Aero Heating Review

8/2/2019 Aero Heating Review

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NASA T M X-54,056

2E &-'THE AERODYNAMIC HEATING OF ATMOSPHERE

ENTRY VEHICLES - A REVIEWBy H. Julian Allen

NASA, Ames Resea rch Cent erMoffett Field, Califo rnia

Paper for Symposium on Fundamental Phenomenain Hypersonic Flow, Cornell Aeronautical La bor ato ry,Buffalo, New Yor k , June 25-26, 1964


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The Aerodynamic Heating of Atmosphere Entry Vehicles -A Review

By H. Julian Allen*National Aeronautics and Space AdministrationAmes Research CenterMoffett Field, C a l i f .

IntroductionIt w a s only a l i t t l e more than a decade ago that aeronautical

engineers were faced with the challenge of designing the f i r s t long-range ba l l i s t i c miss i l es . Since the chemical rocket r equi res t h a tox id izer as wel l as fu el be carried, the energy content per u n i t pro-p e l l an t mass i s poor. I n addition, th e mean propulsive e ff ic ie nc y i slow s o t h a t th e r a t i o of launch weight t o empty weight i s very largeindeed. Hence every e f f o r t must be made t o keep th e payload a s la rg ea fraction of the empty weight as possible.therefore a prerequis i te for th e long-range roc ke t.

Light construction i sThe engine

designe rs were fac ed with the p r o b l e m of designing rocket motors thatwould produce very high th ru st but with l i t t l e weight. The structuralengineers were required t o bui ld the rocket sh el l s t ruct ure - mainlytankage t o hold the lar ge quantity of fu e l needed - the mass of whichw a s but a few percent of th e t o t a l mass a t launch. The guidance andcon tr ol ex pe rt s were c al le d up on to provide systems which would give amiss dis tance of about one m i l e a t a target five thousand miles away.The aerodynamicist was asked t o provide an e nt ry body f o r the warheadthat could successfully withstand the intense convective heatingexperienced upon reentry into the Ea rt h' s atmosphere. Each of these

*Assistant Director f or Astronautics


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2challenging problems - one or tw o orders of magnitude more di f f i c u l t thanthose which had been dealt with previously - w a s succ essfu lly mastered.It i s the purpose of t h i s paper t o review historically the aerodynamicheating problems of the reen try vehicles s ta rt in g with long-range b a l l i s t i cvehicles and finishing with what appear w i l l be the interplanetary spacevehicles of the future .Aerodynamic Heating During Reentry of Ba l l i s t i c Miss il es

A ba l l i s t i c vehi cl e r equi red to a t t a i n a range of the order of one-quarter the circumference of the Earth must be accelerated during theboost phase in to space t o a speed of about 7 km/sec.has a kinetic energy of aLout 25X106 m2/sec2 per u n i t mass which i sabout eight times the amount of energy required t o convert a u n i t mass

The vehicle then

of i ce in to steam.must be converted in to hea t, only a very small f rac t ion of i t can be

Clearly, i f a l a rge f rac t ion of th i s k ine t ic energy

allowed t o hea t t he vehi cl e i f the vehicle i s not t o be destroyed before

reaching the target . Therein l i e s the problem.In order t o assess the f ract ion of the energy which enters the

vehicle , consider the following simplified analysis.of the vehicle , VE, i s high and the tr aj ec to ry reasonably steep, as i sthe case f o r the ba l l i s t i c miss i l e, then the nega tive acce le ra t ion due

If the entry speed

t o d r ag is l a rge compared t o Ear ths gravi ty accelerat ion dur ing thepor t ion of t h e atmosphere e n tr y when th e he at ing is important.sim pli fy th e equation of motion t o

We may

wherem entry body massV ve loc i t y


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3t timep a i r de nsi tyACD drag coefficient

reference area (usual ly base area) fo r def ini t ion of coeff ic ients

Now, the heat ing ra te f o r these vehicles i s very l ar ge compared t othe r a t e a t vhich heat can be reradiated f r o x %he su fa c e, and thedriv ing temperature po te nt ia l promoting th e convective tr an sf er of hea ti s determined ess en ti al ly by the ai r temperature (i .e . , the wall tern-pe rat ure can be ignored by comparison t o th e a i r temperature). Underthese circumstances one may show that the rate of input of heatexpressed i n kin et ic energy units i s

dq - I. C,~V~Aa t 2where CH i s the dimensionless heat-transfer coe ffi cie nt.

Then equations (1)and (2) yield the important resul t t h a tdq = - -H(7)dv2

CD ( 3 )If w e assume for the moment that the mass, the heat- t ransfer

coefficient ,& the drag coeff ici ent may be considered co nstan t, thenthe to ta l hea t inpu t i s

where Vo i s the vehicle speed at sea l eve l .When the to t& heat input is l e a s t it can be shown that the final

speed, Vo, i s smal l compared t o the e n tr y speed so that approximately

The factor CHq = -CD


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4i s the portion of th e t o t a l kinet ic energy which must appear as heat t othe vehicle and 1 - 7 t h e portion which i s given t o the a i r . Clear ly ,we des i repossible.e n t i r e l y a convective one.convective hea t-tra nsfe r c oeff icie nt i s d i r ec t ly express ible as

7, hereinaf ter cal led the energy f rac t ion , to be as small asA t b a l l i s t i c missile speeds the heating process i s e s s e n t i a l l y

Reynolds analogy (ref. 1) e l l s us t h a t the

CF ( 7 )CH = 2where CF i s t he f r i c t ion coef f i c i en t .

In order t o keep the heat shield mass, which i s proport ional t o thet o t a l heat i nput , as small as possible, then, th e extraneous mass (seeeq . ( 5 ) ) should be kept as small as possible, s o t h a t the vehicle massmindicate the optimum w i l l be at tained when the r a t i o of f r i ct io na l forcet o t o t a l drag force is as small as possible ( r e f . 2 ) . A blunt body bestsa t i s f ies t h i s l a t t e r requirement. The energy fr ac ti o n, 7, can be madepar t i cu la r ly low i f laminar flow c a n be maintained a t the usual Reynoldsnumbers of i nt er es t fo r then the fr i ct io n coef f icie nt i s much l e s s tha n

i s no larger than necessary. In addition, equations ( 3 ) and (7 )

it would be f o r turbu len t flow.than one-half of 1percent were obtainable so that even using a so l idhea t sinlc as a sh ie ld - a poor coolant a t b es t - a s a t i s f ac t o ry en t r yvehicle could be designed.

