# Lifting Line Theory (3-D Inviscid Flow)

14.3.2.1 Induced Drag in Cruise

Give the formula for the induced drag Di in (N), in terms of the wing efficiency e, the dynamic pressure 1 pV2, and the other geometric characteristics of the wing.

Give the equilibrium equation along the vertical axis during horizontal cruise in dimensional form (neglect the lift of the tail).

Eliminate CL between the two results and rewrite Di.

Application: calculate Di for V = 20 m/s, M = 24.7 kg and b = 4.877 m, e = 0.9 (use p = 1.225 kg/m3).

14.3.2.2 Turn

In order to turn, the airplane must roll about its longitudinal axis. This can be achieved by using the ailerons, small flaps located along the trailing edge of the wing. Assume that the wing loading in cruise is given by:

Г [у (t)] = 2UbA1 (sin t + ^ sin 3t) „

b, 0 < t < n

у (t) = — 2 cos t

What is the induced drag coefficient during cruise in terms of A1?

The turn will require to add the antisymmetric mode A2 sin 2t. Sketch mode 2.

14.3.2.3 Drag Penalty

Find the drag penalty associated with the turn by calculating Cdl, given that A2 = A1/3. D