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National Advisory Committee for Aeronautics, Report - A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth's Atmosphere at High Supersonic Speeds

A simplified analysis is made of the velocity and deceleration
history of ballistic missiles entering the earth’s atmosphere at
high supersonic speeds. It is found that, in general, the gravity
force is negligible compared to the aerodynamic drag force and,
hence, that the trajectory is essentially a straight line. A con-
stant drag coefi‘icient and an exponential variation of density with
altitude are assumed and generalized curves for the variation of
missile speed and deceleration with altitude are obtained. A
curious finding is that the maximum deceleration isindependent
of physical characteristics of a missile (e. g., mass, size, and
drag coeflicient) and is determined only by entry speed and
flight-path angle, provided this deceleration occurs before impact.

The results of the motion analysis are employed to determine
means available to the designer for minimizing aerodynamic
heating. Emphasis is placed upon the convective—heating
problem including not only the total heat transfer but also the
maximum average and local rates of heat transfer per unit area.
It is found that if a missile is so heavy as to be retarded only
slightly by aerodynamic drag, irrespective of the magnitude of the
drag force, then convective heating is minimized by minimizing
the total shear force acting on the body. This condition is
achieved by employing shapes with a low pressure drag. 0n the
other hand, if a missile is so light as to be decelerated to rela—
tively low speeds, even if acted upon by low drag forces, then
convective heating is minimized by employing shapes with a
high pressure drag, thereby maximizing the amount of heat
delivered to the atmosphere and minimizing the amount delivered
to the body in the deceleration process. Blunt shapes appear
superior to slender shapes from the standpoint of having lower
maximum convective heat-transfer rates in the region of the nose.
The maximum average heat-transfer rate per unit area can be
reduced by employing either slender or blunt shapes rather than
shapes of intermediate slenderness. Generally, the blunt shape
with high pressure drag would appear to ofier considerable
promise of minimizing the heat transfer to missiles of the sizes,
«weights, and speeds of usual interest.