Question

Consider an infinitely thin flat plate of chord c at an angle of attack α in a supersonic flow. The pressure distribution
can be approximated as follows:
i) Upper surface: Cp constant at -0.8 from the leading edge to 60% chord, then increasing linearly to +0.1 at the trailing
edge.
ii) Lower surface: Cp constant at –0.4 from the leading edge to 60% chord, then increasing linearly to +0.1 at the trailing
edge.
Estimate the lift coefficient and the pitching moment coefficient about the leading edge due to lift.

Answer 1

first 60%
Cp lower - Cp upper = -.4 +.8 = + .4 = delta Cp front
last 40% = average from 60 to 100% = (.4 +0 )/2 = .2 = delta Cp rear

Cl = 1/c integral 0 to c of delta Cp dx
front part 1/c * .4 (.6 c)
back part 1/c * .2 (.4 c)
sum = .24 + .08 = 0.32 = Cl , lift coef per unit span
for the moment integrate with the distance x from the leading edge in the integral