D4 PARTNIEU+L\RNI C opy No t'Prelimnargy Design and Analysis of a Ram.Jet Missile" Project M-679 GA Project Wizard Prepared by _ C. E. Vandenberg Approved by M. A. Mi9ls June 10, 1948

:Nl I \ l 1RsIV (N I. MWHItI(;.\N Ai TjBLIE OF COITE IT rlS Eage Introduc t i on........., * * 1 Sumary,......,........,..,............S...... 2 Discussion..,........,. 0 o. fo............. ~ 3 Third Stage Design *. 3 Second Stage D3sign.................... 3 First Stage Design 5 iei'hrst Sta.e * es*n*. *.*...............,.* 5. W'e i g ht s. ~ ~. ~. * * *. ~. ~. ~ ~ 5 Performunce cLulysis ~~*............... 6 Conclusions and Reconendations.............. 12 Referene s............,.....,....,.,........ 13 Appendix.... ~. 1 14 Derivation of Equations.....,........ 14 Boost 4iiz;e Calculations...........,... 18 Wieight breaakdown...................... * * 19 SampleCaiif ~ Calcuat tion.....,.. *... 22 Figures..................... ~ *O** *.. ** 23 L...... a.

[)IT:rT RmT.NrT O1 ENGJN;:,rfFM; RI.: \.R('ft VN\'V:RSITY OFU xt I;AN ii LLST OF ILLU iTRiTI01i4O Figure Title kage 1 Horizontal Distance, Vertical Didtance, and Velocity vs. Time.... 23 2 Initial Gross Wleight Vs.,laxiratm Accoeleration......*...**..*...... 24 3 Approxinate Skiri Temperature vs. Tir:e and ~ltitude................ 25 26 4 Ct and Cd vs. Filight Liach Number..... 5 &ltitude vs Lach rumber of Launching. 27 6 Initial deight vs Lae.h Number of Launching and Weight of Fuel (10 g).. 28 7 Sane as (6) except for 25 g.......... 29 8 Jsiaie as (6) except for 40 g.......... 30 9 Launching iLach I'Nunber ahd i.axi:um~ 31,hcceleration vs. Latunclingi Time. 10Q.g) 10 Jame as (9) except for 25 g.......... 32 11 Same as (9) except for 40 g.......... 33 12 Conplete Lissile Design............. 34 j i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

T T T. (TUC T r)~ T Thle prnosc of this report is to present a prelimins-y analysis E7^0~ ~islen of a missile which fulfills the reqlirements si ecifi-d Vy Project MXJ -794 as ortlioned in thPe Uniiver;sity of Alvichigan ec rt, IT Th,8 for the UMA -1 Uiissile, eand wlhich utltizPs ram-jet p;ropulsicul for thie major portion of its thrust. Final dimensional and v;eight d-ta C-.re to be compared for equal ei l condition of altitu-de, horizoxitIal distance and time, to model 7MA -1 liquid-rocket missile. Particulpr attention hEs been paid in this analysis to the structuar16 design from high temperature and high acceleraticnl standpoint, in order Lo insure that tne missile conforms closely to the structural requirements of an actual missile. Drag coefficients eave been revised apward to give decidedly maorF cztoz vative performance resmits thrn heretofore. Analyses of the variol-s components making up the missi le ar de scribo-d nd. eyl. i ia-a8- in detail. A section on the homing stage thV. —st requirements has also been included to show promise of further reducing the initial weight of the missile. Fowwver, to alntai.: a.. n,3 rly equal beses of com -ariso wl.it.-. model UkLk-1 missile, as possible, identical horming stage thirlst requirements are used. Graphs and farmulas are presented I.m thle 1appendim p with brief comments on their derivation.

