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AMC HARRIET АМСР 70S-242 ENGINEERING DESIGN HANDBOOK DESIGN FOR CONTROL OF PROJECTILE FLIGHT CHARACTERISTICS Kuminu, ix шт шппн chiui KFTEIKI INI
HEADQUARTERS UNITED STATES ARMY MATERIEL COMMAND WASHINGTON. О. C. 20315 AMC PAMPHLET NUMBER 706-242* 26 September 1966 AMCP 706-242, Design for Control of Projectile Flight Characteristics, forming part of the Amy Materiel Coamand Engineering Design Handbook Series, Is published for the information and guidance of all concerned. (AMCRD) FDR THE COMANDER: OFFICIAL: Colonel, ф Chief, Administrative Office SELMYN D. SMITH. JR. Major General. USA Chief of Staff DISTRIBUTION: Special •Thia pamphlet aupereedae OtDP 20-246, Nay 1957, redealgnetwd 4NCF 706-246
ЛМСР 7W-942 PREFACE The Bugiuoenag Deaign Handbook of the Amy Materiel Command it a enordinatod aerie* of handbook* joutaining braie inforaMtion and fundrmeatai data ’rnefut in the dceign and develop- ment of Алау vatanel and ayateaaa, The Hand- bent* are wthoritatiro refetwnee book* of practical information and quantitative facta helpful io the datig* a ad devetopaacut of materiel that wilt meet th* мот of th* Araaed Force*. Tbi* handbook, oar of a aerie* on аашншйоа, proarr.t* a goner*) eorvry of the principal factor* offering th* flight of projectile*, and deaerihe* the method* commonly need for predicting and in- flneaemg the flight performance. The eoeAeianta which ebaraetenm th* aero- dynamic forom and momenta on a moving bodv an identified, method* for determining the eoefll- cientn applicable to a projectile having a given ahap* and «enter of gravity location are daaeribed, and the eaetteiente of a nomber *f projectile* and paojaetU* ahapaa *r* given. The mm of aerodynamic ee*ttti<ate in pradirtiag atabihty, rang* and aeeuracy it dmtribed. Th* effect* of variatioM ia projectile ahap* and center of gravity location *n range, aeeoraey and lethality are dtaenaaad. Soaa* material on prototype tatting and th* «ffbet* of rvnnri to mood variatioan ia prodnetioa lota ia proaauted. It ia no longer peaaibie, if it ever waa, to eram into a few hundred pagan all of th* information required to intelligently daaign every type of con- ventional projectile. The author mutt ebocne bo- tween eonatrneting a digeat of available infoma- tion, or directing the daaigner to tie aourcea perti- nent to hie problem, together ’ri-h enough back- ground aaaterial to make it pavable for him to uae th* data in the original report*. The aaeoad ap- proach haa bean ehoeen in th;a handbook; th* ma- terial praaanted ia intended to place the daaigner ia a pomtian to пае new information a* it ia pro- duced by the variona reneareh farilitie* Thia text waa prepared by K. L. K«arier, aaaiated by D. Vipeberg, both of th* ataff of The Budd Company. Much of the material and many helpful eoaamenta were anpplied by the U.S. Amy Ballinti* Hmm reh Leboratoriee and by the Picotiony and Frankford Aracnab. Final editing and arranging wer* by the Kngineering Handbook Otte* of Dake Univermty, prime contractor to the Army Bmmreh OfltamDurham. tthmante of the U.S. Army Materielг’-—- boring need for handbeaka may aobmit rrqai*rti*wa or attdal raqwato directly to tb* Pnblienticaa and Bepeaductiaa Agency, Lattorkoany Army Depot, Cbaaabcnbarg; PaMuyivaaia 17901. Cantraatar* ahoald aahmit aaeh regowitiaae er ragteate to their «ontraetiag offlmn. CesflNeto wd ш tbi* b**dbook wt wricome and abojald b* addremad to Amy Be- atareh Ottm-Dorbam, Box CM, Dak* Btatiw , Dnrham, North Carolina ТИЧА
ЛМСРЖЗа TABLE OF COXTEXTS rvrv^rvpe *W* PREFACE................................. i LIKT OF ILLUSTRATIONS .................viH LIST OF TABLES......................... ix LIST OF APPENDIXES ..................... X LIST OF SYMBOLS ....................... xi CHAPTER 1 INTRODUCTION 1-L Gamal .................................. 14 1-2. Maaaarw af Perferauner ..................14 1-4. Lqpctieal CcssdraatMos................ 14 CHAPTERS TRADE-OFFS ЕЙК»? t Ц щ Gamal Ismaaat Easts va Wariest Vtm......................... UtiBty st Staadard Prajastila Ахмат! Basal to •m far Siaadard Easts......................... instar 9t ЬааЛыЛ PnjKitib Aasmed Staal to Uaity tar Saaadart Вам»....................... Caaaaariaaa st Emits tar Utility Eras! to Ears asd Utility Eqaal to Unity........................ Tabslettos af Psasibli Tiaih aft....................... 24 M M 24 CHAPTERS AERODYNAMIC COEFFICIENTS Gsaaaal............................................... Bstjr Aafadysaaica.................................. Castriiaats ttystaaa............................ Taw ............................................ 2-1 Castor at Piiasaia................................... Asratystaria Pearse sat Meeaasto ***•«•**»«•••••••••••• Gaesrai.............................................. Lift aat Dtm .........................................
АМСР 706-342 TABUS OF CONTENTS (crat'd) /’ereffrupk Pegt ХЗЗ Magnus Furer’.................... .................... 3 3.4 Static Moment......................................... 3-3.5 . Damping Moment.......................................... 3-3.6 Мартов Moment......................................... 3-3.7 Roll Damping Moment ................................ 3-4. Foree and Moment Coefficient*................ ............. 3-4.1 ' Aerodynamic Force Coefficient* ... л.................... 3-4Л . Moment Coefficient* and Moment*......................... 3-4.21 Moment Coefficient*.............................. 3-4.22 Jfn Moment About Horizontal Ай».................. 3-4.22 3tt. Moment About Vertical Axia.................. 3-4.24 Moment About Longitudinal Axia............... 3-4X5 Relationship Between Balliotie and Aerodynamic System* of Coefficient*....... ............... 3-42 Complex Yaw .......................................... 3-44 .Марти* Moment .Sign Convention....................... 34. Method» of Measuring the Coefficient* ............................. 3-5.1 Дм»—1 .......................................... ..... 3-5.2 Method* of Measurement .................. ............ 3-52 Factors To Be Considered in Selection of Method....... 3-52.1 Free Flight (Balliatie Range) ...................... 3-52.2 Wind Tunel ...................................... 3-5.4 Data Resulting from Balliatie Range Teats............. 3-52 Data Resulting from Wind Tunnel Testa................. 3-5.4 Test Facilities ...................................... 3-6. Methods of Estimating the Coefficient*............................ CHAPTER 4 TRAJECTORY CALCULATIONS General ................................................. Dtfirratial Cocffiuants er Sensitivity Pastors.......... Digital Csmputor Pragiaam for Trajectory Calculations ... Simple Particle Trajectory ......................... Six-bcgrce-ef-Fraedam Partieie Trajectory .......... Example of Simple Paztirk Trajectory Cake latten (FORTBAN Program)................................... Desk Computer Method ter Trajectory Caleulatioa......... Method of Calculating Direction of Tangent to Trajectory .. Effect of Projectile Mam on Trajectory ... ............. .Horieoatal Trajectory.............................. Vetoeity ...................................... Time of Flight................................. TerminalVeiaeity .............................. Curved Trajectory. Antiaircraft Fire ............... Efeet of Drag on Trajectory............................. General ....... .................................... ttttt 888888888888 4-722 4-722 6-724 Axial Drag ...................................... ' Effect of Moeh Number............................. Swbeeuk Ragiou. 0 < If < 02 to............... Tiraeuaii Regia*, 26 * < M. < U to........... duparuani* Regie*, 1 * < M <i................ Hypmeai* Regiaa. N > i.............. ........
ЛМСР TOMtt Paragraph <-7.10.2 4-710.3 4-710.4 4-7.11 4-7111 4-7112 4-712 TABU OF СОКТКГГв (eeat*4) Bffeet of Reynolda Number oa Drag Coefllcitut....... Subaonie Drag....................... ............... Surfaoe Bougtoneaa and Irregularities.......... Bloat Noae ........................... ..... Bofttiftiling ..... ............................ ' Pin-Stabilized ProjeetileB ............. ........ Traaaooie Drag .................................. SpiaAtabiliaed Projectile............ .......... Pin-Stabiliced Projectile ..................... Supamaie Drag....................................... Deeroaae of С», with Kadi Number .............. Meet of None Shtpe oa .......................... Meet of Boattailiag on ........................ Dual Plow........................................... 8pike-Noaed Projettika ........................ Undercut Projeetilea........................... Hoaakpharieal or Sharply Cooieal Baae Projeetilea Drag Venation with Yaw ............................. Muazk Bloat..................................... Yawing Velocity Due to Tnaareroe Vibration of Mode ........................................... . Tranworw Preacure Gradieata.................... Pialkabiliaed Projeetilea ia Brrnnad Plow...... Otemooa....................... ................ СпшяпаА .......................'............... Wind Seoaitirity............................... Lateral Deflection ............................ VahMBofCe, та Mach Number.................... ...... CHAPTERS CHOICE OF METHOD OF STABILIZATION RtabQiantioa .......................,.......... 5-121 Agaiatt...................................... 5-122 For ......................................... 5-2 Bpio^taMHaed Projeetilea .................................... 5-21 Gyrooropie Stability............. ................ 5-211 Qyraacopie Stability Faeter..... ............ 5-212 Caaditiona oa Value of ц far Stability....... 5-22 Taw of Пересе .................................... 5-221 General ..................................... 5-222 5-223 5-224 5-225 5-23 Formula for Angie of Bepoee ................... Trailing ...................................... Projectile Aaymmitrim.......................... Method of Computation of Projectile Spin....... 5-24 5-241 5-242 Dynamic Stability of SpiaAtaMWI ProjeetSm.... Mttpttuii of Modal Vortma................ Dynamic Stability Factor, *.............. £ зззззззз3552 3255533 33555555 ззз ззззззззззззззззз
▲MCP 71)6-242 vi TABLE OF COMTEMTS (cant*d) /•ray rep* 5-2.42.1 5-2.422 5-2.4.3 5-2.5 5-24.1 5-2.52 5-243 5-24.4 5-244 5-2.56 5-24.6.1 5-2.5.62 5-33 5-3.3 5-33.1 5-332 5-34 3-3.5.1 3-342 5-3.8 5-3.6.1 5-3.62 5-3.63 5-3.63.1 5-3.633 5-3.633 5-3.63.4 5-3.6.4 5-3.6.4.1 5-3.6.43 5-8.6.44 5-3.7 5-3.7.1 5-3.72 5-3.72.1 5-3.722 5-3.733 5-33 5-8.10 Peg* 54 54 Stability for X ............................. Stability for 1 = 0......................... Further Discussion of Magnitude of Modal Vectors and Stability ................................... Aerodynamic Jump of Spin-Stabilised Projectiles .... General............................................... - Aerodynamic Jum? .................... Magnitude of Ae .. asrfeJamp........................ Orientation cf Aeroc.углск Jump................... Distribution cf A rr-iv .w jac Jump............... Relationship Aerod? <tmic Jump and QJs. Ml ------------ 5-11 5-12 5-12 5-12 5-12 5-12 5-13 .5-13 5-13 5-13 5-13 5-13 5-14 5-14 5-14 5-14 5-14 5-14 5-15 5-15 5-15 5-15 5-15 536 5-16 5-16 Variation of Magnitude of Taw with Asymssetry 5-16 ----------------- 5-17 5-17 5-17 5-17 5-17 5-18 5-18 Vertical ( ja7«..;ent................ Horisontul Cci-pone>.t .............. Fin-Stabilised Projectiles ....................... General ...................................... C.P.-C.G. Separation ......................... Fin Type............. ...... ................. Fixed Fine............................... Folding Fins ............................ Obturation ................................... Arrow (Subealiber) Projectiles................ General ................................. Sabot .......................... ........ Aeroelastieity .......................... Dynamic Stability of Fin-Stabilised Projectiles General...................................... Zero Spin................................ Equilibrium Roll Rate.................... Equilibrium Spin..................... Torque .............................. Computation of Equilibrium Roll Rate Sample Calculation .................. Computation of Dynamic Stability......... General.............................. Sample Calculation .................. Magnus Moment CcefieientB............ Resonance Roll Rote, p, ....................... Computation .................................... Sample Calculation ......................... Ratio of p,/p, to Avoid Raaonaaea Instability Roll Loeh-in......................................... Aerodynamic Jump of Fiu-Stabiliaod Projectiles....... Fin EEeetiranMB at Supersonic Speeds................. CHAPTER 6 ROCKET-ASSISTED PROJECTILES 54 54 54 54 54 5-11 5-11 6-1. General .................................................6-1 4 8-2 Momentum Limited Situation .............................. 6-1 6-21 Variation of Massie Energy, Chaarter Pnasun and Propellant with Weight of Projectile.............................. 6-1
ЛМСР 706-342 TABLE OF C0X7EKTS (cMt*4) Psrsgrepk Pepe 6-24 Variation of Setback Acceleration................... 6-2 6-2.3 . Effect of Roeket Addition* on Projectile Design Parameters ................................ <4 6-24 Effect of Rocket Addition* on Accuracy.............. 6-2 CHAPTER 7 LIQUID-FILLED PROJECTILES 7"*1 7-1 7-2 Effect of Sloshing of Liquid Filler ................... 7-1 7-3. Computation of Design Parameter* .......................7-1 7-3.1 Oyroeeopie Stability Factor........................7-1 7-32 Dynamic Stability Factor......................... 7-2 7-44 Spin Bate....................................-.....7-2 7-4. Rigid Body Theory.......................................... 7-2 CHAPTER 8 RANGE TESTING OF PROTOTYPE PROJECTILES XL General ..............................................8-1 8-2 Data........................................ 8-1 8-3. Teatinc ...............................................84 8-3.1 Static Testing......................................M 8-32 Flight Testing .................................. 8-2 8-3X1 Vertical Target Accuracy.................... 8-2 8-3.21.1 Measurement of Accuracy................... 84 8-3.21.2 Temperature Range......................... 84 8-3X1.3 Data Recorded ............................ 84 8-3X2 Range (Distance) Accuracy..................... 84 8-3X21 Measurement of Accuracy................... 84 8-3X22 Dau Recorded ...........................84 8-8X24 Instrumentation ...........................84 CHAPTER 9 MANUFACTURING TOLERANCES XU xu Analysis XI XI
ЛМС? 7O»i-*A42 TABU 07 С0ГГЖМТ8 (смРА) 9-Z Predicted Probable Bang» Error..................................9-1 9-3. Dynamic Stability of 175-mm Projectile, M437 .................. 9-2 GLOSSARY ......................... G-l APPKNDIXB8 ...................... A-l RRFBRBNCES ........................ B4 BIBLIOGRAPHY ..................... B-l LIST OF ILLUSTRATIONS Fipwv go, ftft S-l Coordinate System ......................... ................3-1 4-1 Diagram of Gravity Force oa Projectile................... 44 4-2 Flow Pattena on Varying Length. Cooatant Caliber 43 Diameter Spike Noam at Snpenonie VeloeitiM .............4-11 S-l Abbreviated Graph of 1/», va «« ............................54 5-2 Graph of 1/a, vo g........ ............. MO
AMCP 70042 LIST OF TABLSS Fable No. Pajje 3-1 Eatimrted Accuracy of Aerodynamic Coefflej^ats Obtained by Ballistic Range and Wind Tunnel Teat*................................... 3-3 GoeAciait* of Typical Projectile» Measured in Free Flight . and Batimated ....................................................... 3-3 Partial List of Ballistic Tert Ranges in North America.............. 3-4 Partial Liat of Wind Tunnels in North America....................... 3-5 List of Reports Containing Methods of Ratimsting CoefBdenta .. 4-1 Typical Output of FORTRAN Simple Particle Trajectory Program ............,. 4-3 Sample Trajectory Oleulatrd on Desk Computer (Seineh Sample Projectile) ............................................. 3-1 Sample Trajectory for Spin-Stabilised 5-ineh Project at Q.E. = 3* ................................................... 5-3 Sample Trajectory for Spin-Stabilised 5-ineh Projectile at Q.E. 70* ................................................. 5-1 Probable Variability af Rorket-Aanstad Projectile Characteristic* and Sensitivity Factor* Which Affect Range................... .......... 5-3 Sample Trajectory for 175-mm Spin-Stabilised Projectile, M437, at Q.E. = 46* .................................................... »-f Aerodynamic Date Sheet for 175-еии Projectile, 1(437 ........ •-4 Dynaau* Stability Estimate of 175-mm Projectile. M437............... П St t 2SU S
АМСР 706-342 Appendix No. LIST OF APPENDIXES Ряде I Sample Spin-Stabilized Projectile....................................A-l II Calculation of C.O. and Radius of Gyration..........................A-2 III Gyroscopic Stability Estimates A. Spin-Stabilized Projectile With Boattail ................... A-3 B. Spin-Stabilized Projectile Without Boattaii (Flat Baae).... A-S IV Comparison of Estimates of Ballistic Parameter! By Various Methode ........................................A-6 V Dynamic Stability Estimate.................. ..................A-S VI . Static Stability Estimate of a 5-ineh Fin-Stabilized Projectile'.. A-9 VII Projectile Geometry.........................................A-10 VIII Aerodynamic Data Sheetz A. 30-mm HEl Projectile, T306E10............................... A-ll B. 20-mm HEI Projectile, T282E1 ............................ A-12 C. Drag re Truncation: Conical Heada........................... A-13 D. 2.75-inch Roeket, Tl?l ......................................A-14 E. 90-mm HE Projectile, M71................................... A-15 F. 105-mm HE Projectile, Ml (Modified) .........................A-16 G. 4.9-ealiber Projectile at Transonic Speeds.................. A-17 H. L J. L. M. N. 0. P. 0- R. 8. T. U. V. w. X. T. z. 90-mm HE Projectile, T91 ............................. ........ Effects of Head Shape Variation................................ 120-mm HE Projectile, M73....................................... Com Cylinder ..................................... .......... Effect of Boattailing on Co, .................................. Effect of Boattailing on Co, at M = 2.44........................ 90-mm Model of l?5-mm Projectile, T203 ........................ 7.2-ineh Spinner Roeket, T99................................... 5-ealiber A-N Spinner Roeket................................... 7-caliber A-N Spinner Roeket................................... 7-ealiber A-N Spinner Roeket and 9-ealiber A-N Spinner pocket ....................................... 10-ealiber Cot e Cylinder ..................................... 105-mm HEAT Projectile, T171 (Modified) ....................... 60-mm Mortar Projectile, T24................................... 105-mm Mortar Projectile, T53............... ............ 57-mm HEAT Projectile, T188E18................................. 90-mm HEAT Projectile, T108.................................... 90-mm HEAT Projectile, T108.................................... 10-ealiber Arrow Projectile ................................... А-Э0 A-32 A-33 A-34 A-35 A-36 A-37 A-38 A-S9 IX Trajectory Program in FORTRAN Language........................ A-40
AMCF 706-242 LIST OF SYMBOLS A A a b c e-P- CD cal C,. Ct. Ch, C"t. Ct, С*, + C*» Ct» . A conatant deecribing the kind and degree of aaymmetry of a projectile, radiana D d Bore area, ft* e Setback acceleration, ft/aec* 0» Conatant in Q function в Fin epan, tip4o-tlp, ft к Conatant in Q function I. Fin chord, ft 11 Conatant in Q function л9 Center of gravity t Center of preaaure Dreg coefficient Ki Caliber k. Drag coefficient at aero yaw Yaw-drag coefficient, per rad* k, lift coefficient, per radian L Normal force coefficient, per radian Zu (Cm, С*., + С» for email yaw) M Mangua force coefficient, per rad/aec, per radian at Static moment coefficient, per radian N Mag".ua moment coeftcient, per rad/ n вес, per radian N, Damping moment coefficient, per rad/sce P. Rolling dariping moment coefficient, P perrad/aec Roll moment coefficient due to fin cant (at aero epin), per radian О Drag, lb Maximum body diameter, ft Baae of natural logarithm! Feet per ascend Acceleration of gravity, ft/aec* Altitude above aea level, ft Axial moment of inertia, alug-ft* Tranavene moment of inertia, alug- ft* V-l; in complex notation indicateo rotation by 90* Modal vector, radian» Axial radiuc of gyration, caliber* Tranavene radiua of gyration, mlibera Lift, lb Bore travel, ft Natural logarithm Mach number Maae, aluga Normal force, lb Twiat of rifling, cal/turn Magnua force, lb Chamber preaaure, Ib/ft* Roll rate, rad/aec Equilibrium roll rate, rad/aeo - - o + Mf
AMtT 706 242 LIST 0Г SYMBOLS (cant'd) Dynamic prrenurr, &,'?•? (f - **V») Angular velocity at a noorolling nuamle-fixed coordinate rynem about a boriaootal axia, rad/aec (in damping moment expreaaion) Radian» Frontal ana ft* Trawl at projectile, caliber» Dynamic (tabibty factor Dynaamc XabOity factor for U. S 0 Gyrcaoopie atabihty factor Temperature, *F Tune of flight, aee Time, aac Utility Velocity or aimpeed, fpa Volume of projectile (indudiag bauadary layer over the boattail, if ряапы). ft* Weight, a> D*aare along trajectory, ft Vertaeai oorepanant of yaw, rad Beriauntal eoreponeot of yaw. tad Yamaatfo,nd Samfa maaaoat factor, ib-fl/radiaa CaaAaiaataf naeaatty Spin (aomSmaaakaual) » » pd/F Acute >mgfa between a horiaoMnl pinna and the tiaynt to the trajec- tory nt the eg. of the project de Angle of roi Aagb af anewtatien of a modal wet ar, re liana Danaity, thg.'ft* Pertain» to nutation vector Periaine to pre г ramen vector Pertain* to aaymmetry vector Maximum value Standard value Dummy index: to be replneed by a aaqoance of apedfic indioea when the «aJjc-ripted quantity uaed in t computation Sama definition an auhacript • Aerodynamic jump Damping exponent, par caliber of trawl Repone Rwoaaat Derivative with reaped to angle of sttftck Aoouatie (V. - apeed of aound) Body Bum RSaetiw Equilibrium Fin Initial eoadfticn» Stanza* vahm Dnriuatiw with reaped toapia Derivative with reapaat tn time Derivative with reapaat to antihare trawled, Kg., • p, ЦТ
АМСРЖЭС1 СМАЯЛ* 1 IMTRODUCTIOM J—L GMMSKAL Thia handbook м гоомниД with th» doaign of projection flrod free guan. The pro- jeetihn aoModerad m of greater мм and weight than sea пеемаИу be And fnm a hand-held weapon, aad they are wot equipped with guidaoce ya fa It win be aaouawd that they an bodice of rivfhuiie, aoaaetiaoee equippod with flno, aad fly ia the gawara! direction of the Inwgifniliaal axis. J—X MBASCU8 ОТ ПЖГОКМАМСЖ The pemcipol an Mateo of the perferManti of а pnjeetile art: b. Lethality e. Aeeuruoy d. Tineoffligh. The eohtea taben on by tbeae neaaune arban a reend. ar group of twaada, io trod are detenaiaed by atMeopberte eeudxiooa, maaaie velocity, gun orieatatiau, tarpot ar barot riot elite relative to gaa, aad by flight ehorneteriotMO draagnod aad boUt iate the projMlilo, The рпамгу flight 'horaeterietka which dinetly inAoaaee tbe trnjoeteey are: a. Drug b. АогоАуаамй jaa^ bat both drag, which rhwfly adret» range aad tiaae of flight, aad jenp, which ehiepy afloete aaewraey. an tboanarivaa detonemed by a aaatber of prejeetik aharaatariattea wbaab we will aoM enoadwy flgbt a. Stro-yaw drag ooaAeiant b. Taw-drag MiMriant e. Serfianal deaaity A Lift eoeflkieat a. Stability t Aqyaaaetry effects g. Wiad eenortnity h. Meade bleat MMiiivity The lift aad dra* eaodfeieate are funrtioao of projectile ohape aad airop nd. Stability ia primarily a fwartioo of chape, airepoad, air deaaity, aad opin rate, aad of the Meaner ia whieh the мам of tbe projectile ia distributed. Mank biaot araeitivrty depeadi on enoeatially the aame paraaeteH aa atability. Vind Moatirity deponde on tbe lift aad drag eoeflfeienta, *• atability, and, ia tbe сам of rocket aeaioted projeetihn, on the ratio of throat to drag. Practically all projectile bodiea (aad flat) an deaigaed with rotational ayaaotey; tbair MjnMitry ariaa ia tbe aMoofaetaring peooaaa. Рама, boweeor, an aeaally aaysaaetrie iateraaQy; the eenter of gravity of tbe faae dan sot be ia tbe praj(ctik axis. AS of tbe above aaeaadary flight abaaaater- iatiaa, aad therefore the priaary flight ahem- terietMo. an controllable by tbe daaigner to withia a narrow range; roead to naad oariatieaa ariaa owing to Monofaetariag toteroaea aad to obaaga ia aaaaia nleeity. air deaaity and wiad pattea». Striageat aaaatetariag aienni: m aaay ba Mo- poaed by the daaigner if the аопгму йпреоеемпК obtained eaa jaatify the iaaeeawd aaet of anao- faetan. 1-4. LOOtSTSCAL СОЯГОПАПОЖа hgiattak The fl edge re май еаааМаЦу bear th 14
AMCPTOd-242 Kind the dement* of eoat, atorability, and trans- portability. He should avoid, where роиШе, the we of material» likely to be in «bort «apply during wartime. He will often be limited by the facilities for loading the projectile into the gun, and by the design of the gun chamber. Moat of thane eon- aiderationa are beyond the aeope of thia particular handbook, bat ate eocered ia other draign hand- books of this aeries. It is not difficult to deaigu a projectile having long range, a relatively abort time of flight, and л «mail round-to-roand diapetmon. However, the projectile might, and probably would, have aueh a mill Jeatnietive value, or lethality, that it would be ttsrieas *» a weapon. THE PRIME FUNCTION OF THE PROJECTILE DESIGNER IS TO FIND THAT COMPROMISE AMONG RANGE, ACCURACY AND LETHALITY WHICH WILL BEST SUPPORT THE MISSION OF THE WEAPON SYSTEM UNDER CONSIDERA- TION. Foe eaample, maiiHhatita of an eaiating pro- jectile by increasing the length of ita ogive, while preserving the overall length cf the projectile, should decrease its drag coefficient and, therefore, increase it* range. However, the stability of the round will be altered, with some effect on accuracy; the volume of the projectile will be decreased, with resulting decrease in lethality (or other measure of usefulnem, as in the ease of ansoke or illuminating projectiles). These trade-offs are disenssed in de- tail in the body of thia handbook. ' In most of the discussion* in this handbook it will be tacitly assumed that the designer i* given the projectile disaster and the characteristics of the gun from which it m to be flred, i.e4 upper limit*, on chamber pressure, muasie energy and murnie momentum have been established by the gun designer. Occasionally, but not often, the pro- jectile designer may be able to apaeify the twist of the rifling. If the deeagner i* equipped to make correct design decision* for any one ealiber, he will be аЫе to cope with the problem of eboosiug an optimum ealiber far a given miasma, should that problem arise.
