Hypersonic aircraft design

Hypersonic Aircraft Design

UNIVERSITY

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Student Authors: H . Alkamhawi, T. Greiner, G. Fuerst, S. Luich, B. Stonebraker, and T. Wray Supervisor: Dr. G. M. Gregorek Assistant: R. L. Reuss Department of Aeronautical & Astronautical Engineering Universities Space Research Association Houston, Texas 77058 Subcontract Dated November 17,1989 Final Report May 1990 - - - - { N A S A - C . 9 - 1 8 7 G 0 5 ) H Y Q E R S O W I C A ERG WAFT UESTGY - - - F i n 3 1 Keport tnhio S t a t e Univ,) 174 p GSCL 81C

Hypersonic Aircraft Design

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UNIVERSITY Student Authors: H . Al kamhawi, T. Greiner, G. Fuerst, S. Luich, B. Stonebraker, and T. Wray Supervisor: Dr. G. M. Gregorek Assistant: R. L. Reuss Department of Aeronautical & Astronautical Engineering Universities Space Research Association Houston, Texas 77058 Subcontract Dated November 17, 1989 Final Report RF Project 7679191722941 May 1990 Hypersot7lc A i r c r a f t Design .

AAE-4 I 6'H Professor Dr. Gerald fl. Gregdrek

Teaching ~ssistant: RoGyn &uss

Abstract T h i s report outlines the preliminary design and characteristics of a hypersonic aircraft for a flight at Mach 10 using only scramjets for t w o nvnutes at 100,000 feet. There are many design problems that have to be addressed for such a highspeed flight. These include aerodynamic, t h e r ~ a 1 , l o g i s t ~ c a l and structural problems.

T h ~ s r e w r t contains ideas to deal w i t h these problems that have been exarrilned by our research team, the gold team. Aerodynamic calculat Ions, Inn>-.

!,.e,..=:ical s o l ~ f t ions are gresented along w; t h thermal and structural CFSICjn~. Yap:, ;deaf f cr hyperson:c a;rcraf t are based on theory ac$ haice ? . c . - : i t f i ~ d \\.r.hr.-n, . , ; : ..,- , , ~i,..f;; !:;,estzl f i>:~?,batlon.

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z- I cQ PI57 .-. 7 r-7- P \ I n c v L L ~ PURUI 6 i ~ T L ; + ......................................................... I c c c C O S T ? f OTAL DEVE!-Ot)MEMTfi,Ni! E't/ALUATiON . . . . . . . . . . . . . . . . . . . . I \ 9 Aspect R a t i o Span o f A i r p l a n e A/C Drag c o e f f l c t e n t C o e f f i c i e n t o f Drag a t Zero l i f t S k i n F r i c t i o n Drag C o e f f i c i e n t F r i c t i o n C o e f f i c i e n t Wave Drag C o e f f i c i e n t Leading Edge Bluntness t e r m Base Pressure Drag C o e f f i c i e n t Subsonic Pressure Drag C o e f f i c i e n t Supersonic Wave DragCoef f i c i e n t Nose Wave Drag C o e f f i c i e n t Body A f t e r Body Wave Drag C o e f f i c i e n t l n t e r f erence Drag C o e f f i c i e n t L i f t C o e f f i c i e n t L i f t Curve Slope Moment C o e f f i c i e n t About Aerodynamic Center Moment Coefficient About C.G Slope O f C , us. *Curve /deg Root Chord f t T i p Chord f t Diameter o f A/C f t Time o f Impulse sec Wing Efficiency Factor Wing Planform Efficiency Factor Temperature degrees Nose Fineness Ratio A f ter-body Fineness R a t i o Height of Landing Gear Gravitational Acceleration lnviscid Drag due t o L i f t Viscous Drag due t o L i f t Drag due t o L i f t Length of Airplane Liquid Hydrogen Maximum Landing Weight 1 bs Subsonic Suction Parameter Mean Aerodynamic Center f t Location O f Aerodynamic Center f t Leading Edge Radlous in Wetted Area of Wing ft2 Exposed Planform Area f t2 Maximum Cross SEctional Area ft2 o f Body Thickness t o Chord Ratio Turbo Fan Ram J e t Kinetic F r i c t i o n Coefficient Landing Velocity Landlng welght or Airplane Location of Center of Gravity Angle o f Attack degrees Glige Angle degrees Leading Edge Wing Sweep degrees degrees Trailing Edge Wing Sweep Taper Ratio lntroduct ion The design group project chosen this year i s t o design a hypersonic aircraft which uses scramjets to accelerate from Mach 6 t o Mach 10 and sustain that speed for t w o minutes. Initially the main difficulty was deciding on a propulsion system to propel the aircraft from the launched speed cf Mach .8 to Mach 6 at 100,000 feet. The different propulsion systems belnl; cccsidered were solid rockets, liquld rockets, rarnlets, and

t;jrn3f 25-mp.v.- I 6 , il]?ts. The f lnal decision was that the aircraft wculd use cr;e

fuli C F - . ~ e tcr30fan-ramdet. Later it was decided t o add t w c solid rocket Socsterf t o save fuel and help the aircraft pass through the transanic regi er,.

After the propulsion system was decided each member of the group was

assirjrte3 a task sucb as: aerodynamics, aircraft design, stabi 1 i t y and

csntrrj), coclincj systems, mission profile, and landing systems. The members researched their specific area of assiqnment and tried to get a ?PI;/sicat understanding of how the!r system interacted w i t h complete P:jpersoni c aircraft.

A f t e r two weeks o f research the group was ready t:, begle to set the

21rc:aft ccnf iguration. The two possible chcices available for t t ~ e

czr!f :c:irat:cri $ 6

. . . ere 2 waverl&r GT conver;t ionai &sign, Tpie c,^,nvent?~:-~z!

,!?.;:$:: wzs :!:(;ser dye tc i t s landinq characterjstlcs z y i e the relat:ve c . . .-r G r - C ~ ~ , . v ? - ~ ~ g T ( L..s.ir...lb.~ Y V I . 5 h , u . . L ' t o a wz:.erider. I t was apparent from the start t5at t.i:e 9 , y P . t S . , ?

,,, ;.,.... , o f fij?! requ;red t o c n . ; $ i e t e t h e m i s s i ~ n g:eat?): e f f e c t e d tp!e reizt:ve size c:' :re aircraft, Also the i ~ t e r ; r a t i o n - of the efiqlfie - systerr:f 33c tptmT i r . ~ a t p ! : : . 13 affected the aircraft c.onflcjumtion. Each o f :he follcwrng

sfcticns sf the repcrt ccn:ribute t~ the f;nal &sign of the hypersonlc

a;rcraft ancl 1s l~ir:tten by an irrdividual member.

An unmanned hypersonic researched vehicle was designed t o test a SCRAMJET, This vehicle had t o meet the followlng performance specifications: 1 ) The aircraft had t o be carried t o 40,000 f t . and launched from a carrier aircraft a t M=.8.

2) The aircraft w i l l be capable of accelerating to M=6 and climbing t o 100,000 f t . using i t s internal engines, 3 ) The aircraft w i l l carry aprototypeSCRAMJET engine that w i l l be employed to accelerate the aircraft from M=6 to M= 10 and i s to maintain M= 10 for 2 minutes of study level flight.

4) The aircraft w i l l then decelerate and land back at i t s base, NASA Dryden Flight Test Center, CA.

The aircraft .design process started by choosing the propuision system t o meet performance specification 2. Sol i d rockets were considered because of their simplicity, high thrust, and the fact that they can be

dropped t o reduced drag, but they were found t o welgh too much of the total

vehicle weight. Liquid rockets were considered because of their high thrust but the iuel and oxtdizer wo!lld require too much volume. Ramjets \#ere considered because of thelr simplicity and llght weight but were found to be lacking performance i n the subsonic and high drag transonic region. Finally, a General Electric hydrogen fueled augmented turbofanram j e t was chosen.

The turbofanramjet was selected over the others T o r several reasons. li

produces good thrust and efficiency within the Mach range of .8 t o 6, It has at1 acceptable weight, It burns hydrogen, the same fuel as the scramjet.

And in addition, the aircraft could have a powered landlng, The turbofanramjet was selected f u l l scale; 22.1 ft. long, 6.92 f t . i n dia., and 6100 lbs. in weight. The reason for selecting it f u l l scale was t o assure enough thrust around M= 1 since this region would have the highest drag and the least thrust avaf lable.

Since the alrcraft would burn liquid hydrogen, which has a very low density of 4.43 lb/ft3, most of the aircraft volume would be taken up by 1 iquid hydrogen. Thus, in order to get a preliminary sizing of the aircraft, a rough estimate of total fuel consumption was needed. This was done by approximating the average vehicle weight at 45,000 lbs. Next an average l i f t t o drag ratio of 2.5 was assumed. From this an average drag of l$,0001bs was calculated. Next a preliminary altitude versus Mach number flight path was selected for the turb~fanramjet uslng the General Electric data. From this an average thrust of 60,000 lbs., an average fuel flow rate of 60,000 lbslhr., and a SFC of 1,O was approximated. This resulted i n an average accelerating force of 42,000 lbs. This then allowed the calculation of a flight time of 3 minutes from Mz.8 at 40,000 f t , to M=6 at 100,000 ft., which meant 3000 lbs. of liquid hydrogen would be burned by the turbofanram jet. From M=6 t o M= 10 the SCRAMJETS would be turned on. An SFC of 2.0 and a thrust of 35,000 lbs. was assumed for the SCRAMJETS, The SCRAMJETS would then operate a t M=10 for 2 minutes. From this the estimated SCRAMJET on time was calculated t o be 7.48 minutes i n which time

they burned 75'33 lbs, of liquid hydrogen. Thus the estimated t o t a l

m o u n t or' hydrogen burned was 10593 Ibs. This meant a fuel tank w l t h

239 1 ft3 was needed.

A conventional configuration was next selected because the aircraft was hypersonic research vehicle for a SCRAMJET which would only f l y for short amounts of time covering a Mach range from 0 to 10 and would not be a t any one Mach number for a long period of time. A conventional design would also keep the plane simple and within current technology.

A simple conventional design and the fact of wanting a sletider low drag aircraft led to using one fuel tank placed i n front of the turbofanramjet, Since some l i f t was wanted out of the fuel tank i t was made slightly wider than i t i s high and i s curved longer on the bottom, As a

result the fuel tank was made 8 f t , wide , 6.5 f t , high , and 60 f t , long. This

resulted in the fuel tank having 2450 ftS3 which met the fuel requirement.

The plane, however, resulted in being 90 ft. long and resembled a missile w i t h a SCRAMJET strap to the bottom (figure Dl.).

After intial exact calculations were done on the plane i n figure Dl, it

was found necessary to decrease the wing loading by one-half and add l i f t i n g surfaces t o the front part of the aircraft in order to keep the nose up.

This was done by increasing the wing span 10 f t . and strecthing the wing 40 ft. up the side of the fuselage (figure D2.1. The wings extending up the side of the fuselage were blended into the body l i k e that o f an SR-71. This also allowed for more fuel storage. The exact SCRAMJET data from General Electric also caused a reconf iguration of the SCRAMJETS' locat ion. Since the SCRAMJETS produced small net thrust of on the average of 6500 lbs at 100,000 f t , from M=6 to M=10, It was decided t o use t w o ~ i ' them. And

slnce they required large exlt areas o f on the avenge o f 35 ft2 they vdere

placed on either side of the fuselage and under the wing so as t o get some inlet compression from under the wing. The exit nozzles expanded under and -. \ L . . . *+ over the wlng and then expanded into the turbofanram jet nozzle to satisfy I . .

the necessary exit area requirements. The turbofanramjet nozzle was now made t w o din?ensional- and resembles a 6 x 7 ~ 10 rectangle. This was done i n order to expand the SCRAMJET nozzles into the turbofanramjet nozzle.

The f u l l expanded SCRAMJET nozzle areas are shown i n blue on figure D2.

This expansion Into the turbofanramjet nozzle also elimanted the base drag from the turbofanramjet nozzle when it was off. The base drag from the SCRAMJETS was eliminated by folding the nozzles into the side of the fuselage when not i n use and expanding them outward when ..,_ i n use (figure D2.1. The inlet t o the turbofanramjet was placed on the bott6m of the fuselage i n order to assure a good compression surface for the inlet. The inlet t o the turbofanramjet as well as the inlet to the SCRAMJETS w i l l be closed off when not i n use i n order to reduce drag.

After more exact ca1culation.s on the design i n figure 02, the design in figure 03 was arrived at. I t was found necessary to add two more SCRAMJETS i n order to achieve an accelartion quick enough to keep the flight time and distance reasonable, fe,, under 30 minutes and under 2000 miles. The t w o SCRAMJETS were added by just making the existing SCRAMJETS twice as wide (figure D3,l The SCRAMJETS expansion nozzle area i s shown in blue on figure D3. A detailed view of a SCRAMJET itself in both the on and o f f stages I s given I n flgure 04, The aircraft wlngs were to reduce drag (figure D3>, The landing gear was also also smoothed out reposition i n order to reduce flexure stress on the ground. The front nose wheel i s keeped cool by the fuel tank. The avoinics i s positioned i n the front of the plane, This design (flgure D3) resulted In aircraft 90 f t , long, 15 f t , tiigh, fuselage width of 8 ft, and height of 6.5 f t . I t has a wing that has a span crf 40 ft., thickness t o chord ratio of .05, an area o f 850 f t . 5 aspect r a t i o of 1.88, and a wingloadlng of 42.68 l b / f t 2 empty and 56.20 l b / f t 2 full. The aircraft has a gross weight of 47,774 lbs. and a empty weight o f 36,274 Ibs.

The aircraft in figure 03, however, was larger than the French's carrier . .

plane's l i m i t by 5 feet, that is, their maximum plane length l i m i t was 85 feet. This meant that this design had t o be reduced by 5 feet. This could have been brought about in 2 ways.

The f i r s t way was t o scale down the entire aircraft as it i s now. At . T- , f i r s t a 50% scale down was studied. This evalution discovered some important characteristics about drag, lift, weight, and volume i n scaling down the aircraft. Since when the plane i s scaled down the surface area arid

cross secttonal area go down by the square. This reduces the drag by the

square. The inlet and nozzle areas are reduced by the square, This reduces the mass flow rate by the square and thus the thrust i s reduced by the square. Sfnce the drag and thrust are both going done by the square it seems relatively simply t o scale down the aircraft. The catch i s that the volume

i s going down by the cube. This means the fuel volume i s being reduced t o a

greater degree than the drag and thrust. This means that aircraft w i l l run cut of fuel before completing i t s mission, The good part about the volume going done by the cube, however, i s that the structural weight also goes down by the cube.

The second way was to simply remove 5 feet of length from the aircraft's fuselage and readjust the plane accordingly.

AIRCRAFT DESIGN I I Gerry Fuerst The final aircraft configuration was the result of a long evolution of aircraft designs. Originally, the plane resembled a missile that was powered by a turbofan-ramjet (TFRJ) and a scramjet. However, the lenght had to be shortened and the wing area increased. The nozzles of the scramjets had to be reworked inorder to make them workable. The final design turned out to be that of a delta winged, tailess airplain (see figure Dl1 1).

The overall volume of the fuselage was dictated by the number of engines and the enormous fuel requirements. The plane uses one full-sized TFRJ to take it from Mach .8 to Mach 6. After Mach 6, the plane w i l l use four full-sized scramjets to take it to Mach 10. Because of the large amount of fuel that i s required t o power these engines, the length of the .

plane was set at 85 feet (the maximum length that the French w i l l allow).

The scramjets are located a t the rear of the aircraft- t w o on each side of the TFRJ. When the 2-0 nozzle of the TFRJ closes, it provides two verticle expansion surfaces for the scramjets (see figure Dl1 2). These expansion surfaces, along w i t h pressure boundaries, w i l l be used as the nozzles fcr the scramjets.

The aircraft has three seperate inlets. A variable geometry inlet for the TFRJ i s located on the bottom of the fuselage, and a mixed cornpressicn inlet i s located on each side of the plane. These two mixed compression inlets supply air to the four scramjets. The scramjet inlets actually s t z r t about 18.5 feet upstream of the actual scramjet units. This i r b b r h ( 2 +,~tere the sides o f the fuselage turn outward at a 6.5 degree angle. This tur? i n the fuselage produces an oblique shock that rests on the outer llp of the scramjets a t Mach 10. This shock creates the i n i t i a l compression of the air entering the scramjets.

co The planform of the aircraft i s basically a delta shape. Because of the fact that the aircraft w i l l f l y at Mach 10, the wing was designed w i t h a high sweep angle and a low aspect ratio. The surface area of the wing i s relatively small. However, this area could be even smaller for a plane flying at. hypersonic speeds, but due t o the fact that the plane must be landed, it was not reduced any further. The following parameters apply to the planform: Wing Span, b = 40 f t Root Chord, C r = 40 f t Tip Chord, C t = 5 f t Mean Aerodynamic Chord, MAC = 27.037 f t Taper Ratio, A = 0.125 Sweep Angle o f Leading Edge,ll,, = 69 deg Sweep Angle o f Trailing Edge,ATE= 23 deg Exposed Surface Area, Se = 722.5 f t 2 Aspect Ratio, A = 2.21 5 Maximum Thickness Ratio, t / c = 0.0370 Zero L i f t Angle of Attack, d o , = 0 deg Aerodynamic Center, Xac = .S(MAC) The following parameters apply to the vertical stabilizer: Surfac Area, Sv = 120.75 f t 2 Root Chord, Crv = 27.5 f t Tip Chord, Ctv = 7 f t Sweep Angle of Leading Edge,&.,,= 73 deg Sweep Angle o f Trailing Edge,&; 2 0 deg Xvs = 17.69 f t Zvs = 6.335 f t Weight Analysis Thomas Greiner To better estimate the hypersonic aircraft weight f o r a l l o f i t s f l i g h t systems an analysis was performed using a computer program developed by both the United States A i r Force and the National Aeronautics and Space Administration . The i n i t i a l program, P.D.W.A.P (Preliminary Design and Weights Analysis Program) requested basic preliminary design data such as fuel weight, number of crew men, type and number o f engines t o act as an i n i t i a l data f i l e f o r a larger more comprehensive weight program. The larser program called W.A.A.T.S, (Weight Analysis of Advanced T r a n s p o r t a t i ~ n Systems) bases i t s findings on a data base containing Informatlor: on a i r c r a f t already i n existence. Not only does the program pro*~./lcfe vieisht estimates f o r the t o t a l aircraft and i t s subsjstems but it also slzes the a i r c r a f t for fuel and f l i g h t regime.

Wker, the program was run f o r the hypersonic aircraft, one problem that arose was that i t did not allow f o r scramjet engines. Since there are four scramjets an the current design t h i s could introduce substantial error, h2:,4;e$ ",. lo* (J,.,,~ - i t , . the englnes provided by the program, the most reasonable choice x a s to descriSe the scramjets as ramjets. When the turbcfan-ramjet onboard was entered into the program a highly exzgcjeratet weight estimate for the iniet (over 200,000 pounds) was returned. Thts error was compensated for by considering the engine t o be a camjet a x ! then adding t o the weight of i t s i n l e t t o adjust it t o the 2c:ual weight or the turbofan-ram jet.

The Cata returned by the program indicated that the i n i t i a l weight e s t l x a t e s viere very reasonable. The take o f f weight computed by \hI.A.A.T.S was 43,? 33 pounds, see figure weight 1 while the group used 4Z,CCO pounds , see figure w e i g h t 2 That eight percent difference i s acc?s:al;ie, h ~ ~ d e ' J e r the computeS Program underestimated for the thermal ~ r z t e c t i o z sytems so the higher number w i l l s t i l l be used. The computed height of the aircraft matched the 8 feet that i s used i n the current design while the calculated span i s 32 feet while the aircraft's current span i s 40 feet.

Overall the W.A.A.T.S. program computed a very similar weight estimate for the aircraft and i t s subsystems reaffirming the intial estimates used by the design team.

Rocket Boosters Thomm Grcincr Since the main driving f o r c e i n sizing the hypersonic aircraft was the need to hold large volumes of liquid hydrogen, solid rocket boosters were considered for the main propulsion system that would be used to accelerate the aircraft from the launch speed of Mach .8 t o the Scramjet operating speed of Mach 10. The solid rocket was considered because of the hish thrust and accelerations which would not be a concern to the l~nrnanned aircraft, also the booster could be jettisoned after i t s use.

?reliminari/ calculztions indicated that the rocket weight would be 75.,300 pcunds which was almost twice the aircraft weight. The idea of usins rockets as the main propulsion system proved to heavy.

