The entry of manned maoeuvreable spacecraft into planetary atmospheres

SP ACECRAFT INTO PLANET ARY A TMOSPHERES

a lecture by B. ETKIN

OCTOBER, 1961 UTIA REVIEW NO. 20

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SPACECRAFT INTO PLANETARY ATMOSPHERES

a lecture by B. Etkin

OCTOBER, 1961 UTIA REVIEW NO. 20

FOREWORD

This review is a written version of a lecture given by the author' at the "Symposium on Interplanetary Explorations", held at the

Into Planetary Atmospheres

by

B. Etkin

INTRODUCTION

The title of this lecture suggests that the active partidpation of a human crew is an advantage, if indeed not essential, for the success -ful accomplishment of certain space missions. 1 take this to be an esta-blished facto It is then both logical and efficient to utilize the control capa ..

bilities of human pilots to help in bringing the vehicle down to a pre-selected destination on the Earth. We are concerned in this lecture with the nature of the flight path followed by such a vehicle after it enters the atmosphere of aplanet, and with the particular Engineering problems which relate to the human occupanc)*of the vehicle.

The parameter whose effect overshadows all others in its influence on entry flight paths is the velocity of the vehicle at the time it comes into the atmosphere (altitude approximately 300, 000 to 400, 000 ft. for Earth). The values of these velocities at entry into the atmospheres of four of the planets are shown in Fig. 1. We have listed here the cir-cular speed(the speed of a space vehicle which is tra versing a circir-cular orbit near to the planet) and the escape speed (the speed required for interplanetary missions). The ratios of the speeds are also shown here,

taking the value for earth as unity. We see that the range of speed with which we may have to contend ranges from 8, 000 mph for circular velo

-city at the planet Mars all the way up to 135, 000 mph for the escape speed of the planet Jupiter. This is a tremendous range of speeds. The values for Venus are seen to be near to those for earth; those for Mars less than half as great; and the values for Jupiter 5 1/2 times those for Earth. We shall see presently when we consider the problems which are presented in bringing a vehicle to rest on the surface of the planet that these pro

-blems tend to increase with the square of the speecL The (speed)2 factor for Mars landi.ngs is seen to be only 21% of that for Earth but the factor for Jupiter is 29 times as great! The quantity responsible for the (speed)2 law just mentioned is the kinetic energy. On Fig. 2 are presented the

values of the kinetic energy per pound of vehicle in terms of the heat energy

of gasoline. As we see from the figure, at circular velocity of the planet Earth the equivalent energy is ten gals. of gasoline per lb. of vehicle.

This goes up to something like 20 gals. per lb. at escape speed for Earth and at circular speed for Mars all the way down.1o about 2 gals. per lb. of gasoline. We have not shown the values corresponding to Jupiter on this graph. To do so would have entailed compressing the horizontal scale so much that the details shown here for Mars, Venus and Earth would have been. too crowded. (As I mentioneq a moment ago, the energy equivalent for Jupiter is 29 times that for Earth).

For the purpose of this lecture we are going to consider three main problem areas for the landing of space vehicles. The first concerns

the deceleration to which the vehic1e and its occupants are subjected.. The second concerns the heating of the vehic1e, i. e. the ternperatures which are oeveloped in the skin and structure; and. the third problem area ilil thij.t of the navigation or guidance of the vehicle to a desired point on the ,surface _{. I} .

DECELERATION

I would like to turn to the first qf these problem areÇis now;, that of the deceleration of the vehicle. Figure 3 Shows some results for the acceleration tolerance of human beings. This is dependent on the time of exposure and the orientation of the body to the direction of the acc:,eleration vector. The most favourable condition is seen to be that in which the

direction of the acceleration is perpendicular to the outstretched body; next best is the feet-first orientation (in accelerated motion), and finally, head-first. During deceleration, such as occurs in reentry, the head-first position is, of course, better than feet-first. On the assumption that the vehicle design takes advantage of the increased capaoility of passengers to withstand accelerations by putting them in the right position, we see that for times in the neighbourhood of 10 ~ 100 secs.! which are the sort of times with which we have to be concerned for high acceleration, human beings a:re limited to accelerations in the general order of 10 g. That is a figure we should bear in mind wh en we look at the graphs which follow.

Figure 4 presents the definitions of some of the terms we shall use:

"w"

is the weight of the vehicle acting along the radius "r" towards the centre of the Earth; "y" represents the altitude measured from the surface of the Earth; "V" is the velocity; '( the angle of the velocity vector below the local qorizon; "s" the distance m easured along the flight. path; and "L" and "Dil are the lift and drag, the aerodynamic forces which are the primary source of both the deceleration and manoeuvre capability of the ve hicle .

Now this is not going to be a mathematical discourse. and we are not going to discuss the methods of solution of the equations )Vhich govern the motion and heating of the vehicle. However. I thought that the equations themselves (Fig. 5) should be displayed in order that the general

nature of the mathematica! problem might be shown for the benefit of those

who are interested. We have here two equations of motion. The first is ...

the component in the direction of velocity vector (the 'drag' equation); it contains the aerodynamic drag term, a gravity term, and an acceleration term. The second equation is the component perpendicular to the direction of motion, (the 'lift': equation). It contains the aerodynamic lift force, (the first term). the expression in

v

2

_/r',

_{which is the centripetal acceleration}

due to Earth curvature; rnc;t, the weight term; and the normal acceleration associated with rate of change of flight path angle relative to the horizon,