АК<ЖЖ4Н2 СНАРТХЛ 2 TRADE-OFFS 3—L GBVXKAL If th* eolutioa of * tradeoff pro&Hm to ex- pmeed in ввааЬеп, an intelligent eompramtoe be- tween eoufbeting geek eon only be roeeted when the eont of falling abort of each geal ana be ex- prvmed in number*. Furthermore, them penalty number* mum b* in the aame eyetem, Le_, they maat be capable of being added or multiplied to> gMh*r t* grv* a eigniheant number. One nerful concept, borrowed from ceoneauca, ie that of •‘utility", enpiemtd at a number which lie* between aero, etoadiug for naeBw, and unity, ataading for am visum uarfulnem attainable ia the given aituatioa. If the utility of each element of a aituatiou can be computed, the utility of the over- all aituatioa ean be touad by muitiplyiag, ar. ia tome aaom, adding, tbe utilitiee of the element*. (The earn atay be divided by the washer of ceat- poaenta if the teaviatiea that Utility leaner trend unity ia to be r Hamid.) In order la oeaetnmt the enrauo which expram the utilitiee of tbe rnriom etemmne of projeetito perfaramaaw, tbe durigaer meat obtain, from the agency rmposaibie far dednine the military rugate*- meat, atatemento about tbe roUtrvo value* of war- head* of diliriut valamm dor the purpaoaa, and at to nsgaa, pertinent to the mtoetos of the pea- (йвйвмммш weNi Ъ* obvM the uerfulaem of increaoed rang*, dmmneod toe of tight, and improved accuracy While the otate- meate obtained may be mainly gnalitetivo, anob a* “•eeon toad a tola mduottom warhead veto**, but a 90% ntoetton would be aaowaptabto," •* ‘‘anything 'Mt thou tom tbe proem* range to ooaaHemd to be b^end to «Шив of Me pew- joetto’* toy to b» trastotod tom immiHiil utility eurree. Tbe deeigner ahouU dtoeum th* utility eurm with the esmtomer befor* proceed- ing with the daaign; oom* elariSeation of dmign objective* ia likelyt* reauit. Ixamplm of trade- off ar* given below. 3—3. DICRXASXD KA10F VS WAMRAD vouna 3-ЗД Utility of Sttndaxd Fiojectite toe moi Xgaal to Zare far Standard Bang* A* an totopia, onppom that the peobiam to tto> deeign of a rorhat eentotel projectile to be dr* from an «xietiag gun. Range to iaeroaaed by th* addition of roehat fori; howavnr, th* overall length of tbe projectile to limited by etability or handling eoaeidcratioaa, m that an the amount al rochet fuel to iaeraaeed, the volume of the warhead, and tor** fere toa lethality, to dm ream it Tfea deaigne* can compute the tradeoff «uro* of rang* vo warhead valame, and dt thia earm with a eimpla algabmi* iipuwim. Foe mempto, to our** might ba m
лмсртсвш Неге Хм cad FoIm repeoeent the raage cad warhead volume, reopoetivdy, of the ataadard pro- jeetile toed from the given gua. The deaign prob- lem ia to inereaae the raage above X«m withost ааогШм “too maeh" warhead volume. The equattoa for the enrve abowa would be: of range uaefulnem approaebm aero aa the raage approaebee the upper limit. replacing the fnetieaa by mnnboto-. Tbto naatiaa might M the carve wall only over the raage Ц < 1, bat it wffl ten oat that in thia еамарй we ate act iatoroated ia mlutmaa out- todt of thia raaga. Wa aww that the utaity of the warhead MW W w* WHB ОТСЯМММф wnM) thru paeeiptoooaty, and «not votaaam torn thaw 0-3 Ac atondtod vehmm are werthloea, Le4 P>»0. Ito Mtowtog cam abeam that any raage lying oonga it of hrtaaen^ and that the ante of inmnaa we aan tap tom Ot ia term» of 2, «'—ft-y-Sf- On the aaaumptton that the utility of the rem pre mtoe eolation ia proportional to the product of the ntUitiea of range and warbead volume, wa have Й?* ;*i.5 . Tbere to an teteroot Wbw » = M aad the boot iimpromtoc Um at В = O.K where U = BM, and X = LM X<o Ttoe aatattoa may bo reached by orthm graphiaal er aaalyttoal matbada Note that the rmaitawt utiMiy of the ataadard projmtUe to ano by thto artoartoa. h-U Vtttty af htmtoard Frtjirtito ЛшшЛ Bgaal to Baity tor htaated Жа^а It it ahoeM ba thought more naltotto to give the ttoadard paadaotUa a raaaitoat utiMty at ana, raauitoat. la thto earn M
AMCP 708-242 a>>d the bo* ecmpromioe Un at ff = 0.80, where F = 138, and X - 1-67 Х~ Tbe reouHant utility of the atandard-projectile being 1.0 by the cri- terion, we hare an rotimate of the iaemer ш пае- fulnea gained by going to the roehet-aaeiated pro- jectile, ria, 58%. 3-U Comparioea of Beechs tor Utility Bgnal to Zero and Utility Kgnal to Unity In car example* it don not sake mueh dif- ference which criterion we war, however, thia will not ahrayi be the cane. In general, it eaa be «aid that tbe nee of the additive criterion plaem the optimum ti the point where tbe eaa of tbe olopeo of the utility curve* ia aero. In tbe muhiplieetive method tach aiope i muhiplird by tbe peodnet of the other etilitiee before being anaimed to am. After beating tbe area of optimum miutMaa, the flaal aototiaa win be pinpointed only by coa- aidaratiouo of accuracy, timi if flight, and bgbtica. 2—3. TABULATIOB OF FOSSIBU TRADE- OFFS Deaign change* whieh inervaae accuracy aoaw- timea decnwee range; range and accuracy aught both be improved by inereaaing the coat of manu- facturing the round. Tbe trade-off method out- lined above can be uaeful in them and mauler atten- tion*. Many different trade off aituationa are men- tioned in the баепипоаа in thia handbook. For ex- ampl*: a. CocLputiag time to* accuracy of anaulatioa in trajectory calculation*. h. Warhead vohnne tor abort time-of-flight by me of a «nbealiber projectile. e. Bange or time-of-flight for accuracy where improved atability aaay be obtained by em- ploying a high drag rouflguraiiou. d. Warhead voluaae for range or tim*-of-flight by boattailing. er by lengthening the ogive. Unfortunately, inereaaing range uaually di- nin i*h re tbe nrwfubim* of even an undimin- iahed warhead by ineraaaiag the diapenaan (in meter») и the target. * Drag for manufacturing eeat in the ihoirn at flapoaflie. f. Bange or tme of flight rodneed ataengo aad handling apaae in the oaae of a W*e- naaad round. g. Bimpiirity tor warhead volume by uaiag feid- gflna, М/Ы
АМСР70МС1 chapter з AERODYNAMIC COEFFICIENTS 3—1. GEXEEAL A large part of thia handbook ia concerned with the interactions between a projectile and the air through which it Hies Frequent use ia made of the fact that many aspects of thia interaction are in- dependent of which of the two, projectile or air, ia actually moving; their relative velocity is the signi&eant quantity. The basic characteristics of the How of a fluid, sueb as air, around a body are described in Posndorioss of Aerodyncmaes by Knethe and Scbetaer, and in Physical PrindpUf of .Vcehcsies and Aeoerttca by Pohl, which pre- sent many interesting drawings and photbgnuha of the flow of flsnda, using dye or reflecting ~-rti- eiaa to aaake the motion visible. The Bibliography at the end of thia handbook lists those and other hooka on aeredynamae theory. 3—J. BODY ABB0DYBAMIC8 A projectile flying through the ai.' mates vertexes, turhalrnia and, if its speed is ufllciently gnat, shock wares in the air. Both the air and the projectile are heated. The energy content of these motiuna is supplied by the kinetic energy of the projectile, end thia transfer of energy implies & force, or foree system, between the air and the projectile. This force system may be analysed into components which produce changes in the linear and angular velocities asroeiated with each of the throe orthogonal axes which ему be efaoaen as a eootalineto system for the description of the asoticn of the projectile. 3—XI CoordinMe Byatea The Meediaate t>seom employed in this hand- book. Figure S4. for deeerihiag the leeoso and momenta acting on a projectile has its origin at the eenter af gravity (eg.) of the projectile, its X-axie pointing in the direction of the tangent to the trajectory (note that thia direction changes as the projsetile moves along the trajectory) and its Y- and Z-axes in a plane normal to the X-axis. The Y-uia is horiaontal; the Z-axia ia normal to the other two. Many diFerent coordinate ay ate am are employed by writers on projectile osrodynaaaiaa, the aheiee of a ayotem being iaflneased by earn of derctep meat of the mathematics involved. However, nearly all of those eystema ^tvee in having the origin at the raster of gravity of the projectile arose the motion of • body ean always be rseeivod into
AMCKTUS-M2 translation cf. and rotation about, its center of gravity. 3-23 Taw Tbe aerodynamic forces nrc functions of the attitude of the projectile with respect to the di- rection of motion of the e.g. rdatire to the sur- rounding air. If there i* no wind, thia direction of relative motion is along the tangent to the tra- jectory. (Since wind velocities arc small compared with projectile velocities, wind effects are usually introduced as corrections.) Yaw to defined as the angle between the tangent to the trajectory and the direction of the longitudinal axis of tbe pro- ject ile. Thix angle varies continuously throughout the Hight, rapidly at first, but, in a well behaved peejectilr, less rapidly an time goes on; apin- stabiliard projectiles should quirt down to a nearly rv actant yaw, called the yaw of repose, while tbe yaw of fin-stabilised projectiles should damp to very small values. In mathematical analyses, the position of the projectile axis is usually projected onto the Y, Z-plane. giving a horisontal and a “vertical” component of yaw. These components are related to the yaw by the eosine and sine of the yaw orientation angle, and are usually handled matbemstirally by the use of complex numbers. 3—13 Cantar of hmsn , Tbe aerodynamic forces on a projectile are de- termined by the pressure distributee'Which exists •ver tbe whole exterior surface, but in order to simplify the miasurrmrnt end mathematical ma- mpulatioM of these forrrs, we «leal only with a (Verified set of the resultants of the distributed foeees. These resultants have a amgniinde and direction, and also point of application on tbe body, ie., a point through which the resultant seta. This point, called the eeater of pressure (e.p.) of the force in question, is assessed to lie in tbe longi- tudinal axis of tbe projectile, but its position on that axis depends on the shape Л the prajsetile, hs sir opwd (Mach amnber), axial spin rate, and, ttefoeHnateiy, аапийама on tbe magnitude ef tbe Я*. In this handbook, the center of pteanme Л the fidt foeoes io aoouased to be bsdopeerfeat at yaw angle; thia ia made psooMe by considering moly "linear” projectile behavior in whieh I he yaw seldom exceeds 10*. (hie pnr]Mss- of good design is to keep the yaw well below thia figure; not greater than 5*. However, the center of pressure of the magnux forces can move an appreciable distance when the yaw angle changes as jiueh aa 10*. and some attempt to describe tbe effects of thia e.p. movement will be made. 3-^3. AERODYlfAMICS FORCES ATO MOMENTS 3—3.1 General The (resultant) forces and momenta whieh are significant for projectile design are: a. Normal fores b. Lift c. Dreg d. Magnus force e. Static moment f. Damping moment g. Magnus moment h. Roll damping moment 3—33 Lift and Drag Tbe resultant of the pressure forms on a sym- aaetrfeal nouspaming projectile lies in tbe plane ooataiaing the tangent to the trajectory and tbe longitudinal axis of tbe projectile, called the “yaw plane”; the point on the projectile axis through whieh this nsultant paassa ia called the center of prnsuirr of the lift er normal force, einoe the re- sultant may be resolved either into lift and drag components, or into norma) force and nxial drag. Lift is parallel to the Y, Z-plane, drag is parallel to tbe X-axis; norma) force is perpendicular to, and axial drag ia in line with, the axis of the projectile. Rack possible psir of components lies, of course, in the yaw plane. 3—33. Kagans Vens When в projectile is spanning about its longi- tudinal axis, tbe pressure distribution over its sur- face to altered so that the resuhast force na longer lies tn the plane of yaw. Tbe asvodynamietet tabes earn of this stonstiea by tartrsdusiag a terse oom- poaent normal to tbe yew plasm, together with Ms
ЛМСР 700-242 aeeoriatni moment. Thia foree, called the “magnus force”, ia alao perpendicular to the longitudinal axb of the projectile, and paaaea through it* own eenter of preasure. Vector aubtraction of the magnus foree from the total foree on the projectile leavm a force in the yaw plane, which ean he re- solved into lift and drag. 3—J.4 Static Moment The static moment ia the product of the normal foree and the distance between ita e.p. and the eg. of the projectile, which ia considered positive when the e.p. b forward of the eg. as it practically al- ways i* for apin-stabilixed projectile*. The axis of thia moment is a transverse axia through the e.g., normal to the yaw plane. Fin-stabilised projectile* have the e.p. aft of the eg., so that the static moment opposes an increase in yaw (in normal flight), and ean be called a “restoring moment”. 3—3J Damping Moment When the yaw of the projectile b ehanging, the swinging of the projectile about its eg. change* the pressure distribution so as to produce a eouple about an axb through tbe eg. normal to the plane of tbe yawing velocity (which b not necessarily the plane of yaw). Thb eouple, called tbe “damping moment”, usually oppoem the yawing velocity. 3-34 Xagami Memaut The magnus forte produces a aaoeaent about an axb through the eg. parallel to tbe normal foree. Thb aaagnua moanent changes the yawing velocity in a way which depends ou the location of the center of pressure of tbe amgnue force, aad on its direc- tion. The magnus foree and moment are a result of spinning the projectile, and are shot nt on a non- rotating projectile; however, even flnotabiliaed projectiles шау have spin. 3—ЗЛ ЯЛ Damping Moment Tbe roll damping moment b a couple about tbe longitudinal axb of the projeetib; thb aaoeacnt on a spinning body b related to tbe friction be- tween projectile and air. Fins produce large roll damping moments owing to the angle of attack induced by spin. 3—4, FORCX AMD MOMXMT CORFFICttMTS It has been found that the aerodynaaue forces and the static moment are proportional to the dimension* of the projectile, to the dynamic pres- sure of the air, and to the yaw of tbe projectile. The three moments arising from rotatiora are also proportional to their appropriate angular veloci- ties. The factors of proportionality are known as “aerodynamic coefficient*1’. They are not constant for a given projectile, but an themselves funetioca of Mach number, Reynolds number, spin rate, aad yaw. A brief dbcnaebn of tbe foree and moment coefficient* follows. For a more complete ilierue sion of the aerodynamic forces and aaoownto am Murphy, The Free PtigU Uotoe* of Sgaaaairie MittOu, Ref. 12*. 3—4.1 Aerodynamic Form Ceoffidenta The moat significant of the aerodynamic foree coefficient* are defined aa follows; when is the dynamic pressure, 8 = - d1 is the frontal arm of the projectile, aad a b the yaw in raitiana; r N_ a = air density, alug/ff F ~ apoed of peojeeUe ral- д stive to air, ft/am p = roll rate, rad/ом _ d = maximum body diaaa- C* - -s etar of projectile, ft If = normal force, lb c,_______If» 4 = lif,lb D=dreg,lb If» = magnua fore* All of thane eoaffieianta an expected to be func- tions of the yaw angle, o. For assail angles (e < 0.17 radian), all, except C>, ean be aaoumed to vary linearly with ynw; thb leads to the no* of the alepe of the ma of coefficient venue yaw angb m a more eouvonbnt deoeriptioe of the ehwactartatim of the projeetib. Using th* subscript e, to denote a derivative with raped to e, we san write:
АМСР 705-242 N-^gSe-Cs.gSa L - ^gSs - Ct,p8« M Drag varies with the square of the yaw, ao we write D « (C*. + «8 where С», ia the drag coefficient at aero yaw aad C»,» ia the rate of change of Ca with a*. 3—42 Meanest CaeSdeata aad If ascents The momente produced by the aerodynaaaie forces an referred to the eenter of gravity of the projectile, uateaa othenriae stated. The moment eoeflejenta, ia the terminology of thia handbook, an derivatn-ea with respect to yaw, or with mpeet to appropriate angular veloeities. 3—42.1 Momsnt Cosffideuto Than* eoeffitients an defined aa follows: “ = C*, = static anaaent coefficient damping aaoaaent eoeffieiewt -----Cw_ = magnus non ent coefficient de 3 4.22 My. Mem eat Abent Hocizonin' Ata The total mocaest about a heriaontal ata through the eg. b given by abase p in the aaoand tom b the angular velocity abont the bertasrtal ata when e, the yawing velaa •«tew tea swmms teem total dbeeMen b peegeriteaal to ta Я» b ta Г awmUm. Cm pmagne* •—40. ity about that axis, ia aero; i.e., the total angular velocity about the horiaontal aqb ia q 4- i. f ariaes from th» curvature of the trajectory. Therefore, in coefficient form M, - Ы M [cr.a + C.jffi + CWi(^) + M$'] The first term of the expansion b the static moment, the next two an the damping momenta, and the last term is the magnua moment (Note the eaeh term inside the brackets must be multiplied by 4nF*ad to obtain the moment) 3 423 1Ц, Mament Abent Vertical Ata M., the aerodynamic moment about the “verti- cal” axis through the e<, ia obtained by a similar expansion, interchanging a and 3, substituting 0 for «, and r for q, where r 4- 3 is the angular ve- locity about the z-ata 3—4X4 M., Маем* About tengtadinal Ante The aerodynamic moment about the longitudinal axis of the projectile ia, in the abaanee of a apin- indueing torque seek as might be provided by canted Ina, simply and Ci^ is called the toil damping moaaent co- efficient. The diseeneionlem ratio pd/V which ap- pears above ia often designated by a, the spin in radians per ealiber. 3-423 >ahfbnta| Betam BaHtotis and ЛмшКумнбс СмАсЬвШ The earlier work in this am uaae a system at coeffieiects within which дРе mfcm toe place at the dynamic proaaure, aad dF taken the plane of frontal am. Thb system is, of course, dimanainn ally correct. It was the system used in AMCP 704 Md, Knginseriag Design Handbook, Aaamunition Benes, Boctwu 3, Design fer Cental Plight ChamterMoA aad b dbaardad bare in the in- ternet at unifying the natatbn of aaredywaaaiabto teUtatitttMb мм* th® letter on israd to wm M
AKOP 704-242 * Urge amount of wind tnnnel data obtniiml by aertMlynnmirUU. The ballwtie notation will lie around for a long time, an it ix iiewssacy Io know that rorfllriruLs in the balimtie system (which are usually denoted by the capita! letter К with a subscript) ean be converted into the corresponding aerodynamic coefficient slopes (or directly into those coefficient* which are not function» of yaw) by multiplying the ballistic system coefficient by 8/x, e.g, C»a - . For example, N " C". 0pV» I <₽) a - лЦрР <₽ j Ш a When ain a * a, C»a * | Ku by cancellation, h should be noted that for Ci^ + C<; , »“d the multiplier ia - (Some authors пае - aa a multiplier, since they use 2 V as the denominator of their spin terms, e.g^ pd/2F in- stead of pd/V.) 3—43 Complex Yaw In the foregoing discussion, for the sake of simplicity, the symbol u was used for yaw angle. In the notation of Ref. 12a, a is the component of the yaw angle in the “vertical” direction; the com- ponent in the horiiontal direction ia 5, and the total yaw angle, 8, ia given by » = » + *• where the orientation of the yaw is tan-' 9. The aerodynamic coefficient slopes, or “aero- dynamic derivatives", ean be defined in terms of a because of the rotational symmetry of a projectile; their values ean be derived from measurements made on a model whieh is given a ya* in one plane, identified as the о-plane. (See MeShane, Kelley and Reno, tzteriar BaUirtiet, Ref. 7.) 3—4.4 Magnus Mem eat Sign Coaveutieu If the projectile m viewed from the front, 0 is positive to tbe right and в ia positive upward. A project?!* with righthand spin (eounter-eloek- wie» rihen looking from the front) experiences a magnus force downward when 0 is positive. If the neuter of pressure of this maguus force is aft of the e.g. of the projectile, then the magnus moment is positive since it add» to the static moment produoed by positive e and (*na. In the study of the effect of e.g. position on the aerodynamic properties of the A-N spinner (Ref. 49), it will be seen that CMpa increases as the eg. moves forward. 3—5. METHODS OF MEASVRIMG TH.* COEFFICIENTS 3—5.1 General la order to be able to predict the performance of a proposed design, a good bit must be known about the probable pattern of the air flow over the projectile in flight. Thia air flow is mathematically described by the aerodynamic coefficients, as these must be measured or estimated. Estimation, by methods referred to below, is adequate in tbe pre- liminary design stages; however, if the coefficients are not well established before prototype rounds are manufactured, the designer runs a great risk of a totally unacceptable performance when the first test firings are made. Furthermore, the proeeea of maximising one desirable characteristic, such as lethality, which involves reducing other per- formance characteristics, sueh as stability, to their minimum acceptable values ean not be intriligently carried out if the principal aerodynamic eoaffiriente are not known to a dose approximation. 3-12 Methods of Mease rsmeat Two methods are in common use for the measure- ment of coefficients, both of whieh yield values whieh are adequate to permit eonfldent design compromises. That is, they yield not only sufficient- ly accurate values of tbe coefficients of the design being tasted, but also good estimates of the changes in those coefficients whieh would result from small changes in the design. Tbe two methods are: a. Ballistic range tasting b. Wind tunnel tasting Tbs method ehornn in a particular ease stay depend on tbe technical eonsidarationa listed be-
ЛМСГ 7(MU242 low; if not, it depend* on factor* of time snd co*t. Major considerations are tbe availability of the range or the tnnnel, and the «peed with which the necessary data reduction ean be performed at tbe available facility because costa are usually not widely different Estimated accuracy of aerodynamic coefficients obtained by ballistic range and wind tunnel tecta ia abown in Table 3—1. 3—S3 Factor* to ba Cansidsred 1* Selscttea of Method The condition* and objective* of tbe teat should be thoroughly discussed with personnel of the facility ehoeen before any work ia started on test models or prototype*. However, to assist the de- signer in the preliminary djsenasion, significant difference* between the two method* of testing are dearrihed below. 3—53.1 Free Flight (BtlHotic Bange) a. Good control of Maeb number, velocity, temperature, and premure*. b. Little control of modtl attitude. e. Medel must be statically or gyroacopieally яСяЫв, d. No strut to interfere with baa* flow. a. One teat cover* a range of Maeh number*. t Data obtained from shadowgraph*, photo- graphs, and yaw cards, with the poaobility of telemetering асам data. g. Data reduction i* eompHeated. h. Models usually full aeale. L Baynolds number ean be varied by varying sire. 3-433 Wiad Tunnel a. BxceUent control of Mach number, -velocity, temperature, and proaouie*. b. Excellent control of model attitude. a. Can obtain data on both stable and i natalil г couflgarstioM. d. Model anpport may interfere with baaa flow, o. Only ом Maeh number per toot. f. Data obtained from fore* and moment hal- амаа, maars tape, aohVoren photograph* or shadowgraph*. g. Data reduction ia simple. h. Models usually reduced in aiae. i. Bcynold* number ean be varied by varying tunnel premure (it may not be possible to teat at free-flight Reynold* number). 3—53 Data Basnlriag tram Ballistic Baage Teats For a test of thia type a projectile is manu- factured in accordance with the preliminary design drawings; if length or diameter is too great, a geometrically sealed model with a proper mam distribution may be made. The projectile is fired along a nearly flat trajectory in a suitably instru- mented building. For a description of sueh a range, it* instrumentation and method of operation, see Ballistic Research Laboratories Beport 1044 (Ref. 13). (The U.8. Army Ballistic Research Labora- tories at Aberdeen Proving Ground, Maryland, will be hereinafter referred to by the initial* BRL.) The designer should be familiar with the capabili- ties of BRL, aa this installation ean be of major assistance to him ia any design problem. A* the projectile flies along the instrumented range, a number of parameter* of ita motion are very carefully measured at successive stations along the range. They ar* a. Velocity b. Roll rate e. Ta* angle d. Taw orientation e. Swerving motion From the position versus time (velocity) data, the deceleration of th* projectile can be inferred. Knowing the ант and diameter of the projectile, and having observed the current value* of baro- metric preaeure, tea^onture, and humidity; wo an able to compute the drag and drag eoeAsient, C*. Befaat brings at the mm* velocity eaa give tbe variation of С» with ya* angle (equated), end sate of flring* at different mnarte velniitieo will gh* the variation of C* with Maeh number. If the pro- jectile ia rofkot sestets 1, teat flrings with rceket ignition wil! gh* not thraat. All of the eseAsteete hated above aun be de- termined in a baMatb rang*, anopt that C»f and Cai » hhrnya determined aa a ana. Tbe yawing fiequMotm aad the damping ан deter-
лМСР 708-242 TABLE 3—1 ESTIMATED ACCURACY OF AERODYNAMIC COEFFICIENTS OBTAINED BY BALLISTIC RAMGE AMD WIND TUNNEL TESTS Ccrfident EeitmaUd Maximum Error" in Percent BaUuHc Наяде Wind Tunnel C, Drag ± 0.5 ± 2. Co. Lift ± 5. ± 1. Cm. Static moment ± 2. ± 1. Cm, + Cm; Damping moment ±10. ±10. C“>. Magnus moment ±15. ±10. Roil damping moment ±1. ± 1. e.p.-c.g. ' Separation ± .10 cal ± 0.10 cal Magnus force ±25 ±10 "Maximum error equnb 3 std. deviation* mined early in the procev of the reduetion of the data, and indeed the dynamic stability of the projectile at various Mach numbers can be directly observed. Dynamic instability may be catastrophi- cally apparent; cbeervation of the projectile in a free flight condition ia.one of the major advantages of testing in a ballistic range. If it is desired to assess the effects of varying initial roll rate, this may be accomplished if suitable gun tubes are available. Usually, however, the designer does not have roll rate at hia disposal because even if the projectile is not designed to’fit an existing gun, rotating band strength or tube wear usually puts a limit on the allowable spin rate. Coefficients of typical projeetilea, determined in a ballistic range, with estimates of their accuracy, are given in Table 3-2, and in the Aerodynamic Data Sheets, Appendixes VIII-A through VIII-Z. A list of the ballistic ranges in North America which are uaually used for projectile testing ap- pears ia Table 3-3. 3—&S Data Easultiag from Vlad Tunnel Testa A test of thio type is usually madb on sealed medeb having the exterior configuration of the projectile’s preliminary design. The interior of the model is hollow and contains suitable provisions for mounting the model on a sting or strut which in turn is supported by a structure attached to a stationary portion of the wind tunnel If the model is to spin, the internal provisions inelude bearings and often a drive motor. Internal strain gage balances are generally used to measure the aerodynamic forces and momenta. All of the .aerodynamic coefficients previously diseuaaed can be determined in wind tunnel testa C«( and Cs; can be determined separately if deaired. Very accurate determinations can be aaade if the need for sueh accuracy justifies the eost Coefficients of a typical projectile, determined in a tunnel, with estimates of their aeeuraey, are given in Appendix VI1I-Y. 3—5A Tact FadUtbs A partial liat of ballistie ranges and wind tun- neb in North America vhid are suitable for artil- lery projectile model testing appears in Tabb 3-3 and Table 3-4, respectively.
АМСР 706-242 TABLE 3 I COEFFICIENTS OF TYPICAL PROJECTILES MEASURED Uf FREE PLIGHT AMD ESTIMATED Identification: С», (peak value) Constants ia Q function (See par. 4-7.7.1) Range of validity C»f (avg) • 105 mm Ml 0.401 .01 1.54 0.22 .2.70 1.13MS2.5 6.0 Cm^Cpfadr j. 41 ±0.01 1.62 0.20 2.» 1.2SM^3.2 7.0 7-Cal A-У Spwcwr 0.46± .01 1.50 0.25 2.60 1.1SMS2.6 8.0 Свфейп1» of Jf - 1.3: determined by free flight measurements Gre 2.310.2', 2.010.1 2.0510.15 сф. (eaL from base) 3.4510.2 2.7Ю.1 5.410.1 eg. (eaL from base) 1.75 1.05 2.95 Cm. 3.910.1 2.7510.06 5.210.06 Gw. + Cm; -71Г —9 —2010.5 C-w 0.0310.05 0.25 0.401.08 4 -0.191 001 CoffiatnUaiM - / .3: estimated by Simmons-Wood methods <i. 2.40 2.80 2.80 о.рь (eaL from base) 3.10 2.00 4.90 3.25 2.05 . 5.40 3—6. METHODS OF ESrUUTIMG THE COEFFIOEMTS Sines it is waatefnl to constmet a projectile or projectile model for range or wind tnnnd test whieh has no rhanno of вместе, and which aty even destroy walls or fasti ostentation of the V11****» range when fired, it is neeereary to make prelimi- nary astimatea of the principal eerndynemiu eo- ef&eients before tasting. The methode of making such eetmatao an given in the list of reports, Table
▲MCF7K3C2 TABU 3-3 PARTIAL LIST OF BALLISTIC TXST RABGXS U SORTR AMXRXCA Ифпм» CMMNMt ВаДаяй йммгеЬ Laboratoriea Aberdeen Proving Growti Maryland Ref I# BRL Report 1048, W. fhaua Two tang* Projectile up to 8 inehea max. diameter Na val Ordnance Laboratory White Oak, Maryland NAVORD4069 Three range, two praaanrimid NASA Лама Reaearch Cwtar Motet №, Caldera* NACARapcnISS Several range Canada* A**et Rerarrh aad Devrinpewt Embhhant Qoetee Gty, Canada Caaadua A«ra- aaatMal jMnaai, May IBM Large rang»
AJSCP ТО-342 TABU 3—5 UST 07 REPORTS CORTADTTHG METHODS OF BSTDKATIBG COEFFICIENTS Quentty J^wwnaaa CeawMal Or. aad C„a Simmon* (Ref. X) Hitchcock (Ref. 81) Wood (Ref. 21) Kelly (Ref. Ifi) Not readily available ' limited range of uoefalnem Raced oa Simmon*; nerd ia thia haadbook (See Appendia III-A) C„, + См; Hitchcock (Ref. 81) Domace (Raf. 15) Conventional apia-eUbiliaed projeetilea af length L (fairly good for 3 < L < 5) d Reproduced ia Murphy aad Schmidt (Ref. 40) C»e- Martin (Ref. 40) Kelly (Raf. 3») See ateo Ref. 48 34. Sample mlniteticae ar» ahewa ia the Ap- peodixM. Three methode ar* faadaaMBtally baaed oa aa iaterpetetioa ef data from wry maay wind tuaael aad baUietie raage tecta of a erid* variety of prejeetih* ahapee. Uae ia made of linear aero- dyaaaeie theory ia eeaotrartiag formula* for per- forming the intarpetetieaa Wbtte theac fermutee heald of ooaree act be and ter Aapea which lie outaide of th* raage of the data on which they an baaed, it may be a re emery to am them for aammal •hapee when no other method of eotiwiation ia available. Such abapm ahonld be tooted ia a vr ’ tuand; moot balliotic raage operator* would ref to fire thaw hetimated eoeAeieata of typical projectile ahapaa, for eempartean with vahrne obtained ia ballietie raage toot*, an pnoeatod ia Table 34.
АМСР 706-342 CHAPTER 4 TRAJECTORY CALCULATIOMS 4—L gxyxral The parpm of a calculation of a trajectory, the rarve ia opaee traced by tbe eeater of gravity of the projectile, ia ooualiy the prediction of the ex- pected pent of import of the projectile, «he* fired at a give* mandr eeteoty and qnadnat elevation, along with the prediction af nmorirtrd gaaathire aaeh oa time of flight, aagte of fall, aad reloeity at impact. Bemetimes the raage ia stated, aad the pnrp-.se of the eoienlatiaa ia to find the eerriopooj- iag marie vrieeity and/or gaadraat ilmtioo; the three eriistaral eaantitioe are still of iateTNt Or the trajectory may he a groaad-teair type, oa for aa satiaireraft projeetile, for which ainaer aititade, tim to raaeh a given attitwie, aad tra- jectory earvntnrv are impertast roonEa. 4-2. ытштт сотквт аж ЖЖПГПТТТТ FACTORS •tee m*. by varying tbe enpata to tbe trajectory aaicalotoea by авий aaeaata, ear at a time, rom- pnte the ebangr in asported raaga, time of flight, or ether gmmtity of ia to rad, canard by a email ehaagv ia raeb mpnt pnraasoter. The percent ehaage ia taagn (or other oatpat quantity) predated by a 1% cbaapr ia aa mpat parameter m ended by came writers a ••didorootad rorifieirot", by others a "seuritivity factor.” Tbe feeters are d^crvnt foe oath deriga. ш weU as for rldhrsot internals of tbe valrn of tbe input pn-nmcters. whieh in why they mast be dotermmod by aamll pertarbatieae aad the partiroiar aoe of oaadrttona for which they arc valid mat be stated. A aneapto ad of oraritrvrty Inelm for a Mchstmdotod projectile fired Isr ав1амаа mage m pwa in Tbbto fi-L 4-3. DIGITAL COMPUTZR PROGRAMS FOR TRAJRCTORT CALCULATIONS MleeAstMdB Ъмв erode. aad are stiU bring mode, for the prodaction of firing tables. Up to tbe advent aad general adopti~n of the high speed digital oompater, those mini latinos were performed by approximate math eda wbiih employed overage or odhetive calm of the drag roeCrient. The varioas methode were named for their developers, the Garre n—imiari—. Siaed, and Mayevoba among others. These smtheda are still naefnl for roped aetiarotiena of the effecto of variations in projectile shape, амв1е velocity and quadrant elevation on range and tiase of flight. The neeoesary charts aad tables with directions for their one, are give* ia AMCP 704-140 (Ref. 97). Digital comptiter programs fall into two dasroe, particle trajectories aad six degrii rf-freedom tra- JtslMiMp вмЬ * 4йяиЫ tabw. 4—3.1 gtmpte Particle Trajectory The rriotivriy eimpie particle trajectory pro- gram amnaroe that the only forma an tbe pro- jectile are gravity, drag, and, if present, thraot. The herieeatal and wrtieal aeerieratioas dwe to these foevm are computed at eueeoarivs potato ia tian, aad tbe rvoatting herisoatal ami vertical eompeneato of tbe projectile's veledty aad petition are competed for roeh time point If tbe time in- terval a aamll eaoagh. the titon lotion of the tra- jectory eaa be very good. With a time interval of O.JS oeeend, the time repaired to eimalate a typical trajectory on aa IBM 1490 eompater mat abent ten time» tbe time of flight of the projectile bring rimtoted. This foealted in an aaenengy of
AMCF 7116-242 simulation better than 1%, assuming that the drag eoefieien' ewe used averaged within 2% ot the true C* at all Mach numbers travened. If no com- putation of yaw ia made, C*t, the axilc drag eo> efloent, ia the eocffeient uaed. Since projectile velocity and altitude are known at саек time point, Maeh number ia ahwaya available for entering a stored table of С», vs Maeh number. Tbe particle trajectory ia very naefnl in com- puting trade-offs of range, time of flight, aad lethality, particularly in eaae of a rocket easiitrd projectile. Bxtenawan of tbe program to com- pete muzzle vehnity under tbe limitations on muzste energy and musrie momentum, aad then the merinos set beet aeeeteration, ем further aato- mrie the donga proeom. 4 । U fix Degree of У reed ms Particle Trajwnocy Tbe stx-degree-ef-frmdam system ia seldom coded fee anything smaller than tbe «inivaMut of an IBM 704. Thio program computes tbe position and velocity of the projectile relative to all thiyv asm of the coordinate system(s) chasms, aa wen as the portinent aagtee aad angular veioeitAe. All of the aerodynamic tsrffriiets ru be mod (although many meind order tones are usually left out), aad the rmuttisg eimnbtieu of the trajectory is earn- plots, down to ysw angle, yaw ersoMataen, and sen list ambon. dt redye am к jump to on unto- emtio by-prodnet of this system. Wmd ean be intendawd ma variable. If nil rata, and the vortolion of Ca, with Math sombre were iaeludid ia the particle tra- jectory program, thou either program could esn- tlaaoueiy cheek the gyroscopic stability of the projectile and calculate the jaw of repose, Tbessx- degrooW-frvedem cyst ms ossdd ahs riatinwousiy chock the dynamic etahiiMv of the projectile. 4—3J Banmpto of Nmpio httkh Trajectory Catentettoa (УОЖТЖАВ Pngna) The FOBTBAX particle tmjistory avogram pomoatml belew wes written fee м IBM 1O0 com- puter with ЖЦКМ unite of aw miry. it will oem rocket-asaisted projectiles, either spin- or fln- htabilized. and single-stage roekete. The spin, yaw >f repose, and gyraeeopic stability computations do uot allow for the presence of fin eant or nocxle «•ant. The limited memory available nude it aeeeesery to read the headings for the output (see Table 4-1 for a sample output) from cards. Appendix IX dewribn the input cards forming the data deck; the numbers on the iuput eardc describe tbe pro- jectile and its launching environment. Heading cards are a part of the data deed and follow tbe numerical data, except that the first eard of the data deck identifies the projectile heiny pro com rd. An experienced programmer, or one having scrim to s computer having a larger rm згу, will be able to make many improvemeuts in and ex- tensions to the program, presented here. For ex- ample, this program isterpolatm haeariy ia find- ing C>, or C«, from the tables provided by the data deed; it nmy be iiffenlty to represent a given curve eufliriistly wed with only nine data pointe. Furthermore, while the computer will print out CNSTABLA whoa 8, is lem than unity, dynamic stability must bo computed by hand. A typical output produced by the program given bri.'W is presented ia Table 4-1. Projectile data an for the sample peojeetites uaed to illustrate the methide of mtimetisg gyromspie atability (Appmdiim I-VI1). The form farter relating tbe drag of the oample projectile to that of the fi-ineh/M Navy projectile stored in the eoosputer mesmey was mtimafied to be 106 since the only significant difference in chape is the shorter oom of tbe cample projectile. The form farter relating tbe static moment eoeffeieat of the sample projectile to the С», table stored in memory wm mtimeted to be 1.142, booed on tbe Wood-BioMconestimate oik з 1.72. The loot Uno of the computer output givee the time of flight ia amoate, the range in meters, the vrierity at impact, angle of toE, aad the ф!п and gyroimp is stability faster at hapmet. Ths target to at the come etovwtioa ш the gun (ma level) in thio example, bat му dwirsd target itovotiis ем be M with the data.
