Control Surface Hinge Moments Questions and Answers

Answer: A

Applying the gearing directly:

\[ F = 320 \times 0.25 = 80 \ \mathrm{N} \]

so 80 newtons, a firm but manageable pull. 1280 N divides by the gearing instead of multiplying, and would be far beyond any pilot. 320 N ignores the gearing altogether. 40 N halves the correct answer. Gearing is the designer's cheapest lever on stick force, limited by the column travel the cockpit can accommodate.

Answer: B

The float ratio is \( -C_{h_\alpha}/C_{h_\delta} \), so

\[ \begin{aligned} \frac{\delta_f}{\alpha} &= -\frac{-0.10}{-0.40} \\ &= -0.25 \end{aligned} \]

so the surface floats a quarter of a degree trailing edge up for each degree of incidence. -4.0 inverts the ratio, a very large float that would imply a nearly free-floating surface. -0.04 slips a decade. -2.5 does the same in the other direction. A small float ratio means the stick-free and stick-fixed neutral points lie close together, which is generally desirable.

Answer: C

With no float tendency the released elevator stays where it is, so the tail keeps its full contribution and the stick-free neutral point converges on the stick-fixed one. Increasing the float ratio is what drives them apart, moving the stick-free point forward and reducing the free static margin. Nothing here pushes it aft of the manoeuvre point, which lies aft of both neutral points, and the quantity remains perfectly well defined throughout.

Answer: D

It is \( C_{h_\delta} \), the derivative of the hinge moment coefficient with respect to the surface's own deflection, and it sets the self-centring of the control. \( C_{h_\alpha} \) is the derivative with incidence, which drives floating. \( C_{m_{\delta e}} \) is the aeroplane's pitching moment per unit elevator, the control effectiveness. \( C_{l_{\delta a}} \) is aileron rolling effectiveness. Two of these are hinge quantities and two are whole-aeroplane ones, and the distinction is the crux of the topic.

Answer: A

Hinge moment carries dynamic pressure, so it goes with the square of the speed at a fixed coefficient: doubling speed quadruples the force. That single fact explains aerodynamic balance, tabs of every kind, and ultimately powered controls. A linear dependence would have made manual controls viable to much higher speeds. A cube law belongs to power rather than force. And independence of speed is the behaviour of an artificial feel unit that has not been scheduled with q.

Answer: B

A spring tab does: the spring in the linkage deflects more as the hinge moment rises, so the tab takes on a growing share of the work and the balance grows with dynamic pressure. A horn balance gives a fixed proportion of balance at all speeds. A trim tab holds a deflection without force but does not change the gradient. A bobweight responds to normal acceleration rather than to speed.

Answer: C

A force gradient that lightens and then reverses is overbalance: \( C_{h_\delta} \) has gone positive at large deflection, so the surface drives itself further from neutral. The fix is to reduce the balance, often by trimming the horn or reducing the set-back. Insufficient mass balance shows up as flutter, not as a force reversal. A tab at full travel limits trim rather than reversing gradient. Gearing scales the force uniformly and cannot reverse its sign.

Answer: D

Growing amplitude with increasing speed is the signature of flutter approaching, and the correct action is to reduce speed at once and land for inspection of the surface balance and the control run for free play. A trim runaway shows as a steady, one-way change of force rather than an oscillation. Overbalance gives a force reversal, not a vibration. Buffet is broadband and driven by separation, and it does not grow smoothly in the way an approaching flutter mode does.

Answer: A

Free play lets the surface move independently of the control run for small displacements, which reduces the effective stiffness of the system and can lower the flutter speed. That is why inspection limits on play are quoted in thousandths of an inch and taken seriously. The aerodynamic coefficients are unchanged. Static margin is a whole-aeroplane property. Tab authority depends on tab size and travel rather than on play in the run.

Answer: B

That is mass balance, and its purpose is flutter prevention rather than force reduction. Aerodynamic balance uses area or pressure ahead of the hinge to reduce the hinge moment and therefore the stick force. Static balance is a term used loosely for the same mass condition but is not the standard name in this context. A spring tab is a device, not a class of balance. The two kinds of balance are routinely confused, and they solve entirely different problems.