Aerodynamic Derivatives Questions and Answers

Answer: A

Assembling the definition:

\[ \begin{aligned} \frac{S_t l_t}{S\bar c} &= \frac{8 \times 12}{40 \times 2} \\ &= \frac{96}{80} \\ &= 1.20 \end{aligned} \]

so 1.20, a healthy value for a stable transport. 0.40 divides by the arm rather than multiplying. 2.40 omits the chord from the denominator. 0.05 is the area ratio alone with a decade slipped, and it ignores the arm entirely - which is the quantity that makes a small tail effective when it is far enough aft.

Answer: B

Pitch stiffness scales with area times arm, so the two match, but damping scales with area times the square of the arm, so the long-armed configuration has more of it. That is why a long, slender aeroplane feels better damped than a stubby one with the same static margin, and it is a genuine design argument for a long tail. The matching volume coefficients guarantee equal stiffness only, which is the trap in the third option.

Answer: C

The hinge moment derivative is a control-system quantity, describing the load on the elevator itself, and it governs stick force rather than the aeroplane's motion; it appears in stick-free stability and in artificial feel design. The other three differentiate a whole-aeroplane moment with respect to a motion variable and are stability derivatives in the strict sense. Hinge moments matter enormously to how an aeroplane feels, which is why they are studied under a heading of their own.

Answer: D

The cross-product term \( I_{xz} \) survives whenever the chosen body axes are not aligned with the principal axes of inertia, which is the usual case, and it couples the roll and yaw equations independently of any aerodynamic coupling. Mach number affects the aerodynamics rather than the inertias. Non-dimensionalisation is a scaling choice. Sweep changes the aerodynamic derivatives and the mass distribution, but the product of inertia arises from the axis choice.

Answer: A

It is a control derivative, because its independent variable is a commanded deflection rather than a state of the motion. Stability derivatives differentiate with respect to motion variables. Rate derivatives are the subset of stability derivatives taken with respect to angular velocities. Static derivatives are those taken with respect to displacements such as incidence and sideslip, so the distinction between static and rate cuts across the stability set rather than describing the control one.

Answer: B

The steady roll balances the aileron moment against the damping moment, so the rate is aileron effectiveness divided by roll damping. Multiplying them has no physical meaning here. Dihedral effect over directional stiffness is a ratio that characterises the slow lateral modes rather than roll performance. Roll damping over inertia gives the reciprocal of the roll time constant, which describes how quickly the rate is reached rather than what rate is reached.

Answer: C

Reynolds number governs boundary layer behaviour, and therefore separation, maximum lift and the incidence at which derivatives depart from their linear values. That is why low-Reynolds-number tunnel data can mislead near the stall while being perfectly adequate in cruise. The speed of sound belongs to Mach number. Reference area is geometry, chosen by convention. Mass distribution is an inertia matter, entirely separate from the aerodynamics.

Answer: D

The first and third hold. Non-dimensionalising removes the dynamic pressure dependence at fixed Mach number, but the coefficients still change with incidence and with flaps, gear and stores. The second is false: a coefficient is defined against a particular reference area and length, and quoting it against a different reference changes its value. That is why data sheets state their reference geometry, and why mixing two sources without checking references is a reliable way to introduce a large error.

Answer: A

Such devices control separation, so they act on the lift curve slope and maximum lift in the high-incidence region, where the linear derivative model is breaking down. Their effect at cruise incidence is small. Rolling moment with yaw rate is a kinematic effect of differing local speeds. Hinge moments concern the flow over the elevator itself. Rudder effectiveness depends on the fin's flow, which wing devices do not reach.

Answer: B

A plug ahead of the wing adds destabilising forward side and normal area and shortens the effective tail arm relative to the new centre of gravity, so pitch stiffness weakens and the variant may need a larger tail or a revised loading envelope. Roll damping depends on the wing span, which is untouched. Rudder side force is a fin property, though its arm changes a little. Elevator lift certainly does not halve.