Aerodynamic Derivatives Questions and Answers

Answer: C

\( C_{m_{\delta e}} \) is a control derivative: its independent variable is the elevator deflection, a commanded input rather than a state of the motion. The others differentiate with respect to incidence and pitch rate, both motion variables, so they are stability derivatives. In the state-space form the two kinds occupy different matrices, and that separation is what makes it clear why a larger elevator changes the response to the pilot without changing the aeroplane's modes.

Answer: D

It is \( C_{l_\beta} \), the rolling moment with sideslip, negative on a stable aeroplane, and it receives contributions from geometric dihedral, wing sweep and wing vertical position. \( C_{n_\beta} \) is directional stiffness. \( C_{l_p} \) is roll damping, a rate derivative. \( C_{y_{\delta r}} \) is the rudder side force, a control derivative. Of the four, only the first describes how sideslip rolls the aeroplane.

Answer: A

The criterion is \( L_\beta N_r - N_\beta L_r > 0 \), so \( C_{l_\beta} \), the dihedral effect, appears multiplied by the yaw damping. That is why dihedral improves spiral stability while fin volume, entering through \( C_{n_\beta} \), degrades it. The other three are longitudinal quantities: pitch damping, elevator lift and the drag derivative with incidence, and none of them can appear in a lateral criterion at all.

Answer: B

Pitching inertia is a mass property, obtained from the mass breakdown or by swinging the aeroplane, and it divides every moment derivative in the conversion to dimensional form. The other three are aerodynamic derivatives. The distinction is practical: inertias change with loading and fuel state, while derivatives change with flight condition and configuration, so the two are tabulated separately and combined only at the point of forming the equations of motion.

Answer: C

One radian is 57.3 degrees, so the per-radian value is that many times the per-degree one: a slope of 0.1 per degree is 5.73 per radian. Six is roughly \( 2\pi \), which is the numerical value of a thin-aerofoil slope per radian and easy to confuse with a conversion factor. Three is about half of that. One hundred and eighty is the number of degrees in \( \pi \) radians, not in one radian, and using it introduces a factor of \( \pi \) error.

Answer: D

DATCOM is the cheapest and quickest: geometric parameters go in and derivatives come out, with no mesh, no model and no aeroplane. Its accuracy is adequate for sizing and for spotting problems early. CFD costs orders of magnitude more effort per condition. A free-flight model is expensive and slow, and a prototype flight test cannot happen at concept stage by definition, since the aeroplane does not exist yet.

Answer: A

The reference is the trim condition about which the equations were linearised, and it is why every set is labelled with a speed, altitude, weight and configuration. The stall is where the linear model breaks down and is studied by other means. Never-exceed speed and maximum thrust are limits rather than reference conditions, though sets are certainly evaluated near them as part of exploring the envelope.

Answer: B

The approximation retains \( M_\alpha \) for stiffness and \( M_q \) for damping, together with \( M_{\dot\alpha} \) and \( Z_\alpha/u_0 \). The speed derivatives \( X_u \) and \( Z_u \) belong to the phugoid approximation instead. The third pair are lateral derivatives that appear in the spiral criterion. The fourth are rudder control derivatives, which appear in the input matrix rather than in any modal approximation.

Answer: C

Every dimensional derivative carries a factor of dynamic pressure, so they all scale up in proportion, which is why modal frequencies rise with speed and fall with altitude. The non-dimensional coefficients are what stay put at a given Mach number. Nothing scales down with dynamic pressure, and the effect applies to stability and control derivatives alike, since both are dimensionalised the same way.

Answer: D

By convention it is the wing reference area, including the notional portion carried through the fuselage, and every whole-aeroplane coefficient is defined against it. Tail area appears in the tail volume coefficient rather than as a reference. Wetted area is used for skin friction estimates, and frontal area for some drag work on bluff bodies. Because the choice is a convention, a data sheet must state it, and two sources using different definitions cannot be mixed.