A f u l l scale turbofan-ramjet,(T.F.R.J.) was chosen t o accelerate the aircraft forn Mach .8 to Mach 6 but a problem arose because the engine's b ~ r n i n g of liqtiid hydrogen increased the aircraft's size.

Ancther problem that occured was the efficency of the T.F.R.J. inlet t o produce a rzasonable pressure recovery at the low Mach numbers.

Estimates made by the U.S.A.F. showed that a loss i n thrust of 30% would . - , C p l , J L L U ~ ? t h r o q h the transonic region, where the aircraft drag increases shzr;:~. Thn* I I ici e i s some c~ncern-whether the engirres could produce enough tPLrtist t c ~ L I S ~ the aircraft thrgugh the sound barrier and that it would take m c x fuel t o do so became of the lower accelerations.

These ? r c h , l e ~ s were great concerns that needed to be corrected '::lths:~: ;eriallzlns the desisn by increasing i t s size to add more liquid hLirjrcr;er,. C)ce s ~ l u t i c r . was tc; put the aircraft into a d i \ ~ e and use gravity + h ..: G2ln SpeeC 2fter seperatfon from the carrier aircraft. This method .--%I _,.Juiu , : A :,{iork S ~ l t i t wouic' take more fuel to climb back to the original Anot5er s ~ l u i i o n was to use strap o~ booster packs t ~ ? accelerate thraush the transcr,ic region. These boosters would be used from Mach .8 t o Mzch 2.5 to accelerate the aircraft while the T.F.R.J. would produce ORIGIN&I ~ A z IS I O e)F B W R Q u A b m enough thrust to overcome drag. This T.F.R.J. was not used a t f u l l thrust to reduce the amount of fuel needed t o span the transonic region but it was kept operating to allow for a smooth propulsion tr'ansition when the solid boosters were jettisoned.

The two boosters are integrated into the aircraft body, one under each wing, see figure Booster1 mounted next to the scramjets. The booster's nose i s slanted t o lower the drag and also the two-dimensional exit nozzle i s located partially behind the aircraft body to reduce the drag. The length o f each booster is 15 feet and their combined weight i s 15,000 lb. This additlona? weight puts the aircraft's takeoff weight at approximately 62,OCg pounds.

The size 2nd welght of the booster rockets was calculated using a sgreadsheet, see figure Eooster2 which was based on the constant acceleration that was assigned. An acceleration of 1 -G, (32.2 ft/sA2) was chcsen tr, reduce the range traveled and the amount of f ~ e l used. Using tke given acceleration the amount of fuel required t s rxaintain the chosen C l i o h t I I d y l I C grzfile I s calculated and then the required volume i s determined.

Thr, r q i r ( 1 1 ~ ;,dlIu p r s p e l l a ~ t chosen was J.P.N. which has a specific impube of 249 r a i q n d r . This was the upper l i m i t f c r a solid rocket fuel impulse. The rnltial %eight c f the aircraft was 62,003 pounds and the weight of the fuel Burned 5y both the solid rocket boosters and the T.F.R.J. were subtracted from the aircraft weight as i t accelerated. The thrust rewirecf to accelerate the adjusted mass was calculated and then x z v e r t e d into pounds of propellant. Knowing the density of the >rapellafit the volume required t o ccntain the propellant was detern-iined.

\+ijth t q i c i ,nformatlon a rocket diameter o f 2.5 feet was determined to be .

exce2table in terns of drag and volume for the roclcet's tube.

The overall Senefi t s cf using the booster pack i s a reduction i n range of ,> ; 1 P. P.

.

. ~ 3 due tc; the large acceleration, a reduction of 500 pounds of fuel r. h d rl

. lc.=ile:: :cr thi: T.F.R.J. Ir, the transonic region, and the additional thrilst t o

offset the thrust lcst due to an inefficent T.F.R.J. subsonic inlet.

I I CENTER OF GRAVITY LOCATION Gerry Fuerst The center of gravity for the entire aircraft was found by taking the weighted average of the center o f gravity for individual aircraft components. The Analysis was as follows: COMPOf.IEf.IT WEIGHT (LBS) LOCAL C.G. (FT)

Nose *

Eody Fuel Tank TFRJ Scram je ts Inlet Front Landing Gear Rear Landing Gear Wing Vertical Tai 1 flote: the nose section contains a portion of the main fuel tank.

When the fuel tank i s empty, it not only affects the weight of the fuel tar\\: but also the weight of the nose. Therefore, the empty weight of the fuel tank and nose i s 441 3 Ibs and 1365 lbs respectively. With the above infr!rwation, the center of gravity was calculated as follows: Sum (WeightSC.Local C.G.)

xcg = .......................

Sum of the Weight Xcg ( f u l l tank) = 35.102 f t Xcg (empty tank) = 29.053 ft * The C.G. i s measured w i t h respect t o the rear o f the aircraft.

r I I ~ I - l t vt-or IIe I .

Thomas Greiner A necessary requiremet f o r any hypersonic vehicle is to minimize the size and weight o,f the aircraft. The size and weight requirements f o r t h i s niission were specifled by the French based on their launching a i r c r a f t requirements. Since the hydrogen fuel used has a large storage volume it i s necessary t o nlnirnize the amount of fuel required f o r the f l i g h t profile.

This mission p r o f i l e consisting of a f i v e phase f l i g h t was i n i t i a l l y used to minimize fuel.

phase One) Acceleration from Mach .8 t o Mach 2.5 a t 30,000 feet.

Phase Two! Following the Q-Curve of 1850 a t Mach 2.5 a t 30,000 fee!: and accelerating t o Mach 6 a t 75,000 feet while maintaining a climb angle of four degrees.

Phase Three) Leaving the Q-Curve at 75,000 feet and climbing t o 100,000 feet w h i l e maintaining Mach 6.

Phase Four! Leveling off a t 100,000 feet turning on the scramjets, turning o f f the turbofarr-ramjet and, accelerating t o P'!act; 10 3\76 c,us:atnirig that speed for tid.+$ nlnut:~, Pr,~$,e =:~;e; T~:'",l:g c f f the 1=,cra!r; lets a 1 ; c f s l o w ; y dc..::!] &]oyi Maah1 J ' ;>,-.A t s $et-,i , , , . , , I I , n ~ tfie turbof an-ram jet or, and t:ea.?inq t o Drycen .Air Force Szse In Califcrnla under acwer.

Thf! preczc?:rig pt-~ases were analyzed using a spreaGheet, see f iqbr?

g ? 3 ~ i ~ P 1 , ,,<. .

fh:c:, uses cc;nditlor,s such as accelerat;cin, time-c;f-flight, and t L h ~ A climS anqle t.6 mit'flm:ze rue! consumption. Calcu!ztigns Idere cond~ctec! t o follcw a constant dynamic pressure line, a C-curve, which w i l l a!low the a l r c r a f t t o maintain a constant angle of attack from 40,C)00 t o 100,000 f e e t . 9riqinally, a Q based on Mach 6 a t 10'3,000 feet was attemptec: 5st a u l d not be used due to t w o factors, the maqni tude of the +@!.,> 4,.

L.. d,ynemic f ~ r c e s a t the lower altitudes and the lack of thrust of the , = . - , - + t h t - . - i a ~ t - . - , ~ . j : - . - ~ t ~ t t . - ~,-.n.-.

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altituded required t o stay on the Q-curve f o r the entire f l i g h t . The Q value i s above 2 0 0 0 which implies there would have t o be a substantial increase in structural weight t o accept the loads. For a hypersonic a i r c r a f t a Q should be about 1 800 therefore a new value was chosen based on Mach 6 a t 75,000 feet w i t h a Q of 1850. This an acceptable value that w i l l not greatly e f f e c t the i n t i a l estimate of the structural weight.

The a i r c r a f t follows this Q-curve i n phase t w o u n t i l it reaches Mach 6 at 75,000 feet. A t this t i m e the a i r c r a f t enters phase three were it !eaves the Q-cunle while nlaintainlng a climb angle of four degrees an6 cl!mbs 100,000 feet while sustaining Mach 6. In t h i s high altitude pet'iod : : f the f l i g h t p r o f i l e the thrust of the turbofan-ramjet f a l l s o f f , however the thrust r-ec;uired also clr,:ps, Since there are r ; o cther acceler-atici; requ?ren:ent";t:: meet cther t3an those causecl by the change in the speed 3' 3 i ; ~ d Cue to ttse atn;c;sar;eric temperatur'e,at t h i s point the thrust has ? n ? y t c overcorrie the drag and the force from the weight compcnent, :+?refore tbe thrust available IS s t i l l large enough to meet the thrust TeG!;:red.

In phzse four of the f l l q h t the a i r c r a f t levels o f f at !00,C00 feet, the turSof3n-ramjet i s turned o f f and the scramjets are turned on. Based on :he data 5upplled by the spreadsheet it became obvious that the a t r c r a f t Ceeded more t9rust to recuce time of burn and, i n turn, the fuel requlrec' t o zccelerate frcm Mach 5 t s Mach 10. Two additlonal scramjet modules ;tbtere added t o the a!rcrsft. Adding the engines increased the thrust anc!

.-,i f i t ' C , : . . l L t Y J L : ~ fcr considerable ir~crezses in acce!eratlon and reduced the an:r;uf-~t % * t ' l : L ; Lur:;ee cur!t;c,;. this St-lase 3 f the f 1 lc;ht, d ' u\.

" T :-i;-;a!\y 1 : ' ; ;p,i:se f l * ; ~ after- tp,e t w o m],]l~te e;;c:;;e tes: t $ e s--,-?p-;at,= : , c.i i ; . ! : b-. , -1 .-:.?.-,, j. ,\.I: ,.'f , ..2,1~2 ?,-? the ;;ia:,e 15 Ce~eiei'ated by the fcr'ce 3 f draq. The a!rr,raf :: . .

. : -.',.,,v : ,.. , , , c -, $ ! ; : t ; n t,s X3::t: a t 5O,;!CO fee: and the tcrbofan-ramjet 1s turned or: . , . i . . , ! + .b . - ti:e aii-:raf t cc=:~t:r-~i;es to slow down. The h y ~ e r ~ c t ? i ~ aircraft xa!r;tz;r:s Plach .8 and f ? ! e s t o Dr'yden A i r Force Base California a!%!(?

lands. The actual fllght path along the west coast of the United States i s illustrated in figure Prof i le2.

To further reduce the 1 iquid hydrogen necessary to accomplish the mission an energy state program,was written.

PATH nnN (ENERGY STATE OD) BY Bob Stonebraker The accelerated accent from release to Mach 10 at 100,000 feet was broken into two phases based on the engines used. Phase 1 employs the turbofan-ramjet and two booster rockets to reach Mach 6 at approximately 76,000 feet (q = 1800 psi.). Phase 2 then continues the accent under power of the scramjets to Mach 10 at 100,000 feet to begin the two minute test. The energy state method showed that the altitude vs Mach number flight path which consumed the least fuel was simply one of a constant high dynamic pressure.

Temperature limitations determined the highest dynamic pressure to be 1800 psi.

The data provided forthe General Electric augmented turbofan- ramjet engine consisted of net thrust (Fn) and specific fuel consumption (sfc) for various Mach numbers and altitudes. To make this data easier to incorporate into a computer program, it was used' in a subroutine (SUBROUTINE TFRMJT) to produce values for any Maizh number at any altitude. To do this, Fn and sfc were separately plotted vs Mach number for a constant altitude. This was repeated for various altitudes yielding several curves, one for every 10,000 feet from 40,000 to 100,000 (Figure ES-1) .

A plotting package was then used to obtain best-fit equations of these curves which modeled the given data quite accurately. These polynomials were then used in the subroutine in conjunction with the cubic spline interpolation method for values at altitudes between those of the equations. In this way, the subroutine yields a corresponding net thrust and sfc for any Mach number ( . 8 - 6 ) at any

altitude (40,000~ - 100,000'). Where several values of Fn and sfc

were given for the same Mach number and altitude in the original data, that for the best fuel economy was chosen for the plots.

The given data for the experimental SCRAMJET was also reduced in a similar manner through a subroutine (SUBROUTINE SCRAMJET)' which yields values for a range of Mach numbers (6-10) at any (See Figures ES-2 & ES-3). The data altitude (80,0001 - 100, 0001), provided, gave thrust (Fn) and specific impulse (Isp) values as a function of dynamic pressure and fuel/air equivalency ratio for various values of altitude and Mach number. Because the data for this engine was given in terms of various dynamic pressures (q) instead of altitude, the best-fit equations in this subroutine have altitude as the independent variable with Mach number held constant. Then the cubic spline interpolation subroutine (SUBROUTINE SPLINE) finds the desired net thrust and Isp for non- integer Mach numbers from 6 to 10. Once the Isp(sec.) is found, the sfc is computed by the following;

3d 0 0

S F C =

ISP

Two additional subroutines had to be written for the Energy State program; one for standard atmospheric data as a function of geometric altitude (SUBROUTINE ATMOSFR) and another for the total drag of the aircraft as a function of Mach number and altitude (SUBROUTINE DRAG). The total drag data, computed by another team member, was received in tabulated form and was therefore also reduced through curve-fit polynomials and cubic spline interpolation.

khe energy state method can be used to determine the minimum time or minimum fuel required to reach a Mach number and altitude.

To compute the minimum fuel accent required five separate programs.

The first code (PROGRAM HECONST) determined lines of constant He

(ft) , which defines the amount of potential and kinetic energy that

He an aircraft possesses at a certain Mach number and altitude.

is given by; Two additional codes determined contours of constant Fs for phase 1 and phase 2 of the mission (PROGRAM FSCONST & PROGRAM FSCNST2).

Fs is the vertical distance traveled per pound of fuel burned and is given by; The minimum fuel trajectory is one in which the lines of constant Fs are tangent to lines of constant He. These plots showed that a greater thrust per pound of fuel is obtained at high Mach numbers and low altitudes. However, aerodynamic heating obviously limits flight in this realm. Therefore, the minimum fuel accent was chosen to be one of a constant q = 1800 (Figure ES-4). For comparison, the quantity of fuel requiredto accelerate from Mach=6 to Mach=lO all at 100,000 feet was determined to be approximately 25,000 lbs. This is obviously unacceptable.

Once the flight path was determined, several values could be computed along the trajectory. Figure ES-5 shows the thrust available and required curves. The last two codes (PROGRAM PHASE1 and PROGRAM PHASE2) were used for this and to compute the fuel consumed and elapsed time for phase 1 and phase 2 of the mission.

The fuel burned is given by;

P dfz

The elapsed time is given by; The range required for these accents was also computed, as shown below, and found to be approximately 130 miles for phase 1 and 970 miles for phase 2 .

Originally, the plan was for Edwards A.F.B. to be the base of operation over all phases of the mission, from carrier aircraft takeoff to test vehicle landing. The plan incorporat$d a triangular pattern with one leg over the ocean for the accent, acceleration and scramjet test phases. The aircraft was to be carried to the release point approximately 300 miles southwest of base. This would allow a return, either to Edwards or Vandenburg A.F. B.

under power of the turbofan-ramjet in the event of scramjet misfire. However, after a better estimate of required acceleration distances, it was necessary to alter the plan. It was decided to originate the mission from Seattle and release the aircraft over the ocean, then run approximately 100 miles off the coast to land at Edwards. This plan still fulfills the requirement of non- supersonic test vehicle flight over populated areas.

Control of the mission from release to landing is to be fully automated. Based on this, it was determined that the avionics should include a receiver, transmitter, inertial navigation equipment, stability augmentation systems, and a computer. This equipment was estimated to weigh approximately 1000 lbs. The aircraft cooling system was not included in the avionics. The control program will originate from systems based at Edwards and be communicated to the aircraft via satellite. Real time communication between the aircraft and Edwards A.F.B. is also necessary to monitor data from the test scramjets. The on-board computer will maintain a backup control program in addition to its' stability augmentation and engine monitoring functions.

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The l i f t and drag d f an airplane are the key factors i n det.ermining [he type o f engines and the perf ormance of the airplane. For the f i r s t phase of

the design process , an in1 t i a l configuration was approved, an estimate of

the C D , of out- ail-plane was calculated usiny the build up method. Tho itlitfa1 calculations indicated that using one f u l l scale GE tur-bofan-rzrr~jet wouid be sufficient t o overcome the drag of the airplane a t the uario:!s

phases of f i ight where GE's turbofan-ram j e t would be use6 A f t e r the!' f trst

ghase o f the design process was completed, the drag of the airp?zi:e wt?s more accurately calculated using Nfcolai's (chapters 2 S , I 11, and the Datcom reference. A f t e r Several lteratlons on the drag numbers becaclse of slight modifications t o the airplane design , final drag numbers were calculated t o the f i n a l airplane configuration. This data was then given t o the f l i g h t Path group whlch was responsible f o r determining the f l l g h t path arici the fuel requirements of the mission. A f t e r the fuel requirerrient and

t i m e of filgrit for the mission profile were calculated uf l n g the thrust

provided by the t w o scram-Jet engines it was obvious that an addl tional t w o scram-Jets, one on each side of the airplane, woulcf be required t o cut :,i;e fuel r e ~ u i r e r f ~ e n t and t i m e of f l i g h t . These additions effects on the drag

w?r;: iriciuaed a ; a 1 OX increase t o the CDo of the airplane Dec:;ij+e t k p f e

:nodiiitations were dorie the day before the final presentatjot-) for \n,'jnter.

Quarter. Therefore, the effects of these additions had t o tje r;hi::ul~ted mgr.2 >:a , , , , , , A t ? , rt-.9t+; , y i n Sprlrlg quarter, The l a s t rnlrsute tnodlflcatlotss, that were Itltroduceo at tiie etid ~i Wlnter quarter, were studied more closely a t the beglnig of Spring quarter and ~t lvas obvioils that some modiflcatlons to the shape of the airplane had t o be done. A f t e r the flnal shape of the a ~ r p l a n e was modified and approved, the f lnal drag numbers were calculated . The drag numbers for- the 016 conf lguratlon could not be mod1 f led t o account f o r the changes In the alrplane conf lguratlon malnly because the fundemental parameters used In calculating the old drag numbers were drastically changed by the new design; these parameters include the airplane fineness r a t l o (Ig/d), the nose fineness r a t i o (lN/d), the af ter-body fineness r a t i o ( I A / d ) , the aspect r a t i o o f the wing, the surface area o f the wing, the taper- r a t i o ? %r7d f i n a l l y t h e leng t h o f tile ail--plane. ~ h e r e f o ~ e , the drag nulilbers for t h e new . .

c ~ j n f iguyatiofi !]as t o be calculated f p ~ l m scratcil, The t t y e e c o e f f fcie/]ts t!;at had to be calc,~lated t o provide us w i t h sufficiently accur-.ate dr'ag nut-17bers w e r e C D , , I( (factor o f drag due t o I l f t), and CL . These three coef f lclftnts

need t o be calccllated seperately for the four f l i g h t regimes i n our- flight

p x n .

SUBSONIC For the wiriy, the zero 1 i f t drag i s composed of t w o parts, skin fr-icttc~rr drag and ~ressclre drag. As for skin f r i c t i o n drag, it is caused by shear-inc( S[fxpS:e5 i~/jt!7.1!'1 a tt?jfl !a)!@- o f yet.aft.erj i311- tj-je sijrface o f tile w ~ f i ; ~ ~3iii;f:j the boundary layer. The amount of viscous resistance depends on whether the f l o w In lamlnar o r turbulent; f o r our alrplane turbulent f l o w was assumed f o r a l l f l l g h t reglmes. As f o r the pressure drag, ~t IS usually s;'riall cornpared t o sk~n f r i c t i o n and it 1s prlmarlly caused by the d ~ s p l a c e m e ~ t thickness of of t h e boundary layer. Methods f o r ~ r e d i c t l n g subsonic C D , fcr*

w lngs are essential ly empirical and are based on strezmw ise a i r f oi 1

thickness r a t i o it./c!, For the body, a t stlbsonic speeds the dray of sri~ooth slendtir isiidies 1s $r:marily skin friction. The Reynold's nclmber i s based on body lenqtt;, so!~ndary layer ccnciition, and surface roughness. The pressure drag i s also generally small for fineness r a t i o s above 4 ( The airplane's finess r a t i o 1s 7.083) but becomes significant f o r blunt bodies. A t the subsonic reigon, A C D , of 0.0 129885 was calculated a t M-0.8. Also a t M-08 and a t 40,000 ft, the dt-ag is 7508.25 Ibs w i t h a L/D of 6.433.

