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NASA Technical Memorandum 86760 

NASA-TM-86760 19850024864 

A Review of Shock Waves Around 

Aeroassisted Orbital Transfer 

Vehicles 

Chul Park 

June 1985 

NI\S/\ 

National Aeronautics and 

Space AdministratIOn 

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I 

JUL 2 7 E:~ 

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NF00027 
NASA Technical Memorandum 86760 

A Review of Shock Waves Around 

Aeroassisted Orbital Transfer 

Vehicles 

Chul Park, Ames Research Center, Moffett Field, California 

June 1985 

NI\S/\ 

National Aeronautics and 

Space Administration 

Ames Research Center 

Moffett Field California 94035 
A REVIEW OF SHOCK WAVES AROUND AEROASSISTED JRBITAL TRANSFER VEHICLES 

Chul Park 

Ames Research Center 

SUMMARY 

Aeroassisted orbital transfer vehicles (AOTVs) are a proposed type of reusable 

spacecraft that would be used to transport cargoes from one Earth-bound orbIt to 

another. Such veh1cles could be based on the proposed Space StatIon and used to 

transport commercial satell1tes from the Space Station to geostationary orbIts or to 

polar orbits and return. During a mission, AOTVs would fly through Earth's atmosphere, thus generatIng aerodynamIc forces that could be used for deceleratIng the 

vehicles or changing theIr direction. This review of published AOTV research find1ngs was concerned wIth the shock-wave-1nduced, h1gh-temperature a1rflows that would 

be produced around these veh1cles during atmospher1c fl1ght. In the survey, specIal 

emphasis was placed on the problems of (1) the chemIcal phyS1CS of muititemperature, 

loniz1ng, nonequilibrium a1r flows, and (2) the dynam1cs of the flows 1n the base 

region of a blunt body with complex afterbody geometry. 

SYMBOLS 

AOTV aeroassisted orbital transfer veh1cle 

Cd drag coeffic1ent 

Cp specific heat at constant pressure 

Cv spec1fic heat at constant volume 

c.g. center of gravity 

g grav1tational acceleratIon of the Earth = 9.80 m/sec2 

GEO geosynchronous Earth orbit 

HEO h1gh Earth orbit 

Ip peak radiation intens1ty behind shock 

LEO low Earth orbit 

LID lift-to-drag ratio 
M 

Ma 

Mf 

Ml 

OTV 

Ps 

Pm 

qc 

qr 

R 

ReS 

T 

Te 

Tr 

Tv 

t 

V 

Vf 

V· 1 

Vj 

X 

- Xe 

Xp 

y 

mass of vehicle 

mass of air displaced by a vehicle 

flnal mass of a vehicle at end of a rocket engine burn 

Inltial mass of a vehicle at the beginning of rocket engine burn 

orbital transfer vehicle (without aeroassist) 

stagnation pressure 

free-stream pressure 

convective heat-transfer rate, kW/m2 

radlatlve heat-transfer rate, kW/m2 

nose radlus, m 

reaction control system 

heavy-particle translational temperature 

electron translational temperature 

heavy-partlcle rotatlonal temperature 

vibrational temperature 

tlme, sec 

fllght velocity, m/sec 

vehlcle veloclty at end of rocket engine bUrn or of aerobrake 

vehlcle veloclty at beglnning of rocket engine burn Or of aerobrake 

exhaust veloclty of rocket engine, m/sec 

dlstance from shock 

distance for chemical equilibrium behind shock, where radiation intensity IS 

1.1 times the plateau value 

dlstance for peak radiation Intensity behind shock 

2 
'. 

~V Vf - Vi 

A mean free path 

~ v1scosity 

p free-stream dens1ty, kg/m3 

INTRODUCTION 

Starting about 1970, near-Earth space became a realm not only for sC1ent1f1c 

explorat1on but also for commerc1al enterpr1ses. The most notable commerc1al use of 

space is 1n telecommun1cat1ons. For the nat10ns fortunate enough to be located 1n ~ 

relatively low latitudes, the geosynchronous satell1tes, located 42,210 km away from ' 

Earth's center, provide a relatively 1nexpensive means of transferr1ng 1nformation 

from one ground pos1tion to another over a large d1stance. For the nat10ns that are 

located near the North or the South Poles, high satellite orbits that can serve 

slm1lar purposes have been found and are be1ng used. These h1gh-Earth-orbit (HEO) 

satell1tes are used not only for telecommun1cat1ons, but also, for example, 1n 

mak1ng weather and crop forecasts; detect1ng crop-destroying 1nsects and diseases; 

find1ng new Earth resources, such as natural gas or 011; detect1ng sh1pwrecks and 

forest fires; and space manufacturing. In add1t10n to these HEO satell1tes, there 

are some scientif1c satellites that are in low-Earth-orbits (LEO), either over or 

near the Poles. Del1ver1ng satell1tes from the ground to these various orb1ts 

became a profitable commerc1al activ1ty, and, in some instances, 1t has been shown 

that retr1eving defunct satellites could also be done profitably. 

Var10us nat10ns have developed d1fferent rocket veh1cles for the purpose of 

carry1ng such satell1te cargoes. Most of these veh1cles are still in development, 

and so 1t 1S d1ff1cult to assess and compare their performance on a common bas1s. 

In add1t1on, because they are 1n the process of development, a great deal of pert1-

nent informat1on about them is st1ll proprietary. This makes the task of rev1ewlng 

the subject matter rather d1ff1cult. Under this constraint, therefore, the present 

author chooses two basic guidel1nes: (1) any information avallable to the general 

public without restr1ction will be freely referred to, and (2) the author will 

freely upgrade available performance data 1f, in his op1n1on, such upgrad1ng can be 

cons1dered a reasonable certa1nty. 

F1gure 1 shows two such typ1cal carr1er vehicles: the U.S. Space Shuttle and 

Ar1ane of European Space Agency (ref. 1). The Ar1ane Veh1cle 1S shown here with 

four solld-fuel boosters, even though such a comb1nation has not yet been flown. In 

the opinion of the author, adding four boosters in this way seems to be a reasonably 

easy thing to do. As shown in the f1gure, the Space Shuttle and Ariane are expected 

to deliver, respectively, with the antic1pated upgrad1ng, about 30,000-kg and 

4,500-kg payloads to LEOs. 

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To transfer such payloads to an HEO, such as a geostationary Earth orbit (GEO), 

additIonal propulsIon IS necessary. In figure 1, the upper stage vehicle for Ariane 

IS visible as the top part of the assembly. For the Space Shuttle, the additIonal 

stage IS stowed insIde the cargo bay of the Orbiter and does not appear In the 

figure. The payload that can be delivered to an HEO will be determined principally 

by the specific impulse of the rocket engine of the upper stage vehicle. The specIfIC Impulses of the systems vary greatly depending on the fuel used. The liqUId 

fueld that do not requIre cryogenic cooling (which are known commonly as storable 

fuels), deliver specifIc impulses of about 250 sec; liquid hydrogen, which requIres 

cryogenIc cooling, can deliver a specIfic impulse of the order of 450 sec 

(ref. 2). At this time, one cannot judge the relative merits of these fuels. For 

purposes of thIS review, therefore, a specIfIc Impulse of 350 sec (the average 

between the hIgh and the low) wIll be assumed. The correspondIng exhaust velocIty 

Vj , WhICh is by defInItion a product of g (Earth's gravitational acceleration) and 

specIfIc impulse, becomes 

Vj = 3,430 m/sec (1) 

The fInal payload wIll depend partly also on where the vehicle is launched. For 

example, the least fuel is required for launches from the Equator. In the interest 

of sImplIcIty, therefore, equatorIal launches will be assumed in thIS analysis. 

To transfer from a LEO to a GEO, one must follow an elliptIc orbIt wIth perIgee 

and apogee COIncIdIng wIth the LEO and GEO, as shown in figure 2. The average 

cIrcular velocIty around the center of Earth is well known: at an altitude of 

150 km (LEO), It IS 7,768.5 m/sec; at an altitude of 42,210 km (GEO), it IS 

3,069.8 m/sec. For the elliptic orbit wIth perigee at 150 km (LEO) and apogee at 

42,210 km (GEO), the perIgee velocity at an altitude of 150 km (LEO) IS 

10,342.4 m/sec; and the apogee velocity at an altitude of 42,210 km (GEO) IS 

1,580.7 m/sec. In order to transfer from the circular orbit at LEO to the ellIptIc 

transfer orbIt, therefore, a velocIty Increment ~V (=Vf - V ) of 2,573.9 m/sec IS 

necessary. After reachIng the GEO, there must be another veroclty Increment ~V of 

1,489.0 m/sec In order to stay In the cIrcular orbIt. 

