Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech III AIRCRAFT STABILITY AND CONTROL Previous Question Paper (February/March - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
Derive the equations of motion of a rigid body. State the underlying law of physics. Use the suitable diagram labeling the forces and moments on an airplane.
Answer
The equations of motion for a rigid body are derived from Newton's Second Law of Motion, which states that the rate of change of momentum of a body is proportional to the applied force and occurs in the direction of the force. For a rigid body in three-dimensional space, this is expressed as the summation of forces equals mass times acceleration and the summation of moments equals the rate of change of angular momentum.
Considering a body-fixed coordinate system with the origin at the center of gravity, the force equations are:
The moment equations, derived from the Euler equations for rigid body rotation, are:
In these equations, u, v, w represent the linear velocity components, p, q, r represent the angular velocity components about the body axes, and I_x, I_y, I_z, Iₓz represent the moments and products of inertia. The forces X, Y, Z include aerodynamic, gravitational, and thrust components, while L, M, N represent the rolling, pitching, and yawing moments respectively.
To visualize the airplane, imagine a body-fixed frame where the x-axis points forward through the nose, the y-axis points toward the starboard wing, and the z-axis points downward. Forces act at the center of gravity (thrust, drag, lift, weight), while moments are generated by control surface deflections (ailerons for L, elevators for M, and rudder for N) and aerodynamic coupling.
Why deflecting the aeroplane produces a yawing moment. Explain.
Answer
Deflecting the rudder produces a yawing moment primarily due to the generation of side force on the vertical tail. When the rudder is deflected, the camber of the vertical tail airfoil is effectively changed, creating an asymmetric pressure distribution. This results in a side force acting at a distance from the aircraft's center of gravity, thereby generating a yawing moment about the vertical axis.
Additionally, the deflection induces a change in the local angle of attack of the vertical stabilizer. The resulting lift force, acting perpendicular to the chord line of the vertical tail, creates a moment arm relative to the center of gravity. Furthermore, in some aircraft configurations, the rudder deflection may cause flow interference or changes in the pressure distribution over the rear fuselage, which can contribute secondary effects to the overall yawing moment.
Discuss the aircraft stability for different loading conditions.
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Explain the effect of power on aerodynamic stability in aircrafts.
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Derive the expressions for control derivatives for aerodynamic stability.
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Explain the difference between stability when the stick is fixed and when the stick is free.
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Consider an airplane with W = 22500 N, S = 15 m2, aspect ratio = 6, c̅ = 2.50 m, lt = 3c̅ = 7.5 m, Cmδ = -0.01 deg-1 and τ = 0.5. Calculate the difference between maneuver point stick-fixed and neutral point stick-fixed.
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Explain the criterion for longitudinal static stability. What are the desirable values of Cm0 and Cmα? Explain.
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Explain about the phugoid, short period dutch roll and spiral modes.
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Explain about the coupling between rolling and yawing moment.
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