TRANSONIC I

For- the w in^, the transotlic ranye vat-des great iy * i t h atrt'oi i shape an6

thickt!ess, but fur sitnplicity i t can be considered t o begin at. approxit-iiateiy !;1=0,9 and end a t r.1= 1.2, Because o f t!*,e ~ 1 i s e d flows, drag tfje transonic . -, r y 1 yon does 17fjt jefi(-j j t ~ e j f tc) tj]egt-atical or e;;perjlnefitai a!>ai*ys;s, 1 ~5

-

1ng drag a t t i l e trar7sonic 1-ei got) is tr;air]ly corriptjsed of skin fr-ictior] a!](j ;&/3\i$ f:irag, As for si:.in f r i c t i o n , a l i t t l e increase i n tlrag i s exf.,erlenced (:l!.-!e t.6 v1scocity. Therefore, the skit) f r i c t i o n drag w i l l be assumed cotsstanl

arirl equal t o the subsonic skin drag throughout the trat'rsot~ic range. As for

the wave drag, the variables involved i n a wing design that e f f e c t the manner i n vv'hich shock waves develop on the surface are many; they include sweep, aspect ratio, taper ratio, thickness r a t l o variations between root at70 t i p thickness, posi t ~ o n of the maximum thickness, incidence an3 leadit;:; edge thickness. As a result i t s very hard t o predict the wave drag 11s the transonic reigon. Estimates f o r the wave drag can be obtained by f l n d ~ n g the drag divergence Mach number and then using figure 1 1.10 i n Nicolat's to find CDo .

For the body, the general approach consists of predicting the skin friction, the drag divergence Mach number, the variation o f base drag w!th Plach nutilber, and the variation of pressure drag f o r Plach numbers above I Ther:efore, the drag of the body a t transonic speeds consists of skin friction, base pressure, subsonic pressure drag, and supersonic wave drag. A t the transonic reigon, as predicted, a C D , of 0.039493 a t M= 1.2 was the lsrges t.

Also 3 t PI= 1.2 a t 43,000 St, the dray was 145983.92 lbs w i t h a L/D o f 3.273.

SUPERSONIC

Fa- the wing, a t supersonic speeds an increase i n the tYlach number

results in a deCrease in the skin f r i c t i o n coefficient a t constant Reynolds numbers. This variation i s primarily due to the variation i n the temperature and density at the surface. The full reduction In skln f r l c t l o n a t supersonic.

Mach numbers IS justified only when stabilized conditions and zero heat t.ra;?s:'er are at.t.aii;ed, For t.rans!ent. f l l ~ h t . the skin f'r!ct.loi; w i l l he 8ssumed equal to the incompressible value although in reality ~t varles between this value and the zero heat transfer. Another important factor f o r estimating drag at the supersonic speeds i s the Reynolds number, this can be accounted for by taking into account the ratio of compressible to incompressible skin frlction coefficients. As for the wave drag, the well known linearizecl s~;personic theory i s used in predicting wlng wave drag. For the alrplane the [Afave coefficients were obtained using equation in Nicoiai's which are based on the supersonic linear theory.

For the body, the characteristics of compressible skln f r i c t l a dr'q fot- Sodies are similar t o those of wlngs; the skin frictlon coeffictents decrease 3s the Mach number increases. A s f o r the wave drag, two niethods for es:!mat ing the fore-body and af ter-body wave drag are presentecl In the Oatccm ref e r e ~ c e . The second method, which was used, i s based cn s:ml lari ty parameters, The wave wave drag i s seperated into the f ore-body drag, the Isolated after body drag, and the interference drag of the fcre-body and center section of the after-body. In the supersonic relgon, a CDo o f 0.0242 was calculated a t M=3.0. Also a t M.3.0 and a t 65,5000 f t, the drag was 40666.36 Ibs w i t h a L/D of 1.1592.

HYPERSON l C For the wing, due t o the non-linearity of hypersonic flow, approximate methods f o r est imat lng force characteristics are very desirable. Among the methods used, Newtonian and modified non-New tonian f l o w theory have

Dt-Ovftd very useful, New tottlan theory is based on the assumption that. ti::?

shock coticldes w i t h the wtng surface and no frictiott exlsts Dettveet; t h e

wing and the boundary layer. The f l u i d particles ahead of the w lng are ncit disturbed u n t i l they encounter the w inq.

For the body at hypersonic speeds the drag of the body i s caused primarily by the pressure and skin f r l c t i o n drag of the nose, Both the af ter-body and the base drag become insignlf icant a t hlgher Mach numbers.

The drag coefficient was calculated a t M=6.O and a t M=10.0 using NewtonIan f l o w theory and i t was also calculated using the supersonic linear theory; the discrepancy between the t w o methods was less than 10% (the Newtonian f l o w provided the lower drag values). I t was deccided to stick w i t h the CDo1s found using the supersonic 1 lnear equations since the discrepancy was calculated and a t M= 10.0 a CD, of 0,0 155 17 was calculated A t M=6.0 and a t 76,000 f t the drag was 32294 Ibs w i t h a L/D o f 1.4002, and a t PI= I 0.0 ac 100,900 f t the drag was 26036 i l b s w i t h a L/D o f 1.449.

After the CDo was calculated for the various fllght regimes a 10% increase was added t o CDo t o include the i'nterfernce effects. In addition, the coefficient of drag due to l i f t (K) had t o calculated in order t o accoutst for the effect of l i f t on the drag of the airplane. For the subsonic reiyon t i l e equatior~s in Micolai's (Chapter 1 1 ) were used. For the supersonic and hupersonic reigons the K values were calculated uning the supersonic linear theory. Finally the values of K for the transonic reigon had to be approximated. After obtaimng the CD,'s and the K values for the various Mach nurnbers, the drag a t the various a1 t i tudes and Mach numbers was calculated. Three seperate prograrrls were written t o calculate the drag and angles of attack a t the various Mach numbers and altitudes. A listing o f the equations and procedures used in calculating the drag are 1 isted in Appendix b 2nd the listing o f the programs used in calculating the drag can b? f o i ~ n d 1r7 Appendix 8. The tables AD 1 -AD6 and the figures AD 1 -A138 irioiuBe l h i r ~ s f i l t s o f this chapter.

BASIC STABILITY ANALYSIS Ocrry Fucrst Due t o the large amount of fuel on board the t e s t plane, there w i l l be a considerable s h i f t in the C.G. during flight. The C.G, w i l l s h i f t down and towards the rear of the a i r c r a f t as the fuel i s burned. The distance towards the rear of the plane that the C.G. w i l l travel was computed as follows:

C.G. Travel = 35.102 - 29.053 = 6.05 f t

For stability, it i s necessary t o have a positive s t a t i c margin. The SM i s directly related t o the distance between the center of gravity and the aerodynamic center.

Although the C.G. travels back 6.05 feet, it always remains ahead of the aerodynamic center.

This means that the s t a t i c margin always remains negaive. The calculation of the s t a t i c margin was as follows: Static Margin: SM = (Xac - XcgVMAC Full Tank: SM = 13/27.037 = 0.4858 Empty Tank: SM = 6.875/.037 = 0.2543 For an a i r c r a f t t o be statically stable, i t s value of Cm(alpha1 must be negative. When this i s the case, the aircraft i s trimmed at a positive ancjle of attack.. When the angle of attack i s suddenly increased, the aircraft w i l l generate a negative moment t o push the nose back down t o the origional trimmed angle of attack. The Cm(alpha1 for the t e s t plane was found t o be neyatiSde for both the f u l l and ernpty tank cases. I t was cr:l;;;~i;ted as f ~ l l o w s : Case 1 : Mach .8 Full Tank: Cm(alpha)= -.7965/rad Empty Tank: Cm(a1pha) = -.42 13/rad Case 2: Mach 10

F u l l Tank: Cm(a1pha) = -. 1957/rad

Empty Tank: Cm(a1pha) = -. 1035/rad The Cm cg of the test plane was calculated for three different cases:

subsonic (M=.5); supersonic (M=2); and hypersonic (M= 10). Refer to tables

S 1 thru 53 for Cm cg versus angle of attack, CL, and CD. Cm cg i s plotted versus angle o f attack i n figures S 1 thru 53.

LANDING GEAR Gerry Fuerst The landing gear of the test plane w i l l consist o f two rear skids and one forward wheel. This configuration was choosen primarilly for i t s reliability and simplicity. The rear skids are better suited i n handling the high temperatures that w i l l be experienced during flight. A forward wheel w i l l be used because it w i l l allow for the steering of the aircraft after it

has landed. his wheel w i l l be kept cool i n flight by surrounding i t s

compartment w i t h the liquid hydrogen fuel tank. The rear skids are located 1 1 feet from the rear of the aircraft, while the front wheel i s 50 feet frcm the rear.

In desrgnlny the landing gear, tt IS necessary to determine the

maxlrnurn loads that w i l l be experienced during landing. These maximum loads w l l l occur as a short impulse when the landing gear touches down. It is assumed that the test plane w i l l land at a velocity of 21 1 ft/s, and i t w i l l be descending w i t h a glide angle of 5 degrees. The glide angle i s the angle that the plane's descent makes w i t h the ground. The 5 degree glide angle w i l l be the maximum that the plane experiences and was chosen t o determine the largest possible loads on the landing gear. Finally, the last assumption that was made i s that the time of impulse w i l l be 0.5 seconds.

A simple free-body diagram of the landing gear i s as follows: Constants: Landing Weight of Plane, W = 47000 lbs

Height of the Landing Gear, h - 4.0 f t

Kinetic Friction coefficient, Uk = 0.6 Landing Velocity, V = 2 1 1 .O f t / s Glide Angle, Theta = 5 deg Time o f Impulse, dT = 0.5 sec GravitatTonal Acceleration, g = 32.2 f t / s 2

The maximum force, on both skids, in the vertical direction (Fy) can be

calculated from the following formula: (W/g)*Vy

Fy = --- ----- ---

where Vy = V sin (Theta)

dT Vy = 2 1 1.0 sin (5) = 18.39 f t / s (470O0/32.2)jC 18.39 Fy = ....................

.

Fy = 53'685.093 lbs This i s the maximum vertical load that w i l l be experienced by both skids together. Each skid will, therefore, experience half o f Fy or 26842.547 Ibs, The maximum force experienced by both skids in the horizontal direction (Fx) can be calculated from the following formula: where N is-the maximum normal force The maximum normal force on both skids is eqlial t o the maximum vertical force on the skids (53685.093 lbs!.

Theref ore:

Fx = 0.6 * 179279.503 Ibs

= 322 1 1,056 1 bs - The maximum horizontal force on each skid seperately w i l l be half of Fx or 1 6 1 05,528 I bs.

The maximc~m moment produced by each skid (Mz) can be computed from the f 01 low irrg formula:

Mz = (Fx/2) * h

= ( 16 105,528) * 4.0 f t

=64422.1 12 f t Ib The following i s a free-body diagram of a skid w i t h the maximum loads in place:

Materials and Cooling Systems

been olaa!!ea - %:rn i n ? o r ~ n i g - f i s r = -I I wha; ~ ~ ~ ; ~ r ~ a i ,! 5 ; z e

s r r e n ~ t ? , 2~;;;:

cooling S)isie<r;s Trb CISG, T t 7 ; a r g nwst b g n e f i c i a i 1.o the !nissjor!

iilqr!

thermal ioadinqs and DOG^ f ~ r c e ~ actinq a i m q tr!e entire a i r c r a f t r e ~ u j t - 5 new techr!gio$ies j e G ~ L ' ~ ; C ! Q F - I . This SeCijQr~ c f tne repor; qeals wit:.

lrJeaS anil LL,l i.n!.rcl- 1.- .,;'.':. - -, yns- .. 1'4, :-?t-~ -. , : . oe ;I=:'P -, -.-. -.I 'r, t g : roo .. ,... (i;je.\;$iopmer;; c: ;p:;s z!rcyzr;.

,' , , . : + ,. . , , .- , . . , -

..L . ; . C I I . . I i ' . c The fir?.: z:ecj ; : ! ~a~s:;i:.rri:+~~' rrle r ~ g ; e y i ~ l : ~ at!a i < , < j i i , l i , ;>Ici, , , : :=.

-.

caic,giate a ;smsei-a;u;+ cjstribi;;;i;c ~/c,;-~c ';fie a;rcrzf 1, r;+ -2- \cil!t,t~ - - -.*-.--* dL.i.if+ , * C ' -.

distri buclon i s SI.IOA~~ i l i r ~ ~ ~ i ) cojor cooing i!7 i i a i i r t I Id , I t 7 ( ? pro$:-am an$

-

data t a b i e j are sr~own it; aooenaix 3, I his oroaram i s uaset't (]!-I e;~!fi;rica: . .

d a t a ant: ~ 4 5 qec!rrierr;c ztr\l::r;j!-e ! ; ; ',!-,$ a::-::raf;.

;; s;-lotli:-j ~5 :;.:a:

-

the proarars ~ 7 e ' ; e ~ 15 13: j - j ~ W O ~ S ; c a ~ e scenaric i r!i.s p - ~ q r a m g;lies . ;;:-:- . . -.. .

. .

Figure MS i ; i rje S P Q ~ , . . v tf~:a; t.;-<e $ . ) ~ ~ a ~ a r ; i j ~ y + r cfian~es f ; - ~ b - - ~ jamifizr- ~ $ 1 , '.

edges, the ncss, the !r,ietg, an: t ? ! ~ t!$y:;cal tall: , .-- -., -.-+ r c - . - . - . . . r . C . ! ,-...-..-.- g : .- ! - I ~ I ~ ~ ~ , : ~ ~ ~ i ,< : ;. -+-. -;- but ~ l t i l 2 SDs~i2i bjac!: <cayriG, :!?,-E C,r, IT+ 3 e - i I . . .._. _... -. ._. _: . .-. .

.' '

The m a t e r l a ] c>n t ~ l e tr!;cy,r!es? tr3r.r; . !

v;?l) a\!erar;e !!-:. t i \ ... J . , .> !I-! - . .

The t i t a n l u m ailuminlde can withstan:: terriperar,!jres c f ~3 t c 15612 F .

which 1 9 :)cry he?efjc,;al!.Fiei ! j : r.,ec?use 29 F ; Q G ~ $ "z.7 S ~ Q W ~ :??: the next o b , j e c t ? \ ~ e i s t o gict;c a coc\ling system t , ~ use, barrG\>:l~~q 0 6 ~ ; z i 132 choices there seems

pe three rjsef [J] choices ( f i ~ y - e : ~ .4 pjS:,qSssp;SS>

I -.

Figure MSS sno\*:s a pane! con? luurzti~n for t h e inlet.

t v!ic; !S trte or::..;. 2r?2

d.C t nU , % " "' ; >. .-. -.--; - " -. -.: 2 , --

>?.*! ! s ( : . i n I , t % - .-.,: I ? k

pane], the nyarza~efi t~let-1 acts as a ~ e a : sick: ?y*rc

, . s . , . . : ' , I . . ,.- b.,...,#,, i tnen the T1!40?30en 15 /rlrc!JOr: 3 neat e:<cfiarlger WFjer.2 jt i.; ~ r ! e t ' is. . .. - .. : \ ' ; , : :

The nose !s ver.)f ror:,~'lex \,vfierl It cor.r!es t o heatlna. Tne <-:aze:ey ci

!t?e nose an2 t,ne curvzture ',Re cone a l l a(-j(-j tc:, tr!e C C I ; ~ : ; ~ ~ , ~ ! ~ L ~ C ' tr'+ - - i.. L t 3-.

3 ; + 3 6 e i ~ : ? , " ~ ~ f p . r . > tr. -.

' " . . ..,".. . : !-.: .:..- -. _. -..- . , . L b . b ._ -. - ,.

- Ld . bl)z \js? 0 ' 2 i'cs? czp 1s t h e p r ~ p ~ y <-,T;:;Z~

- 3

cap 15 COMc';;'zeQ Q : 2 JT:A: c z r ~ c c c ~ c s c ~ l t e ! I % : $ . - J KJ.. ..-I \;p,-..\,. $ :,: ':rrC,-,y .- ... ,., ci "'.,- .- Ourab!e, D ! ! J ~ [r!: reusabi !it!, ;;f tn!s czp 1s a n a j o r a ~ \ , p ~ < ~ ~ ~ , .cCS: i,,21:ze The \ e z $ l x egges ~ ~ ~ i ; ~ ~ ~ t h e r,-jgst work., aria pre A < % . 7r-g .. . . . , .--..-.+-. iiit2:!,*:. .-.-.-..-.: ; , . ! . . . ::-.. ..---.

'.- .. . . , . .

The wings a . : o . e r t i c a j t a i l "qijlre heatlpa . . , W I J ~ z i a y ? ci;8>tor;-. .-.? .- i. .*.. . T~~ . id leading eapez. car: ce c o ~ i e d t \ \ ~ tittc metflobs, L )P$ V=.A . . . , zp2s:.i,r.:, : > . , .=+-.:Pv: .-..,. ' . . .

- ~ 0 0 l i n ~ w sy5Ler:'i ! r!e o ~ ; ~ c ~ ! \ , i ~ 2 i lr!!~_. c ; v s ~ ~ ~ T ) 15 t ~ 2 ~ .:f i ? ~ : - ; ? < : !s t.2 :y cJjy&/e$ I,?;-..?;*;<!-.: 2 z...??:.; T i e ; ; ; ;::;: 3 .:.TT;:-:T< < - . : ; -pi: ;A;:~:-:.:+-..-. - . - s - . - - 7 3 . . . . - .-* ....,. "i::. . - i i . : : - - " ' : - - . ; i . '* . . . . . - . . .. . . -. .- ~ R ! G ~ N A % PAGE ri>i>\?qr! .,.-. % . ) , % . . ~.r,e +<!FIG q : - , ~ t , *..... t t - , + ? ~ ? ? :q *yip:-.- . - - . . . . , . . . . . , . . . . i .-:,. -!..OPT . . . . . , & ! ' ! , , ~ , J ; ~ ~ \ J ~ ~ l ! j t ~ ~ 5 :$ : ! 5 5 ~ ; OF P m R QkfAli,m

exchanger, the system then s t a r t s over again i n a contior~ous cyc!?. The

maJor.ar&aet.age of this type ~f System 1s $2; ';he ';eae;n;: . . ~ G G E ._ raJ;i czn

be very =;rslall, tliA t h e rslaj~r Cfi$ad~ar\tage 1s tt-!at !I i s i:nt~rgivin::: to iocai failure.

The secona type of leading edge system is a l u b e sysiem, Fiaure M S .

The concept Deh;nd thls system Is that the ieaainr? w. ecae %I wotlld oe cornposeo

of a carbon-csrbcjn composite which is rneskeg or. ern!;ecae$ t + q h Iupes

that run ti?;'o:ignc~~. tne ieadirtr,, edges, Tr!e tt~nes f!'i!e$ w!tr: 2 j i ~ l ; i d run

through the leacling edge acting heat sir;::,, :her; t,ne ~.:Q!,J:Q if trar;sgcrterj

to a heat exchanger where the cycle s t a r t s ail over amiri. Tne a$u2ritaae . , .

t o this systerr~ 1s that t h e cooling systerri caii a c t ass'. I:!? i t a g i n g edpe, even t0 six f e e t past, the leadTn~ edge, onto t h e win:!? \+&:-ete ?r.,:s rieeaea.

These t w o types of cooilna ., have aooa ./ po!nts! oijt. t,ke cer;!cj?na *- factrjr

i s that i n the carpon-carbon composite tuue c ~ o l i n p Ice 1393 97 c o o i ~ n r ! 3

-.

Past the leading edge outways any aspect that the s::ray cool:tng t7z.z. ! ne

carbon-carbcn tube cooling will act for the i ~ r s t filteer! ieet. of' the winr; . , I

a f t e r that, areas that needed cooling can be cool ea w It t-~o~t, carbon-carzor), just tube cooling w i l l be used aPter(Ref. 3).

The vertical tail i s quite similar to the leadinu .I. eeges o f the wing,

except tha': irle maxlrnuirn terrlperatures expected w l l ]

~n the Qrder of

2000 F; The t a i l will be coolea w - f t t ~ i u ~ t , 2 ~ j ~ t : , ) e ~ Q D ? ~ , ~ ~ j j p g . , s ~ J ' s ~ ~ ~ ~ ! , f

With Carbon-~csrtjo:; just a t ttle f jrst f 001 of IT!^ ~ e r t l ~ z j taj!

DRIQjrg&g* p;&;< a>;:

w PrnR QLk,&,;.:;y,,- 4 x

!

The fuel tanks are very d i f f i c u l t t o keep at the proper temperature.

On one side of the fuei ~ a n k the temgerature i s approx~rnately -41 g F, w h i l e on the othersicie the ternperz-ture 1:s approxlrnately !ROO F. There are t w o types cf purge syslerris that can be vsed.