The well-known rocket equatIon relates the velocity Increment ~V to the 

requIred mass of fuel by 

where Ml IS the InItial mass, which Includes the mass of the expended fuel, and 

Mf is the fInal mass. For the case under consideration, the mass ratios become 

For perigee burn Mi/Mf = 2.118 

For apogee burn Mi/Mf = 1.544 

The mass ratio product = 2.118 x 1.544 = 3.270 

4 

(2) 

(3) 

(4 ) 

(5) 
At present, the upper stage vehicles used for this purpose are expendable, that 

is, they are discarded after one use (see f1g. 2(a». This expendable upper stage 

1S becoming expens1ve for the following reasons: (1) the cost of manufacturing and 

testing, and (2) relatively high insurance premiums because of low rel1ab1lity. By 

making the upper stage vehicle reusable, one could eliminate both these problems and 

ach1eve a considerable commercial advantage. Such a conceptual veh1cle, operating 

solely on rocket engines for produc1ng ~V's, as depicted in figure 2(b), is 

referred to as orbital transfer vehicle (OTV) (ref. 3) . 

. ~ The OTVs suffer from one seriOUS handicap, however. After delIverIng the 

payload to the GEO, the OTV must now expend the mass rat10 of 3.270, the same mass 

ratio as for the ascent, 1n order to descend to the LEO. Slnce there 1S a f1xed 

mass for the eng1nes, fuel tanks, and control and command components, th1S mass 

ratio requirement of 3.270 greatly reduces the true payload capac1ty of the OTV. 

The idea of aeroassisted orbital transfer vehicle (AOTV) was 1n1t1ated orig1-

nally to alleviate this difficulty (refs. 4,5). An AOTV would be equipped w1th an 

aerodynam1c surface that would produce drag (and some lift, if poss1ble) and withstand whatever heat 1t would be exposed to. On return from the GEO, the AOTV would 

d1ve 1nto Earth's atmosphere and Sk1P out of 1t as shown schemat1cally 1n f1gure 2(c). In doing so, the veh1cle would be decelerated by drag, an operat1on 

referred to as aerobrak1ng. A small course adjustment would be necessary after the 

veh1cle skipped out of the atmosphere, but 1t could be accompl1shed by uS1ng only a 

very small amount of fuel. By th1S operation, the mass ratio required for the 

return tr1p is reduced from 3.27 to about 1.55, an advantage of a factor greater 

than 2. Though this type of AOTV theoretically requires no 11ft, a small amount of 

11ft 1S needed 1n real1ty because of the need to correct for the unforeseen deviat10n of the fl1ght course from the planned course. We can call th1S class of AOTV 

low-lift AOTVs or aerobraking AOTVs. 

The advantages of the AOTV can be determined fa1rly eas1ly (by uS1ng 

eqs. (1)-(5» 1f one knows, for example, the weight of the hardware (rocket engine, 

fuel tanks, and the command and control components) and the start1ng mass at the 

LEO. Before making such calculations, however, one must f1rst recognize that an OTV 

and AOTV have three different appl1cat1ons: (1) delivery of payloads from LEO to 

GEO, (2) retrieval of payloads from GEO to LEO, and (3) excursions to GEO in which 

no transfer of payload takes place. A retrieval may be requ1red 1f 1t 1S necessary 

to br1ng a malfunctioning satellite back to the Space Station or to Earth for 

repair. An excursion mission may suffice if the requ1red repair 1S simple enough 

that 1t could be accompl1shed in orbit. By add1ng and multiplying the numbers glVen 

1n equations (1) to (5), one obtains the payload capac1ties for these three functions, as shown 1n table 1. The values in table 1 are based on the follow1ng 

assumpt1ons: that the LEO is on an equatorial plane, that the rocket engine has 

Vj given by equation (1), and that the small amount of fuel necessary for minor 

course adjustments is neglected. As shown in the table, an AOTV can improve the 

payload capac1ty considerably over that of an OTV, although the maximum deliverable 

payload by an AOTV is st1ll less than that of an expendable rocket under the given 

assumptions. An expendable rocket cannot perform the second and the th1rd functions 

5 
at all, however. Besides, an AOTV can ?eliver payloads greater than that of an 

expendable vehicle simply by carrying extra fuel in an expendable fuel tank. For an 

AOTV, the LEO takeoff mass of 30,000 kg can be exceeded with no adverse effect; by 

attach1ng any number of expendable fuel tanks, the takeoff mass can be increased 

w1thout a limit. One interesting point to note in table 1 is that the maximum mass 

of the AOTV at the time of atmospheric entry is of the order of 10,000 kg. Detailed 

calculat10ns of this type have been carried out by various authors in recent years 

and are available in the open literature (refs. 6-12). 

Another reason for proposing an AOTV is for changing orbital inclination angle 

w1th respect to the equator (refs. 4,5). To illustrate this pOint, let us imagine a 

satellite in an equatorial orbit at the altitude of 150 km with a circular velocity 

of 7,768 m/sec. For some reason, it is desired to change to a polar orb1t. The 

requ1red ~V is 1.4142 x 7,768 = 10,986 m/sec, as indicated in figure 3. If this 

~V 1S achieved entirely by burning rocket fuel, the required mass ratio is 22.60. 

If the veh1cle is to return from the polar orbit back to the equatorial orb1t, the 

requ1red mass ratio 1S 22.60 x 22.60 = 605.4. Such a large mass ratio requ1rement 

could be reduced 1f the veh1cle could ut1l1ze aerodynamic lift. Assuming that the 

veh1cle had an aerodynamic lift1ng surface, it could dive into the atmosphere w1th 

an expend1ture of a small amount of fuel. The vehicle would fly in a h1ghly banked 

attitude so as to produce a large sidew1se force. This sidewise force could make 

the necessary direction change efficiently. This operat1on 1S referred to as aeromaneuvering (ref. 4). The vehicle would slow down dur1ng this aeromaneuver1ng 

fl1ght because of its drag. Th1S velocity decrement must be compensated for by a 

propuls1ve means, that is, by operating a rocket or an air-breathing eng1ne. 

Therefore, the amount of fuel necessary to make a given angle turn would be 

inversely proport1onal to the Ilft-to-drag ratio LID of this veh1cle. As was true 

for the aerobraking AOTV, this maneuver1ng veh1cle must skip out of the atmosphere 

and attain and des1red alt1tude expending a small amount of fuel also. For this 

type of vehicle, a large LID is preferred, and it can be designated a high-lift 

AOTV, or an aeromaneuvering AOTV. 

Unl1ke the aerobraking AOTV, the benef1ts of an aeromaneuvering AOTV are not 

easy to predict for m1ssions involving large orbital-plane-angle changes because 

there are too many arbitrary parameters that affect the payload calculation: little 

such 1nformation appears in the open literature (refs. 4,8,9). Hence, no attempt 

w1ll be made here to assess the benefits of the high-lift AOTV for this kind of 

application. However, a high-lift AOTV can be designed to perform all the functions 

of a low-11ft AOTV, in addition to its special capability (ref. 13) .. Consequently, 

much of the following discussion is also pertinent to the high-lift AOTV. 

FLIGHT REGIMES 

Since there is no reason for the AOTVs to land on the ground, the most economic 

way of operating them would be to base them in space--on the proposed Space Station 

(ref. 14) or on some similar space structure. This means that the Space Shuttle 

6 
need transport the AOTV from Earth to space only on!e. Thereafter, the Space 

Shuttle would only carry the ultimate payload cargo (satellite) and the fuel needed 

by the AOTV. The AOTV fuel could usually be transported without diff1culty, because 

on most of 1tS missions, the cargo-capab1ty of the Shuttle 1S not filled. When the 

Space Shuttle reached the Space Station, it could transfer the AOTV fuel into a 

large fuel-storage facility. In this way, the load-factor for the Space Shuttle 

could be ma1ntained at close to 100%. When an AOTV took off from the Space Station, 

it would start from zero-g. Hence, its rocket engine could be arbitrarily small in 

compar1son with the weight of the assembled AOTV. (When a rocket takes off from the 

ground, it must at least overcome Earth's gravity.) The optimum Slze and thrust of 

the rocket eng1ne can be determ1ned from other constra1nts, free from the requ1rement that 1t be greater than the takeoff weight. 

