Aerodynamic Derivatives Questions and Answers

Answer: C

One radian is 57.3 degrees, so a derivative per radian is 57.3 times the per-degree value; both are dimensionless in the strict sense, since an angle is a ratio, but the numerical values differ enormously and mixing them is a classic error. The equations of motion require consistent units throughout, and radians are the natural choice because the small-angle relations assume them. A lift curve slope of 0.1 per degree and 5.7 per radian are the same physical quantity.

Answer: D

Multiplying by the number of degrees in a radian:

\[ 0.09 \times 57.3 = 5.16 \ \mathrm{rad^{-1}} \]

so about 5.2 per radian, a plausible figure for a moderate aspect ratio wing. 0.09 is the per-degree value unconverted, which used in the equations of motion would understate the lift by a factor of nearly sixty. 0.0016 divides instead of multiplying. 57.3 is the conversion factor itself reported as the answer.

Answer: A

The distinction is in the independent variable: a displacement such as incidence or sideslip, against an angular velocity such as pitch or yaw rate. Both kinds can be measured in a tunnel, the rate ones needing a forced-oscillation or rotary rig. Both have non-dimensional and dimensional forms. And both apply throughout the motion, since a manoeuvre involves displacements and rates together.

Answer: B

The rotor is a lightly damped dynamic system in its own right, so the coupling between rotor and fuselage matters and the assumption of quasi-steady aerodynamics is much weaker. Rotorcraft models therefore carry rotor states explicitly rather than folding them into a fixed-wing style derivative set. Derivatives do exist and are used, linearisation is still possible about a trim point, and reference areas are defined by convention as usual.

Answer: C

With that derivative negative, a sideslip produces a moment that increases the sideslip, so the aeroplane diverges in yaw rather than weathercocking into the wind. It also drives the spiral criterion the wrong way. A Dutch roll needs positive stiffness to oscillate at all, so it cannot be better damped. And the short period is longitudinal, so no lateral derivative can change it.

Answer: D

Roll derivatives are excited by aileron inputs, with reversals in both directions so that trim asymmetries cancel, and a well-shaped doublet separates aileron effectiveness from roll damping in the fit. A throttle step excites the phugoid. An elevator ramp excites the longitudinal set. A steady climb is a trim condition and contains almost no information about any rate derivative, since nothing is changing.

Answer: A

All four pairs are correctly labelled. The two moments are derivatives, one a stability derivative and one a control derivative; the inertia is a mass property; and the chord is reference geometry. Keeping the three categories apart matters because each is measured differently and changes for different reasons: derivatives with aerodynamics and flight condition, inertias with loading, and reference geometry not at all once the aeroplane is built.

Answer: B

The usual cause is a prediction error in one derivative at that particular condition, often a moment derivative near a Mach number or incidence where the flow changes character. Mass matters and is checked, but a weight error alone rarely flips a sign. Technique errors show up as inconsistent records rather than a repeatable divergence. And the equations of motion themselves are not in doubt: it is the coefficients in them that carry the uncertainty.

Answer: C

Induced drag grows with the square of lift coefficient, so above the minimum drag point drag rises with incidence and the derivative is positive. Below the minimum drag incidence it can be negative, which is the back side of the drag curve and the source of the speed instability felt on a slow approach. It is certainly not zero throughout, and the last option inverts the region in which the sign changes.

Answer: D

Yawing moments use wing area and span, as rolling moments do, because the span is the natural lateral reference length. Mean chord is reserved for pitching moments. Tail geometry is not a reference for whole-aeroplane coefficients, though it appears inside the estimates. Fuselage dimensions are never used as the reference. Mixing chord and span here changes a lateral derivative by the span-to-chord ratio, which on a transport can exceed ten.