The f i r s t purge system i s a K2 purge system (Figure MS6). The major advantage of this t y p e of systen 1s :hat you can use available Insulations

and It i s rezsonably inexpensive. I t s ma joc Oisadva~tages Is tnat it has

The 5eCOna purge system 1s [ne C o p pu;pe . . syfterri (Figiit-2 M57). Ttle

major advzntage cf this type o f system i s that it iirriits liquid hydrogeri boll off an0 there i s no liquid phase. I t s major disadvantages i s that there are c o r ~ ~ i e x grouncl har~d;;ng r e q ~ i r e m ? n l s a n d it t o i s a i f f icul: ',o ;nspec:'., dioxide 1s b e t l e r suited for the heating and cooling, and also because it l i m i t s liquid nydrogen #oil off: i ~ q u i r l hydrogen Ooii off i s of major importance i n deciding what t o use, because you could ultimately lose 36

Percent of your f u e l t o hydrogen b o i l o f f . The additicn of a vapor shield on

the tank.

w i i \ further decrease t'ne boiloff inside the tar\lc(~ef. 3).

The cholce of which coolant t o use f o r the cooiirq systems f a r the

leading e d g 6 \wzs s l r n ~ i e t o cnaosi: The only liquid w i t h a hiah .d specific heat 50 a5 to au~rjru 1'71rjr.e enerav . , . 15 ' i i t i l i ~ r f ~ . The other 1 iquias

comparslon are nor. even dlose

!t, will be easy t o u;? anr; 1s the mgj; eff lcient.

Fuel Tank - W a t l o n Thickness For a

E

By John 0on Tong & Gerry Fuerst In hypersonic flight, it i s necessarily t o have t o have sufficient insulation around the tank t o maintain the hydrogen i n a liquid fan-1-1. A slight increase in temperature of liquid-hydrogen fuel may results i n tremendous increase i n pressure. For example, hydrogen a t i t s 1 iquid state at -4232F has a density of 70.1 g/liter but at i t s vapor state, it has 1.3 glliter. i f insulation i s not used adequately, the tank w i l l explode. It i s our goal to design an insulation system that M!l insulate the fuel used for a cruising time of approximately 20 minutes.

The derivation of the equation used to calculati the thickness o f insulation was taken from NASA Technical Memorandum Paper TM X-2025 by Hark 0. Ardema. The author used standard analytical techniques to develop procedures for calculating the insulation's thickness. The assumptions that were used are : 1. Only heat transfer by conduction i s considered since radiation and convection effects are negligible compared w i t h conduction.

2. Thickness of insulation used i s much smaller than the diameter of the fuselage.

3. Conductlvi t y of insulation i s much smaller than the conductivi ti^ c s i

s i i structural elements.

I 4. Thermal constants are independent of time, temperature, and position.

5. Insulation i s continuous and homogeneous.

6. The temperature a t the wall of the inner fuselage i s the same as the temperature of the liquid-hydrogen fuel.

7. Exterior surface of fuselage i s exposed t o square temperature pulse.

With the above assumptions, the following equation i s obtained: where the definitlbn of the symbols used are as f 0 l l o ~ ' s :

- hydrogen heat of transformation, (Btu/ft 3)

h f ! 3

k - diffusivity, (fta2/hr)

K - insulationconductivity,(Btu/hr-ft-QF)

Ls - tank thickness,(ft)

tf - cruise time,(hr)

TH - liquid hydrogen fuel tempersture,(gF)

To - i n i t i a l exterior surface temperature,(gF)

Ts - cruise exterior surface temperature,(gF)

4 3 - insulation densi ty,(l b/ft'3)

@ , - tank density,(i b/f t 3)

@ , , - hydrogen fuel dens1 ty,(lb/ftJ); It can be seen from the equation that for fixed materials and temperatures, the optimum insulation thickness i s proportional to the square root of the cruise time. The above equation can be simplified further i f we consider the steady-state condition. The steady-state equation can be obtained by setting the initial exterior temperature equal to the cruise exterior temperature. The equation i s as fotlows:

For our design, the insulation must keep the hydrogen fuel at -

43SGF to ensure that it w i l l remain i n i t s liquid state. Furthermore, the cruise exterior temperature i s approximated to b'e 120EF. The material that was chosen for the insulation i s Silica Fibers. In the calculation of the insulation thickness, the thickness of insulation was found t o be 0.34 ft. The weight of this insulation i s approxi mate1 y 450 I bs.

The thickness of insulation can be reduced further i f a bo,t!sr / insulaticn i s used. One such insulation i s Quartz Fibcr which has a lower density (.66 at 7 0 @ F ) , and a greater maximum temperature l i m i t (25002F). The reason we have not included such fiber i n the tiesigri was that we wer e uriutrie tu ub t u i r ~ i 1s lher rr~ai vurrslar~ts.

We strongly believe that there are better insulation material 3 o t h ~ i iiidri thirse rr~entioned above. I f further inforrrsatiofi on insulation materials can be obtained, the thickness of insulation w i l l reduced substantially.

Cost Analysis Thomas Greiner The cost analysis method used i n determining the total cost of the hypersonic aircraft design was found i n a book by Nicolai, Fundamentals of Aircraft Design (see references) and refered a l l dollar amounts t o the cost in the year 1970. The final cost estimate was multiplied by the inflation factor of 2.35 t o adjust for the current year 1990. The analysis based the ccst or, three main parameters, 1 ) AMPR W e l ~ h t w h ~ c h i s the weight of the dry aircraft minus the we!$-~t of the engines, the starter, a l l cooling fluids, wheels, brzkes, ~ n ~ - t r . t , il i , l , - l Llrcents, a:;%! ia:-; power and Satteries. The value used was an average c f tr;e qold desian team and the WAATS program weight estimate, A"tPR= 1 8526 Ibs.

2 ) S w r i ~ c h IS the maximum speed a t the "best" altitude in knots.

This description 1 s vague therefore the velocity for Mach 6 at 80,000 f e e t was Gsed due t o the large avai lable thrust, S=5 178.22 knots

3) O which i s the combined number of test aircraft and the number

to 5e bui 1 t durincj productior:. Since there IS to be only one test aircraft t o 5e 3:;llt C=1,

ljslnc; tt;e eq:lat!Gn supplied ir, the book the cost o f enqifieerlng hours

..',a8- I,,,z :rte ?2r:)e5: c c ; ~ t at 1 7 Oflli~n dotlars, see figure costLt w h ~ l e the

s::'?ilest $;<;5?'ze :s t!;e n?a$2factui-?;lg acd n l a t e r i a i cost a t 1 1 nlilliori

dcllars. The nzte!-:als estimate apgears to be t o o low due to the unique

at!::;~s needen t c socl ar;d maintain structural integrity in the intense heat.

of r~yl;ersoi;ic flight.

The t o t a l prtce of the aircraft i s 3.3 b i l l ~ o n dollars which 1s most

4 9

likely a gross underestimate. The intial development costs o f the 0-2 Stealth bomber was approximately 40 b i l l i o n dollars. Although the hypersonic a i r c r a f t would not need the technology of the 8-2 bomber it stands as a good indication of the expense of applying new technologies t o a i r c r a f t design. This a i r c r a f t would use the s t a t e of the a r t technologies in structural composites, ceranlics i n cool~ng, and propulsiot7 t o achelve i t s mlssion requirements. This t o t a l cost would be spread over a period of approximately f i v e years.

WIND L HODEL by Bob Stonebraker A 1/65 scale model of the preliminary design was built for tunnel testing and to aid presentations. This scale was selected to match that of other designs for relative comparison and to avoid overloading the tunnel measuring device with too large of a wing area. The model was constructed of wood and finished with black pigmented lacquer. Pine was chosen over balsa or fiber-glassed styrofoam for reasons of better durability and lower cost. Lacquer was chosen as the finish to allow polishing and provide a smooth, low drag surface. Construction took place only after approval of the preliminary three-view drawing.

The model will be used to study the longitudinal stability and landing characteristics of the design. Tunnel testing will yield lift, drag and pitching moment for various angles of attack.

Reynolds numbers up to 1.8 million can be obtained in the available tunnel with reference to the longitudinal dimension of the vehicle.

Since this is a preliminary design, it is subject to change.

Data from this model will be used in an additional design iteration and another model will be built and tested to incorporate changes.

Conc 1 us i on This report has described and presented many concepts on how and why a hypersonic aircraft should be designed similar to the gold design for the given mission requirements.

This paper attempted to f i n d answers to questions concerning the areas of aerodynamics, thermodynamics, structural design, and aircraft configuration in a hypersonic enviroment. It can be concluded that these major design concerns have been addressed but the aircraft st i 11 remains in tt7e ezrly stage o f development.

Some ;roS?ems as inlet design, fuel reduction, and dynamic stability s t i l l need t c be resolved for the hypersonic aircraft. These problems c~trrently exlst within the aerospace industry and w i l l have to be solved SeTore hyperscnic flight t o be commonplace References Anderson, John 0. l ntroduct ion t o Fl ioht. McGraw-Hi 11 Book Company, New York, 1985.

Ardema, Mark D. NASA Technival Memorandum P a ~ e r TM X-2025.

Carriero,L. E., Preliminary Design and Weights Analysis Program for A ? ~ o s D ~ c ~ \/chicles, 1 Lt. ,Wright Research and Development Center A i r Force Systems Command, Wright-Patterson AFB, OH., WRDC-TR-90-2005.

DATCOM, United States A i r Force, Wright-Patterson Air Force Base, *Revised 1 975.

Ellison, D. E.,"U.S.A.F, Stability and Control Handbook (DATCOM)," A i r Force F ? ight Dynamics Lzboratory, AFFDL/FDCC, Wright-Pat terson AFB, Ohio, August 1968.

Glat:,C R. Weichts Analysis C f Advarlced Trans~ortation Svstems, Aeroghysics Research Corporation, Hampton,Va. ,N.A.S.A. CR-2420.

I i i 11 h Peterson. Mechanics of Thermodynamics of Propulsion.

AdGIson-Wesley P~blishing Co., Reading, Massachusetts, 1965.

Nicolzi, L. M., Fl~ndarnentals of Aircraft Desian, University of Dayton , 32j.'tcc, Oh13 , I 954.

Flcskarr,, J. Aimlane F ? ight Dynamics and Automatic F l i Roskom Aviztio:: and Efigineerong Corp., 1979.

::ern ,B. & Walter I l l q h John Buckley., Structural Materials : o r Hycersonic Aircraft., Langley Research Center, NASA Report 74f.173077, 1 974.

5'3 Stone, 3. €. & L. C. Koch, H y u c r ~ o n i c A i r f r a m e Structure Tcchnoloav.Need3 and F l iuht Test Retlulreinents.. NASA Center, NASA Report 3 1 30, ~ u l y 1970.

Q Based On R-6 at 75,000 ft.

- CLIMB ANGLE-9 DEGREES Uint 1909.8'43 M-.8-779.353FT/S Altitude Temp. Density Q U N CFt, 3 CR) Cslug/ftA3) CSLUGISa2 CFT/S)

Mach 4# - - ; A l t i t u d e .-.',--:. ::;-Mass +flow . . : '. Area "

.-'Corrected Area Y . . - - - . - .

- . .

. . f t ) . : - . s:.(lb/k;cf - , ( f t * * 2 ) t f t * * 2 ) ( f t * * 2 ) - Table IN3 : RAMP LENGTHS VS. MACH NUMBER.

~ i ~ ~ ~ @ k ~ • t;!c&.G8&;- -:;.-? 6 pi/ C y f b r-+'

. - . ; ; ..$&& G7-&3F;?: . SF+.;-- : .

'1.40 ,i:+&:p::,~..

. . . .: <:&$%;-:.% . . . ..-<.' .'. ,

------------------------------------------------------------------------------

THETA BETA M ( 1 ) M ( I + l ) P O H , . . , ; ;:-:- PR TR XT . - . .

-------------------------------------------------<----.-------------------------

c- 5 - 2 3 &a. 23 1.400 1.205 .99815 1.3005 1.0785 2.80 ............................. ...........................................

TPOR TPR . TTR TPOTH TPTR TTTR M N T .

.99815 1.3005 ' 1.0785 .99043 1.9881 1.2203 .8388 Mach # = 2.00 ------------------------------------,,,,----------------------&--------------- THETA BETA M ( I ) M ( I + l > PQR P R T H XT I

--------------------------------------------------------------------------------

5.25 .

34.53 2.000 1.812 .99758 1.3331 1.0864 5.45 5.16 .

38.32 1.812 1.634 -99806 1.3063 1.0799 4.75 --r

1 . 4 1 50.28 1.634 1.261 . 98607 1.6773 1. 1639 2 . . .12

*

----------------------------- 99********Y*******+)C***~Y**.M***8*8~K9*.fi.+*.R**

TPOH TPH TTH TPQTR TPTR TTTR MNP .98 178 2.9209 1.3655 ,96753 4.9344 1.5928 .8064 Mach # = 3.00 ...............................................................................

THETA BETA M ( I ) P l i I + l ) POI3 , P H TR XT ------------__----_---------- 9**+8.fi.99**9***8**~&99)C**+*Si.**9*99*+.E*ii-.ii.JI.**** TPC)H PPH TTH TPQTR TPTF? TT'TF: MNT .92452 li:). t647 2. (31 1 1 .88575 22.6281 2. 5.24~1) --..

. / 2.95

.. .. .. ... .. .. .. .. .. .. .. .. .. .. ... .. .

F . : . F Ti7 X 1.

THE'Tfi BETA M i I ) M i 1 - i - 1 ) PBR

___-__---_-------------------- ********.k**********+**+.+********.E*.:*.**n.*.%+*

TPiJTF! TP'TR 'TTTF: MhIT TPOH TPH TTR -. n = - . . . . . . .-,. ....

-- 7 ' > c ~ f i , . a&c-"' 83.6254 . 3 . c , 9-7'"; .

-86929 -1 . . : , .-? . : : , c\ . : , . LLdb 2, d . , * . . '. ~ F L L , )

--* ---"- -.-----------.----.-------------.-.--.-----.-------" -.-..--.------.--------.-----.-.-- -.-- ----- --.---- -.. * I l-iETf? B E T A P i i I ) M i l + I l POR PR T F : X T I

Mach # = 6 . Ct i:)

.. ....

~'p;-ji-: .. I - . r.'F( , . . y . f. 1:;; i ,- yr<:).'l'R -r 1 : ' I F~ . --. - - I ._ I I i I t? 8 . ;,I "I" ...- . .

.." ..-v.

...... . . . . . - * * .7

; . . , ,.. " I--.*'-' ( 3 K"

7.i 3,52 , : , . . . : , . j , p , ' ; : , :j 1 fi . ,,.j '7 2: tr . ti '3 5 y 1

8 n ._ .*_ 7 L ,.:I / " . . : , L , .L, . /, , / 45

TABLES

TABLE AD1 Components o f the drag coefficient for the wing a t d i f f e r e n t

"ch numbers.

TABLE AD2 C o m p o n e n t s of t h e d r a g c o e f f i c i e n t f o r the body a t d i f f e r e n t Mach n u m b e r s .

TABLE A D 3 CDo f o r t h e d i f f e r e n t Mach numbers.

.

TABLE AD4 Shows CL f o r the d i f f e r e n t Mach numbers.

TABLE AD5 CL Irad, CL /drgree, and K f o r d i f f e r e n t Mach numbers.

TABLE AD6 CL, CD, and CL/CD f o r o u r m i s s i o n p r o f i l e .

MACH .8 Cm cg A n g l e OF A t t a c k C L C D ............................................................

. .0009005 0.0 . 0.0 .0129885

- , 096966 3.959 0.1 ,016090

- .099903 6,917 0.2 ,025900

-. 191908 10.376 0.3 . 090920

- ,187989 13.835 0.9

,062690

- ,239129 17.293 0.5 .030569

- .279899 20,752 0.6 ,129705

- ,325128 29,211

0.7 ,165097

- .369982 27.669 0.8 ,211596

- .919905

31.128 ' 0.9 ,269351

- ,958398 39. 586

1 .O - ,323312

............................................................

Table 5 1 : &Go) V 5 . d , C L , C b i H = , P ) MACH 2 Cm cg A n g l e of A t t a c k C L C D ............................................................

.0019975 0.0 0.0 ,028809

- ,0957967 2.563 0.1 ,033679

- ,0528155 5.126 0.2 , 098289

-, 1392088 7.689 0.3 ,072639

- ,1899266 10.252 0.9 ,106729

- ,2299690 0.5 .150559

12.815

- ,2793360 15,378 0.6 ,209129

- ,3180279 17.991 0.7 ,267939

- ,3610939 20.509 0.8 .390989

- ,9033839

23.067 0.9 . 923279

- . 9950'489

25,630 1.0 , 515809 ............................................................

Table S Z ! &a? VS, dl L L , ( ~ ( f i z z ) MACH 10 Cm cg A n g l e of A t t a c k . C L CD .............................................................

.0010761 0.0 0.0 ,015517

- .003715 1 ,909 0.01 .01576

- ,008Lf72 2.816

0.02 ,01650

-. 013195 9,223 0.03 .01773

- ,017889 5,631 0.09 .0199S

- ,022539, 7.039 0.05 ,02166

-,027160 . 8.Lf97 0.06 .02936

- ,031796 9,859 0.07 .02756

- ,036299 11.262 0.08 ,03129

- . OY0817 12.670 0.09 .03592

- ,095302 19.078 0.10 .09009

- ,088272 28.155 0.20 ,11380

- .12783Lf 92.233 0.30 ,23665

- ,163989 56,310 0.90 . 90869

- ,196735 70.388 0.50 ,62977

- ,226079 89 ,966 0.60 .90009

.............................................................

Tuble 5 3 : c m c q Vs. 4, C A , c l ) ( f i = 1 0 ) Uehicle Summary Uehicle Name: tscram cle Discription: UrlANNED SCRAMJET TESTBED File = E:GOLD.DAT Output File = B:GOLD.OUT Date = 01-01-1980 Date = 01-01-1980 Tim5 = 00:01:27 Time = 00:03:13 .

t h =

8 73 Height - Span = 32 TRoot - 5.1

d y -

1,570 Swing = 508 SUert = 51 SHorz = 0 b e r OF: EarnJets = 5 of:

- 100,000

st LOX = ~ t s : G T O W = LfLf.133 Pagload = 0 Ory = 33,303 Landing = 3 Y , 013 Entry - 3'3,093 .

AR a 1.980 T 'GTOW a 11.33 T/S = 385.39 Wsin%t Statement ................................................. ------------ -------- Group 1: 42r0 surfaces Wing Vertical Horizontal Fairing Group 2: Eody structure . 12,821 Easic body 6 , 1 8 2 Secondary 1,539 Thrust 3,199 Integral Fuel tanks 1,906 Integral Ox tanks 0 Group 3: Thermal Protection System Uehicle insulation Cover panels Group ? : Launch and Recovery Gear Launch gear Landing gear Group 5 : Propulsion Rocket engines *..I Ramjets T~rrboram jet Nonstructural Fuel tank Nonstructural Ox tank Fuel tank insulation Ox tank insulatiqn Fuel system O;:idizer system Pressurization system Inlets Weight statement For:tscram Page 2 Group 6: Orisntation Control System 89'4 Engine gimbal system Attitude control system Aerodynamic controls Seperation system ACS tankage Group 8: Power supply Electrical System Hydraulic/Pneumatic Sys Group 10: Avionics Group 1'4: Crew Provisions Uehicle Dry Weight' Group 17: Crew 35 Group 18: Payload 0 Group 21: Residual Propellant 75 Trapped Fuel 75 Trapped Oxidizer 0

-------------

Landing Weight 3'3,013 Group 22: Reserve Propellants 80 Fuel 80 Oxidizer 0 ACS Fuel 0 4CS oxidizer 0 ------------- Entry Weight 3'4, 093 Group 23: Inflight Losses Fuel Oxidizer Group 25: Main Propellants Fuel Oxidizer 4yos.s Weight '3'3,133 Gold Weight Estimate Thomas Greiner Structure- Skin 7955 lb.

Internal 2386 lb.

Total 10,341 Ib.

T.F li.J 6500 It;. 65(>(] ! 9 Total 18,500 Ib.

Electrical Computers 75 l b Batteries 300 Ib ?afid!n$ Gear 200 Ib. Empty Weight 36,274 I b Gross Weight 47,774 10 !"el i 1,50C It;.

Figure: Weight2 R o c k e t B o o s t e r F u e l E s t i m a t e f o r H y p e r s o n i c V e h i c l e A i r c r a f t w e i g h t 47000 l b E s t i m a t e d b o o s t e r w e i g h t 15000 l b E s t i m a t e d t o t a l w e i g h t 62000 l b .