(the last ter.m). The third equation is a simple kinematical relation, and the last one gives the variation of density with height. This is an extremely im portant relationship, central to problems of reentry flight. It applies strictly only to an isothermal atmosphere. It is quite easy to show that in that case the value of the exponent (j which occurs in this equation is fixed by the temperature (T) and the gas constant (R) by the expression shown. In changing from planet to planet all three of the quantities R, T. and g may in general be expected to change, so that (2) is subject to substantial variations from one planet to another

<pee

Fig. 8). We shall see later on th at these variations in ~ are resp~nsible for many of the technically important differences between entry flight into the atmospheres of the vari-ous planets . These equations have as the principal unknowns the quantities

y'L and

't

They are complicated by the presence of the variable coefficient (( ('j) and by the. presence of trancendental terms. To obtain exact solutions it is necessary W. resort to machine computation, either analogue or digital. However, a great deal of useful information and under-standing of reentry phenomena can be obtained by solving them for certain simplified cases. Perhaps the simplest of all these is the ballistic entry (Fig. 6). In thls case we assume that the flight path angle ~ remains constant right down to the surface of the Earth, and we further assume that the decelerations are sufficiently large that the neglect of the gravity term is not too serious an omission. This leaves us with one simple equa-tion of moequa-tion as shown. When the exponential expression for the density is substituted in, this equation is readily integrated to give the result shown for the speed--a simple relationship. The value of the maximum accelera-tion which we obtain from this calculaaccelera-tion is, quite remarkably, seen to be independent of the drag coefficient Co and of the mass parameter 'Tv\/S. The quantity CD S

/'rn

is a variation of the so-called "ballistic coefficient"

W

Ic

s .

What is especially important about this result is that the

maximam acceleration depends on only three quantities: the flight path angle 't , the entry speed YË and the value of (:> , which is determined

by the planetary atmosphere. The effect of entry angle is shown on Fig. 7. Here we see the maximum deceleration in units of Earth-surface g plotted against entry angle. For Earth we find that a vertical plunge into the

atmosphere (900 _{entry angle) gives a deceleration of almost 160 g. This}

of course would be quite unacceptable for human occupants. In order to reduce the accelerations to acceptable levels, that is to 10 g or less, we see that the entry angle for Earth would, on the basis of this calculation, have to be kept down to something of the order of 4-50 . On the other hand,

because the value of ~ is so much less on the planet Mars, and also because the circular speed on the planet Mars is substantially less than it is on Earth, the curve of the same quantity for Mars shows that accelera-tions of the order of 10 g would not be exceeded until entry angles of the order of 500 _{were reached. Figure 8 shows how the relative value of f-> YE.1.} (an important factor in the expression for the acceleration) varies for the four planets . . We see that with the value for Earth being taken as unity at circular speed, at escape speed we get just twice that value. The lowest value shown'on the table is .083 at circular speed for Mars--the largest value 22.8 at escape speed for Jupiter. Thus we see that the accele-ration problem is much less severe for entries into the Martian atmosphere than it is for Earth and that entry into the atmosphere of Jupiter may be extreme-ly difficult to achieve. It would probably be necessary, at circular speed, to enter the atmosphere of Jupiter at angles of less than 10 in order to achieve acceptable decelerations. The values for Venus are seen to be almost identical with those for Earth.

The results above are for a ballistic entry, that is one in which the only aerodynamic force is drag, the lift being zero. Another fairly simple solution of the equations of motion shown on Fig. 5 can be obtained by assuming that the Earth is flat and that there is no gravity. These two assumptions cancel one another exactly at circular speed; as the vehicle slows down, the approximation becomes progressively worse. Ex-perience shows that for reasonably shallow entries of the sort one deals with for manned vehicles this approximation gives useful results. Figure 9 shows the situation for a lifting entry in which the approximation above-mentioned has been made.. The coefficients of lift and drag (C\... 1t CD are assumed to be constants, so that the ratio LID is also a constant. The equations are readily integrated, with the exponential density function, leading to the results shown. The minimum height is seen to depend on the atmospheric gradient param eter ~ ,the 'lift loading Parameter' CL

slm

and the entry angle o"f. . However, it is independent of the drag parameter Cc S

/1-..

"

.

Application of this formula for the case indicated here, 30

entry angle, and CL S

l'm

unity, gives ab out 240, 000 ft. as the minimum altitude on Earth and more than 500, 000 ft. on Mars. This result, which seems remarkable at first sight, is due primarily to the effect of the

factor ~ which is considerably smaller on Mars than on Earth, ( ~Mars

I

~ Earth

= .39,

see Fig. 8). If the parameters of the entry are such that the flight path actually does have a minimum, (i. e. there is a skipping motion). then the speed at the hottom of the first 'skip is given by the simple expression shown. It is seen to dep end only on the lift/drag ratio and the entry angle. At the same point on the flight path we get the expression shown for the acceleration. I draw your attention to the fact that it con-tains as a parameter the quantity ~

V[

,

the same expression which we found as a factor in the acceleration results for ballistic entries, and the relative values of which we showed on Fig. 8. Thus for given values of the drag/lift ratio and the entry angle, the relative values of the accelera-tion during lifting entries into the atmospheres of the four planets are the

same as those we saw earlier for ballistic entries. Examination of the equation for the acceleration reveals that an increase in the lift

I

drag ratio leads to a reduction in the maximum acceleration. Figure 10 shows this effect. Plotted here are the peak accelerations for entry into the Earth's atmosphere from an interplanetary mission (velocity 35.000 ft. per sec. ). Practical values of LID for reentry vehicles would be from zero up to 1 1

12

or 2. We see that at entry angles such as 60• for which the ballistic

entry would lead to about a 10 g acceleration ... the use of even a very small amount of lift. corresponding to a lift

I

drag ratio of only 1

14.

reduces the peak acceleration to less than half. The use of larger amounts of lift such as LID

=

1.0 permits entry angles of up to 70 _{or 8}0 _{to be used while}

retain-ing moderate decelerations.