Such a space-based, reusable AOTV demands, however, that most parts of the 

veh1cle be reusable, w1th only m1n1mum maintenance. One of the most cr1tical components of the AOTV that must meet th1S requirement 1S the aerodynam1c surface (the 

aerobrake for the low-lift AOTV or the 11fting surface for the h1gh-l1ft AOTV). The 

aerodynam1c surface w1Il be subject to heat transfer from the hot shock layer flow 

around it. To be ma1ntenance-free, such a surface must not only w1thstand the heat 

but be chem1cally unaffected by atom1c oxygen that eX1sts 1n the shock layer flow. 

Presently, such mater1als are used on the Space Shuttle Orb1ter (refs. 15,16). 

These mater1als can w1thstand heat-transfer rates of the order of 200 kW/m2. For 

th1S rev1ew, therefore, 1t will be assumed that the tolerable heat-transfer rate 1S 

200 kW/m2. 

In order to roughly define the reg1me of flight of the AOTVs, we w1II assume 

the AOTV to be a sphere, which has no lift, and the drag coeff1c1ent, calculated 

from the Newton1an theory, to be Cd = 1. Equations of mot1on of such a body are 

well known (ref. 17). We w1II assume that the AOTV 1S return1ng from the GEO, and 

that 1tS mass is 10,000 kg, a typ1cal maximum value seen 1n table 1. After the 

veh1cle Sk1PS out of the atmosphere, we will assume that 1ts new apogee w1Il be 

200 km above the ground. As a trial value, we will assume the radius of the sphere 

to be 10 m. The convect1ve heat-transfer rate to the stagnat10n p01nt of a sphere 

can be approx1mated by 

(6) 

where p 1S free-stream density in k1lograms per CUb1C meter, R 1S nose rad1US 1n 

meters, and V is fl1ght velocity in meters per second (ref. 18). F1gure 4 shows 

the results of the calculat1on. As seen here, th1S vehicle approximately sat1sf1es 

the maximum allowed heat-transfer Ilm1t of 200 kW/m2. Its perigee 1S approx1mately 

80 km. 

One wonders how the nose radius R affects the convect1ve heat-transfer 

rates. Accord1ng to equat10n (6), the heat-transfer rates are 1nversely proport10nal to the square root of the nose radius. However, th1S 1S not really true 

here. For an AOTV, there exists an implicit relationsh1p between the flight 

dens1ty p and the nose rad1us R 1mposed by the fact that the veloc1ty decrement 

1 
through the aerobraking flight be the desired value. To illustrate this relationship, one begins with the equation of motion along the flightpath in the form 

dV 2 2 M dt = -(1/2)CdPV ~R (7) 

Integration of equation (7) leads to 

(8) 

where Vi and Vf are the velocities of the AOTV at the time of entry into and exit 

from Earth's atmosphere, and Ma is the mass of air displaced by the AOTV: 

Since the ratIO Vf/V l is fixed at approximately 0.75, equation (8) leads further 

to 

Ma = 0.572 x M (9) 

That is, an AOTV must displace an air mass that is about 57~ of its own mass. In 

order to accomplish this, the density regime an AOTV chooses to fly must be 

inversely proportional to the square of its radius R, that is, 

2 

p = const/R (10) 

By introducing equation (10) into equation (6), one obtains the scaling relationship 

q = canst x V3.15R-1.5 

c ( 11) 

Equation (11) shows that the convective heat-transfer rate is relatively sensitive 

to the choice of nose radius: one cannot vary the nose radius too far from the 

value of 10 m we determined earlier. 

Conversely, because of equation (10), the flight density is also sensitively 

affected by the nose radius: one cannot vary the perigee height too far from the 

value of 80 km we determined earlier. The flight regimes are, therefore, fairly 

narrowly defined. These are shown in table 2 at the perigee for an aerobraking AOTV 

with zero lift. 

More detailed analyses of the trajectories and the associated flight r~gime 

parameters have been performed analytically (ref. 19). Such calculations include 

the effects of variations in nose radius, allowable heat-transfer rate value, and 

lift-to-drag ratio LID. The results of these analyses, as well as the numberical 

calculations referred to earlier (refs. 6-12), indicate that these additional 

8 

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parameters affect the flight reglme parameters rela,ively weakly. Hence, for the 

purpose of this revlew, the parameters gIven in table 2 will be used throughout for 

the aerobraked AOTVs. 

CHEMICAL KINETICS AND RADIATIVE HEAT-TRANSFER RATES 

The shock standoff dlstance for a sphere is a function of the density ratio 

across the normal shock wave, or, equlvalently, a function of the effectlve speciflc 

heat ratio y = C ICv (see, e.g., ref. 20). The relatlonshlps among the three 

parameters are we~l known for an inviscid flow. Since the characteristlc Reynolds 

number for an aerobraked AOTV IS relatively large (1.5x105 In the tYPlcal conditlons 

shown previously), the lnvlscid assumptlon may be appllcable ln estlmatlng the shock 

standoff distance. However, the density ratlo is a strong function of the chemlcal 

state behlnd the shock wave, which is yet to be determlned. If the chemlstry is 

frozen behind the shock wave, the denslty ratio is 6, and the shock standoff distance for a sphere of 10 m radius would be about 1.2 m. If the flow behind the 

shock is In equlllbr1um, 1t would be about 0.4 m. In the low-denslty regime of 

lnterest, however, the chemical state IS most likely ln the process of chemical 

relaxatlon, that is, vlbratlonal excltatlon, dissoclatlon, and lonlzatlon. For thlS 

reason, nelther of these standoff dlstance values would be valld for the AOTV. 

There is one well-known standardized computer program that computes chemlcal 

reactions for a one-dlmensional lnvlscld flow (ref. 21), and one mlght thlnk that 

the chemical state beh1nd the shock could be est1mated by operatlng such a computer 

program. Unfortunately, such eXlstlng programs assume that all 1nternal modes of 

energy (rotation, vlbratlon, electronlc excltation, and electron translational) are 

ln equllibrium wlth the translatlonal mode of the heavy partlcles, that lS, w1th the 

gas temperature. ThlS one-temperature assumption was believed to be valld for most 

past appllcatlons. It lS well known that rotatlonal temperature equillbrates wlth 

translatlonal temperature very quickly (ref. 22). V1brat1onal excltatlon 1S somewhat slower, but ln the envlronments encountered ln past space mlsslons, lt was 

usually faster than the rates of dlssoclatlon (ref. 23). Both the vlbratlonal 

relaxatlon rates and dlssoclatlon rates are proportlonal to denslty, but dissoclation rates are more strongly dependent on translational temperature than the vibratlonal relaxation rate. At temperatures below about 10,000 K, typlcally, vlbratlonal excltation lS flnished before any slgnlficant dlssoclatlon can occur 

(ref. 23). For the AOTV, however, the translational temperature behlnd the shock IS 

over 40,000 K. Hence, vlbratlonal relaxatlon and dlssoclatlon are llkely to proceed 

simultaneously. 

It is known also that electron klnetlc temperature lnteracts strongly wlth the 

vlbratlonal modes of a molecule (ref. 24). If there is any ionizatlon or dlssoclatlon by impacts of electrons, the energy content in electron gas lS reduced by the 

corresponding amount. The equllibration between the electron translational temperature and heavy-particle translational temperature is slow because of the large mass 

9 
disparity between them (refs. 25,26). This causes the electron translational temperature to deviate from the heavy-particle translational temperature. 

Recent studies show that the low electronic states of atoms and molecules are 

easily excited to their Boltzmann values on impact by electrons (ref. 25). As a 

result, for the purpose of approximately determining the total energy contents in 

the electronic excitation mode, one may assume the electronic excitation temperature 

to be the same as the electron translational temperature. 

