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National Advisory Committee for Aeronautics, Report - Heat Transfer to Bodies Traveling at High Speed in the Upper Atmosphere

The general method has been deceloped, using the methods of
lrinetic theory, whereby the surface temperatures of bodies can
be calculated for steady flight at any speed in a rarefied gas.
The particular solution was made for a flat plate; however, the
calculations can be easily extended to bodies of arbitrary shape.

It was found that the aerodynamic heating problem in the
absence of solar radiation, that is, for the case of nocturnal
flight, becomes of negligible importance at altitudes of 125 miles
and higher and up to steady flight speeds of 36,000 feet per
second. The efiect of solar radiation, for the case of daytime
flight, becomes increasingly important as the flight altitude is
increased. At an altitude of 150 miles and higher, solar radia-
tion is the predominating factor that determines slcin tempera—
ture. Owing to the strong effect of solar radiation on skin
temperatures at high altitudes, the desirability of nocturnal
flight is indicated in order to minimize skin temperatures.

In order to maintain low ski-n temperatures, it was found
that the angle of inclination of the body with respect to the
flight path should be kept as small as possible. Ibis may be
accomplished in practice by designing the body to be finely
tapered and by flying the body at small angles of attack.

It is pointed out that skin temperatures may be reduced by
insuring thermal contact between portions of the shin inclined
at positive and negatire angles with respect to the flight path.
As much surface as possible should be inclined at negative
angles. Practically, this may be accomplished by boattailing
the body.

In the event that an internal skin-cooling system is employed,
it is shown that the rate of internal cooling must be of the same
order of magnitude or greater than the rate at which heat is lost
naturally by emitted radiation. If the cooling rate is below
the natural radiation rate, cooling has little eject upon ski-n
temperatures.