Question

The airfoil on the Lockheed F-104 straight-wing supersonic fighter is a thin, symmetric airfoil with a thickness ratio of 3.5%. Consider this airfoil in a flow at an angle of attack of 5o. The incompressible lift coefficient for the airfoil is given approximately by cl=2παcl=2πα, where αα is the angle of attack in radians.
Estimate the airfoil lift coefficient for
(a) M = 0.2
(b) M = 0.7
(c) M = 2.0.

Answer 1

We have a problem with three different state of the ratio of flow velocity to speed of sound.

That is,

a) Mach number to evaluate is 0.2, that mean we have a subsonic state.

The equation here for lift coefficient is,

$c_1 = 2\pi \alpha$

where $\alpha$ should be expressed in Rad.

$\alpha = \frac{5}{57.3}= 0.087$

So replacing in equation for subsonic state,

$c_1 = 2\pi (0.087)=0.548$

b) In this situation we have a transonic state, so we need to use the Prandtl-Glauert rule,

$c_{t}=\frac{\c{t_0}}{\sqrt{1-M^2_{\infty}}} = \frac{0.548}{\sqrt{1-0.7^2}}=0.767$

c) For this case we have a supersonic state, so we use that equation,

$c_s = \frac{4\alpha}{\sqrt{M^2_{\infty}-1}}=\frac{4(0.087)}{\sqrt{2^2-1}}=0.2$