Question

An airplane glides in steady flight (T = 0), and its lift-to-drag ratio is L/D = 4.

(a) What is the flight path angle γ ? 

(b) If the airplane glides from an altitude of 1000 m to zero altitude, what horizontal distance does it travel?

Answer 1

The angle between the thrust vector and the positive x axis is α:

The drag: D = -|D|i +0j. The angle between the weight vector and the positive x axis is (270 - γ);

The equilibrium conditions are

Substitute and collect like terms:

Solve the equations for the terms in γ.

Part (a): Take the ratio of the two equilibrium equations:

Divide top and bottom on the right by |D|.

Part (b): The flight path angle is a negative angle measured from the horizontal, hence from the equality of opposite interior angles the angle γ is also the positive elevation angle of the airplane measured at the point of landing.