Assume the hinge moment is given as

$HM = 0.5\rho v^2*C_{h\delta} \delta*S*c$

$\rho$ = air density

$v$ = air speed

$C_{h\delta}$ = Hinge moment coefficient

$S$ = Control surface area

$c$ = average surface chord

the resulting moments / actuator loads are mainly influenced by the aircraft's altitude (air density $\rho$), speed $v$ and the control surface deflections $\delta$. (AoA is neglected to keep it simple)

Can there be anything said about the actuator loads regarding different mission types or flight phases? E.g. does cruise (high altitude and speeds, small surface defelctions) cause higher actuator loads than approach (low altitude, low speed, larger surface delections).

I was planning to use X-Plane to investigate this, but as far as I know it will only output the rudder's deflections, not the hinge moment itself.

Any ideas about this?

  • $\begingroup$ have you tried plugging numbers in the equation and see what happens? $\endgroup$
    – Federico
    Feb 27, 2017 at 13:38
  • $\begingroup$ @Frederico, thanks for your comment. Actually i didn't because i do not have any reliable data concerning the rudder deflections ($\delta$). Of course I could generate some data by simulation (X-Plane) - but I'm not sure how realistic this approach will be... $\endgroup$
    – Henrik
    Feb 28, 2017 at 14:01
  • $\begingroup$ Notice that the the hinge moment is proportional to dynamic pressure ($\frac12\rho v^2$) and deflection ($\delta$) and so is the aerodynamic force on that control surface. $\endgroup$
    – Jan Hudec
    Mar 1, 2017 at 21:08
  • $\begingroup$ For a passenger plane or a jet fighter? $\endgroup$
    – Koyovis
    May 6, 2017 at 22:47
  • $\begingroup$ For clearification: I'm interested in the actuator loads for an uav, which will be used in different mission scenarios. However, I started to set up a simulation environment via X-Plane to investigate this further. I'll let you guys know what I'll find out once I have some data. Many thanks so far for your comments $\endgroup$
    – Henrik
    May 8, 2017 at 12:50

1 Answer 1


Indeed the hinge moment equation is (with index $_s$ for surface) $$H_s = C_{h_s} \cdot ½ \rho V^2 \cdot \delta_s \cdot S_s \cdot \bar{c_s}$$

The moment coefficient $C_{h_s}$ depends on aircraft angle of attack, surface deflection (!) and trim tab deflection, as depicted in the figure below (from this answer). It is not a simple constant linear function due to shading of horizontal tail in the flow of other bits of aircraft structure.

enter image description here

So of course, hinge moment calculation depends on aeroplane configuration and geometry. But as @JanHudec mentions in a comment, the two main variables here are dynamic pressure and surface deflection.

Full surface deflection at cruise speed results in the largest hinge moment. It may also result in structural forces higher than the limit design forces, for instance load factors > 2.5g. It would be safest if the actuator force can never exceed the hinge moment required to reach maximum load factor, which would require making plots of (hinge moment for max. load factor) vs. airspeed, at different c.g. at maximum weight.


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