I 'N!\'ART'RN'T" {Of I,IIKRI('. RlI..N IR H SUMMARY The missile presented in the report is a three stage missile utilizing a solid propellant stage for launching, a ram-jet stage to accelerate it to a high altitude and velocity, and a rocket stage for controlled flight outside the atmosphere to the target. Initial weight and overall length of the ram-jet missile are considerably lower than that of the liquid rocket missile for identical interception conditions, and are due primarily to the extremely high specific impulse of the ramjet. The possibility of further reducing the initial weight of the rarjet missile with consequent reduction of its physical dimensions appears quite favorable. It should be stated, however, that the performance results of the ram-iet are contingent upon the practical solution of combustion problems and upon the d esign of a practical, completely variable diffuser and tail nozzle. I

| NI' VRS,I'TV 01 M li(Cl N I Discussion The prelimnary analysis and design of the missile was begun with an attempt to determine quantitatively the following conditions in order to fix its structural requirements: (1) maxium axial and radial accelerations; (2) mnaximum internal and external temperatures; (3) maxlmum internal and external aerodynamic forces; and (4) stability requirements. Brief calculations of these conditions showed that axial acceleration and internal and external temperature, would be the most important design considerationr. Internal pressures were calculated to be approxim-) ately 300 psia maximum throughout the flight path. (See Fi.gure 1, Ref )' erence t4l-14)..... Third Stags Desip < a s 1,6 2 Since, from IlC-.46, third stage equipment was known, the problem remaining was to position each piece of equipment to hold a f.ixed c.g. position and to perform its job properly. Thrust requirements were based. upon the method used in IMC-46 (see page ). From these, fuel requirements giving tank and motor isizes were found, and the bulk of the third stasge miessile dmersions were known, permitting the ram jet stage to be deeigned. Second Sta*ge Desig -- Ram Jet The diffuser selected was of the Oswatitsch type, utilizing the ird stage mieessile for the central body. An of noseas selectd for the central bodry to protide optimum pressure recovery in the pubs~,portion of the diffuser. Dimensions of the diffuser were compromieed to give optimum preasure recovery throughout

1 | II"I.\Rf'MIF\NI' I1: I:N(;1I tII I,.(; Rf -:,II I \ I,"' a wide range cf Mach numbers, and were obtained from USCAL report R-4-7. " Stability of the normal shock is obtained by means of bleed holes located in the forward part of the diffuser hood, according to experiments by Evvard of NACA. Proper design of the bleed holes will minimize/the loss in mass flow through them, while still insuring stability, and almost isentropic pressure recovery. ontraction ratios for Mach numbers from 1.5 to 6.o were provided for as well as possible in the design by a maximum of fore and aft movement of the central bidy. Fuel is injected into the subsonic air stream forward of the flame holders by means of a tubular ring fitted with injection nozzles. The fuel is preheated in tanks surrounding the subsonic portion of the diffuser, and is pumped to the ring frcm a circumferential tank holding 1200 lbs of fuel, through four high volume, medium pressure fuel pumps. ("Ignition of the fuel is continuous and provided by a hot wire syster $. 'latticed across the flame holders at the forward part of the ccmbuetion chIamber. el^,;1 1 1 The combustion chamber is designed to wlthetand combustion texrlperatures up to 3500~ F, and incorporates a heavy skin plus a ceramic coating. Heavier guage skin is also provided for other parts of the missile subjected to high temperatures. ( Tail nozzle design was ccmplicated by the requirement that for ma|imum thrust coefficients for Mach numbers of flight less than approximately 3, the tail nozzle should be a straight tube. Above flight Mach ' numbers of 3, contraction ratios of combustion chamber area to throat ( area should be greater than 1. These requirements could not be designed

1 )'.f'-\R'I' l1t'-I ' (I ); K'R,'N'Ot N II N(G II:lG.\RA ' 11 - - -,. "I'lN qNI\I(RSI'IY (Wt- *II('!I(;.AN into the nozzle section, and a compromise was made. Control systems for the fore and aft movement of the after body and forward body are provided by means of hydraulically actuated pistons, actuated by an interconneted~ (draulic pressure source. Hydraullc pressure is maintained by high pressure hydraulic pumps. Regulation of the positions of the inner bodies is aeccmplished automatically by a valve operating between subsonic diffuser pressure and atmospheric pressure. Jet deflectors, similarly controlled as the inner bodies, are provided at the aft end of the ram jet, to control its direction in the atmosphere. i ~'-t - "e - S 7 First Stage Design - Boost Solid boost attachment ccnsists of four solid propellant rockets, each capable of delivering approximately 75,000 lbs of thrust for a period of fr seconds. The boost rockets were located on the outside of the ram Jet shell for three reasons: (1) reduction of overall length for ease of handling; (2) operation of the ram Jet during boost; and (3) action as part of the required fin surface. Reason (2) is probably most important, since at the low Mach numbers of boost, any retarded operation of the ram j3et could conceivably result in an unsuccessful flight due to the high drs. Provision for jettisoning the boost rockets is made by means of explosive bolts attached to each boost unit. Fins were added to the boost units to coeplete the required total fin area. / V,h~eighis of each component 6 the ahell structure were calcultod according k tandd aircraft praictiehaoi o intappeihdldiI w_..~~~~~~~~~i~ppni L~~~~~~~~~~~~~~~/S~