Values of t he energy fr ac ti on of l e s s

The next important step was to incorporate ablat ive heat shieldsi n t he des-6 - that is, sh ie ld s which would vaporize during th eheat ing so that advantage could be taken of the la te n t heat of vapori-zati on t o gre at ly incr ease the heat removed pe r un it of heat sh ie ld mass.The ablat ive shields have a second recognized advantage of great impor-tance (see refs. 3 t o 6 ) which i s that the issuing vapor from theshi eld s fends off th e a i r so as t o reduce the shear a t the vehicle


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5surface and hence reduce the heat- t ransfer coef f icie nt i t s e l f . Thisreduction i s approximately i n the ra t io

whereinf vk

the energy required t o vaporize a uni t mass of the shielda constant depending upon the molecular weight of th e ab la te d vapor

and upon whether the boundary-layer flow i s laminar or turbulentValues of th i s constant (r e f. 6 ) are character i s t ica l ly about 0.3

f o r laminar flow and about 0 .1 for tur bul en t flow. The important fe at ur et o no te i s th at the reduct ion of heat- t ransfer coef f icie nt with abla t ionincreases with increasing speed.

There i s a third advantage of the abla t ive shie ld which i s notgeneral ly appreciated that w i l l become important a t higher entry speeds.It is t h a t as abla tion occurs, the coo lan t,a fte r accepting all t he hea tof which i t i s capable, i s automatica lly je tti so ne d. The ensuing heatload i s therefore lessened by the continuous reduction of unnecessarymass. For the ablat ive heat shield the mass t ransfer equat ion is

With equation (1) hen

so tha t for constant heat-transfer coe ffi cie nt and drag coeff ic ien t , thef i n a l mass i s , f o r a l o w speed a t impact,


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6s in ce t h e f i n a l mass i s , of course, th e payload i n an optimum de sign ,For th e heat si nk shie ld, on th e other hand, even supposing the co olanti s as e f f i c i en t as the ab la tor and that no allowance i s made for thefavorable effe ct of ablat ion on the heat- t ransfer coef f icie nt , theoptimum r a t i o of payload t o t o t a l mass of payload plus coolant i s

Figure 1 shows th e optimum r a t io of payload t o en tr y mass as aFor the nonablativeun ct ion of the energy parameter CHVE2/2C~(v.

shield the payload vanishes when t h e energy parameter reaches 1.the ab la t ive sh ie ld some payload i s ava i l ab le fo r indef in i t e ly l a rgeva lue s of t he energy parameter although it may be uneconomically small.

For

Reentry Heating for Space VehiclesThe negative accelerations of ba l l i s t i c veh ic l es en te r ing the

a tmsphere on s t eep t r a j ec to r i es are lar ge compared t o th e a cce lera tionof gravity, as noted earl ier , s o t h a t the equation of motion can beapproximated by equation (1) nd the t ra jectory i s es s en t i a l l y ast ra ig ht l i ne . In planetary atmospheres the densi ty varia t ion withal t i tude i s es se nt ia ll y exponential i n form

-PhP =where

sea-level densi tyPoh altitudeP inverse of the scale height

Under these circumstances it may read i ly be shown ( r e f . 2) t h a t t h emaximum accelera t ion , if it i s reached before impact, i s


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7whereye Naperian base

angle between t he t ra je ct or y and the lo ca l horizon tal

This i s a rather curious resul t s ince it indicates t h i s accelera-t i o n t o be independent of th e vehicle shape or mass and only dependenton ent ry speed, tra je ct or y angle, and the sc al e height of the atmosphere.For th e ty pi ca l ba l l i s t i c m issile the maximum acceler ation s can reachabout -60 g but t h i s i s of small significance since such vehicles can berat her ea si ly made su ff ic ie nt ly robust to r e s i s t such loads.

For manned space vehicles, of course, maximum accele ra ti on s mustbe l imited t o values of the order of 10 g during entry.gives the clue t h a t t h i s can be accomplished with a shal low trajectory.This equa tion, however, cannot be used t o f in d th e permissible t rajectoryang les because gr av it y e ff e c ts were ignored in i t s formulation.( r e f s . 7 and 8) has considered this problem with grav i ty effects includedas well as t h e e f f ec t s of the use o f aerodynamic l i f t .manned satelli t ies, such as for Project Mercury, a sa t i s f ac to ry r een t rymay be made without the use o f aerodynamic l i f t i f t h e en t ry t r a j ec t o r yis ne i ther so s h a l l o w 88 t o over ly ex tend the t ra j ect ory due t o i n s u f f i -c i en t drag nor so steep as t o promt e excessive accelerat ions. In fa ct ,by the use of a modest re t rorocketwi th proper ly d i rected th r us t alanding a t a preselected spot can easi ly be eff ec ted without th e use ofaerodynamic lif 't, as has been demonstrated with the Mercury spacecraft.When the entry speed is increased t o values corresponding t o Ear thparabolic speed o r grea ter, the attainment of a permissible approachtr aj ec to ry becomes more di ff ic ul t . A t Earth hyperbolic speeds, in fa c t,i f the approach i s too shallow the drag may not be su f f i c i en t to assu retha t t he veh ic l e will be "captured" by the atmosphere.

Equation (14)

Chapman

For near-Earth

Generally, the


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8si.tuation w i l l be more re st ri c te d than has been indicated , fo r i f t h eveh icl e on the sha llow t r a j e c to ry l ea ve s t h e atmosphere, it may t r av e r s et h e Van Allen b e l t s before i t s next approach t o E a r th and so sub jec tt h e occupants t o a l e t h a l radiat ion hazard.assumed t h a t a manned veh ic le must be captu red and kept i n th e atmosphereduring the " f i r s t pass."manned en tr y veh ic le problem i s the so-called en t ry corr idor definedhere in as the range of a l t i tu de s requi red as aiming points for theapproach t o assure t h a t t h e vehicle nei ther experiences excessiveaccele ra t ions nor f a i l s t o be captured in a s ing le pass .th e 10 g corr idor as a funct ion of l i f t - d r a g r a t i o for en t r y a t Earthparabolic speed. The advantage of using aerodynamic l i f t i s apparentand the subject has been treated extensively in t h e l i t e r a t u r e ( e .g . ,r e f s . 7 t o U ) .

