Aerodynamic Derivatives Questions and Answers

Answer: A

It is negative: a roll to the right produces a rolling moment to the left, opposing the motion, which is what makes the roll subsidence a stable first-order decay. A positive value would mean autorotation, which is what happens beyond the stall when the down-going wing loses lift instead of gaining it - the mechanism of a spin. Zero would leave roll rate undamped. The magnitude varies with speed and incidence, but the sign does not change in normal flight.

Answer: B

\( C_{m_q} \) is a rate derivative and needs a rate, which a static test cannot produce; oscillating the model and resolving the in-phase and out-of-phase components of the moment is the standard method. \( C_{m_\alpha} \) comes from a fixed-attitude sweep. Maximum lift and zero-lift drag are both static measurements as well. The distinction between static and dynamic rigs follows directly from the distinction between static and rate derivatives.

Answer: C

\( C_{n_p} \), the yawing moment due to roll rate, is the culprit: the down-going wing gains lift and with it induced drag, dragging the nose away from the direction of roll. Aileron profile drag adds to the effect. \( C_{n_r} \) is yaw damping, \( C_{l_p} \) is roll damping, and \( C_{y_\beta} \) is the side force with sideslip - all three present in the roll but none of them the source of the initial adverse yaw.

Answer: D

Lowering the flaps changes the aerodynamic shape and therefore the coefficients themselves. Climbing at fixed Mach number changes dynamic pressure, which moves the dimensional derivatives while leaving the coefficients nearly untouched. Burning fuel and offloading cargo change mass and inertia, which matter in the conversion and in the resulting dynamics but are not aerodynamic properties at all.

Answer: A

Tail volume coefficient is that ratio, area times arm over wing area times reference length, and it is the primary number in tail sizing because pitch and directional stiffness both scale with it. Aspect ratio describes a surface's own shape. Static margin is the distance from centre of gravity to neutral point, a result rather than a geometric input. The downwash gradient is the factor that reduces what the tail actually achieves.

Answer: D

The air velocity, angle of attack and sideslip angle are [100.995, 5.71, 5.68].

\[ \begin{aligned} V &= \sqrt{100^{2} + 10^{2} + 10^{2}} = \sqrt{10200} \\ &\approx 100.995\ \text{m/s} \\ \alpha &= \tan^{-1}(w/u) = \tan^{-1}(0.1) \approx 5.71^\circ \\ \beta &= \sin^{-1}(v/V) = \sin^{-1}(0.0990) \approx 5.68^\circ \end{aligned} \]

The angles differ slightly because the angle of attack uses the tangent in the x-z plane while the sideslip uses the sine against the full speed. The entries 0.1 are the ratio \(w/u\) left unconverted, and 5.73 is 0.1 radian expressed in degrees; 120 and 100 are not the magnitude of the velocity vector.