S p e c i f i c I m p u l s e 240 s lg a c c e l e r a t i o n .

T o t a l R o c k e t Mach V e l T h r u s t t t W-dot F u e l SFC # ( f t / s > ( l b ) ( s ( s ) ( l b / s ) (11) S e c o n d s ........................................................................

0 0 0 0.8 774.35 0 0 0.000099 1 967.94 62000 6.012111 6.012111 258.3333 1553.128 0.0002 1.2 1161.53 60436.18 6.012111 12.02422 251.8174 1513.954 0.000196 1.5 1451.913 58888.26 9.018105 21.04232 245.3677 2212.752 0.000194 2 1935.854 56610.25 15.03015 36.07248 235.8760 3545.254 0.00021 2.5 2419.85 52887.42 15.03 51.10248 220.3642 3312.075 0.00021% F i g u r e : B o o s t e r 2 TFRJ TFRJ A/C r o c k e t S e c t i o n F u e l F u e l Weight Volume l e n g t h Drag ( l b / s ) ( l b . ) ( f t A 3 ) f t ( l b s . )

----------------- ........................... ----------

7177 0.710523 0 62000 0 0 0 8886.99 1.777398 10.68591 60436.18 15.30176 3.117252 74.55013 14413.38 2.825022 33.96870 58888.26 14.91580 3.038626 71.21642 15984 3.100896 65.25007 56610.25 21.80051 4.441168 103.0257 23442 4.92282 177.5783 52887.42 34.92861 7.115604 178.6305 31258 6.845502 349.8221 49225.52 32.63128 6.647595 174.0826 I F i g u r e : B o o s t e r 2 c o n t i n u e d .

Q based on M=6 at 70,000 CLIMB ANGLE=4 DEGREES Vin t 1404.843 M=.8=774.353FT/S Altitude Temp. Density €2 V M ( R > (slug/ftA3) (SLUG/S"2 (FT/S) (ft.)

..........................................................

389.99 0.000587 774.3537 0.8 40000 0.000587 967.9421 1 40000 389.99 40000 389.99 0.000587 1161.530 1.2 40000 389.99 0.000587 1451.913 . 1.5 40000 389.99 0.000587 1935.884 2 C) & ..5 40000 389.99 0.000587 2419.855 40000 389.99 0.000587 2359.837 2834.595 2.925786 45000 389.99 0.000462 2359.837 3195.274 3.301100 50000 389.99 0.000364 2359.837 3601.297 3.720571 55000 389.99 0.000287 2359.337 4058.621 4.193041 60000 389.99 0.000226 2359.837 4573.796 4.725278 65000 389.99 0.000178 2359.837 5154.053 5.324754 70000 389.99 0.000140 2359.837 ,5807.651 5.999999 75000 389.99 0,000110 5807.651 5.999999

80000 389.99 o . boo087 5807.651 5.999999

85000 394.32 0.000068 5839.803 5.999999 90000 402.48 0.000053 5899.918 5.999999 95000 410.64 0.00004 1 5959.426 5.999999 100000 418.79 0.0000:32 6018.274 5.999999 lUU000 418.79 0.000032 6519.798 6.5 lOO00C 418.79 0.000032 7021.321 7 100000 418.79 0.000032 7522.844 7.5 lOOOQO 418.79 0.000032 8024.367 5 100000 4 18.79 0.000032 8525.890 8.5 100000 415.79 0.000032 9027.413 9 1000UO 4 18.79 0.000032 9528.936 9.5 4 18.79 0.000032 10030.45 10 100000 100000 418.79 0.000032 10030.45 10 F i g u r e : P r o f i l e 1 T o t a l T o t a l T o t a l d i s t t t x Dist D i s t a c c G ( a n g l e 4)(seconds)(seconds) (ft) (ft) (miles) f t / s 6 2 ........................................................................

0.733289 0 0 5 5 3871.768 3871.768 9.679421 0.300603 20 25 17422.95 21294.72 4.033092 20 4 5 21294.72 42589.45 8.066184 9.679421 0.300603 1 3 . 0 1 5 8 8 1 4 . 5 1 9 1 3 0.450904 20 6 5 26134.43 68723.89 0.751507 20 8 5 33877.97 102601.8 19.43217 24.19855 24.19855 0.751507 20 105 43557.39 146159.2 27.68167 t i m e m i n u t e s x - d i s t m i l e s ....................................

939.5427 15.65904 5217306. 9 8 3 . 1 2 6 2 M=6 t o 10 t i m e m i n u t e s x - d i s t m i l e s ------------------------------------ 626 10.43333 5345231. 1012.354 F i g u r e : P r o f i i e l h ' l 7 a I 7717 , % 1 T h r u s t Drag T h r u s t SFC SFC l b / s Weight A/C b u r n e d Weight ace r e q h o u r s e c o n d s --------------- -------- .................................................

45000 0 5977 5977 0.357 0.000099 0.592719 2.963595 0.721 0.000200 4.161421 83.22843 44997.03 13526.25 7252 20778.25 44913.E0 0.709 0.000196 4.949456 98.98913 13501.23 11630 25131.23 0.7 0.000194 6.427597 128.5519 44814.81 20207.2i 12849 33056.21 18795 52377.05 0.8 0.000222 11,63935 232.7870 44686.26 33582.08 0.78 0.000216 12.66454 253.2969 44453.47 33407.13 25046 58453.13 20553.09 12849.4 36571.53 0.63 0.000175 6.452518 176.0325 44200.13 20725.63 11500.0 35296.59 0.7 0.000194 6.863227 163.1603 44024.15 26220.89 11000.0 40280.48 0.73 0.000202 8.167986 172.2824 43860.99 33154.72 10153.7 46355.98 0.75 0.000208 9.657497 180.7408 43688.70 41916.43 9000.0 53931.39 0.845 0.000234 12.66359 210.3005 43507.96 52945.65 1OOOO.C 65965.94 1 0.000277 13.32387 270.0326 43297.66 66782.81 10158.0 79942.26 1.063 0.000295 23.60517 305.7058 43027.63 11300.0 14279.91 1 0.000277 3.366644 48.95629 42718.92 11300.0 14276.50 1.02 0.000283 4.045009 49.92347 42669.97 3457.624 10990.0 17420.64 1.03 0.000286 4.984240 61.34564 42620.04 6506.606 10750.0 20225.34 1.043 0.000290 5.870969 71.69152 42558.70 6495.645 10670. I 1 20129.38 1.045 0.000290 5.843113 70.63167 42487.01 6476.899 10652.0 20087.71 1.12 0.000311 6.249311 74.79773 42416.37 15336.78 10652 25988.78 2 0.000555 14.43821 1241.686 42341.53 14878.42 11233 26111.42 2 0.000555 14.50634 1247.545 41099.89 5856.467 11790 20646.46 2 0.000555 11.47025 1605.836 39852.34 8499.1632 12292 20791.16 2 0.000555 11.55064 1617.090 38246.51 8139.354 12832 20971.35 ' 2 0.000555 11.65075 1631.105 36629.42 7776.427 13406 21152.42 15 0 , 0 ~ 3 - 5 5 J.J 11.76801 1647.522 34998.31 7409.848 14007 21416.84 2 0.000555 11.89824 1665.754 33350.79 7038.647 147128 21746.64 2 0.000555 12.08147 1691.405 31635.03 14703 14728 2 C.000555 8.171111 1961.066 29999.63 f u e l Vo lurne ------------------ 15006.36 3387.441 F i g u r e : P r c f i l e l C o n t i n u e d

FIG AD2

/STRUCTURAL SKIN

STRUCTURAL I

SKIN--\ VIEW A-A

POTENTIAL I POTENTIAL

ADVANTAGES DISADVANTAGES/LIMI TA TIONS

e USE OF LOW TEMPERATURE METALS WEIGHT 0 REASONABLE COST RELIABILITY LEADING EDGE RADIUS REQUIREMENT COOLANT RETURN V I A a UPPER PANEL--\

COOLED END C A P 7 \

COOLANT SPRAY BAR COOLANT RETURN VIA TITANIUM CONCEPT .

SUPER PLASTICALLY

COOLANT

FORMED SKIN 7

PASSAGE DIFFUSION BONDED

STIFFENER

VIEW A-A TYPICAL COOLED PANEL CONNGURA TIONS STRINGER-STIFFENED INGER-STIFFENED SKIN HONEYCOMB SANDWICH INSULATEDICOOLED PANEL PLATE-FIN SAIJDWICH SUPPLY MAN1 F RETURN MANIFOLD LIQUID HYDROGEN EXCHANGER b TO ENGINE FROM TANK POTENTIAL POTENTIAL ADVANTAGES DISADVANTAGES/LIMfTA T/ONS REQUIRES LARGE FUEL HEAT SINK USE OF ALUMINUM MATERIALS .4 COMPLEX SYSTEM ARRANGEMENT e LOW WEIGHT MAY REQUIRE ADDITIONAL THERMAL VOLUMETRIC EFFICIENCY PROTECTION DEVELOPMENT Total Develo~ment and Fvaluation Airframe Engineering Development Support Flight Test A i r c r a f t Englnes & Avlonlc Manufacturing Labor Material & Equipment Tooling Quality Control Flight Test Operations 32,259,4 1 0.80 Test Facilities 0.00

Total $3,6 i 5,972,876.80

Figure: Cost 1

APPENDIX A

WIHG: SUBSOPl l c: =C = Cf [ l + 2 * t / c + l 0 0 * ( t / c l 4 1 Swet/Srer CDO D f

CDf : Skin f r l c t l o n drag c o e f f i c i e n t w h i c h i s constant i n t h e

subsonic region.

: Turbulent f l a t p l a t e s k i n f r i c t i o n c o e f f i c i e n t , C f (Nicolai, Figure E2).

TRANSON I C: CDo=CDf+ CDoZCf [ 1 + t i c 1 Swet/Sref +ACDo b CDo : Wave drag c o e f f i c i e n t (Nicolai, Figure I 1.10).

SUPERSON1 C:

For w i n g s w i t h round-nosed a i r f o i l sections and supersonic leading

edge use : CDo'CDftCDlef [ I 6 / 3 / ~ ] * ( t/c12 *Swet/Sref C D ~ = C ~ *Swet/Sref C f = I C f c / C f iIXCfi

-(2.56/ b)*[r, e * ~ ~ * c o s 2 ~ , ~ / [ / -t -

' ~ l e - B o o ' ' 1 45Z/Jk;

C f c / C f i : Account f o r c o m p r e s s i b i l i t y e f f e c t s above Mach * I

(Datcorn, Figure 4.1.5.1-1 5 ) .

: Leading edge bluntness term.

Cole The CDo f o r t h e w i n g i s l i s t e d in Table A D l .

BODY: SUBSONIC; CDO'CD~+CD~

cDf=l .02*tfX( 1 + 1 . 5 / ( W 4 ~ + 7 / ( 1 8 / 4 ) ~ ) Sref/Sg

c ~ ~ ' o . o ~ ~ ~ ( ~ ~ / ~ I ~ / ( c ~ ~ ) ~ ' ~ where CDb : Base pressure drag c o e f f i c i e n t .

TRANSONIC: C D O ' C D ~ + C D ~ + C D ~ + C D ~ C ~ f = 1 .O2*Cf*[Cfc/CfIY Sref/SB '= 1 .02*Cf[ I . ~ / ( 4 / 4 ) ~ + 7 / ( @/414jx Sref/SB C~~ ~ ~ ~ ' - ~ ~ ~ * ( d ~ / d ) ~ Cpb: Base pressure c o e f f i c i e n t (Datcom, Figure 4.2.3.1-1 7).

c&: Subsonlc Pressure Drag.

Cop: Supersonic Wave Drag (Datcorn, Figure 4.2.3.1 - 18).

SUPERSONi C: C ~ o ' C ~ X S r e f / S ~ ~ C ~ ~ ~ 2 + C ~ ~ + C ~ ~ ~ ~ ~ ) + CDE12: Nose wave drag (Datcom, Figure 4.2.3.1-501.

COA: Body a f t e r body wave drag (Datcom, Figure 4.2.3.1-136-381).

CDA(NC): Interference drag c o e f f i c i e n t a c t i n g on a f t e r body due to center body and nose (Datcom, Figure 4.2.3.1-54).

: Base pressure drag c o e f f i c i e n t (Datcom, Figure 4.2.3.1-44) cob The Coo f o r the body i s l i s t e d i n Table AD2.

The f i n a l CD, value can be obtained f r o m the f o l l o w i n g equation:

*S /S

C~o'IC~o]wing+IC~olbody ref 3

The ( C ~ o ) ~ o t a l i s l i s t e d i n Table AD3 W ING-BODY COMBINATION; SURSONI C : 2 4

c ~ = c ~ ~ + K ' ~ c ~ + K *[CL-CLmlnI 2

if= i /[rr"AR*e]

e=ct/xll - ( d / b ) 2 1

K? l n v l s c l d drag due t o l t f t (Induced drag).

K//. Viscous drag due t o l i f t due t o f l o w seperatlon and increased sLli; f r i c t i o n (Nicolai, Figure 11.6).

e : Wing efflclency factor.

e? Wing planform e l f iciency f a c t o r (Nicolai, Figure 1 1.5).

TRANSONIC: The values f o r CL and K have been estimated u s i n g Figure AD7 and

Flgure AD8. In these graphs the values of CL and K were estimated

by simply connecting the subsonic and sofrerscnic values and t h e n just

reading the corresponding CL and K f o r the transonic region.

SUPERSONI C: CD=CDo+KY [CL-CLminI 2 K = l /CL - P N f o r subsonic leading edge.

0( A N = 1 / C -(kS+K") #el. 0 L%cn.,.o K: Drag d u e t o I i f t factor.

b N: teatling edge suction parameter.

CL : supersonic l i f t curve slope (Nicolai, Figure 11.2).

( 6Nf bN 1 : Nicolai, Figure 1 1.7.

&f+O

Tables AD4.AD5, and A06 list values l o r CL /degree,& N, and

A K,respectively, f o r the d i f f e r e n t Mach numbers.

CALCIJLATIONS FOP THE SUBSONIC REGION) :rogram A A E V 5 5il; const s = 722.5; pi = 3.141597,; cdo = 0.0 129885; xk = 0.3 103235; var xm, cl, cd, d, v, h, t, r, xx, %la, cla, W : real; outfile : text,; tt : boolean; aaa : integer; ;legin .*k-,fi<,+:t 31 lid # 6 ~ E E ! ; rewrit.e(outfi?e, 'hani:out4'); t t := false; w h i l e not tt do begin wr?tein('input W,h,t,rl); readln(Wfl; read1 n(h); readln!t); read? tt(t-1; vfri t e l n('w = ', w : 1 : 2, ' 1 bs'); write?n(outfile, ' w = ', w : 1 : 2, ' lbs'); xrn := 0.1; cla := 1.6566 * pi / 180.0; while (:sm <= 0.9) do begin := xm * sqrt( 1.4 * 17 16 * t); cl := 2 * Cw) / r / s / (v * v); ~d := cdo * 1.1 + (xk * c l * el); d := c d * s * ('J * v) * r * 0.5; x x := c1 / cd; a l a := cl / cla; I I ' I , v : 1 : 2, w:lte(or~t,iile, h : I : 1 , ' ', x m : 1 : 1, , cl : ' I : 5, '); I I I I 1 I , a j a : 1 : 3 ) ; wr:t.eln(ol:tfil~, cd : 1 : 5, , x x : 1 : 5, , d : 1 : 2, I I , , , I # t l r . h : l : l , : 1 : 1 , , v : l : 2 , , c l : l : S , 1; I I writ.elnfcd ; 1 ; 5, , x x : 1 : 5, ' ', d : 1 : 2, ' ', a i d : : : 2); zrcl := ><K + g, ? ; xm := x m + 0.1 ; end; w r i teln(' h i t I t o exit'); readln(aa3); i f (aaa = 1 ) then tt := true; end; 2nd.

CALCULATIONS FOR THE TRANSOPIIC REGIONS) var xm, el, d, cd, cdo, xk, V, h, t, r, xx, ala, cla, w : real; infile, outfile : text; tt : boolean; saa : integer; procedure d e t c d o x k (xm : real; var cdo, xk, cla : real); begin i f (xm = 9.0) than begin x k := 0.3 1 ; C ~ O := 0.0 147 19 1 ; cla := 1.683; end; i f !xm = 10.0) then begin ~k := 0.30; cdo := 0.034345; cla := 1.7%4; e n d ;

i f i z m = 1 1.0) then

begin

;rk := 0,285; cdo := 0.039222; cla := 1.753; end; i f ( x m = 12.0) then begin xk := 0.28; c d o := 0.039493; cla := 1.722; end; end; :awri te(outfiIe, 'Hsni:outS'); tt := false; w h i l e not t i do begin writeln('input W,h,t,rl); readlnlw); readln(h); read1 nCt); readlnk); writeln(outfile, 'w = ', w : 1 : 2, ' lbs'); writelnC'w = ', w : 1 : 2, ' lbs'); xm := 9.0; while (xm <= 12.0) do begin Y := xm * s q r t ( l . 4 * t * 1716) / ( l e 0 l ) ; cl := 2 * ( w ) / r / s / (v * v); detcdoxk(xm, cdo, xk, cla?; cr; .= cdo * 1 , I + (xk * c l * ~ 1 ) ; d := e l * s * ( ! , * V ) * r * 0.5; : ~ m := ::n: / 1201; ::x := C l / Cd; a l a := e l / Ccla * pi) * 1 a0,O; I t I I w r ~ t e ( o u t f i l e , h : l : l , , % m : 1 : 1 , , v : 1 : 3 , I ', c1 : 1 : 5, ' ' f ; ' ' d : 1 : 2 , ' ',ala: 1 : 2 ) ; w r i t e l n ( o u t f i l e , c d : 1 : 5 , ' ' , x x : 1 : 5 , , ',wri!e(autfile);) t I I I s 15 write(h: 1 : 1, , % m : 1 : 1, , v : I : & ' ' , c l : 1 :5, 1; writeln(cd : 1 : 5, ' ', xx : 1 : 5, ' ', d : 1 : 2, ' ' , a l a : 1 :2); I w r i teln;) xm := xm * le01; xm := xm + 1.0; end; %~tri t e l n('Hi t 1 t o exit'); rezdln(a5ej; i f aaa = 1 then tt := true; en G; e x ? .

CALCULATIONS FOR THE SUPERSONIC AND HYPERSONIC REIGONS) v 4 r xm, cl, d, cd, cdo, xk, v , x x , ala, cla, h, t, r, W : real; i n f i l e , o u t f i l e : text.; tt : boolean; saa : integer; procedure detcdoxk (xm : real;) ! j a r cdo, xk : real);) aegi 3) 2 fi d;) legin r e s e t ( i n f i l e , 'Papers:data 1');) showtext; r e w r i t e ( o u t f i l e , 'Hani:outS1); :t. := false; w h i l e not tt do begin w r i teln('input. V4,h,t,r1); readlnCw); resdln(h); rearflnCt); read1 n(r'); w r t t e l n ( o u t f i l e , 'w = ', w : 1 : 2, ' lbs'); w r i teln('w = ', I V : 1 : 2, ' tb5'); xm := 15.9; w h i l e Cxm (= 100.0) do begin Y := Xm * ~ q f t ( , 1 , 4 * t * 1716) / ( f e O f f ; c ? := 2 * ( 5 / ; 1 ) / r / 5 / (1,) * v); ".