FLIGHT PATHS

In order to show how the main variables affect the reentry flight path we have carried out a number of analogue-computer solutions of the complete equations of motion given in Fig. 5. The next five figures show the results of these ca1culations.

*

Figure 11 shows the effect of entry speed on the flight path in the atmosphere of the Earth. The lift/drag ratio is

112.

the lift-loading-parameter CL 'S

/rn

is unity. and the angle of attack is 620_{. The lowest}

curvè on the graph is for a speed of 10. 000 mph. which corresponds to the reentry into the atmosphere of a vehic1e following a ballistic path having a range of about 2.000 miles. The middle curve (18.000 mph) is for a speed slightly greater than that of a circular orbit. and the topmost curve

(26. 000 mph) is for a speed slightly greater than the escape velocity for the Earth. The tendency of the vehic1e to skip out of the atmosphere at the highest speeds and to follow a wavy path at the lowest speeds is c1early evident from these curves.

Figure 12 shows the effect of entry angle. which we saw was so important in determining the maximum acceleration of the vehicle. The steeper angles are seen to lead to oscillatory motion whereas the shallower angles (about 20 ) lead to much flatter and longer-range trajectories. The entry speed for all these cases is circular velocity.

Figure 13 shows the effect of the angle of attack of the vehicle on its flight path. The lift and drag coefficients were assumed to be functions of the angle. of attack as shown. These functions were deter-mined on the basis of simplified hypersonic flow theory applied to a vehicle having a delta plan form and a relatively flat under surface. at high angles of attack. The .numerical values shown are considered to be representative of those which may occur in practice. As shown in the table on the figure

•

This does not agree with the approximate result given on Fig. 6. The latter is not valid for such small angles.

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The curves shown were traced by the x-y plotter of the analogue com-puter automatically during the computation process.

the angles of attack were chosen to correspond to uniform increments in the lift/ drag ratio and the value of the lift coefficient corresponding to each case is shown for reference as weIl. The 900 _{curve, the lowest one} shown, is of course a ballistic entry, since the lift is zero. The remaining curves show that the effect of changing the angle of attack is quite complicated.

Figure 14 shows the effect of changing the wing loading or lift-Ioading parameter of the vehicle by a factor of 10. The two curves shown are both for entry at circular speed and the upper curve is for the more lightly loaded vehicle. It is evident that the two lines are parallel to one another, that the upper one can be obtained from the lower simply by

shifting it upwards about 50, 000 ft. The speed, acceleration, and flight path angle are the same at corresponding points on the two curves. This result is a general one that can be deduced from the equations of motion. The wing loading can be shown to act as a kind of altitude scale that simply determines the height at which any given speed and acceleration will occur.

The last figure of th is set, Fig. 15, shows the effect of changing the p1:anetary atmosphere. The two curves shown, one for Earth and one for Mars, are for entry speeds in each case equal to the circular speed for the planet. Now although the Martian atmosphere is much "thinner" than that of Earth, in the sense that the surface density is much smaller, nevertheless, as can clearly be seen, the vehicle entering the Martian atmosphere slows down at much greater heights than it does at the Earth. The two factors which contribute to this result are the lower circular speed and,equally important, the much smaller value of the atmospheric gradient parameter f-> . As a result of the smaller value of th is parameter for Mars, the Martian atmosphere is relatively much deeper than that of Earth, and its influence on the entry flight path commences at a relatively much higher altitude.

AERODYNAMIC HEATING

We now leave the question of flight paths and deceleration and turn next to the problem of heating of the vehicle. Figure 16 shows the two main mechanisms of heating. On the left is a blunt body preceded by a shock wave, and on the body itself, a boundary layer. On passing through the shock wave the air is heated non-isentropically to a very high temperature (eg. 8, OOOOR) so that the region between the shock wave and the boundary layer consists of extremely hot gas. lf the body itself is cool then the situ-ation is essentially one of the conduction of heat through the relatively thin boundary layer from the hot gas outside to the cold body inside. The temp-erature distribution through the boundary layer is indicated in the left-hand graph. On the right-hand ,side of the figure we see the flow-field of a slender body, which is very different from that of the blunt body. Here the shock wave, being very much inclined to the flow, is much we aker and has a much smaller heating effect on the air passing through it. The gas between the shock wave and the boundary layer is therefore relatively cool. However,

it has an extremely high velocity and hence there is a very high rate of dissipation of energy by friction within the boundary.layer. The heat gener-ated in the boundary layer causes it to become very hot. and conduction of the heat takes place in both directions. into the cooler gas on the one side and the cooler body on the other. The temperature distribution in this case is as shown in the right-hand graph. A major aim in the design of any re-entry vehicle is to keep the heat transferred to the body to a minimum. In comparing the mechanisms which we see here for the blunt and slender bodies we find that they are very different from the standpoint of the amount of heat transferred to the body. In the case of the blunt body most of the energy goes into heating the air outside the boundary layer. and with suit-able choice of the shape less than 1% of the total energy may be transferred to the body in the form of heat. This is not so with a slender body. Here a much larger fraction of the total energy dissipation takes place in the friction processes within the boundary layer. and of the heat liberated with-in a boundary layer approximately one half is conducted with-into the body. The net result is that a substantial fraction of the total energy dissipated may find its way into the body in the form of heat. Thus a practical reentry vehicle will inevitably be a bluff body. or if it is slender. it wil! be oriented during the critical heating period at a large angle to the stream so that the flow-field is like that of a blunt body.

