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Differential Aileron Motion versus Bellcrank Angle

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cwilliamrose

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The subject of aileron differential comes up from time to time and since I'm working on that very thing for my project I thought I'd post the results of my work. For those not aware of the reason for differential and why some of us want to eliminate it I'll explain. When the ailerons deflect they increase lift on one side and decrease it on the other side which causes the airplane to roll. The aileron increasing the lift also increases the drag and that's adverse yaw. What most GA airplanes have is an aileron control geometry that limits the deflection on the aileron adding lift so that aileron also has limited drag and therefore limited adverse yaw. The pilot doesn't need as much rudder to compensate for the drag so the airplane is more 'pleasant' to fly. If you want maximum roll rate the last thing you would do is limit the aileron travel. And if you intend to fly negative G maneuvers the differential that works so nicely during positive G works backwards during negative G. So, for an airplane with a primary mission of flying akro, you want the ailerons to have symmetrical travel.

I just completed a study of aileron differential travel versus bellcrank angle for my Pitts S-1S based project. The aileron system is very similar to a stock S-1S. I'm using a Solidworks model of my airplane to model the control system which makes changes to the geometry very easy to do and the results can be accurately measured.

I started by going from the idler out to the aileron. I found that ±20° of idler deflection yielded an almost perfectly symmetrical (0.13° of differential) travel at the aileron with a 90° bellcrank angle. But that's not the real world, there are many other components in the system that play a part in the aileron travel.

I looked at the idler's motion with a ±26.5° stick travel and found the left side idler moves 20.19° with full left stick and 21.99° with full right stick. This differential motion is due to the idler's angle to the pushrod. Without compensation this would give you negative differential (see table below).

ScreenHunter_901.jpg

The idler has two separate pairs of holes where the pushrods are attached which means there's an angle between the centerline of the idler and the holes where the pushrods mount. There's also an angle between the idler and the pushrod coming from the torque tube which adds to the V-angle of the idler. I'm not sure why this pushrod angle is there but it may be necessary for the flat wings and was carried over to the round wings so that a wing swap would not require a different torque tube. All these angles create the 1.8° differential at the idler.

The Pitts S-1S specs say the airplane has about 2° of positive aileron differential using a 75° bellcrank. By 'positive' I mean the upward moving aileron travels 2° more than the downward moving aileron. This is typical of many airplanes in order to reduce adverse yaw. Most airplanes have more than 2° differential. My goal is to eliminate this differential motion for my airplane.

I did several iterations in order to achieve zero differential;

Stick travel = ±26.5° (this results in a minimum of around 25° of aileron travel)

BC Angle = 90°, UP travel = 25.33°, DOWN travel = 27.53°, ∆° = -2.2°

BC Angle = 81°, UP travel = 25.84°, DOWN travel = 25.95°, ∆° = -0.11°

BC Angle = 81.5°, UP travel = 25.85°, DOWN travel = 25.85°, ∆° = 0.0°

BC Angle = 80°, UP travel = 25.85°, DOWN travel = 25.75°, ∆° = +0.1°

BC Angle = 75°, UP travel = 25.77°, DOWN travel = 24.68°, ∆° = +1.1°

BC Angle = 72°, UP travel = 25.63°, DOWN travel = 23.98°, ∆° = +1.65°

In practical terms using 80° or 81° will result in zero differential but I'm fixturing the bellcrank for welding so I will use 80.5°.

ScreenHunter_902.jpg

I think the important point here is that in order to have zero differential you have to treat the aileron system as a whole and not just assume a 90° bellcrank is what you need. All airplanes are different and even though my aileron system is virtually identical to an S-1S I have only 1.1° of differential using a 75° bellcrank. Maybe a stock S-1S is short of 2° as well. Not eveyone has a 3D CAD program and the experience to use it but this can be done with actual parts very much like I did using SWx. You will want to leave one of the arms on your bellcrank unwelded and create a way to attach this loose arm temporarily so you can make some deflection measurements with all the other parts of the system in place. On a Pitts you could use a long hose clamp or maybe use a tack welded tab on the loose arm. You could also use a dummy arm to determine the angle needed. However you do it the adjustable arm just has to be stable enough to stay put for some quick measurements. Once you determine the required angle you can tack the arm in place and check the travels one more time before finishing the welds.
 
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