АМСР 706-242 The. fundamental equatione undeiying the com- puter program preeentod below are: дг - дв.^^вдх AX - (F eo* 0) At AX - (Ужав) At Averaging technique are uaad to imptv*» the ac- curacy of the aimuiatinn 4—4. DESK COIMTH METHOD FOR TRAJECTORY CALCULATIOR Reference io made io Tahie 4-2 for the format of the drok eomputaiioo. Note that the eoeditioae, в. and appear ia column* 2 and 5 in tba dnt row. Starting with thane initial eraditicno, we now proceed with the rempntatina aa ItUowa: a. Compete the lemaininet ertriee in Ant row. b. Proceed to neat row: locate С» oa the drag curve of the projectile; calculate the drag, D, reelerotica, D/ue, where m ia the projectile aMaeiaaia^. e. Compute: (1) dF, _ _ Deeeft (2) <У, Dam 8 Л “ m " ’ d. Multiply the above darivativon, dF,/dl aad d1\/dt, by the earrewtly ahaeea time interval. The nonIto aee AF, and AV, in the third row. *. Compute V, aad V, at the tad of the time interval (they appear in the fourth row), aad am avenpt veloeitim over the Ant tim* interval to rrmpwte Ax and At (third row) and the new g aad a (fourth row). t. Compute th* new V from V = >/77T7? determine в from в = tan -» V./V,; fad oo* 8 aad aia •; aad romplrtr the fourth row, uatag np |—SI x 10-‘r| and V.» in«-aoote. g Continue aa above far remaining entrim to 4—5. METHOD OF CALCULATIHG DIRECTION OF TAMGXMT TO TRAJECTORY It may be of internet to diacum the equation uaed in the computer program for the calculation of the direction of the tangent to the trajectory at the en^of each time interval la a partide trajectory, where lift and magnon force are negieetod and drag io aoeumed to aet in line with the velocity vector, the only force ье-iag to change the direc- tion of motion ia the weight o£ the projectile. figoro 4—1. Diograw of Gravhy Ferae oa Prajeddo The inertial force, or centrifugal force, arieiag from th* curvature of th* trajectory, m given by a»V*/Jf, where m m the projectile maaa and i a th teeal rodbm of enrvataro of the trajectory. Thia m balanced (Figure 4-1) by the eoaopenawt of the projectile weight in the diroetien of the rediuo of earvaturo, mg am •, aa we ana write But F/R i* the time rate of change of the diraetiea of the radraa, aad i* therefore ateo the liaoe rote of charge of the direction of the trajectory tangent, tone* the tangent i* alwayt normal to the rodiua rorter. Dena ting the rote of change of direction by dB/dt, w have AD--poaaiLAVV
АМСВ ФЖ. ДО TABLE 4—J TYPICAL OUTPUT OF PORTRAIT SIMPLE PARTICLE TRAJECTORY PROGRAM 5-IECH SAMPLE PROJECTLIE (SEE APPERDIX I) FFD FFM TYPf AGA RGT D.FT 1.050 1.142 5.540 .381 1.030 .4150 WTO , vo • 46.08 1925. WTB ZO 46.06 .001189 1116.0 SPIS SBT DTM TWIST QE .0 .400 28.00 45.000 TEMP DTL DTE CDD2 CLP 59. 4.0 .350 6.00 -.014 TIME X DIST V CO CHA DR MASS THETA Z THRUST DRAG YAW MACH SPIN SG 50*. 11 *:й 6682. 6188, 3210. 3109. • 1925.0 .331 197.4 .000 3.59 1.000 1.72 224 4469. 1578.0 .362 3.79 905 131.3 .001 1.42 261 9110*. 1265.9 .398 4.14 820 84.1 .002 1.16 311 14166. 993.0 .290 34.3 .004 4.91 .92 744 379 20596; 786.3 .168 4.32 676 11.3 .010 .73 456 26412. 684.8 .169 8.3 .016 *:a 654 502 26686; 682;4 .169 4.20 654 8.2 .016 .64 503 32099. 686.1 .168 8.6 .014 4.20 .64 37859. 762.2 .168 4.28 w 11.7 .009 •70 414 44371. 866.5 .176 4.42 866 18.4 .004 .78 .344 9.80 1.43 TIMERS RAMGE,M V.TPS THETA.D SPIN SO Mils 12281. 929. -59.$ .303 2.19 44
TA*. —I ПЯТИ TRAJECTORY C'-CULATBD 01» DBSK COMPUTER S-1XCH SAMPLE PROJECTILE (SEE TABLE 5—1 FOR SAKE TRAJECTORY USIBO BLBCTR0N1C COMPUTER) t. •ее e. ooe8 0.0 3.00 о9986 0.90 2.10 .9993 1.04 1.95 .9994 1*74 1.21 .9998 2.94 -0.02 1.00 4.09 -1.70 ААЛ/ • WtQ 5.15 -3.17 •9985 5.72 -3.98 •9976 •tn 8 V, fp« Vx ^x/dc AVx .0523 1925 1922 -138 -124 .0367 1799 1798 -124 - 17 .0342 1782 1781 -122 - 85 •0212 1696 1696 -113 1561 -135 -.0038 1561 - 99 -114 -.0297 1447 1447 - 89 - 94 -0554 1555 1353 - 80 - 46 -.0696 1310 1307 x, V. dv«/dt ft ft A Ax Ae 101 -39 0.0 0.0 -35 1674 76 66 -37 1674 76 - 5 251 9 61 -36 1925 85 -25 1217 34 36 -35 3142 119 -42 1955 18 - 6 -32 5097 137 -37 1730 -28 ' -43 6827 109 -30 -32 1484 -62 -75 -28 8311 47 -16 758 -47 -91 9069 0 2765 eaters P.p. v* M D/n D,lb CD 1.0 1116 1.72 138 197 .331 .998 1116 1.61 124 178 .342 .997 1116 1.60 122 175 .344 .996 1116 1.52 113 162 .351 •996 1115 1.40 99 1<*Z .365 • 996 1116 1.30 89 127 .378 • 998 1116 1.21 80 115 .390 2.61 error compered with result In Table 5-1 AMCP 706-242
Ткж —utia—hip ш also need in derma* the oqna- taan tar p/7 whieh to presented ia paragraph ЛЛЛЛ. 4-4- EFFECT OF PROJECTILE MASS OB TRAJECTORY BiaeeCa, dote not vary greatly with inereeaing length to iiiameter ratio, a tony, and therefore heavy ronnd will experience a tower drag deceleration thaa a lighter round of the same ealiber aad general shape. Thia ia the reaaon for the пае of anbealiber or "inw" peojoetilm for antitank or antiaircraft Are, where a abort rime of flight to a givea target ia at great importance. The man- ner in which the паза of the round aT'eta the velocity, time of flight, range, and terminal velocity io shown in the treatment whieh foltowe. 4—4Л Hoeiaontal Trajectory la thia ease С» ia aoauaaed to be a constant, and the gravity curvature of the trajectory in aaauawd to be negligible dF d7 dt DI Cao PS U”1 S’’ “ a"v" SsF 80 ^-dhsF - InOegmtiag ghno bsF C (4-1) 4—AU Yotodty If we onbotitnte the iniriai eenditioaa, 7 = 7. when X, = 0, into Bganba* 4-1; C-toF. F-F.e«p[-^a] (<4) whieh chows the importance of a aasall С» aad a large там if a high velocity ia to be maintained aa X, the range, inmeaes. Replacing the frontal area S by (*/4)d* and m by W/g, we have F - 7.exp[ -- The ratio W/d* ia called “sectional density”, and in moat of the older publications ia written an ж/d1, using ж as a symbol for weight. 4-6.1 J Time of Fligjtt The time of flight to a given range ean bo obtained by eohsririrting dz/dt tar 7 and re- arranging Equation 4-3 Integrating and substituting intial eonditiook, a « 0 at i “ 0 If T ia the time of flight to a given range X, then (♦4) where Fr = terminal votoeity, or votoeity at« = X. Bines Г = X/7M aad 7W > 7n tho gmmtity in the parontbaem of Equation 44 io negative and the time of flight to a give* target deeroaom in pro- poetion to the relative in erases in the mono or weight of the projectile, Aas/ns, providing that 7. ie independent of projectile weight However, when designing a reend to *t an ototiag gen, muaoto votoeity 4 ep— de in a very direct manner on projectile weight If it to decirod to make the mam of the projectile greater than the
AMCP 706-242 mass, M.M, of tbe standard projectile fired from that iron, then 1’. will be Im than the mutzle velocity, <>f the x'auilunl projectile. Thix м due to the шчччыНу of ktx-piug tile inunde nioinen- tuiu, and therefore the load mi the recoil xyxteiu. at or below the rapacity of the xystetu. We can write Г. _ *•**••*{& at 2 Ч1.Ы and substituting this in the Equation 4-4 for time of flight we get 2ж» i 1 * "w V-CawS I “P . гт vr x____ gm ” at mVr -*(£- /,) Since tbe average velocity is usually not much dif- ferent from the terminal velocity for the flat trajectories of interest to the designer (and indeed cannot he if tbe assumption of constant C* is to be be valid), we can conclude that increasing the projectile weight in a momentum limited situation will usually increase tbe time of flight. If the projectile mam is less than ацм, then V. is limited by chamber prmnra (a constant energy constraint, mF*. = atue^iw) and ЭТ/Э m = 1/m (3T/2 — X/l'r). Here there in more likelihood of decreased tiam of flight. 4—4.13 Ttrmfasl Vetodty Increased projectile weight ean, however, im- prove tbe terminal velocity. If we substitute F, = ацм Pmin tbs velocity equation, 4-2, m we get avr 9b So г- -|- decreases with increased projectile weight for ranges which are shorter than 2m/ (f'opX), and increases for longer ranges. For a typienl 20-mm projectile weighing 0.22 lb, C&B might be (1.4 X .IMK37H x s/4 (0.066)»= 4.1 x 10 * and the range beyond which inereuaed projectile weight will give increased terminal ve- locity will be about 1000 meten. At thia range Г/V. will be e~‘, which makes the assumption of constant Co questionable. The accuracy of the estimate of tbe eroes-over range eould be improved by performing the calculation in steps. Since pro- jectile weight generally increases faster than frontal area with increasing diameter (m = Ы», approximately), tbe cross-over range generally in- creases with projectile caliber; for a 105-mm pro- jectile weighing 32 lbs, 2m/(Cep 8) would be about 7000 meters on tbe assumption of a constant C* of 0.40. 4- 82 Curved Trajectory, Antiaircraft Fire The analysis of antiaircraft Are is complicated by the ehanging air deaaity aad tbe inability to neglect gravity and trajectory curvature; it will not be attempted here. 4—7. EFFECT OF DEAO ОЖ TRAJECTORY 4-7.1 General Tbe drag of a projectile has a direct effect on its range, time of flight, and wind sensitivity; and leas directly affects both static and dynamic sta- bility. In order to obtain long range, abort time of flight, aad minimum lateral defleetion due to side winds; the drag of tbe projectile should be as amall as possible. Sometimes stability eocsids-ntions will lead to the acceptance of a high вето-yaw drag. A reduction in yaw, obtained by improving atability deereaem the yew drag aad may improve aeeuraey by decreasing asrodynaaue jump. The material on drag which follows is eoaflned to tbe drag of a projectile flying ia line with the tangent to tbe trajectory of its e.gM La., at aero yaw. The drag eoeflkient at aero yaw, C\ , san in thb situation ba sailed the axial drag eoeflhient. Tbe increase in drag with yaw, and its ooaflteient, win be dbemosd h рал«тарЬ 473. For a won behaved projectile the initial yew damps rapidly to
АМСР1Ш442 a ff"*” value, «о that by fnr tbe prater component of С» ia С», . The minimisation of Co, is, there- fore, of primary importance in nearly all cases. The designer most seek a projectile shape whieh will have a «mall axial drag coefkient, Co,, and yet h/ve anfleient internal volume to carry the re- a-'ired lethal charge, lie must also avoid, as far as possible, surface irregularities such as alota, de- pressions or protrusions. The effect of general surface loughntm varies with the velocity regime of the projectile; thia will be diaruewd later. the carfare of the model in a way whieh depends <hi its ahape. 4—73.1 Subssak Bagion, 0 < M < 03 ± The aerodynamic eoefleiente of a conventional projectile are fairly constant when the projectile io flying (or being tested in a wind tunnel) at Ma< h numbers lean than some critical number, whieh ia usually in the vicinity of 0.8. This is the model or "free stream" Mach number at which the flow over some port of the model reaches Jf= 1.0. 4—73 Axial Drag The axia) drag at aero yaw may be divided into three components: wave drag, friction drag, and Ьме drag. The relative importance of the various components depends strikingly on the Maeh num- ber regime. For example, wave drag is absent in subsonic flight. For this reeaou the designer will ehoose different shapes for rounds whieh fly pre- dosainantly in different regimes; however, many artillery projectile fly in all throe regimes and a trajectory calculation of some sort must be made if the optimum drag ahape is to be found. Wind tunnel testing with pressure surveys will provide a division of Ca, into its components; ballistic range testing gives only the overall value. The designer is urged to refer to Hoeraer, Flvid- Dys cetin Drug (Bet 27) in all matters relating to drag. 4-73 Meet of Mach lumber The mmplaot way to dineum drag is from the point of view of a paraoa observing a peojeetile flxad ia a wind tunnel, with air flowing around it The aanpeed of tbe peojeetile is then dearly the voteaity of the tunnel air far enough upstream of the model aot to be mgnifaaatly altered by tbe peossnee of the model. Tbe speed of sound, in the tunnel air at the point at whieh the air velocity is measured then gms the Meet number, V/V„ at whieh the toot is being conducted. At points in tbe neighborhood of the model the air vskieity is altered in magnitude aad direction but the speed ef мшЫ1 to mmmmA to ta w thto total M*ta wntocF wto* tras petal to peel ew 4—733 Transonic Bogies, M л < M < 1.1 ± At a free stream Maeh number slightly above the critical value, the eoefteients such so or <’/>, begin to increase rapidly and the projectile is said to have passed from tbe subsonic to the transonic regime. 4—733 Supermaic Bagtea, 1 < M < S At some free stream Maeh number greeter than 1.0 the wave system characteristic of compressive flow is fully established, and the projectile is said to be in the supenonie regime. 4—73.4 Hypersonic Bagioa, M > 5 Above M=5 the flight is tensed hypersonic. This regime will not be diocnsssd so very flaw con- ventional artillery projectiles fly at such high epMck 4—7.4 Xfcct st Bsyaolds Member on Drag Caodktent Drag eosfleients are also influenced by Boyuolda number; geoasrtrieally similar projoetilas of dif- ferent calibers win bare slightly different Ca, vu Maeh number curves. 4—73 Subeaate Drag la the subsonic range (0 < Jf < 03 ±) wa would like to have a rounded, but nut noeoemrily pointed, мое and so aaull a base diameter as san be ja-t-vieed in view of the ашу eonsiderationa whieh afftrt projectile shape, sash as required in- ternal vshsam, weD strength, propulsive method. 44
АМСР 706-242 type of stabilization, fuzing, etc. The eSect of pro- jectile shape is discussed below. 4—7.S.1 Surface Roughness asd Irregularities Surface roughnem corresponding to ordinary industrial practice wilt have little effeet on the drag coefficient. Surface irregularities, ouch aa dots, shallow holes, and protuberances may increase the drag very greatly, depending on their location and orientation. Fuzes are often poorly designed in thia respect nnd consideration may be given to covering them by a windshield. 4—7X2 Bloat Item Blunting the none of a projectile will, in the subsonic regime, have little effect on overall drag. The important effeet of blunting (short of a com- pletely flat face) is to lower the critical Mach num- ber. Small flat faces, such aa appear at the nose in many point-detonating fazes, have little effect on drag. The integral of the dynamic pressure forces over a properly shaped head will be dose to zero, and the forebody drag will accordingly be dose to aero. The base drag is thus the result of a pressure deficiency over the base of the projectile; the existence of this sub-static (less than atmospheric) pressure ia evident in everyday life in the wake of trains and automobile*. 4—7X3 BeettaiBag Reducing the diaaseter of the base below that of the cylindrical body, called “boattailing*’, is a very effective way of reducing base drag in the subeonie regime. Boattailing also reduces the lift coeflteiont and changes the position of the eenter of pressure of the normal force, moving it forward. This reduces the stability of the projectile, placing another limit on the amount of boattailing that ean be tolerated. The extent to whieh thia ean be done on a spin- stabilized projectile is limited by the necessity of applying a rotating band, which moat be supported by s relatively thick wall, and by the fact that the projectile walk aft of the rotating band are ordi- narily exposed to the full chamber peemure so that they must aloe be thick. These considerations limit the length of the boattail aad may also limit the amount of reduction in bees area. Um of a hollow boattaii avoids these limitations, bnt sacrifices in- terna! volume. Г sc of a large bouttai! angle (greater than about 16°), without a rounded transition from the cylindrical body, ean cause the air flow to separate at the junction, cancelling all of tiie drag reduction. 4—75.4 Fin-Stabilized. Projectiles The zero-yaw drag of fine ia. of course, related to their shape and siae, but these arc dictated primarily. by stability considerations. While it is true that some fin profiles have less drag than a simple flat plate, the extra cost of manufacturing the double wedge or streamline profile fins must be weighed. 4—75 Transonic Drag 4—7X1 Spin-Stabilized Projectile The transition from the subeonie to the super- sonic drag regimes is clearly illustrated, for a typi- cal low-drag spin stabilized projectile, in K. D. Boyer, Aerodynamic Properims о/ the 90-mm HX M71 Shell (Ref. 79). The ogive of this projectile ex- tends over about half its length, the boattail is half a caliber long and the boattail angle ia 7*. Its subsonic Cd, is 0.15, even though the rotating band area has four circumferential slots. Shadowgraphs at M = 0.88, M = 0.97, and If. = 1.05 show the initiation of the shock waves at the points of abrupt ehenge in diameter and their growth to fully developed wave*. <’», ram from 0.15 to 0.39 in thia Mach number interval, as ean be seen from the drag curve in Appendix VHI-B. No shock wave appears over the nose of the projectile before photograph at If = 1.05, when a separated bow wave is present 8o we ean eay that for this projectile the transonic regime rovers the Mach number range from approJasatriy 0.88 to 1.05. Note thia is only one example; the numbers would be different for a different pro- jectile. The development of the oboek waves on the body and fins of an arrow projectile is shown by the shadowgraphs in BRL Report 934 (Ref. 89). The greatest pert of the increase in drag in the tranao. ie regime eaa be attributed to the proaenee of the ahoek waves aad b called “wave drag**. The bane drag peaks at about if = 1.0; the friction 44
AMCP 706-242 drag becomes relatively amah ax the total C„t in* ereaar*. 4—7.A2 Fla-Stabilbod ProjectUe The draff of ty| й-al 'ui-xtabilised projectile in the tranaonb regime incresam in about the name •ay ax d«terihed nbovr, aa may be noeti from the drag curves presented in Appendixes VII1-T through VII1-Z. The designer should obtain aad study a number of shadowgraphs or Schlieren photographs of projectiles of varying shapes in conjunction with their drag curves. 4—7.7 Saparaaak Drag 4—7.7.1 Decrease of Cq* with Mach Bumbar After tbe shock wave system is fully developed, which usually oeeun at a free stream Maeh number batwean 1.1 and 1Д wa £nd that С», decreases with inerescing Maeh number. In faet, wa ean use Q = y/e-f-C», iP — a 4- Mf aa aa interpolation formula; a typical set of values of the constants might he a = 1.4, b = 0.2, e = 2.7. 4—7X2 Effect of Kass Shape on Cq* The aba of Cs, in the supersonic regime de- pends largely on the shape of the мае. By the Tayior-MaceoU formula (BaL Э0) wa have-. Cs, - (ли + where C*r is the forebody pressure drag (wave and drag) component of C*,, • b half of the cone angle, in degrees, and Jf is Maeh number. While by thb formula the lowest drag shape tor the глее would be a вопя, an ogival nose hav- ing a large ogival radius will have slightly lower drag (and abo afford a greater warhead volume). В. B. Diekiaaon (Bef. 24) found from ballistic range drugs at M = 2.44 that the minimum drag head shape at a caliber £0 projectile (d = 0.0417 ft) wm a secant ogive having a radius twice that af the tangent ogive af the sasse length and maxi- mam diameter (ratba between 1.7 and 2J5 were asarty as goad). The presmn of a araaD flat (or rounded) sur- face at the front of the мое, called the mfplat, has only a small effect on Co, , and indeed, if not top large, may reduce Си, slightly below that for a |M>iutn! iw of the same ie.igth. 4—7.73 Effect of Beattailing ea Сщ Boaitailing reduces the drag *>f м|м*лмшЬ pro- jectiles as long sa the airflow b abb to follow the contour of the body. For each projectile shape there b a critical angle (generally stout 8*) and a critical boattail length (about 1 caliber at ths critical angle, longer for smaller angles) beyond which the flow win separate from the projectile forward of the base, reulting in a Co, which b greater than the minimum attainable, and which varies from round-to-round with consequent deg- radation of aeeuncy. Bee Beta. 25 and 24. 4—7 A Dual Flow As a general rule, we assume that projectiles having the same shape and eqj. location will have the same set of aerodynamic eoefleianta when tired at the same Maeh number (and Reynolds number), and that small differences in shape and surface finish will produce only small differences in the euefficienta. The few outstanding exceptions to these rules are diseased below. 4—7.8.1 Spflm-ltaed PrajoctBm It waa found some time ago that replacing the ogival bead of a projectile by a slender cylinder protruding from the flat forward foee of the body would stove the e.p. of the normal foree rearward, reducing and reducing tbe spin nue required to stabilise a spin-stabilised round, or reducing the length of the tail required on a tin-etabilixed round. These spike-noeed projectiles had higher drag co- efficients than the corresponding projectiles with ogival heads. Aho, for some designs, projectiles from tbe seme lot, tired under the asase conditions, exhibited drag eoeOeients which fell in ом or the other of two groups, with tte aversgm of the two groups as much as 30% apart. Examination of spark photographs showed that the low drag coeMeients were associated with rounds on which the airflow separated from ths spike at its tip, whib oa tbe high-drag rounds the flow separated at a point about half-way down ths spike. Thb phenomenon wm called “dual 4-10
АМСР 706-242 М = 1.73 M=2.75 M-3.80 L=I.O CALIBER L'1.0 CALIBER L-I.O CALIBER L« 1.5 CALIBERS L=l,5 CALIBERS L-1.5 CALIBERS L-2.0 CALIBERS L-2.0 CALIBERS L-2.0 CALIBERS The pitiurea, taken ia the ERL мрегаоак wind taaael. ahow that the character of the low orer a apiko мае depeada «• Mach auarber aad near length. The tow aepantioa ia delayed, with ronaeqoeat inereaac ia drag, on the three photographa at the loner right hand eornerf-t. Thieher apikea ahonod delayed reparation at nhorter lengtha (Ref. Mb). Figaro 4—2. How ЯвИегт on Varying lengUi, Coaetant CaUbtr .33 Droaietar Spika Noaoa of Svpartonk Voiocffioa 4-11
АМСР 704-242 How”; it* rxmti'im* wax a function of tin* geometry of the spike. In order to avoid the oecnrrewe of dual flow, with it» Mcrionx effect on neenracy, modern apike-iKxed round* an* fnrnixlo-d with a maall ring near tbe tip of the mw whieh insure» the early ae|>aratio«i of the flow. Figure 4*2 ahowa the rffiwl of Maeh number and nose length on the .flow pattern prnditred by a spike-nosed projectile. 4—7Л2 Uadercut Prsjectilee Another example of dual flow was found in ballistic range firing» of projectile» haring the central part of the body deeply undercut; drag and moment coefficient» «tried from round-to-round by aa much as 50%. The flow pattern, whether high- or low-drag, was stable; i.e., onee established, it persisted throughout the observed flight of the projectile. The possibility of dual flow may some- times be detected by wind-tunnel tests when bal- listic range flrings do not reveal its existence. 4 7.8.3 Hemispherical er Sharply Conical Base Pnject&aa The point of separation of the airflow from the base of a projectile having a hemispherical or sharply conical base will also vary from round- to-round, but in a continuously distributed manner, ao that thia behavior й wot classified as '‘dual flow”. The hemispherical shape allows the wall of the base to be thinner, ao that more HE ean be earned, but extra care must be taken to insure dynamic stability (see Appendix VHI-H). 4—7.9 Drag Variation with Taw The increase in drag when the attitude of tbe projectile changes from sero yaw to a yawed posi- tion is called by some writers “induced drag.” This term is borrowed from airplane terminology, and is equivalent to "drag doe to lift.” For small yaws, the axial drag is very nearly unchanged from its aero-yaw value, and its component parallel to toe trajectory is also very little changed, since cos 8 =: 1 when 8 =: 0. Tbe normal force is inclined rearward at an angle 8, so it has a component in the drag direction which ia given by Cx, VqS when 8 = sin 8. The expression for the drag coefficient then becomes С. - С., + С», I» However, the nbservt*<i coefficient of variation of drag with yaw squared. <'„?, й usually about twin* as large as Ctt, . While the induced drag may be reduced some- what by rhutMtng a body shad's having a small dynamic stability may be impaired so that the act effect on drag may be unfavorable. The above observations apply to fine as well as to bodies. It will be seen that over-atabiliaing a finned projectile by means of a large fin lift may result in a C> penalty aa well aa increased muzzle blast sensitivity. 4—7.10 Muzzle Blast 4—7.10.1 Tawing Velocity Due to Transverse Vibration of Muzzle Nearly all projectiles emerge from a gun with essentially zero yaw. Even mortar projectiles, which have large bore clearance to facilitate drop flring, ean lie in the tube no more than 0J* out of line with the tube axia Tbe possibility exists thnt transverse vibrations of the muzzle may move the rear end of the projectile after the eg. has passed the muzzle; thin action, as well as any over- all motion of the gun tube, can impart yawing velocity, to the projectile*, but no significant exit yaw. Equations for aerodynamic jump, whieh is one of the two primary flight characteristics, will b>- presented later in this handbook. It is noted here that jump is primarily a function of initial yawing velocity, and not of initial yaw. 4—7.102 Transverse Prassure Gradteta TrSnsvent pressure gradients in the muzzle blast elnunpart some yawing velocity to the pro- jectile if the eg. of the projectile does not coincide with the center of pressure of the transverm fores. This effect is most prominent when firing with a worn gun tube. These transverse рпыше gradients are probably related to the bon yaw of the pro- jectile. Good obturation reduces the pt t mere dif- ferences in the blast aud shortens the effective blast zone, thus reducing initial yawing velocity, aero- dynamic jump, and dispersion at the target An improvement in accuracy of hot rounds over cold *For a ttiiivtiiil m4 azparimaata) sta«y af the atsrt» at gaa амСйа, aee >£. L 4-12
ЛМСР 704-242 rounds of the mum projectile* arises drit£r from their better fit in tbr tube, partly because bin- yaw is reduced and partly because obturation is unproved. 4—7.103 Fin-Stabilised Projectiles ш Bcwraed Flow Pm-atabiliard projectile* arc affected by the saiuxle biaet ш yet another way. For n abort lime after eaergrwer from the nusxlr the blast gases are flowing forward orer the fin surfaces, resulting in a large demobilising seoaseat which ean impart a significant yawing veioeity ron though the time of action is abort. it ia of great importance that the aerodynaanie moon rut rveSeirat of the fins ia re- amed flow be hept aa small as possible. Many photograph* of the Buazie blast are available in firing test nporta of the Devriopomt and Proof Services, Aberdeen Prosing Ground. Maryland. Sines the camera nasally takes thousands of pietarm per served. the imrrgram of the pro- jectile frees the smoke flood caa be eboerred, and the tiane spent ia reversed fiow estimated. The data frees the photographs ean be correlated with the dieperoioa of hits on the target; these correla- tion* Hearty shew the importance of ebtnratian for finntabilieed rounde 4—7.MM Obtnewtian Мшимо» of the rotating bond sterol into the groom of the riffiag aaualiy eesmideved to furan* odegMte eb.aratiea foe apinwtabrbaed rounds However, aeaae recent prajoetde designs here inciwdrd special obturating ring* or dines- miler to the drum remeieuty need an fin- stabilised rounds, these desires are deembed in paragraph 5-34. ♦—7.H Cramubad 4—741.1 WM fliaawidty While too projectile drsigwee cannot de any- thing about the wind, be ran de eomething about the eran№vity of baa project de to the effeet at wind. A etnde proysetde win am into the wind. Le, the tlw вжШ W trifle V0 ba Ш hue wt*b the mnltani of prajeotite votoeity and wind velocity. The net drag force (drag minus rorket thrust) will then have a component at right angto* to the projectile velocity. In the absence of rocket thrust, or ir drag exceed* thrust, the pro- jectile will acquire a downwind lateral velocity and displacement; if thrwrt exceed* drag, the projectile will aaove upwind. 4—7.1 14 Lateral Dodhrtira With no rocket thrust, a conatant eromwind, and making the usual assumption that the projectile aligus itself with the rmultant air-stream a* soon aa it leaves the muazle of the gun. we can write a very aim|>)e exprrmion for the deflection of a flu* trajectory by a t torn wind (асе II. P. Hitch- eoek. The Motion of ? Verj Stable 8MI at Short Beafct, BBL Report 1047, April 1958. p. 19). r-f.(T-p-) where T= lateral deflection at impart, ft F< = crosswind velocity, fpa T = time of flight, see X — raage, ft V, = mtusie velocity, fps The only variable in the above exprtmion ia the time of flight. Kubatitutiag for T ita equivalent, as given in paragraph 4-4-1Д we have From thia eqaatiaa we caa find that the lateral de- flect iea m mils deerraaaa with inirraaail projectile weight er snail vetaeity, aad iaoeawo with ia- ervaee ia C*. Theos relatmaa taramb the desigwr with addi- tions! rsaaoas for arebiag toe* drag and high aertiraal draaity (nairas bin projectile contains a rochet aaetar, when the trade-off aituatioa besnaaea mare eaatpbm). 4—7.1J VataaaotC^ so Mach Rumbee Corvee of C*, ve Mach number for typical prajeetitoe are diawn ia Appaadiara VUI-A through Vtlt-Ж. The raatgnfgtiea ef the pre. jaetUr ia Aewa an rar* pagr la seder in raobie ths drainer to iMrrpilaii between ahapae 4-И/4-И
AMCP 70С-М2 CHAPTER 5 CHOICE OF METHOD OF STABILIZATION 5—1. STABILITY 5-1.1 GemI In order tn have a «mall induced drat, a pev- jaetile niuat be иаЫе, i r„ the yaw of tbe projectile moot damp to a «mail equilibrium aagie mrty in ita Hight. if not atatieatly М>Ыг MT gynwwpi- enlly ataMe, tbe projectile will entnawnev to tuaMr an anon aa it leaven the retuxlr of the gon; if not dynaairally atable. tbe yaw of the projectile will grow eocrtinnomiy with tune, ou that the project tie will taa.bie nr go into a bat «pin mile- the eipeeted tune of flight ia very abort. 5—1Л Static aad Gyrwecapic Stability Static atabatty b related to the pout мп af the ।enter tt aiemari of tbe патам! fnrre with reopect ta tbe eg. of the proyretile. If tbe e p b aft a( tbe eg.. tbe projectile -tatieaUy Mabie, re. any yew of tbe prejnetde produre* о maaarnt abaart the eg. «hath tend* to ret am the aria of the prajectiie tn tbe arm-yaw pamtion. if tbe e.p. ahead of tbe eg., the aneowl faevr prmtueco an overt new tag aaaorent lending to ineimv the yaw. However, if tbe projectile ► «running rapidly reoufh ah tot гл owe mX the yaw will net grow rapidly bat oowmly eflange direction; tbe projectile b Mtd to be rrmomptenlly i table. even though atat trolly nawtable. Stare the e p. of a cylindrical body of remla- that b woolly throe of an eentroed. a typml pee- >etlh ahope b aaolobb nahna: a. Mare of tbe prejeetde u м «oamntrawd at tbo fattened ^^ad no bo aaove tbe e t • ahead of the e.p. (thia b rarely a practical eola- tion >. or b. Projectile b provided with a flaring rear end or with flat eurfaceo (flaw) at the rear of the body which move tbe e.p. rearward of the eg., er e. l*rojevtilr in nanih* gyraaevpiraHy atable by pin. 5—U Factor» to ba Caabdarai ia Cbaaco of Fia-Suhduatiae 5—1.11 flpiwa Fixed flat take no length without adding to tbe payload volume of the .projectile, exrapt ia the ipectai caae at an arrow, er aubealiber, pro- jectile Foldiag flan either add to the length ar rrdnre tbe volume, departing on the daoiga adopted, bat b any eaae add to tbe rerepJenity of tbe projectile. Since tbe naafolaaao of a pro- jectile of a given maxiaiaaa diaaaatar aad ornar- all length b re dm id when ba payload rotaaM m reduced. and. м general, agio atabllbsl pro- jectile» are cheaper than and aa arcaretr м tbe reempomlmg KoMobtliaod projectile haring agnal peyl«ia*l. pmpvtrbw are alabiherrl by apin aalnm their are oveereduig reman* to the contrary. 5-1.12 Far three af the reooam fae ehioa ng flnotahilim tie* are: o. A tn-wtabdiaMi prajeHile roa he larger in pwpnrtian to d* diameter (hare a greater flaretrea Mtbi than oae which b flphre M
ЛМ4Т иж-м: stabilised. If thr logixlic limitation* on length («toeing, handling, loading into tbe gnn > are not exceeded, the fin-«tabilivd pro- jectile may be long enough to nave an interna! volume greater than that of the correspond- ing «pin-stabilised round. b. The lethality or other terminal umfulnem of the round at; be impaired by spin. An example in thia category n the «hoped charge round. r. Tbe Hussion of thr projectile nay require that it he fired al high quadrant elevation*. Coo rent tonal «pia-otabilisrd round* suffer severe degradation in arenne-y when fired at quadrant deration» greater than about fH*. fin-stahilianl rounds du M d Tbe internal structure .af thr projectile siay be ым-Ь that the round become i dynamically unstable when spun, er even su.-h that .t can- not he spun rapidly enough foe gyroscopic stability by the gua available. e. Thr projectile may be designed 10 be fired from a smooth-bore gun. f. Pia-stabiliaed projectiles ean be fired from a rifled кчр without peeking up enough spin to lose seCuracy Thu is done by tbe use of aa obtutator whieh engages tbe rifling but slip* aa tbe pcojsetile. S—2. Sraf-«TA*aiZBB nOJBCTXLBS The first requirement we place on a projectile at that it be staMr *t must be sial wall у or gyro- srepirnMy stable, it mtme aha be dynamically stable OSlein it* expected trajectory is very short. ГЪе stability »f iq>«a-siab«liaed pr»jrvtile« at treated ia the paragraphs which follow. 5—X! Oyrmciyk flcnbOtty I—3.1.1 Oyroacopte BtaMMy Factor Tbe gyroscopic wabUrty of a ipm stabilised peojoetile van be maesaed by computing s*. tbe gyrsmeepir stability Carter. whew I, — axial moment of inertia, *lug-ft: I, — traaswnr moment of inertia, slug-ft1 p — axial angular velocity, ead/arv # = static moment factor. Ib-ft/radian i bi the атшпрйоа that the static moment varan linearly with yaw, the ezpevmiou for the static . moment per radian of yaw ia О ц — air density, slug/ft1 d — maximum body diameter, ft F — airspeed, ft/sev — static moment eweflk-irat. pec radian t’lme attention must he paid to the units used in these nprvwuoim, a* some of them are not tor units customarily employed ia reportisqr mi1 asurrments »f the quaatMaa. 5—2.L2 СоекШам on Value of sg for Stability if 0 —s»^l the projectile ia unetabi* and will "tumble” within a few hundred feet of the guu. If ц is greater than one. the projectile m gyro- scopically stable, aad we then investignu >*• dynamic stability, aa deaeribod later. Sines », is inversely proportional to the density of the air, projertdm whieh are stable at standard simas l«herie csmditisen amy be umstablt «hen fired under arrtie er other noswtaadard iwaditiem of tempera- ture and premmre. hsmnMe mvironmewto mtsd be i shea into account in computing «,. thin fart, wepW with the uacrrlaiatie* ia the ether factors entering into *a ha* fed some designers to set 1.3 aa a tosrrr limit oa *, ia th* preliminary deesgn stage, nig standard air density in tbe somputaUoa. Nate that at tbe muasie we can write vrherr Ci sb »и nets st hot p/F = fls/mf, where a w th* twist sf tbe riflw* st thr muasie. in calibers per tom. Ilwsoow tbe miiiol stability of tbe projectile dipt ads oa tbe rdhag twist and only indirectly on mnmle vobrity. If this wow not am aaued fire. Lt, fins* with re> M
AMCH7MUM3 «liwnl propelling ebargc, wuuhl I» impmctica). The indirect influence of muzzle vclucity arises from the depcndroev of »n Mach number; this de- prudencr ran rsuse instability at гн'ит! muzzle velocities. t'onvrutiuual projectile» ka<r airspeed much more rapidly than they kw spin Tbe value of *, thus nearly always increase» aa tbe projectile file» liowii range. Tbe atability factors of projectile» fired at high quadrant elevation* ran. unless projectile velocity ia ataintained by roeket thrust. rroeh quite large value» at tbr summit of tbe trajectory. ourirg to drvrraer» ia both vet wit у and air density. Throe larye vnlue» are not detrimental in themselves, but tbe rouditbun which produce them abu bring about lance inrrraara ia tbe equilibrium ya* of the pro- jeetile. S-2J YrwofBopeM $-2,2.1 GmtjI Tbe gravity mrvatere of tbe trajretocy five» rise to aa angle of ya* large enough to rotate a premauoa rate whieh will permit tbe azh of the projectile to follow tbe taagent to tbe trajectory. Thia equilibrium requirement ranees tbe projectile to porat to the right of it» flight path (right-hand ya* of repcor) when tbe spin of tbe projectile м ehehwhe aa viewed from tbe rear, which ia tbe eaae with nearly аП I'aitod Htatro artillery ammuaitba The lift force associated with thm angle canoe» a drift to tbe right, aad an rolimate of tbe magnitude of thb drift io gma ia the flriag tabtao for tbe projectile. The demgner ia iatoroHad ia beeping tba> drift email aad a* .uniform, from round t* roand, as реайЫе. The ya* of repose proport maul to Р/П If it beeomrs Urge, the projretib may become dynamieaUy амСаЫг with matting Um ia nagr aai seewrucy. • 5—2X2 Bormob lor Aagb of Вором Aa appmimote rxprtmuu for the aoual right- hand ya* of гор roe b Thb equation shows that at tbe imasmit uf a high aitgir trajectory. where иш W a: 1 and д b con- siderably Ina than its sea level value, if Г is anal] the ya* may be very Urge; it may eveu shift over to tbe left-hand equilibrium angle with disastrous result* for the trajectory predietion. Hee Bef. flfl, p.392. 5—2-2.? Traihag An analysis of the flrat (and most aigniflraat) term of the expmaioa for ya* af гора* may 4hed Mine- light on tbr mechanism by which n spinning projectile “traih” as it нагого along it* trajectory. Keamnging tbe abnrr equation gives ipPSdC^fc - I*1—? On tbe left aide of tbe aquation wv have the static aerodynamic moment, a* the right aide me have the axial angular momentum, Z,p. multiplied by the rate of change of direction of the tangent to the trajectory, g roe в/К (aee paragraph 44). The product b a rote of change of angular omaoentum, earned by the aerodynamic meanest; Mavsrsrty, the aerodynamie moment orbing from the ya* of rap mi b just eu£eie*t to «bangs the angular momentum of the peojectib at the rote required for the asm of tbe peojeetib io remain langoat to tbe trajectory (in the vertical piano tbe ya* b ia a plane мета! t* the trajectory phar and tbe static onmrwt b af right a ng Im t* tbe rotatimt, er 'регомма*, af the projretib axb. *hbb b tbe well knows gyramepii brim rise). $2.2.4 Projoetib teywmilrbs Aaymamtrim of a projeetib, aribag from tbo Maufaatariag proevaa, «Ш add (vrotoiieity) a small eoaolaM ya* to the ya* of ropnro, iaeroaaiag tbepwnibilityof troobb at the ешммС. Aaymmotry aba introdMso a forcing function *kbh ran bad to rvseaaaee; the rvwultiqg ya* M* be large lor fla etobilbwl projevtiba, aad tbr onhjeet will be dbeMoad further in paeagroph 14.