There are several ways in which the heat which is trans-ferred to the body may be dealt with. The first. and perhaps the most ob-vious. is simply to provide sufficient mass in the body that it can absorb the total energy involved without overheating (the heat sink method). In th is solution. the total heat-transfer is the quantity which must be kept small. . A second method is to use a thin heat shield which quickly comes into

thermal equilibrium with the boundary layer that envelops it. It then radiates away the heat energy at the same rate at which it is coming in from the boundary layer. A third method is what is known as ablation. That is to use a surface material which melts or vaporises at the tempera-tures which develop. The change of state provides a major contribution to the heat absorption. and in the case where the material becomes gaseous. the evolved gas assists by providing a barrier to further heat conduction. A fourth cooling method can involve the application of coolants carried alo ft in the vehicle and evaporated from the surface as required. I don't think that it is clear which of these methods if any win ultimately prove to be most useful ior reentry vehicles carrying human occupants. It may well be that all of them. singly or in various combinations depending on the miss ion. will find practical application. Certainly radiation cooling is likely to be one of the methods seriously considered for reentry vehicles at shallow angles. for then the times involved are sufficient that the heat energy can be radiated away without excessive surface temperatures. It is also possible that the heat sink approach may be useful when used in con-junction with auxiliary drag devices. as shown later on in the lecture. Figure 17 shows the results of some calculations made in connection with the Dyna-Soar program in the U. S. A.; it is for a. reentry at about 20. 000 fps.

It has plots of the radiation equilibrium temperatures at two points on a

vehicle, one the nose stagnation point and the other 4 ft. back from the

leading edge. For a moderately lightly loaded vehicle, i. e. wing loading

of 201bs. per sq. ft., we see that the maximum ternperature reached at

the stagnation point is substantially higher than 3, OOOoF. It occurs at

about 250, 000 ft. altitude .. at which point the speed is about 22, 000 ft. per

second. The maximum temperature reached at the point B on the

under-surface is considerably Iess, about 2, OOOoF, and is reached somewhat later

in the flight at a. lower altitude. The rate of heat transfer to the body at

both the stagnation point S and at the point on the under-surface varies

approximately as the square root of the atmospheric density and the cube

of the speed. The integral of this rate is therefore dependent, in a manner

that is cleá.rly not simpie, on the actual flight path, that is, on the manner

in which (( and V vary with time. Detailed ca1culations show that if the

flight path is designed, by the use of lift or shallow entry angIes~ to keep

the vehicle at very high altitudes and relatively high speeds for a relatively

longer time, then the total heat transferred is greater than if it deseends

rapidIy to low altitudes. On the other hand thel?e very flight paths are those which perm it a greater proportion of the heat transferred to the vehicle to

be radiated back into space, and hence the best design compromise for each

particular mission requires a detailed investigation of all of these factors. One may say however that the understanding which has been arrived at of the

heat transfer problems, and-the developments which have taken place in the

field of materials have certainly put us in a position where satis~actory

vehicle designs can be produced from the point of view of heating problems. There is no thermal barrier; and in retrospect it may even be said that

there never was. The problerns of reentry heating have yielded to entirely

conventional engineering solutions; no 'breakthrough! has been needed.

NAVIGATION

We now Ieave the problern of heating and turn to the third a,nd final one of the major problem areas which we said we were going to

discuss--that is navigation, the proble.r:n of bringing the vehicle to rest on

the surface at the desired location. The graphs which we saw earlier

show-ing families of reentry flight paths, in particular Fig. 13 which shows the

influence of angle of attack, made it fairly evident that quite large varia-tions in the landing point would occur for even relatively small variavaria-tions in any of these flight paths variables. This point is ernphasized by the

flight paths shown in Fig. 18~ to scale in relation to the Earth. The $hort ..

est path is a bailistic trajeetory, the next is one with variabie angle of

atta,ck, and the longest, the skipping path, is one flown at constant

cJ.. .

Evidently if we are to be able to cope with errors in the initial entry

con-ditions, with variations in atmospheric density, (i. e. departures from the

assumed density law) and if we are to be abie in addition to compensate for the effect of unpredicted winds, then it will certainly be necessary to have control of the vehicie during the atmospheric portion of the flight. In con,.. sidering the accuracy with which the initial conditions of the atmospheric

entry can be achieved, i. e. the entry angle, entry velocity, and the point of entry, we have to consider how the vehicle gets to this point from its orbit in space. Consider for example a vehicle in flight at an altitude of 200 m iles on a circular orbit. It begins its descent to the Earth by firing a

retro-rocket inclined at a. suitable angle to the flight path in order to enter the atmosphere at a small angle. Figure 19 shows the errors in range which may accumulate as a result of errors either in orientation or magnitude of the retro-rocket impulse. Considering an entry at about 60 _{we see that an}

error in orientation of the retro-rocket impulse of only 10 _{will result in a}

range error of 30 nautical miles; and that an error of the order of only 1 ft. per sec. in the -impulse would produce a range error of more than 1 mile. Considering the practical requirements of the landing it is evident that substantial, probably unacceptable, variations in landing point would occur as a result of errors in establishing the initial conditions, as well as of the variations in density and wind that can occur after the vehic1e gets into the atmosphere. Another important point in this connection is that the desired landing site may not be in the orbital plane of the vehicle. Since the earth is rotating all the time, then to find the desired landing site in the plane of the orbit would be something of a coincidence. If the entire mission were planned so as to produce this result, small errors in timing would lead to appreciable deviation of the landing site from the plane of the orbit. Thus we find that vehicles that are to land at a desired point must necessarily have the capability of manoeuvering out of the plane of the initialorbit. This capability can be provided by suitable directiçm of the retro-rocket impulse which produces the initial conditions of the reentry, or alterna-tively by the use of aerodynamic lift and banking of the vehicle af ter enter-ing the atmosphere. It may be expected that the latter technique would be required whether or not the former one is used.

