How do you determine the optimum position and angle for a Control Horn?

I've had to move/replace control horns on various planes and it seems that there is a bit more science to the placement/angle of horns than I'm actually aware of...How do you determine the 'optimum' ( always a dangerous phrase) position and angle for a C-Horn ?

Bill, the "science" you're referring to is called in engineering jargon "Kinematics", specifically the study of four-bar linkages. Check your public library for mechanical engineering texts on mechanical systems and mechanism design if you want to get into the grisly details. One text I'm familiar with is "Kinematics and Dynamics of Machines" by George H. Martin, published by McGraw Hill, but I'm sure there are many other books on engineering fundamentals that cover it as well.

In a typical servo/control surface setup, the first "bar" is the structure of the model between the servo arm pivot point and the control surface hinge. The other three "bars" are the servo output arm, the control horn and the pushrod.

In the case of the servo output arm and the control horn, the shape of them doesn't matter. In the analysis, represent them with the imaginary straight line from their pivot point (the output shaft axis for the servo, the control surface hings axis for the control horn) to their connection to the pushrod.

In the most basic case, you want the control deflections to be linear with servo motions, i.e.: 25% travel on the servo = 25% deflection on the control surface, 50% = 50%, 75% = 75%, etc.. This is approximately correct if the angle between the servo arm and the pushrod is 90 degrees, and the angle between the pushrod and the control horn is also 90 degrees when the servo and control surface is at neutral. If the two arms are both the same length, then this system is exactly linear. This is also true if both arms are the same length, AND they are both leaned in the same direction by the same amount (for example, if both the servo arm and the control horn are leaned aft by 20 degrees when the system is at neutral).

In the case of most flight controls, we don't want the control surface to move the same angular travel as the servo. For example, our elevator servo might have a maximum travel of +/-30 degrees, but we only want to have +/- 15 degrees of elevator travel. Easy, just make the control horn (measured from the elevator hinge axis to the pushrod hole) twice as long as the servo arm (measured from the output shaft axis to the pushrod hole). To get equal travel up and down, make sure that at neutral, the angle between the pushrod's back-and-forth "line of action" and the servo output arm is 90 degrees, and the pushrod is also 90 degrees to the line between the hole in the control horn and the elevator hinge.

Now some folks would say "Why not just set them up any old which-way and dial in the travel I want when I program my computer transmitter?" Certainly that will work, but you make some significant compromises when you use that route. If you use only part of the travel of the servo, you lose some of the servo's accuracy and resolution and some of its effective torque.

For example, let's look at two cases, both intended to have an elevator travel equal to half the angular travel of the servo. In the first, we use a control horn twice as long as the servo arm, as described above. In the second, we use two arms of equal length, and re-set the travel setting in the transmitter back to 50%. Let's also say that the servo has about 30 in.-oz. of torque, and an accuracy of 5% its total travel of 60 degrees, which is therefore equal to 3 degrees position error at the servo output arm.

In the first, "mechanical linkage determined" system, the elevator travels a total of 30 degrees for 60 degrees of servo travel. This means the servo has a mechanical advantage over the elevator of 2:1, so if the servo torque is 30 in.-oz, then the torque available at the elevator is 60 in.-oz.. Likewise, the error in elevator position is half the servo position error, or 1.5 degrees. About the only negative is that the servo speed is also divided by 2, so elevator deflection rate is half as fast as the servo's.

In the second, "transmitter programming determined" system, the mechanical advantage is one, so the elevator deflection rate is equal to the servo's. This is just about the ONLY advantage to this arrangement. With a mechanical advantage of one, the torque available at the servo is only half as good at 30 in.-oz., and the elevator position error is double the other system's, at 3.0 degrees. I don't know about you, but considering that the typical speeds of today's servos are a lot faster than my fingers need to move the sticks, I'd much rather have the better torque and lower position error of the mechanical system!

Now let's look at differential. In a 4-bar linkage like this system, if we lean the control horn and/or servo arm towards each other, we will get greater control surface travel when the pushrod is pulling, and less travel when the pushrod is pushing on the control horn. If we lean them away from each other, the opposite happens.

Let's look at an example, a typical aileron system. We want to have some "positive differential" (more up travel than down) built into the linkage, to prevent adverse yaw (the undesireable situation where upon deflecting the ailerons, the aircraft rolls one way but yaws the other way). The linkage uses a servo in each wing, with the servo arm and control horn both on the underside, connected by a pushrod. When the pushrod is pushing in this system, aileron is going up. Checking the paragraph above, we see that for more travel when the pushrod is pushing, we need to lean the servo arm and the control horn AWAY from each other. One easy way to accomplish this is to mount the servo arm at 90 degrees to the pushrod, but mount the control horn further aft than normal on the aileron. This means that the line between the control horn's pushrod hole and the aileron hinge line is angled back, away from the servo. From the servo's point of view, when the aileron deflects up, the apparent length of the control horn seems to get shorter, making it move farther. When the aileron deflects down, the control horn appears to get longer, reducing the aileron's travel. Voila! More up than down!

Of course if we had the aileron horn on top of the aileron, we would mount the horn AHEAD of the hinge line to accomplish the same effect.

One last consideration: how long should the arms be? We've already discussed the issue of how the ratio between the length of the servo arm and the length of the control horn determine control surface travel, but is there any difference between a 0.2" servo arm with a 0.4" control horn, versus a .6" servo arm and a 1.2" control horn? Kinematically, no, they both have a 2:1 ratio (control surface angular travel is half the servo angular travel). However, in the real world there is another factor to consider. Real linkages have slop. Even if you fit the hinges and pivots perfectly, even if the pushrod fits the horn so tightly that the friction threatens to stall the servo, eventually the pivots will wear, the gears and bearings in the servo will wear, and the system will develop some looseness or "slop". In this situation, the resulting angular play in the surface will depend in large part on the length of the control horn.

For example, let's say there is .005" slop (.0025" either side of the center of the hole) in each pivot at the end of the pushrod in the two examples above. In the first system, we have a linear play of +/-.005" at the end of a 0.4" control horn. The total angular play will be twice the arcsine of (.005/0.4), or a bit more than 1.4 degrees. In the second system, we have +/-.005" play at the end of a 1.2" control horn. The angular play with the longer horn will be 2 x arcsine(.005/1.2), which is not quite 0.5 degrees, about three times better. Obviously, unless there are other limiting factors, we should use the longest control horns we have room for, and whatever servo arm length required to get the necessary travel.

So that's it. Use the longest arms and horns you have room for (provided that they aren't so long you have to start worrying about control horn flex!), and in general try to keep them 90 degrees to the pushrod unless you have to tilt them towards or away from each other for differential (usually by mounting the control horn forward or aft of the position that results in the 90 degree angle with the pushrod). Try to use the full travel of the servo rather than using transmitter programming to do it the lazy way, and try to make sure all the parts fit well with as little play in the pivots as possible. Occasionally there are some other factors, such as dealing with things that like to suck open in flight (spoilers) or drag on the ground on landing (flaps), but for the most part, the principles discussed above should keep you out of trouble.

Don Stackhouse @ DJ Aerotech