Ilt.:t'.\R'I'~i<.XT OF1 E:N(;l'.':I,:RIX!. ': \R~ | NI\1!RS1'I'V 01t MIC'IGAN PERFORmANCE ANALYSIS The final requisite for the oerformance analysis of the ram Jet missile, is, of course, to determine the thrust and drpg coefficients as functions of Mach number annd. altitude. From Report UJMfli-7, thrust coefficient curves wrere calculate-d (see Fir. 4- ). The diffuser efficiencies used are considerably lower at low slUersonic!,>.ch numbers than can actually t et4> *' t.,:., A ic? /. >; be retlizede tonding "to keep performance results conservative. It must be stated at this point, hoTrevr, that the thrust coefficient curves 1equire s straight/\tube of combustion chamber diameter at Msach ntmbers less than 3, end further, requireytha.t the dffluser entrance area equals the combustion chamber area,,a.t Mr~ch numbers greater than 3. Although these requirements are not entirely met by the ram jet missile designed as shown, it is felt that by the time an actual flying missile is built, sufficienteorogress will heve been made in (dsegn to insure the/thruct coefficent s used, rnd hatth oerformance given is not at all ontimistic. Drag coefficients for the first two stages were obtained from Continental Aviation and Enrineering Report 340, which used a missile of similar design (see Fig. 4- ). Coefficients plotted Pre based upon combustion chamber area. Drag coefficients for the third stage Pre taken from NACA report ACRL5H08 and are based upon a missile of L/D = 5.5. With thrust snd drag coefficients plotted, it wrs tentatively decided to launch to 1M - 2.0 with a total burning fr'~

I|NIV'iRSITI' 01 MII(CHI(;AN { time for Stazes I and II of 23 seconds. A few climbq to reauired Pltitude were run to check the nerformance. The altitude Pt the end of boost was calculated from the relationship (see oage 1+ for derivation): (_o_)2 - Iz,- oD v- o + 2gS3gS 2g$., ~,;i,-( o cM c - velocity of sound - fps A 3 - vertical distance - ft. I - s'-)ecifc impulse - sec. w - hate of burning - lbs/sec wo - initial weight - lbs. D - averaze draq durinr lsunchlng Launching is vertical, andf the missile is swvung through an angle of 26~ from the vertical at the start of ram jet oaerat ion. Severrl clculatlonq to the reauired final altitude were then made, uqin ra sten by sten orocess for the second and third stages (see Appendix, page ). When the drag became les'- than 100 pounds, the following equations were used (UMRF-8, Appendix A, npate 6): V(n) V(n-l) w W!o (n) g t (nn)

I,-I\\RTM -1 - 1 I R \ ' ); T 1, I. J = V + T sin log wo (n) + (1))()1 t (n) H(n) H(n-l) wo - )t(n) T gcos Wt(n) - (wo - Wt(n) )log 2 L.. t (n) H H H t(n) (n) (n-l) (n-l) 2 nWo VV - vertical velocity - -fps. VV - horizontal velocity - fos. SV - vertical distsnce - ft. 3 - horizontal distance - ft. H T - thrust - lbs. g - 32.2 ft/sec2 w - rote of burninr - lbs/sec n - store number - tiThe of burninm dIlTrinrr nth stnge - qec. (n) - weicht at beginning of nth stpre - flight oath angle from vertiopl = 260 Rates of burnins of the third stage control end stsbillzation motors were calculsted by the method given in IMC-46 pp. 1 -4........