Let us return to the problem of coming into the atmosphere with the required initial conditions. As shown in Fig. 20, displacement of the entry trajectory from the desired value in either the upward or down-ward direction can cause the entry to fail. lfthe angle is too steep, that is to say if the vehicle undershoots the atmosphere, then the acceleration or the heating will exceed the design limit, even with the maximum use of lift, as shown in the lower flight path. On the other hand, if the vehic1e overshoots, that is if the entry angle is too small, then it might miss the

~tmosphere altogether, or by only coming into grazing contact with it emerge again into space to complete another circuit around its Keplerian orbit . . A vehicle which has a negative lift capability can extend the upper limit substantially as shown in the upper flight path. When the maximum capability with respect to negative lift has been considered on the one hand, and the limitations of heating and acceleration on the other, an entry corri-dor is defined. The width of this corricorri-dor for a vehicle returning from a Moon mission and using the purely ballistic entry technique would be of the order of only 8 miles in width. Thus after travelling some quarter of a million miles on a return trip from the Moon the vehicle must hit this tiny target. However, by the use of high lift/drag ratio and relatively

sophisticated manouvres (rolling over so as to produce either positive or negative lift) this entry corridor can be widened to greater than 100 miles.

From any given set of initial conditions a vehicle capable of aerodynam ie manoeuvring has accessible to it as a landing point a certain area on the Earth. This area*" is limited by several factors. As we see in Fig. 21, it is limited at short ranges by the steepness of the flight path which can be followed. This will in turn be fixed by deceleration and heat-ing limitations. At the other extreme, the maximum range which can be achieved is governed

py

the maximum lift/drag ratio of the vehicle. The sideways.limits indicated as "maximum manoeuvre boundary" are fixed by the vehicle' s ability to manoeuvre out of the plane of the initialorbit by means of aerodynamic forces. If the possible landing area shown shaded contains the destination of the vehicle then all is well, and it can presum-ably manoeuvre to .that point. Of course the diagram shown here would be predicted upon certain assumptions concerning the density variation in the atmosphere and the wind structure. If these were not as anticipated in the computation then the destination might at a later stage of the flight turn up outside the shaded area. This would presumably be unfortunate!

. When a human being drives an automobile or steers a ship or flies an aeroplane to its destination he is ordinarily capable of applying

the necessary correction manoeuvres utilizing only the information pro-vided to him by his own senses to close the feedback loop (that is, when-ever the destination is visible). It is doubtful whether this will be the case for reentry flight paths. As can be se en from some of the examples we

have shown the paths followed are sufficiently complex and sufficiently sensitive to variations in vehicle parameters that human control of this simple sort may not be possible. The pilot who has to bring the vehicle to its destination will probably require some rather sophisticated aids. One such which has been proposed by R. C. Wingrove and R. E. Coate of the NASA in a recent report (NASA TN D-787) is a navigation computer whieh produces a display showing the pilot both the location of the destination and the availablefootprint of the vehicle, (see Fig. 22). The contour lines drawn here represent the landing areas which can be achieved for the veh-icle parameters indicated by the numbers. For example, to reach the point shown as the destination it will be necessary to fly the vehicle at an angle of attack of about 130 _{and a roll angle of about 220 . A display of this kind}

would ge used during the entry until a relatively low altitude and low speed had been achieved--eg. a low supersonic speed at the order of 100,000 ft. altitude . . From this point on normal flight procedures could be followed to bring the vehicle to its final landing point.

:+- The area is known as a "dyna-soar footprint"--after the U. S. Dyna-Soar project.

UTIA RESEARCH

In the foregoing portion of this lecture, I have presented a review of well-known material. I should now like to tell you about some of our own research, here at the Institute of Aerophysics. We have for the past 2 years been engaged in theoretical work±- related to reentry flight paths and I should like to conclude my presentation with a brief description of one of the analyses which we have carried ou~.

It concerns the entry of a vehicle into the Earth's atmos-phere fr om a low circular orbit. The entry is presumed to be initiated by the application of a suitable impulse which leads to an initial velocity (at 400, 000 ft. ) equal to the circular speed

V

_{c (see Fig. 23). The objective}

of this investigation was to find a flight path which would pro vide a suitable transition between the circular orbit and what is known as 'an equilibrium glide. The equilibrium glide is defined by the condition that aerodynamic lift plus centrifugal force equals weight. In this condition the rate of change of flight path angle can be neglected in the equation of motion and the vehicle proceeds along a smooth curve, with steadily decreasing speed,

It is th is kind of path which is followe d by a boost-glide vehicle during it.s glide phase and which it is intended will be followed by the Dyna-Soar veh-iele. Such an equilibrium glide at a high value of lift/drag ratio would seem to be a very suitable mode of flight for the later portions of a reentry. However, it is unsuitable for the beginning of the entry because of the smal! rate of descent, and consequent excessive range. As the equilibrium glide is followed upwards in altitude it becomes flatter and flatter, so that the path would encircle the Earth many times before it reaches satellite alti-tude. This would make the problem of navigation to a preselected landing site extremely difficult.