For these reasons, the chemical reactions in the shock layer over an aerobraked 

AOTV reqUires, in general, the recognition of three different temperatures: heavyparticle translational and rotational, vibrational, and electronic eXCitation and 

electron translational (ref. 26). If the flow conditions were such that the interaction between the electron translational energy and vibrational eXCitation is 

allowed to proceed frequently, then one could further assume that the vibrational 

temperature and the electron-electroniC temperature are the same, leading to a twotemperature situation (refs. 27-29). 

To compute the reacting flows under this two- or three-temperature environment, 

reaction rate coeffiCients must be expressed in terms of these different temperatures. At present, very little is known of this multltemperature description of 

rate coeffIcients, although work is in progress in an effort to understand the 

phenomena (ref. 30). 

ThiS problem can be approached from a purely experimental viewpOint. Unfortunately, however, even the experimental data are contradicting and confusing. Beginning in the late 1950s and continuing until about 1970, shock tubes were operated to 

observe the flow behavior behind strong shock waves (refs. 31,32). Shock velOCitIes 

In excess of 10 km/sec have been generated in such facilities. The free-stream 

denSities in such tests were, however, tYPically 5 to 10 times higher than those 

given in table 2. In such tests, the intensity of radiation was measured With an 

Instrument located outSIde the shock tube, looking through a window, as a functIon 

of the distance from the shock wave. The wavelengths of the observed radiatIon were 

varied over a wide range. In all such tests, it was found that the radIatIon intensity was zero at the shock wave, rose to a peak, and decayed and approached a 

plateau (see fig. 5(a». The distance (or, equivalently, the time) to the peak x

P' 

the distance to the eqUIlibration pOint Xe (defined as the pOint where radiation 

emiSSIon Intensity becomes 1.1 times the plateau value), and the peak Intensity 

value Ip have been measured over a wide range of conditions. 

The peak intenSIty Ip was seen to be between about 2 and 15 times stronger 

than the plateau values, depending on the wavelength (ref. 31). ThIS phenomenon 

became known as nonequillbrlum overshoot, or nonequilibrium enhancement, of radiation. The quantities x

P' xe ' and Ip were found to approximately obey the 

so-called binary scaling law (refs. j1,32). That is, xp and xe were inversely 

proportional to the gas denSIty, and Ip was proportional to density. As a result, 

when xp and xe were multIplied by the free-stream density and then plotted, all 

data fell within two narrow bands. The area under the intensity curve in fIgure 5(a), from x = 0 to x = xe became approximately independent of free-stream 

10 
r 

denslty. This integrated intensity was referred tj as nonequilibriurn radlatlon 

lntensity (ref. 31). Figure 5(b) shows schematlcally how the various temperatures 

mlght be varying to produce the observed radlative behavlor. 

The shaded areas 1n f1gure 6 show the exper1mentally determined x and xe 

values (ref. 31). Until recently, there has not been any serious effor~ to quant1-

tatively expla1n the observed data. Most recently, an effort was made to understand 1 

the observed phenomena, using the best available computing techniques. To do so, J 

however, the form of dependence of var10US react10n rates on v1brational and 

electron-electron1c temperatures had to be assumed (ref. 28). The results of such 

calculat10ns are glven 1n reference 28, and are reproduced In flgure 6. The symbols 

1n the figure show the results of the calculations obta1ned uS1ng varlOUS different 

chemlcal k1net1c assumptions. Readers are referred to reference 28 for the mean1ng 

of the assumpt10ns represented by each symbol. It 1S apparent from the flgure that 

we are not yet able to quantitat1vely explain the observed nonequ1l1br1um rad1at1on 

enhancement phenomenon. 

In f1gure 7, which 1S also reproduced from reference 28, the measured and 

calculated lntegrated intens1ty are compared 1n a slm1lar manner. The calculated 

values are somewhat closer to the measured values 1n th1S plot than 1n f1gure 6, but 

are still not satisfactory. One not1ces also that the measured 1ntegrated 1ntensities show scatter by a factor of nearly 4 at the most cruc1al veloc1ty of 9 to 

10 km/sec. (Although the per1gee velocity 1S approxlmately 9 km/sec, the maX1mum 

rad1atlon occurs Sllghtly before perlgee 1S reached, at which t1me the fllght veloc1ty 1S about 10 km/sec.) Th1S extent of uncerta1nty 1S perhaps too large to be 

tolerated for the purpose of des1gn1ng an AOTV. 

In add1t1on to the shock-tube exper1ments, fl1ght experiments were conducted 1n 

the early years to 1nvestlgate the chem1cal k1netic behav10r 1n the shock layer over 

a reentry vehicle. Those fl1ght-test projects are named F1re (refs. 33,34), Apollo 

(ref. 35), PAET (Planetary Atmospherlc Experlment Test) (ref. 36), and RAM (Radlo 

Attenuation Measurement)-C (refs. 37-41). The Flre veh1cle was an approxlmately 

1/4-scale model of the Apollo entry module. In both the Flre and Apollo experlments, the total radlatlon power lncldent on the stagnat10n reg10n was measured, 

uS1ng several different lnstruments. In the PAET experlment, a multlple of narruwband monochromators were 1nstalled to measure the rad1at1on lncldent on the stagnat10n reg1on. In RAM-C test, m1crowave exper1ments (attenuat1on, reflect1on, and 

phase Sh1ft) were conducted to determlne the behavior of electrons 1n the shock 

layer. 

However, the results of these fllght tests dld not lead to any deflnlte explanatlon or conclus1on. In the case of Fire and Apollo, the radiat1ve heat-transfer 

rates measured near an alt1tude of 80 km were much lower than those deduced from the 

shock-tube exper1ments. This observed phenomenon prompted a hypothes1s known as 

"coll1s1on-l1m1ting" (refs. 33-35). Rad1at1on 1S a result of decay1ng of h1ghly 

exc1ted atoms and molecules lnto lower excited states. The exc1tat1on occurs as a 

result of colllsions wlth partlcles (atoms, molecules, and electrons). The rates of 

such exc1ting collisions are proport1onal to gas density, and the rates of radiatlve 

decay are independent of gas density. By equat1ng the rates of coll1sional 

11 

t 

I 
excltation and radiative decay rates, one finds that the radiation intensity 

decreases rapidly when the gas density is less than a certain critical value: there 

are not enough collisions to maintain the population of the highly excited states 

under this circumstance. That lS, radiation lntensity becomes "collisionlimited." The nonequilibrium radlation data taken in shock tubes were obtained at 

densitles higher than that at 80 km. If the collision-limiting phenomenon occurred 

at the altitude of 80 km, then the phenomenon could explain why the flight data were 

lower than those obtained in the shock tube. This explanation was accepted in the 

days of Apollo and was used in the deslgn of Apollo missions. 

In retrospect, however, this "collislon-limiting" theory is flawed. In the 

Apollo days, one thought that the excitation of atoms and molecules occurred mostly 

through collisions of atoms and molecules. In recent years, lt became known that 

electrons are many orders of magnitude more efficlent in electronically and vibratlonally exclting atoms and molecules (ref. 25). USlng the avallable data on 

electron-impact excltation rates, one finds that the colllslon-limltlng phenomenon 

occurs at altltudes of about 100 km (see ref. 25), instead of 80 km. 

An alternative explanation of the observed low radlation intensity ln Fire and 

Apollo lS the effect of boundary-layer growth, WhlCh is known as the "truncatlon" 

hypothesis (ref. 31). Accordlng to thIS hypothesis, the profile of electron temperature may develop a thIck, cool boundary layer near the wallowing to the hIgh 

thermal conductivlty of the electron gas. The electron temperature boundary layer 

may have grown so thick that it may extend almost to the shock wave, thereby preventing the occurrence of nonequillbrium overshoot In electron and vlbratlonal 

temperatures. That lS, the rIse ln radiatlon Intenslty lS "truncated" by the cool, 

electron boundary layer. To prove the hypothesis, however, one must carry out a 

detaIled fluId-mechanical calculatIon accountIng for the multIple-temperature chemical kinetics, WhlCh is presently beyond our capability. 

The PAET experiment (ref. 36) confIrmed that the observed radiation at a 

selected wavelength (390 nm) was higher than the equilIbrium value. Unfortunately, 

however, the experlment dld not measure the global (integrated over the entIre 

wavelength range) radiation. Also, the flight speed was considerably lower than 

that of AOTV. Analysis lS in progress to explain quantitatively the values obtaIned 

ln the PAET test, and has met with partlal success. For a thorough verlflcatlon, 

however, one must awaIt generation of all the multltemperature rate coeffIcients 

mentioned earlIer. 

