NAVWEPS 00-601-60 
HIGH SPEED AERODYNAMICS 
in pressure without apparent changes in den- 
sity. Such a condition of airflow is analogous 
to the flow of water, hydraulic fluid, or any 
other incompressible fluid. However, at high 
flight speeds the pressure changes that take 
place are quite large and significant changes 
in air density occur. The study of airflow at 
high speeds must account for these changes 
1 in air density and must consider that the 
1 air is compressible and that there will be 
“compressibility effects.” 
A factor of great importance in the study of 
high speed airflow is the speed of sound. 
The speed of sound is the rate at which small 
pressure disturbances will be propagated 
through the air and this propagation speed 
is solely a function of air temperature. The 
accompanying table illustrates the variation 
of the speed of sound in the standard 
atmosphere. 
TABLE 3-I. V.r;afIm < 
Altitude in 
,I T< 
the - 
-- 
- 
D F. - c. K?uI, 
59.0 15.0 661.7 
41.1 5.1 650.3 
23.3 -4.8 6%. 6 
5.5 -14.7 6X6.7 
--12., --24.6 614.6 
--30.2 -34.5 602.2 
-48.0 -44.4 589.6 
-65.8 --w.3 516.6 
-69.7 -56.5 573:s 
-69.1 -56.5 573.8 
-69.7 -56.5 573.8 
As an object moves through the air mass, 
velocity and pressure changes occur which 
create pressure disturbances in the airflow sur- 
rounding the object. Of course, these pressure 
disturbances are propagated through the air 
at the speed of sound. If the object is travel- 
ling at low speed the pressure disturbances are 
propagated ahead of the object and the airflow 
immediately ahead of the object is influenced 
by the pressure field on the object. Actually, 
these pressure disturbances are transmitted in 
all directions and extend indefinitely in all 
directions. Evidence of this “pressure warn- 
ing’ ’ is seeii in the typical subsonic flow 
pattern of figure 3.1 where there is upwash 
and flow direction change well ahead of the 
leading edge. If the object is travelling at 
some ,speed above the speed of sound the air- 
flow ahead of the object will not be influenced 
by the pressure field on the object since pres- 
-sure disturbances cannot. be propagated ahead 
of the object. Thus, as the flight speed nears 
the speed of sound a compression wave will 
form at the leading edge and all changes in 
velocity and pressure will take place quite 
sharply and suddenly. The airflow, ahead of 
the object is not influenced until the air par- 
ticles are suddenly forced out .of the way by 
the concentrated pressure wave set up by the 
object. Evidence of this phenomenon is seen 
in the typical supersonic flow pattern of 
figure 3.1. 
The analogy of surface waves on the water 
may help clarify these phenomena. Since a 
surface wave is simply the propagation of a 
pressure disturbance, a ship moving at a speed 
much less than the wave speed will not form 
a “bow wave.” As the. ship’s speed nears 
the wave pro$agation speed the bow wave 
will form and become stronger as speed is 
increased beyond the wave speed. 
At this point it should become apparent 
that all compressibility effects depend upon 
the relationship of airspeed to the speed of 
sound. The term used to describe this rela- 
tionship is the Mach number, M, and this 
term is the ratio of the true airspeed to the 
speed of sound. ,-I 
M=; 
where 
M=Mach number 
V= true airspeed, knots 
d= speed of sound, knots 
=a& 
aO=speed of sound at standard sea level 
conditions, 661 knots 
e= temperature ratio 
= T/T, 
Revised January 1965