What we have done here is to find that particular family of transition paths which have end condition at M , the match point, which fit exactly the conditions of the equilibrium glide. That is to say the speed, the altitude, and the flight path angle match at this point. In addition we have required that the lift force be same on both sides of M • but we allow the drag force to change. The reason for this is that for each pair of entry angle ('Ol:) and match point angle (DM) a unique value of the ,LID ratio is required. The value of LID so obtained is small and may be too low for the-Iateral manoeuvring requirement of the subsequent glide. In order that the latter may proceed at a higher value of the LID ratio. we allow a sudden reductiqn in the drag at the match point M. This can be achieved by jetti. -soning a drag device or parachute. This procedure has a significant ad-vantage with respect to the total heat load. The slowing down of a vehicle towing a parachute during transition is produced not only by the aerodynamic forces which act upon it. but additionally by the cable which connects it to • Supported by the United. States Air Force Office of Scientific Research.

the drag device. Thus the heat load on the vehicle is necessarily less than if the slowing down were produced entirely by aerodynam ic forces.

It turns out when one calculates this class of transition path that the maximum ~cceleration, shown in Fig. 24, depends on the reentry angle only. The quantity plotted here, load factor, is the acceleration in units of ear~h-surface g. We see that, the human tolerance level of about

10 g is reached at entry angles of about . 09 radians, (about ,50 ). Of the total kinetic energy of the vehicle which exists at the time of reentry the fraction which is ·dissipated at the vehicle itself is shown in Fig. 25. We see that for the steeper entries, in the neighbourhood of 40 _{or 5}0 , some-thing like 20-30% of the energy is dissipated at the vehicle, and the remain-der, some 70 to 80%, is dissipated by the auxiliary device. This necess-ar!ly makes the the.rmal design of the vehicle an easier task, since the total heat load which it has to carry is less. It may for example make it feasible to use the heat sink concept, and ease the requirements on the structural materials. Of course, a penalty is paid for this, since it is necessary to carry along the extra drag body, which is a weight penalty, and the thermal design of the drag body itself may present difficult problems. However, it should be noted that it is only required of the drag body that it shall not collapse. High temperatures are quite acceptable since there is no payload to be protected there. The radiation equilibrium temperatures Which we re calculated for a particular entry at

'Ct:

=

40 _{are shown on}

Fig. 26. This figure shows the stagnation-point temperatures reached on the vehicle (assllming a 2 ft. stagnation-point radius) and on the drag body (which is assumed to have a 20 ft. stagnation-point radius)." The values of these temperatures, although fairly high, are well within the capabilities of modern high-temperature materials. We see that the peak stagnation-point temperature of the vehicle is not reduced to a low value by the llse of an auxiliary drag body which reduces the total heat load substantially. ln-deed, the r,adiation-equilibrium temperature is not a suitable criterion for showing the advantage which accrues from a reduction Of tot al heat load. For this purpose, one must calculate _.the actual transient temperature in the vehicle, including proper allowance for the method used to absorb the heat. This has been done for our example, and Fig. 27 shows the result. The upper curve, the radiation-equilibrium temperature, gives the average temperature over the entire surface of the vehicle which would be achieved if the vehicle were in radiation-equilibrium at all time~, that is, if the heat capacity were vanishingly small. The average temperature shown on this curve is of course smaller than the peak value at the stagnation-point shown on the previous figure. Now, if we assume that 50% of the mass of the veh-icle uniformly absorbs the heat which is being transferred to it (with the specific heat of steel) then the average temperature obtained is as shown in the lower curve. As a re sult of the low total heat load, the peak value obtained is only about 8000_{R or 340}0_{F. The indication is that reduction of}

*"

The value of the stagnation-point heat transfer rate varies inversely as as the square root of the radius.

the total heat load by a substantial amount has probably made feasible the heat-sink approach to the solution of the thermal problem. The relatively low average temperature indicates that much of the structure rnay be made of conventional materials.

CONCLUSION

In coilclusion, it appears that none of the three major pro-blem areas, i. e. deceleration, heating,and navigation, wiU present in-superable difficulties for the reentry of manned space vehicles. The nor-mal processes of applied research and engineering development may con-fidently b~ expected to lead to the successful accornplishment of such missions in the future.

24 20 16 12 8 4

o

Circular Escape Ratios

-Venus 16,300 23,000 0.92 Earth 17,700 25,000 1. 00 .. Mars 8,000 11,400 0.46 Jupiter 95,500 135,000 5.40

FIG. 1. TABLE OF ENTRY VELOCITIES FOR THE FOUR

PLANETS VENUS, EARTH, MARS, AND JUPITER

FIG. 2. KINETIC ENERGY PER LB. OF VEHICLE COMPARED WITH HEAT ENERGY

/

OF GASOLINE 1/

//

.... _z /

/

:J 0 en

"'

C)

"-V/

0 en ...J

"'

C)

/

/

~

---

n(Vc~ar.

(Ve)Man (Vc)Venus (~arth (Ve)yenu .tv~Earlh

4 8 12 16 20 24 28 32 36 40

LEVEL

(G-UNITS)

1 1 _{10 100 1000}

TIME (SECONOS)

FIG. 3. GRAPH OF HUMAN TOLERANCE LIMITS TO ACCELERATION

II

(Fig. l(b) of "The reentry of manned Earth Satellites" by R. H .. P1ascott, R. A. E. Tech. Note Aero 2640, Aug. 1959)

,

\

CL~P~V2S

+

m cosy(f

-g)

+

mv

:

=

0

..Qy=-sin y

ds

P

= Po

e-[jy

Crucial parameter:

(provided R, T const.>

FIG. 5. EQUATIONS OF MOTION FOR REENTRY VEHICLES

\

\

\

\

\

\\~'"

Equation of motion:

mat-:- - --

dv .:.

D -

C

1.

,\~

2

D2

P\J/V

5

Results:

y=const.