The results of the RAM-C test have been analyzed by several investlgators 

(refs. 37-41). Each Investigator was able to explaln a portion of the data produced. However, there IS no unlfYlng analysis that explalns all aspects of the 

data. 

These uncertainties about chemlcal klnetics have a serlOUS Impllcation for the 

deSIgn of an aerobraked AOTV. If the shock-tube data shown in figure 7 are correct, the radlative heat-transfer rate qr could be 

40 ~ q ~ 400 kW/m2 (12) r 

12 
This additional heat-transfer rate imposes a seriou~ burden on the heat shield. If 

the collision-limiting theory is correct, this large radiative heat-transfer rate 

WIll not occur; if the truncation theory is correct, however, thIS heat-transfer 

rate may have to be added to the convective rates of 200 kW/m2 (see table 2) In the 

design of the heat shield. This is because, since the AOTV IS larger than Apollo, 

the truncatIon phenomenon is less lIkely to occur for the AOTV than for Apollo. 

To remove thlS uncertainty, three efforts must be undertaken slmultaneously: 

(1) there must be a fluld-mechanical computer program that calculates flow fIeld 

around a gIven multIdimenSIonal body, accounting for the effects of multltemperature 

chemical klnetics; (2) chemical and physical parameters needed in the above calculatIons must be generated; and (3) after computing the flow propertIes USIng the two 

items above, one must be able to compute radiative characterIstICS for the multitemperature nonequillbrium gas. 

Of these three, task (3) is relatively the easiest. A computer program named 

HF730 was wrItten in 1969 that allows differences among translatIonal, rotatIonal, 

VIbrational, and electron temperatures (ref. 42). However, this program assumed a 

Boltzmann distribution of internal states at these given temperatures. In the 

nonequl1ibrium flow under conslderation, the internal state populatIons are governed 

not by the Boltzmann relation but by one known as the "quasl-steady-state" relatlonShIP, which states that the sum of all electronic transltlons lnto a state lS 

approXImately equal to the sum of all transitions going out of the state 

(ref. 25). A new computer program named NEQAIR (ref. 25) has been wrltten by lncorporatlng thIS prInciple into the HF730 program. The NEQAIR program reqUIres a large 

set of eXCItation rate-coefflclent values, only some of which are presently available; however, work is in progress ln all these areas. 

STABILITY, GUIDANCE, AND CONTROL 

In the foregoing dlScusslons, the aerobraking AOTV was assumed to be spherIcal 

and hence to have no 11ft. In practIce, a small amount of 11ft IS necessary for 

maneuverIng. The velocity and flight angle at the tIme of atmospheric entry can be 

dlfferent from the planned values because of errors in the operatIon of the maIn 

rocket engines, both in thrust and In dIrectIon. In order to correct for any such 

errors, the vehicle must be maneuvered while ln the atmosphere. 

Also, it became known In recent years that the denSIty of the atmosphere In the 

altItudes of interest can vary over a WIde range, that lS, nearly by a factor of 2 

(refs. 17,43). The vehlcle must be able to vary lts fllght altltude so that lt 

satisfIes equation (9). For these reasons, an aerobraklng AOTV must maneuver to 

attaIn the required altltude. Llft capabllity would also be helpful in makIng small 

changes ln orbltal-plane inclination angle. For the Space Shuttle-Space StatIon 

system, the most likely LEO would be inclined 28.5° from Earth's equatorial plane 

(because the launch pad in Florida lS ln this inclined plane). By bankIng Into the 

13 
appropriate side during the atmospheric flight, the vehicle could approach the 

target LEO orbit partially aerodynamically. 

In space, a spacecraft's control of its attltude is accomplished by firing 

small rocket engines known as reactlon control system (ReS) engines. An AOTV could 

use the ReS engines also for controlling its attitudes during atmospheric flight. 

To do so, however, it would be desirable to have a neutral stability in the mode to 

be controlled by an ReS engine. Otherwise, there will be an aerodynamlc coupling 

between different modes (such as yaw-to-roll coupling). 

To provide a neutral aerodynamic stabillty for an AOTV is not so easy, because 

the center of gravity (c.g.) will vary widely depending on the misslon and on the 

amount of fuel remalning in the tanks. Since it is most likely that the vehicle 

will have a left-right symmetry, the c.g. variation will affect the pltching stability parameter most severely. These considerations lead to the concluslon that the 

primary consideration In the design of an aerobraked AOTV is to have an acceptable 

pitching stability at all possible c.g. locations at the highest allowed angle of 

attack. With respect to yaw and roll, the vehicle must have a neutral stablllty. 

An aerobraked AOTV will thus fly at the hlghest angle of attack allowed by its 

pitching stability crlterion (and other criteria if any; see the next section), by 

controlling the c.g. location. The yaw angle must be kept as close to zero as 

possible, so that there will be minimum interaction between yaw and roll. The roll 

angle wlII be controlled by the use of ReS engines. The effective average angle of 

attack and LID can be lowered by alternating the bank angle between a positive and a 

negative value. A course change can be accomplished also by malntaInlng a fixed 

bank angle. In this way, the vehicle has a two-parameter control in lts 

maneuvering. 

How an aerobraked AOTV can negotiate an atmosphere with greatly varylng density 

lS yet to be determlned (ref. 17). The worst situatlon wlII occur when denSIty lS 

distributed nonuniformly: a high denslty during the descent (entry) flight and low 

denslty durIng the ascent (exit) flIght. It would be highly desirable to know the 

denSIty dlstribution before the atmospheric flight, and that posslbllity lS presently under study (ref. 44). A multiple atmospheric pass is suggested as one way of 

reduclng the effect of density uncertainty (refs. 7,8,11). 

Another benefit of a finite LID is that it enables an AOTV to fly at a higher 

altitude than with an LID = O. By flying at a small negative average LID, such as 

-0.1 or -0. 15--by alternating the bank angle between 1100 and -1100 for example--the 

AOTV can stay withln the atmosphere at hlgher altitudes than with an LID = 0 (see 

refs. 7, 7, and 17). Thls wlII lower both the convective and radlatlve heattransfer rates. Since equation (9) must be satisfied even in this case, the fllghtpath will become longer; but this poses no problem for an AOTV. 

I 

The multiple atmospherlc pass mentioned above has one added beneflt. A multiple pass results in a longer atmospheric fl1ghtpath. In order to satisfy equation (9), the vehicle must fly through an atmosphere of lower denslty than that In 

the single pass case; that IS, It must fly at higher altitudes. This causes both 

14 
convective and radiative heat-transfer rates to be i'educed in relatlon to the 

slngle-pass case (refs. 7,8). 

EXAMPLES OF PROPOSED DESIGNS 

Ballute 

[ In this design, the aerobrake consists of a balloon-llke elastlc gas bag, 

Inflated to the shape of a blunt body (fig. 8); It IS called a ballute (comblnatlon 

of balloon and parachute). Its size will be varled by controlllng the pressure 

InSlde the gas bag. It has been shown experimentally (ref. 45) that such a body can 

vary the drag coefficlent over a factor of close to 2. The rocket englnes could 

posslbly be mounted on the tall side (fig. 8(a» or at the nose slde (flg. 8(b». 

The maln advantage of thlS deslgn is that it could be the llghtest and cheapest to 

make of all the optlons. 

There are, however, two potential problems with the ballute. The flrst IS that 

the varlatlon of drag coefficlent produces only one-degree-of-freedom control. As 

was mentioned In the precedlng sectlon, most of the other proposed deslgns have a 

two-degree-of-freedom control on the motion of an AOTV. A two-degree-of-freedom 

control would be preferable to one-degree-of-freedom control. The second posslble 

problem concerns the questlon of statlc stability when the ballute IS deformed as a 

result of an asymmetrlc external pressure dlstrlbution. No study has yet been made 

of the aerodynamic characterlstlcs of a ballute that IS only partlally Inflated and 

that IS set at a finite angle of attack. Common sense would predIct that the windward side would depress Inward owing to the increased shock-layer pressure there, 

whlle the lee would bulge out because of the decreased pressure there. ThlS WIll 

tend to produce a moment that wlli Increase the angle of attack, leadlng to a static 

Instabllity. To aVOId the occurrence of such statlc Instabillty, the locatlon of 

the c.g. may have to be compromised. Therefore, a careful analysis must be carr led 

out regarding the stablilty questlon, before serlOUS conslderatlon IS glven to the 

ballute scheme. 