AJCCH 706-242 S—2ЛЛ ММЫ of Cesnpatatiea »f PnjKtite Spin Th* gyroscopic «Utility factor is calculated at ♦к» muzzle and и often eaienlated at the summit of high angle trajectories aa an index of summital bdsavior. It ia recommended that the designer com- pote the yaw at repose at the summit of sueh trajectories. and compute the stability factor at the muzzle and at impact. If his computer pro- gram does not inelude a running calculation of spin rate, he must estimate as well as he ran what the spin rate of the projectile will be at summit and impart, uaing the expieaaiiMi (in the absence of racket thrust} where the subscript a refer» to conditions at the btginning of the interval over which the change in р/Г in bring competed, z i* distance measured along the trajectory, and k. •’ = arit/l,. Thia ex- p from an aesuams that p. Clf and CD are eonataats, whieh is not likely. Average values of these parameters moat be used, and it will be seen that the appraximatiou far p/F may be poor. Designers of spin sterilised projectile* have been willing to sesame that the projectile* retained enough spin to be stable at impart and ta aeeept whatever limi- tottoe oa quadrant etovatiaa was found to be aeemaary ia test Mage of the round. While C, ia args tire. C„ is usually at stobr net magnitade that p/F iacremw* as the projectile Ham to the summit. On the draeendiag limb the eosine at the trajectory angle is decreasing, aad p/F will deereem, cnee obviously Г is iaeriaaing white p, ia the absence of some spia-prodneiag meehonimn such aa a canted fin. continue* to de- Mown in Table 5-1 and Table 5-2 are sample trajortortes far a lypiml 5-iaeh projectile, with initial esadittene dtfbriag oerty ia quadrant eteva- tson. The trajectory with Q.K. — 2* ofera aa ippertuniiy far a steeple cheek so the (p/F)/ (P/F), equation pevsewted above. ,1'siag average «stars of g aad Ca, wo have, for p, Г al Impact P £ 2 ”»( ~ 3-У) / (-001186) (0.1355) /p\”e. * йпЗ5 Mpl 1.435 U7. (6.88 ( - .014) + 0.365) 0330 j .9977 * , _ ”.9986* “132S The trajectory calculation give* »/», = .295/224 = 1.32, so the approximate formnla is very good for flat fire. For the trajectory with Q.E. = 70*, the rough estimate* of * and Г• obtained by taking simple means values would be .ОООЙЯ foe g ami 3M5 for •_ ”* < ~ 11 m H-WM8) (0.1355) cos 70* ”₽ | 1.435 (6.89 ( - .014) + 0285) 54100 } .2113 «• ” .3420 * “ 145 The trajectory calculation gives »/», = 289/224 = 1.29, so the approximation is only fair. The uae of values of С» weighted hy the are distance traversed, in calculating the moans, would make ;he approximation for »/». very good. The high angle trajectory io presented princi- pally to show the ssagnitade reached by the yaw of repose at the summit. The actual yaw might be much greeter bocsjse dynaaue instability, owing to nonlinearity of tbs aerodynamic eosflteisuta, is likely to occur at yaws of this magnitade. Conventional prajeetite* attain their maximum range when bred at a quadrant deration of about 43*. For rocket ornate 4 projectiles the Q.K. for maximum range is greater than 46*, rwaniag ap to •0* or 70* when using а losv-barafa* racket wit* a high ratio of fuel weight to total prajoetL weight. Reagan shorter than the smximam may bo obtained by ehanging the Q.E., reducing the etse- tire racket thrust, er reducing the muazle veioeity. Reduction of the mmate votoeity in a series of stope, hy reducing the charge of gun propellent, is salted “aontog**; raeh level of musste veiomty ia sailed a “sene”, aad variations of raage within eagh им are obtained by varying the quadrant eievuttea. A peajratiie whose raage te ssattailed bp asaaato
ЛМСР 7W-MS velocity variation muxt be stable over a wide range of Naeh number*, which will ainxwt certainly in- clude tranaouie speed* st sea level air drasitiro Sitter f'j, usually peaks in the trawaniie regime aad the gyruaropie stability factor m inversely pro- portional to CWa , stability may be at a auaimiun in the tromsmie regime. If dau are not avail- able for the full range of speeds, estimates may be amde by use of the shapes of tbe va Mack number curves of projectiles aiarilar to the one in question. Use of aa estimated С», requires a greeter margin of safety on the gytooeopis stability factor toinsurs that it does not beams leas than unity. However, if trajectory ealeulatioM show that the projectile will spend only a abort time in the transonic regime, it easy he possible to aeeept a certain rnnouat of instability for that short time. The gytoseopie stability factor of a esnven- tioaal spiaatabilimd projectile usually has its mealiest value at the aausale. fforbrt assisted pro- jeetiles, on the other hand, are more likely to be- come gyroecopieally unstable on the descending limb of tbe trajectory, near impact. This insta- bility ean be avoided by • a. Distributing tbe mass of tbe projectile •? that its eg. to forward of tbe usual location in a projectile of the given aerodynaade shape. h. Increasing tbe rifting twiat of the gun. e. Casting tbe roehet aieshs. or providing in- ternal meaaa of rotating tbe jet from a tii gh Baade. S-X4 Dynamic Stobttty ef •yte-fttabMrod nVJKaHi S—2A1 Magnttuii of Hadal Vectors Tbe yaw of a tymasetrie projectile acted oa by a Unoar flseoo and moment gtou is giroa by * - Х«,Л*е** ♦ Ж|,Л»о* _ i X< = precession damping ei- ponent, per caliber s .= travel of projectile, eabbers 4t — phase angles of the model vectors (j = 15) i. - equilibrium yaw We are concerned here with the magnitudes and signs of X| and Xt. It will be seen that the magni- tude of a modal vector win increase if its associated X is positive; the larger the value of X the more rapid is the increase in the magnitude of the vector. The term Л ia, of course, simply a sinusoidal oseillariou between +1 and — 1, aad between +♦ and —i. If neither of the two modal vectors, Xi or Xb grows in magnitude so the projectile Aim down range, the projectile is said to be dynes»jolly stable. For dynamic stability, therefore, both X, and X» must be equal to, or lew than aero. From Bef. 12a we have Х.--1/5Г,- L VI - l/ч J and %e differs only in having a + sign between the two terms inside tbe braeketa. и _ c*. - c. - ы (Cm, + Cw,)J r.«[c^ + Ke„] So, since i, is a function of Св. and (indirectly) of Ci,, we see that all of the major aerodynamic eoeflfeiento enter into the dotirminatuin of the dsnptag вфммвЖ S-XU Dynamic Stability Factor, Og Murphy (Bef. 12a) rooemminde that instead of simply requiring that the X, be noapoaitive, we should set an upper limit oa ths greater of the two whieh moat not bo eseeoded if the projectile to to fulfil ito mtooioa. This liasit, represented by uaenbeoriptod X, may be greater than osro be- come souse growth of initial yaw may be tolerable, oopeeiatty ia towrt flights. I—2Л2.1 Stabfitty lscXM.^X Murphy then introduces the . «ability fbotar, ч *bors
АМСР 70*442 27 + 21 * " И + 21 aad by uae of the exprmion for with the reatraintk that )wi — land H + 2 1 > 0, arrive; at the identity ^-a*(2-ad Hotting thia exprawion aa a curve with 1/*» and a« aa coordinatea, we get Figaro 5—4. nbbrwaaotad Graph of 1/t* va Cooditiona aa to atability are a function of the locution of the point determined by the inter- mrtioa of l/t, with it (Figure 5-2), naaody: a. Intmeetioa liea below curve: Projectile ia gyroaeopiealiv «table and aaay he dynami- cally atable, with !*« < 1. b. latenettioe liaa aa the curve: !* = 1 e. Iwtecmetien Km above ewe: Projectile ia dynamically anatabif with > 1 aad may be ругааеерйаПу uaatahh. S—2Л2Х Stability far 1 = • la practice, 1 ia often art egeal ta aero Then the exprnwioa for the dynamic viability factor ia* _2Г SCCi. + MCw^)____________________________ ®* Ci, — C* — *<* (См, + CkJ The earn- in Figure 5-1 h new the leeua of potato where 1=0. И the iutaroactioa of \/t, with a* Bro above the eurve, we ran oeleaiate by ataaroring Да», the change ia a* required to roach the eurve. moving horixontaJly. and uoing the following relation: l-ж - Да» when <1 I — hi, ~ A** ** (Reuwmber that H eontaina th« factor p<«/2ai.) Note that H > 0 ia one of the eoaatrtinta on a»,, *o the l«x computed by the above expreenion in (Maitive, and one of the yaw veetora ia undamped; we can eatimate the growth of thia vector from exp |l«m*l where a ia travel in ealiber*. Similsriy, when the iateraeetion lice below the curve, uae of the above expreeaion for !«, will reault in a negative value with whieh the rate ef dceraam of yaw ean be computed. lieturning to the expremion for it, we note that Ci. й alwaya pooirive and ианаЦу much greater than С» The denominator of % io nearly alwaya poaitive. If it ia not, we aboeld not compute a*, . The numerator contain* the amgnua moment eo- rfieient, С>и. which ia uaually poaitive for cpin- xtabiliaed projeetilea at aaperuouie apeeda, hut often negative at traaaenie aad auboonie apeeda. »», ia wmally poaitive, and indeed the value* of the coeffcient* and radii of gyration (in ealiber*) are aueh that ««, nearly alwaya Um between 0 and 2; if it, ia ouioide them liauta, the projectile eannot be atabiliaed by apin. In BBL Beport 853 (Baf. 48), Murphy dia- rmnm the indneace of aaam diotribntioa on the dynamic otabibty of otatieaUy unatable projeetilea. lie notm that at auperaoaie veloeitim many bodim of rrvotatioa cannot be atabiliaed by apin if the e<. io more than two caliber* aft of the centroid. The centroid ia, of courm, the point at whieh {he eg. would be located if the projectile were of uniform dewoity; it ia none the gooaaetriaal centroid of thj Mlhourtte of the projectile, in any cam, therrja an optimum eg- Ieeatioa whieh minhaiww th* apin rote required foe debility, aad thia optim>jm loca- tion ia aeaally near, aad aft of, the eca'roid. The complete graph of 1/^ va c* tahen from Kef. 12a, appear* m Figure 5-2 Unfectuaately C«w to arooitive to ehangm ia yaw angle. We eaaaot proaarve B’jaarity in the amgnua memant by rvotrietiag 11* lorn thaa 10* aa we have maaawd that wo oenlj far aaaae other tredynamw oeadtoiewta. A tap* Ci, aad b« will
AMCP 7M-242 TABLE S—l SAMPLE TRAJECTORY FOR SPIN-STABILIZED 5-ПГСН PROJECTILE ATQX = 3* (SEE APPENDIX I) FTD FFM TYPE RGA RGT D.FT 1.050 1 .250 5.540 .301 1.030 Д 450 3.0 0. К WTO VO SPIS SBT DTM WIST qe 46.oe 1925. • .0 .400 28.00 3.000 WTB ZO TEMP- DTL DTE CDD2 CLP 46.08 • 59. 4.0 .350 6.00 -.014 .001189 1116.0 TIME X DIST V CO CHA DR MASS THETA z THRUST DRAG WM > IACH SPIN SG .00 • • 1925.0 .331 3.93 1.000 1.43 .05 . • • 197.4 .000 1.72 .224 1.36 .12 .90 1694. 1695. 1804.4 .342 4.01 .997 1.43 .03 75. • 178.9 .000 1.61 .234 1.46 .13 1.04 1937. 1938. 1787.5 .344 4.02 •997 1.43 .03 34. • 176.3 .000 1.60 .236 1.48 .13 • 1.74 3156. 3158. 1704.1 .351 4.07 .996 1.43 .02 .14 118. • 163.7 .000 1.52 .244 1.57 2.94 5125. 5127. 1574.8 .364 4.16 .995 1.43 *.00 137. • 1*4.6 .001 1.41 .259 1.72 • 15 4.09 6867. 6870. 1465.8 .377 4.23 .996 1.43 -.02 113. • 129.8 .001 1.31 .273 1.88 .17 5.15 8375. 8379. 1375.5 .388 4.38 .998 1.43 -.05 .18 55. • 117.9 .001 1.23 .286 1.99 TINE.S RANGE.N V.FPS THETA.0 SPIN SG 5.85 2839. hie. -3.9 .295 2.04 •4
АМСР 706-242 TABU 5-2 SAMPLE TRAJECTORY FOR SPIV-STABILIZED 5-ПСН PROJECTILE ATQJL = 70* (SBB APPEMDIX I) FFD 1 TH TYPE RGA RGT 0. FT 1.050 1 .250 5.560 .381 1.031 i .4 150 WTO VO SPIS SBT DTM TWIST QE №.08 1925. .0 .800 2Г.00 70.000 WTB ZO TEMP DTL DTE CD02 CLP 66.08 59. 8.0 .350 6.00 -.016 .001189 1116.0 TIME X DIST V CD CMA DR MASS THETA Z THRUST DRAG YAW MACH SPIN SG .00 • • 1525.0 .331 3.93 1.000 1.63 1.22 9 • 197.6 .000 1.72 .226 :.36 .22 5.62 3160. 8769. 1260.0 .397 6.53 .770 1.63 1.17 8166. 78.2 .002 1.16 .313 3.00 .35 15.86 7620. 18531. 739.1 .168 6.69 .581 1.63 1.02 16951. 8.6 .013 .70 .696 9.66 .68 31.25 13366. 26588. 360.6 .306 6.21 .687 1.63 •F 22665. 3.0 .151 .35 .971 68.95 .80 36.65 16159. 27696. 336.7 6.18 .685 1.63 -.02 22606. 3.3 .32 1.033 56.07 .80 66.85 17696. 31575. 650.3 .196 6.33 .513 1.63 -.81 20861. 3.2 .069 .63 .757 27.51 .80 60.85 22170. 61728. 819.9 .168 6.79 .683 1.63 -1.23 11898. 12.6 .007 .76 .390 6.95 .80 65.65 23663. 65896. 911.0 .220 6.97 .775 1.63 -1.28 7931. 22.8 .006 .86 •360 3.19 .co 70.65 26617. 50616. 966.5 .253 5.06 .892 1.63 -’:й 3566. 33.9 .003 .87 .307 2.23 TIMERS RANGE.M V.FPS THETA.D SPIN SG 76. 20 775$. 988. -n.S .289 1.82
ЛМСР 706-142 reduce tbe effect of change* in ('л^ > and a email and nearly eonmant yaw angle will reduce the aiae of the change in magnna moment. We aee im- mediately the value of good obturation in keeping the initial yaw email, and the value of high pro- jectile velocity in keeping the equilibrium yaw aaaalL S—2.4-3 Further Diacuacioa of Msgnitud* *f M*dsl Factors aad Stability The following paragraph is taken from Murphy (Kef. 12a): Tbe requirement that the exponential eo- efik-ient* be negative throughout the flight ia much utronger than necemary in a number of applica- tion*. This ean be aeen by the following example. Conaider the earn of a specific projectile whose ex- ponential eodfleienta are strongly negative for It ^2.0 except for tbe Maeh number interval (0.9, 1.]) where both exporunta are positiv*. Ex- act numerical integration showed that an initial maximum angle of attack of four degree* for the launch Mach number of two will decay to a tenth of a degree before the Maeh number decrease* to 1.1. The dynamic instability aaaoeiated with the transonic veloeitie* then will cause tbe maximum angle to grow to approximately one degree and then deereaee a aeeond time when aubaonie atability ia eatabtiabed. Thue the “dynamically unteabte” projectile ha* maintained a smell angle of attack over th* entire trajectory. S—2J Aarsdyasari* Jump ef SpMtahUaad ProjortHaa 5—2A.1 General Th* path taken by a projectile after leaving the muola of the gun ia determined principally by wind, gravity, drift, aerodynamic jump, and, of eoune, by the direction in which th* gun ia point- ing when th* pv*jee*ile emirgm from th* senate Th* designer can reduce the aenmtivity of tbe projectile to wind by reducing С*, er balancing drag by rocket threat; be ean redoes th* round-to- roond dieperaion dn* to varying gravity drop by good obturation which red**** rvund-to-round variations in aanmie velocity. Drift absald Mt vary maeh tram rawed to round If the projectile yaw i* kept aeaall. Ia thia diaewaaie* w* win simply art wind, gravity, aad drift eqaal to ano, aanams that th* teaaoveaas ooaapaaaat of the velocity imparted to tbe projectile by the gun ia negligible, and conaider bow the designer may reduce the re- maining source of inaeerraey, aerodynamic jump. 5 2.5.2 Aaredyaamic Jump Dadaad In the abeenee of wind, gravity, and drift, an average line drawn through the swerving path of the projectile, sueh that the projectile spend* equal time* on eoeh aide (or all aid**) of the line, ean be visualised a* a straight line which intersects the muole of the gun. At tbe mantle thia mean tra- jectory line will make an angle with the line de- fining the direction of the bore of tbe gun; thia angle ia called the “aerodyanmie jump." Note that tbe plane of the aerodynamic jump angle ean lie in any orientation; jump ean be up, down or aidewia*. At a vertical target the effect of jump appear* a* a deviation from the theoretical point of impact, which is computed from tbe bore eight line, corrected for drift aad gravity drop, (in flat firing wiad correction* are seldom made; round* ar* fired aa rapidly as is practical, and tbe wind effect ia assumed to be the asms for all round»). 5—iSJ Magnitude *f Aerodynamic Jump The aerodynamic jump of a agnametria pro- jectile, in radian*, m givan (to a eime appi prime tian) by в/(Н».-й:рЛ) where V, = projectile valecity, fps j, = yawing velocity, nd/bae p. = spin rate, rad/aee g, =y*w, radian* aad th* imaginary multiplier,«, ahoam that the earn- tribation of initial yaw to jump is at right angle* to the dbartte of th* yaw. I*ymeatery st th* papjastfle adds another tern to th* axpraaabn far •a a term wfaiah depend* <m th* *s aad initial ariantatian < the aqymmetty; am Morphy, Ceao ампйапЛге^мМе Jwnp>*at. FT. It in impovtaa*
* «• - Iе l—f •*вМ •>10
АМСР 706-242 that projectile asymmetries be kept as small aa ia economically feaaible. 2, ia usually ao email that the second term in tbe jump rquction ia about an order of magnitude smaller than tbe tint. However, if the bore clear- num* in ununuaily largi*, ur if there ia a strong eroaa wind at the gun, the ynw may be. large ami the aeeond term cannot be neglected. 8. varies from round to round. Good obtura- . tion will reduce ita magnitude.and the magnitude of the variation. For a low drag projectile. C»e /Ct. ia approximately equal to the distance, in calibers, between the c.g. of the projectile and the e.p. of the normal force. Increasing thia distance will reduce в/ for a given 8, but the design changes which increase the e.p.-c<. separation, such as an increase in tbe length of the projectile, often also increase kJ. Boatteiling will decrease Cto and increase , increasing the e.p.-e^. separation without much change in kJ. Since drag ia also decreased, boattailing has a very beneficial effeet on performance unless the stability of the design ia impaired; thia must be checked (see paragraph 5-2.4.). This dieenmion of aerodynamic jump applies only to dynanucelly stable projectiles. 5—45.4 Orientation ef AeNdynaaslc Jump The orientation of the aerodynamic jump angle also varies from round to round, because 8, ia a vector. Tbe dirmtiim of 8, depends «m the pattern of tbe gas flow in the munle blast, whieh in turn drpen de on the born yaw of the projectile. Since projectiles loaded in the gun in the same manner probably ride the lands of the rifling in the same manner (see Bef. 56), the orientation of the hlast pressor* field, and therefore" of K. is probably biased in one particular direction. Hence the distri- bution of jump orientation angles, when a group of rounds is fired, is probably sharply peaked in one quadrant 5-45J Distribution ef Aerodynamic Jump Tbe dietrftotion of impact pointe oa the target is really a eireahr (or elliptical) distribution about the thoerrtieal point of impart of all the rounds, summing no change in gun direction. The Mao described in tbe preceding paragraph produces a hit pattern whieh appears to be a rectangular dis- tribution about a mean point of impact whieh ia the “renter of gravity*' of the pattern. Artillery targets arc always analysed so though this were tin* true situation, ainee tbe center of. impact and the vertical and borixontal probable errutn arvvery easy to compute from the coordinates of the'hita. The location of the theoretical point of impact ia very difficult to obtain from the coordinates of the hits and eannot be computed from the boresight line with any certainty, which makes the derivation of the true Sj distribution impractical. The above diornarinn is presented because of its implications for design dmeisiniw baaed oa the results of firing testa. Sines the P.B.v aad P.K.W method commonly used is theoretically inappro- priate, design changes should not be baaed on small srmplea, ix, groups of fewer than 15 rounds. Furthermore, ainee moot design changes are aimed at reducing only the magnitude of в; and not at reducing ita directional dispersion, the statistically indefensible procedure of eliminating “maverick" rounds from the error calculations may be justified by the eont>mtion that their pointe of impact on the target were the result of unusual orientations of the jump angle, not large changes in ita magni- tude. 5 454 Betatiesskip Between Aerodynamic Jump aad QX 5—454.1. Vertical Component In firing for range, tbe importance of the verti- cal component of depends on the quadrant elevation of the gun. Differentiating tbe expression for range in a vacuum gives an approximation of the effeet of changes in angle of departure on range. When ». = 45*, the change in raage ie negligible. At в» = 15* «be change in range, in mils, is shout 5-11
AMCP70fi-242 3J> Нтр— as great м the change in departure angle (in milliradians) due to aerodynamic jump, ao at tow quadrant elevations jump is an important factor in range accuracy. 5—23.63 Horizontal Component The horizontal component of produces a horizontal deviation at the point of fall of the projectile, which is proportional to the are length of the actual trajectory. Since the deflection die- pennon of rounds fired for range is usually re- ported in mils based on the mean range, the effect of a given horiaontal jump ia multiplied by the ratio of the are length of the trajectory to its horiaontal projection. Again we can estimate this ratio from the vacuum condition, giving Лге _1Г 1 .__________1 u ( oos в. \1 7* 2Lcos0. tan 0. \1— ain0jj and at®. = 45*, 4^ =1.15, while at ®. = 15*. X £=1.01. H— <-««. ы woifa.1 in estimating deflection P.E.’s from aerodynaaue jump, when 0. > 40*. 5—3. FIR-STABILIZED PROJECTILES 5—3.1 General The inconvenient fact that the eenter of pressure of the aerodynamic forces on a projectile body is abnoot invariably forward of the e.g. of the body can be counteracted by placing lifting surfaces (fins) rearward of the eg.. If, when the projectile is yawed, the moment produced by the lift forces on the fins is greater than that produced by the forces on the body, the net moment will oppose the yaw and the projectile will be statically stable. In symbolic notation, we have Gra — Cm, ” Gva> (Xe^.y — 'Xe.e.) + Gr^ (Xe^.r — Xc.sJ CJ. - C.O. where the subscript В refers to the body and the subscript T refers to the tail. Unauboeripted quantities apply to tbe whole projectile. The X’s are distances in calibers, measured from the base of the whole projectile, which ia usually the base of the tail. The tail comprises all of the fins and the (usually) cylindrical boom os whieh they are mounted. Arrow or subealiber projectiles have the fins mounted directly on the body, so the base of body, base of tail, and base of whole projectile may coincide. Folding fins may require an arbi- trary definition of their base location, depending on the design. 5—12 CP.-C.G. Separation It will be noticed in the above equations that Xor.r —Xco. is negative, and C«a will be negative if the projectile is statically stable. О J*.-C.G. is then also negative, but this quantity is often re- ferred to simply as “e.p.-eg. separation,” in cali- bers, aad treated aa though it were unsigned. The optimum magnitude of the c.p.-eg. separa- tion is not well defined. For minimum sensitivity to muzzle blast the tail moment coefficient, ^"•T —ХОл.) should be small; to minimize the yaw angle due to projectile asymmetries, the total static moment coefficient, СКл, should be large. The writer believes that the design value of the e.p.<g. separation should be far enough above 0.5 caliber that inaccuracies in estimation of and С»,, including the effects of amnufaeiuring varia- bility, will not reduce tbe e.p.-eg. separation of any round hzlow 0.5 ealibor. On tbe other hand, e.p.-eg. separations greater than one caliber have been found to be accompanied by meroamd disper- siou at the target. 5—33 Fin Type The eboiee of fin type is obviously a trade-off problem, involving the utilities of projectile volume, range, accuracy and eoct Establishing trade-off curves for each design, determining optimum points for each design, end then comparing the optima would be a long proosoa. It is doubtful that the eboiee win ever be made explicitly in this way, but tbe intuitive narrowing of ehoaoas Burnt follow Ml
▲МСР 706-242 them lines. Д hrief discussion of the type» of fins follows. 5—33.1 Fixed Fina Fixed fina of one caliber span are easy to make, and —у to make uniformly; thia promotea ac- curacy. However, «расе m required between the leading edge of the fina and the location of the full body diameter in order to reduce fin-body interference and allow the fina to develop their expected lift. This reduces the projectile volume-to- langth ratio. If low drag ia important, the long boattail required further reduces tbe netful pro- jectile volume. 5—332 Folding Fina Folding fina which are bunched behind the projectile when in the gun tube and fanned out to more than one caliber span by aome mechanism after the projectile has left the muxxle blast ean produce large e.p.-eg. separations without large mnzxle blaat effect». They are expensive and con- ducive to large projectile asymmetry. They need not reduce the volume-toJength ratio of the pro- jectile aa much aa do fixed fina. Folding fina which are wrapped around the projectile near ita baae when in the gun tube and spring out after the projectile leave the muxxle, ean produce the required atability with reduced sensitivity to music blaat and very little reduction in projectile volume. They are not cheap; the asymmetry they produce ean be effect by a large 5-3.4 Obtnratien Good obturation ia important for both spin- and fin-atahilised projeetilea, especially so for the fin-stabilised rounds. It haa been achieved by the use of rubber or plastic ring» on or near the cylin- drical portion of the body, or by the use of a к of suitable material placed behind the projectile (puaher obturator). The obturator ia sometimes given the added function of holding folding fine in the doaed position; the obturator must then break up <m sMtgenee from tbe muxale, usually no prob- lem with rubber or plaatie obturators which can be notched or, if nesamry, segmented. Obturator» on mortar projeetilea moot break-up into assail non- lethal fragment» on emergence; thia behavior may be required for other weapon «yatema. Obviously, retailing the obturator in flight increases the drag. , Fin-atahilired projectile» are often fired from rifled guna. The obturator muat be designed to fill the groove» of the rifling, but it muat not impart a high «pin to the projectile. Friction between obturator and projectile will impart a alow spin which ia usually remarkably uniform from round to round, and which can to some extent be con- trolled by the designer by varying the material of the obturator and the area of ita surface of con- tact with the projectile. 5—33 Arrow (Subcaliber) Projectiles 5—35.1 General The large muxale energy obtainable with large caliber guna offers the possibility of launching a light projectile at very high velocity. If the light projectile is reduced in caliber, ita weight per unit deceleration due to drag would be so great aa to aoon reduce it» velocity below that of a heavy pro- jectile fired from the same gun. But if the light projectile is reduced in caliber ita weight per unit of frontal area (sectional density) can be in- creased up to the point at which it becomes a use- ful item for employment against armor, owing to ita high striking velocity. Since these subealiber projeetilea are usually very long in proportion to their diameters, they must be dnutabilixad; they are referred to aa “arrow” projeetilea. 5-332 Sabot The space between the subealiber projectile and the gun barrel ia filled by an annular device called a “sabot.” The fina, attached to the body near its base, have a span equal to the gun caliber ao that they and the aabot, which ia usually plaeed near the eg. of the projectile, form two riding surface» which keep the bore yaw of the projectile malL If the projectile is propelled by a puaher obturator, the aabot has only a centering function and can be relatively light and lightly attached to the projectile. However, the aabot must often pro- vide the obturation and transmit most’^of ths aeoeisrating fora to to the projectile since the aabot MS
АМСР TOfi-242 аге» often greater than the bate area of the projectile. The xabot it then heavy, aad attached to the projectile by ore nt of groove* around the projectile body. Tbeee groove» naturally give roe to abode wave» whieh inrreaw th.* drag. If fired from a rifled tube', provnioa sta*. be Made for rotational ilippagr between obturator aad pro- jectile. Tbe eabot meat leave the projectile by break-up or aegnwntatMn ehortly after leaving tbe muaxie beeaaac » drag would be intolerable. Fragwente ef «be eabot ay atrike the Аац an the fin met be rtrcwg For thia reaaon, aad to improve the ridii< of the fin» oa the interior «efface of tbe gun tube, the fine are often end-plated While tbe traaeverae piatee on the Up» of th* fine Mtereaee tbe drag, they abw in veer the lift of tbe fiat, penaituag a redaction in fia area whieh largely eCeeto the drag of th* platen Socw mtiroerrig eabot dawgna are deaenbed by AQna w BSL Вере ММ» Pan 1 (Baf. fill. MacAibater and Bwbfri (Bet O) riwpdif and onaljaid tbe drag data obtained ia wvural Hl1—*" mage firsage of anww projection. They found tbar the addifiaa of four ooreahber aquarv а.- м ж t«n lebibtr coat ryhntev body in- rreaeed tbe drag to about of tbe drag ef tbe body atone, when the fia tbwhw woe of the fin eord When the fin thwfrn»* waa 1<%. tike dreg atereaaed to about 230“% of the bedy alone vane. When thear fine wee* canted t* the drag ~ by an addatnaai ДО ef the body ptoe tad valor. Ttoto torn» f», vtonv are wade triatn- hb by Ito tort that they aw band on the Ammeter of the den to, bed? f- f <» Aaouatentteaey Beeaaar of the togh «etorrty of the am* made, the amdynam* Сосем and епкм to *hwh they at* euhjeriad earn tovnm* «о terp» aa to eaaar a tong «tender ywjartri* to drfoe* «о Bqfb* mao a dighT be* tower the to*» «hnape duvotmn nr the yowi aad eufl» rtrvb. the bowoeg defertwo town* «• ианйаьв* wtert Unde to tbe M*fa4 are art kbefy to gm tenable bee. w tbe evuat that adgwiflaaot pevbaa of «he body a iteteeM. the antenl tooqnewrlm of the hidy ribnewg aa a tad apgfid be entoedehne and eetepneafi wdb the frequency — e/^v ie radiaat per er rend Large deformatioae inereaae the drag of the projectile wen if they do not threaten ita integrity. 5—ЗА Dynamic Stability af Fia-StahiliMt Projeetilea S-3A1 C to oral Aa dirmeri (at greater length) ia the aub- Mvtioa toi eptn etebiliwd projeetilea, a projectile t» aaid to be dynamically atabie if ita trenrieat yaw does not iaervaae during flight. Statically atabie fin-rtabiliaed projectile* having aero apin are alwaya dynamically atabie; the yaw whieh ia plauar, do- —гад».according to the expreaeton • - Ao1* +1? “ where C* — t'! ♦ Cwj J e it tbe travel in rolihirv. and A, a the eauataat ya* doe to projecute aajnwitrj, er "trim eagto ” Yhe addit.oaal ya* whieh anew from th* cunenure of th* trajectory * nagtigtlto Car neraal trajoe- torim S-3jU Zee* Span A inn ditto* ef an* open ateaart moor exart» wner wie»factoring toteeuneaa pmnb eatoe abght *wo< of the han roenitmg in a epin prodnamg tooqer 1» fart, an* apin ia very undenmbie. be* nuw the* th* Uft prndneod by the trine nagle. will alm the peojevuto away fme йп peodtetod trajectory, th* defiertw* doe to naywitotry on* to- catebrably gnnt if the reB rate of the prajmie n near am ewer math *i tbe trajoetory Ifil BqefiMbnato Bag Bate $-ААЛЛ BqnMbrtoto Byte Naariy *3 fiaotetohoad prajirtitei an do- «wed to eeqawv о ooetarn «ndibrvu* epen* ealterl a •*»• «pen to-kj» it * etwab ownlte* than the nil nuotoid tor ^wwn dwotw* The «pin «мфее a
АМСН 704-342 |«мг»Пг prodneed by "caaUay’’ tbe inn, or, if the projectile » reefrrt «girted, «*y be produced by eaatiny Aa rochet ina 5 -3.4.1J Torqne Whea the terqne ia predated by twiabay ar aunberiny the daa. er by eaatiny, Le, bendiay ap a portion of aaeh da, the spin tarqae ia produced by the lift e* tbe dm, whieh seta ia eppotote di- гмЬеаа aa ippierti ade* ot the peoyeeOie ахж The apple at which the air tew aver the projectile etnhaa the tea tepee dt aa the apta rate; aa the epia rate mcreaaos, tbe aapie of attach of the coated port ton of the ds deemara and the ара» terqee deewaeta anti] it jael balances the deederatiny torque pMdneed by «bin frietiea. 5—ЗЛ1Х Caanpatatiea of lyilrtrt— BaB Bate Th» aqaiNbrwMi rail rate ia given by where f, — eqsabbriow roll rate, md/aee C»( = rail »t»mt eoeflkieat doe to da cent (at aero spin) = roO daapuay nwaeent eoedbeient = da not anyie, radians Ct, to a fanetiea of tbe pirmtepe of fat area whirb to canted, C»t ia ateayc aayatiaa. Ttaa aa- рамс tonactei «Ban C,t baa been drtaemiaed in a wind teaaei teat. Ibwtru, C,t /C^ may be aettawtad teas the appreeiwat ia, valid only far Baa with a tip radiao at kaat these tiaras as ymt aa tbe wet radtea - il® i «bare C*. to tee te Mt eoedbeeat toepc baaed on la am, Ct* to the reO daeeptey aeewewt enedMoM of tbe body atone, F* to the total la am (act tea wetted am wteeb to twice aa ymt) aad <a» to tee tetai aaated am Вааса tbe ntte 4m/4e» to tee peapaetiaa tt la am white to aaated. * to baatal am, * to ia ypyp aad d to aataaa dtaartav ef tee body 5—1Ш Samph Calcalatiaa Per exaaple, a < meh projectile with one* caliber das (b = d) nuyht have the feitowiay Ci^ - 2.0 per radian - — 0.02 s - am ft* &--Uft* 3», - 0.1 ft* U • 4* « 0i073 radian Г - IdOOfpo c«. 3 /0Л\ 0.6 ш - 0.57 •1 л - 057 (ОЛ73) - 133 rad/aee -21 rnv/aee Thia ini rale tim to net very aeaaitive to C^, whieh can be ti—trd by tbe rzpreaaiea C, - С», £ *y te where b = span of daa, aad e = avaraye da dteed. If the das have more than 44* nwnephnak, the nbnwt irprmna dor C»( /С^ ему ant yrve a 5—XM CitepatetoM at Ttjuaii ttellfty S—ЗЛ4.1 Caaneal It in importaat te have a yaad oatimate of the oqaitibriaw epia toare tbe bhebhoed at dyaaatit instability iaenaaw with ineraatmy ipia rate. Tbto to often rape»4 by myiay "the epia ma aaat ba tept tow eninyh te sveid toaqnoa edtecta** Marphyto dyaatnie stability teeter, к vn d» earned ia paeayraph d-d.4. This atotbed at die- piaytey tee tycrmii atability at a pvoyoetite eaa be aataadad, wtobent ebaaye* te atytieaay atabto penjrotilee, tee aaaptote earn a< 1/t^ w te to teewn ia Plyan К Fw taai^iUard репуаКйм, tear*** opomate hi oat to^Mo^wawetnsM^eeato
AMCF70*-W t, » negative taarr CWa ia BnpUi* Hr mnall wlura of apia, t, approoebau aero aad 1/*, beeoawa a large negative number. Hence, the pomibility of dynamic mutability ia «mall when the apia ia email. S—ЗДА2 Sample Cakubte Our d-ineh gamer need an aa example in the diaeuaaioa of apia due to tn. eaat ia. preceding paragraphs aaight alae haw the following char- aetariotian: J. - OiUriurft* I. - 1Л ah*ft' Cm. “ - Xlparmdma Then we haw 1 tfjy* «См. s, " V (4) <2.0) (.001 It) (ИЮУ (ft Ito) (<U) (—2-5) “ (ftuy (iw - -.22.5 fa any eaae, the magnua аммаеп! corftciacta of fin-atobiluad projeetilea are lem predictable than tboae of apin-aiebiiiied projeetilea. kor thm reaeon it it wiee to allow as great a margin of dynamic atability aa ean be secured without falling into r.mniaei batability, which ie itieewsid in the next paragraph. S—17 Вааомпее Instability While spin Mebiliaod projeetilea can thooreti- еаЦу experience coincidence of epin and yaw fro- q-мпема, thb phenomenon ia aa much mere fitdy to occur with in efabitiaed projeetilea that it in diaewaed here. S-3X1 Variate ef Magnitude of Taw with Aapaneetry Murphy (Bef. 12a), in hia dbewmien af the angular mote of a slightly uaaymmetrie teaile, abowa that the augnitade of the yaw due to wym- nmtry ia usually well approximated by и- "Л + M where Dcipg Murphy 'a ententes |--4a-4)hrh - he <• we tad that tbe peojaciite ef thia enamyto ie tyaimiielly etaMe if a^ lien between -U and +«Л к terid wee be dMiu.l ta deafen a •*- aad degree ef aaynwoatry. otohihoad pcwjactihi with a sqtoe of % lying bo- tween thane bmito. If tbe doMteatar b aat equal to Ш» and aaiwd ter a, the ruauit b S-4jMJ Hague Моим Ceetoteto but thb b peoebely the мргеааюа for fie fro- queweiae tt the two amda) wetace of yaw (Bef. 12a). 8o if either tbe mtateol froqvancy or the preaaeeieaal fraquaocy b nearly equal te the apia frequency, the magnitude ef the yaw due ta Офап* matry can baaome wry large The ebbbrity to a cpring-aaae <etom subjected to an евМгм! ohsr- fae yaw inenaaa. The inareaee to year, ante toe growth ef toe aanpiitade af an ocdkanry qpringwaw bbte M bounded net w much by toe dmaping to
AMCP 7004*2 th* и by ita аваПамгйу; th* aaanaat yaw *f pnjaatitai any Ъ*мп* la*** *anngh to «ан tan of reap* а*Л anaiaey ttawogh taqe d*w iNKto bat art a* tarp* a* to *aaa* th* pn> jaatite totnabte. 5-4X2 BmaaoaoM Bat*» pr $-3.7X1 CiByetktiM Th* apia ia nart likely to eaiaeida with th* to-dX2X ВвпрйСМпйШв Pa* the gdaab tear ari a* aa aoanpte la PRWll-U ________ at 7 = MOO p, ш . /-—— = 1C2 nd/«« fpa at aaa ' \ ЦО - C.15 ' JL Th* aaaffihriaai *oU nt* to far thia fianar aaa 133 rad/aae, a* to й w*U abao* to Biaa* both to aad to an dineQy pnpwtiaaal to ainpoad, «haaga* ia V aiaaf th* t*K,o*ta*y d* art altar tba 9^9, ratio. 5 3 7.7J Batto of fe/>rto A*wid Вамамас* laatatahty It wiin b* aaaa fnn th* аараоавма far * that dBenan ia air deaaity with aititod* damn 9,; if tba agailibrian nU «at* it greater thaa to ftriag at high gndraat «tontiaa* will doeraan th* •haa** of гаамаам iaatahiltoy. Tbn*fan, ia triag Iran a nfled gaa, th* ebtantar ahooid ba do- aigaad to prods** a rail nt* at anargawe* boa th* aaaaate at taart thn* ttarta a* gnat a* the eai- oototad **aoa*at toil rata, y^aad thadnaahoald bo daigwad for aa agoilihnan apto (». = p^/7 abaat th* mb* aa the apia at оавацуаам. Th* *. of oar <4aeh daaar, 0.0*1. to аааомааагЦу high ia aw* of й» r, of (МШ; atthar th* ta oaat aagto ar th* panaaiag* of ia araa oaatad ««aid bo oat ia half. Caaaaatinaal projiititoa trod fnaa a naortb- ban gaa aaaaga fraat the Mart* with aaarttiaRy aan tpia. Kaaa M**ai aaaaBfaatanag *•*** mU sBftM gAaga ton ваваааааа, the taa an аоаайу aaatod to peadan a to gpaator thaa to- Th* nt nto at th* pnjaetito art thaaaton pao* thnagh to •>/ to toi if thto paaaag* to aapid aaaagK the twaperary growth te yww do* to паааам will b* aagtigibli Th* gnator th* p^to lb* ahertor th* tiaa* apart te th* TMteity af to ah* th* dtoartnaa pbaaaaenaa aaB "nO totete" oeaaaa, f -ya gafilaBtola MfaaiaMrt aad tehan han aade ав «tantea VMM WK ton
AM СР 706-242 momenta not considered in tbe dhenaaioao in thia handbook ean offiet the fln torque, causing the spin to naii' at the reetmant frequency long enough for the yaw due to asymmetry to grow eataatrophi- caily. Giving tbe pro.ieetife a epia at emsrgcnee— and at equilibrium greater than >„ the Method roeemmended ia thia handbook for avoiding roll loek-in. S—3.9 Aerodynamic Jump of Fin-StaMHiod Frojoctilee All of the Material oa the aerodyaaaaie jump of «pia^nabiltaed projectiles (paragraph 5—25) ap- plies erithoot change to flaotabiliaed ammunition, with tbe eseeptioa that the drift of a destabilised projectile in kept tad! by railing the projectile slowly. However, it requires very good design and manufacture to keep tbe aerodynamic jump (aad therefore the dispersoe) of ftn-otabiliaed ronada to ы low a level so that of standard opin-otabiliaed rauads flrod from the same gun. This hoc been observed aaaay times ia test fringe of da-etobiliaed teak rounds, where spin-stabilised rounds were need as control raundo. The aerodynamic jump aagie Gz, ’• rodweed by increasing the e.p.-eg separation, so is веса m tbe oquatioa ia paragraph 5-2ЛХ (e.p.-eg. — C«. / Ci, for assail yaw). Unfortunately, if this in- oroam ia achieved by meroaoiag tbe momewC cm eflbioat of the teal, aa by greater da area er a loafer boom, then the rffwtivvasm of the fas ia the re- wound dew rsintia* m the Meet aenr is iaoroaood. with nnuftiag iniranw la teitial yawing wfeeity. If thin mereane it I, > greater than the йаегааае in r.p.ug. separation, and it may well be, then tbe aeredynamie jump is iaeraaosd, not reduced, by the change ia ep.-eg. mparatisa. Tbe e.p. tt the normal force oa the body alone can be awved rearward by changing the ahape of the body: thio can increase tbe ep -eg. oeporetioa of tbe whois projectile with Mttie or no eboagr ia tbe tail moment If thio body eha^e h made by oabstitatiag a apibe fee tbe often, tbe deaf b la- Fte-otobilmsd rounds are probabiy mere ooaoi- ties to taaaoee^oe peecaaore geedba^e in the Moot tadteote that Лв «fleet of feme рампе* grodfento on aerodynamic jump minimised if the raoultant of the transverse pressures oa tbe projectile passes through the normal flight c.p. of tee round. How- ever, since little is knewn about the dbtribmioa of muscle blast pressure in either space or timt, the best way to reduce mumle blast efleet io to reduce I be magnitude and duration of the blast pressures on the projectile by good obturation. It will be noticed that aerodynamic jump has been di te nosed only for dynamically stable pro- jectiles where initial yawing velocity sad e.p.-cg. separation are tbe quantities of interest. Fin- >uabiliied projectiles whieh are statically stable are also dynamically stable unless they have an un- usually high roll rate. 5—3.10 Fin Effoctivoum at Supsnenic Spoofs (Kef. 12b) With low aspect ratio* fas of tbe ardor of 10 or loss, the span io the predominant factor for producing high normal fores oooflfeieata. However, when spans are limited to no greeter than ano full body diameter, the optimum chord length must be determined. For a flsod span there is a dedaite limit to the chord length that still giro the boot combination of normal foree and swot rearward C.P. The normal foree baaed oa body frontal area derrrams with iaereaeing Maeh aaasber for ft Mwtftftt фвя ftftd ftMHtftet chevdg ftsd it dMNMM more rapidly aa the chord is shartaaad. Thio means that as aspect retie inereaem, the «fleet of Maeh number h greeter oa the fla normal fence, Tbe must Hhrwat chord tragth appears te be between calibers .70 aad 1.0, dep indent oa Maeh number. Thr larger chord should bo weed for the hi***» Maeh numbers. The effect of leodiag-odge swoopback io negligi- ble m far es normal ferae eoaeeeaod if oeaotant am and aeport ratio is held. From tbe wing theory tbe lift within the tip Moab ooarn b appreai- amiely И af the twmdiaMaabaal value.*• Tbb ia eaaaed by a permute leakage arouad the tips from gfefllfe te m^nmmn^a^k
АМСРТММ tbe tower to tbenpper aurfaew. If met ef the 1* wrfiet a affected by tbe tip Mach сома, the tower the total normal foeor will he and the further for- ward the C.H. will aarw. if by типе method wr could prevent thia pnurr leakage around the lipa, wr would be аЫе to two-dimruniaaaltor a thru1 dimmwinaal aurfaee. Bad plating the tea waa attempted. By thia method it waa found that the fa normal force could be inrrmerd aa much aa 4O5< depending upon the aaeount of fa area afaetod by the end platee and the amount of end plate width. Tbe end plated fa m agoinot tbe plain tail oa the TWK triage had notoring momenta 31% greater aad much better accuracy. The damping enefaienta were alee larger far tbe end-plated taih aa agaiaat the plain tail, and thia t enerd the more atabie round todaatp to % amptirodr in fewer cyetea. A complete end piate width would be etenated ш a ehrouded or ring tail Bxperimental evidence at lew Meeh mmbem ebowed that tbe ehroud had a otroug tendency to ehohe er Uock the air few over the fa eurfawe, thereby enuring poor faw ever them eurfaem. Th» in turn canoed poor lifting rooulte. However, mace the Sight veieritim bare been reieed to high Maeb number*, the ten- dency for tbe faw to choke between the fae and ahroud ia eiimioeted, aad fa normal foreeo are iaervaced aad C.P.’a moved rearward. The number of fae neeeaeary for optimum normal force appear* to be ux. Theoretically eia flee. acting independently ef each other, ahould gi** 1 'A timn> the force of four fan. however, experi- mentally they MuaUy produce only 10% to S0% more, dependent upon Meeh number. If autre than nix fae are employed, tbe fae interfere with ем another m far m the faw faida are eaneernid, aad the normal force aufen In order to obtain татпаме tail rffutiumm. ом would want the tail to be m a uaifocu faw region, ix, outaide of nay body wake infaeneee. Thia, however, ie only p Baribin when wing folding faa whom oweep aagim are relatively entail For faod fa ooudguratioM (except in the earn ef arrow projeetilm) the fae an epent-ag mainly ia the boundary layer faw from tbe body. Maaaa of giv. iag the fa the moot effective lifting eurtaec an to make the cupporung body m email aa practical, La., beep the epsa to auppert body diameter aa large aa poaaible aa that a greater portion of the fa in mat- aide of the body boundary layer, aad boattail the ntoin body m that emieth uniform faw io pre- rented to the aurfooe. ЫДОВ
АМСР Т06-М2 CHAPTER 6 ROCKET-ASSISTED PROJECTILES 6—1. GENERAL The kinetic energy whieh a gun ean impart to a projectile to limited by the diameter of the bore, tbe length of travel of the projectile in the tube, and by the curve of chamber preecure vo travel The aunle energy ean be increaeed by aaing a bigger, longer or thither gun tube, thue increaaing the coot of the weapon and, more important, decreaaing ita mobility. Bet raage ia liauted by the kinetic inirgy «applied to the pro- jectile ainee each foot of trajectory aubtraeta from the kinetic energy an aamunt equal in magnitude ta tbe drag foeee. To inrrami raage, or to inmem the pay- load earned io the came range, or to inereoae the votoeity at target impact, without det tearing the mobility of the gun, the tat «top to io rodwee the drag ooeft-tat of the projectile to m tow a value aa to compatible with the projectile votane required by the projectile *a mtorina Tbe next atop to to add kinetic energy to the projectile in fight By i a creeping the length of tbe projectile, or by aaerifleing воем of the warhead volume, a rocket motor ean bo ineluded in the projectile. The rocket thruet adde kinetic energy to the pro- jectile ia flight. The rocuHing projectile to called a "roeket amietid projectile,'* or, equivalently, a"gun-booetod racket" Tbe burning of tbe rocket fuel can be controlled, or "progromaeed,’’ to bo lorn than tbe drag force, anptoxtoutoly equal to drag, or very much greater for a abort ported. Tbe addition ef a reeket motor iaenmaee the eart of tbe paojeetito aad iacreoapa tbe etonge apace required ta a givea daatrurtivo capability. Aa added ttoeHattoaea aeaaeie energy to Ktoodweod by the maximum aet-beck acceleration whieh the propellant can tolerate without eruahing, but thio limiting acceleration to aurpriaingiy high. 6—2. MOMENTUM LIMITED 31ТПАТ1ЭЖ 6—2.1 Variation of Muzzle Energy, Chamber Pm- euro and PropeUaat with Weight of Pro- jectile Became of the aet-baek aeealention limit, tecket-aariated projeetilea are rnually made heavier than the conventional ammunition flrod from the юте gun. The muxale velocity ia then limited by the capacity of the resoil ayrteaa, and deeroaam in proportion to the inrroam in projectile weight. If we uae the aubeeript “ftd" to identify the •tymboto relating to a projectile whieh to launched at tbe mmole moauntum limit, then mV “ m«M (oeuotant momentum) aquaring, rearranging, and dividing both ridm by two givm | .1» . (Sto), \ ш / мегаж). Equating muxale energy to the integral of the work done on the projectito by geo preoowe in tho guu givm where P, m chamber pronmro A shore area A a bore travel Ы
AMCP 706-242 timing th* preesure-travel curves have the tame shape, P,=.kP.* and P,= then muxxle energy and chamber pressure, and conse- quently tbe weight of gun propellant, are inversely proportional to the weight of the projectile, in a aaomentum limited situation. I—12 Variation of Setback Acceleration The setback acceleration, а, ы given by as the setback acceleration ia inversely propor- tional to the square of the mans ratio. •—2J Effect ef Rocket Additions on Projectile Design PusBctsen The ndnetioa in weight, and volume, of gnn propellant allows aoane at the extra length occu- pied by the rocket motor to be inserted in the space previously occupied by gun propellant Whether, aad how, thia io done depends on the characteristics of the gun tube aad loading system involved. Largo inert asm in range require, if warhead watuaw is net to be severely rodwecd, as intrasas in projectile laswtth. lips пенсе has shown that spin- stabiliaed projeetilea laager thaa • calibers usually require a high open rase fee gyroscopic stability; in the ahseuM of rochet thrust tbeae prejeetileo slew down so maeh on a high angle trajectory that their equilibrium yaw baseman daagvrouety large. However, whsu tbe projectile velocity is asainteiaod by a koebot which buran nearly to the summit of the fnjoMsey, opts etabilbwtinn may be used far projectile* a* long as 8 calibers, or possibly longer*. At 10 calibers, fin-stabiiixatioa is almost certainly required. 6—2.4 Effect of Rocket Additions on Accuracy Long-burning rockets, sometimes called “sua- taiuer” rockets, with thrust approximately equal l<> drag, ran have a proving ground accuracy (no wind) very little worse than a conventional round fired from the same gun. Thrust malalignment, which contributes heavily to the dispersion of fast- burning rockets, is a minor factor in the tow-thrust rocket. Variation in racket fuel specific impulse contributes to racket dispersion and accounts for tbe slightly inferior accuracy ef long-burning rockets compared with conventional projectiles when both are fired in the absence of wind. How- ever, a long-burning roehet is lam affected by wind than a conventional projectile, ao that eoasbet» euraey of the racket emitted round might well be better thaa the eenventional. Accuracy analyses of racket assisted projec- tiles, both spin- and fin stabilised, era prmentad in Bullock and Harrington, Sasnswry Eaporf on 6'tsdy ef the Gsa-Boostod Rockst Spates», Ref. I*. These analyses, with supporting experimental date, are very useful for design; an ext assies bibliog- raphy is also included. Initial yawing ulssitj-, ilynasrie uabalanee, and wind era identified as the major sources of dhpensen ef spin stabilised roeheta; thrust saalalignsseut earn be significant in east* af high thrust and stow spin. Dynamic unbalance ie net significant fir finneru but fin asymmetry and thrust malalignment ean be if the roll rata ie too tow; wind b alee a asajor aonrae of dbperaion here. Tbe naaono for tbe mall wind- setmitivity of ouotainer raehste are abe discussed. •eosrtal taUmfag ef the eg. bsMtae nap be mwM is *s4w te saOsm tysani» IsstaMUw st th* anssl* sat saat in m st
АМСР 706-342 СВАРТКК 7 LIQUID-FILLED PROJECTILES 7—LOKJTXJUL Projectiles having an inner eavity whieh ia partially or completely filled with liquid are a special сам of tbe data of projectiles having a nourigid internal structure. The yawing motion st a projectile has anally «“eh a low energy eon- teat that small transfers of energy between the internal parts and tbe wall of the projectile can тгтеем the yaw significantly. When tbe mass of the nonrigid part large relative to tbe имев of tbe projectile, aa it is in the сам of aome bqnid- fiilod projectilea, the yaw may in инеем very rapidly. The inotahiti*y of liquid-filled projeetilm hm Ымв stodiedp thoMratta&Uy *Bd czperiflMstsUy, by Karpov, Scott, Milne, Ota war tarn and others. Boom of thio week in reported in Refs 71 to 73. The iasaetigatioa in not complete*, the statements made in the following paragraphs represent ear- rent (19*4) eeneepta and opiaioaa. 7-4. ДОХСТ ОГ SLOSMIKO ОГ LIQUID ГПШ Difereueec in the thermal eoeSeiento of a- рамаоа of projectile body and liquid make it im- practical to completely fill a projectile cavity with liquid. Meehanim! deviem for allowing the cavity votams to ebaage with tbe change ia liquid volume are peaeible, but not much need. ГШе of are ееамвеа; came projeotibe may be fitted to M*. It Ъав been found that the «Inching about of the Ml ia a ftawtabilbed projectile Som net ia- ' arouse tbe yaw. So a ample notation of the prob- lem of liquid fin b to we fimotabUbatiea. Thb b net alwaga babble) HmbutbuB on projectile length may reduce the volume of a flnnor below acceptable limits, or spin-stabilisation may be desirable for terminal affeeta. 7—3 COMPUTATION ОГ DN8I0N PASAMXTXBS The dbetmaion whieh folloaa apptito only to spin stabilised projectiles. 7—3.1 Gyreocepfc Stability Pnctar The gyroeeopie stability factor of a liquid-filled projectile is given (approximately) by *“4(/,, + c?,J7 when /.y = axial mniamt of inertia of rigid parts, stag-ft* = traaoverM moment of inertia of rigid parts, etag-ft* с = a constant related to the viaeMity of the liquid; for water, о = OJ /»4 = traacvecM amment of inertia of liquid parta, stag-ft* д s |Цй BMMt tMtotg ib-ft/ndbu Tbe rigid parte inetade bath metal parts aad high exptasivo; the traewvorao meannto of inertia are computed about tbe total «4- at the projectile, with the liquid fin distributed м a heDvw eon-
АМСР 706-242 centric cylinder occupying the full length of the eavity. 7—<! J Dynamic Stability Factor The dynamic stability factor—computed in the usual way from aerodynamic eorfirienta, except that hi ia given by Л(,/(’ив*) and M by (I, + c7,t)/[(me + mJ #| — mw<t be such that the projectile would be dynamically atabie over ita trajectory if there wen no interaction between the liquid fill and the projectile wall. 7—33 Spin Bata In the transieut period, during whieh the liquid fill b acquiring a spin rate equal to that of the projectile wall, tbe traufer of angular momentum from wall to liquid will reduce the «pin rate 'Л the walk Thu redaction in apin rate may be very rapid if the liquid fill has a high vbeosity, or if Ъавеа tied to the projectile wall are placed in the liquid. On tbe theory of paragraph 7-33, above, that the angular mom rntarn of the liquid dose not contribute to a* the projeetib may become unstable. However, the transient period b then so abort that bafibe (or high viscosity) may actually improve the flight. Hafirs ean be designed simply on the boob of the torque exerted on tho liquid in g’ ring it angular velocity and on the shear, due to setback, at the roots of the baffles. 7—4. BIGID BODY THBOBT When all of the liquid b rotating with the name angular vebsity aa the projectile wall, the pro- jectile in said to be rotating aa a “rigid body.** If the liquid were not al! of the same density, the heaviest fraction would be eloeast to the projeetib wall aa a result of the centrifugal field, whieh re- sembles * gravitation*! field. The air space, then, is as far away bom the projeetib wail as possible, surrounding the axis of the projeetib or any solid eore, sueh ss a burster tube, which may be posi- tioned along the projeetib axis. Stewartaon’a theory b concerned with the in- stability of liquid-filled projectiles rotating aa a “rigid body.** It was derived for cylindrical eavi- ties completely or partially filed with liquid of uniform density and low vbeoaity; the behavior of test groups of rounds of varying geometry and percentage of cavity filled han been имеем fully predieted by the urn of thb theory. The pro- jectile eavity need not be precisely cylindrical near its ends. The necemery formulae and tables for applying Stewartaon’a criterion of instability are contained in Karpov, DynssuM of Legtrid-FBied XheU. BBL Maemruadum Boport 1477 (Bef. 72).
