Question

Re-derive the coefficient of pitching moment equation for the aircraft in the previous problem.Note: Use the corresponding free body diagram and build-up method for the derivation.

Answer 1

The Moment about the C.G (centre of gravity of the aircraft) in a broad sense is created by 4 factors,

1.Lift, Drag, and Moment about the aerodynamic centre of the wing.

2. Lift of the tail

3. The Thrust of engine

4. Aerodynamic forces and moments of other parts.

Assuming, the thrust vector pass through the C.G and hence zero and aerodynamic forces and moments of the other parts being negligible in comparison to that of wing and tail, we will only consider wing and tail for deriving the coefficient of the pitching moment.

We will derive the coefficient of moment about C.G. due to wing and tail separately and add them up in the end.

Coefficient of moment because of wing:

Consider the isolated wing and forces/moments acting on it as shown in the diagram below.

Coefficient of moment because of Tail:

1. The tail is generally mounted behind the wing and hence it affected by the wake of the airflow behind the wing.

2. The airflow at the tail is deflected due to the downwash of the wing and hence the tail does not see the relative wind in the same direction as seen by the wing.

3. Also, because of the retarding force of skin friction and pressure drag over the wing, the magnitude of the wind is less than that seen by the wing.

Consider the isolated Tail and forces/moments acting on it as shown in the diagram below.