, L ? i.8esAg;&(xm, cdc, ; < k ) ; ) i f (xtrr = 15.0) then begin x k := 0.55; C d D := 1.3 * 0.057375; cla := 2.2355; end; i f (xm = 2Q.O) than begin xk := 0.430; cdo := 1.3 * 0.028804; cla := 2.092; end; i f (xm = 25,O) then begin xk := 0.52 10; cdo := 1.3 * 0.025900; cla := 1.9193; end; i f (xm = 30.0) then begin xk := 0.602; cdo := 1.3 * 00.2420; cla := 1.662; end; i f (:tm = 35.0) then begin xk := 0.72134; c l r ~ := 1.3 * 0.022705; cfa := 1.331; end; i f (xm = 40.13) then begin x k := 0,8202; C ~ O := 1.3 * 0.2 1767; cls := 1.1361; end; i f (xm = 45.0) then begin xk := 1.02; cdo := 1.3 * 0.02077; cla := 0.3'30; end; i f (xm = 50.0) then begin x f : := 1.1cr; cdr~ := 1.3 * 0,020 104; c i ~ .= r: ~5 1 a; end; i f (xm = 55.0) then begin xk := 1.294; cdo := 1.3 * 0.0 19427; cla := 0.773; end; i f (xm = 60.0) then begin xk := 1.422; cdo := 1.3 * 0.0 1 8758; cla := 0.703; end; i f (xm = 65.0) then begin xk := 1.55; cln := 1.3 * 0.0 183272; c i a := 0.645; end; i f (xm = 70.0) then begin xk := 1.672; cdo := 1.3 * 0.0 176583; cla := 0.598; end;

i f Cxm = 75.0) then

begin xk := 1.799; cdo := 1.3 * 0.0 17373; cla := 0.556; end; i f (xrn = 80.0) then begin X % := 1.922; := 1.3 * 0.0 170 12; cla := 0.5203; end; if (xm = 85.01 then begin x k := 2.0.43; C ~ O := 1.3 * 0.8 166643; cla := 0.46%; end; - , -

if (xm = 90.0) t h e n

begin xk := 2.183; do := 1.3 * 0.0 1634; cla := 0,458; end; i f (xm = 95.8) t h e n begin X% := 2.32; cdc := 1.3 * 0,0 15 125; ~1 s := 0.43 1 ; enO; i f (xm = 100.0) then begin xk := 2.457; c d o := 1.3 * 0.0 155 17; cla := 0.407; end; c d := cdo / 1.3 * 1.25 + (xk * cl * cl); d := cd * B * ( % I * v) * r * 0.5; xm := xm I (leOl); x:: := cl / cd; ala := cl / (cls * p i ) * tE30.0; I I sr/rite(cutfile, h : 1 : 1 , ' I, xrn : I : 1 , , Y : 1 : 3, ' ', c1 : 1 : 5, ' '1; wri!e!n(outfile,cd: 1 : 5 , ' ' , x x : 1 : 5 , ' ', d : 1 : 2 , ' ' , a l a : 1 : 2); writ.el,outf ile); , 8 ,?!rfte(h : 1 : 1,

, xm : 1 : 1, ' ', v : 1 : 3, ' ', cl : 1 : 5, ' '1;)

, -.:? I ~ . ~ i ~ t ~ ~ . + * ~ : ? : 5 , + + I ~ / P &

a , ~ ~ : 1 : 5 , ' ' , d : l : 2 , ' ', a l a : 1 : 2);)

,siri?.elfi;) xm := xm + 5.0; e n d ; ;t/n!elnl'Hii I t o e : < ~ t'); read1 n!ssa); i f aaa = 1 then end; p r o g r a m INLETHREA

1-4 ( 3 C ) j ,fr (Si:}) , 'r (30) ,MCSCI-I (36) ,VEl- i31:)) ,BLD i3i:)i

d i m e l ? r , i a n d i m e n s i o n I - A M ( 3 0 j , a i Y ( 3 Q j ,T)'1(30) , l J I R ( 3 0 j , A R E A I 3 0 ) ,E{AREAi3C)j

real iYlA(21-I , B

o p e n ( u n i t = l ,file='INLETf3F3EAIDAAT') A L T - 3 5 0 0 0 .

d o I = 1 , 1 3 ALT=ALT+SOCIC).

H ( I ) = A L T T ( 1 ) = 3 8 9 . 9 9 e n d d o w r i t e ( 6 , 3 i : ) i w r i t e ( 6 , 5 ) w r i t e i 1 , f i j w r i t e ( l , 2 O ) w r i t e l 1 ,5i:lj w r i t e i 1,s) f o r m a t ( ' M a c h % ' , " J ) ! , ' A l . t i . t u d e ' , b X , ' T ' l a ~ s ~ ~ L I W ' , ~ ; . : , ' A I - ~ ~ I ' , & : . :

, ' C o r r e c t e d A r e a ' , 8 X , ' Y ' j

format ( 1 i $ X , ' ( i t ) ' ,BX, ' i l b / . j e c ) ' , 7 X , ' (.fl:.ii.ji.2) ' ,Ti:, ' (f.t+++2) ' , 9 X , ' i f k . j + . ~ " > j " L I d o I = 1 , 1 3 J = J + l w r i t e ( & , * ) ' E n t e r Iblach :#, W:LF":, X b:leed a t ' , t l i : [ j , ' . f t ' r e a d i5,,*) MACHCJ) , W 1 H i J ) , E L D ( J ) I - l P l ( J j = H i P i D M i J ) = 1 3 i I ) T M i J j = ' T i I j

VEL ( 3 1 -MACH i J j uSL!H"r f 1 . 4.H.171 b.ii."I"f") ! J j )

( J ) =WlR ( J ) ; ' (:32,, 2.el)p'l (,j) ,++VEi, ( J j ) Bf>lF<Efi i J ) --.fiF:ZEf!l, (,I ) .+E-(L-D ( J ) ..k.fijr<[i:fi ( J j ORIQ!NIEA& PAGE B S 'yl-EAREA ( J ) ,'7.

OF PrnR QUALO879 w l p i . t e ( & ,/q.i>j p'lhCt.4 ( J ) , H M ( J j ,,W1f<iJ) ,Af:{Ii:A( J j ,E{p,i:';;'E:fi!J) ,,',y' f o r m a t ( l X ,F4.2,8X ,F8.1,5X , F b . 1 ? 1C)X ?Fb. 3,eX 7F6.3, 1 0 X , F 5 . 3 ) W I - i . k e ( b , * ) ' E n t e r 1 t o e n t e r a n o t h e r - Fflach# a t same a l t i t u d e else 2 ' r e a d 1 5 , . % ) L!

i f ( f i . e y . 1 ) g o t o 10 e n d d o claseIl) s t o p end p r o g r a m INLETANGLEM6 d i m e n s i o n M ( i . 5 ) ,MN(15) , E ( E T ( l S ) , T H E T ( l S ) , X T ( 1 5 ) ,F'6R(15) r e a l M,HN o p e n ( u n i t = l , f i l e = ' INLANGM6.DAT7 ) w r i t e ( 6 , t ) ' E n t e r T h e t a , M i , NR7 r e a d ( 5 ; f ) THETA,M(l) ,NR M ( 1 ) = 6 .

NR-8 THET(1)=THETAt3.141592654/180.

BET(1)=EETAt3.141592654/180.

TT=TAN (THET ( I) ) /2.

d o 30 I = l , N R w r i t e ( & , $ ) ' E n t e r T h e t a f o r M1=6 a n d NR=8\ 1 r e a d ( 5 , t ) THETA EETA=THETA+3.

THET(I)=THETAt3,141592654/180.

BET(I)=BETAt3.141592654/180.

TT=TAN (THET (I) ) /Z.

TE=(:).

i f ( AES (TT-TB) . 1 t . ,00601 g o t o 20

BET(I)=EET(I)+(TT-TB)d1.7 A=~M(I)$$2.W(1.4+COS(2.~BET(I)))+2.)$TAN(BET(I)) T E = ( M ( I ) t t Z . t S I N ( B E T ( I ) ) t t 2 . - 1 . ) / A g o t 0 10 X T ( I ) = 4 . / T A N ( B E T ( I ) ) M N ( I ) = M ( I ) t S I N ( E E T ( 1 ) M N ( I + l ) = S Q R T ( (MN(1) $$2.+2./.4)/(2.8/.4$MN(I)$$2.-1)) M(I+1)=MN(I+1)/(SIN(BET(I)-THET(I))

B = ( I. 1 6 6 6 6 6 6 6 6 6 7 t M N ( I) $ f 2 . -. 1 6 6 6 6 6 6 6 6 6 6 7 ) **-2.5

POR(I)=(l.2tMN(I)f%2./(1.+.2tMN(I)tt2.) ) t t Z . 5 % B T H E T ( I + I ) = T H E T ( I ) , E E T ( I + l ) = T H E T ( I + l ) c o n t i ncte w r i t e ( 6 , 5 0 ) f o r m a t ( ' T H E T A ' , 4 X , ' E E T A \ 7 X , b M ( I ) D , 7 X , ' M ( I + l ) 7 , 5 X , 7 F ( : ) R > 7 8 X , ' X T ' l w r i t e ( l , 5 0 ) TPOR= 1.

d o 4 0 I = l , N R BETA=BET ( I) / 3 . 1 4 1 5 9 2 6 ~ 4 a 1 8 ( : ) .

THETA=THET ( I ) / 3 . 1 4 1 5 9 2 6 5 4 * 180.

w r i t e ( 6 , b O ) THETA,BETA,M(I) , M ( I + 1 ) ,P(:)R(I), X T ( 1 ) f o r m a t ( l X , F 5 . 2 , 3 X , F 5 . 2 , 5 X , F 6 . 3 , 5 X , F 6 . 5 , 5 X 7 F 5 . 2 ) w r i t e ( 1 , b Q ) THETA,EETA,M(I) , M ( I + l ) 7 P ( 3 R ( I ) , X T ( I ) TPOR=POR ( I ) tTPOR c o n t i n u e

C = ( i . l 6 6 6 6 6 6 6 6 6 7 * M (NR+1) SP2. -. 1 6 6 6 6 6 6 h 6 6 6 7 ) # # - 2 . 5

TF'TR=(l.ZtM(NR+l) t t 2 , / (1. + . 2 t M ( N R + l ) $ t 2 . ) ) %%3. 5$C%TP(:)R , w r i t e ( 6 , 7 0 1 f o r m a t ( / , ' TF'()R7 , 7 X , TPTR' w r i t e ( 6 , 8 ( : ) ) TFIOH,TPTR f o r m a t ( l X . F 6 . 5 , 6 X , F 6 . 5 ) w r i t e ( l , 8 ( 3 ) TF'Of3,TPTH w r i t e ( 1 , $ 1 ' g o t 0 1 c l o s e ( 1 ) s t o p e n d THETA BETA POR C

. . . I . f)i:) 1 2; . 11.3

.96h24 ii " f ,i:1 15.20 "7598'7

. ..:r -

'7.25 17.7'3 J .."* (-1 4

8.75 21.13 . '34735

it:). 25 25-28 .94765 12. 0i:) 3i:l. 92 .9494.7 13.25 38. 60 ,95887 12.25 49.40 ,97690 --------- -----.----.

THETA XT' C d.25 .16.84 6 - 2 5 14.45 7.25 12. :;&, 9.50 10.38 9.75 8.61

11 . 00

6.98 12.25 5.38 13.75 3.53 ------- ----- - .---__ -- THETA BETA C

J. 25 13.36

h.25 15.47 7.25 17.94

8.50 21 . (37

9.75 24.31

1 1 . i:)~:) 29.82

13.75 38.25 12.25 48.52 BETA 1.3 " 1 6 14. 2 5 9 15. 67 1.7 i:)Z 19.45 22-72 25.65 29. 1i:) TPOR TPTR .a3977 .50516

------------------

-----_----------------

7'1iE-f A BETH M ( I + l ) POW 6. C)C) 13.98 5.182 ,944.91 6.00 15.47 4.541 .96247 6.00 17.05 4. 020 ,97355 6.00 18.74 3.585 .'98QU5 6. C)i:i 28.56

3.213 '. 98583

1 ( 2 ) . i:)C) 25.97

2. 677 ,95641 18.06 30.03

2.237 . 5'7 1 Eli:)

:t 0 . oi:, 35, 22

1.856 . 98 1 i:)2

TPi:iR TPTR -." >

. , , ae!&a . b1478

.--------- FETA 14.84 16" b O 18.49 20. 55 22.82 29-55 35.24 43. 62 . ~pi,-j~\' TF'TF:

. '73353 .67477

THETA BETA 8. 00 15.73 a, 17.77 S . ( 3 0 19.99

8 . r : ) 0 2 ~ ~ 4 6

c> u a.

; a . 27

-.. . : , -., . : , " 59

13.33 1'5.33 41.84

1 : : . :33 r j O . 88

.-----.-.-----.-I--"- -------- -- ----- ---

M ( I 1 M < I + 1 ) POH

6.000 5 . 0 4 8 .9 1777

5.048 4.334 .94705 4.334 3.769 .76435 3,767 3,306 .97519 3,. 306 2,916 .982:3 1 2.716 2.4--' 21 4'2 ,, 96556 2, 434,

1 . YYi:) . 97045

1. 990 1.477 . 96il9.1

---------- ,--------- THE'TA EETA

f ; . 00

13.16

, 5 . i:)tI)

15.20 7.00 17.58 8 . r : r a 20. 4 1 : )

9 . O(:j 23.79

10. CtO 28. CtQ 11.50 34.64 13. 5 1 : ) 44.09 TP8R TPTR

.-.-.. I

. ./ . : , 6 2 1

.60940 --------- THETA 5 . ij!:, 5. '75 6. S O

-

./ 3:) 8.75 10. Of:) 10.'75 11.25

.-----------------------------------..--- --.----- - .--- - -.-.-" ---------.-.----

THETA BETA i l I I ) M I I-t.1) XT C . J ,. <:j [I 13.16 6. CiOi:) C- LI ,, -7- ..::I I 5 ,, 9&24. 1'7. 11

(5 . <:)i:)

1 " ,J . d . 1 . ~ " '" 5.315

4. ,547 9598.7 j. i b 7':3 -.

,i. 25 1'7. 79 4.647 3.397 ,, Y5ZSi_iS 12" 4.b i3 " '75 2 : L ., 1 :3 3.997 -." ...,...-,

2, . . . . , / 2 <;2 4 7 ;r -.,J 1:: 1 (1) " 5

7 -8.-., ,.- j. (,I) ,'7 r 7 ' I-,= "'

. .L s .LJ. 28 .L." / . 9 4 . 7 6 2 ; $3 ,, 4.7

.-, " 2, / A :

1 3 , ( j 9 2; 1 1 . , ? < I ) 2. '74(:) 2 - : L (~$2; 93'7.7 :3 6 - 455

.. . . . -, 12 ,, cj9

. . : a / . 5'[3 2.192, 1 " -739 " 4(,9(3Z; tL- ,-I " :t 2

.I 2 . 75 49. Eli:, 1 ,, ,739 1 . . a : ? ~ , c?73(39 .:- . : , . -+"- .-., ,'

'THETA EET'A 1 2 . -3-7

4 . err:)

5 . 8 1 : ) 14.12 6.00 I&" 15) '7.00 18.64 8.30 21.55 24-22

$ . C)i:)

1C). 00 29.10 12. no 36. (31 -I-POF: TPTR .78848 .62173 -------- B E T A 13. 16 15-20 17;50 20. .li:) 23.79 27. 1i:) - . F -- 32," 98 44.27 TPi:)R TPTR -.-C

/ ~ 4 1 7 . 63881

- 7- "...

I YLJI-; TF'TR

.798$9 . 6015i:)

..r-,----..-.uu--I .,-.---.- i" -,xr-A..-I----.------.-.-. i d -'--------.-.-----jl-- --- - - - ~ - THETA BET'& . M ( I > M(I+11 POR XT

5 . O ( : ) 13.16 6. 0r:)O 5.315 .96624

17.11 6. i:)O 15.20 5.315 4. h4.7 9591r77

14 . 73

-..

./ .25 1'7. 79 4.647 3.99'7

. 953i:)5 12.4h

9.75 21,13 3.997 3.372 .94735 ~("J.zs

1 i:') . 25 25-28 3.372 2 . 790

.9476:3 8.47 11.60 29.96 2.790 . 2.286 .95987 6.94

12.00 56.5~5 2.286 1.820 . '.?672,5

5.39 14.25 49.37 1.820 1.300 -96275 3.43 TPOR TPTR . 7i393 1 .69469 ..

-------------------------------- ------------. --.-------.--

TtdETR BETA MI11 M i 1+11 POF: XT 5.50 13.57 b. OOC) 5.250 .Y5633 1h.58 6 - 5 0 15-74 5 . 250 4.542 .95 188 1.4. 14 8.25 18.94 4.542 3,83(:, .93774 11.66 ' 5 ' . 75 22. 67 3.836 3.175 .93721 9. 513 11.25 27.36 3.175 2. 581. -94224 -7. 73 12.75 53.ht; 2.581

2.U.3/ - -,.-. . 9502i:) h.O:L

1 4'4 , i:10 43. 20 2.037 1.521 "95954 4.26 14%. St:) ++++.E:*Q 1.521 2.059 +**.jc*:* -.- -.. ./ ,, 2 6 T'F'OK TPIR

. '71993 .47905

------- EEIA 13.57 15" '71% 18.29 21.51 24.96 29.56 36.86 49.93 -------em------------ BE'TA M ( 1 1 13.16 6. 000 15. 61 5.315 19. 1s 4.593 21.15 3.934 24.78 3. 34.0 2 9 . 12 2. 8iI6 36.14 2.334 4'48.73 1.851 .--......- ...-- x -r l b . C I b 1 3 " <>'7 1 :L &.....

" >(,.I 9 " 7(3 8 , 1 : : 6, " 1 : : ; 5 4. . -, :....

1 i:: 2.26 program INLETANGLE dimension M(15) ,MN( 151, BET(15) ,THET (151, XT (15) ,F'OR(15) dimension PR(15) ,TR(15) ,DR(15) real M,MN,MNT open (ctni t=l, f i le=YNLANG2. DAT' 1 .

write(6,8) T n t e r MI, NR" read(5,L) M(1) ,NR do 30 I=l,NR write(&, t) 'Enter Theta for M1 and NR\ 1 read(5,t) THETA EETA=THETA+3.

THET(I)=THETAt3.141592654/18(3.

EET(I)=BETAt3.141592654/18(:), TT=TAN (THET (I ) /2.

TE=O.

if (ABS (TT-TB) . lt. . O t : f ( : ) ( : ) l ) goto 20

EET(I)=EET(I)+(TT-TE) 81.7 A=(M(I)tt2.%(1.4+COS(2.*BET(I) ))+2. )tTAN(BET(I)) TB=(M(I)tt2.tSIN(BET(I))4t2.-1. )/A got0 I ( : ) XT(I)=3.5/TAN(EET(I)) MN(I)=M(I>tSIN(BET(I)) MN(I+l)=SRRT( (MN(I)ft2.+2./.4)/(2.8/.4tMN(I)tt2.-1)) M(I+1)=MN(I+l)/(SIN(BET(I)-THET(1))) B=(l. 166666666678MN(I) tt2.-. 166666666667) 8%-2.5 PR(I)=l. 16666666667tMN(I) t82.-. 166666666667 DR(I)=(2.4tMN(I)tt2. )/(.48 MN(I)tt2.+2.)

TR(I)=F'R(I)/DR(I) POR(I)=(1.2tMN(I)St2./(1.+.2tMN(I)tt2. ))%!#3.5*B continue write(&, 12) M(1) write(l.12) M(1) format (3C)X. 'Mach # = \ F5.2) write(6,lS) format ( ' 7 ' ) write (6.50) write(&, 15) format(' THETA\,SX,'BETA',6X,'M(I)',6X,'M(I+1)',4X,'F'OR',7X, T R ' ,?X,'TR\,SX,'XT') write(l,l5> write (l,5U) write(l,l5) TPOR= 1.

TF'R=l .

TTR= 1.

TDR= 1.

do 4 1 : ) 1=1 ,NH BETA=BET(I) /3.141592654t18(:).