AMCP 708-242 \ CHAPTER S RANGE TESTING OF PROTOTYPE PROJECTILES 8—L GENERAL Very few projectile* an completely satisfac- tory aa fint designed. Metal part* failure is ran, but the fint teat firing* usually show that either пце or accuracy is not a* good a* waa demnd or expected. In instance* when the fint group of tea or fifteen teat rounds find gave excellent result*, a aeeond group ha* often failed to confirm the good mult* of the fint Conduaion* an drawn from the behavior of the test round*; design change* an made on tbe basis of then conclusions; and new prototype round* an made and find. Thia teat and change aequence may go ou through many eyele* before an acceptable design i* reached. The difficulty that a designer may encounter in translating a round from the drawing board into a useful weapon is deaeribed in the following ex* eerpt from tbe report of E. R. Diekineou, The £f- ftete of Uttltr Sngt mi Qroooot, and о/ Body fadareatf e* th* Aerodynamic Properties of a Coa*-Cyl*ud*r Projtetilo of M = 132 (Ref. 80): Often, in a projectile’s progress from ths de* signer's drafting board to the assembly line, then an many changee made in the detail* of tbe pro- jectile** contour. A* a result, tbe actual aerody- namic performance of the projectile may differ fNm that of the deaigner’s prediction. Almost all of the baaie deaign data on projec- tile* concern* itself with smooth contour* and stmpl* geometric shapes. When practical eonaidrra- tfoM enter the pietan aad fuses haw to be at* tech cd, relief* han to be machined, rotating band* hen to ba added, a projectile which may han been, originally, aa optimum one, often fall* abort of ex- pMtatioML По engineer, who tranalatea the boUstieiaa'a deaign data into a practical piece of ammunition, should be cognisant of tbe differential correction* that have to be made to the predicted behavior of the projectile. The purpose of thia report (Ref. 80) is to show the effect, on drag, lift, and pitdung moment, of depremion* and protrusions on the surface of a body of revolution. Unfortunately, there were insufficient data to determine effect* op_ the damping and msgnua momenta and foree*. Obviously important to the designer is the soundness of the conclusion* on which th* design change* are based. This soundness is directly re- lated to the care taken in preparing for, firing, and analysing the firing tart. 8—2. PRE-FIRE DATA It is important that the designer know exactly what waa fired and bow it waa fired. He must know what equipment waa uaed for measuring the test parameter*, «neb aa velocity, time-of-flight, aad target impact, in order to aa*em the accuracy of the number* presented to him. Each round fired must be precisely identified ao that ita performance can be tied to its physical characteristics a* deter- mined before firing. For each round, the following phyrieal charac- teristics must be determined and reoordod before firing: a. Individual weight* and dimensions of all of th* significant eoesponenta of the round. b. Weight and center of gravity location of the projectile, iaeladiag it* simulated lethal e. Amount of seeenSrieity ef specific compe- nsate relatiw to a sbeesn raforeaee axis,
▲MCI* 706-241 when atwemhled into lh- complete projectile. <1. Axial and tranaverw momenta of inertia. (Moment of Inertia data may be omitted if the projectile ia fin-atabilixed and it ia known from a previous test that dynamic stability ia not a problem.) e. Surface irregularities whieh could cause dis- ruption of proper boundary layer flow. f. Bound number or other identification, whieh should be permanently marked on the pro- jectile. Spam experiences in the manufacture of proto- Ay^e projectiles indicates that there should he no difficulty in meeting the following tolerances: a. Projectile weight: ±0.6% design value b. Center of gravity location: ± 0.C5 inch e. Eccentricity: ±0.006 inch d. Moments of inertia: ±2.0% of design value Practical methode of measurement of projectile characteristics are described in В. R. гна;»»» Phycioel Мммггееиай of PnjodilM (Bef. 74). of the projectile tact 1л- and unbiased test re- The primary cility is to acquire suits. Engineering unsound; aeeord- 76). It is the usually employed are: responsibility of the tooting овеет to dition whieh will make completion impractical The two types of tecta, static tasting and flight tast- ing, are described below. h. Fragmentation studies c. Smoke tests: chemical type, shape, volume, density, ete. d. Socket motor performance e. Propellant and high explosive ignition sys- tems - Many of there static tacts involve design fac- tors whieh contribute to the mam and maaa distri- bution, and directly or indirectly affect flight characteristics. 8—3.2 Flight Testing The mission of the projectile determiner the type of flight test conducted. The two moat com- mon tacts are to determine vertical target accuracy and range (distance), each of whieh fa diacomud below. 8--32.1 Vertical Target Accuracy For vertical targets, the accuracy is exprsreod in terms of two probable errors, PJB.a and РА». These indicate the distribution, both boriaoctaUy and vertically, about a center of impact 8—32.12 Temperature Mango Test requests generally specify temperature con- ditioning of the test projectiles, for a Sri-hoar a. Hot: b. Standard: 70*P e. Cold: —40*F 1-3.1 atatie Testing Static testing fa an intermediate design tool, whieh fa particularly netful in determination of the followiag: a. Whaped charge pen strati no (1) stand-off dfatanee (fl) User design: thickness, cone angle, etc. (» high expletive charge: type, volume, density, ®Ь|фе» ate. (4) dBret of чИв 8—32.1 J Data Retarded In vertical target accuracy testa the projeetilm are fired on a flat trajectory and the following data are reeorded: a. Projectile identification; round identification b. Gun identification aad condition c. Chaagte in gun elevation « atimnth (if any) between rounds d. Target dfataaee from gun a. Maatie vtiesity 44
АМСР 706-242 f. Coordinate* of point* of impact g. Ground level meteorological conditions h. Terminal velocity \ i. Time of flight ( Not always j. Chamber premare / observed k. Barty yaw ) 8—3X2 Range (Distance) Accuracy 8—3X2.1 Measurement of Accuracy When testing projectile* for distance, the ac- curacy i* measured in these two way*: a Probable error of range; indicating the dis- tribution forward and aft of a calculated mean range. b. Probable erne of deflection: indicating dis- tribution to the right and left of the eenter of impact Deflection P.B. is generally ex- prams d in mils, tweed on the mean range. 8—3.2X2 Data Recorded Those projectiles are generally tested through a range df quadrant elevations and the following data are recorded: a. Gun and projectile identification* a* in flat fire b. Quadrant elevation and aaimnth of gun e. Munla velocity d. Coordinates of points of impact or bunt e. Meteorological data at ground level aad aloft f. Time of flight g. Chamber pressure 1 Not always h. Barty yaw J observed 8—3.2X3 Instrumentation Subsequent field tests may be conducted uadei localised weather conditions, sueh as at the Arctic Test Branch, Big Delta, Alaska. Instrumentation available for recording flight data are: a. Photography: Picture* taken at muscle show growth of smoke eloud whieh is related t<> adequacy of obturation. Sequence photo* record discarding sabots or record spin ac- tivity. b. Taw Cards: The projectile is fired through a series of strategically located softeard- board panels to record the attitude of the projectile relative, to its line of flight e. Radiosondes: A small radio transmitter built into the projectile m actuated upon firing. An on-ground receiver, being sensi- tive to the roll orientation of the transmitter antenna, is able to record th* apin history of the projectile. d. Radar: Radar tracking ean provide position and velocity data throughout the flight.
ЛМСР 704-342 CHAPTER 9 MANUFACTURING TOLERANCES 9—1. DIMENSIONAL CHANGES Cort factor* neceaaitate that tolerance* on part* being produced in large quantity be lea* stringent than prototype manufacturing tolerance*. Dimen- sional change*, to facilitate production, may be made only when the Sight results will not be sig- nificantly impaired by the change; thia implie* that standard* for high production run* can be estab- lished only after statistical analysis of prototype firing tert data. A brief example of the type of analysis considered is presented below. Reference should be made to the Engineering Deaign Hand- books, Ezperimewtal Statistics, AMCP 706-110 through AMCP 706-114, for a thorough treatment of thia important phase of data analysis. 9—LI Problem Fin misalignment relative to the longitudinal axh of the projectile ia recorded during preflight inspection. The assemblies accepted t'. thia time must meet the requirement* of prototype manu- facturing. After tert firing the accepted pro- jeetilea, the impact dispersion at target ia re- corded. 9— 1Л Aaatyrt* A aimpie r*gre*sinn analysis of fin misalignment versus distance of hit from center of impact will produce number* indicating the effect of "»•**4g"- ment. If the analysis indicates insignificant cor- relation, the tolerance* on th* fin dimension* which control alignment may be relaxed. 9—2. PREDICTED PROBABLE RANGE ERROR Table 9-1 presents estimates of the probable variability of those projectile characteristic* which most significantly affect range. Theae estimates were gathered from balliatieiana at Picatinny Ar- senal, Aberdeen Proving Ground, and the Naval Ordnance Test Station. The last column in the table presents sensitivity factors for a particular rocket- assisted projectile when fired for maximum range. These sensitivity factor*, which represent the per- cent change in range caused by a one percent change in the associated round variable, were ob- tained by trajectory computations as deambed in paragraph 4-2. Tbe predicted probable error in .range, in per- cent, due to each variable is therefore the product of the probable error of the variable and its as- sociated sensitivity factor. Under the usual as- sumption that the error* an independent of each other, the resulting rang* probable error of the projectile, in percent, is tbe square root of the sum of the equate* of the individual products. Vector sum* of this type can be significantly reduced only by reducing their large components. Obviously, a significant improvement in the range dispersion of rocket-assisted projectile* could be obtained by reducing the round-to-round variation in specific impulse. In th* absence of rocket thrust, variations in drag coefficient become moat significant; dis- persion might be improved by closer control of the external contour of the projectile. The foregoing paragraph* apply to high angle indirect fire. As the quadrant elevation ia de- creased, the relative importane* of th* various factor* change* ao that in dinet fin th* most im- portant items an quadrant elevation and aerody- namic jump. M
TABU 9—1 FBOBABU VABIABIUTT OF BOCUT-ASSISTED PROJECTILE CKARACTXB1STICS AMD SEMSITIVITY FACTORS WHICH AFFECT RAXGX Jtoaad FrawMc PtoheMe Error et % ef Ммл ef VerieNe e araa. raage Projectile Weight AS At Morale Veioczty AS Л Feel Weight SO Л Fad Spaetoe laipube u® AT Feci Buniac Beat AO AB Dreg CectocMct y. .П Boltietie Deraity of eb AO .П Qaedwat Bhratba <* Л ♦—A DTMAMIC УГАВП.ПУ OF 17S-MM pbojecttu, «и? Пе trajectory еаЬоМЬош га ТаЫв M toe* that toe M4J7 And at 44' qeadroat ebvataoa aad MX® fpe raaato vehiity, vtO if at a Mach aaraher «baa la 1.1S over the catin de* oeaodiag taah ef rte tnjetterj. Bateriag to the terertyevii date ia Totoe *4. aa aw that ia thia Mach aaraher ▼warty the eapeeted ccUac of 4, « ebae to 1®, » that a roead haria* veto* cd the «верам tocaeeat aad daraprag шевем исВмвШ acar to the everape raiara ceoare 4 for the iceato toBtod ia Шс face Bight raage ail he dyacatiraBy ehtob ewe ito vheie tntfectwy. Bewrw, the aapertoMatoi data heat tho паре ▼eaae of the eraaB си» of the ya* beeL Aaaoaa- eeaacaat •< thio watt*. BVj acatapiad the ceaaitmty of the Nttoirty of the peejertili to ▼ariatieaB ia the швата sent aad dawptag treat bt-toJet voriataara b рсефаввЬ chape ее «eater ef gravity hatae The neaMt of raeeat (1M4) ctaAagroaef-boa- <k>« eeapator гам at BBL the* that the MeMT pro jeetile hcheeed property crith eerie tiara of tear foer eUadard deeiataoaB heat toe carve httod to the eeyeriateotal vahtaa hat rartottoaB of tee itaadaed tonebtra predaejd iaatohtttiaa Thera rarapatotbac, Tahh hd, faaMaato toot ether thaa auaer btdabl vwtatiira to chape or e< baaiim eaa had to traahb ewe ahaa the haob draipt ef a p.-ajeatih b <aito ctohto.
▲мер теме TABLE ♦—2 SAMPLE TEAJECTOET POE 175-JUf SPIE-STAEILIZED PEOJXCTXLE, M437, AT Qi. = 45* FFD FFM TYPE RGA RGT D.FT 1.0C0 1.000 .175 .369 1.297 .573 WTO VO SPIS SBT OTH TWIST QE 1*7.50 3000. .0 .300 20.00 1 !»5.nOO НТВ Z' TEMP DTL DTE C002 CLP 1*7.50 .001189 59. 1116.0 2.0 .350 5.80 -.015 TIME X 01 ST V CO CMA DR MASS THETA Z THRUST DRAG YAW MACH SPIN SG .00 • • 3000.0 .203 3.62 l.oon *.58 .78 • • 562.1 .000 2.68 .3:* 1.95 .06 3.*6 6895. 9621. 2577.8 .222 3.73 .806 *.58 -75 6709. 366.5 .001 2.36 .3*2 2.80 .07 7.92 16769. 20213. 2198.8 .2*0 3.87 .6*2 *.58 .71 13815. 229.5 .002 2.C7 .379 *.17 .10 13.6* 237*5. 31770. 1858.3 .260 *,0* .509 *.58 .66 21066. . 1*0.3 .003 1.80 .628 6.38 .12 21.01 3*165. 66262. 1552.6 .279 *.30 .608 6.58 .52 27972.4 86.6 .007 1.5* .691 9.86 .16 30.8* *6693, 58090. 1282.1 .307 6.61 .322 6.58 .31 3371.1. 50.1 .015 1.30 .572 15.85 .23 *3.01 60831. 72*79. 1108.3 .332 *.99 .289 *.58 -.00 3605*. 36.2 .023 1.1* .6*1 20.68 .30 $8.01 76566. 88752. Ю92.1 .335 5.08 .362 6.58 -.*»3 32635. 62.0 .019 1.10 .627 16.ЗО .30 73.01 90373. 105836. 1193.6 .326 6.93 .686 6.58 -.78 22521. 69.6 .010 1.16 .565 8.93 .30 88.01 101738. 126610. 7882. 1265.5 .32$ *.92 .777 *.58 .673 *.21 -1.02 126.2 .005 1.16 .30 ИМЕЛ 85.16 RANCE, M V.FPS 3233). h*7. ТНГТА.0 spin -63.1 .*52 SG 2.95 M
AMCP 706-242 »>u »-з АВЖООТВАИЗС BATA 8ЕХГТ FOB ITSJOI FBOJACTtLl, ЯШ «epost DATE TYPE OF TEST BRL-UmklitMO Oat* 1903 Free flfflfct 3000 23Q_____ 0.573 0.3i4 147.5 k^eol _Д.Ж __ it. cri 1.207 Я * 0.85 я « 1.0 Я • 1.0 Я • 2.0 o' Cements - 4%. -0.75 • 0.25 -2 • 1 -0.7 • 0.2 •0.0 • 0.5 cw 5.0 *t all йкя мот Рг» ML HR MO (Mf. 470) C^, 9.П «.25 1.2$ * .П 2.4 » .2 3.0 ' .2 -1» * W too carw Mm -» • W -0 • 2 -W • 4 • -о.» • .1 0.1 • .4 0.33 • .25 0.22 • .25 4 f-r «.2 •.» *2 3 t • 0.1 3.1 • 0.1 «•110m frm кем Rg 1.02 * .00 1.30 • .00 l.n • .03 I.M * .11 -0.3 • 0.3 1.0 * 1.0 1.20 • 0.0 1.00 * 0.40 • / • *’*• ** * «1.30 *f «1.0 0.32 «у «1.0 0.75 «у «1.0 ж л МВШЦ 0.73 «.03 0.07 • .03 жшгтс зттх« о.и ».оз 5ТЖ2 •to Ml» tMt
АМСР 70А242 TABLX •—4 DYFAM1C STABILITY BSTIMATB OF 175-MM PROJXCTILB М4П Prujeetilr Type: !7S«nai М4.Ч7 Им4ь ишвЬсг: l.M Air daaaitgr: D > А0Ш88 aiuc/ft* at ЭАО6О ft above aaa leva! Avarafa «окна of aaodjnuaue омвемМв: См. - AO C*, _ U From Uopubliahad C>. -033 - A2S См, + Сш, - -AS BBLdatalM3 Spfa, « = AUnd/«al Inamatar.d sAFTSft Axial radiai of ajialim, i, = A3W «al Traaovan* radial of pirtioa, A = U9T «al Prafaatib maaa, at m AM aiau Oyvaaaapaa atabAity faataa, 2 (AM) (AW (AMP_________ т (1Л7? (AU) (10*) (АМЗЯАО) " tlyaaaiir ataMNty farter. •<, ч О + 4) . Ifl м/м
ЛМСР 706-242 GLOSSARY accuracy. Tbe quality of eomctaem or freedom from error. С*, precision. accuracy of fire. ТЪе eonectncm of firs as judged by tbe distance uf the center of impact from tbe eenter of tbe target. acoustic aoteiity. Toe Priority of sound wave*, or tiaular waves, in a given medium. For variation with altitude. in air, •< <Standard Atmosphere. eeeifjaiciir jump. Tbe avenge defleetion of the trajectory whieh anas from the alternating lift forem on a yawing projectile. Drift, whieh arisen from a non-aerv equilibrium angle, in not included in aerodynamic jump. inpmd. The speed of a projectile relative ta *br air ia whieh it is imawreet1 AMC fabhrj. Army Materiel < naviaad. angle •! jump. The aagic bet». ti 4 line of ele- vation aad the hne of dv.iertur- angle of yew. The angle between t'> dunelion of motion of a projectile a->c di.-v-tios. of ifc aria. In computing secv<fi.-tic Чгое* m the presence <f a InMral wind > tv angle is baaed oa tbe directmu of tbe relative »i»d, mtber thaa the ditvrtion nt wetioa of the iл atmospheric eaadltieea. #«v: mofe^ «logical data, aahd drag. Tbe component of thi aerodynamic foree oa a body ia tbe dmetioa of U« toagitud- iaal axis of symmetry. ante Vnlem otherwme specified, the lacqpuu’nal us vf symmetry baBtetic oaoAdaaL A numerical measure at A- ability of a projectile te evocomao aar rmioterv It ш в^в® tM* AiMMtw ям! teem tarter, aad mm widely med ia tmjeeteey ^^В^^^ВпЯЖпВ^^в >Wv OV emu w^Bmw^^®®®^ ballistic range. A suitably instrumented area or enclosure in whieh projectile trajectories ean be closely observed, aa by park photography; anal- ysis of the observations ean yield good estimates of the aerodynamic cnefBewnta of tbe projectile. blast man. The sone of turbulent air and propel- laut gases through whieh a projectile must fly as it leaves the mussie of the gun. The blast sone ends where, aad when, the projectile entom undisturbed air. beattail. The bene of a projectile when shaped like the frootum of a eone (к like a reversed ogive). < if: agnate bnm> boom. The central stalk or sleeve to whieh the fins nf a fin-stabilised projectile are attached. bore. The interior of a gun barrel or tube. boundary layer. A thia layer of air (or other fluid) next to a body, distinguishable from the mala flow by ebamstcriatier of its own, aat up by trietiou The layer within whieh tbe major efforts of viasemty are ssmeeatrabed. bourrelet Tbe eyiiadrieal surface of a projectile ea whieh the projectile beam white in tbe been of the weapon. Conventionally the bourrelet b located jwet aft of tbe egive aad baa a slightly larger diameter thaa the main body. Ia асам caem tbe bourrelet exteexte the full length of tbe cylindrical body. Ia aocae designs a middle bourrelet ia provided juat forward of the rotating bead. In aeaee other deeigm a rear bourrelet is provided behind the rotating bend, aad ia tn- etahiliaed designs a ahmad or end plalm oa the fine provide a rear bourrelet. Murrslot diameter. The maxtiama diameter of the projectile. Tbe frontal am med ia the computation of aerodynamic oeedteientB is baaed vu An diameter. 04
AMIT 7WMM2 GLOSSARY (coat’d) bew wave. A shock wave caused by the ronpmuon of air ahead of a projectile Li (light. When thia wave touches the tip of the nose of the projectile, it is called an “attached bow wave” or “attached shock.*' IU (tibrj. UK Amy Ballistic Research Lab- oratories. turaiag rata. Eor «Jut nn>|wl!ani furl», tbr rate of motion of the burning surface (nonaal to itself). burnout. Tbe teminatzon of eooBbuttion ia a roeket sector owing to ev ha nation of the propellant sup- ply caliber. The diameter of a projectile or the di- ameter of the bore of a gun. In ririnl anas, the caliber й meonnd from the surface of one land io the surface of the land directly opposite Often the caliber designation й booed on а мев- inal diameter aad repnaents a close appresima- tioa rather than aa exact mtmurement. Caliber may be aaed aa a unit of length; for example, a 6-ineh S&ealiber gun (6*750) would hare a bore diameter if • inches and s tube length of SO calibers ее 25 feet, measured from the breech face to the muzzle. catotto. See: twpist. aemtoc of (aspect. Center of the dispenses pattern. Calculated at though it wen the ten ter af gravity ef a qpatem at diaente mut maaom placed at the peieta of impjet of the individual rounds of tbe group. oaotor of ргсавам. The point on the ахй of a projectile (er on the the rd of a tn) through wtueh the me heat of a given set of eat r dynamic Свеет paaaea chamber pram to. The решаете existent wtthia the gun chamber ot nay time ao a mult of the burning of the pnpeDant charge. Thm pmeurv мепмПу varies from atmaepbme pressure to a paak preueerv whseh b attained when the pen* jectilc non traveled a abort distunes, thus de- esoesm steadily until the yrojeetih nairgm hem the atusaie. In thm handbook F, й identided irtth ths pnaaan exirtieg ot too baas ot the pro- jeodit, akhnegh the two paoaaarm an not exact- ly oyael. the bon pcaonan being pethaps fi% smaller than after tbe projectile haa aequired a large fraction of its (Inal velocity. complete round. AU of the components of am- tunnitiou nevessary to fire a given gun onee. control rounds. Set: ntmat» rounds. damping exponent. A numerical measure of the rate of rhantre of the amplitude of an uaei(iatiug motion. defiection probable error. The directional error, rawuvl by linpenion. which will be exceeded aa often a» not. iu a large number of rounds final at a siujrt- gun setting. It й approximately one- eighth tbe greatest width of the dapenioa pat- tern (far large samples). density ef air. The maar ef a unit volume of air. ft varies with altitude, generally decreasing as the altitude inert ааи, since it varies with the rurrent temperature and baranetrie pmsnrv. When > й altitude in feet (h < 90,000) above sea level. It ,) — 3.2 X Ю~* A a. the stan- dard deiiaity of dry air at 5#*P and 14.7 psi, й 0002378 slug/ft* (KACA W42). derivative. The rate change of one variable with respect to another. In projectile mrodynaatiea, the rate of change of aa aerodynamic coefficient with mpeet to a change in the aeagaitude of the yaw angle. r-g- tbr stope of the C« vs о curve give» the static atoment derivative, C*,. dileraattol esadMant Ле.- aaarttMty fatter. didermttol eBecta. The edeeta upon the elements of the trajectory due to variattoam fram standard ruuditioaa. , dtoponiea. The scattering of abets feed on a target by the оси gmi (or group ef gnus). dtoperetoa ocroc. Chen ее varieties in a aeries of shots even though firing eoadittoua are kept so constant as possible. Far practical purpoaaa tbe «liapentoa mor of a particular shot in eomndond the distance from the point of impost or bunt ef that «hot to tbe center of impact er bunt diepentoa pattern. The distribution of the points of totoort of a series ef shots obtained under rooditieae aa nearly identical aa poaaibto. diatributiaa. Pattern of pnjeetitoa about a point. Tbe art of vahma tabea on by a rundem variable ia auemrtw triab. 04
лмсртоедо GLOSSARY (coat’d) dhorgiag yaw. In thr Hight of a projectile, if the angir of yaw iuereaws from the initial yaw, the ynw ia mid tu hr diverj-iug. «rag. < '<impuMa4il of air rnuxtauvr in the direc- tion opposite to that of the motion of the renter of graviiy of n projectile. drag ceefeoeat. A iiunilirr relating drag forre to the dynamic prroaurv of the air stream ard to the frontal area of the projectile. grift The lateral deviation of the trajectory of a spin<tabilised projectile, die to the equilib- rant yaw. dynamic prmsure. The premure exerted by a fluid aolely by virtue of ita relative motion when it «trike* an object. Proportional to density and the square of relative velocity [q= (Ц)е V’i. it ia obviously related to the kinetic energy poo- seeaed by, er imparted to, the fluid. Sometime» called "velocity head." end plate. A narrow rectangular plate integral with tbe tip of a fln, forming a T when viewed in the chordwiac direction. The other surfai> ef the plate ia curved to conform to the radius' of th* gun bore, as the end plate »uppiies a rid- ing surface for the fln in the barrel, as well as increasing the lift of the fln by preventing tbe flew of air around the fln tip from the lower to the upper surface. equilibrium yew. The yaw angle to whieh the yaw of a dynamically stable projectile decays. Part af this angle is due to asymmetry of the pro- jectile, part to the effect of gravity. tmr. 1. The differ» ace between an observed or calculated value aad the true value. 2. In gun- nery. the divergence of a point ef import from tbe eenter of impart. flaeaam ratio. Ratio ef length to diameter (l/d) of a projectile. fln ata hili tod Of a projectile, made statically stable by the aerodynamic asoerent arising from the presence of lifting surfaces aft of the eg. flring tahto. Table er ehart giving tbe data needed fer flring • ff*” aeeurote’y on a target under ——* conditions and also tbe correetioos that nit be made tor special conditions, sueh as winds er voriotieue ef temperature. flat boon. Deeeriprim of a projeetiW with a tylin- drival bs*e section, an opposed to a beattail, which Sometime rallnl “square hone.*' form factor. Factor introduced into the denomi- uator of the ballistic ruelBeient (q.v.), hued on lhr xliapr of the projectile. free stream. The flow of air or other fluid audio, ‘urbed by the premier of a (relatively) moving lady; specifically the relative flow of air ahead of s shock wave. fringing groove. A groove eut into a rotating band to collect metal from the band while it travels through the bore. Exeom metal so colleetad io prevented from forming a fringe behind the rotating band. Fringe formation has been a cause of exeem dispersion and short range. frontal area. The ana of the greatest circular cross-section of tbe body of a projectile j S = (a4)<P1; used as the reference area ia de* fining tbe aerodynamic eooeeienta. gravity drop. lu ballistics, the vertical drop due to gravity; equal to one-half the acceleration due to gravity multiplied by the aquare of the time of flight. HEAT (ebbr). High explosive antitank. A term used to designate high explosive ammunition .ontainiag a shaped charge. hit. An impart on a target by a projectile. bit probability. The expected ratio of number of hits to Lumber of projectiles flred at tbe target. HVAF fobRj. Hyperveieeity armorpicreiag. hypersonic. Of or pertaining to tho speed at ob- jects moving at Modi 4 or greater. impact velocity. The velocity of a projectile at the instant of impact on the target or target area. Also ealled "striking velocity.*’ impulea, total, la rocketry, tbe product of tbe av- erage thrust (in pounds) dcvetopod by the motor, tiasm tbe burning time (ia seconds). iacreamaL An amount of propellant added to, or taken away from, a propeUiag charge of aami- flood or separate boding ammunition to allow for differences in raage. direct Are, Gunflre delivered at a target which cannot be aeon from tbe gun parities. iahibitae. A material applied to aurfaaaa of pro- peilaat graiao to prevent burning on tho seated aurtacca G4
АМСГ 7U6-2<2 GLOSSARY (coat’d) initial M* Thr mam sf » rorkrt-amiMted pn> jretilr a.J. the Mart of burning nf the rorkrt pro pellant. вШ yaw. The yaw of a projectile «a it (carve the muscle htet sone. initial yawing vs io city. Tbe rate of change of the yaw ol a projectile aa it leaves tbe muscle blast coos. jump. 1. Mowment of a gun tube when the gun ia fired. X Angle of jump (q.v.). Sm: aerodynamic jwap. кШ ^rehabstity. Probability (/*<) that, given a hit, a single projectile will hill (ie, destroy) the target against whieh it is fired. The overall hill probability of a single shot is tbe product P«P<, where Pa iu the hit probability, amumrd to be indepeudrat of P«. teriaar lew. A OMtneMent airflow. lead. One of the rained ridgeu ia Che bore of a rifled gun barrel. bmaal i eristics. Horiaontal distance (normal to the line of Are) between tbe point of impact of a single round and the center of impact of the group. Utt. The eompoacat of the total aerodynamic force perpendicular to the relative wind, aad acting ia the plane of yaw. Hee of departure. The path of the projectile aa it leaves the maarie; tbe direction of the pro> jwtite st Um iMtMt it *4^^ Um mms!> the gun, providing it ban no swerving Motion. tee of rievaten. The penteugatioa of tbe bore when tbe gun is out hi ire logarithm, natural. Mned by * = «*', where t— 2'1828 . . . let. Ouaatity of str riel, the units of which were amaafaetarod under identical conditions. II fabbrj. 1. Maeh nuasber. x In aueh usage as М2*, designates a ctandardiaed (teas. Hoch. (Named for Bract Maeh. 1838-1*16, Aus- trian physicist.) Pwgnoetly used for Math number, whieh ace. Mash angle. Tbe acute angle between a Mach tea aad the tee of flight of a snoring body. •« > tar* 1 *4^ - 1 Mach effect. Ai> rrauhing from the feet that an object ш moving al transonic or supersonic speed; ж cotnprvmibility effect. Maeh effort may be eviuudered in terms of (a) The changes in the air brought on by a aboek wave, La, changes in рггмшге. velocity, density and temperature and (u) Changes in aerodynamic confidents, each an drag, lift, and moment coefficients. Mach tee. A theoretical line representing the back- »weep of a eone-shaped aboek wave made by aa assumed infinitely small particle moving at the same speed and along the same flight path as aa actual body or projectile. This tee, ao repro- aented on any plane bieroting the shock-wave «ми-, forma an angle with the flight path usually wimewhat wore acute than tbe angle formed by the aboek wave of the actual body, whieh depends among other thingi upon the shape of the body. Mach somber. Tbe ratio of the velocity of a body to that of sound in the modivm being eoasid- i-red Thus, at ace level in the UM Standard Atmosphere, a body moving at a Maeh number of one (M = 1) would have a velocity of 1116.2 fpe (the speed of sound ia air under those oon- ditions). Mach number, critical. The free stream Maeh num- ber at whieh ths relative speed of air aad pro- jectile attains aoaie velocity at some point oa the projectile. Mach Masher, bee stream. The Mash number com- peted on tbe basis of the velocity of the pro- jectile relative te air which in undisturbed by the psveenee of the projectile. magnas force. The lateral thrust on a rotating body whan acted on by an airstream having a velocity component normal te the body’s aate of rotation. magnus meaesnt The moment about the body eg- produced by the magnus foree. mesa. The в on stent of proportionality between the fens oa a body aad the roaultiag aaeelerotion. m m W/p. Date Miaately, in previous refer- ernes, “mesa** is eemetimm need as syueaymnno with “weight.*' materioL la a roetrieted осмо, these things used la oombet or legmtie support operations, each as
