JNTU B.Tech III FLIGHT MECHANICS II Previous Question Paper (February - 2022 - R13)

For a steady pull-up maneuver at a constant load factor n, the airplane undergoes a circular motion with a normal acceleration a_n = (n-1)g. The equations of motion in the normal direction and about the center of gravity are used to determine the required elevator deflection and stick force.

The normal force equation is L - W = (W/g)V(q), where q = (n-1)g/V is the pitch rate. Substituting L = nW, we obtain the lift requirement. The pitching moment equation about the center of gravity is M_cg = I_y(dθ/dt) = 0 for a steady pull-up, implying the sum of moments must be zero: M_ac + L(x_cg - x_ac) + M_tail = 0.

The elevator angle to trim δ_e is derived by accounting for the increased angle of attack required to generate n times the weight. The total lift is L = C_L(1/2)ρV²S. The elevator angle δ_e is given by:

Substituting the load factor n, where C_L = nW / (1/2)ρV²S, the elevator angle required to maintain the maneuver is:

The control force F_s is proportional to the elevator deflection and the aerodynamic hinge moment. Since the hinge moment H = C_h(1/2)ρV²S_ec_e, and C_h = C_h0 + C_hαα_t + C_hδeδ_e, the stick force is expressed as:

where G is the mechanical advantage of the control system. In a steady pull-up, the stick force per g is a critical parameter defined by the rate of change of stick force with respect to the load factor n, representing the pilot's effort to maintain the maneuver.

The power effects on longitudinal static stability refer to the influence of the propulsion system (propeller or jet engine) on the aircraft's pitching moment characteristics. These effects are primarily categorized into direct effects of the thrust vector and indirect aerodynamic effects caused by the slipstream or exhaust flow.

The total pitching moment about the center of gravity is modified by the thrust as follows:

The term C_m,T represents the contribution of thrust, which depends on the thrust magnitude, the vertical distance between the thrust line and the center of gravity (thrust offset), and the angle of the thrust line relative to the longitudinal axis. If the thrust line is above the center of gravity, an increase in power creates a nose-down (negative) pitching moment, which is stabilizing. Conversely, if the thrust line is below the center of gravity, it creates a nose-up (positive) moment, which is destabilizing.

Key power effects include:

• Direct Thrust Effect: A thrust line passing below the center of gravity induces a destabilizing nose-up moment as power increases. This effectively reduces the static margin of the aircraft.
• Propeller Normal Force Effect: At non-zero angles of attack, the propeller disk experiences a normal force that acts at the propeller plane. This force creates a pitching moment that is generally destabilizing as the angle of attack increases.
• Slipstream Effect: The high-velocity air from the propeller flows over the wing and the horizontal tail. This increases the dynamic pressure at the tail, which can enhance the effectiveness of the horizontal stabilizer, but it also changes the downwash angle at the tail. The net effect depends on the relative geometry of the wing, tail, and propeller.
• Nacelle/Exhaust Effect: For jet aircraft, the exhaust flow can induce changes in the pressure distribution over the rear fuselage, potentially altering the tail's contribution to stability.

In summary, the longitudinal stability derivative C_m,α is modified by power. A design where the thrust line is positioned to counteract the destabilizing effects of the propeller normal force and slipstream is preferred to maintain consistent handling qualities across different power settings.