THETA=THET ( I ) /3.141592654t180.

write(6,6(:)) THETA,BETA,M(I),M(I+l) ,F'OR(I) ,F'R(I) .TR(I) ,XT(I) f0rmat(lX,F5.2,4X,F5.2,4i(~F6.3,4X,F6.~,4X,F6.5~4X,F7.4,4X,F7.4,4X,F5.2) write(1,tc:)) THETA,EE'rA.M(I) ,M(I+i) ,F'OK(I) ,F'R(I) ,TR(I) ,XT(l:) TPOR=PI:)R f I ) ; k T P l : ) R TF'R=F'R ( I) %TF'R TDR=DH ( I ) tTDR TTR=TR I I) $TTR continue \35 C= ( 1 . 1 6 6 6 6 6 6 6 6 6 7 8 M ( N R + i I f 82. -. 1 6 6 6 6 6 6 6 6 6 6 7 ) # % - 2 . 5 MNT=SQRT( ( M ( N R + l ) %%2.+2. / . 4 ) / (2.8/.4%M(NR+l) f f 2 . - 1 ) ) TF'OTR= ( 1 . 2 f M ( N R + l ) *f2. / ( 1. +. 2% M ( N R + l ) f f 2 . ) 1 *#3.5fCfTF'(:)R TPTR=~l.l66666b6667%M~NK+l)at2.-.lbbb66666667~tTTR TDTR= ( 2 . 4 f M ( N K + l ) $ 6 2 . ) / (. 4 % M ( N R + i ) f f 2 . +2. ) bTDR TTTR=TPTR/TDTR w r i t e (6.17) format("---------------------------- t l f f f f t b f f i f f f f $ f $ # l t ' , " * t t t $ t t t t t * * t t t t X t t ~ ' ) w r i t e ( 6 . 7 0 ) f o r m a t ( ' T T O R ' , 6 X , ' T T R \ S X , ' T T F \ " , 1 1 X , ' T F ' ( ~ ~ T R ' , 7 X , ~ T T R ' , 8 X , ' T T T R ' , 8 X , ' M P J ) w r i t e ( 6 , 8 8 ) TPOR,TFR,TTR,TF'OTR,TF'TR,TTTR,MNT formattlX,F6.5,3~,F8.4,4X,F7.4~7X~Fb.5,6X~F8.4,4X~F7.4,4X,F6.4) w r i t e ( l , 1 7 ) w r i t e (1.70) w r i t e ( l , 8 0 ) TP~:)R,TF'R,TTR,TPOTR,TF'TR,TTTK,MNT w r i t e ( 6 , t ) w r i t e ( 1 , $ 1 g o t 0 1 c l o s e ( 1 ) stop e n d FOR MACH # ' S M=5.0 8 c M=6.0 program INLETLENGTH dimension M,HET,THET

, M e t MN5 , PI6 , MN6 , M7 , FIN7 , MNN2

rea 1 MI, MNl , M2, MN2, M3, MN3 , M4 MN4

real M N N 3 , M N N 4 , M N N S 3 M N N 6 , M N N 7 XPI=3.141593/180.

write(&,$) ' ENTER THE VALUES FOR THETA1 AND M1' read(5,L) THETA,Ml write(&,$) 'ENTER THE VALUE OF Y AND Ll-L5 ' read(5,t) Y,XLl,XL2,XL3,XL4,XL5 M1=5.0 THETA=5.25 Y=J. 5 XL1=7.27C) XL2=3.(:)8523 XL3=1.703.5117 XL4=1.103C)2 XL5=1.6 THETAz8. 0 THESE ARE VARYING LENGTHES

XL1=7 . (:)81003

XL2=2.04934137 XL3=1 .09605 XL4=0.714048 P1=1.0 BETA=THETA+3.

THETl=THETAtXPI RETI=B&TA$XPI TT=TAN(THET1)/2.

'TB=<) .

if (ABS( TT-TF) . 1 t. . C ) C ) S ) C ) l ) goto 20

BETl=BETl+(TT-TB)#1.7 A=(M'1$$2$(1.4+CUS(2.%EET1))+2.)*TAN(BET1) XXX=(SIN(BETl))$P2 TF=(M1%#2*((SIN(FETl))td2)-1.)/k gcto 1 s t write(b,b) 'BET1 =',HETI MMl=tIl*SIN(BETl) write(6,$) 'MN1 = ',MN1 M N 2 = 5 Q l ? T ( ( M N l X # 2 + 5 ) / ( 7 # M N 1 $ # 2 - 1 ) ) write(&,%) ' MN2 =',MN2 write(&,*) BET1,THETl M2=Mk42/ (SIN(HET1-THETA) ) P 2 = P 1 % ( 1 + ( 2 . 8 / 2 . 4 ) $ ( M N l ~ K # 2 - 1 ) ) PO1=Plt( (1+(:).2%Mlt:K2) )1t3.5 P02=P2$((l+0.2#M2#%2))##335 write(&,'#) M 2 continue da 40 I=1 , NF: BETk=HET( 1 ) 13. .1415?2654#13S).

T'HETFr=-~HET(1)/3.141592b54f138.

write(&, t ) BETA,TNETk,XT( I ) ,M( I ) ?M( I-b1) corrtir-~~~e BETA=BETl/XPI write(&,$) ' BETA = ',BETA U T T A - ~ C I ~ a v r ~ T THETT3, MN4, M4 w r i t e ( 6,BC) ) f o r m a t ( l X , ' T H E T 3 = ',F6.2,3X5'MN4 = ' , F 6 . 3 , 3 X 3 ' M 4 = ' , F b . 3 ) BETA3=BETA3/XPI w r i t e ( & , # ) ' BETA3 = ',BETA3 EETA3=BETk3*XPI r e a d ( 5 , # ) X3=XL3#COS(THET3+THET2+THETl) 't f - , - X t 3 # S I N ( T H E T 3 + T H E T l + T H E T 2 ) 7- w r i t e ( 6 , 6 2 ) X3,Y3 format(10X,'X3=',Fb.3,3X,'Y3='aF6.3) BETA4=ATAN((\{-\{1-Y2-Y3)/(X-X1-X2-X3))-THETl-THET2-THET~ A3=((2/TAN(BETA4)*(M4#12.t(SIN(RETA4))t*2-1.))) T H E T 4 = A T A N ( A 3 / ( M 4 # $ 2 . t ( l 1 . 4 + C 0 S ( 2 t E { E T A 4 ) ) + 2 ) ) MNN4=M4 tS I N ( BETA4 ) MNS=SaRT ( (MMN4%#2+5) / (7WMNrJ48#2-1) ) P15=MN!5/ ( S I N ( BETA4-THET4 ) ) F 5 = F 4 ~ ( 1 + ( 2 . B / 2 . 4 ) # ( M b l b 1 4 d # 2 - 1 ) ) F05=P5%((1+0.2WM5t#2))$#3.5 THETT4=THET4/ XP I w r i t e ( 6 , 3 0 ) TMETT4,MN5 ,MS f o r m a t ( l X , ' T H E T 4 = ' , F 6 . 2 , 3 X 3 ' M N 5 =',F6.3,3X,'M5=',Fb.3) BETk4=BETA4/XPI

w r i t e ( 6 , d ) ' BETA4 = ' , BETA4

BETA4=BETA4#XP I r e a d ( 5 , * ) X 4 = X L 4 # C O S ( T H E T 4 + T H E T & + T H E T 3 ) Y4=XL4#SIN ( TIiET4+THET1+THET2-(-'TIiE'TJ) w r i t e ( 6 , 6 3 ) X4,Y4 . . . - . , , < < " . - . - - . . . . . - . - . -.

- . - A - - l ~ r - i ~ , G T L - ~ - i . r ~ , - , r 7 - - ~ r - L i . i . - f . - t r x $ - I - r - ? I ~ m u > BETA5=ATAN((Y-Yl-Y2-Y3-Y4)/(X-Xl-X2-X3-X4)) BETAS=EETA5-THETl-THET2-THET3-THET4 A4=((2/TAN(BETA~)%(M5#%2.#(SIN(BETAS>)#~2-1.1)) T H E T 5 = A T A N ( A 4 / ( ~ 1 5 % # 2 ~ d ( l 1 4 - t C O S ( 2 % B E T A 5 ) ) + 2 ) ) MNNS=MS%SIN(BETA5) MN&=SaRT((MNNS##2+5)/(7*MNN5*#2-1)) M&=MN&./ ( S I N ( BETAS-THET5) ) P&=PS#(l+(2.3/2.4)#(MNNSt*2-1)) PQ&=P&%((l+0.28M&*S2))%#3.5 THETTS=THET5/XPI w r i t e ( & , 9 1 ) THETTS,MN&,M& f o r m a t ( l X , ' T H E T S = ',F6.2,3X5'MN& =',F&.3,3X,'M&=',F6.3) BETA5=BETAS/XPI w r i t e ( & , # ) ' BETAS = ',BETAS BETA5=BETA5#XPI TQTFD=P06/POl F'D=F'&/P1 w r i t e ( & , # ) ' THE TOTAL PRESSURE DRPUT OBLIOL.FOHOP I S ' ,TOTPD w r i t e ( & , % ) ' THE PRESSURE R I S E I S ',PD r e a d ( S , # ) s t o p end N Z Z f 5.

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E z W r t

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Z * 1 . 9 t . . : 1 W X = . . .

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I r 4 z II U J 11 IF--** a \ . . . . 11 * M .

II t I- l c S 4 N I- e m - - H N A rJ I

I - Z Z 4 r 4 r 4 -.4 . Z Z w 4 4 . 4 a a r.~ E = E E

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I - - i . - i X Z 4 I - C 4 * * it I - I I - a w l

n W I - Z * Z t - W X N N W W l L - W W u + \ I

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- x m w r - 1 w m m - = r 4 H H ~ I I I X X X ~ E I X W ~

m Z Z

. . . . . Z .sir . a . z . m w . u Z * a Z * E

& . & Q + + V \ . . w m a : -- f Z N t t X X ~ - V U - . N A r . n r.C;d V W , % 4 Z + a ~ z - u n n w w 4 . 4 n \ n W w m z z Q s Z t X ~ = * X Q Z Z I a I- Z * ~ ~ - - * n u i + w - * ~ w a m o w ~ t - u ~ ~ ~ c E t2? I - W r.C-J ..+ . . ..-4 W V ..ill+ ..+ -oCn+-CLJ ..4 . . 4 W * + + .

0 . . Z w x .d 4 z x I- - 0 * 4 K 4 4 \ u * * 4 Z i W 4 U Z * * C ~ 4 V - 0 V ~ C c \ Q t- II - 4 w E w - r 4 x 4 N w C U j - i 4 Q 4 4 ! I !I - - - ~ J - - e t II fir4 1 1 : ln z r I 1 .4 c i l l = @ui ill o l Z 4 I l C L IL II i - A J 1 ; 1 I . 4 ill 15 ill r C C ' 4 - - ~ 4 a I- +J II +J II +J+'ECL II II + J + J Q + J ~ \ X X ~ S Q + J E + J E ~ u - - I - !

..+ 4 -I r 4 .4 ..+ 11 11 .-I r 4 c I- .d t - 1 11 11 I- I- .d I .d L I - a 11 w , E d * I -4 d ll W I - W L L C 4 . I C . l g Q I O W L W II 4 4 U W L O L O U o l d X i -4 ill aJ aJ L m 4 I W I L Z I Z D L L L 3 L E I - I- 3 Z 3 Z 3 3 E C L a L 3 u m 3 m x x r m m P Y - 3 u . m L a b , - - - - "- -..- ,.r,, ' ,L-.-,,L 4,i,Air\L,L,r,i, -. ---... --" - -- - - -. * - - - = - - - - - - - w r i t e ( b , * f c ) ' MM1'42 = ',MNN2 MN3=SnRT((PlNN2%%2+5)/(7*MNN2%f2-1)) MS=MN3/(SIN(BETG2-THETZ)) P3=P2#(1+(2.B/2.4)%(MNN2*82-1)) ~03=P3#((l+o.2#M~#*2))**3.5 THETTZ=THETz/XPI w r i t e ( 6 , 7 0 ) THETT2,MNZ9M3 f a r m a t ( l X , ' T H E T Z = ' , F 6 . 2 , 3 X 5 ' M N 3 =',Fb.3,3X,'M3=',Fb.3) r e a d ( S , * ) X2=XL2%COSITHET2+THET1) Y2=XLZ!*SIN(THET2+THETl) w r i t e ( b , b l ) X2,Y2 format(10X,'X2=',Fb.3,3XP1Y2=',Fb.3) B E T A 3 = A T G N ( ( Y - Y l - - Y 2 ) / ( X - X l - X 2 ) ) - T H E T l - T H E T 2 A 2 = ( ( 2 / T A N ( B E T A 3 ) $ ( M 3 % % 2 . * ( S I I ' 4 ( E E T G 3 ) ) * * 2 - 1 . ) ) ) T H E T 3 = A T A N ( G 2 / ( M S * * 2 . % ( l 1 . 4 + C 0 S ( 2 # B E T A 3 ) ) + 2 ) ) MNN3=M3PSIN(BETA3) PlN4=SnRT((MNN3$%2+5]/(7fMNN3*%2-1]) M4=MN4/ ( S I N (BETAS-THET3 ) P 4 = P 3 % ( 1 + ( 2 . 8 / 2 . 4 ) * ( M N N 3 d % 2 - 1 ) ) ~ o 4 = r 4 * ( ( l + o . 2 * ~ 4 8 * 2 ) 1 ~ $ 3 " 5 THETT3=THET3/XPI w r i t e ( 6 , 8 0 ) THETT3,MN4,M4 f ~ r r n a t ( l X , ' T H E T 3 = ',F6.2,3X,'MN4 =',Fb.3,3X,'M4=',Fb.3) BETA3=BETA3/XPI w r i t e ( & , * ) ' BETA3 = ',BETA3 BETA3=BETG3#XPI r e a d ( 5 , t ) TOTPD=PO4/PO1 PD=P4/P1 w r i t e ( 6 , t ) ' THE TOTAL PRESSURE DROP I S ',TOTPD w r i t e ( 6 , l o ' THE PRESSURE R I S E I S ',PD r e a d ( 5 , t ) s t o p ertd MACH # 3 AND MACH # 2 p r a g r a m ' INLETLENGTH d i m e n s i o n M,BET,THET r e a l M1,MN1,M2,MN2,M3,MN3,M4,MPJ4,M53MN5bM6IMN6,M7,MPJ7,MN~J2 r e a l MNN3,MNN4,MNNS5MNN6,MNN7 X P I = 3 . 1 4 1 5 3 3 / 1 3 0 .

w r i t e ( 6 , t ) ' ENTER THE VALUES FOR THETA1 AND M I ' r e a d ( 5 , # ) THETA,Ml w r i t e ( 6 , l O 'ENTER THE VALUE OF Y AND L l - L 5 ' r e a d ( 5 , S ) Y,XLl,XL2,XL3,XL4,XL5 M1=3.0

THETA=3 . C 1 6

y = 3 * 5 FOR MACH # 3 X L 1 = 5 . (2 FOR MACH 2 XL1=3. ( : ) XL1=9,13034937 XL2=2.04934137 L 3 = 1 . 7 0 3 6 2 L4=1,1C)302 XL3=1.09665

XL4=1 . 1(:)3(:)2

P1=1.0 BETA=THETA+3.

THETl=THETA#XPI BETl=BETA#XPI TT=TAN(THET1)/2.

TE=8.

i f (ABS(TT-TB) . lt. .00(:)01) g o t o 2 0

H E T l = B E T l + ( T T - T B ) # 1 . 7 A=(Ml##2#(1.4+COS(2.6BET1))+2.)tTkN(BETI) X X X = ( S I N ( B E T 1 ) ) # # 2 TB=(M1##2#((SINiBET1))#*2)-l.)/A g o t 0 10 w r i t e ( & , # ) ' B E T 1 = ' , B E T 1 M N l = M l * S I N ( B E T l ) w r i t e ( & , * ) 'MN1 = ',MN1 MN2=SnRT((MN1#*2+5)/(7#MNl#*2-1)) w r i t e ( 6 , b ) ' MN2 = ' , M M 2 w r i t e ( & , # ) BET1,THETl M Z = M N 2 / ( S I N ( B E { T l - T H E T l ) ) P2=Pl#(l+(2.a/2.4)#(MN1**2-1)) P O l = P l * ( (.1+(3.2#M1*%2) )*%3.:1 p o 2 = r 2 * ( ( l + o . 2 # ~ 2 * * 2 ) ) t # s . 5 w r i t e ( 6 , b ) MZ can t i n u e BETA=BETl/XFII w r i t e ( b , * ) ' BETA = ' ,E(ETA HETA=BETAXXPT X=Y/TAN I BE'TA ) X l = X L l $ C O S ( T H E T l ) Y l = X L l * S I N ( T H E T l ) B E T A 2 = A T A b J ( ( Y - Y l ) / ( X - X I ) ) - T H E T 1 BETA2=BETAZ/XPI ~ ~ r i t e ( 6 , 5 0 ) X , Y write(&,&O) EETA2,Xl ,Y1 format(lOX,'EETAZ=',F6.293X,'X1=',F5.3a3X,'~l=',~5.3) BETA2=HETA2* XP I read(5,%) A1=((2/TAN(BETAZ)$(M2t82.%(SIN(BETA2))%~2-~.)~) T H E T 2 = A T k N ( A 1 / ( M 2 $ % 2 . t ( l 1 . 4 + C 0 S ( 2 t F E T A 2 ) ) + Z ) 1 MNNZ=M2%SIN(BETA2) write(&,#)' MNNZ = ' 3 MNNZ MN3=SnRT((MNN2%*2+5)/(7%MNN2*%2-1)) M3=MNZ/(SIN(BETAz-THET2)) P3=P2%(1+(2.8/2.4)%(MNN2%%2-1)) PO3=P3*( (l+(:).Z#M3##2) ) t%3.5 THETT2=THET2/XPI write(6,70) THETT2,MN3,M3 farmat(lX,'THET2 = ',F5.2,3X,'MN3 =',F6.3,3XF'M3=',F5.3) read(5,W) TOTPD=P03/F'Ol PD=P3!P1 write(&,%) ' THE TOTAL PRESSURE DROP IS ',TOTPD write(&,*) ' THE PRESSURE RISE IS ',PD1 read(5,Y) stop end ,:=*..-. . . .

k teal :" LAMBD, MHU , N , MACHI , LAEF , LEF ' ': '- '- - . - . -.

RHO I N=O . i:)i:)i:)<)3211.4

-RHOAT=C) .0C)2357 ' VELIN=9913.2 . . .

' R & D N = 0 . 5 .

LANED=5?.53 ALPHA=<). C)

ANOFA=O . O

MHU=<). 00i:)<)093 N=O. 0s) MACHI=lO.i')

EETA=O . O

RADLE=';). 02085

EM I SS=O . €39

STEFB= . O<)i:)000i:)01714

GAMMA=1.34 TNOT=7533.2 c HDLAM= i : i . 1 i : t 5 5 d ( R H O I N . , ' R H D f i T ) $ $ . 5 % ( V E L I f . j i I . Q ; i i % < 4 ) X t _ t .ib HaTUR=i:).437#! (F;HOIN/HHOAT) # L -78% (YELINIf1i:)%ht4) %%L. 54 HNDSE=HOLAM/KADN%*.5~ LAEF=5INiLAPlaD?%COS(AtPHAl LEF=ASIN:LAEFZ PF1=(1.33%MACHI%x2+2.5>%( (iL:Gs(iEF) >g1<2+i:im<!i:ti9) P F z = l . ~ ~ $ ( P 1 & C H I : K ( C o S ( L E F ) j );Sf2+1 PF=PF~/F'F:I H L l = H O i A M I (PFItKADiE) #$:. 5 HL2=i3.72b(CDS<LE=) 1 % t i i I E I + . . ~ ~ ~ S S I ~ : J ( L E F ~ HLSTAG=HL.l 8HLZ d p 10 30=1, 105 XX=JO/Z.O XDIS=JD%l.O RN=RHOIN%VELINtXDIS/MHU i f (RN. l t . 3 . 5 E 5 ) then H L A N l = H ~ L A M ~ i P F ~ ( 1 + 2 # N ) / ( 3 . t X ' D I S ) ~ % ; i c . 5 HLAM2=1.75#SINiBETA~-.86O(iSIN(FETA)l~B2l HLAMZ=i:). (236,s' ( ( pi&cH 3 %S I N ( EiETA 1 1 $ t z + i . [If : : H L A M = H L A M l * ( H L A M 2 + H L k M 3 ) U E = V E L I N I S I N ( L E F ) T&&=TNiJT- ( I - , , 1 5 ) %UE$$z1'12?312. i:i g 0 . t ~ 2i:) e n d i f HTI,JKF1=HQTUF;t ( x D I S / i i : > , 0 ) 8 % (-2'O)b ( i 1 . g + l .25;1;.N::,/ ( 2 , 2 5 9 : : : D I S ) j ;C;$:::;,;;: HTuREtz=PF%$Q.a* ( 2 . 9 % ( S I N ( l . s%BET&) )-1 m & g ( ( S ~ P X ! ( E E T G ) > ;Kg<::*Sj j HTUHB~=CI~.OZ/ ( (pjACHI*sIr.i(E{ETA) } *%2+1 .i:)] HTUKH=HTURBl8(HTURB2+t-;TUHB3] T k W = T N O T - O . l # V E L I N t t 2 * ( ( S I N t L E F j ]LW2f ,/lZQ12.:3 HWU=HTUHB goto SC) HWU=HLAM . .. . do 90 J=l,lE4,1C) . T T = J I 1 . 0 A=TT*14+HWU%TTi(EMISS#STEFE) B=HWUITAW/(EMISSISTEFB) g ? t o 4i.I con tin^^^ -- write (6,10(:!) Hb;U,TTI20,XDIS/2 LIST OF Y STAm F C 3 Bob Stonebraker (ft.).

PROGRAM HECONST - Computes lines of constant He

PROGRAM FSCONST - Computes contours of constant Fs (ft./lb.)

for phase 1 of the mission.

PROGRAM FSCNST2 - Computes contours of constant Fs (ft./lb.)

for Phase 2 of the mission.

PROGRAM PHASE1 - Computes fuel consumption, elapsed time and

range for Phase 1.