АМСР 706-242 GLOSSARY (coat’d) Mi raage. Average distance reached by a group of shots fired with the same firing data. stoplt* The flat nose formed by truncation of thr ogival portion of a projectile or point fuxe. Sometimrx the meplat ia convex, and auty h* railed a “calotte.” mttrmlflgi-i* data. Peeta pertaining Io the nt moapherr, raperially wind, temperature* and air denaity, whieh nrv used in determining correct- ing* to basic firing data. Often ahortened to “metro data.” medal vectors. A pair of. rotating arm*, called the precession vector and the nutati an vector, which when added together give the magnitude and orientation of the variable part of the yaw of the projectile at any inatant. Adding the equilib- rium yaw to the variable part gives the total yaw. The preremion vector ia often visualised aa originating on the tangent to the trajectory, and rotating alowly. The outer end of thia pre- cession vector ia taken as the origin of the nuta- tion vector, whieh rotates more гарЗДу, and tbe resulting epieyelie motion of the outer end pf tbe nutation vector represent* the motion of the nose uf the projectile (neglecting the equilib- rium yaw). mauls blast. Sudden gas pressure exerted nt thr muule of a weapon by the noth of hot gases and air on firing. Muxrie blast precedes tbe emer- gence of the projectile, and forma a soar of tur- bulent air, gas, and smoke through whieh the projectile must fly. The length of the projectile** path in the blast «one varies from about 20 feet to 200 feet, depending on the aim of the gun aad tbe aasouat of gas leakage post the pro- jectile while ia the lore. made energy. Kinetic energy of the projectile as it tmergm from the muxxle (plus a small amount of energy picked up in tbe muxxle blast, where for a abort distance the muxxle gases out raa the projectile). Thio io a measure of the power of the weapon SMsafo measentum. Tbe momentum of the projec- tile (ue., product of mam and velocity) aa it loaves tbe arassie. Limited by the capacity of the resell system built into the gun meet амшй velocity. The projectile velocity at tbe moment that the projectile ceases to be r.»3d upon by propelling foiee* (other ths» the thrust uf a rocket motor). It ia obtained •< measuring the velocity over a dixtanee forr .rtl of the gun, anil correcting back to t’zi 'puxxle for the re- tardation iu flight. KBS (abbr). National <iureau of Htandarda. MOL (abbr). Naval Ordinance ’laboratory. normal force. The component of the total aero- dynamic fur-- |>erpendieular to the longitudinal axis of the projectile, and acting in tbe plane of yaw. MOTS {вЪЪт). Naval Ordnance Test Station. nutation. The oscillation of the axis of a rotating body such as a spinning projectile. This oscil- lation is superimposed on the slower motion of the projectile axis whieh is known aa procasriea, which see. obturation. Tbe act of, or sseana for, preventing the escape of gases. obturator. 1. A device (usually a ring or pad) in- corporated in a projectile to make the tube or a weapon gas-tight. 2. A device incorporated in a rocket motor to prevent unwanted gas leakage. ogive. The curved or tapered front of a projectile. Tbe fuse may or may not be included as a part »f tbe ogive ogive, secant. An ogive generated hy an are not tangent to, but intersecting at a small angle, the cylindrical surface of the body. A secant ogive may have any radius of curvature greater than that of a tangent ogive for the same projectile, np to an infinite radius of curvature (Le., a xireight, eonieal ogive); a radius twice that of the tangent ogive is common ogive, tangent An ogive generated by aa arc tangent to the generator of the cylindrical sur- face. Called “true ogive" bf the British. erieatatioe ef yaw. Tbe direction of the plane of yaw (q.v.) relative to scam reference direction sueh as a vertical plane containing tbe tangent to the trajectory. overturning moment Aa aerodynamic moment tending to ineroam th* yaw of the projeetde. particle trajectory. The trajectory determined by gravity aad mro-lift drag which would be de- scribed by a projectile which maintained sere 04
АКС? 706-242 GLOSSARY (coat’d) atiglt* чГ yaw. A., useful approxinuitlull tu the trajectory <>Г an actual projectile. piezeatotrk oflkiency. The ratio nt I hr work ilutie on the projectile hy the propellant gases io the work that eoukl have breu iloiie if the maximum chamber pmoutre barf acted on the projectile base for the full travel in the bore; i.e.. tbe ratio of average ргиЛипе to peak pressure. plaae of yaw. The plane containing both the longi- tudinal axis of the projectile and* the tangent to the trajectory. / ' procession. A eirariar motion, of the axis of rota- tion of a spinning body which ia brought about by tbe application of a constant torque about an axis perpendicular to the axia.of rotation. A noneonstant torque produce» a noncireular pre- cession. pradsiea. The property of having small dispersion about tbe mean. Cf: Accuracy. pressure treat. Ям,- shock treat. preamro-travel curve. Curve showing chamber pressure plotted against the travel .of the pro- jectile within the bore of the weapon. probable error. In general, a value that any given error aril! aa likely fall under as exceed. In gun- nery, a measure of the dispersion pattern around the eenter of impact; half of the observed im- pacts will within a band two probable errors wide and centered on the eenter of impact. quadraat elevation. Vertical angle between a horiaontal plane and axis of bore of gun, just prior to firing. radius of gyration. Tbe distance from the axis of rotation at which the total maos of a body might be concentrated without ehanging ita moment of inertia about that axia. In this handbook radii of gyration are usually expremed in calibers. rang* correction. Changes of firing data nreceaary to allow for deviations in range due to weather, material, or ammunition range deviation. Distance by which a projectile strikes beyond, or abort of, the target measured along a line parallel to the gua-target line. range error. Difimaee between the range to the point of impest of a particular projectile им! the raago to tbo mater of impact af the group of «hots died with the eaaae data. range probable errar. I. Error in range that n кип >r ntln-r wrafion may lw rx|M*etai tn exeecil as often пн iu>L Itiuigr probable error given in the firing tables fur a gun niny be taken as an index of tin* accuracy of the piece. 2. in describing the dispersion (tattern of a group of shots, the prob- able error in the range direction. range wind. Horizontal component of true wind in the direction of the line of fire. reference rounds. Ammunition rounds of known performance which are fired during ballistic tests of ammunition for comparative purposes. Also called “control rounds.” relative velocity. The velocity of relative motion, especially in respect to a projectile and the air- stream. relative wind. The velocity of the air with refer- ence to a body in it. Usually determined from measurements made st sueh a distance from the body that the disturbing effect of the body upon the air is negligible. Equal and opposite to the relative velocity of a projectile. restoring mefueat. A static moment (q.v.) which ie negative when the angle of attack is positive, and vice vena. reversed flow. Flow of the airstream from the base toward ths nose of tbe projectile, sueh as exists in the mnsxis blast where the blast gases are mov- ing faster than tbe projectile. Reynolds number. (Named after Osborne Reyn- olds, 1842-1912, a British physicist aad engi- neer.) Aa index of similarity used ia the analysis of tbe fluid flow about seals andda in wind tun- nel testa to determine the results to be expected of the flow about full-seals models. The Reynolds number ie expressed in a fraction, the numerator consisting of the density of the fluid multiplied by its velocity aad by a linear dimension of the body (aa for example ita diaamter), the de- nominator nonsisting of the eoefleienta of vis- cosity of the fluid (R* = *П/a). RMS error. A*.* standard error. rochet motor. A nonairbrrathing reaction propul- sion device that oouaiota вгамНаПу of a fuel ehambor(s) aad exhaust ueado(a), aad that car- ries its own solid oxidiser-fuel ooabiaatisa from which hot gaam are generated by eemhmtioa aad G4
АМСР 706*242 GLOSSARY (coat’d) expanded through a nozzle (a). (If the fnei is liquid the device ix called a ’‘rocket engine.") rolL An angular displacement about the longi- tudinal axis of a projectile. nil rata. The tine rate of projectile rotation about ita longitudinal axis. nil rate, nonditneiisieaaL The product of roll nte and a reference length, for example a di- ameter, divided hy the airspeed (» = pd/V). Usually called “spin.” rolling moment. An aerodynamic moment about the longitudinal axis of a projectile, tending to ehange the roll nte*. rolling velocity. Angular velocity; roll nte. net moan aquare. The square root of tbe arith- metical mean of the squares of a set of numerical values. rotating band. Soft metal band around a projectile near ita base. The rotating band centers the projectile and makes it fit tightly in the bore, thus preventing the escape of gas, and hy en- gaging tbe rifling gives tbe projectile its spin. round (af ammuaitioa). 1. Short for complete round, whieh see. 2. A shot fired from a weapon. scale effect. An effeet in fluid flow that resales from changing tbe aeale but not tbe shape of a body around whieh tbe flow parses Reynolds number is useful in the amt mm ent of aeale effeet. achHerea. 1. Gradients or variations in gas density, from tbe German word. 2. An optical system whieh either euts off or pannes a large ehange in light intensity, owing to the slight refraction of the light panting through the gas. This phe- nomenon ix often used to make turbulence awl shock waves visible by photographic means: hence, ‘‘achlieren photographs.'’ aectioaal density. The ratio of the weight of a pro- jectile to tbe aquare of its diameter. A measure of the maaa per unit of frontal area, and there- fore of tbe deceleration due to drag. sensitivity factor. The percent change ia range (or defleetion) produced by a one percent ehange in a parameter affecting range (or deflection), sueh aa mussle velocity or initial yawing velocity. Aho called “differential eoeflkieaL” flee.* dif- farartial affects; aaparation. i. The phenomenomin whieh tbe bound- ary layer of the fiow over a body placed in a mov- ing stream of fluid (or moving through the fluid) separates from the surface of the body. 2. The point on the body at which tbe separation be- gins. Aho called “separation point.*’ aetback acceleration. The peak acceleration ex- l>erieneed by the projectile during launching. I'sually expressed in terms of the acceleration due to gravity, e.g., “the aetback acceleration was 40000 g’x’’ or about 1,286,40 ft/oee*. shock front. The outer aide of a shock wave, at which the prexxure rises from aero up to its peak value. Also called a “preaaure front.’* shock wave. 1. A boundary surface or line across which a flow of air or other fluid, relative to a l»dy or projectile passing through the air or fluid, changes discontinuously in premure, ve- locity, density, temperature and entropy within an infinitesimal period of time. 2. Such a bound- ary surface or line that comes into being when an object moves at transonic or supersonic speeds. 1. 8ueh a surface or line produced hy the ex- pansion of gases away from *n explosion (or through a nozzle). shroud. A tubular section encircling the tips of the fins, and usually integral with the fins. The shroud often forma a rear riding surface for the projectile in the bore of the gun. slug. The engineering unit of mass, chosen such that n force of one pound acting on a unit mam will produce au acceleration of one foot per second )s*r second. Since the weight of a body is equal to the product of its mam and the accelera- tion of gravity, the weight of a body having a mam of one slug is 32.17 lbs (at sea level at 45* latitude). spaa. Tbe maximum dimension of an airfoil (e.g„ a coplanar pair of fins) from tip to tip. spark raage. A flring raage in whieh projectiles in free flight ean bo photographed by tha light from an electric spark whieh is triggered by passage of the projectile, flee: baUotic raage. spodfle taapnlae. Tbe total impulse produced by burning a pound of rocket fuel. At constant thrust and авам burning nto, the threat pro-
AMCP 706-242 GLOSSARY (coat’d) dueed per unit of mass bunting rate, i.e., pound» per Ib/see. specific weight WeighJ^per unit volume. spike. A subeajjbef'eylinder, often slightly tap- ered. whieifreplaces the ogive of a projectile, increasing the drag but moving the eenter of pressure of the lift force nenrer the 1шж nf the projectile. spin. Mee: roll rate, i—dfmsnsional spin rata. Mee: roll rato. spia stabilization । Method of stabilizing n projec- tile during flight by causing it Io rotnle about ita own longitudinal axis. spotting charge. A small charge such aa black powder, in a projectile under test, to show the location of its point of functioning (usually ita point of impact). square base. Descriptive of a projectile with a cylindrical base section, as opposed to a beattail, which see. Abo called “flat base.” stability. A characteristic of a projectile that causes it, if disturbed from ita condition of equilibrium or steady flight, to rrtum'to that condition. stability factor, dynamic. A number related to the ynw damping characteristics of n projectile. Stability factor, gyroscopic. A number relating the angular BMimentum of a projectile to the slope uf ita aerodynamic overturning moment. Loug used as a sole criterion of projectile stability and called simply the “stability factor.*’ ». A neves, мгу, but not sufficient, condition for atability b that thb factor be greater than unity,'or nega- tive. stability, static. Stability in tbe absence of spin. In general, a meebanims b statically stable if any dbplacement from a rest position creates a foree or moment opposing tbe displacement. Standard Atmssphsr*. Tbe standard atmosphere for the United States Armed Services b the U.S. Standard Atmosphere which b that of tbe International Civil Aviation Organisation (ICAO). Thb standard atmosphere aasumm a ground pressure of 760 mm of mercury (14.69 psi) and a ground temperature of 15*C (56*F). Tbe temperature throughout the troposphere ex- tending up to 11 kilometers (approx. 36,000 ft) b given by: T(*F) = 59 - QJtic56 * where * b the heigh&^bove sea level measured in feet. In the stratoaftberv, extending from 11 kilometer* to 25 kilometers (npprox. 82ДЮ0 ft) tbr tei(i|ierature b SMuimed to be a constant 21<>.6(>"K (—69.7aP). Above the stratosphere other laws are assumed. Temperature b signifi- cant IsTaust* the aeoustie velocity iu feet per «croud b given by V. - 49.1 V 460 + T T in *F standard deviation^ In the field of testing, a mea- sure of the deviation of the individual values of a serie* from their mean value. Tbe standard deviation of a sample b expressed algebraically by the formula. . - J«» - " X ’ я the sum of N individual squared differeneas, the Si are the individual values, * b the mean (i—X r</M), and N b the number of individuals in the sample. The best estimate of «, the stan- dard deviation of the lot from which the sample was drawn, b obtained by multiplying the sample value, *, by vW/(M-l). standard error. The square root of tba average of the squares of all the errors. When error b identified as the difference between an observed point and the means of the observations, standard error becomes identical with the sample standard deviation. It might also he called the “BM8 error.’’ standard muzzle velocity. Velocity at which a given projectile b supposed to leave the muzzle of a gun. The velocity b calculated on the basb of the particular gua, the propelling charge used, and the type of projectile. Firing tables are based on standard muzzle velocity. standard projectile. That projectile which a given gun was primarily liorignod to fire. static moment An aerodynamic moment related only to angle of yaw. static pnanre. The pressure which b snorts it by <M
GLOSSARY (coat'd) n fluid al real, or which would be indicMl-ri by n gage placed in the Htream and. moving with the name velocity их the Htreani. It ia thr prwwun- arming irom the random motions of the mole rules of the fluid, rather than their organised suit ion in the direction of the flow. steady state. The condition of a system whieh is essentially constant ifter damping out initial transients or fluctuations. sting. A rod or type of mounting attached to, aad extending backward from, a model, for conven- ience of mounting when testing in a wind tunnel subsonic. Pertaining to relative motion between a body and a surrounding fluid at a speed iem than the speed of sound in the same fluid. summit of trajectory. Highest point that a pro- jectile reaches in its flight. swerving motion. In flight, the motion of the cen- ter of gravity of a projectile perpendicular to its particle, or zero-lift, trajectory. r;etem reliability. The probability that a system will perforin its specified task under stated tac- ;‘-eal and environmental conditions. This will in- clude accuracy. T (subscript). In aerodynamic data, relating to tail alone configuration. terminal velocity. I. The constant velocity of a falling body attained wben the resistance of air or other ambient fluid has become equal to the foree of gravity acting on the body. Sometimes called “limiting velocity.'’ 2. Velocity at end of trajectory, Le., impact velocity. time of flight. Elapsed time in seconds from the instant a projectile leaves the gun until the instant it strikes or bursts. tolerance. The permissible difference between the two extremes in dimension, weight, strength or other quality whieh will not cause rejection of an item. trajectory. The curve in space traced by the eenter of gravity of the projectile. traaaitiea flew. A flow of fluid, about a body, that is ehanging from laminar flow to turbuient flow. traaaeaic raage. The range of speeds between the speed at whieh one point on a body reaches su- personic speed (relative to the airflow in tbe vicinity of that point) and the speed at which the shock wave system is fully developed. transonic speed. A speed within the transonic range. transverse axis. In a projectile, any axia normal to the longitudinal axia and paaaing through the eeater of gravity. trim. Tbe equilibrium attitude of the longitudinal axis of the projectile relative to the tangent to the trajectory; equilibrium yaw. turbnleat flow. An unsteady flow characterised by the super-poaition of rapidly varying velocities on the main velocity of flow, in contrast to the smooth, steady laminar flow in whieh velocity varies with distance but only slowly with time. twist (of rifling). Inclination of the spiral grooves of the rifling to the axia of the bore of the weapon. It ia expressed as the number of calibers of length in whieh the rifling (and therefore the projectile) makes one complete turn. A right hand twist is such as to impart a right hand (clockwise) rotation to the projectile whan viewed from the rear. Most U.8. guns have right hand twist utility. A numerical scale for comparing prefer- ences between alternatives. Usually defined on tbe interval 0, 1 because of its relation to prob- ability. vacuum trajectory. The path of a projectile sub- ject only to gravity. A first approximation to tbe trajectory of an actual projectile. vector. 1. An entity whieh has both magnitude and direction, sueh a* a foree or velocity. 2. In con- nection with the yawing oscillations of projec- tiles, the rotating arms whieh can be used to rep- resent the components of the yaw are termed modal vectors, whieh see. velocity. Speed, or rate of motion, in a given di- rection and in a given frame of reference. In many contexts no distinction in meaning is made between speed and velocity, tbe symbol V often being used in equations in whieh the magnitude of the velocity, i.e., tbe speed, is the only attri- bute of velocity whieh is beiag considered. velocity head. 8м; dynamic pressure. viscosity, ceeflciaat uL The ratio of the shearing strem to the velocity gradient in a boundary G4
АМСР 706-242 GLOSSARY (coat’d) layer. Dependent on the fluid and on ita tem- perature. м ы, at 59* F = 3.72 X 10" » Ib-sec/ft» «aka. The xone of turbulent flow liehind the baae of projectile. wash. The «urge of disturbed air or other fluid resulting from the paaaage of something through the fluid. Include» the wake and bow and aide waves. wave, expansive. An oblique wave or tone set up ia supersonic flow when the ehange in direction of the airflow is such that the air tends to leave the new surface, sueh as flow around the juncture of a cylinder and a eone (e^., at the forward end of a boattail). Thia condition is called "flow around a corner. ” The air after pasaing through an expansive wave or none has a lower density, static presure, and freestream temperature and has higher velocity and Mach number. Visible cs a darkened sone in aehlieren photographs, these waves are often called "expansion fans." wave length. 1. The distance traveled in one period or cycle by a periodic disturbance. Z Of yaw of a projectile, the distance traveled by the pro- jectile during One eyele of yaw. yaw. 1. Thr angle between the direction of motion of a projectile uud tbe direction of the longi- tudinal axis of the projectile, Z The oscillation uf the direction of the longitudinal axis (aa in ' wnvelength of yaw”). .7. To acquire an angle of ynw; to oscillate iu ynw. yaw of repose. That part of the equilibrium yaw which is due to gravity. yaw drag. Drag due to yaw. yawing moment due to yawing. Term sometimes itsed for the damping moment. yawing vslodty. Time rate of ehange of yaw; the change may be a ehange in magnitude or direc- tion, or both. zone charge. The number of increments of propel- lant in a propellant charge of semifixed rounds, corresponding to the intended sone of firs. zone of fire. The raage interval whieh ean be cov- ered by a round containing a given number of in- crement. of propellant, Le., the eovenge obtain- able by changing quadrant elevation at a constant muzzle velocity. zoned ammunition. Semifixed or separate loading ammunition in which provision is made for add- ing or removing propellant increments. G-10
AFPBJTOIX I SAMPLE SPIN-STABILIZED PROJECTILE
ашт Ms-эа лтяпях и CALCULATION OF С. G. AND RADIUS OF GYRATION Apprexuutr forwalao for high expicarve pro- jectile* ore prevented by Hitebeoek ia BBL Bopart. «20 (Ref. 81). i 0375^ k». = 0140 к», =OOTO+ 0l0M4^) where Xrl. ia the riwtianr free the tear of tbe projectile to ita «enter of gravity, ia aolihcea, aad 1/d m tbe in>»a ratio at tbe projectile. a. A!trr»eu MtM: For tbe вамрАе projectile ia Appendix I, the panMoeten eatatiated by aae at tbe "Altanaie Method” 'we Appeadix VII) are: Хел = L5. P. = 0145 H, = LOT . A MildUecb Method. By HitHMark n fonaalat, we weald got Jre 0XK x Ala -= 1.Ы h*. = 0140 IF, = OOTO + OOhM (4.3?)’ = 1Л
AMCP 706-242 АРРХКЫХ Ш GYROSCOPIC STABILITY ESTIMATES A. SPIH-STABaiZRD PROJECTOR WTTE ВОАТТАП. . Tbe fallowing * sample calculation for a epin-etabiliaed projectile with boattail, uaing the awthoda of Wood (Ref 21) and Siaaoune (Ref. 20) to eutiaute the nonaal fore* aad static ao eat eoeAcienta The geometric and там eharae- tericties ot the projectile are given in Appendix I. Effective Base Diameter: where d - Rear body chain. « 4.88" (0.416 ft) d» - Baae diaaa. - 442" 4. - у/ 21.7314 - 4.66" Effective Baae Si - .7854 £ - .7854 (4M? - 17.0664 in* Frontal Area: X - .7854* - .7854 (446)» - 16.4783 ia* Baae Area Ratio: Xi . 17.0554 X ”18.4782 - 04756 Volume of Projectile (iacAiitag boattail bouadary Myer): V» - 30X5412 * (aee mlnriitina below) 1 Я1Я '4125) |(3CO)» 4- (SOO) (56) > (.SA)*] 11.8*76 2 Prato Harvard Table Caten'atioaa* ЛМ40 8 7864 (8.382) (4.88)»= 188,2660 4 2618 (280) |(4.M)* 4- (4.M) (4.66) > (AM)*) 46.6826 V, Total Bouadary Layer VehtaM « 308.5412 * Мегмае Appendix Tit.
АМСР7ММ2 лтпа ш (сме<> <Jeulrr <d < «rarity (faaa App aifa I); C. (,'. - 1.Л2 oJihrfli (гим her C. /•. (!. t:. » XN5 - tJS • IJB мКЬма DrtrrwM—йов «/ /, nd fc фве graph Appradn IV) At аиргпм*е taead: X - VM’-l - 04» far X - 1.П VjSd Static Muaxat Cotgcirat: С», - CK, (С. A - C. 0.) - (2.TO) (14» ш IM * ~ 1 - 0142 aad VX» - I J* 7™1 - aits VSTZi ..J, - 1.1007 aadX - 1.2300 Ncnaal Fcrca CnrOrirol. - I 2 (ATM) 4- A 1(1.1007) - 270 rad • Moanmt Coeftqeat (abcat baae): C«. - ](1 2300) Gyroaeopic Siabtfcty Factor, Velocity: Vel - 1Я25 (pa Twiat: a - Я eahbaaa par tan Airdaaaity: * - 000072 аЦДО /.*//, - OOOMA«4t* ,-t^PC,, i - IM tat* _______(LOOM X >T) *“ i^cooncb (J0U) (зЗомм X (X0j - LM
лмсгжде АРРДОЫХ Ш (eaat’d) GYROSCOPIC STABILITY ESTIMATES A SPLM-STA BQ. IZED PRO JECTILE WITHOUT BOA* TAIL (FLAT BASS) Aaaaaae only change from previoat exaatple » м volume aad C. G. location. New volume: К = Э0&5412 ia.» Mena Finenem Ratio: V. r 306.5412 .Sd (19.4782) (4.96) “ llrtrnntnation of /i and/«: (Ser graph Appendix IV) N - 044 fur M - 172 - 1 A - 1 vm* — i L & I* Bn^ VX* — i ” ® *** ../> - LOWaadA - 12337 Normal Fore* Coeftciaat: C"‘ " (’ * *)1 ***"S " Я - (2 (1.0) +• .14 (».990) - Х0О rad ’ Moawat Coe . (about bear): C*e ” (* S’) h ~ <ЛИ (l аяп - 7-Miad-* Center of Pbeawre; • L*. P. ” •• X60 caliben from baae Center of Gravity: C. G. ia nov located 1.50 eaubero from baae P. - C. G. - X60 - 1J0 - 1.10 ealiben Static Momc.it Cocggeat: < a. - О. (С. P. - в.) - (xoo) (i.io) - xao Gyroeeopie Stability Fbctor, a» Suter the parametera V*L, p, a, d. a, /J//»—are the ааш aa the example ia part A: Z^a. with boattail \ ** “ I’4® Wa. *aithout boattail / • ла an ’ l *(xao) “ , e= ConduMOtt: thB boMtMl httB UMNMBd the gyroaeopic atabduy ItMt (bwt aho iaanaaaad the aaro-yaw drag Modheicat).
AMWNe-МЗ Ш1Ю1Х nr COMPARISON OF ESTIMATES OF BALLISTIC PARAMETERS BY VARIOUS METHODS For eompanaoa with the other eariMttee, oeJ- ndotkMM by Hrteheoek’a awtbod, BBL Report OO (Ref. 81), far At мте boattailed projeetile. A*- prndiz I. are preamted Wo»: X. = lies r «, =4 *. = 2-M (wXTOby Weed’a method) a (beetle il eagle) = 75 degree* b (boattail Vogth) =05 мКЫн <• (eyliadrieal body liagth) = L58 oalihera d (opnl heed leagth) =100 ealihere r (radia*atogival ore) = 5-12 eaSbero IjO/« = .1» Crater of Ргнвог»: h = .0747 + 4443e 4- 1JHM 4- MUt 4- JMSOd 4- AOOS (LO/o) h = .0747 4- ЛКЛ 4- JSO№ 4-14494 4 .4910 4 .157» Хашм! ('urMeieat: (мм* a. h, e. d. aad • shove) * 2.91 ralibm from the bar (ea 18& by Woad’a aMthed) K. ~ 453 + AS3o — 4UM — ЯВП» 4 ЖЫ 4- Ml* <L0/«) r. = ЛМ + .im _ дт - ооа» + xno 4- IMS This agrreowat ia camadrrad to be better thaa average- While Hitabcack’n aril atm are very mod for peojretihe whieh lie withia the reage •>< bio ezperuaeata] data, the Weed-SmaaoM eoti- matea will >a goaera) he atom reliable. A4
ЛМСВ ТООДЭ
АШТ 704-242 APPEVDIX V DYNAMIC STABILITY ESTIMATE РгаЫмм: То drtenniae v,. Tbe projectile will beatable if: _L <a4,(20-s4) (Ref. par. 5-24 21) . • a (Cl. 4- «•" ex. - u л- * (с. Д c.j Snee nur projectile has the hum baBbtk shape as projectile, 90-mm, HE, M71, ths baffistio coett- rieato for the 9(Xmm projectile at Mach “ L72 iief. Appendix VIII-E) any ba naad, namely: - 020 См, + Cm, --AO C. - 042 Ihta: For pratutype projectile (Appendix I). Cl, - 270 rad-» Mach - 1.72 * - 4АМПЛЛЛч* d - 01415 ft J. - 00350 shuH^ 2,, - 04040 sh<-ft7 *-5--T7 . (**\1*^. им 1»2 ) (.0Ы4, **"£“77 /МО<\(4ЛУ)_ \324 ) (4040) Solution: 2(2.70 4- 54M (40)1 114 4 " 270 - 043 - 0933 (-10) "10707 - 0736 Eram Appendix Ш4:4 “ L40 < (20 - - O7M (20 - 0754) - 004 Ccochмйа: Projectile is stable am: _1_< 4^ (29 ¥ i&: 0471 <004
АМОР 706462 АРРКХЫХ VI STATIC STABILITY ESTIMATE OF A 5-IKCH FIN-STABILIZED PROJECTILE l*n>bli-a>: I Jrb-nniw normal f«m* atul n-nti-r of imtwun* of the Ixuly alow. and normal fora* and renter of 1И1КШЛ* of the tail alone in onlrr Io solve for statir «lability: ; P- — С. 4. ; > 0.5 caliber Solution: (1) Body alone coeffictents at sufasomc muxzlc velocities Data; The effective base are г. 31, and total boundary layer volume are determined in a manner similar to that shown ia Appendix Ш-Л. 4, - 2.672" and о - 5" SI - .7854 4 - .7854 (2.672)’ » 5.6074 in1 X - .7854* - .7854 (5>* - 19.635 S3 - 19.635 3 - 19.635 (5) - 98175 V» - 487.0151 №> Solving by Simmons' Equations НИ. 20: См, “ 2 + 0.5 ’(Sb—- ’® -’(та1) 9.9212 C»t> 9.9212 • ~ C„“ 1.071 - 9.26 calibers from base of fins (2) Tail alone eoelbarut» at subsonic velocities: Data: effective tail length: / “ 3.0’' In span: X “ 5.0" effective base diameter: d, * 2.67" j- 0.6 and y- 0.53 Solving by Simmons’ Tables : f’i.T — *2.20 (for 6 rectangular fins) - <’tp (0.74) 1.628 (body interference factor « 0.74) Gr - Ci (1.80) - 2.9304 (allowance for end plates and shroud - 1.80) C. P- u.i “ 0.61) caliber from base of fins (3) Static Stability | С. P. - C. G. | > 0,5 caliber (Ref, par. 5-3.2): Data: From parts (1) A (2): Ся, - 1.0710 at a С. P. located 9.26 calibers from base of fins f 'vr - *2.9304 at a С. P. located 0.60 caliber from base of fine < v. - Си, + С„т - 4.0014 rad*» C. fl. * Ж68 calibers from bane of 6na «'. P.„ - C. (! ) - 9.2h - 3.68 - 5.58 cali x*n« P.r - C.«.) - 0.60 - 3.68 - - 3.08 calibers Solving (ref, pir. 5—XI): См. - См, (С. P., - C. (?.) 4- C,T (C. P.T - C. ff.) (1.071) (5.58) + (2.9304) (- 3 08) 4.0014 X0494 n„ -4Л61Г- ~°n P. - C. G. | - 0.76 caliber Condumoo: Static stability seems adequate sinoe | C. P. - C. 0. | > Л5, iA, a78 > as
AMCPTCIMt лтпих vn PBOJECTUB GXOMETBY Th* deeiga parameter* rotated only to th* Material* aad geenMtry of th* projiotiie an: Weight Crater of gravity location Axial aad traaawrar momenta of .nertia Method* of Ccmpetation: I. Mechanical Integrator (Ref. 95): *. A aeale drawing ia Made of the part or aa- ata^ty. (1) Th'miaeinae ia the z dirratioe av not attend (X) Птепемпа ia the у duration are al- tered hy letting ih = y*/S h. The drawing ia travomd by the mo- ehaaieal inti grot nr (a fam af planieo- eter). r. Dial iadiratore provide nambera, relative to the transformed plane arena d. Bquatioaa convert dial readinga to weight, center of gravity, aad eoomrate of inertia of aalide of iw station. 2. Harvard Tebin Btaadard Method (Hot «21 a. Analyte wortei from dimraeioned ahetehee, or drawian, to evahtato weight, eg, and MMste of iMvtifc» h. Table* provide expedient method to aap> piement etandard egnation* for aolida'of revelation. X. Alternate Method: Aaotyat nma venation* of form]** for limited xaaeber of аоШ ohapro, aad waiplibm ammary ef parte and aaembty. A Competer (Ref. 98): The weight, heatira of frntOT of |iniitj~TnlaoM. polar moment of inertia, tranever** moment of inertia aad total momeat of inertia eon be obtained throogh пае ef a digital ilietrnrir eompeter.
AMCP 706-242 АРРКЖС1Х УШ—A 30-MM HEX PROJECTILE, T306E10 AUTHO₽(s) E. T. Roeckar and E. D. Boyar REPORT BRL MR 1098 DATE 1957 TYPE OF TEST Free Bight Weight, lb Q.,56 Muzzle fVolodtyfpe Vari ahi, (Spin rate, rpe Yana bl it d.ft . 0.098 y, rad/col - °-38 eg. location fra* bot%cafiber* 1.33 M Subtonic fQ.6 Tranaonic Pbofc 0.9 к col 0.372 t «1 0.845 Superaonic 2.0 CowwiHHfci c«t* 1.7 2. l<0.2 2.4*0.2 ^Ma 1.9 2.3*.05 1.50.05 ^a|..O 4 C.P 2.3 2.350.05 «3.501.0 «0.13О0.10 1.850.05 Without arming ball rotor |4-aC**.|«o tM « 2.0 b « 90 -- - f. — 8- (noAm » 5.4*0 1 Computed for itaadard 1:25 twiet ( 0.25) ч£“К? • 0.500.« Vithout arndag ball voter aad at mail yaw STABLE at mull yaw* ar/o armlag ball rotor. UaaaUy UNSTABLE with arming ball rotor A«H
АМСР 706-242 author(s) Е. О. Boyar АГГКМШХ VIII—8 20-МЖ НЕ1 PROJECTILE, T282S1 REPORT BRL MR 813 (Raf. 78); BRL MR 916 DATE 1954 1955 TYPE OF TEST Free flight Mexlo 0.216 Variable Variable" 0.0655 0.209 or 0.251 Mosh No. C.Q- locoHon faora bomvcofibora -L)L kecd ♦ 370 kfCd -1-015 M Subocnie 0.98 . 1.15 Supononic 2.4 tow» CBA 6.6 (oetimated) 5.3*1.0 1.4£M£3.6 1.9*0.1 2.0*0.1 2.6*0.2 cn. - % c* Vk -4.8*0.6 . -0.20*0.04 aoa curve -7.5*0.6 -3.8*1.1 0.07*0.04 0.16*0.07 Г-0.7*0.3© M> l-4.3*0.3©M« 3.5 3.5 w/o arming ball rotor 4 Not maaeu-i Bd; aesumad to be -0.01 ia computatioaa •e 2.85*.05 1.75*.06 2.70*. 05 1.85*.07 2.25*.05 oa 2.6*. 12 Ihm tram born 1 0.15*. 12 0.58*. 10 1.25*. 10 Whu’ *-1» 11 0.26*.20 0.57*.02 UNSTABLE 0.82*.08 0.54*. 02 STABLE 0.93*.05 0.38*. 02 STABLE Far large yav (/£43*) flrlaga at M* 2.3 aoo E.T. Roe char, BBL MR 888. 1955.
