Aerodynamic Forces and Moments Questions and Answers

Answer: A

Lift and drag are defined with respect to the oncoming flow, which is what makes them useful in performance work. The alternative resolution into normal and axial components uses the body axes instead and is convenient for structural loading.

Answer: B

Normal force acts perpendicular to the chord and axial force along it, so at zero angle of attack the two systems coincide. As the angle grows they diverge, and converting between them requires the sine and cosine of that angle.

Answer: C

Because the cosine of a small angle is close to one and the sine is small, lift and normal force nearly coincide at low incidence. The approximation fails badly at high angles, where the axial contribution to lift is no longer negligible.

Answer: D

Correct answer: The free-stream dynamic pressure

The pressure coefficient is

\[ C_p = \frac{p - p_\infty}{\tfrac{1}{2}\rho V_\infty^{2}} \]

Dividing by dynamic pressure is what makes it dimensionless and comparable between conditions: the same shape at the same angle gives the same \( C_p \) distribution whatever the speed or altitude, within compressibility limits.

Its value is 1 at a stagnation point, where the local pressure equals the total pressure, and negative wherever the flow is faster than the free stream - which is most of a wing's upper surface.

Answer: A

At stagnation the local pressure exceeds free-stream static by exactly the dynamic pressure, so the ratio is one. It is the maximum value the coefficient can reach in incompressible flow, whereas negative values over the upper surface may be large.

Answer: B

Negative values mean suction relative to the free stream, and it is the large suction peak near the leading edge that produces most of the lift. Separation is indicated by a flattening of the distribution rather than by the sign.

Answer: C

Integrating the pressure distribution around the section, with a small contribution from shear, gives the resultant force whose component perpendicular to the flow is lift. Friction contributes almost entirely to drag rather than to lift.

Answer: D

Placing the whole resultant force there produces the same moment as the real distributed loading, so no additional moment is needed. Its position moves with angle of attack, which makes it awkward as a reference point.

Answer: A

With lift approaching zero but a residual pitching moment remaining, the point at which the force would have to act recedes without limit. This awkward behaviour is precisely why the aerodynamic centre is preferred as a reference.

Answer: B

Correct answer: The pitching moment does not vary with angle of attack

The aerodynamic centre is defined by that invariance: \( dC_m/d\alpha = 0 \) about it, so the moment there is a constant of the section.

Thin airfoil theory places it at the quarter chord in subsonic flow, moving towards mid-chord supersonically - the shift that causes Mach tuck. The property is what makes it the natural reference point for stability analysis, since the lift's contribution to the moment about any other point varies with incidence and the aerodynamic centre's does not.