PROGRAM PHASE2 - Computes fuel consumption, elapsed time and

range for Phase 2.

SUBROUTINE ATMOSFR (ALT,T,RO,P) - Computes standard atmospheric

variables as a function of altitude.

SUBROUTINE TFRMJT (M,ALT,FN,SFC) - Computes net thrust and sfc

from given data as a function of Mach number and altitude. (based on economic sfc)

SUBROUTINE SCRMJT (M,ALT,FN,SFC) - Computes net thrust and sfc

from given data as a function of Mach number and altitude. (based on equivalent fuel/air ratio of 0.8)

SUBROUTINE DRAG (M,ALT,D) - Computes drag from given data as a

function of Mach number and altitude.

SUBROUTINE SPLINE (X,F,XF,FN,N) - Interpolates between points

(X, F) for point (XF,FN) .

PROGRAM HECONST ROBERT STONEB R COMPUTES VALUES OF CONSTANT He (ft.)

IMPLICIT REAL(A-H,O-2) REAL M OPEN ( 5,FILE= HECONST. DAT ) Rz1715.621 "-32.1578 HE=2. E4 DO 200 I=1,10 HG=O .

100 CALL ATMOSFR(HG,T,RO,P) M=SQRT((HE-HG)*2.*G/(1.4*R*T)) WRITE(S,*) M,HG,HE WRITE(*, *) M,HG,HE HG=HG+4000.

IF(HG.GT. 110000. ) GOT0 200 IF (HG.LT. HE) GOT0 100 200 HE=HE+2.OE4 CONTINUE STOP END PROG FSCONST ROBERT STONEBRAKER COMPUTES VALUES OF CONSTANT Fs ( f t / l b ) OVER PHASE 1 WITH NET THRUST, SFC, AND DRAG A S FUNCTIONS OF ALTITUDE AND MACH NO.

IMPLICIT REAL ( A-H , 0-2 )

REAL M OPEN(5,FILE=@FSCONST.DAT') 'ENTER INITIAL VEHICLE WIEGHT IN LBS.'

WRITE(*,*) READ(*,*) W M=. 8 Rx1715.621 MACH NO. LOOP DO 100 I=1,27 ALT=40000.

ALTITUDE LOOP DO 200 J=1,30 CALL ATMOSFR(ALT,T,RO,P) A=3600*SQRT(1.4*R*T)

CALL TFRMJT ( ALT , M, FN , SFC)

IF(FN.EQ.0.) GOT0 200 IF(SFC.EQ.0.) GOT0 200

CALL DRAG ( ALT , M , D )

FS=M*A* (FN-D) / (FN*SFC*W) IF(FS.LT.0.) THEN FS=O .

ENDIF WRITE(*,10) M,ALT,FN,D,SFC,FS 10 F0RMAT(F5.2,3X,F8.1,3X,F10.1,3X,F10.1,3X~F6.3,3X,F7.1) WRITE(5,20) M,ALT,FS 20 FORMAT(F5.2,3X,F8.013XIF7.1) 200 ALT=ALT+2000.

W=W-100.

100 M=M+.200000 STOP END PROG FSCMST2 C ROBERT S T O N E B m R C COMPUTES VALUES OF CONSTANT Fs ( f t / l b ) OVER PHASE 2 C WITH NET THRUST, SFC, AND DRAG AS FUNCTIONS OF C ALTITUDE AND MACH NO.

C IMPLICIT REAL(A-H,O-Z) REAL M OPEN(~,FIIJE='FSCNST~.DAT') 'ENTER INITIAL VEHICLE WIEGHT IN LBS.'

WRITE(*,*) READ(*,*) W M=6.

R=1715.621 C MACH NO. LOOP DO 100 I=1,41 ALT=70000.

C ALTITUDE LOOP DO 200 J=1,16 C SPEED OF SOUND (ft/sec)

CALL ATMOSFR (ALT, T , RO , P)

A=SQRT ( 1.4 *R*T) Q=.5*RO*1.4*R*T*M**2 C IF(Q.GE.1800) THEN C FS=O C GOT0 300 C ENDIF C

CALL SCRMJT (ALT, M, FN , SFC)

FN=4 * FN

SFC=SFC/3600 IF(FN.EQ.0.) GOT0 200 C

CALL DRAG (ALT , M, D)

C FS=M*A* (FN-D)/ (FN*SFC*W) WRITE(*,lO) M,ALT,FN,D,SFC,FS 10 F0RMAT(F4.1,3X,F7.0,3X,F10.1,3X,F10.1,3X,F9.6,3X,E12.5) 300 WRITE(5,20) M,ALT,FS 20 FORMAT(F4.1,3X,F7.0,3XIF12.3) 200 ALT=ALT+2000.

W=W-14 7.

100 M=M+.10 STOP END C C COMPUTES THE FUEL CONSUMED ALONG PREDETERMINED FLIGHT PATH C FROM (M=.8 AT 40,000' TO M=6 AT 76,000') IMPLICIT REAL (A-HI 0-Z) REAL M OPEN(5,FILE='PHASEl.DAT') OPEN(6,FILE='PHASEll.DAT') WRITE(*,*)'ENTER INITIAL VEHICLE WEIGHT' READ(*,*) W WRITE(*,*)'ENTER MACH NO. STEP SIZE' READ(*,*) DM R=1715.621 G132.1578 M=.8 HG=40000.

HGO=40000.

Ax968.1 C COMPUTE INITIAL HE AND F=l/FS AT M=. 8 AND ALT(HG) =40000 HE1=49326.186

CALL TFRMJT (HG , M, FN , SFC)

SFC=SFC/3600.

C A U DRAG (HG , M , D)

Pl=W/ (M*A* (FN-D) ) Fl=FN*SFC*Pl C N=5.2/DM+l DO 100 I=l,N M=M+DM CALL FLTPTH (MI HG) CALL ATMOSFR(HG,T,RO,P) CALL TFRMJT(HG,M,FN,SFC) CALL DRAG(HG,M,D) SFC=SFC/3600.

A=SQRT ( 1.4 *R*T) HE2=HG+.5*(1.4*R*T*M**2)/G TR=FN-D IF(TR.EQ.0) GOT0 100 P2=W/ (M*A* (FN-D) ) F2=FN*SFC*P2

DTIME=(HE2-HEl) *. 5* (P2+P1)

DF'UEL- (HE2-HE1) *. 5* (F2+F1)

W=W-DFUEL TIME=TIME+DTIME ACC=DM/(M*DTIME) RNG=RNG+SQRT((M*A*DTIME)**2-(HG-HGO)**2)/5280.

HGO=HG FUEL=FUEL+DF'UEL ELT=TIME/60 WRITE(*,10) ELT,RNG,M,HG,FN,D,W WRITE(5,lO) ELT,RNG,M,HG,FN,D,W 10FORMAT(F7.3,2XlF8.1I2XIF6.2,2X,F8.0,2X~F8.O~2XtF8.Ot2XtF8.O) WRITE(6,20) RNG,M,HG,ACC,FUEL 20 FORMAT(F8.1,2X,F6.2,2X,F8.012XIF7.412XtF7.0) HE 1=HE2 Pl=P2 0 100 Fl=F2 TIME=TIME/60

WRITE(*,*) ' M =',M, ' ALT ,HG, 'ft. I

W fuel =l,FUEL,llbs.l WRITE(*,*) 'T =*,TIME, 'min.

PROG ROBERT STONEBRAKER COMPUTES FUEL CONSUMED ALONG PREDETERMINED FLIGHT PATH FROM (Ma6 AT 76,0001 TO M=10 AT 10Ot00O1) IMPLICIT REAL (A-H, 0-Z) REAL M 0PEN(5,FILE=1PHASE2.DAT') 0PEN(6,FILE='PHASE22.DAT1) WRITE(*,*)'ENTER INITIAL VEHICLE WEIGHT' READ(*,*) W WRITE(*,*)'ENTER MACH NO. STEP SIZE' READ(*,*) DM WRITE(*,*)'ENTER NO. OF SCRAMJETS' READ(*,*) K R=1715.621 G=32.1578 M=6 HG=75835.

HGO=75835.

A=968.1 C COMPUTE INITIAL HE AND F=l/FS AT M=6 HE1=600433.

CALL SCRMJT (HG , M, FN,SFC)

FN=K* FN SFC=SFC/3600.

CALL DRAG(HG,M,D) Pl=W/ (M*A* (FN-D) ) Fl=FN*SFC*Pl C N=4 ./DM+30 DO 100 I=l,N M=M+DM C C FLIGHT PATH ALONG 421800 IF(M.GE.10.) THEN M=lO.

HG=HG+300.

IF(HG.GE.100000.) GOT0 500 GOT0 50 ENDIF HG=-7.35005*M**4+262.753*M**3-3749.61*M**2+29936.5*M-l6027.

C 50 CALL ATMOSFR(HG,T,RO,P) CALL S C m T (HG,M, FN,SFC) FN=K* FN SFC=SFC/3600.

CALL DRAG(HG,M,D) A=SQRT ( 1.4 *R*T) HE2=HG+.5*(1.4*R*T*M**2)/G TR=FN-D IF (TR.EQ. 0) GOT0 100 P2=W/ (M*A* (FN-D) ) F2=FN*SFC*P2

DTIME= (HE2-HEl) *. 5* (P2+Pl)

DPUEL-- (m2-NE1) *. 5* (F2+F1)

W=W-DFVEL TIME=TIME+DTIME ACC=DM/(M*DTIME) RNG=RNG+SQRT((M*A*DTIME)**2-(HG-HGO)**2)/5280.

HGOIHG ELT=TIME/60 FUEL=FUEL+DFUEL WRITE(*,lO) ELT,RNG,M,HG,FN,D,W WRITE(5,lO) ELT,RNG,M,HG,FN,D,W 10FORMAT(F7.3t2XtF8.l~2XIF6.2,2X,F8.0,2XtF8~Ot2XtF8eO~2XtF8~O) WRITE(6,20) RNG,M,HG,ACC,FUEL 20 FORMAT(F7.3,2XtF6.2,2XIF8.O,2X,F7.4,2X,F7.O) HEl=HE2 Pl=P2 100 Fl=F2 500 WRITE(*,*) 'FUEL =*,FUEL STOP END SUBROUTINE ATMOSFR(HG,T,RO,P) C ROBERT STONEBRAKER C COMPUTES TEMPERATURE, DENSITY, AND PRESSURE GIVEN A C GEOMETRIC ALTITUDE HG.

IMPLICIT REAL ( A-H , 0-2 )

REz2.08646637 H=HG*RE/(RE+HG) C IF(H.LT.36000.)THEN HO=O.

T0=518.69 I R00=2.37693-3 PO-2 116.2 A=-3.566273-3 T=TEMP(TO,A,H,HO)

RO=ROSLOP (ROO,T , TO,A)

P=PSLOP(PO,T,TO,A) GOT0 500 ENDIF C IF(H.LT. 82000.)THEN HO=36000 T=389.99 ROO-7.08583-4 P0=474.7098 RO=ROLNR(ROO,T,H,HO) P=PLNR(PO,T,H,HO) GOT0 500 ENDIF C IF(H.LT.154000,)THEN HO=82000 T0=389.99 R00=7.76643-5 P0=52.03 A=1.64355E-3

T=TEMP (TO, A, H , HO)

RO=ROSLOP(ROO,T,TO,A) P=PSLOP(PO,T,TO,A) GOT0 500 ENDIF 500 RETURN END FUNCTION TEMP(TO,A,H,HO) TEMP-TO+A* (H-HO) RETURN END FUNCTION ROSLOP(ROO,T,TO,A)

ROSLOP=ROO* ( (T/TO) ** (- (32.1578/ (A*1715.621) +l. ) ) )

RETURN END FUNCTION PSLOP(PO,T,TO,A)

PSLOP=PO* ( (T/TO) ** (-32.1578/ (A*1715.621) ) )

RETURN END FUNCTION ROLNR(ROO,T,H,HO) ROLNR=ROO*EXP(-32.1578/(1715.621*T)*(H-HO)) RETURN END FUNCTION PLNR(PO,T,H,HO)

PLNR=PO*EXP(-32.1578/ (1715.621*T) * (H-HO) )

RETURN END SUBROUTINE T T(HG,M, FN,SFC) C ROBERT STONEBRAKER C COMPUTES THE NET THRUST AND SFC OF THE FULL SCALE C TURBOFAN-RAMJET AS A FUNCTION OF ALTITUDE AND MACH NO.

C BASED ON CURVE FIT POLYNOMIALS AND NATURAL CUBIC SPLINES.

C IMPLICIT REAL (A-H,O-Z) REAL M DIMENSION HGA(15) ,FNA(15) ,SFCA(l5) C IF(M.LT.0.8) THEN FN=O SFC=O GOT0 500 ENDIF IF(M.GT.6.0) THEN FN=O SFC=O GOT0 500 ENDIF C K=7

C *** 0.8 TO 3.5

HGA(1) =40000 ENA(1)=-2879.52*M**5+28051.4*M**4-101019.*M**3+172092.*M**2

* -112116.*M+37378.7

SFCA(1)=-.0430727*M**6+.570346*M**5-3.00762*M**4+8.02043*M**3

* -11.2762*M**2+7.86021*M-1.40087

C

C *** 2.0 TO 4.5

HGA(2) =50000 FNA(2)=2569.33*M**3-15206.7*M**2+53954.5*M-37169.1 IF(M.LE.3.5) THEN SFCA(2)=.0640001*M**3-.492*M**2+1.316*M-.424001 GOT0 60 ENDIF ' SFCA(2)=.034*M**2-.237*M+1.312 C

C *** 2.5 TO 6.0

60 HGA(3) =60000 IF(M.LT.3.5) THEN SFCA(3)=.0880001*M**2-.422*M+1.299 GOT0 70 ENDIF SFCA(3)= -.0020003*M**3+.0522861*M**2-.28693*M+1.34922 C

C *** 3.0 TO 6.0

70 HGA(4)=70000 SFCA(4)=.0103333*M**3-.130929*M**2+.613024*M-.lO77 C

C *** 4.0 TO 6.0

HGA(5) =80000 FNA(5)=-2007.67*M**3+30631.5*M**2-137628.*M+212654.

SFCA(5)=.00866667*M**3-.105*M**2+.486334*M+.O959986 C

C *** 4.0 TO 6.0

HGA (6) -90000 FNA(6)z-1233.33*M**3+18722.*M**2-83600.7128444.

SFCA(6)=.0076661*M**3-.0854991*M**2+.372829*M+.311008 C

C *** 4.0 TO 6.0

HGA (7) =100000 FNA(7)=-683.667*M**3+10277.5*M**2-44661.8*M+66948.

SFCA(7)=.024*M**3-.320001*M**2+1.476*M-1.37301 C

CALL SPLINE (HGA , FNA, HG , FN ,K)

IF(FN.LT.0.) THEN FN=O ENDIF CALL SPLINE (HGA,SFCA,HG, SFC,K) IF(SFC.LT.0.) THEN SFC=O ENDIF 500 RETURN END SUBROUTINE S T(HG,M,FN,SFC) C ROBERT STONEBRAKER C COMPUTES FG(lbsf), FN(lbsf), ISP(sec), SFC(lbsm/lbsf/hr) C AS FUNCTION OF ALT. AND MACH NO.

C CURVE FIT EQUATIONS BASED ON F'UEL/AIR RATIO OF 0.8 IMPLICIT REAL (A-H,O-2) IMPLICIT REAL (MI I) DIMENSION MA(15),F(15) C DATA MA(1) ,MA(2) ,MA(3)/5.0,7.5,10.0/ N=3 C

C *** FG ***

C F(1)=-4.92613E-10*HG**3+1.45585E-4*HG**2-14.8904*HG+534062 C F(2)=-4.91975E-10*HG**3+1.71206E-4*HG**2-20.445l*HG+845486 C F(3)=-4.99582E-10*HG**3+1.95693E-4*HG**2-26.l568*HG+l201470 C CALL SPLINE(MA,F,M,FG,N) C

C *** FN ***

F(1)=-1.61294E-lO*HG**3+4.71692E-5*HG**2-4.77752*HG+l69622 F(2)=-1.04412E-10*HG**3+3.57416E-5*HG**2-4.20399*HG+l71214 F(3)=-4.13576E-ll*HG**3+1.7587E-5*HG**2-2.52803*HG+l23291 CALL SPLINE(MA,F,M,FN,N) C

c *** 1sp ***

F(1)=-5.79888E-12*HG**3+1.19854E-6*HG**2-8.53+66E-2*HG+5398.13 F(2)=-9.88777E-12*HG**3+2.55155E-6*HG**2-Om22344*HG+9l42.38 F(3)=-7.61882E-12*HG**3+1.98524E-6*HG**2-0.174684*HG+7093.69 CALL SPLINE (MA, FIX, ISP,N) C SFC=3600./ISP RETURN END

SUBROUTINE DRAG (HG , M , D)

C ROBERT STONEBRAKER C COMPUTES DRAG OF 515H VEHICLE DESIGN AS A FUNCTION OF ALTITUDE C AND MACH NO. BASED ON CURVE FIT POLYNOMIALS OF GIVEN DATA.

IMPLICIT =(A-H, 0 - 2 ) REAL M DIMENSION HGAA(15) ,DA(15) C K=13 HGAA(1)=40000 DA(1)=981.718*M**2+10219.2*M-5885.21 HGAA(2) -45000 DA(2)=777.411*M**2+7952.26*M-4088.61 HGAA (3) =50000 DA(3)=617.958*M**2+6144.13*M-2528.24 HGAA (4) =55000 DA(4)=494.109*M**2+4690.13*M-1114.06 HGAA (5) =60000 DA(5)=398.678*M**2+3505.97*M+235.57 HGAA(6)=65000 DA(6)=326.16*M**2+2523.4*M+1598.03 HGAA(7)=70000 DA(7)=272.36*M**2+1685.99*M+3051.45 HGAA (8) =75000 DA(8)=234.18*M**2+945.452*M+4678.9 HGAA (9) =80000 DA(9)=209.415*M**2+259.422*M+6572 HGAA(10) =85000 DA(10)=196.64*M**2-409.555*M+8834.34 **NOTE**LAST THREE EQUATIONS ARE NOT VALID FOR M < 4 IF(M.LT.4.0) THEN x=10 GOT0 500 ENDIF HGAA(l1) =90000 DA(ll)=-59.1967*M**3+1483.62*M**2-10103.l*M+31674.9 HGAA(12) =95000 DA(12)=-69.7467*M**3+1732.75*M**2-12589.8*M+39067.1 HGAA(13) =100000 DA(13)=-83.6275*M**3+2064.89*M**2-15665.8*M+48294.5 C 500 CALL SPLINE(HGAA,DA,HG,D,K) -1. l*D RETURN END SUBROFPTINE SPLIWE(X,F,XW,FX,N) C ROBERT STONEBRAKER 4/10/90 C COMPUTES VALUES OF AW UNKNOWN F'UNCTION FROM UNEVENLY SPACED C DATA USING A NATURAL CUBIC SPLINE.

IMPLICIT REAL (A-H,O-2)

DIMENSION X(15), F(15) ,A(15) , B(15) ,C(15) , G ( 1 5 ) ,R(15)

C C DETERMINES WHICH INTERVAL OF THE DOMAIN.HOLDS X DO 100 112 ,N IF(XN.LE.X(I)) THEN J=I-1 GOT0 200 ENDIF 100 CONTINUE C C DEFINES MATRIX COEFFICIENTS 200 DO 300 I=l,N DELX=X (I+l) -X (I) A(1) = (X (I) -X (1-1) ) /DELX B(I)=2* (X(I+1) -X (1-1) )/DELX C(1) =l R(I)=6*(F(I+l)-F(I))/(DELX**2) *-6* (F(I) -F (1-1) ) / (DELX*(X (I) -X (1-1) ) ) 300 CONTINUE A(1)=0.

C (N) =O .

C C THOMAS ALGORITHM FOR G(i) DO 400 I=2,N FACTOR=A (I) /B (1-1) B(I)=B(I) -FACTOR*C (1-1) 400 R(I)=R(I) -FACTOR*R(I-1) G (N) =R (N) /B (N) DO 500 I=2,N NI=N-1+1 500 G (NI) = (R(NI) -C (NI) *G (NI+l) ) /B(NI) G(1)=0.

G (N) =O .

C DELX=X (J+l) -X (J)

FX=G(J) * ( ( (X(J+l) -XN) **3)/DELX-DELX* (X(J+l) -XN) )/6

*+G(J+1) * ( ( (XN-X(J) ) **3)/DELX-DELX* (XN-X(J) ) )/6

*+F(J) * (X(J+l) -XN)/DELX+F(J+l) * (XN-X(J) )/DELX

C RETURN END