A MCP 706-242 APPKND1X VIII—С DRAG VS TRUK CATION: CONICAL HEADS AUTHOR^) A. C. Charter» and H. Stain REPORT BRL R Ы4 DATE 1952 TYPE OF TEST Free Hight 0.0655 0.25 &0. location from Ьс^сойжг» ----------1^, dur*’-------- k-Cal __________________k.,cd _________________ <r г Commmti 5.4*1.0 >.6*1.2 2.0 approx. 1.0 approx. 0 approx. About 10 rounds of each typo. A-1S
A МСР 706-242 A/PIND1X VIII—1> 2.7S-IXC8 ROCKET, T13J AUTHOR^) L. С. MacAlliater aad W. K. Roger» REPORT BRL MR 948 DATE 1955 TYPE OF TEST Free flifht INERT ROCKET Weight, ib 5.3 Muzzle (Velocity, fpa Variable (Spit? rata tpa Variable d,ft 0.228 1/, rad/col 0.523 Modi Na Mach Na eg. looCian Ikm baaacafiben 1.77*. 01 >>.01225 kecd JLHL-— кь«1 M 0.85 1.0 Cewmate 1.15 1.95*.05 2.04.05 2.04.08 ^Me 3.15*.05 3.454.08 3.45*0.1 -4.5*0.5 -7.5*1.0 • 1042 •0.23*0.1 -0.23*0.1 -0.07*0.07 ijcoHun *0 Ы - •-i-- wvon vram вявв hS2^? 4" Л-14
appxxdix vin-E AMCP706-242 90-MM HE PROJECTILE, M71 AUTHOR^) E. D. Boyer REPORT BRL. MR 1475 (Ref. 79) DATE 1963 TYPE OF TEST Free flight Dimensions, calibers Meeh No. Mach No. eg. location from basecofibors _ I^slug-f»8 Q.QQ87 skig-ft8 0.0815 к _col °- 369 k^cd »•*« Transonic 7 Subsonic fbak Supersonic M 0.8 0.95 1.8 2.4 c<* 5.53*.15 5.17*.05 1.5*035 1.4*0.5 2.35*0.05 2.55*0.05 с*. 4.0O0.08 4.7*0.5* 3.55*0.08 3.30*0.08 Jindependent of yaw oxcept in (interval stated -tel -7.5*1 -9*1 -8.5*1 At M * 1.05 Cu + Cu • -5.5*2.5 -0.2t0.I5 40.2*0.15 40.2*0.05 40.2*0.05 At M x 1.05 Cj^* 0*0.2 4 ЮС0МЗН 4.000.2 4.25*0.25 2.8*0.15 2.7*0.15 calibers from base 1.07*.02 0.93А.Ю 1.20*. 03 1.30*.03 ‘Ho 0.0*0.47 0.85*.50 0.86*. 16 0.924.16 Increasing ths twist of rifling to ?5 cal/turn (Г » 0.251) stabilises uS*“k? o.o+o-n -1.16 0.79*.21 0.954.05 D.97*.03 projectila over whole Mach ao. range. 0.93*.02 1.104.12 0.53*. 02 0.77*. 02 V UNSTABLE METASTAB LX STABLE STABLE 10^ A«15 * Strongly dependent on yew whin 0.938» M£ 0.98; CM* *5.2-
АМСР 706-242 APPSMD1X VIU—У 105-MM HE PROJECTILE. Ml (MODIFIED)* autho«(s)e. T. Roecker; E. D. Boyer REPORT BRL MR 929 (Ref. 85): BRL MR 1144 DATE >«55 1958 TYPE OF TEST Free flight Free flight Dimenticrts, caliben Wiohtjb (Velocity, fpt (Spin ratal qpa d.ft V, rad/cal Rifling twist 32,12 1510 220 0.344 0.314 nt mussle 20 cni/tum M Subeonie оЛ Ticmcnie fbok 0.95 a Supemcnic 1.35 "" 1»— Ccmmatda c* 6.1*0.5 1.4*0.2 2.0 8.1*2.0 1.9 ^Mn 3.0*0.1 4.9*0.13 3.85*0.05 -7.4*3.0 • 12.7*3.5 -4.9*0.7 , fVarias markedly with yaw at aubecuic and ^^4 c»s- «0.3*0.25 0.55*0.07 0.03*0.05 (Jraaaenic speeds Roeckor Boyer 3.9*0.2 4.5*0.2 3.4 соНмп from Ьсм ЬаМои 'в 2.4*0.15 2.15*0.1 2.7 Subeooically, СМр* ** vary markedly • > 0.15*0.47 0.94*0.14 0.43*0.14 with yaw. Projectile ie dynamically uaotahle o.is^*57 ”•“-1.03 0.90*0.02 0.85*0.12 at yaws leea than 3*. _1 0.30*0.02 0.47*0.02 0.37 See comment STABLE STABLE A*16*The cylindrical body diameter waa undercut by .03 iach ie increase the yaw.
AMCP 706-242 APPSMDIX VIII—G 4.9-CALIBER PROJECTILE AT TRAESOXIC SPEEDS литнояк) L. E. Schmidt REPORT BRL MR 824 DATE И54 TYPE OF TEST Free flight 42.5 Variable Variable 0.341 0.314 Dimensions' calibers Mach Na Mach Na cq. location from baset calibers *-23 ^sluQ-ft’Iy,slug-ftl к cal 0--34S k.,cal °-’7S Subsonic Transonic Pbok O’ Supersonic Comments M 0.83 1.03 1.3 с«г b. 1 (estimated) Used over whole Maeh no. range 2.3*0.! 2.1*0.1 4.4*.04 4.7*.04 4.7*.04 -1.8*0.8 -5.0*1.2 -3.5 -0.4*.05 -0.1*0.! -0.05 c.₽ c.q location 3.0*0.1 3.0*0.! 3.o*o.l cdbers hoe bow *8 3.1*0.! 3.0*0.1 3.0*0.! ‘do -0.83*0.4 Ю 0.42*0.30 0.71 -1.7*1.4 o w*®-46 0,6*-0.43 0.92 0.32*.01 0.33*.01 0.33*.01 • UNSTABLE METASTABLE STABLE A-17
AMCP 706-242 AFPUDUl VXU—M 90-MM HE PROJECTILE, T91 AUTHORCs) L. C. MuAWlUr REPORT BRL UR 990 (Ref. 13) DATE 1956 TYPE OF TEST Free flight IB,64 Variable Variable ___0.292 0.25 cq. locotian haa boM^cafibcrs I-?5 Modi Na JL2®*L_ ly. Ajb-** 0.0645 M Suboomc 0.7 Transonic 0.95 k®e°* SupSflOCMC 1.8 _°L3.70 kb Cd Ь14 Comnmds сог 2.1O0.1 2.7*0.2 2.1*0.1 Valuee shewn ar* for tracer aot i^ited. With tracer ignited, C_, eo ie reduced about 6%; Cwt ia not См. № 18*1.1 0*1.5 -6.5*1.0 changed very much; dynamic stability ia improved. -1.0*0.15 -0.9*0.3 •0.2*0.15 cv 3.65*.05 3.35*.15 3.55*.05 « яя bom Ьом loccAort *8 4» 4" - Coefficiente vary with yaw. See BRL TN 1119 (Ref. 84) for data on variation. Tracer off—UNSTABLE at all Mach nos. tested (0.6 A M « 2.0) Tracer on—UNSTABLE 0.6<MA1.6 STABLE above M • 1.6. A-18
AMCP 706-242 лтшых viii—। EFFECTS OF HEAD SHAPE VARIATION AUTHOR^) E. R. Dickinson M = 2.44 REPORT BRL MR 838 (Ref. 24) DATE 1954 TYPE OF TEST Free flight Weigh», lb _____________ (Wlodty.fpe 2720 (Spin rate, rpe -------- d,ft eg. loooticn hem Ьом^соСЬеге various R 9.47 14.20 18.94 37.88 « edben «Ат 1.0 1.5 2.0 4.0 «(cone) .235*.007 .210*.006 .205*.005 .210*.005 .217*.005 C0»»x Ю.0 for all types 2.8*0.1 2.7*0.1 2.65*0.1 2.55*0.1 2.5*0.1 All values are at M s 2.44 «•A - ОыЯОП 3.05*.05 2.93*.05 2.82*.03 2.71*.03 2.57*.05 --»« — • - 1 GDHDwV IWm DKBB R^ is the radius of a tangent ogive, in calibers. For this projectile R^ * 9.47 calibers. A-19
АМСР 706-242 лижжвхх тш-j 120-ММ НЕ PROJECTILE, М73 AUTHOftls) Н. Р. Hitchcock REPORT BRL R 569 DATE 1945 TYPE OF TEST Fro* Flight Woiphr.lb Muzzle (Meloeityfpe (Spin rato.rpe d,ft 4/, rad/cal . M.T. M61 Fuse 50 (approx.) -3010 —Й4______ 0.392 0.209 eg. location from bca%oa№ors . Subsonic Transonic Psok M -0.0125s. 0008 Determined by averaging over time intervale ao long ao 60 oec cdbm from beat ^(2Tlo)
AMCP 706-242 JPPEIDIX VUI— К . COME CYLINDER AUTHOfifc) L. E. Schmidt Muzzle REPORT BRL MR 759 (Ref. 52) DATE TYPE OF TEST Type 21 - Weight, lb (Velocity, fpe (Spin rate, rps d.ft V, rod/cal 1954 Free flight «olid bronze 0.582 Variable Variable .0655 20mm 0.25 Dimensions, calibers Mach Na eg- location from ЬамьаЬЬеп -1,65 Mach Na 5.55x10-6 Ty «IvQ-ft* 57.2x10-6 kaed 0.330 к», Col 1.06 Transonic Subsonic Supersonic ** 0.8 1.25 1.9 C0|« 2.3O0.06 2.6*0.06 2.7*0.1 2.3 2.9*0.06 2.5*0.03 2.75*0.02 2.3*0.64 -0.3*3,1* -9.0 -4.8 -0.7*0.1 *0.25 40.05 4 2.3*0.02 -6.0 (from ci.rve) 0 (from curve) C-P 2.7*.05 2.75*.05 2.5*.05 2.45 I .Г wQDROn •g 2.86 2.75 3.24 2.33 0.87 0.87 0.68 ^2^) 0.98 0.98 0.90 -J- 0.36 0.31 0.43 ТВ UNSTABLE STABLE STABLE STABLE • Positive values of *re reported for 3 rounds. calibers from base Computed from curve data A-a
АМСР 706*242 APPIUDtX УП1—t ‘ EFFECT OF BOATTAILIEO 01 Cos AUTHOflfc) E* R* »*ckin.<»n BRL MR М2 (Ref. 24) ЭД7Е 1944 TYPE OF TEST Free flight variable | .19 |4o| |—15 DtaMmicft», coliben PART I Effect of adding to length of projectile, and diminishing the area of the baee. by adding boattaU. d« .0417 ft Boattail Square Baee Boattail Length, calibers Лпд1е 0.5 1.0 1.5 C_ at M * 1.2 »o 0* 0.42 4* 0.372 0.350 0.330 7*15’ 0.376 0.340 0.324 9* 0.39 0.35 0.345* at M * 1.8 bo 0* 0.32 4* 0.288 0.27P 0.25 Г 7*15' 0.298 0.270 0.261 9* 0.31 0.275 0.27* C_ at M » 2.4 0* 0.26 4* 0.254 0.220 0.220 7*15’ 0.246 0.22 0.22 9* 0.25 0.225 0,22* The C_ values ebown were read from the curves ia MR 842. The ecattar ua of the observation» averaged about *0.005. Variatiaa ia surface finish, by affecting th* boundary layer transition, may account for much of the scatter. •The 9*. i.5 caliber boattail was a dynamically unstable configuration; these data ar* for a 9*. 1.25 caliber boattail. A-22
AMCP 706-242 АРРВИНХ VIII—L EFFECT OF BOATTAILIMG OM (crat’d) AUTHOR^) e- *• Bick.nson Dimension», caliber» REPORT BRL MR 842 (Raf. Z5) DATE TYPE OF TEST Free night PART Ц Effect af increasing the length of the boattail, and diminishing the area of the base, while keeping the overall length of the projectile constant. d = .0655 ft = 20mm Boattail Square J3as£ Boattail Length, calibers Angle 0.5 1.0 1.5 C atM« 2.4 0* 0.256 »o 4* 0.243 0.224 7* 0.237 0.216 0.207 C_, at M - 3.2 »o 0* 0.208 4’ T* 0.19* 0.179 0.169 C_ at M x 4.0 »• ...72 “° 4* 7* 0.165* 0.151 0.144 The Cjj valuee shown were read from the curves in MR 842. The scatter of the obee^vabons averaged about ±0.003. Estimated effect of adding a driving band (rotating ring) is to add 0.01, or lees , to the valuee shown assuming'that the band does not extend to within less than 0.25 calibers ai the bjtttaii. •These valuee were read frem aa interpolated curve.
АМСР 706-242 AUTHOR^) лтятх vin—м EFFECT OF BOATTAIL ОН С* AT М = 2.44 T. Hailperia REPORT BRL MR 347 (Ref. 26) DATE 1945 TYPE OF TEST Fr«‘i n*** M> 2.44 Boattail Length, caliber* Baee Area Square Base 0.5 1.5 1 Frontal Area 1.0 0.76 0.39 c_ 0.263 0.248 0.228 Do *.027 *.004 *.005 CD«i 6.7 5.1 4.5 A-24
AMCP 706-242 АРРХЖШХ УШ—Я 90-MM MODEL OF 175-ММ PROJECTILE, Т203 AUTHORtS) В. О. Karpov, к. s. Krial and В. Hull REPORT BRL MR 956 DATE 1955 TYPE OF TEST Free flight Weight, lb 21.82 Muzxle (Velocity, fpe (Spin rate, rpe Variable Variable d,ft 0.295 1/, rad/cal d.tVb (For etandard 175mm gun,V ® 0*314) Mach Na eg. location from Ьсм,саСЬ*га 1.94 »00?S -0535 k Cd k cd 0.952 QF f* Tranacric Supenonic Comment* M 1.15 1.65 2.6 5.8 5.8 5.8 1.4*.08 3.0*.05 3.5*.05 4.75*.05 4.3 3.7S -7.8 *8.0 -6.7*,35 0.28*.15 . 0.28 0.19*.04 4 ioection 4.7 3.25 2.95 M. - . £ 1 GQRWl TTOlW DQiv ’« 1.48 1.65 1.90 calculated withy ж 0.314 ЧН? Projectile ie dynamically etable over thie range of Mach numbere when fired from a gua with 1:20 twiet (V • 0.314). * A-25
АМСР 706-242 шипи vin—ж (coat'd) AUTHOR(s) В. G. Karpov, К. S. Krial «ad B. Hull REPORT BRL MR 956 DATE И55 TYPE OF TEST Free Hight Muzzle Weight, lb |spinrat«,rp» d.ft V, radZoal 21.21 Variable Variable" "07295---- ~В.Ш or 0.251 eg. location from biweontfaau 1 •85 ^dug-ft’—______________Iyrdug-ft* .094 kacol 0-™ kf.el 1-065 M 1.2 1.6 Sm&ereonie 2.6 Coenmonh 5.8 5.8 5.8 2.3 2.95 3.5 Cm. 3.0 3.1a.05 2.8*.02 -9.4 -9-7*0.1 -9.5 0.18 0.18 0.16*.05 4 «•P ОыЯОП 2.98 2.80 2.60 cdbot* from boro 2.37 2.30 2.52 calculated with* » 0.314 *d© W4? Projectile ie dynamically stable over thio raage of Mach numbers when fired from a gua with 1:20 twist (9 a 0.314). А-И
APPKKDIX УШ—О 7J-IMCK SPIRRER ROCKET, T99 АМСР 706-242 AUTHOR^) T. Hailpenn REPORT BRL R 572 DATE 1945 TYPE OF TEST Free night Weight, lb . Muzzle IVelocity, foe 1500 KiT.Sejp. d,ft (model) 0,0655 V, rod/cal Z0<t>3 Mach No. eg. location from base, calibers . various Mach Na ^slug-ft1-----------ly.dug-ft’^________ _ kaCal -----------------kt««> ------------ Transorac Subsonic Peak Supersonic Comments M 1.17 9.4*0.5 2.7*0.03 >0.025 3>M others from base 4, ' А4П
АМСР 706-242 ЛРРПГЭ1Х VIII—F 5-CALIBER A-И SPIHMER ROCKET AUTHOSCS) с. H. Murphy and L. E. Schmidt Muzzle REPORT BRL R 876 (Ref. 49) DATE 1953 TYPE OF TEST Free flight Intermediate c.g. location WMQht.lb Variable (Vblodlvfm Variable dft пятг V, rad/eol Mach Na Mach Na cq. location from bae<ediben 1,96 ^dug-ft1 I^dug-ft1 kacal °-340 bt,«d -1.19 Supcnonie Commenti M 1.3 1.8 2.5 COH 7.9*1.5 6.642.3 6.948.4 2.140.1 2.540.1 2.940.15 Cm. 3.954.05 3.804.05 3.354.05 -13.5*1.5 -12.540.5 -11.5 0.434.06 0.194.08 0.19 4 -.0134.001 -.011*.001 -.0104.001 f-»- DQDHOn 3.540.1 3.340.1 3.040.1 adban from bam CNp* -0.35 -0.30 -0.15 approximate 4" A-28
AMCP 706-242 APPBTIDIX Till—Q 7-CALIBER А-'Л SPINNER ROCKET AUTHOR^) L. E. Schmidt «ad С. H. Murphy REPORT BRL MR 775 (ReX. 53) date 1954 TYPE OF TEST Free flight Type 2 model: intermediate e.g. location Waioht.lb 0.33 Muzzb |VUf-dty,fpe X>rUble (Spin rata,rpe v*r^« d ft .0655 » 20mm 1/, rad/col °-63 (Pucher aabot) к cd °-364 к к cd 1.48 Traneonic O' Г Subcode Peak Si upanonic Ccmmotdi M 0.8 1.01 1.28 cm* 6.6*1.3 7.1*0.8 2.0*0.05 2.0*0.1 2.2 5.2*0.1 5.7*0.1 6.2 c +C -21*1 -19*1 -25 Me4** -0.40*.05 -0.35*0.1 +0.40 Chang* due mainly to change in magno* e.p. 4 -0.024*.0005 -0.021*.001 -0.019 e-p location 5.4*.05 5.35*.05 5.3 M t 1 QOBDW ТТОП1 ООЯ •e 6.0*C.l 5.6*0.1 5.0 •Moviag th* e.g. forward 0.8 caliber* makee thie ehape etable at Mach sumbere •«io -0.26 -0.20*0.13 0.78 greater thaa 0.9. vS’Ho’ -0.59 -0.46*0.31 0.95 1 0.17 0.18 0.20 UNSTABLE UNSTABLE* STABLE А-»
АМСР 706-242 APPKMDIX viu—X 7-CALIBER A-N SPIKIER ROCKET AUTHOR^) С. H. Murphy aad L. E. Schmidt Dimnaiom, caliber» REPORT BRL R 876 (Ref. 49) DATE 19S3 TYPE OF TEST Free flight Intermediate c.g. location Wight, lb .Variable Muzzl* jYalocitu fas Variable <ир<ппяяФ> т.н; - ~ V, rad/col - Mach No. eg. location from Ьом,cafibors 2.96 Mach No. kacol 0.M5 kf.cd M 1.3 1.8 2.5 Solid dural model СошпвиЫ cm 12.0*4.5 6.6*1.5 6.9*2.3 e|d*O 2.2*0.15 2.5*0.1 2.8*0.1 с. = с. IA ♦ ь C* Ln La|0 Cm. 6.2*.05 6.8*.O5 6.6*.05 M> 1.3 1.8 2.5 b « 45 26 110 -26*0.5 -31.5*1.0 -33*0.5 4 0.40*.08 -.019*.001 0.50*0.12 -.016*.001 0.70*.05 -.014*.001 «•* - 5.4*0.1 5.4*0.15 5.15*0.05 edbars from Ьом 4> -0.50 -0.50 -0.40 approximate A40 All teet round* were dynamically etable;
АМСР 706*242 лтяшх vin-к 9-CALIBER А-Л SPIBBER ROCKET AUTHOUfe) С. Н. Murphy aad L. Е. Schmidt REPORT BRL R 876 (R«f. 49) DATE 1953 TYPE OF TEST Intermediate Weight, lb (Velocity, fps (Spin rata, rpe d,ft V, rad/col Free flight c.g. location Variable Variable Variable" Mach No. ^,elu8-ft’---------------------------------- M 1.3 1.8 k col 2.5 °-34.7 k},cd 2-30 Homogeneous modele Commants c* Cu|ce 8.6*3.0 2.3 5.9*2.3 2.6 7.4*7.5 2.9 M* LS l.t 15 См«|а*О 8.5 9.5 10.0 b' <4% bo Th •Л -85 -I5O -142 -50*3 -72*4 -74*8 Л**0"* C.. **|*O 0.5 1.0 1.0 % c-p -.024*.001 7.05*.05 -.021*.001 7.1*.05 -.018*.002 7.1*o.l catbars from boss loocfiun •« •do Mo^ 1.14 0.98 1.40 0.84 1.35 *\ 0.88 J Based on aero yaw values Dynamically stable (at aero yaw) at all 3 Mach not. when a >1.2 ♦CL. ia also a function of yaw, increasing in magnitude. 8 A-a
ЛМ(Т 706-242 лррных vin-s 10-CAL1BER CORK CYUMDER AUTHOflts) E. D. Buyer REPORT BRL MR 1258 (Ял1. 57) Muzzle DATE WW TYPE OF TEST Free flight Forward c.g. configuratioa 0.535 Variable Variable" .0655 * 20mm 0.63 Pucher sabot DiiMmicn*, eoliben Mach No. C.Q. location from boe^oafiber» 3.752 Mach No. . 9.3xlO~” 2.8x10-* к cal °-ul Comment» Cnm-C.. 1.98 ▼ & iranmc Subsonic Peak Supereonic M 0.8 1.3 5.88 11.2 (estimated) 2.3*0.15 2.3*0.15 Г 7.85*0.2 9.15*0.2 '"Me C +C -42*5 .45*5 8 2 M s 0.8, b « C . -0.4*0.1 [ и . U, b* . *1*0 L M £ -.032*.0005 *.027*.0005 •e c.p 6.8*0.2 7.0*0.2 crfben from bate ОыЯОП •_ 3.6*0.1 3.0*0.05 0 *j -0.75*0.23 -0.13*0.15 calculated at sero yaw 250 340 -2.1*0.8 -0.30*0.34 —L- 8.33 д __ TR UNSTABLE UNSTABLE A-iK at yaws lees than 5* at email yawe
appixdix vni—т AMCP 706-242 105-MM BEAT PROJECTILE, T171 (MODIFIED) * AUTHOflts) M. J. Fiddington REPORT BRL MR 1215 (Ref. 41) DATE »»» TYPE OF TEST Free flight Weight lb 17.54 Muzzle |Wlocity,fps (Spin rate.rps Variable variaoie d,ft 0.344 1/, rad/col Six-finned, end-plated tail ср. location from Ьом^соБЬоп - 3,22 0,0072 Iy,A»p-fta 0,088 к col °-341 kbcol Transonic ° h Subsonic _____ Supersonic Cowwnenls 2.5*0.2 -28*7.5 No significant variation with Mach number 5 rounds 14 rounds colbm from bone Static instability (C^_> 0) is to bo expected at about M*« 2. Mo(2%) The else of the yaw for the rounds tested ranged from about 0.5* to 4*. •Modified by eliminating the wrench slots ia the forward section of tba i A48
AMCP 706-242 AFTUDXX УШ—о М*ММ MORT ЛЯ PROJECTILE, Т24 AUTHO«(s) Ж. D. Boyer REPORT BRL MR 1020 (Ref. 07) DATE 1956 TYPE OF TEST Free flight Afazzb Wright, lb IVriod^fpa (Spin rato,rpa d.ft y, radZooi 4.05 500 Vartable^leaa thaa 1 rpe) 0.197 5.3*1.0 2. 3*0.1 *2.1*0.05 -20 (approx.) 0^.45*13 CMf ' -» ‘ 5 edban from boa* B*ao4 a* 5 rooada with ao fia caat, aa* 7 rouada with the aft eectioaa af th* Haa «acted. No appareat effect of caat (op to 4*) oa drag, lift or pitchiag mcauat.
AMCP 706-242 AFFXXDU УШ-V IOS-ММ MORTAR PROJECTILE, T53 author(s) m. J. Pidctington REFORT BRL MR 1354 DATE 1961 TYPE OF TEST Free flight Weight, lb 23-35 Muzzle (VWocity,fp. • 925 (Spin fate, rpe variable . d,ft 0.344 V, rad/cal C 0,08 | 0.13 lo-lb eg. location from baeetcaSber» . 4.87 Mach No. .OU 0.253 kecal °-345 fct,cal Tramcnic Subionic Reofc Supenonic - Comment» M 0.82 7*2 C. -3.5 * 0.1 at »«ro «pin - 4.2V C.. » C -55 4 5 -1.4* 0.3 смижСм^|.-25х'*зв5*’ t-P fl в 0.08 -0.0454.001 » 0.16 -0.1654.005 ’<*o -3.70Й.57 1 For etability at nearly aero yaw, V ebould not exceed 0.11 (45 rpe at V в 900 fpe) -9.7542.8 -22.2*0.3 STABLE (Computed from coefficient* tabulated above) -6.0540.2 UNSTABLE (but STABLE at about 4^ в .094 rad A-85
AMCP 706-242 ШПО1Х Till—W 57-MM HEAT PROJECTILE, T188E18 Weight, lb Muzzle (Vblodty.fpt (Spin rote,rpe d.ft "V, rad/eol REPORT BRL MR 1112 (Ref. 35) DATE 1957 TYPE OF TEST Free flight 2.75 1200 6 * 1 0.187 Mach No. c.g. locoKon fccn boa^cofibera - 4,95 Tramonic Subeonk _____________ M 0.8 ~ 0.95 Led Led _ Cr Г Trcnaonk Comment» 1.06 0.54 Mil.07 2.80 0.8 3.6 0 1.2 3.1 о 0.3 €au -6.4*0.3 -8.501.5 -6.0O0.3 -7OO10 -6209 -7508 The Urge rarUtion U may be due to yaw aad to dual flow. locrti» -0.05O0.05 Computed from cur re; fin aaymmetry caa nullify ekia friction, cofem hem bow W4? •Cylindrical body undercut 0.22 inch to lacroaee yaw level (to about >•).
AMCP 706-242 AWJWB1X УШ—X M-MM HEAT PROJECTILE, TIM ДЦТНОЙЬ) В. G. K*rpcv REPORT bRL MR 4% (RM. 47) DATE 1953 TYPE OF TEST Free flight Subeonie Suoononie Couvnontt M ------------- oT? ---- -------------------- 1.2<M<1.8 Cu 2.7 3.0* 0.5 -A. 5 See curve C.p - c.g.. caliber* - -2.0 -1.1*0.4 baton *8 MR 1
4МСР 706-242 APPXFDIX VUJ-T 90-MM HEAT PROJECTILE, TIM AL*THO₽fr0L- J- lbd *• H‘ Krl*8er: R. Pisiali and L. C. MacAUiater Lfint Muzzle nrn_-T BRL MR 763 (Ref. 93)1 RErORT BRL MR 1076 (RM. 41) DATE 1956; 1957 TYPE OF TEST Wind tuaael; Free Right d, It (w-t modal) 0.118 Dimenuons, caliber» Mach Na 7.13 (w-t) с.®, lasaticn fccm Ьом^соМж* 6,г* M 1.72 I.72 2.45 Body aloM Body + tail Cu^*C*<\1*3 2.8 +5.6 -3.2 Wiad tunnel 3.0 41.5 + 75(Л) -75 (approx.) -8.3 (approx.) Fran flight V * roll rata la rad/cal Рт-'/actile becomes dywamlcrlly uaatabla above 16' .*pe (» - 0.11). Raductica of boom leaf th by 1.5 calibers cut ia holf (when ueiag shrouded tail), c.pre.g. eeparatioa was also halved. This relatioa Mould hold for the six-fia uaahroaded tail aa well. Л-88
APPixDix vin^z AMCP 706-242 10-CALIBER ARROW PROJECTILE AUTHOR(s) L. C. MacABieter REPORT BRL R 934 (Ref. 89) DATE 1955 TYPE OF TEST Free flight Variable Variable ” IA .066 Cruciform tail kacd _Oifi-----k^cri ____ M Tmcnic Supersonic «sSSSSS^L 1.1 1.8 2.4 C«H 12*1 9*1 Cu 21*3 12*1 8.5*0.5 Cm. -42*0.5 -21*0.5 -12*0.5 -220*50 -290*50 -270*50 S t-A baton ъ 2.1 2.1 2.6 CGHDwl ПСП® DCBO Ч" A-39
АМСР 706-242 лтятх ix TRAJECTORY PROGRAM IM FORTRAM LANGUAGE C L_____ 1 FORMAT 6 FORMAT , BBSS’ W*'9-2’- eH“&2.ms 6 format п.г.гб.о.гв.о.гт.т.гб.з.гб.г.п.з.гб.г) 9 FORMAT F6.3,F6.3.F8.3,F6.3,F6.3,F8.Aj 10 FORMAT i F8.6-F7.1) “ FORMAT (2Я ) READ 1 READ 6,D,ZT,WT0,WTB.SPIS,S8T,QE.V0 READ 6, FFD,FFM,CD02,TWIST,CLP,PINT,RCA,RCT,DTE,DTL,DTK,20,TEMP DO 11 1-1,9 READ 9. COO(I,1),CDO(1,2),X,CMA(I,1),CHA(I,2) PRINT 1 PRINT 7 READ 1 --------a, PRINT 1 .----------------- PRINT 9,FF0,FFM,X,RtiA,RGT,D PAUSE IF (SENSE SWITCH 1) 21,22 ACCEPT 6, QE. SBT IF (SENSE SWITCH 2) 23,26 : ACCEPT 6, FFD, VO,DTL,DTM i READ 1 ---------1 PRINT 1 ~---------------------- PRINT 6,WT0,V0,SPIS,SBT,DTM,1WIST,QE READ -----------v PRINT 1 -------JL----------t>---- PRINT 6,WTB,ZO,TEMP,DTL,DTE,CQ2,CLP PRINT 7 THST - 0.0 IF (WTO-WTB)29.29,96 96 THST-(WT0-WTB)*SPIS/S8T DMASS-THST/f32.17*SPIS) 29 TEMPR - 5l8./(A59.*TEMP) VAO • 1116./(TEMPR**O.5) RHOOS - .OO1189*TEMPR PRINT 10, RH005, VAO PRINT 7 PAUSE IF (SENSE SWITCH 6) 20,97 97 READ 1 PRINT 1 READ 1 PRINT 1 PRINT 7 PI МП TIME > 0.0 X - 0.0 DIST > 0.0 7 100 11 20 21 22 23 26 0.0 Di»t V CO сил OR мам A-40
АРРВЮ1Х IX (CMt*4) АМСР 706-242 тнт z - - QE ZO ZF - ZO S « .7854*O**2 PMASS - WTO/32.17 THETA - .01745329*QE V » VO IF (TWIST)30,31,30 30 SGC - RGA**4/(4.O*RHOO5*S*O*RGT**2) GNU - 6.2832/TWIST . YRC - 32.17*RGA**2/(RHOO5*S) C EH) OF INITIALIZATION 31 32 IF (Z-30000.) 32,33,33 RHO - EXPF(-3.2£-O5*Z) GO TO 34 RHO - .3828WXPF(-4.6E-O5*(Z-3OOOO.)) „ IF (Z-365OO.) 35,36,36 35 VM . V/(VAO-(VA0-970.)*Z/36500.) GO i'O 37 36 VM - V/970. 37 IF (COO(9,1)-VM) 38,38,39 38 CO - CD0(9,2) GO TO 43 IF (OIFF) 41.41,42 41 CO - C00(I,2)*0IFF*(C00(I,2)-C00(1-1,2))/(C00(I,1)-CDO(I-1,1)) GO TO 43 42 l« 1+1 43 44 45 46 47 48 49 50 GO TO 40 CD - FFD*CD IF (WIST)44,95,44 IF (CMA(9,1)-VM) 45,45,46 CM - CMA(9,2) GO TO 50 51 52 53 95 I «2 OIFF - VM-CMA(I.I) IF (OIFF) 48,48,49 CH - CMA(I ,2)-*OI FF*(CMA( I,2)-CMA(l-1,2))/(CMA(l,!)-CMA( 1-1,1)) GO TO 50 l»l+1 GO TO 47 CM FFH*CM SG - SGC*(GNU**2)*PMASS/(RH0*CM) IF (SG-1.0) 51,51,53 PRINT 52, SG FORMAT (FI0.3.10H UNSTABLE) YR -(YRC*PMASS*GNU/(RHO*CM*V**2)) * CO - CO + CD02*YR**2 GACC • -32.17*SINF(THETA) DRAG - RH0O5*RKO*(V**2)*S*CD ACC - GACC ♦ (THST-ORAG)/PMASS CO5F (THETA) A-41
AMCP 706-242 APPRKDIX IX (CMf *) 59 60 55 56 70 57 58 61 63 62 % DT - DTL/(ACC*ACC)**OTE IF (DT-OTM) 60,60,59 DT « DTM IF (SENSE SWITCH 1) 57,55 PI NTT - PI NTT-1.0 IF (PINTT) 57.57.56 IF (THT*THETA) 70,70,58 ZF - ZT PRINT 6,TIME,X,DIST,V,CD,CM,RH0,PMASS PRINT 6, THETA,Z.THST,DRAG,YR,VM,GNU,SG.DT PINTT - PINT IF (SENSE SWITCH 2)54,58 54 ACCEPT b,DTL,DTM IF (TIMF-S8T) 62,61,61 IF (THST)64,64,6i TMST - 0.0 PMASS - WTB/32.17 GO TO 57 IF (TIME40T-SBT) 69,68,68 OT - DTM/6.0 PMASS- PMASS-OMASS«OT DRAG - DRAG*(1.0s2.0*ACC<DT/V) ACCT - GACC ♦ (THST-ORAG)/PMASS VBAR - V ♦ (ACC*ACCT)«0T/4.0 OS - VBAR«OT 2.0*VBAR - V - DIST ♦ DS - TIME ♦ DT - THETA - THETA - 16.O9*COSF(THETA)«OT/VBAR ♦ DS*COSF(THBAR) ♦ 0S*SINF(THBAR) - THETA - 32.17*COSF(THBAR)-*OT/VBAR GNU*(1.0 4((DRAG*CLP/(PMASS*CD*RGA**2))-ACCT)*0T/V) DIST > TIME > THT - THBAR X « X Z - Z THETA GNU ” VEST FOR END OF TRAJECTORY x IF (Z-ZF) 67.67,31 67 OS - (ZT-Z)/SINF(THETA) TIME - TIME ♦ DS/V X -(X 4 0S*C0SF(THETA))/3.28l THETA - THETA/.01765329 REAO 1 PRINT 1 PRINT 6, TIME, X, V, THETA, GNU, SG PAUSE IF (SENSE SWITCH 6) 20,100 END SW 1 ONFOR SYMBOL TABLE FED Ratio of drag coefficient curve to typical curve in eeeory FFM Ratio of static aoeent coefficient curve te typical curve in TYPE Identification of typical drag and none nr. curves in епакту RGA Axial radius of gyration, calibers RGT Transverse radius of gyration, calibers D Maxinun body diaeeter, ft A-42
АМСР 706-242 АРПЖО1Х IX (cMt'4) WTO Projectile «Might at launch, lb VO Projectile velocity at launch, fps SPfS Specific impulse of rocket fuel, вес SBT Rocket motor burning time, sec TWIST Twist of rifling, calibers per turn ПЕ Quadrant elevation, deg WTB Projectile weight at rocket burr^t, lb ZO Elevation of launcher, ft ZT Elevation of target, ft TEMP Air temperature at launcher, 9F COO 2 Yaw-drag coefficient, per rad2 CLP Roll damping moment coefficient DTL Numerator of expression used to compute time intervals DTE Exponent in expression used to compute time intervals DTH Maximum length of time interval permitted PINT Number of time intervals between automatic print-outs CDO(1,1) Element of mach no. column in drag coefficient table COOK 1,2) Element nf drag coeff. column in drag coefficient table CMA(l,1) Element of mach no. column in moment coefficient table CMA(l,2) Element of static moment coeff. column in moment coeff. table THST Rocket thrust, lb ®HASS Rate of change of projectile mass, slugs/sec TEMPR Ratio of std. absolute temp.to absolute temp.of air at launcher VAO Sea level (Z»0) vel. of sound in air at temp.of air at launcher RH005 one-half air density at sea level at air temp.at launch, slugs/ft^ X Horizontal distance from launcher in range direction, ft DIST Arc distance along trajectory, from launcher, ft THT Variable carrying sign of traj.angle at beginning of time interval S Frontal area of projectile, ft 2 PMASS Projectile mess, slugs THBAR Trajectory angle at middle of time interval, radians THETA Trajectory angle at end of time interval, radians V Projectile velocity, fps SGC Constant in computation of gyroscopic stability factor GNU Spin of projectile, rad/cal . _ YRC Constant in computation of yaw of repose, ft2/ slug . sec2 Z Altitude of projectile, measured from sea level, ft RHO Ratio of air density at altitude to density at sea level VM Mach number CD Drag coefficient DIFF Mach no.diffarence from tabular value, for interpolation in table CH Static moment coefficient, per radian SG Gyroscopic stability factor YR Yaw of repose, radians FINTT Counter for automatic print-out TIME Elapsed time since launch, sac . GACC Projectile acceleration along trajectory, due to gravity, ft/sec2 DRAG Drag, lb ACC Proj.acceleration along traj.at beginning of time interval, ft/sec2 ACCT Proj.acceleration along traj.at end of interval, ft/secz DT Length of time interval, sec VBAR Average velocity over time interval, fps DS Arc distance traveled during time interval, ft A-43
АМСР 706-242 REFERENCES General 1. R. fl. Fowler, E. G. Gallop, C. N. H. Lock and 11. W. Richmond, ‘.‘The Aerodynamic* of a Spinning Shell,” Phil. Trana. Roy. Soc. (Lon- don) (A), 221, 295-387 (1920). 2. H. P. Gay, Note» on the Weight» of Cunt, Morten, BecoUlett Weapon» and Their Am- munition, ERL Memorandum Report 1360, Aberdeen Proving Ground, M<1, 1961. 3. H. P. Gay and A. 8. Elder, The Lateral Motion of a Tank Gan and It» Sftd on the Accuracy of Fire, BBL Report 1070, Aberdeen Proving Ground, Mil, 1959. 4. J. L. Kelley and E. J. McShane, On the Motion of a Projectile With Small or Chang- ing Yaw, BBL Report 446, Aberdeen Proving Ground, Md., .1944. 5. B. H. Kent and E. J. McShane, An Blementary Treatment ef the Motion of a Spinning Pro- jectile About It» Center of Gravity, BBL Re- port 459, Aberdeen Proving Ground, Md., 1944. 6. C. G. Maple and J., к Synge, “Aerodynamic Symmetry of Projectiles," Quart. App. Meeh., Vol. VI, No. 4 (1949). 7. E. J. MeShane, J. L. Kelley and F. Beno, Ex- terior BaUittica, Univerrity of Denver Preet, Denver, CoJon 1953. 8. J. von Neumann and O. Morgenatern, Theory of Gem re and Xeonomie Behavior, Princeton University Prine Princeton, N. 1953. 9. J. D. Nieolaidea and L. C. MaeAUiater, “A Re- view of Aerobelliatic Bange Reeeareh on Winged and/or Finned Mimilee,” 3rd Havy Bympoeium on AerobaUiitiu, Applied Phyaics Laboratory, Silver Spring, MiL, NAVOBD Bo- port 5338, 1954. 10. Ordnance Technical Terminology. June 1962. Special Tert ST 9-152, UJ. Army Ordnance School, Aberdeen Proving Ground, Md. Alao available from CJearingbouee for Federal Sci- entific and Technical Information, Springfield, Va. aa PB 181465. 11. R. W. Pohl, Phytical Principle» of Mechanic» and Acoustics. Translated by W. M. Doana, Blaekie A Son-Ltd, London, 1932. 12. a. С. H. Murphy, The free Flight Motion of Symmetric MittHu, BBL Report 1216, Aber- deen Proving Ground, M«L, 1968. b. R. H. Kreiger, Addrett Delivered Before the Commute» on FimStabUiaed Ammunition at Picatmny Anenal on 15 September 1954, BBL Technical Note 962, Aberdeen Proving Ground, McL,1954. Estimatien and Measurement of Aerodynamic Co- cAcisnts 13. E. Bluestone, Flexible Hoetl» Tunnel Ho. 3, Model Detign Criteria and Tunnel Operating Condition» (BBL Supertoaie Wind Tunnel), BBL Memorandum Report 711, Aberdeen Prov- ing Ground, McL, 1958. 14. W. E. Buford and 8. Shatnuoff, The Xfeete of fineneu Batio and Mach number on the Normal Pore» and Center of Preuvn of Conical and Ogival Head Bodin, BBL Memo- random Report 760, Aberdeen Proving Ground, Mil, 1954. IS. W. H. Dorrance, “Non-oteady Superaonie Flow *-1
