However, if high speed flight is the primary 
consideration, the airfoil must be chosen to 
have. the highest practical critical Mach 
number. 
Critical Mach number has been defined as 
the flight Mach number which produces first 
evidence of local sonic flow. Thus, the air- 
foil shape and lift coe&ient-which determine 
the pressure and velocity distribution-will 
have a profound effect on critical Mach number. 
Conventional, low speed airfoil shapes have 
relatively poor compressibility characteristics 
because of the high local velocities near the 
leading edge. These high local velocities are 
inevitable if both the maximum thickness and 
camber are well forward on the chord. An 
improvement of the compressibility character- 
istics can be obtained by moving the points of 
maximum camber and thickness aft on the 
chord. This would distribute the pressure and 
velocity more evenly along the chord and 
produce a lower peak velocity for the same 
lift coefficient. Fortunately, the airfoil shape 
to provide extensive lamiaar flow and low 
profile drag in low speed, subsonic flight will 
provide a pressure distribution which is favor- 
able for high speed flight. Figure 3.12 
illustrates the pressure distributions and 
variation of critical Mach number with lift 
coefficient for a conventional low speed airfoil 
and a high speed section. 
In order to obtain a high critical Mach 
number from an airfoil at some low lift 
coefficient the section must have: 
(u) Low thickness ratio. The point of 
maximum thickness should be aft to smooth 
the pressure distribution. 
(6) Low camber. The mean camber line 
should be shaped to help minimize the 
local velocity peaks. 
In addition, the higher the required lift 
coefficient the lower the critical Mach number 
and more camber is required of the airfoil. 
If supersonic flight is a possibility the thick- 
ness ratio and leading edge radius must be 
small to decrease wave drag. 
NAVWEPS 00-801-80 
HIGH SPEED AERODYNAMICS 
Figure 3.13 shows the flow patterns for 
two basic supersonic airfoil sections and pro- 
vides the approximate equations for lift,drag, 
and lift curve slope. Since the wave drag is 
the only factor of difference between -the two 
airfoil sections, notice the configuration fac- 
tors which affect the wave drag. For the 
same thickness ratio, the circular arc airfoil 
would have a larger wedge angle formed 
between the upper and lower surfaces at the 
leading edge. At the same flight Mach num- 
ber the larger angle at the leading edge would 
form the stronger shock wave at the nose and 
cause a greater pressure change on the circular 
arc airfoil. This same principle applies when 
investigating the effect of airfoil thickness. 
Notice that the wave drag coefficients for 
both airfoils vary as the SQUARE of the 
thickness ratio, e.g., if the thickness ratio 
were doubled, the wave drag coefhcient would 
he four times as great. If the thickness were 
increased, the airflow at the leading edge will 
experience a greater change in direction and 
a stronger shock wave will be formed. This 
powerful variation of wave drag with thick- 
ness ratio necessitates the use of very thin air- 
foils with sharp leading edges for supersonic 
flight. An additional consideration is that 
thin airfoil sections favor the use of low aspect 
ratios and high taper to obtain lightweight 
structures and preserve stiffness and rigidity. 
The parameter JMz-l appears in the 
denominator of each of the equations for the 
aerodynamic coefficients and indicates a de- 
crease in each of these coefficients with an 
increase in Mach number. Essentially, this 
means that any aerodynamic surface becomes 
less sensitive to changes in angle of attack at 
higher Mach numbers. The decrease in lift 
curve slope with Mach number has tremendous 
implications in the stability and control of 
high speed aircraft. The vertical tail becomes 
less sensitive to angles of sideslip and the