.-Y=exp

[

-~

m

p

J

V

E

2,Bsiny

Note:

p~)

=

e.

e-/3y

o

/3=~

RT

I

BALLISTIC ENTRY APPROX. SOLUTION 160 ~= CIRCULAR SPEED

/

~ VEARTH 140

/

L

/

/

1

/

120 ~IOO z 0 ~ ct: 80 w ..J W U W 0 ~ ~ 60

/

/

40 20

L

M4RS

J.---

r---r

o 20 40 60 80 100 ENTRY ANGLE

RELATIVE VALUES OF

I

a

I

MAX"-I,sV~

at V c at V e _o/,sE

Venus 0.99 1. 98 1.175

Earth 1. 00 2.00 1.0

Mars 0.083 0.166 0.392

Jupiter 11.4. 22.8 0.392

·FIG. 8. TABLE OF RELATIVE VALUES OF MAXIMtTlVI

\ t \

V

\

\

\

\

\

\

\ \ \

Approx. equ'ns f or

VE=~,

const.

'0 :

-mvy

= L=C

_L

~p(y)V2S

-mv =

D=CD~

p(y)v

2

s

P

=

p,.e-fJY

o

\ \ \

Results:

min. height,

Y.t,.i'

$ln(~S

t3'})

\ \

e.g.

">'

=

3~ ~s

=

I,

YM.i

237,

000

ft. (Earfh)

=

0

508,000ft.

(Mars)

speed af first bottom,

Vv.

=

1-

J2

>t

I

L

acceleration at firsf bottom ,

FIG. 9. EQUATIONS OF MOTION AND RESULTS FOR LIFTING ENTRY

c o ... ro

....

Maximum,

CL/CD

=

0

30

1---- - --- -- - - + - - - , f - - - - 4 - - - + - - - - i a>

20

a> u a> -0 .::.::. ro a> a...

°3~----~~~~:ï6==~---9~---J12

Entry angle. 8 F. (deg) at 400,000 ft

(V f:

=

35,000 ft/sec)

FIG. 10. GRAPH OF PEAK DECELERATION VERSUS ENTRY ANGLE AND LID

(Fig. 18. 12 of "Reentry and Recovery" by J. R. Sellars, Chapt. 18 of "Ballistic Missile and Space Vehicle Systems" edited by H. F.

400

ENTRY SPEED, MPH

300

AlTITUOE,

18,000

:

KllOFEET

14,000

'.

MANNED VEHICLE ENTRY FLIGHT PATH

,- 200 1111111111111 1'

10,000

ENTRY ANGLE

=

3.0

0 els

=

1.0

m

...b..

I

= "2

D

a

₌

63.0°

111111111110 LI Li U l l l l lll l l l l l l l lll l l l l l l l : 11111111 111' I1111 , " '11111111111111 111 1111 I 1 , 111 111111 11 11 1111111111111 t I t t lil! II I I III

100

OISTANCE FlOWN, MllES

o

200 400 600 800 1000 1200 1400

11111111

_,,_ :-j±;p,---;--....

+r::'::j::.:::'

._ .... +-;-;! ." I

+1-±ti

~ 400 !TITT1

ENTRY ANGLE, DEG

I i 111 11I I I I 11 11 I I I1 I I I I 11 I 0.0 ' '>,' 300

2.0

: ALTITUDE,

4.0

KILOFEET 6.0 200

8.0

-100

o

200 , 400

MANNED VEHICLE ENTRY FLIGHT PATH

ENTRY SPEED

=

17,700 MPH eLS 1.0

----rn-

=

J....

I

D

=

2""

a = 63.00

DISTANCE FLOWN, MILES

600 800 1000 1200

FIG. 12. ANALOGUE COMPUTER SOLUTIONS SHOWING EFFECT OF ENTRY ANGLE

400 300 ALTITUoE, KILOFEET 200 100

o

CL

=

2 sin2a cos a Co =

0.03

+

2

sin3a 200 400 ENTRY SPEED =

17,700

MPH ENTRY ANGLE

=

3.0°

W

S

=

22.7

PSF

aO

43

.

7

:63.0-31.0

20.

~lllmi

1111111111

aO

90.0

63.0

43.7

90.0

_31.0

20.0

olSTANCE FLOWN, MILES

600 800 1000 L CL

1f

0.00

0.00

0.50

0.72

1.00

0.69

1.50

0.45

2

.

00

0.22

1200 1400

400 111111111111111111111111111111111 111 300 . 1 " " " " I ALTITUDE, KILOFEET 200 100

o

200 400 ENTRY SPEED = 17,700 MPH ENTRY ANGLE = 3.00 L

₌

_I 0 2

a

=

63.00

els

m

1.0

0.1

DISTANCE FLOWN, MILES

600 '800 1000 1200

FIG. 14. ANALOGUE COMPUTER SOLUTIONS SHOWING EFFECT OF WING LOADING

'

eoo

111

1

11

i

I1111I

1

11111

i

III

I

IIIIIJIII

I

II

I

600 ALTITUDE. KILOFEET 400 200

o

500 1000 ENTRY ANGLE

=

4.00

els

1.0 m

=

b..

=

I

0

2

a

=

63.00 MARS, V

_c

=

8,150 MPH . EARTH, V

_c

= 17,700 MPH .

DISTANCE FLOWN. MllES

1500 I III I I I IIIII~I 2000 2500 3000 3500

TEMPERATURE

OUTER EOGE OF aOUNOARY

LAYER

DISTANCE FROM SURFACE

TEMPERATURE _OUTER

[OGE OF aOUNOARY LAYER

DI STANCE FROM SURFACE

BLUNT BODY SLENDER BODY

FIG. 16. THE EFFECT OF BODY SHAPE ON THE

MECHANISM OF AERODYNAMIC HEATING (Fig. 2 of "The influence of aerodynamic heating on the structural design of aircraft" by Morris W. Rubesin. AGARD Rep. 207.