AMCP 706-242 REFERENCES (cant’d) About Pointed Bodies of Revolution,” J. Aeronaut. Sei. 18, 505 (1951). 16. H. R. Kelley, The Esiimation of Normal Farce end Pitching Moment Coefficients for Blunt Bate Bodies of Revolution at Large Angles of Attach, Naval Ordnance Test Station Technical Memorandum 998, China Lake, California, 1953. 17. J. C. McMullen, Wind Tunnel Testing Facili- ties at the Ballistic Research Laboratories, BRL Memorandum Report 1292, Aberdeen Proving Ground, Md., 1960. 18. С. II. Murphy, The Measurement of Nonlinear Forces end Moments by Means of Free Plight Tests, BRL Report 974, Aberdeen Proving Ground, Md., 1956. 19. W. K. Rogers, Jr., The Transonic Free Flight Bangs, BRL Report 1044, Aberdeen Proving Ground, Mil, 1958. 20. N. Simmoca, Bimplifnd Methods for Estimat- ing Static Stability of Air end Underwater Projectiles, AD.E. Project Note 21, Fort Hal- stead, 1952. See also: AD.E. Technical Report 3-54, 1954. 21. R. M. Wood, Quick Methods for Estimating the Static Aerodynamic Coefficients of Shell, BRL Memorandum Report 854, Aberdeen Proving Ground, Md., 1954. Drag 22. Л. C. Charters and R. II. Kent, The Relation Between The Skin Friction Drag and the Spin Reducing Torque, BRL Report 287, Aberdeen Proving Ground, M<L, 1942. 23. A. C. Charters and R. A. Turetsky, Determina- tion of Base Pressure from Pree-Flight Data, BRL Report 653, Aberdeen Proving Ground, Md., 1948. 24. E. R. Dickinson, Some Aerodynamic Effects of Bead Shape Variation at Mach Number 3.44, BRL Memorandum Report 838, Aberdeen Proving Ground, Md., 1954. 25. E. R. Dickinson, The Effect pf BoattaHimg on the Drag Coefficient of Cone-Cylinder Projec- tiles at Supersonic Velocities, BBL Memoron- dum Report 842, Aberdeen Proving Ground, Md., 1954 26. T. liailperin, Comparison of Boat-tail and Square Base: Part 1, BRL Memorandum Re- port 347, Aberdeen Proving Ground, Md., 1945. 27. S. F. Hoerner, Fluid-Dynamic Drag, Published by the author, 48 Busteed Dr., Midland Park, N.J., 1958. ' 28. L. C. MaeAlliater, The Drag of a % Scale Model of the 3000-lb. Bomb M118 from e Meeh R«m- ber of 0.7 to 1-2 as Obtained from Free Flight Firings, BRL Report 927, Aberdeen Proving ' Ground, Md., 1955. 29. С. T. Odom, A Drag Coefficient of HE Shell for the New Series of Field Artillery Weapons, BRL Memorandum Report 1013, Aberdeen Proving Ground, Md., 1956. 30. G. I. Taylor and J. W. Maeeoll, “The Air Pres- sure on a Cone Moving at High Speeds,” Proc. Roy. Soe. (London) 139, 278 (1933). 31. N. Tetervin, Approximate Analysis of Effect on Drag of Truncating the Conical Nose of a Body of Revolution in Supersonic Flow, NOL Technical Report 62-111, Naval Ordnance Lab- oratory, White Oak, Md, 1962. 32. R. N. Thomas, Some Comments on the Form of the Drag Coefficient at Supersonic Velocity, BRL Report 542, Aberdeen Proving Ground, Md., 1942. Dual Flo* 33. B. G. Karpov and M. J. Piddington, E/ect on Drag of Twa Stable Flow Ceuffguraiione Over the Nose Spike of the 90-mm T316 Projectile, BRL Technical Note 955, Aberdeen Proving Ground, M<L, 1954. 34. A. S. Platou, Body Nose Shapes for Obtaining High Static Stability, BRL Memorandum Re- port 592, Aberdeen Proving Ground, McL, 1952. 35. a. С. P. Babin, The Aerodynamic Properties of • Spike-Nosed Shell at Transonic Velocities, BRL Memorandum Report 1112, Aberdeen Proving Ground, MdL, 1957. h. R. H. Krisger, paper pnasntsd at the Fin- R-2
▲МСР 706-242 REFERENCES (coat'd) Nlabilistil Ammunition Nyru|xauitm, Picatinny Arxcnaf, 19-20 October 1955. Magnus Farce aat Manat 36. E R. Benton, "Supersonic Magnus Effects on a Finned Missile,’’ Al A A Journal, January 1964. 37. E. D. Boyer, Free Flight Range Tests of a 10- eeliber Cone Cylinder, BRL Memorandum Re- port 1258, Aberdeen Proving Ground, Md., 1960. 38. W. E. Buford, Magnne Efectc tn the Сале of Rotating Cylinder» and Shell, ERL Memoran- dum Report 821, Aberdeen Proving Ground, Md., 1954. 39. 11. R. Kelley, An Analytical Method for Pre- dieting the Magnue Poreea and Momenta on Spinning Projeetilea, Naval Ordnance Test Sta- tion Technical Memorandum 1634, China Lake, California, 1954. 40. J. (3. Martin, On Magmu Efectc Canoed hy the Boundary Layer Dicpleeemeni Thiekneaa on Bodice of Revolution at Small Angela of At- tack, BRL Report 870 (Reviaed), Aberdeen Proving Ground, Md., 1955. 41. R. Piziali and L. C. MaeAUister, Efect of Magnue Torque oa ths Erne Damping of the 90-mm T108E45 Shell, BRL Memorandum Re- port 1076, Aberdeen Proving Ground, Md., 1957. 42. A. 8. Platou and J. Sternberg, The Magnue . Characterictiee of a 30-mm Aircraft Ballet, BRL Report 994, Aberdeen Proving Ground, Md, 1956. 43. A. S. Platon, The Magnne Poree on a Short Body at Bupenonie Speedo, BRL Report 1062, Aberdeen Proving Ground, Md, 1969. 44. A. 8. Platon, The Magnne Poree on t Rotating Cylinder in Trmmonie Croce Plain, BRL Re- port 1150, Aberdeen Proving Ground, Md., 1961. 45. A. 8. Platon, The Magmu Poree on a Piemed Body, BRL Report 1193, Aberdeen Proving Ground, Md, 1968. Dynamic Stability 46. R. E. Bols and J. D. Nicolaides, A Method of Determining Some Aerodynamic CoefftTiente from Supenonic Pree Plight Tecta of a Roll- ing Miacile, BRL Report 711, Aberdeen Prov- ing Ground, Mil, 1949. 47. a. B. G. Karpov, Aerodynamic and Flight Char- acterictics of the 90-mm FmStabiliecd Shell, HEAT, T108, BRL Memorandum Report 696, Aberdeen Proving Gronnd, Md, 1953. b. B. G. Karpov, S. Krial and B. Hull, Aero- dynamic Characteriatiea of the 175-mm ТЯ03 Shell aid the 175-mm Sqnare-Bate Shell With Puce M51A5, BRL Memorandum Report 956, Aberdeen Proving Ground, Md., 1955. 48. С. H. Murphy, On Stability Criteria of the Kel- ley-McShane Linearieed Theory of Taming Mo- tion, BRL Report 853, Aberdeen Proving Ground, Md, 1953. 49. С. H. Murphy and L. E. Schmidt, The Efeet of Length on the Aerodynamic Cheracterwttes of Bodice ef Revolution in Superconic Flight, BRL Report 876, Aberdeen Proving Ground, Md., 1953. 50. J. D. Nicolaides and T. F. Gridin, On a Fluid Mcehamcm for Boll Lockin end Bolling Speed- up Due to Angle of Attack of Cruciform Con- figurations, Navy BuOrd Technical Note 16, Washington, D.C., 1955. 51. J. A. M. Schmidt, A Study of the Recounting Taming Motion of Asymmetrical Missiles By Meanc ef Analog Computer Simulation, BRL Report 922, Aberdeen Proving Ground, Md., 1954. 52. L. E Schmidt, The Dynamic Properties of Pure Canas and Cano Cylinders, BRL Memoran- dum Report 759, Aberdeen Proving Gronnd, Md, 1954. 53. L. E Schmidt and С. H. Murphy, The Aero- dynamic Properties of the 7-oeEber Army- Navy Spinner Socket ш Transonic Plight, BRL Messorandum Report 775, Aberdeen Proving Ground, Md, 1954. 54. W. E Soott, The Efeet ef a Rotating Band Upon Some Aerodynamic Caeflmenta ef Che 7 ealiber Army-Navy Spiamor Rocket at Mach
AMCP 706-242 REFERENCES (coat’d) /.8, BRL Memorandum Report 1302, Aber- deen Proving Ground, Md., 1960. 55. R. A. Turetsky, Dynamic Stability of Spinner Roeket Models Fired in the Free Flight Aero- dynamic Range, BRL Memorandum Report 526, Aberdeen Proving Ground, Md., 1950. Aerodynamic Jump 56. J. G. Darpas, Transverse Forces on Projectiles IVhich Rotate in the Barrel, translated by H. P. Hitchcock, BRL Memorandum Report 1208, Aberdeen Proving Ground, Md., 1959. 57. С. H. Murphey, Comments on Projectile Jamp, BRL Memorandum Report 1071, Aberdeen Proving Ground, Md., 1957. 58. С. H. Murphey and J. W. Bradley, Jump Due to Aerodynamic Arymmetry of a Missile With Varying Roll Rate, BRL Report 1077, Aber- deen Proving Ground, Md., 1959. 59. \V. E. Simon, Investigation of the Causes of High Dispersion of the Production 90-mm Fin- Stabilised Snell, ИВАТ, T108E40, BRL Mem- orandum Report 967, Aberdeen Proving Ground, Md., 1956. 60. S. J. Zaroodny, On Jump Due to Musslc Dis- turbances, BRL Report 703, Aberdeen Proving Ground, Md., 1949. Arrow Projectile 61. W. II. Allan, "Sabots Used at the Thompson Aeroballiatiea Laboratory,'’ Proceedings of the Aerodynamic Bangs Symposium, January 1957, BRL Report 1005, Part I, Aberdeen Proving Ground, Md., 1957. 62. L. C. MacAllister, Drag Properties and Gun Launching Long Arrow Projectiles, BRL Mem- orandum Report 600, Aberdeen Proving Ground, Md., 1952. 63. L. C. MacAllister and R. J. Roaehke, The Drag Properties of Several Winged and Filmed Cone-Cylinder Models, BRL Memorandum Re- port 849, Aberdeen Proving Ground, Md., 1954. 64. S. T. Marks, L. C. MaeAllister, J. W. Gehring, H D. Vitagiiaao and В. T. Bentley, PeaaAOity Test of an Upper Atmosphere Gun Probe Sys- tem, BRL Memo, idum Report 1368, Aber- deen Proving Ground, Md., 1961. <»'»_ G. Taylor, Sabot-Launching Systems for Ex- penmental Penetrators, BRL Memorandum Re- port 1505, Aberdeen Proving Ground, Md, 1963. Rocket-Assisted Projeetilea 66. L. Davis, J. W. Follin and L. Blitser, The Exterior Ballistics of Rockets, D. Van Noe- trand N. Y, 1958. 67. С. H. Murphey, Advances in the Dynamic Analysis of Range Data, BRL Memorandum Report 1270, Aberdeen Proving Ground, Md, 1960. 68. S. J. Zaroodny, Ok the Scaling of Rockets, BRL Memorandum Report 1421, Aberdeen Proving Ground, Md., 1962. 69. R. C. Bulloek and W. J. Harrington, Summary Report on Study of the Gun-Boosted Rocket System, PSR-9/8, North Carolina State Col- lege, Raleigh, N. C, 1962. 70. S. J. Zaroodny, Accuracy of Ungmdad Finned Rockets, BRL Report 1232, Aberdeen Proving Ground, Mil, 1964. Liq aid-Filled Projeetilea 71. B. G. Karpov, Experimental Observations of the Dynamic Behavior of Liquid-FUlod Shell, BRL Report 1171, Aberdeen Proving Ground, Md, 1962. 72. B. G. Karpov, Dynamics of Liquid-FUhd Shell, Aids for Designers: e) Milner’s Graph, b) Stewarison’s Tobies, BRL Memorandum Re- port 1477, Aberdeen Proving Ground, Md, 1963. 73. K. Stewartaon, "On the Stability of a Spin- ning Tep Containing Liquid," «. Fluid Maeh. 5, Part 4 (1959). Prototype Testing 74. E. R. Dwftinaon, Physical Measurements of Projectiles, BRL Technical Note 374, Aber- deen Proving Ground, Md, 1954.
АМСР 706-242 REFERENCES (coned) 75. АМСР 706-110, Engineering Design Hand- book, Experimental Statistics, Section 1, Basic Concept» end Analysis of Measurement Data. Iе AMCP 706-112, Engineering Design Hand- . book, experimental Statistic», Section 3, Plan- ning end Analgtis of Comparative Experi- ment». 77. Tut and Evaluation Command Materiel Test Procedures, TECP 700-700, Aberdeen Proving Ground, Md. Aerodynamic Data-Spinners 78. E. D. Boyer, Aerodynamic Characteristics of 20-mm Shell, HEI, T2S2E1, BRL Memorandum Report 813, Aberdeen Proving Ground, Md., 195-.: 79. E. D. Boyer, Aerodynamic Properties of the 90-mm HE M71 Shell, BRL Memorandum Report 1475, Aberdeen Proving Ground, Md., 1963. 80. E. R. Dickinson, The Effects of Annular Rings end Grooves, and of Body Undercuts on the Aerodynamic Properties of a Cone-Cylinder Projectile at M = 1.72, BRL Memorandum Report 1284, Aberdeen Proving Ground, Md., 1960. 81. H. P. Hitchcock, Aerodynamic Data for Spin- ning Projectiles, BRL Report 620 (1947), with Errata Sheet (1952), Aberdeen Proving Ground, Md. 82. II. K. Kelly, The Subsonic Aerodynamic Char- acteristic» of Several Spin-Stabilised Rochet Models, I. Static Coefficients. Naval Ordnance Test Station Technical Memorandum 375. China Lake, California, 1953. II. Magnut Coefficients, Naval Ordnance Test Station Tech- nical Memorandum 376, China Lake, Califor- nia, 1953. 83. L. C. MaeAUiater, The Aerodynamic Proper- ties and Related Dispersion Characterittiu of a Hemiepherieal-Bue Shell, 90-mm, HE, T91, With and Without Tracer Element, BRL Mem- orandum Report 990, Aberdeen Proving Ground, MxL, 1958. 84. L. (.*. MaeAUiater, Comments on the Effect of Punched and Plain Fuse Covers on Йо Aero- dynamic Properties of the 90-mm T91E1 Shell at M = Id, BRL Technic d Note 1119, Aber- deen Proving Ground, Kd., 1957. 85. E. T. Roeeker, The Aerodynamic Properties of the 105-mm HE Shell, Ml, in Subsonic and Transonic Plight, BRL Memorandum Report 929, Aberdeen Proving Ground, Md., 1955. 86. L. E- Schmidt and С. H. Murphey, Effect ef Spin on Aerodynamic Propertiu of Bodies of Revolution, BRL Memorandum Report 715, Aberdeen Proving Ground, Md., 1953. Aerodynamic Data-Finners 87. E. D. Boyer, Aerodynamic Propertiu of 60- mm Mortar Shell, T24, BRL Memorandum Report 1020, Aberdeen Proving Ground, Md., 1956. 88. R. H. Krieger and J. M. Hughes, Wind Tunnel Tuts on the Budd Company T153, 120-mm HEAT Spike Nose, folding Pin Projectile, BRL Memorandum Report 738, Aberdeen Proving Ground, Md., 1953. 89. L. C. MaeAUiater, The Aerodynamic Propertiu of a Simple Non-Rolling Pinned Cone-Cylinder Configuration Between Mach Humbert 1.0 and 2A, BRL Report 934, Aberdeen Proving Ground, Md., 1955. 90. L. C. MaeAUiater and В. T. Roeeb*«, ^ero- dynamic Properties, Spies, and Launching Char- acterittiu of 105-mm Mortar Shell T53E1 With Two Types of Piss», BRL Memorandum Report 618, Aberdeen Proving Ground, Md4 1952. 91. M. J. Piddington, Some Aerodynamic Proper- tiu of a Typical Pin-8tabilis»d Ordnance Shell, BRL Memorandum Report 1215, Aberdeen Proving Ground, Md., 1959. 92. A. 8. Platou, The Effect of High Stability Notu on Finned Configurations, BRL Tech- nical Note 707, Aberdeen Proving Ground, Md., 1952. 93. L. J. Rose end R. H. Krieger, Wind Tunnel Tests of the TlOd, 90-mm HEAT Projectile at Mach Number 1.72, BRL Memorandum Report 763, Aberdeen Proving Ground, Md., 1954.
АМСР 706.242 REFERENCES (cont’d) Projectile Geometry !M. Tublri for thr Drniiii of Uunln, Klaff, <Ioiu- pntation Ijaboratory, Harvard University. Cambridge, Майн., 194#. 9Я. Mc.ehanical Integration for Solid* of Revolu- tion, Development Engineering Division, Ar- tillery Ammunition Department. Frankford Araenal, Philadelphia, Pa. 96. АМСГ 706-^47, Engineering Design Hand- book, Ammunition Series, Section 4, Design for Projection. !(?. AM(‘1‘ 706-140, Engineering Denign Hand- book, liallixlies Sa*ri<*H, Trojeetorie», Differen- tial Кficr.lt, and Dote for I‘rojeetilc4. llx. JMy b. Politser, “Shell” A Computer Program for Determining the Phytieal Propertiu of Artillery SMI end Related Исаи, Technical Memorandum lieport No. ORDBB-DR1-14 (SAAS No. 36). Pieatinny Arsenal, Dover, N.J.. 1962.
АМСР 706-242 BIBLIOGRAPHY General 1. H. J. Coon, Evaluation of Shell, HE, 81-mm, M362, Modified, BRL Technical Note 1288, Aberdeen Proving Ground, Md, 1959. (Con* fidential) 2. E. R. Dickinson, Design of a Ductile Cast Iron Shell for the 155-mm Howiiser, BRL Technical Note 1196, Aberdeen Proving Ground, Md., 1958. (Confidential) X B. G. Karpov and J. W. Bradley, A Study of Causes ef Short Ranges of the Mach T317 Shell, BRL Report. 1049, Aberdeen Proving Ground, Md, 1958. (Secret-Restricted Data) 4. L. C. MacAlliater, Comparative Firings of 105- uun Shell T131E31 and 105-mm Shell Ml from Unmodified and Counterbored M2A1 Howitzer Tubes, BRL Technical Note 739, Aberdeen Proving Ground, Md, 1952. (Confidential) 5. L. C. MaeAllister, “Some Problems Associated with the Determination, from Range Firings, of Dynamic Stability of Ballistic Mismle Re- entry Shapes,” Proceedings of the Aerody- namic Range Symposium, January 1957, BRL Report 1005, Part II, Aberdeen Proving Ground, Md, 1957. (Confidential) A R. Sedney, Aerodynamic Healing of the Pro- jectile 20-mm, HEl, M56A1, Past M505, BRL Memorandum Report 1037, Aberdeen Proving Ground, Md, 1956. 7. R. Sedney, Aerodynamic Heating Problems in Shell Design, BRL Report 1043, Aberdeen Proving Ground, Md, 19M. Rodmatiea and Measurement of Aerodynamic Co* ofldenta 8. F. DeMeritto aad A. May, "A Comparison ef fiorodynamio Data from Wind Tunnell and Free Flight Ranges,' * 3rd Navy Symposium on Aeroballistics, Applied Physics Laboratory, Sil- ver Spring, Md, NAVORD Report 5338, Paper 22,1954. 9. G. E. Hanson, A Method for Estimating Pereas, Moments and Drag Due to lift Ailing on Blender Bodies and Piss-Stabilised Bodies at Supersonic Speeds (Includes IBM 1620 pro- gram.) Report No. R8-TR-63-2, UB. Army Missile Command, Redstone Arsenal, Ala, 1963. DDC No. AD 335484. (Confidential) 10. R. H. Krieger, Ths Aerodynamic Design of Pin-StabiHcsd Ammunition, BRL Memorandum Report 971, Aberdeen Proving Ground, Md, 1956. (Confidential) 11. A. S. Platou, Body Nose Shapes for Obtaining High Static Stability, BRL Memorandum Re- port 592, Aberdeen Proving Ground, Md, 1952. 12. W. E. Scott, Sems Aerodynamic Properties of a 105-mm Modal of the 155-mm T358 Shell BRL Memorandum Report 1369, Aberdeen Proving Ground, Md, 1961. IX a. R. H. Whyte and H. E. Hudgins, Bfoots of Nose Shape and Boattail Angle on Static Aero- dynamic Characteristics of a 105-mm Shall at Meeh 4Д 4Л and 59, Pieatinny Armnal Tech- nical Memor**^dum 1248, Dover, NJ. 1964. b. Elisabeth &. Dickinson, Some Aerodynamic Egsets of Varying the Body Length and Hoed Length of a Spinning Projectile, BRL Memo- randum Report 1664, Aberdeen Proving Ground, Md, 1966. Arrow FrojsctSm 14. R. C. Huystt, “Aerodynamic Characteristics of Fin-Boattail Combinations at M s= XOO,”
AMCP 706-242 BIBLIOGRAPHY (confd) 3rd Navy Symposium on Acroballutics, Ap- plied Phyxiot Laboratory, Silver Spring, Md., NAVORD Report 5338, Paper 14, 1954. (Con- fidential ) 15. F. G. King and R. U. Kent, Kill Probability of the 127/60 Gun for Two Drag Estimate!, and Comparison with the Loki Rocket, BBL Memorandum 721, Aberdeen Proving Ground, Md., 1954. (Confidential) 16. A. R. Krenkel and J. F. Mello, “High Angle of Attaek Aerodynamic Rolling Momenta and Stability Phenomena for Cruciform Wing- Body Combination», * * 3rd Navy Яутрммиа on Aeroballistics, Applied Physics Laboratory, Silver Spring, Md., NAVORD Report 5338, Paper 13, 1954. (Confidential) 17. M. J. Piddington, Retardation and Velocity Histories of an 8-grain Plechette, BRL Memo- randum Report 1140, Aberdeen Proving Ground, Md., 1958. (Confidential) 18. M. J. Piddington, The Drag Characteristics of а 10.2-grain Plechette (ХМ110), BRL Mem- orandum Report 1501, Aberdeen Proving Ground, Md., 1963. (Confidential) 19. M. A. Sylvester, Wind Tunnel Tests of Myper- •seloaty Cone Cylinder Finned Projectiles at Mach Rambert 4M, 4A3 and 4JB9, BRL Mem- orandum Report 1166, Aberdeen Proving Ground, Mo., 1968. Dug 20. R. R. Dickinson, Design Data for a Series of MR Projectile Shapes at Mach Number ЗЛ, BRL Memorandum Report 920, Aberdeen Prov- ing Ground, Md., 1956. 21. E. R. Dickinaou, The Efcctioencu of Base- Bleed m Reducing Drag of Boattailed Bodies at Supersonic Velocities, BRL Memorandum Report 1244, Aberdeen Proving Ground, Md., 1960. 22. G. D. Kahl, Supersonic Dreg and Base Pres- sure of e 70* Соы Cylinder, BRL Memoran- dum Report 1178, Aberdeen Proving Ground, McL, 1958. 28. M. J. Piddington, Berne Brief Comments on the Dreg aad Stability of the 37mm Spotting Pro- jectilr, BRL Technical Note 1416, Aberdeen Proving Ground, Md., 1961. (Confidential) 24. E. J. Roechke and M. J. Piddington, Drag end Dispersion of Banded Spheres With and With- out Strings, BRL Memorandum Report 995, Aberdeen Proving Ground, Md., 1956. 25. M. A. Sylvester and R. H. Krieger, Wtnd Tunnel Tests of the T340E11, 90-mm ME Pro- jectile With Varying Spike Nou and Spool- Type-Body Parameters, BRL Memorandum Report 1146, Aberdeen Proving Ground, Md., 1958. Dual Flow 26. E. D. Boyer, Drug and Stability Properties of the AVCO 52 Nou Cone Model, BRL Tech- nical Note 1145, Aberdeen Proving Ground, Md., 1957. (Confidential) 27. E. D. Boyer, Drag and Stability Propertiu of the AVCO 13 Nou Cone Model, BRL Tech- nical Note 1147, Aberdeen Proving Ground, Md., 1957. (Confidential) 28. H. H. Album, Spiked Blunt Bodies in Super- sonic Flow, Air Force (Mee ot Scientific Re- search Report 307, w—hington D. Cn 1961. Dynamic Stability 29. B. G. Karpov and 8. Krial, Aerodynamic Char- acteristics Of the UOmm ME, T194 Shell and Its Modifications, with Fuse M51AA, BRL Memorandum Report 1057, Aberdeen Proving Ground, Md., 1957. (Confidential) 30. L. C. MacAllister, Some Instability Problems With Re-entry Shapes, BRL Memorandum Report 1224, Aberdeen Proving Ground, McL, 1959. (Confidential) 31. M. J. Piddington, The Efieets of Spin and Magnus Torque on a Spike-Nose, Fin-Sta- bdiud, MEAT Projectile, 76mm T180B23, BRL Memorandum Report 1310, Aberdeen Proving Ground, Md., I960. (Confidential) FeWag Fin Characteristics 32. В H. Krieger, Wind Tunnel Tests of the T84 75mm HEAT Projectile, BRL Memorandum
BIBLIOGRAPHY (cost’d) 'Keport 518, Aberdeen Proving Ground, Md., ftSO. (Confidential) :B. K. JI. Krieger «nd J. M. Hughes, Wind Тамме! Tecta of the Chamberlain Corporation 7G-mm T310 EEAT Projectile, BBL Memorandum Beport 790, Aberdeen Proving Ground, Md, 1954. (Confidential) 34. R. H. Krieger, W*rd Tunnel Tecta of a 76-mm EEAT Projectile With Thin Folding Fine, BBL Memorandum Beport 8i6, Aberdeen Prov- ing Ground, Md, 1954. (Confidential) Liquid-Filled Projectflea 35. a. G. Sokol, Some Ecperimenta ВОД the Liquid-Filled, Impulawely Started, Spinning Cylinder, BBL Technical Note 1473, Aberdeen Proving Ground, Md, 1962. b. B- G. Karpov, Dynamize of a Liquid-Filled Shell: Inatabiliiy During Spin-up, BBL Mem- orandum Beport 1629, Aberdeen Proving Ground, Md., 1965. 36. H. M. Stoller, Apparatus for Study of Fluid Motion tn a Spinning Cylinder, BBL Tech- nical Note 1355, Aberdeen Proving Ground, Md, 1960. 37. В. H. Wedemeyer, The Unsteady Plate Within a Spinning Cylinder, BBL Beport 1225, Aber- deen Proving Ground, Md, 1963. Magnaa Force aad Moment 38. 8. Fagin, “Magnus Charaeteriatica of Typical Projectile Configurations (12.75-ineh A8 Roc- ket; Called ‘Weapon A* and 7-ealiber A-N Spinner Rocket),” 3rd Navy Sympoemm on AerobeUictier, Applied Physiee Laboratory, Spring, Md, NAVOBD Beport 5338, Paper 2. 1954. (Confidential) 39. H. R. Kelly and G. R. Thaeker, The Effect of High Spin on the Надпив Force on a Cylinder at Smail Angler of Attach, NAVOBD Beport 5036, 1956. 40. W. Lnehuck aad W. Sparta, Wind Tunnel Magnate Charaetendiee of the 7 oaUbti A-N Spinner Backet, NAVOBD Beport 3813, 1964. Beckot-Aaabtod Projeetilm 41. B. D. Boyer, Comparioon of Aerodynamic Charaeterielice of Live and Inert 70-mm T331 Gun-Booctcd Rockcta, BBL Memorandum Be- port 1086, Aberdeen Proving Ground, Md, 1957. 42. S. J. Harnet and S. Waaaarman, Second Statue Report, Reaearek and Development of Booeted Artillery Projectilee, Picatinny Arsenal Tech- nical Memorandum Beport 1183, Dover, NJ, 1963. DDC No. AD 339982. (Confidential) 43. F. H. McIntosh, The Theory and the Calcula- tion! of the Behavior of Self-Aligning Rockett, BRL Beport 1228, Aberdeen Proving Ground, Md., 1963. 44. G. J. Pietrangeli, I. Faro and W. Amoa, “Ram- jet Bngine Design Optimisation and the Com- parative Performance Evaluation of Super- sonic Diffusers for Long Range Triton Mis- sile, ” 3rd Navy Sympoaium on AerobaUietice, Applied Physics Laboratory, Silver Spring, Md, NAVOBD Beport 5338, Paper 7, 1954. 45. Deaign Studiea on a 105-mm GumBooated Pocket. Final Beport, A D. Little, Ine, Cam- bridge, Maas, prepared for Picatinny Arsenal, Dover, NJ, 25 January 1963. DDC No. AD 336539. (Confidential) 46. 5-ineh 38-ealiber Socket Buctainod Projectilu, The Budd Company,. Philadelphia, Pa, pre- pared for Bureau of Naval Weapons, Study Project RM-2061, November 1961. (Confi- dential) Spin ef Fin-Stabilized Projeetilm 47. B. D. Boyer, and M. R. Yeager, Aerodynamic Fropertiea of 30-mm, EE-T, T34O Shall, BRL Technical Note 1094, Aberdeen Proving Ground, MA, 1956. (Confidential) 48. J. W. Bradley, A Comparioon of Hectored Spin Hietoriea of 105-mm Mortar Shell T53E1 With Solutiona of Liaenrioed Roll Equation, BRL Memorandum Report 1074, Aberdeen Proving Ground, Md, 1967. 49. J. W. Bradley, A B4
АМСР 708-242 BIBLIOGRAPHY (crat'd) Ярй» Hiotoriot of 81-mm Mortar 8hM T28XS Wilk SoMioiu of Lmoaritod Boll Eqpatim, BBL Technical Note 1234, Aberdeen Proving Ground, Md., 1958. (Confidential) 50. B. G. Karpov and W. R. Sinton, Egectwoout of Booonl Simple Methode of Aorodpawme Control of Bpm of the 90^mm, MEAT, T108.H0 8heU, BRL Memorandum Report 879, Aber- deen Proving Ground, Md., 1955. 51. M. J. Piddingtoa, Borno Aerodynamic Prop- ertier of Two 90-mm Bpmod-Kata Shell, T300E53 aad T316E0, BBL Memorandum Re- port 1082, Aberdeen Proving Ground, MA, 1957. (Confidential) 52. A. 8. Platou, Beil Chaeueieriehee of Of-amt Pm Coafigmvtioa, BRL Memorandtns Report 938, Aberdeen Proving Ground, Md^ 1Э55. (Confidential)
ENGINEERING DESIGN HANDBOOK SERIES lilted below are Uh HeniPi—ti which haw be— published or are currently bring printed. HandbookI alt* p—licet!— dote* prior u I Aug—t 1*2 — p—Hiked и 20-carle* Ordnance Corp* pm—1*1'. NC Circular 310-M. It July 1443. redesignated the— publication* at Юк-teri— АИС panpklrtt (I.a.. OAOP W-IM wa* rod—Igreted АИС? 2M-I3B). All a—, reprinted. or reviled Haadbooki or» —lag pHIlihed и 2114-tarlat —C pan—let*. .Anu—/ «ап/ Via.u I tew-uwe Pubjorte Sb. Title UM Ele—at* of Aw—cut Engineering. Port 0—. Source* of Energy 107 Elaneet* of Ana—ent Eaginoerieg. Port Tuo, Mllittic* 100 Elonert* of Аиаа—nt Engineering. Port Thm*. Wup— Sy* ten* Md Co—on—t* И0 Eaperi—aul Statistic*. Section I. tosfc tea- cept* and f ly*1* of Maatur——t Dau III Eaperin—ul '.u iitlc*. Secti— 2. Analyli* of fm—rLti i aad Cl—ilficatory Dau III Eeporla—ul Sutiitlc*. Section 3, Planning and Mwlyii* of Con—rati— Experin—t* 113 Expert annul Sutiitlc*. Section ♦, Special Topic* II* Experin—ul sutiitlc*. Sect!— S. Такl*> III Packaging and Peek Cn*ine*r1ng IM Maintain—llity Sul de for te*I— 13S In—ntlon*. Pat—U. and Delated Matter* (A—11*4) 13* Sr—ech—I—a. Sect!— I. Thagry 137 oer—neckMl—*. Sect!— 2. Moetur——t and Signal ten—rten 13* Ser—neck—i*m. Section 3. J—pliflcatio* 134 Sor—neck—l—o. Section 4, Onur Elen— and Sy*un 0—iga 170(C) Amor and Iti Appltuti— te «chicle* (U) 270 Propel Imt Actuated Device* 230(C) Иаг—a—-General (U) 331 C—I mating Cl——t* (Fire Centre 1 Serie*', ——Ctiow —4 1—Coot—e Sweden IPS Solid pre—II—t*. Pert Ono 170(C) Solid Pro—II—ti. Part Ten (U) 177 Preportle* of Upl—(vol of in 11 Ury Inter—t. Section I 170(C) Prop*rtle* Of Expl—iv— of —11 Ury In—it. Sectl— 2 (U) IT* Ca*l—1— Train* 210 Fun*. Cenc—I and Mach—teal 211(C) tea—. Pr—laity. electrical. Part 0— (0) 212(5) Fea—. Pro» laity. electrical. Port Two (U) 213(5) Faw*. Pr—laity, electrical. Part The— (U) 214(5) Fu**. Proxtoity. electrical. Part Four (U) 213(C) Fun*. Pro* laity, electrical. Port Ft— (U) 242 0—1— for C— trel of Projectile Fit—t □Mrocuriitlcl 2*4 See lion I, Artillery Anu—Iti — —ml. with Takle of tent—. SI—aery and fer S*W*t 245(C) Section 2. 0—1— for Tomi—I Effect* (u) 24* Section 3, о—I— for tentrel of *M—t Characteristics lawk ef pHoaf 2*7 Section 4. 0—<— for Prayut tier. 2*1 Seet’co 5. ,Mpectl— A—ecu of Artillery Zba—Itlon o—iga 240 Section *. —factum of Meullic С—репам* of Artillery AnaaltIon iMs*!fntac<si The Au—<i— АеииРly Me —< о Saape—lan* MldaCdn an'—(te Serf— ZaeU/aadZ Ml. Title 2*3 Aerodynaericl 284(C) Trajectories (U) 2M Structure* BoIIcartee terUa 140 Trajectori—. Oiffer—tial Effect*, and 0*U for Projectl I— 150 Interior Balletic* of Gu— 130(5) El——u of Terniaal Belliltici, Part (be. Introductt—, Kilt Mock—io—. end Vulnerability 'U) I4I(S) Ela—fit* of Temi—I BalUltlcl, Part Two, Collect!— and A— ly*1* of 0ou Concerning Tar—t* (U) I32(S-AO) El a—nti of Tomi—I Balliitlct. Port Three, A—licatlon tn Midi Io and Spec* Tar—U (U) Пп п ине md — KarCwe 340 Carriag— a— Mo—t*- Co—I Ml Cradle* 3*2 Aecoil Sy*U— М3 T— Carriage* 3*4 Aotten Carriage* 45 Equilibrator* 34* Elevating —c—a1—* Ml Tro—r*lag HeckMi—* Cww Strict 250 Cun—Ceneml 252 Sun Tn—* —‘I*— ArroUi—r*m Sertee IM Part T—. Safety. Pre co du mi and Al—oary IB7 Part niroo. p—perti— of Material* Ikod io Pyrotechnic c—ilttvna IM Pert Fi—. Itkllofraphy 3to^bap-ae-4<r HitrlU Suit» Ml Part 0—. Syitan Integration 232 Part Too. heap— tentrel М3 Part Thro*, tea—ter* 234TS) Part Four, M1**1lo Amaeeot (U) 235(S) Port Fi—. Co—oaaum* (0) 2M Part Six, Structum* and Power Source* M7(S) Pert So—n. Sa—Io Pmblm (U) —rioto *onue* 143 Mber and A—Air like Material* 212 Baiket Material* (hornetalllet 431 Adh—1—* 332 let— to Selection of h—or 0-Din— ИЗ Mega— 1— and Mega—1— Allay* 444 Al—in— and At—in— Allay* И1 Tlteat— and Tlteni— All—* 3M C—r aad Capper Allay* BM laid* te Spar 1 fleet Ion* for Fl— Iklo tebker Product* ЛЮ Plattic* 721 Carr—I— aad terr— 1— Prokecti— of Natal* m «le- 201(5-*) Moip— S—teo Effect!—am* <V) Ж Pm— ill— —d Pro—II—to ant мага—— пап— о—ага. —о о • a—o— Omani