ConIcal Llfting Brake 

In this concept, the aerobrake conslsts of a sphere-cone, WhICh resembles 

spacecraft of past NASA mlSSlons (ref. 46). The configuratIon currently favored 

uses a 70° cone with the sphere radIUS equal to the frustum radlus. The 70° cone 

was selected because It showed the largest range of allowable c.g. locatIons 

(ref. 47). This vehicle could be utilized in two ways, dependlng on ItS mlSSlon. 

For a delIvery mission, the payload could be placed on the opposite slde of the 

rocket engine, as shown in figure 9(a). For a retrieval mIssion, however, the 

payload would have to be on the same SIde as the englne (fig. 9(b». 

In addition to the fact that thIS design allows WIdest varlation In the c.g. 

locatlons, it has an advantage in that the stress on the components occurs only In 

15 
one dlrection: the direction of rocket thrust and the dIrection of the aerodynamic 

drag coincide approxlmately. 

The maln potential problem of this design concerns the yet unknown phenomenon 

WhlCh somehow increases both pressure and heat-transfer rates in the base region at 

a flnlte angle of attack (ref. 48). If the phenomenon IS genuine and insurmountable, thlS design could be used only when the dlstrlbution of densIty in the atmosphere is known beforehand. 

Raked Cone 

The raked cone IS an eillpsoidal body truncated strongly asymmetrlcally 

(ref. 12), as shown in figure 10. Notice that the fuel tanks are SplIt into two (or 

more) parts and are placed far apart. By controillng the relatlve amounts of fuel 

In each tank, the vehicle could adjust ItS trlm angle of attack to a certaln 

extent. Its optlmum LID IS about 0.3, the highest of all eXlsting deslgns. The 

hlgh LID makes it posslble to fly at the hlghest negatlve LID, thereby at altitudes 

substantially higher than 80 km. Conversely the nose radlus of this vehlcle can be 

made smaller than 10 m and stlll satlsfy the llmlt on the heat-transfer rate glven 

In table 2. The comblnatlon of the high altltude, WhlCh tends to induce the 

collislon-Ilmltlng phenomenon mentIoned earller, and small nose radlus, WhlCh tends 

to induce the truncation phenomenon, could cause the radiative heat-transfer rate to 

thlS body to be smaller than that glven by equatlon (12). 

There are two problems associated wlth the raked cone. The first is the dlfficulty In placlng the c.g. on the thrust llne of the maln rocket englnes; dependlng 

on the mass and dlmenslons of the payload and the amount of fuel remalnlng In the 

tanks, the c.g. point may vary over a wlde range. Glmbaillng the maln englnes to 

accommodate this c.g. change wlil be dlfficult. The second problem IS that the 

structures must withstand stresses In two dlrectlons: the dlrectlon of the thrust 

llne when the englnes are flrlng, and the dlrectlon of flight durlng atmospherlc 

deceleration. 

FLUID MECHANICS OF BASE FLOW 

In both the conical llftlng brake (flg. 9) and the raked cone (flg. 10), the 

payload may have to be carrled In the base reglon to form a protrudlng afterbody, as 

shown In the figures. If there is any amount of heat transfer from the base flow 

Into the protrudlng afterbody, then the payload may be overheated. A satelilte IS 

deslgned usually so that when deployed It can wlthstand radlatlve heatlng from the 

Sun and its reflection from Earth, the sum of WhlCh IS about 2 kW/m2. A deployed 

sateillte has large protruslons such as solar cells and antennae. How these ,protrudlng parts can be folded so that they flt wlthln the confines of the base reglon 

IS yet to be determined. Whatever the Solutlon, however, the maxlmum allowable 

heat-transfer rates to the payload are llkely to be falrly small. 

16 
Convective and radiative heat-transfer rates to the base region of a reentry 

vehicle have been studied over the years (refs. 49-52). It is known that both 

convectlve and radiative heat-transfer rates Increase with base pressure. In most 

past reentry vehicles, the base pressure was quite small, that IS, of the order of 

1% of that of the front stagnation pOlnt value (ref. 52). As a result, the base 

heat-transfer rates were also usually very small. 

One cannot necessarily expect this to be the case for an AOTV. For the reentry 

vehIcles studied in the past, there were no protruding afterbodies. For both the 

conlcal lifting brake and raked-cone configurations, however, there would be protruding afterbodles at the time of entry when they are used for retrieval mlSSlons. The experimental data taken in a hypersonic wind tunnel wlth a conIcal 

llfting brake (ref. 48) show that both pressure and convective heat-transfer rates 

can be very high over certaln portlons of the afterbody when the vehicle IS at a 

finite angle of attack. Under certain circumstances, the convective heat-transfer 

rates are so high that It seems as If the flow expanding from the frustum may be 

hitting the afterbody to produce an obl1que shock wave, or that a shock wave may be 

Imping1ng on the spot (ref. 48). 

In order to understand the nature of the flow In the base of a conlcal llfting 

brake, an effort IS presently being made to study the phenomenon in a different type 

of facility. At Ames Research Center, scale models of such vehIcles are flown 1n a 

hypersonic, free-flight range, and shadowgraph pictures are taken of the flow field 

around the flying models. The results are being analyzed wlth the help of computat10nal fluld dynamics (ref. 53). A slgnlficant dlfference 1S appearIng between the 

base flow f1eld of this type of AOTV and that without a protrud1ng afterbody 

(ref. 54). The computed flow field shows that there are two rec1rculating reg10ns 

In the flow rather than one: one between the aerobrake and the afterbody, and the 

other beh1nd the afterbody. The fIrst recIrculatIng regIon resembles a twodimenS10nai separated flow produced by a backward-facIng step (refs. 53,54), and the 

second IS an aXlsymmetrlc base flow. It is known that the two-dImensIonal separated 

flow over a backward-facing step produces a recirculat1ng regIon pressure WhlCh IS 

substantially higher than in the base of an aXlsymmetr1c body WIthout protrudIng 

afterbody (refs. 52,54). Thus, one sees a possiblilty of relat1vely hIgh base 

pressure for the AOTV, which may cause high convectlve and radIative heat-transfer 

rates. However, the geometrlcal and flow parameters under WhICh such nearly twodImenSIonal behavior occurs are totally unknown. 

The base flow for the raked cone has not been studied at all. One interestIng 

aspect of this flow is the possible effect of a strong asymmetry In the base flow. 

In order to produce the relatlvely large lift coefficient inherent wlth this deSIgn, 

the flow 1n the base must have a substantial downward velOCIty component. There IS 

a possibility even of vortices resemblIng wing-tip vortIces, In order to accommodate 

this large downward velocity. The flow behavior under thlS configuration and 1tS 

effect on the protruding payload have yet to be studled. 

17 
CONCLUSIONS 

Aeroassisted orb1tal transfer veh1cles are useful for two purposes: they can 

carry satellite payloads between GEOs and the Space Station, and between nearequatorial orbits and near-polar orbits on a reusable basis. Because of 1ts reusabil1ty, high reliab1lity resulting from the reusab1l1ty, and substitution of aerodynamic forces for a rocket engine burn, the AOTVs can introduce a substantial advantage 1n commerc1al utilization of space. The fl1ght regimes of the veh1cle are 

defIned relatively narrowly from the varIOUS practical constraints; the regimes are 

such that nonequilibr1um v1brational excItatIon, dissociation, and Ionization wIll 

proceed slmultaneously in the shock layer over the veh1cle. Present understanding 

of these chem1cal kinet1c phenomena 1S poor. The requ1rement that these veh1cles 

may have to carry the1r cargo In the base reg1on, as a protrudIng afterbody, Introduces a un1que flUId-mechanical problem of base flow. 

18 
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19 
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20 
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Nelson, ed., Amerlcan Institute of Aeronautlcs and Astronautlcs, New York, 

N. Y ., 1985, pp. 3-53. 

27. Park, C.: Radiation Enhancement by Nonequillbrium in Earth's Atmosphere. J. 

Spacecraft & Rockets, vol. 22, no. 1, Jan.-Feb. 1985, pp. 27-36. 