Oct. 1958)

NOSE OIMlETEA • I FOOT Ct" .2 Q = 2r!' 300

.

• • 0 " .9 3000 F

I

I!IOO°F 2000° F

,

I

400r!'F 200 3000"F ~ ... RADIATION 7 EQUILI8RIUM 0 TEMPERATURES J: 100 - - f - -EQUILIBRIUM FLIGHT - --STAGNATION POINT S - - - POINT 8 - TURBULENT FLOW

10 20 25

FIG. 17. DEPENDENCE OF WING LOADING ON STRUCTURAL

TEMPERATURES FOR A RADIATION-COOLED VEHICLE (Fig. 8 of "Dyna-Soar; a review of the technology" by Y. A. Yoler. Aerospace Engineering. Vol. 20. No. 8, Aug. 1961)

JlOjnt ",here a retarding rocket is fired. Route ending at a is the

and care, respectively, samples of paths that could he followed

hy vehicles wilh variahle nnd with constant lifting power_

FIG. 18. REENTRY FLIGHT PATHS

(from "Reentry from Space" by J. V. Beeker,

o o 00

....

o

....

NO I ""'"

/

V

I

velocity error, nautical miles/(ft) (sec)

I 00

V

I I I ... N

---

J

-0'1 N o

"

I N o I """'" o

--...

~

_~

"-I I

g

_~ ...

8

Range error tor each unit of retrorocket orientation error, nautical miles/deg

....

N o N 0 0 I I N 00 ~-c:: ... ö· QI

-ê

.

i D -0 .., 0-;:::;:

....

"""'" o

FIG. 19. RANGE ERRORS DUE TO ERRORS IN RETRO-ROCKET ORIENTATION AND VELOCITY INCREMENT

(Fig. 18.9 of "Reentry and Recovery" by J. R. Sellars, Chapt. 18 of "Ballistic MissIe and Space Vehicie Systems" edited by H.F. Seifert and K. Brown; John Wiley and Sons, 1961)

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

.

:~~~~~~~~~~~~~~~~:s~~~~:-s-~-~-_~---_________

SKIP PATH ... ..." ,.;. .. ...

-

...

....

... , ' ... _...

ENTRY CORRIDOR defines vertical limits for approach to at· ing lift temporarily downward, vehicle can land from initial paths rno>;,;Jerc'. Limit, ure widened by maneuvers to vary lift. By direct· that would otherwise result in an overshoot or undershoot.

FIG. 20. THE ENTRY CORRIDOR

(from "Reentry from Space" by J. V. Beeker,

1_

I

FIG. 21. DIAGRAM OF THE ACCESSIBLE LANDING 'AREA ON THE EARTH

(Fig. 2 of "Piloted simulat.or tests of a guidance system which can

cOl1~ir..üously _predict landing point of a low LID vehicle during

atmosphere reentry" by R.

C.

Wingold and R. E. Coate.

NASA TN D-787. March 1961)

"'~

..

AOA -..

-.

__ 2 5 °

-I

I 15° Boundary tor acceleration or heating limit Trim tor maximum

LID

Trim for LID = 0

FIG. 22. REENTRY GUIDANCE DISPLAY SHOWING THE DESTINATION WITH

RESPECT TO THE MANOEUVRE CAPABILITIES OF THE VEHICLE (Fig. 3 of "Piloted simulator tests of a guidance system which can

continu0usly predict landing point of a low LID vehicle during

atmosphere reentry" by R. C. Wingold and R. E. Coate, NASA TN D-787, March 1961)

--

_{- -}

- -

V

_c

r

Circular Orbit

--_._

..

---

-->;:

~

Transition Path -- - - - -_

v.

=

v.

~...

~

Match Point E

c

~__,/

-0-. _ _ (Jettison 'chute)

M

- - _

-... _~ Glide . - - . / ...

"-"-

_...

_,

,

FIG. 23. DIAGRAM OF HIGH-DRAG TRANSITION FLIGHT PATH

)C c 12 10 I: 8 c 2

L/

_ 02 APPROX.

/;

' " EXACT

I-/

I

r

/

V

_ 04 _ 06· _.08 .10

ENTRY ANGLE, tF. RAD_

• 8 • 7 .6 .5 .4 .3 .2 .1

o

~---+

-

~---+---+---t---t---1

~

\f\--+---~--+---;

h

~

~---~---~r----', ~~----r----~----4

'I~

r.:

1 _2° ,.. I '

FIG. 25. FRACTION OF TOTAL ENERGY DISSIPATED AT VEHICLE CLS/m=l.O

3000

V

\ ' 2 ft. (VEHlCLE)

/

/

\

i/

L

TOR

I

R=20 ft (DRAG-BODY)

\

.

1\

/ -... /

V

\1

~

I

/

L

/

[7

\

\

_'"'"

~~

I

i/

/

\

MATCH POINT

~

/

\

2000

/

/

't

~

)

"-"',

1000

/

.

~

FIG. 26. RADIATION EQUILIBRIUM TEMPERATURES AT STAGNATION

\-POINTS OF VEHICLE AND DRAG BODY

I I I I I I I I I I I I I

TOR 1400 1200 1000 800 600 400

ti

200 I

o

•

-r

"

.

,

~

\

RADIA TION - EQUILIBRIUM TEMPERA TURE

----

_~

~

I

'\

/

---'.

~~

\ \ \

Ä

\ \ / TRANSIENT TEMPERATT.JRE t (SEC) I I _1 I I 3 I I ~ 60 ₁₂₀ 180 ₂₄₀ 240

FIG. 27. AVERAGE VALUES OF RADIATION-EQUILIBRIUM AND

'T'RANSIENT VEHICLE TEMPERA TURES.

~ ..l