JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year FLIGHT MECHANICS - II Previous Question Paper (March - 2021 - R15/R13)

Static margin is a measure of the static longitudinal stability of an aircraft. It is defined as the distance between the neutral point and the center of gravity, expressed as a fraction of the mean aerodynamic chord. A positive static margin indicates that the aircraft is statically stable, meaning the aerodynamic center is located behind the center of gravity.

To derive the expression for the stick-fixed neutral point and static margin, consider the pitching moment equation about the center of gravity:

Where h is the center of gravity position, h_ac is the aerodynamic center, and V_h is the tail volume ratio. For the stick-fixed condition, the elevator deflection is zero. The lift coefficient of the tail is related to the wing lift coefficient by the downwash gradient.

The neutral point (h_n) is the position of the center of gravity where the aircraft has neutral stability, meaning the rate of change of the pitching moment with respect to the lift coefficient is zero:

By differentiating the pitching moment equation with respect to C_L and setting it to zero, we derive the neutral point position:

The static margin (SM) is then defined as the difference between the neutral point and the center of gravity:

A stable aircraft requires SM > 0. If the center of gravity moves aft of the neutral point, the static margin becomes negative, resulting in static instability.

Autorotation is a flight condition in which a rotorcraft or a wing operates in a state where the aerodynamic forces are such that the rotor or wing continues to rotate or maintain a specific flight state without the application of engine power. In the context of fixed-wing aircraft, it refers to a lateral instability where a rolling moment is induced by a sideslip, causing the aircraft to roll continuously until it reaches a stalled or spinning state. In rotary-wing aircraft, it is a controlled descent maneuver where the rotor is driven by the upward flow of air through the blades, allowing for a safe landing during engine failure.

The stick-free neutral point is the center of gravity position where the aircraft's longitudinal static stability margin is zero, meaning the elevator deflection required to maintain trim does not change with speed. To determine this via flight test, the following procedure is used:

1. The aircraft is trimmed for a specific speed at a constant altitude and power setting.
2. The pilot releases the elevator control (stick-free) to allow the aircraft to seek its natural trim speed.
3. The elevator trim tab or the control force required to maintain various speeds is measured.
4. The test is repeated for different center of gravity positions, achieved by shifting ballast.
5. The stick force per unit speed (dF/dV) is plotted against the center of gravity position.
6. The neutral point is identified as the center of gravity location where the slope of the stick force versus speed curve becomes zero (i.e., the stick force gradient vanishes).

Mathematically, the stick-free neutral point is defined where the rate of change of the elevator angle or stick force with respect to the lift coefficient is zero, indicating that the aircraft has lost its inherent tendency to return to its original trimmed state.