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National Advisory Committee for Aeronautics, Technical Notes - Determination of Transient Skin Temperature of Conical Bodies During Short Time, High Speed Flight

A short and simple method is presented for the determination of
transient skin temperature of conical bodies during short—time, high-speed
flight. A differential equation is presented for this purpose,-
giving the fundamental relations between the transient skin temperature
and the flight history. For the heat—transfer coefficient and
boundaryhdayer temperature, which are needed in the differential
equation, Eber’s experimental results for conical bodies under super—
sonic conditions are adapted and summarized in a convenient way. The
method is applied first to flight at constant altitude to illustrate
the effect of acceleration on transient skin temperature. The method is
then applied to arbitrary flight. Several examples are given; for one
example measured data are available and are in good agreement with the
calculations.

When air flows over a body, the air immediately adjacent to the
body is brought to rest by skin friction. As a result the air is
heated to a higher temperature and, hence, heat exchange between the
air and the skin occurs. This phenomenon is generally termed
"aerodynamic heating."

At high speed the temperature increase of the air is very large
and the aerodynamic—heating problem.becomes of great concern to
designers. The problem.is related to the characteristics of the
boundary layer and the local heat—transfer coefficient. In.reference l
a method is given for the determination of the skin temperature at A
supersonic speed, which makes use of the formulas for heat—transfer
coefficient and boundary—layer temperature derived for flat plates at
subsonic speed. In reference 2 a different approach is made for the
determination of skin temperature of a body of revolution in superSonic
flight. Both papers, however, deal with equilibrium skin temperature
for steady—flight conditions at constant altitude.

In several German papers (reference 3, for instance) it is shown
that for a short—time flight during which the speed and. altitude vary
with time, the transient skin temperature may be considerably lower
than the equilibrium skin temperature. In the present paper, therefore,
emphasis is given to the transient skin temperature, rather than the
equilibrium skin temperature. A differential equation is- presented for
this purpose; and for the heat—transfer coefficient and boundary—layer
temperature needed in the differential equation, Eber’s experimental
results (reference It») for conical bodies under supersonic conditions are
adapted and summarized in a convenient form for immediate application.
If, however, better emerimental data become available, they can be
adapted readily to the present method.