Accordingly, it usua l ly i s

A concept convenient t o disc ussi on of t h e'

Figure 2 shows

This d igress ion i n to t he d iscuss ion of t ra je ct or y requi rements i spert inent to the heat ing problem.ra ther low mass, s t eep t r a j ec t o r i e s are general ly preferab le fo r min i-mizing ablative heat-shield weight, i f aerodynamic l oadin g i s not afac tor , s inc e th e heat pulse though intense i s but of very shor tdurat ion so t h a t l i t t l e hea t i s conducted into th e subst ructure .add ition , ab la ti ve s hi el ds which melt before being vaporized have at h i n melt so that the flow of the melt layer c r ea t e s l i t t l e d i f f i c u l t y .In contrast, for manned vehicles which must employ shallow-angledt ra j e c to r i e s t o avoid excess ive acce lera t ions , t h e heat ing rate i s moremodest but l a s t s f o r a considerable period.i s so severe t h a t insu la t ion i s required t o prevent overheat ing of th esubst ructure .

For small rugged e nt ry vehicles of

I n

The conductivity problem

The choice of ablative materials i s re s t r i c t ed s ince many


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9w i l l flow unduly because the liquid f i l m layer is r e l a t ive ly th i ck .On the other hand, the re ar e some compensating factors favoring theshal low trajectories:of heat t o be radia ted f ro mt he vehicle surface, thus reducing therequired mass for the ab la tor .f l i g h t Reynolds numbers are lower so t h a t a laminar flow can often bemaintained where otherwise t.l~rbvlent. low wnlll l ! C?CC??IT~ ence +,heheat ing ra te i s lessened.the problem since the surface distr ib ut ion of heat ing r a te v ari es withthe veh ic l e a t t i t ude .

The long heating time permits a sizable amount

Also f o r lar ge heavy vehi cles the

The use of varying aerodynamic l i f t complicates

Up t o t h i s point the t a c i t assumption has been made t ha t convectiveheat ing cons t i tu t es the to t a l .f o r Ear th , th is i s essen t i a l ly the case.things being equal, only increases as about the square of the speed.It i s not immediately apparent that there i s a necess i ty t o considerentry speeds above parabolic speed f o r Earth return from travel to theneighboring planets. For Hohmann transfer trajectories from Mars orVenus t o Earth, the atmosphere entry speeds a t Earth are es se nt ia ll yEarth parab olic speed.required fo r the minimum energytrips are long, subs tan t i a l f r ac t ionsof a year.t ravel time.promote some difficult psychological problems.weight of l i f e support equipment increases with voyage t i m e .obscurely, th e veh icl e weight, as determined f o r equal meteor impacthazard, fo r example, gives advantage t o sho rt t r i p durat ion. Thus, f o reven modest sojourns in to space there a r e val id reasons f o r considering

For speeds up t o nearly parabolic speedThus the to t a l heat input, other

However, as shown in figure 3, the t imes

There are many good reasons f o r wanting t o shorten theBbr the occupants, long f l igh t durat ion w i l l probably

Certainly, too, theMore


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10atmosphere entry speeds in excess o f the parabolic speed.d i s t a n t journeys of the future the demands are even greater.

For more

A t these higher speeds one must contend w i t h an addit ional heatingcontribution which arises i n t h e following way:shock layer i s d ra st ic a ll y slowed down re la ti v e t o th e body and i shighly compressed.L V L l v c I kcu w l ~ a k . r ~ l a A L C : I ~ ~ I , I U L Ia t tiie higher E i g h t speeds i ssu f f i c i en t t o d is soc i a te and ionize a lar ge fr ac tio n of th e compressedga s. These atomic and molecular specie s become impo rtant so urc es ofra di at io n which serv e t o promote add itio na l heating of the vehicle (see,e .g . , r e f s . 12 t o 1 6 ) .

The a i r enter ing the

The high kinetic energy i s then almost ent i re ly---.---+*a +,. L A - & rm. - - - - - . L - I - . - . -

The phenomenon i s a complicated one since a chain of processes i srequired to es tabl ish chemical and thermodynamic equilibrium.radia t ion f romthe shock layer var ies a long the s t reaml ines as a i ri n i t i a l l y out of equi librium subsides to the equil ibrium s tate . For thepurposes of t h i s discussion it i s suf f ic ien t t o note t h a t one can regardthe shock-layer rad iat ion as having two components, one from t h a tf r ac t i on of the gas which i s in equilibrium and one from the nonequi-l i b r i u m f r ac t i on . When ra d ia ti ve heating becomes comparable t o orexceeds the convective heating, it has been found tha t the equi l ibr iumcomponent f a r overshadows th e nonequilibrium component.we s h a U concentrate our at tent ion on the equil ibr ium ra diat io n herein.

Figure 4 shows the equil ibrium radiation rate per u n i t shock-layer

Thus the

Accordingly,

gas volume as a function of U, the upstream velocity component normalt o t he shock f o r several values o f f l i gh t a l t i t ud e . These are calculatedcharacteristics (shown by the symboled points) and the lines composed ofs t r a ig ht segments a r e a rb i t ra ry fa i r ings . A t a given veloci ty U, the


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11varia t ion of r adia t ion with al t i tu de corresponds t o a var ia t ion w i t ha i r densi ty to the 1.8 power.veloci ty , U, from about 8 km/sec t o 13.7 lun/sec, the in te ns it y i sincreased four orde rs of magnitude, th e i nt e ns it y varying with theve loc i ty to the 15.45 power.rad ia t ion cont inues t o increase but only as t h e v e l o c i t y t o t h e 3.05 power.It i s r ead i l y q g a r en t that. althnijgh radia t , ive heatring const i tu tes at r i v i a l con tr ib ut io n a t the lower speed, it becomes the dominating factora t h igher speeds, par t ic u lar l y i f these h igh speeds a re a t t a ined a t lowa l t i t u d es .

