RE: Flight control article workshop
I've been thinking about the above, and might have the answer.
The pushrod is not at 90 degrees to the control horn when it matters. Take the example of the aileron above, the pushod may be at 90 degrees to the horn when the control surface is at neutral, but at that time the control is not generating any torque. The control generates max torque when at max deflection, at which time due to rotation of the horn the pushrod is no longer at 90 degrees to the horn. Because it is no longer aligned with the force vector generated by the torque, the force applied to the pushrod will be in the order of cosine of the angle off from the tangent to the horn, so the force on the pushrod will drop as the angle changes away from 90 degrees. Similarly the force applied at the servo arm to convert into torque applied at the servo will be reduced by its angle off the tangent to the radius of the arm, I can't be bothered to work out if sine or cosine but either way it will be well reduced since as you can see the servo arm rotates in the region of 40 degrees. But that works in reverse too, so the servo will need much more torque to be able to generate the same force on the pushrod when it is rotated away from 90 degrees to the pushrod, compared to when it is at 90 degrees
If you are struggling to imagine all that, imagine taking things to the limit. Imagine the control surface deflects 90 degrees, then so does its control horn. At that point no matter how much torque the control exerts on the horn, it has no fore or aft movement so it can't exert a gnat's wotsit of fore and aft force on the pushrod. When the control is only partially rotated, the force the horn can apply to the pushrod is somewhere between full force and that zero force. The same applies when it reaches the servo arm, if the servo had rotated as far as 90 degrees then you could apply all the force in the world but it won't make the servo rotate and the servo will need zero power to resist it - you would need a strong mounting and servo case, but you couldn't make it turn! With servo typically rotating 40 degrees or more, the translation of pushrod force into torque to try to turn the servo is hugely reduced, and that reverses in that the servo needs extra torque to apply a force since its max force is at 90 degrees to the arm and has reduced force at other angles.
That would explain why the spreadsheet gets lower values for Fp than my simple calculation that ignored the angles, and why the low Fp converted into a much higher servo torque requirement.
H