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Like the one above. Is it just so that you can hinge closer to the leading edge of the aileron? Why did the designers of the ATR-72 elect to use this feature?

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There are two coefficients which determine the forces needed to deflect a control surface (besides the physical parameters like area and dynamic pressure):

  • Change in control surface hinge moment coefficient $c_r$ with angle of attack $\alpha$ : $c_{r\alpha}=\frac{\delta c_r}{\delta\alpha}$
  • Change in control surface hinge moment coefficient $c_r$ with control surface deflection $\eta$ : $c_{r\eta}=\frac{\delta c_r}{\delta\eta}$

By shifting the hinge line back, an overhanging nose of the control surface is created which reduces hinge moments because the forces here will counteract the forces on the rear part of the control surface. This overhanging nose will reduce both coefficients equally.

In contrast to that, the horn, while also creating counteracting forces, will affect $c_{r\alpha}$ more than $c_{r\eta}$. This allows the airplane designer to tailor the ratio between both coefficients. Why this is important becomes clear once you look at the floating angle of a control surface: $$\eta_f = -\frac{c_{r0}+c_{r\alpha}\cdot\alpha}{c_{r\eta}}$$ Normally, both coefficients are negative and the absolute value of $c_{r\eta}$ is a bit higher than that of $c_{r\alpha}$. And that is good: A positive $c_{r\eta}$ means that propelling hinge moments will increase with flap deflection, making the flap unstable and run into its stops immediately. But a positive $c_{r\alpha}$ just means that the control surface will deflect into the airstream when angle of attack changes, increasing stick-free stability over stick-fixed stability. So it is desirable to make $c_{r\alpha}$ very small while keeping $c_{r\eta}$ decidedly negative. This can be accomplished with a horn on the control surface.

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Because the horn extends ahead of the hinge line, the slipstream tends to pull the rudder deeper into deflection. This reduces the amount of control force needed to work the rudder without servo-boosting it. This is called aerodynamic boost and can be used to boost the ailerons and the elevator as well.

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