A t any given alti tude on increasing the

Above the speed of 13.7 km/sec, the

One concludes that when atmosphere entry speeds exceed about Earthparabolic speed (11km/sec) t he blunt-body so lu ti on i s no longer theoptimum. Conical shapes for vehicles become attractive in t h i s higherspeed range since the bow shock essentially i s no longer normal t o th ed i rect ion o f motion.nearly 14 km/sec, the pri nci pal r adia tive contribution va rie s a s some-th in g more than t he fi ft ee nt h power of t he v el oc it y component normal t othe shock. Thus, fo r a given f l i ght speed, th e radia t iv e rate var iesas th e fi ft ee nt h power of t he sine of the bow shock angle, and so theradiat ive input i s dr as ti ca ll y reduced fo r even very modest inc lin ati onof the bow shock. The con ic al shape i s l e s s favorable than the bluntbody from th e convective heating aspect, but sin ce th e re quire d coneshape i s not one of high fineness r at io , th e penalty i s small. Thisi s re ad ily apparent i n the next three fig ure s, taken from reference 17which contains an extended analysis of the heating of conical entr yvehicles a t speeds in excess of Earth parabolic speed.th e f ra ct io n of t he e nt ry ki ne ti c energy of the v ehi cle which must be

As w e have seen f o r normal shock speeds up t o

Figure 3 shows


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contended w i t h as heat t o the vehicle as a function of en tr y speed fo ra conical shaped body having a half-cone angle of 30 of a rc .ablator assumed here i s Teflon, and the d imensionless bal l i s t icparameter

The

CDPoApm s i n yB =

has a value of 200 which, as estimated from our meager present knowledge,i s about as small a s can be allowed i f the flow, as assumed fo r t h i s case,i s t o be laminar. Note, here, that the rad iat ive heating does notcontr ibute substant ial ly unt i l speeds of the order of 20 kilometers areexceeded after which i t dominates.butionrad ia t ive cont r ibu t ion qe and the laminar convective portion, q 2 .

The nonequilibrium radiative contri-qn , as noted earlier, remains small compared t o th e equ ilibr ium

Figure 6 shows th e to ta l. energy fr ac ti on as a funct ion of e ntr yspeed for a range of cone half-an gles f o r th e same va lue of t h eb a l l i s t i c paramete r. The optimum energy fra ct io ns f o r t h i s value of Ba r e shown by the envelope (dot ted cur ve). These values a r e but a smallpar t o f 1percent of the e ntr y kine tic energy.

If one assumes t h a t laminar flow can be mainta ined up t o a Reynoldsnumber of lo7 based on body length and lo ca l f low ch ar ac te ris t ic s, thef r ac t i o n of the entry mass which must be ablated as a funct ion of ent ryspeed for two abl at or s (subliming Teflon and vaporizing qua rtz) i s showni n f i g ur e 7.a reasonably small f rac t ion of the en t ry mass even t o f a i r ly h igh en t ryspeed - well i n t o the range of e ntr y speeds of meteors.flow occurs, the mass l o ss f r ac t ion i s much greater since the energyf r ac t i o n i s increased about an order of magnitude. Considerable fu tu re

It i s seen t h a t the ablated mass can apparently be kept

If tu rbulen t


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13resea rch on the age-old tr an si ti on problem i s cl ea rl y needed a tthese high speeds. W must learn the fac tor favorable t o themaintenance of laminar flow i n boundary lay e r s composed of a i r andablat io n vapors.

There i s another problem w i t h conic al ly shaped ent ry vehicles t otouch on before we leave th i s subject. The convective heat tra ns fe ri s iiigiiesi a i ihe cone apex and diminishes toward tne cone base.Thus %he cone ab la te s t o a round-nosed, near-cone shape with increased

cone half-angle a s the atmosphere en tr y prog resses.speed i s high, th e rounded nose becomes f la t ten ed and extended i n width

I f the en t ry

by the radiative heating contribution a t the lower al t i tudes. Much ofthe advantage of the original conical shape may thus be lost . Inreference 17 t h i s problem i s treated in some detail and it appears thatthe pendty can be kept small, provided excessive shape change i savoided by extra f i l m cooling a t t h e apex.complication attendant with t h i s cooling i s undesirable but it i s a

O f course, th e mechanical.

price which perhaps m u s t be paid t o e f fec t a sa t i s fac to ry so lu t ion tothe problem.

]For manned vehicles a t these higher speeds the problem of providingAs shown i n f ig ur e 8, forn adequate alt i tude co rr id or becomes sev ere .

an assumed fixed maximum deceleration of 10 g, a higher and higher l i f t -drag r a t i o i s required as entry speed increases un t i l a speed i sreached f o r which the corridor vanishes. For t h i s decele ra t ion thel i m i t speed i s about 26 km/sec, t h i s being th e speed f o r which, withzero drag, the centrifugal force experienced i s 10 g . f o r a f l i g h ttrajectory having a curvature equal t o the radiu s of the Earth. Therequired aerodynamic lift force is, of course, di re cte d toward the


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14Ear th ' s cen ter .for manned vehicles, a t l e a s t , w i l l have t o be l im i ted t o values le s sthan perhaps 20 km/sec and t h a t l i f t must be provided.shaped l i k e half-cones, perhaps, may provide sa t is fa cto ry configurat ions( r e f . 10) fo r high-speed en tr ie s.

From the foregoing it appears that the entry speeds

Entry vehicles

Up t o t h i s p o in t it has been ta c i t l y assuned t h a t aerodynamicbraking of a vehicle i s preferable to rocket braking to e ff ec t a landingon Earth.well known ( see r e f . 18) the specific impulse of a rocket i s defined as

It i s well t o digress, here, t o make a comparison. A s i s

whereiT

g0dm/dt

sp ec if ic impulse, secthrust , kg m/sec2grav i ta t ional accelera t ion a t Earth surface, m/sec2time r a t e of mass flow of rocket propel lants

For rocket braking th i s thr us t provides the negat ive accele rat ion

d V Td t m- = - -

Equations (16) and (17) can be combined t o give

Comparing t h i s equation with t h e corresponding one for the ab la t ionrate with aerodynamic braking (eq. (lo)), one sees that the equivalent

heat sh ie ld i s


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15where 7 i s the energy f ract ion

For the optimum conical vehicles of reference 1 7 w i t h laminarboundary-layer flow, and assuming

