Control Surface Hinge Moments Questions and Answers

Answer: A

It is the aerodynamic moment about the hinge line itself, and it is what the pilot must overcome through the control run, so it sets the stick or pedal force. The moment about the centre of gravity is the control effectiveness, a quite different quantity: a surface can be very effective and still light to move, which is exactly the combination designers seek. The bracket loads are a structural matter. Trim is a whole aeroplane balance rather than a hinge quantity.

Answer: B

Substituting directly into the definition:

\[ \begin{aligned} H &= -0.15 \times 3000 \times 2.0 \times 0.5 \\ &= -450 \ \mathrm{N\,m} \end{aligned} \]

so -450 newton metres, the sign indicating a moment that tends to move the surface trailing edge up. -900 doubles the chord or forgets a factor of two somewhere. -225 halves the area. -45 slips a decade. Note the reference geometry: the surface's own area and mean chord aft of the hinge, not the wing's, which is why hinge moment coefficients from one aeroplane cannot be applied to another without care.

Answer: C

\( C_{h_\delta} \) is negative: deflecting the surface produces a moment opposing the deflection, which is what gives the pilot a positive force gradient and makes the control feel like a spring. A positive value would mean overbalance, where the surface runs away from neutral and the stick force reverses - a genuinely dangerous condition. Zero would give a control with no self-centring at all. And the sign does not reverse with speed, though the magnitude grows with dynamic pressure.

Answer: D

\( C_{h_\alpha} \) governs floating: with the controls released, the surface takes up whatever angle drives the hinge moment to zero, and that angle depends on the ratio of the two hinge derivatives. It is the mechanism behind stick-free stability being different from stick-fixed. The stick force at zero deflection is a trim and tab matter. Pitch damping is a whole-aeroplane derivative. Actuator travel is a mechanical limit.

Answer: A

Setting the total hinge moment to zero:

\[ \begin{aligned} \delta_{float} &= -\frac{C_{h_\alpha}}{C_{h_\delta}}\alpha \\ &= -\frac{-0.20}{-0.50} \times 4 = -1.6^{\circ} \end{aligned} \]

so the surface floats about 1.6 degrees trailing edge up. -10 degrees inverts the ratio of the derivatives. -0.4 divides by ten as well. -4.0 assumes the surface simply follows the incidence, which would require the two derivatives to be equal. Float direction matters because it decides whether releasing the stick helps or hurts the aeroplane's stability.

Answer: B

Both statements are correct and together they are the whole of stick-free stability. When released, the elevator floats up as incidence rises, unloading the tail and so reducing the restoring moment the tail would otherwise supply. The consequence is a forward shift of the neutral point and a smaller static margin with the stick free than with it held. That is why certification examines both cases and why the free-elevator factor appears in the tail contribution.

Answer: C

The factor is built from \( \tau C_{h_\alpha}/C_{h_\delta} \), so it combines the float tendency with how much moment a degree of elevator produces. Area enters through those derivatives rather than on its own. Elevator mass and its balance weight matter for flutter and for inertia effects in manoeuvres, not for the steady float. Stick gearing scales the force the pilot feels but cannot change where the surface floats to, since floating happens with the stick free.

Answer: D

Overbalance means \( C_{h_\delta} \) has gone positive, so beyond some deflection the surface moves itself further from neutral and the stick force gradient reverses. It can follow from too much aerodynamic balance, and it is why balance is applied in measured amounts and checked across the whole deflection and incidence range. Mass balance is a separate anti-flutter measure. A tab at full travel is a trim limitation. An excessive stick force per g is the opposite complaint.

Answer: A

Force at the stick is the hinge moment multiplied by the gearing of the control run, the mechanical ratio between column movement and surface deflection. That is why two aeroplanes with identical hinge moments can feel quite different, and why gearing is one of the first things adjusted when a control is too heavy. Elevator area enters the hinge moment itself rather than the conversion. Weight and static margin affect how much deflection is needed, not the force per unit deflection.

Answer: B

The hinge moment carries a factor of dynamic pressure, so it grows with the square of the speed for a given coefficient, and the stick force follows. This is the central problem of manual controls on a fast aeroplane and the reason aerodynamic balance, tabs and eventually powered controls exist. Gearing is fixed by the linkage geometry. Surface area does not grow, though the surface does twist. And the pilot is unchanged.