28. Park, C.: Problems of Rate Chemistry ln the Fllght Reglmes of Aeroassisted 

Orbital Transfer Vehicles. Progress ln Astronautics and Aeronautics, 

Vol. 96, Thermal Design of Aeroassisted Orbital Transfer Vehlcles, H. F. 

Nelson, ed., American Institute of Aeronautlcs and Astronautics, New York, 

N. Y ., 1985, pp. 511-537. 

29. Park, C.: On convergence of Computation of Chemically Reacting Flows. AIAA 

Paper 85-0247, Reno, Nev., 1985. 

30. Jaffe, R. L.: Rate Constants for Chemical Reactions ln High-Temperature Nonequlllbrlum Alr. AIAA Paper 85-1038, Wililamsburg, Va., 1985. 

31. Allen, R. A.; Rose, P. H.; and Camm, J. C.: Nonequilibrlum and Equlllbrlum 

Radlation at Super-Satellite Reentry Velocitles. Research Report 156, AVCOEverett Research Laboratories, Everett, Mass., Sept. 1962. 

32. Arnold, J. 0.; and Whitlng, E. E.: Nonequillbrlum Effects on Shock-Layer 

Radiometry durlng Earth Entry. J. Quant. Spectrosc. Radiat. Transfer, 

vol. 13, no. 9, Sept. 1973, pp. 861-870. 

33. Cauchon, D. L.: Project Fire Flight 1 Radlative Heating Experiment. NASA 

TM X-1222, 1966. 

21 
34. Cauchon, D. L.: Radiative Heating Results from the Fire 2 Flight Experiment at 

a Reentry Velocity of 11.4 Kilometers per Second. NASA TM X-1402, 1967. 

35. Lee, D. B.; and Goodrich, W. D.: The Aerothermodynamic Environment of the 

Apollo Command Module during Super-Orbital Entry. NASA TN D-6792, 1972. 

36. WhItIng, E. E.; Arnold, J. 0.; Page, W. A.; and Reynolds, R. M.: 

of the Earth's Atmosphere by Shock-Layer Radiometry during the 

Probe Experiment. J. Quant. Spectrosc. Radiat. Transfer, vol. 

Sept. 1973, pp. 837-859. 

compositIon 

PAET Entry 

13, no. 9, 

37. Evans, J. S.; Schexnayder, C. J.; and Huber, P. W.: Computation of IonIzatIon 

in Re-Entry Flowfields. AIAA J., vol. 8, no. 6, June 1970, pp. 1082-1089. 

I 

38. Nerem, R. M.; and DIlley, J. F.: An Analysis of Re-Entry Flight Measurement of 

Shock Layer MIcrowave RadIation. AIAA J., vol. 8, no. 7, July 1970~ 

pp. 1295-1301. 

39. Adams, J. C., Jr.: Shock SlIP AnalysIs of Merged Layer Stagnation POInt AIr 

IonIzatIon. AIAA J., vol. 8, no. 5, May 1970, pp. 971-973. 

40. Kang, S. W.: Nonequlllbrlum, Ionized, Hypersonic Flow over a Blunt Body at Low 

Reynolds Number. AIAA J., vol. 8, no. 7, July 1970, pp. 1263-1270. 

41. Kang, S. W.; Dunn, M. G.; and Jones, W. L.: Theoretical and Measured ElectronDensity DIstrIbutions for the RAM VehIcle at High Altitudes. AIAA 

Paper 72-689, Boston, Mass., 1972. 

42. WhItIng, E. E.; Arnold, J. 0.; atl~ Lyle, G. C.: A Computer Program for a LIneby-Line Calculation of Spectra from Diatomic Molecules and Atoms Assuming a 

VOIgt Profile. NASA TN D-5088, 1969. 

43. Talay, T. A.; WhIte, N. H.; and Naftel, J. C.: Impact of AtmospherIc UncertaInties and Real Gas Effects on the Performance of Aeroassisted OrbItal 

Transfer VehIcles. Progress In Astronautics and AeronautIcs, Vol. 96, 

Thermal Design of Aeroassisted Orbital Transfer VehIcles, H. F. Nelson, ed., 

AmerIcan InstItute of AeronautIcs and Astronautics, New York, N.Y., 1985, 

pp. 198-229. 

44. Menees, G. P.; Park, C.; WIlson, J. F.; and Brown, K. G.: 

AtmospherIc Densityh USIng a Space-Launched ProjectIle. 

Reno, Nev., 1985. 

DetermInation of 

AIAA Paper 85-0327, 

45. Woods, W. C.; Andrews, D. G.; ana Bloctscher, F.: Experimental Evaluation of 

an Inflatable Ballute for Appiication to Aeroassisted Orbital Transfer 

Vehicles. AIAA Paper 84-0409, Reno, Nev., 1984. 

2i 
46. IntrierI, P. F.; De Rose, C. E.; and Kirk, D. B.: Flight CharacteristIcs of 

Probes in the Atmosphere of Mars, Venus, and the Outer Planets. Acta Astronautica, vol. 4, no. 7-8, July-Aug. 1977, pp. 789-799. 

47. DaVIes, C. B.; and Park, C.: Aerodynamics of Generalized Bent BIconlcs for 

Aeroassisted, Orbital-Transfer Vehicles. J. Spacecraft & Rockets, vol. 22, 

no. 2, Mar.-Apr. 1985, pp. 104-111. 

48. Shih, P. K.; and Gay, A.: Low Lift-to-Drag Aerobrake Heat Transfer Test at 

Mach 10. Progress in Astronautics and Aeronautics, Vol. 96, Thermal DeSIgn 

of Aeroassisted OrbItal Transfer Vehicles, H. F. Nelson, ed., AmerIcan 

Institute of Aeronautics and Astronautics, New York, N.Y., 1985, 

pp. 378-394. 

49. Murphy, S. N. B.; and Osborn, J. R.: Base Flow Phenomena WIth and without 

InJectIon: Experimental Results, Theories, and BiblIography. Progress in 

Astronautics and Aeronautics: Aerodynamics of Base Combustion, Vol. 40, 

S. N. B. Murphy, ed., AmerIcan Institute of Aeronautics and AstronautIcs, 

New York, N.Y., 1979, pp. 345-367. 

50. Park, C.: ModelIng of Radiative Heating in Base RegIon of Jovian Entry 

Probe. Progress in AeronautIcs and Astronautics: Entry Heating and Thermal 

ProtectIon, Vol. 69, W. B. Olstad, ed., American Institute of Aeronautics 

and Astronautics, New York, N.Y., 1980, pp. 124-147. 

51. ShIrai, H.; and Park, C.: Shock-Tube StudIes of RadIatIve Base HeatIng of 

JOVIan Probe. Shock Tubes and Waves, Proceedings of the 12th InternatIonal 

Symposium on Shock Tubes and Waves, A. Lifshitz and J. Rom, eds., Magnes 

Press, The Hebrew University, Jerusalem, 1980, pp. 419-428. 

52. Brant, D. N.; and Nestler, D. E.: Development of an Afterbody RadIatIve and 

Convective Heating Code for Outer Planet Probes. Progress In AstronautICS 

and Aeronautics: Outer Planet Entry HeatIng and Thermal ProtectIon, 

Vol. 64, R. Viskanta, ed., AmerIcan InstItute of Aeronautics and AstronautICS, New York, N.Y., 1979, pp. 345-367. 

53. Lombard, C. K.; Vankatapathy, E.; and BardIna, J.: Forebody and Base Flow of a 

Dragbrake OTV by an Extremely Fast Single Level Implicit Algorithm. AIAA 

Paper 84-1699, Snowmass, Colo., 1984. 

54. Chapman, D. R.; Kuehn, D. M.; and Larson, H. K.: Investigation of Separated 

Flows in Supersonic and Subsonic Streams with EmphaSIS on the Effect of 

TransitIon. NACA TechnIcal Report R-1356, 1957. 