= 2 . 2 f i ~ / s e c 25,for subliming Teflon and

CV = 16x10~m2/sec2f o r vaporizing quartz, one can calculat e the equivalent specif icimpulse f o r aerodynamic braki ng. The v ar ia ti on of t h i s impulse w i t hspeed for these two assumed ablators i s shown in figure 9.equivalent impulses drop w i t h increasing en tr y speed, t hey are alwayswell above what can be a tta in ed with chemical rocke ts (l e s s than 500 sec)o r nuclear ro cket s (up t o about 1,000 sec) even for a rather i n e f f i c i en tablator such as Teflon. Hence as long as energy f rac t io ns f or veh ic leswi th ab la t ive heat shields can be kept to the order of 1percent or so,rocket braking cannot be considered competitive.Aerodynamic B r a k i n g i n th e Atmospheres of Venus and Mars

Though these

The Ear th ' s c lo se neighbors , Venus and Mars, are objects o fpa rt i cu la r int er es t in the space age. Although t h e atmospheres ofthese pla net s have been the object of study f o r many years, th e f a c tsare few.s t i t u e n t .t o t a l . Nitrogen, presumably, and perhaps Argon are t he o ther p r inc ipa lconst i tuen ts .r e l a t i v e l y small amounts.these plzzets ve m u s t , f c r the p r e s e ~ t , ss'me t h a t t h e r e l a t i v e amun t sof the const i tuen ts are varied over a wide range.

Both atmospheres have carbon dioxide as an important con-The estimates range f ro m a f e w percent t o about half of th e

Apparently oxygen and water vapor are presen t i n bu tIn any study of atmosphere en tr y heating fo r

The Venus atmosphere i s assuredly much more dense than i s th eE ar t h ' s so t h a t atmospheric braking i s not d i f f i c u l t . On th e other hand,


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-

-

16t h e temperature near the surface o f the p lane t i s high so that even aninstrument package may not survive f o r lon g.tenuous.pressure indeed (25 k15 mil l ibars ) so th at braking an en try vehicle t oa low speed a t surface impact maybe impossible without the use of aret rorocket a t touchdown.i s apparent ly even l e s s t.ha-n for Enrthj so vehicle s l ; r x . r i y . r d a f t e r lar,&-jngdoes not appear t o present a problem.

The Mars atmosphere i sRecent observations (ref. 1 9 ) ind ica te a very low surface

The atmospheric temperature near the surface

Convective heat tr an sf er i n the Venus and Mars atmosphere appearst o pres en t no problem. Comparison of co nvecti ve he at i n CO, and a i r( r e f . 20) shows only a minor difference which i s i n es se nt ia l agreementw i t h theory ( r e f . 2 1 ) .t r i bu ted from the shock layer i s generally a more se ri ous problem thanf o r a ir (ref. 22) because of the formation of cyanogen, a s t rongrad i a to r , from the nitrogen and carbon dioxide constituents. A t speedsof 6 o r 7 km/sec the experimental evidence ind icat es t h a t t he rad iat iveheat ing i s about one order of magnitude g re a te r tha n f o r a i r . However,as speed i s increased, the mixtures approach more nearly a i rvalues of rad ia t ive hea t ing . My colleague, James Arnold, has re ce ntl ymeasured the effects of' adding argon and has found, co ntr ary t oexpectat ion, th at t h i s di luent does not appreciably inf luence the

bas i c COz - Rz results.

On the other hand, th e ra dia tiv e heating con-

CO, - N2

Because the actual composition of the Venus and Mars' atmospheresi s doubtful , these estimates of the sever i ty of the heating problemmay be i n consid erable err o r.


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1 7Experimental Determination of Aerodynamic Heating a t Hyperveloci t ies

The accuracy of th e foregoing re en tr y heating an alyses i s only asgood as the accuracy of our bas ic knowledge of th e chemical and thermo-dynamic processes involved. As i n t h e s c i e n t i f i c d e l i nea t i on of a l lna tu ra l philosophy, theory i s v i t a l l y importan t to our understanding oft h e heati ng phenomena i n high-enthalpy a i r flows.case, con stan t input from experimental resear ch i s needed not only t oprogress a t a fast pace bu t t o assu re th a t t he th eo re t i ca l results are,in fa c t , va l id . In hypersonic heat- t ra nsfer phenomena th i s i s par t icu-l a r l y t r u e because many of t he bas ic ph ys ica l concepts involved are nottoo well understood.speed i n o ur ground-based laborabo ry equipment i s only a l i t t l e morethan 13 km/sec.r e ly on ex trapo la t ion by theory. In t i m e we expect the l i m i t ofat t a in ab le speeds in th e laboratory w i l l increase but by unknownamounts.extend our experimental knowledge t o the higher speeds, but such t e s t sare very expensive and so t i m e consuming that they cannot be countedon t o produce the experimental data w e need.experimental sources f o r confirmation.

A s i s of ten the

Unfortunately, th e pres ent upper l i m i t on a i r

For present analyses a t higher a i r speeds, we must

It i s poss ib le to perform f l ig h t te s t s us ing rockets to

One then looks f o r o th e r

Observations of meteor fl i g h t a r e one such source worthy of con-s i d e r a t i o n .speeds ranging from parabolic speed (11km/sec) up t o t h e highest speedthey can have and s t i l l be members of t h e solar system (72 kq/sec) .The e n t r y speed requirements f o r our purposes are, therefore, more thanm e t .t o enjoy continuum flow ar e suff icie nt ly infrequent th a t only occasiona l ly

Meteoroids are known t o en te r the Ear th 's atmosphere a t

On th e ot her hand, t h e atmosphere entry of meteoroids large enough


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..

18can one be track ed a t any one locat ion .exis ted but a few meteor observatories so t h a t the number of continuumflow meteors, f o r which acc ura te tracking data are ava i lab le , i s veryl imited.under construction many new meteor observatories s o t h a t future pros-pec t s as regards the ava i lab i l i ty o f nieteor data are good.

