. Thin Airfoil Theory (2-D Inviscid Flow)

As seen in class

Ci — 2n(a + 2, Cm, o — _2 (“ + 4

For a given value of camber and Cl, the lift coefficient relation can be solved for the angle of incidence as

Ci d

(a)Ci —0.5 — – – 2- — —0.0924rd — -5.3° 2n c

Ci d

(a) Ci —2.0 — – — 2 — 0.1463 rd — 8.4°

2n c

The corresponding moments are

(Cm, o)Ci —0.5 — -0.395 (Cm, o )Cl —2.0 — -0.77

The center of pressure is found from Xf — , that is

(—)q —0.5 — 0.79

ci

(—)Cl —2.0 — 0.385

ci

See Fig. 15.3.

15.2.1.2

Подпись: z/c z/c Fig. 15.3 Relative position of aerodynamic center and center of pressure
. Thin Airfoil Theory (2-D Inviscid Flow)

Supersonic Linearized Flow (Mo > 1)

The lift coefficient Ci in supersonic flow is given by

Ci (a) = 4 a, where в = ^M — 1.

Подпись: Cm,o (a) . Thin Airfoil Theory (2-D Inviscid Flow)

The moment coefficient is

where (Cm, o)a=0 = | q(f’+(X) + f’ (X))cit.

. Thin Airfoil Theory (2-D Inviscid Flow) Подпись: 16 d в c . Thin Airfoil Theory (2-D Inviscid Flow) Подпись: 8 d 3в c

The thickness distribution has no effect on the moment which reduces to the camber contribution

The moment reads Cm, o(a) = — d. — 2a. The center of pressure is given by

xcp 1 e(Cm, o)a=0 1 + 2 d 1

c 2 4a 2 3 c a

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