23 
TABLE 1.- PAYLOAD AND MASSES OF THE UPPER STAGE VEHICLE, IN kg, UNDER THE 

MOST IDEAL CONDITIONS, STARTING FROM AN EQUATORIAL LOW-EARTH-ORBIT AT 

150 km, WITH A ROCKET ENGINE WITH A SPECIFIC IMPULSE OF 350 sec 

Space Shuttle upper stage Ariane 

Mass at takeoff from LEO assumed 30,000 4,500 

Type Expendable OTV AOTV Expendable 

Mass of hardware assumed 2,000 2,000 3,000 300 

Delivery to GEO Payload 

Reentry mass 

Retrieval from GEO Payload 

Reentry mass 

Excursion to GEO Payload 

Reentry mass 

7,174 

o 

o 

o 

o 

o 

2,634 

2,000 

1,160 

3,160 

806 

2,806 

4,542 

3,000 

8,349 

11,349 

2,942 

5,942 

TABLE 2.- TYPICAL PERIGEE CONDITIONS FOR AEROBRAKED AOTV 

Al ti tude, km .........................•.............•.• 80 

Convective heat-transfer rate qc' kW/m2 ............. 200 

Density p, kg/m3 .....••....................•..... 2xl0-5 

Mean free path A, m ....................•...••.... 4xl0-3 

Nose radius R, m ..•.•.......•...•••••......••...•••.. 10 

Reynolds number, pVR/~ •.............••.•••....•.. 1.5xl05 

Stagnation pressure ps' atm .......•..••........... 0.015 

Velocity, V, km/sec •..•..............•.••............. 9 

Viscosity ~, kg/(m.sec) ....••...•••.••.......•. 1.2x10-5 

24 

1,442 

o 

o 

o 

o 

o 
SPACE SHUTTLE ARIANE 

(USA) (ESA) 

LEO PAYLOAD 30,OOOkg 4,500kg 

TAKE OFF 2,OOO,OOOkg 400,OOOkg 

50m 

Figure 1.- Estimated apprOXImate weIghts of Space Shuttle and Ariane vehicles at 

takeoff and of payloads at LEO at their fully developed, future stages. 

GEO GEO GEO 

LEO LEO 

(a) EXPENDABLE (b) REUSABLE OTV (c) REUSABLE AOTV 

Figure 2.- Three different modes of transferring payloads from LEO to GEO. 

25 
776Bm/s /{t~:=10.986m/S / / \ .... I 

/ /i;6Bm/s 

// 

./" 

(a) PROPULSIVE COURSE CHANGE (b) AEROMANEUVERING 

FIgure 3.- Two methods of changing orbital plane inclination angle. 

120 250~ 

HEAT TRANSFER w 

J:N 

110 ,.../ RATE 

I X 200~ ~ E I \ I- .::e. ~ I \ u 

100 I \ 150 w w w 

Cl I \ > 2 ~ => I \ 0 ex:: 

I- 90 I \ 100 u ex:: 

I- \ 1- w 

...J \ TRAJECTORY 2 u. « en 

0 2 BO \ 50 0.. « 

"- (!) ex:: ...... I-

........ - « 

70 0 1-

CI) 

0 100 200 300 400 500 

TIME, sec 

Flgure 4.- Flight trajectory and stagnatIon pOInt convective heat-transfer rates for 

a spherIcal aerobraking AOTV with nose radius of 10 m, mass of 10,000 kg, on 

return from a GEO. 

26 
.. 

> 

IeI) 

2 

w 

I2 

2 

0 

le::( 

C 

e::( 

a: 

w 

a: 

:::> 

le::( 

a: 

w 

c.. 

~ 

w 

IySHOCK 

Xp1 

-Xe 

X 

(b) 

~----------------------------~X 

o 

DISTANCE BEHIND SHOCK 

Figure 5.- Schematics of observed varIatIon In radiatIon Intensity from the flow 

behind a normal shock wave, and probable distrIbution of various temperatures. 

27 
CALCULDA~~~~~ENT UNDER 

ASSUMPTI~8N~OR SEE REF. 

DETAILS 

1 ___ ~, 0---- __ - ,~, 

--- ,', a: rt--- " , , 

~ --- '" ........ ", 

w ___'" ::E 

<! 

a: 

<! Q.E 

::I:~ .... , 

Ox __ ::::::.._ _ __ ~_ .... 

-<t EXPERIMEN T -.................. ---_______ -~~ • 

<t X'I i0 xp ALLEN 31 ................. w 

..J ET AL 

w ,,-, x 11 

a: '"" e 10 10-

51 

7 8 9 

5 6 LOCITY. km/sec . nt x 

FLIGHT . ental VE and theor etical 28. see pa k ref. radIation 28 for Pdoe~ailel Figure 6. - Comparlson tlOn pOlnt o. fthe x experlm e (reproduce d from ref. , 

and equi:lbraf thlS flgure). explanatlon 0 

28 
... 

N 

E 

f.J 

102 -

3: A 

~ CALCULATIONS ~ 0 ... UNDER DIFFERENT 

c- o ASSUMPTIONS. Q) 

x ... SEE REF. 28 FOR 

.- • DETAILS <t 

X 

:::J 

..J 10 u. 

.- 0--

<t 

w 

J: SHOCK-TUBE & 

w 

> FLlGHT·RANGE 

.- DATA, SEE REF. 28 

<t I FOR DETAILS 

c 1 t! 

<t 5 6 7 8 9 10 11 12 13 a: 

FLIGHT VELOCITY, km/sec 

Figure 7.- Comparison of the experimental and theoretIcal nonequilibrium radiative 

heat fluxes (reproduced from ref. 28; see ref. 28 for detaIled explanation of 

thIS fIgure). 

FLOW 

c:> 

(a) 

V ....... f---

J 

(b) 

I __ .~V 

Figure 8.- Ballute configuration. 

29 

J 
70° ~V. 

PAYLOAD i!Y J 

\ ~ .... (y ~ 

\ ....... ) v 

(a) 

FLOW 

c=> 

(b) 

v~ 

J 

Flgure 9.- Conlcal llfting brake conflguration. 

FLOW 

c::> 

~ __ --- FUEL TANKS 

V 

J 

Flgure 10.- Raked-cone configuration. 

30 
1 Report No 2 Government Accession No 3 Recipient's Catalog No 

NASA TM- 86760 

4 Title and Subtitle 5 Report Date 

A REVIEW OF SHOCK WAVES AROUND AEROASSISTED June 1985 

6 Perlormlng Organization Code 

ORBITAL TRANSFER VEHICLES 

7 Authorh) 8 Performing Organization Report No 

Chul Park 85277 

10 Work Unit No 

9 Performing Organization Name and Address 

NASA Ames Research Center 11 Contract or Grant No, 

Moffett Field, CA 94035 

13 Type 01 ~eport and Period Covered 

12 Sponsoring Agency Name and Address Technical Memorandum 

National Aeronautics and Space Administration 14 SponsOring Agency Code 

Washington, DC 20546 506-51-11 

15 Supplementary Notes 

Point of contact: Chul Park, Ames Research Center, MS 230-3, Moffett Field, 

CA 94035. (415) 694-5394 or FTS 464-5394 

16 Abstract 

Aeroassisted orbital transfer vehicles (AOTVs) are a proposed type of 

reusable spacecraft that would be used to transport cargoes from one Earthbound orbit to another. Such vehicles could be based on the proposed Space 

Station and used to transport commercial satellites from the Space Station 

to geostationary orbits or to polar orbits and return. During a mission, 

AOTVs would fly through Earth's atmosphere, thus generating aerodynamic 

forces that could be used for decelerating the vehicles or changing their 

direction. This review of published AOTV research findings was concerned 

with the shock-wave-induced, high-temperature airflows that would be produced around these vehicles during atmospheric flight. In the survey, 

special emphasis was placed on the problems of (1) the chemical physics of 

multitemperature, ionizing, nonequilibrium air flows, and (2) the dynamics 

of the flows in the base region of a blunt body with complex afterbody 

geometry. 

11 Key Worm ISuggested by Authorls)) 18 Distribution Statement 

Aeroassisted Orbital Transfer Unlimited 

Vehicles 

Subject Category - 16 

19 Security Oassll (01 thIS report) 20 Security Classll (01 this page) 

121 

No 01 PIIgH 22 Price· 

Unc1ass if ied Unclassified 31 A02 

"For .ale by the NUlonal Technical Inlormatlon Service, Springfield, Virginia 22161 
End of Document