Unt i l recent ly there have

A s w i l l be discussed mre f u l l y l a t e r , t he r e a r e p r e se n t ly

Astronomers, for a number of years now (se e re f . 23 f o r a review),have s uc ce ss fu lly tracked meteors in the following way:cameras, located a t the two ends of a known base l i n e , a r e provided withrotating shutters which occult t h e meteor image on the photographicp l a t e s a t even time intervals.t r iang ulat io n. The var ia t ion of veloci ty and, in turn, accelerat ion,of the meteoric body along the trajectory i s determined from theinterrupted photographic track.meteor track with the background field of stars whose photographicmagnitudes are known provides th e measurement of th e va ri at io n of th emeteor luminosity along the t ra jectory.assess t h e meteor composition, These data a re su f f i c i en t , i n p r i nc ip le ,

One or more

The meteor t ra jectory i s determined by

Comparison of relative exposure of the

Spectra a re ort en measured t o

t o a l l o w the determination of the var iat io n of s i ze and heat- t ransfercha rac t e r i s t i c s of the meteoric body wi th al t i tude and speed.methods of analysis generally employed are the "dynamical method" and

Two

th e ttphotom etrica l method."paper. The l a t t e r i s discussed in reference 24. Suffice it t o say,here, t h a t th e methods ar e ess en tia lly redundant i f meteor de ns ity i sknown.complete solution.

W shall t r e a t only the former in t h i s

When the dens i ty i s unknown, t h e two methods are needed f o ~he


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In the dynamical method of a naly sis th e ve lo ci ty and ac ce ler ati onh i s t o r i e s a r e all t h a t ar e needed to determine heat- tran sfer charac-t e r i s t i cs , and , i f the densi ty o f t h e meteoro id i s known, t h e s i z eva ria tio n with al ti tu d e can be found as well. However, it i s presumedthat a i r -densi ty var ia t ion wi th a l t i tude, h, and the body shape areknown. It i s usual t o employ a standard atmosphere (e.g., ref . 23) f o r&Ii dellsity V&-ues* InLil e bodj- i s ~ s s - ~ i e do reralr, essentiallyspherical during the atmosphere entry since a sphere represents aboutth e be st mean of p oss ibl e shapes (see re f. 2 6 ) .motion (eq. (1))he product of the meteor den si ty and radius as a

From the equation of#

funct ion of al t i t ud e can be found from

pmr = --cr0&)where 'j = p/po and f o r the assumed sp he ri ca l shape, CD i s approxi-mately unity. If i s known, then the size can be determined.Equations (1)and ( 9 ) combine t o give the heat-tr ans fer parameter

s ince dhV s i n yd t = -

Here we note a major diff icul ty - that even presuming CD i s known,we cannot find CHThere is , however, an upper l i m i t t o the poss ib le value ofthe t o ta l energy required t o bring the surface material from t h e coldstate t o the ~ q o rt .ate so t h a t a.n u?per l i m i t f o r can be foundin any event. For stone meteoroids one expects, a p r i o r i , t h a t vapor-ization would be t he usual ablat ion process since l iquid stone i s

unless the heat of ablation i s known, which it i s not .( which i s

CH


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20rather viscous - but if the ent ry speed i s low o r t h e t r a j ec t o r y i s notsteep, then the mass ablated in the liquid state (as Chapman, re fs . 27and 28,has found fo r te kt it e s) can be a r a ther l a rge f r ac t ion of thet o t a l . On th e ot her hand, fo r large meteoroids which en te r t he atmos-phere on a s t eep t r a j ec to ry and a t high speeds l i q u i d run-off would besmall. However, an important fr ac ti on of the a bl at ed mass may be inU L ~ U A ~ ~W Z ~ C s ince stoiie i s ti. ye& r i t e r i d , aiid, b e c a s e t hethermal conductivity i s low, it may a l so s p a l l as the result ofexcessive t h e m stress. For iron meteoroids one does not expectablat ion t o be important in th e sol id s t a t e except fo r bodies of g rea ts i ze s ince th i s material i s strong and the thermal conductivity i sre la t ively h igh .ab la t ion p r inc ipa l ly as a liquid should be expected.

LL ..A1 2 2 -&-LA

However liquid iron has a very low viscosity so t h a t

A serious weakness of the dynamical method i s th at in passing fromveloci ty t o meteor s ize t o the heat- t ransfer fac tor each funct ioninvolves, in turn, diffe rent iat ion of the l a s t . Hence, unless theve loc i ty i s very accurately defined as a function of t i m e and a l t i tude ,t h e f i n a l results may be subject t o la rg e mean err or .(see ref. 29) of the record of the Canadian meteor "Meanook 132"ind icates that veloci t ies can , i n fact, be determined w i t h about therequired accuracy.fo r t h is meteor.the or ig in al values given i n reference 29 and include a correct ion toone of the acceleration values (private communication from D r . Millman).These data are p lo t t ed i n f igures 10 and 11 along with the curvesdetermined by a sixth-degree le as t squares fit t o all the ve loci ty andacce le ra t ion data.

The analysis

Table I gives the veloci ty and accelerat ion historyThese resul ts (see r e f . 24) are more complete than

The close agreement between the data and the curves


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21ind icates that the veloci ty and accelera t ion data are sel f -consis ten t .I n f igure 12 the dotted curve shows the variation of the meteor density-radius product as computed from the sixth-order leas t squares series.The "point-to-point" values are calculated from each of the individualveloci t ies and accelera t ions . The solid curve gives the photometricalr es u l t s fo r a dens i ty of 850 kg/m3.

Figure 1 3 gives the corresponding variation of the heat-transferparameter w i t h a lt it ud e . The dotted curve, again, i s obtained from thesixth-degree l e a s t squares f i t while the cir cle d points are fromneighboring point values of ve loci ty and of a cc el era tio n to evalua tethe mean value over each al ti tu de i nte rva l. These dynamical resultscompare favorably with the photometrical results, as t h e s o l i d l i n eshows. The dash-dot curves give estimated va lue s of the heat- tra ns ferparameter when i n one case on ly vapor ab la ti on was assumed t o occur andi n the o ther only f l u i d ab lat ion . The implicatio n, here, i s t h a t con-side rabl e abl ati on i n the so li d st at e must have occurred. This l o w -dens i ty material ( less than water dens ity) must ev ide ntl y be porousand, accordingly, weak so that so li d ab la ti on would be expected. Hence,t h e r e s u l t s fo r t h i s meteor do not add t o OU T knowledge of th e heat ingof t y p i c a l man-made ent r y vehic les bu t t he y do show t h a t t he meteor dataderived from the photographic plates must be of high qual i ty .

The data f o r t he Sacramento Peak Meteor 19816 ( ref . 30) analyzedin reference 24 do yield results which ar e encouraging, f o r the y indi ca tet h a t ex trap olat ion of our present knowledge of hea t t ra ns fe r up t o speedsof about 20 W s e c may not be far from fact.t i o n s with the corresponding leas t squares err or s ( indicated by AV andAdV/dt) are given in tab le I1 for t h i s meteor whose spectrum indi ca te st h a t i t s composition i s t y p i c a l of as tero idal s tone (pm = 3400 a/&').