I It '\R'!NMIIN'1 O) F;Nt;It\EI;RIN(G RI.!;\Rt]tI UNI'LRSI S ' ()1: %I'IIt(;A\ 170-10 Rec 23-170 ec Lateral thrust 21.9 lbs/sec 4.10 lbs/sec Pitch, yaw & roll 3.13 3.13 Turbine 1. 26.10 8.30 Totsl fiuel = 26.1 x 10 + 8.3 x 147 = 1485 lbs. (third Otage) Check for Hori,.ontrl Distance Correction (23-170 sec): Required distpnce = 58,300 ft. 1 =~wt(n) (W - wt(n)) 1 t W2 - w0n____ 4.1o 3422w w 4.10x 2800 a 8.3 x 147 - (3492 - 1224) n 492 - 34,92 - 122 31 246 1224 - (2268) ln. 60 000 ft. Since 31 is greater then 58,300 ft. these burning rates sufficed. The motors used were: (1), Lateral thrust motors;1, at 700 lbs. thrust eachi Arranzed in cruciform, two fired in each quadrant, consuning fuel at the rete of 4.10 lbs/second; and (2) Pitch, yaw, and Roll stabilistation motors, t 4)' motors, universally swivelincr, orovidino 400# thrust each. Performance calculations have included the 00 lbs.. thrust from these motors during the entire third staze. I: Ai!;1 ' --,I I I..sRt*.

I' NIV IRS-I'I'' i..il N11,'A.N 0;fl1 3Jet burning time! Vrtl( to f'nd ' h un burnin.g tLne necezsary fmry t'e ftisisle to retch the required )t C Fw sn ieih al t i tude istance, time specified for the UMA-1 nissile. Next, l complete analyses wermt 9 hoe enlmissiles designed forlO0 I, 25 9, Pend 40 rrAto deternine a weight versus accelerstion curv e, - (see Fig. t ). The minim:'::. point showed which accelera tion -ve the missile of the least initipl weight, or,!in other words, the most efficient mislile. Figurea G through 8 show plots of 1'ich number efter lsunchgin Pand boost fuel weight versus initial weight of the missile. Parameters of rates of burning are shown. Three design missiles sre used, 10 g, 25 g, snd 40 g. Equations used are: = Z -Iw -Dav - (wo -wt) In w0 cc~ 2 W - t (Symbols used are the same as on page 7, excent tl.t t = time of boost - sec.) wt = w - 7586 (10 g mssile) 10 1.25 wt = w - 7886 (25 g mlssile) 25 1.25 Wt40 = 0- 8186 (40 g mlssile) (See Apoendix, pp. \5 and G\6 for derivations)

1)! ' N', I AR I '1F ( fI IV l N(8 FE tiN,' I \ t j Plt of rtiurm. accelernation rndR l Ipnchino Ifch number versus lunching time Pre included (See Figs. _ through ) for 10 r,,~5 n, nd. 4~0 g mililes, Maximum accelerations or the flight opth are attained during launching. Equstions used were: _ Iw -:Dv -(o t) w 1wo- -?2 4- -n - w0 -0 2 and t1 = -.- - o7586 (10 f nin' e) 10 1.25 t Wo - 788 (25 g iqlle) 25 1."5 w _ wo - 8186 (40 g:?d' sie) (See Aend. G fr ervaton). (See Annendi, -n. o G <r 'ertvation).

1)i':!AR'T.M!:N'' ()O I:N(; INI G'!.t>i( K, R ':F ('1{ l ' NI\'l RSI 'I'OF Ml * lCIII(;AN | C ONCLUSIONS NfJD REC OIENDATIONS 1. The initial gross weight of the ram jet missile 14460 lbs. as cormpared to an initial gross weight of 17600 lbs. for nodel ULA-l. 2. Lowest initial gross weight is obtained by designing the missile for 25-30 g acceleration. 3.it apl:ears that no great behefit will be derived i~h reanalyzing a ran, et missile until more test data to substantiate or disprove present assumptions are available. 4. It is apparent that the rarq jet indicates a trermendous future as a means of propulsion, primarily due to its extremely high specific impulse. Secondary factors such a ease of servicing, manufacture, and storage stability are also not to beoverlooked in a com-parison with a liquid rocket missile.

