Supersonic Flow (Mo > 1, в = JM( — 1)

The same profile equips the wing of an airplane cruising at Mach number M0 > 1 in a uniform atmosphere.

Pressure Distribution and Flow Features

Using Ackeret formula one finds C + — ±20/в and C- — 0 . This is shown in Fig. 15.32 at a — 0. The flow features are displayed in Fig. 15.33 (shocks, charac­teristic lines, expansion shocks).

x

c

Fig. 15.32 Cp distribution on the half double wedge at a — 0

Aerodynamic Coefficients

Подпись: 4 в Supersonic Flow (Mo > 1, в = JM( — 1) Подпись: dx c Подпись: в
Supersonic Flow (Mo > 1, в = JM( — 1)

At a = 0 , the drag coefficient (Cd)a=0 is given by

Supersonic Flow (Mo > 1, в = JM( — 1) Подпись: 4 в Подпись: c x dx d '(x)xdx 0 c c Подпись: 4 в Подпись: 1 2
Supersonic Flow (Mo > 1, в = JM( — 1)
Supersonic Flow (Mo > 1, в = JM( — 1)

and moment coefficient (Cm, o) 0 by

Подпись: 0Подпись: 4 & в ~4Supersonic Flow (Mo > 1, в = JM( — 1)&

Static Equilibrium About an Axis

If an axis is located at the leading edge, x = 0, the equilibrium angle aeq corresponds to a zero moment coefficient, i. e.

Подпись: & aeq = -~4 Cm, o(aeq) = (Cmo)a=0 – 2в = 0,

The equilibrium is stable because dCm, o/da < 0.

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