The velocity and accelera-


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22"he re su lt s of the dynamical analyses (point-to-point and l e a s t squaress e r i e s ) are shown in figure 1 4 a l o n g w i t h the values estimated whenvapor and f l ui d ablat io n ar e assumed. Even when on ly vapor ab la t ion i sassumed, the data indicate values o f the heat- t ransfer coeff ic i ent onlyabout twice as high as those estimated. A s noted earl ier some fluidabla tion probably occurred fo r th is small s tone ( the entr y radius i sabout 1 cm).so t h a t the data and a proper e stim ate would be i n b e t t e r agreement.

A proper estimate w o u l d be somewhat increased therefore

It i s probable, in fa ct , that a t these higher speeds our estimatesof heat- t ransfer co eff ic ien t are l o w because one additional source ofheating has not been accounted fo r .layer and i n the wake collide w i t h the ablated vapor molecules.these co l l i s io ns a re suf f ic ie n t ly energe tic , as fo r t he a i r -t o - a irmolecular co l l i s i ons i n the shock la ye r, they become a source ofradia t ion . The observed luminosity of meteors is , i n l a rge pa r t ( o rcompletely in free molecular flow), a r e su l t o f t h i s radiation. Thephotometrical method of an al ys is for meteors employs, in fa ct , t h i srad ia t ion f romthe ablated vapor coll isions as a means fo r determiningthe mass loss rate of a meteoric body. The magnitude of the rad ia t ionper unit ablated mass depends not only on the flight speed (i.e .col l is ion energy) but also on the composition of the vapors.r a t h e r low speeds the radiation can be important fo r cer ta in ab la tors .Figure 15 i s a photograph of a Lexan model i n fl i g h t .taken with an image-converter camera by my colleague Max Wilkins a tAmes Research Center. The 1/2-inch-diameter model, which has a roundnosed cone for the forward face, i s i n f l i g h t i n a ba l l i s t i c r ange a ta speed of 7.2 km/sec. A l l of the wake ra di at io n and a l a rge par t of

The a i r molecules i n the boundaryWhen

Even a t

The photo w a s


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23t h e radiation from th e region of t he forward face results from

abla t i on products rad ia t ion . " Some important features of t h i s1r ad i a t i on are t h a t , i n add i t ion t o heat ing t h e forward face, it mayg re at ly augment th e afterbody heating of high-speed re en try bodies.Also, as noted by Craig and Davy (r e f. 31, see a l s o r e f . 24) t h i sra di at iv e h eating tends t o become self-perpetuating a t s u f f i c i e n t l y h ig hspeeds.caref u l ly choose ab la to rs f or heat sh ie ld s which have low abla tio n-product radiat ion.

Designers of fu tu re high-speed en tr y ve hic les would do w e l l t o

To ret urn t o the subject of meteors , it does appear that meteort rack ing records can provide exper imental heat- t ransfer ch ar ac te r is t ic sa t very high en try speeds. In par t i cu la r , we s ta nd t o l e a r n a good dealabout ablation-products rad iati on and about th e ab i l i t y of variousa b l a t i v e materials t o resist s t r u c t u r a l fa i lu re caused by thermal s tress ,provided the meteor composition can be determined.supported a proposal by t h e Smithsonian Astr oph ysica l Observato ry t o

Recently the NASA

construct and operate a network o f meteor observatories covering a l a r g earea i n t h e midwest.t racking data on br ight f i reba l l s with su f f i c i en t p r ec i s i on t o a l low themeteoritee t o be re t r i eved . Improved analys i s of these t r acking recordsshould result s ince, for t h e ret r ieved bodies , t h e f i n a l mass and shapeand th e meteor de ns it y and composition w i l l be known.ea r l i e r , many more tra cki ng records f o r meteors i n continuum flow shouldbecome av ai la bl e than have been availa ble up t o th e pre sen t.

This "Prairie Network" i s intended t o provide

Also, as noted


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2 4References1.

2.

3.

4.

5.

6.

8.

9.

McAdams, W i l l i a m H.: Heat Transmis sion . Second ed ., McGraw-KillBook Co., N . Y., 1942, pp. 162-164.

Allen, H. Julian, and Eggers, A. J., J r . : A Study of the Motionand Aerodynamic Heating of B a l l i s t i c Mi ss ile s Entering th eEarth's Atmosphere a t High Supersonic Speeds. NACA Rep. 1381,1058 f slnawcnaocl nTAnA rnnT J I A ) I ~ ~& j r / " . ( u y r A Y & . u & . Y L l c I v c I A&V W - r l I

Gross, Joseph F., Marson, David J . , and Gazley, Carl, Jr.:General Character is t ics of Binary Boundary Layers with Applica-t i on t o Sub limation Cooling.A u g . 1, 1958 ( r e v . ) .

Rand Rep. P-1371, May 8, 1958,

Roberts, Leonard: Stagnation-Point Shie lding by Melting andVaporization. NASA TR R-10, 1959.

Lees, Lester: Convective Heat T ra ns fe r With Mass Addition andChemical Rea ction s. Presented a t th e Third Combustion andPropulsion Colloquium, AGARD, NATO, Palermo, Sicily, Mar. 17-21,1958

Adams , Mac C.: Recent Advances i n Ablation. ARS Jour., vol . 29,no. 9, sept . 1959, pp. 625-632.

Chagman, Dean R.: An Approximate A na ly ti ca l Method f o r StudyingEntry Into Planetary Atmospheres. NACA TN 4276, 1958.

Chapman, Dean R.: An Analysis of the Corridor and Guidance Require-ments fo r Supe rcircu lar Entry In to Pla net ary Atmospheres. NASATR R-55, 1960.

Lees, Lester , Hartwig, Bederic W., and Cohen, Clarence B.: TheUse of Aerodynamic L i f t During W t r y In to th e Ea rth 's Atmosphere.Space Technology Lab Rep. GM-TR-0163-00519, Nov. 1958.


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2510 . Eggers, Alfred J.: The Pos si bi l i ty of a Safe Landing. Space

Technology, ch. 13, Howard S. Seifert , ed., John Wiley & Sons,New York, 1959.

