# What is the benefit of a horn aileron?

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?

• 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 $$\eta$$ : $$c_{r\eta}=\frac{\delta c_r}{\delta\eta}$$
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.