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Does anyone know how the area, height and width of a rudder affect how well it provides lateral lift? I've heard that the most effective rudders are around 35% of the vertical stabiliser MAC but is there any maths to back this up?

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  • $\begingroup$ I think here the notion of effectiveness has to be defined. If we consider two identical vertical stabiliser and rudder, one could be more efficient than the other, because reaction force applies on lateral surfaces of the aircraft which are indeed the vertical stabilizer itself, but also any other vertical surfaces (fuselage, winglets,...) Is rudder efficiency relative to yaw angular rotation speed? Or ability to provide lateral lift ? $\endgroup$ – qq jkztd Nov 30 '17 at 15:20
  • $\begingroup$ Its efficiency relative to its ability to provide lateral lift. I'm wondering if the area of the rudder control surface is increased, would that allow it to provide greater lateral force? $\endgroup$ – Will Patterson Nov 30 '17 at 16:44
  • $\begingroup$ It provides a greater action force or authority on the reacting lateral lifting surfaces. $\endgroup$ – qq jkztd Nov 30 '17 at 17:23
  • $\begingroup$ "the most effective rudders are around 35% of the vertical stabiliser MAC", that could be me, but I don't understand what it means. The "effectiveness" seems to be defined by the moment generated related to the CG vs. the angle of deflection, and in that case the effectiveness has no limit, the larger the area, the better the effectiveness. It also depends on the distance to the CG. Or do you mean moment generated vs. force applied to the rudder? It still depends on the distance. $\endgroup$ – mins Nov 30 '17 at 19:06
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The figure of 35% might be ideal for a rudder on GA aircraft with decent effectiveness and high enough control forces so a good control feel is achieved.

Generally, a rudder on a vertical tail is like a flap on a wing. It changes both camber and incidence of the vertical when deflected, thus helping the pilot to adjust the lateral lift force acting on the whole vertical. Therefore, the same formulas as those for flaps can be used for rudders.

A simple approximation for the amount of lift coefficient change per flap deflection angle $\eta$ is $$c_{l\eta} = \sqrt{\lambda}\cdot\eta$$ where $\lambda$ is the relative chord of the flap and $\eta$ needs to be in radians.

Hermann Glauert derived a formula using potential flow theory that is sligthly more complex: $$c_{l\eta} = c_{l\alpha}\cdot\frac{2}{\pi}\cdot\left(\sqrt{\lambda\cdot(1-\lambda)}+arcsin\sqrt{\lambda}\right)$$

Flap effectiveness over relative depth

I plotted both together with a correction of the Glauert formula using wind tunnel data above. It is remarkable how close the simple formula matches the experimental data already.

To be effective, the control forces on a rudder must not be too high, but also not too low in order to give good feedback to the pilot. For GA aircraft and gliders, a relative chord of 25 - 35% has been found to give the best combination. Control forces grow with the square of the relative chord of their control surface since both their area and the lever arm of the additional forces acting on them grow linearly with their relative chord.

In order to calculate the lateral lift change of the whole vertical, you need to know its lift curve slope $c_{l\alpha}$ which is affected by its aspect ratio and sweep angle, just like a wing is.

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