LNERSITY (1F MIH1&tN I? 1. University of i-ichigan ULR-8. I-hase I report. (September 1947). 2. University of Michigan ILiC-46. "Desigh Calculations for UL.-1" R. H.. Fredericks. (September 1947). 3. University of Lichigan Ul:L-14. "Aerodynamic Heating of a Supersonic Lissile During accelerated Flight" D. WY. Lueck. (October 1947). 4. University of biichigan UlIL-7. n Simplified Method of Calculating Ram Jet Performance applicable to High 11iach Numbers." J. R, aannett. ( July 1947). 5. Continental aviation and Sngineering Corporation report no. 340. "Estimation of Drag Coeffic&ents of Viach-3 lMiissile." J.1.Roth. (September 1947). 6. NTACA-"CR-L5H08. "Supersonic Tunnel Tests of Projectiles in Germany and Italy." antonio Ferri. (October 1945). 7. JPL CIT, Lemo no. 4-17. "The Applicability of Solid rropellant to High 1lerformance Rocket Vehicles." Sunmerfield, et al. (Octoher 1947). 8. University of Southern California H-4-7. "ierfonrance and Geometry of High Thrust and Long Range Ran Jets." (February 1948).

IUNIVE;RSITY OF MI(CtIGAN APPIENDIX Derivati on of ESuqtions A. Vertical Distance Climbed Durin~ Boost. S o + Vot + at2 S = =0 1 at av 2S aaverage Sr a net av Gross Thrust - Drag av-leighta /t ~ ~ 3 (( nighta -(._)i v 2av - 0 2v - 2 2O Wt wo - t S 2 1*o o -W nhich pl6 near,...........! iine~ -this relation may b _ v f 2f t 22 l sor, = = 2 vf 2I- D - W, aS cL_ = 0v or, 2gS W Q~.

B. Launching Mach Number vs. Initial Weight. Assumptions: Vertical Flight Path J I- t Net Thrust - Gross Thrust - Drag - rWeight ' \ x Sie rt gt 5 I - cP Jr rl 4 _ — I '~ %.,4;-o5 c' ~v: "~0 i! -' t - i -o-_ —' w><, T a,-( -- 7 WI ' — L~~~~~ ~~~~7 - ~.~b -t-~~A LT-eF~i'os C~- ~/cJ ~- ------:ia~~~~~~~~~~~~~~~~~~~~~~~~

i tiVRST! 'V ()1' MI'IIIG(;AN tc.w ArI w - wL C. Maximum Acceleration vs. Initial 'Weight D. Ratio of Initial Launching Weight to Final Launching Weight. spX^ From Alleghiny Ballistics Laboratories: ~ -L Pro;ellant W eight = 0.80 Gross Weight 1ropellant We ight + or Shelli t- 4.0 let W0 -Initial. Weight WO = stage III stage II Wboost fins + Wboost fuel + Wboost shell

DEFPARTMENT Of' ENGINEERING RESE.A(CH, UNIVE st,.F MIC,IGN,, For a 10 g missile: Wo = 3492 + 3484 + 610 + W( 1+ Ws Wf * 7586 + 1.25 Wf = 7586 + 1.25(Wo - W) W! 0.25 Wo + 7586 10.25 o 1.25 W1 o.25 Wo + 7586 Adding 200 lbs. for each additional 10 g: Z\ui \ I t i o C; vI v S k y 'T tA I N-i, lt: o. 1.25 og W 0.25 'W0 + 7886 w1 1.25 `'v 1o o (40 g ) o.25 W + 8186 0

). PARTN INT OF ENG..NU.1 RF.SAR(. Boost Size Calculation - Separate Boost Units For L = 2.1, graph of 25 g missile gives: * 1600 lbs. per sec. Wo = 14460 lbs. Wboost fuel- 6080 lbs. 4 _e d -D V-=r ( D2 - d )1 ( 2 _ d2 ) 10OD 6.98 D3 4 From JPLCIT - Ik- 4-17?, Wboost fuel =84.6 lbs. per cu. ft. Totial volume boost fuel -0 =124000 it3 Volume per cylinder = 31,00..;cu. in. 3 _31000 = 4450 cu. in. D 6.9" D — = 16.4 in. L - 164.0 in.

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