11. L e v y , Lionel L . , Jr.: An Approximate A na ly ti ca l Method f o rStudying Atmosphere E nt ry o f Vehicles With Modulated AerodynamicForces. NASA TN D-319, 1960.

12. Kivel, B., and Bailey, K.: Tables of Radiation From High Tempera-tu re A i r . Avco-Everett Res. Lab. RR-21, Dec. 1957.

13. Meyerott, Roland E.: m d i a t i o n Heat Tr an sf er t o Hy-personic Vehic les.Lockheed Aircraft Corp. LMSD 2264-=, Sept. 5 , 1958.

14. Camm, J. C., Kivel, B., Taylor, R. L ., and Teare, J. D. : AbsoluteIn te n s it y of Non-Equilibrium Radia tion i n A i r and Stagnat ionHeating a t High A lt it ud es . Avco-Everett Res. Lab. RR-93, Dec. 1959.

15. Page, W i l l i a m A., Canning, Thomas N . , Craig, Roger A . , andStephenson, Jack D.: Measurements of Thermal Radiation of A i rFrom the Stagnation Region of Blunt Bodies Traveling a tV e l o c it i e s Up t o 31,000 F e e t Per Second. NASA TM x-508, 1961.

1 6 . Canning, Thomas N.: Recent Developments i n t h e C hemis try andThermodynamics of Gases a t Hyperveloci t ies . V o l . 2 , Proc. NASA-University Conference on the Science and Technology of SpaceExploration. NASA SP-11, no. 56, 1562, pp. 283-290.

17. Allen, H. Ju li an , S ei ff , Alvin, and Winovich, Warren: AerodynamicHeating of Conical Entr y Vehicles a t Speeds i n Excess of EarthParabolic Speed. NASA TR R-185, 1563.

18. Summerfield, Martin, and Seifert, Howard S.: Flight Performanceof a Rocket i n St ra ight- Line Motion. SPACE TECHNOLOGY, Chap. 3,pp. 3-01 - 3-28, Howard S. S ei fe rt , ed., John Wiley & Sons,New York, 1959.


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261 9 . Kaplan, L e w i s D . , Mk ch , Guido, and Spinrod, Hyron: A n Analysis

of t h e Spectrum of Mars. The Astrophysical Jour., v o l . 139,no. 1, Jan. 1, 1 9 4 , pp. 1-13.

20 . Goodwin, Glen, and Howe, John T.: Recent Developments i n Mass,Momentum and Energy Transfer a t Hy-pervelocities. Gas Dynamicsi n Space Ex pl ora tio n. NASA SP-24, Dec. 1962, pp. 41-51.

S a t e l l i t e Sp eeds. ARS J o u r . , vol. 32, no. 10, Oct. 1962,pp. 1344-32.

22. James, Car lton S.: Experimental Study of Radiative Transp ortFrom Hot Gases Simulating in Composition the Atmospheres ofMars and Venus. A I M Jour., v o l . 2, no. 3, Mar. 1964, pp. 470-5.

23 . M i l l m a n , P e t e r M . , and Ho ff le it , Dorret: Meteor PhotographsTaken Through a Rotating Shut ter .Percenkewiry -per 31, Harvard Univ. Obs. Annals, v o l . 105,

Harvard College Observatory

1937, pp. 601-21.24 . Allen, K. J G L Z a n , Ebnd James, Natal ine A, : Prospects for

Obtain-i Aerodynamic Heating Results From Analysis of MeteorF l i g h t Data. NASA TN D-2069, 1964.

25. Minwrer, Raymond A. , Chaapion, K. S . W . , and Pond, H. L.: TheA R E Model Atmosphere, 1959. A i r Force Surveys i n Geophysicsno. 115, (AFCRC-TR-59-267), A i r Force Cambridge R e s . Center,A%* 1959.

26. Allen, H. Ju l i an : On th e Motion and Ablation of Meteoric Bodies.Aero nautics and Astron autics, Nicholas John Hoff and WalterGuido Vin ce nt i, eds., Pergamon Pr es s, 190, pp. 378-416.

27. Chapman, Dean R.: On t h e Unity and Orig in of t h e AustralasianTekt i t e s . NASA TM X-54,004, 1963.


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2728. Chapman, Dean R. , nd Larson, Howard K.: The Lunar Origin of

Tektities. NASA TN D-15%, 1963.Miilman, Peter M. , and Cook, Allan F.:

Spectrogram of a Very SlowMeteor.no. 2, Sept. 1959, pp. 648-662.

29. Photometric Ana lysi s of aAstrophys. Jour., vol. 130,

30. Cook, A. F., Jacchia, L. G., and McCrosky, R. E.: LuminousEf fic ien cy of Iron and Stone Aster oida l Meteors.Contribu tions t o Astrophysics.and Physics of Meteors, vol. 7 , 1963, pp. 209-20.

W t h s o n i a nProc. Symposium on the Astronomy

31. Craig, Roger A. , nd D a v y , W i l l i a m C.: Thermal Radiation FromAblation Products Injected Into a Hypersonic Shock L a y e r .NASA TN 0-1978, 1963.


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28

TABLE I.- FLIGHT DATA FOR MEANOOK METEOR 132( s i n 7 = 0.868)

t,sec0.1.2- 3.4-5.6-7.8*91.01.11.21-031.41.51.61*71.81.92.02.12.22.3-

67 5964.5661.5558 5755.5852.71-49.8747.1244.5142.113919838.2137 46

. .

17.4217 3917.351.73017 2517.1817.1017.0016.8916.7516.5816-3716.1215.8215 4515.0114.4913.8613.1012.2411.2810.259.16(8.00)

av/at ,km/sec2-0.31-.36-.42-. 0-.a-*73-.88-1.06-1.28-1.55-1.88-2.28-2.76-3- 4-4.77-5.67-6.97-8.18-9.08-9.97

-io. 58-11 21

-4.02

TABLE 11.- FLIGHT DATA FOR SACRAMENTO PEAK METEDR 19816( s i n y = 0.716

1.135 I 74.02 I 20.57 I 5.021.860 64.16 19.87 k.05dV/dt , AdV/dt,----km/sec2 km/sec2-0.158-2.02-2.75-5 92-8.45

-.416 9.009f.0182.05+.lok.llk.18-9.67 I 2.193-90 +.29


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Aero Heating Review

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