how to calculate force on control surfaces?

[Bob Chiang]

Hi all,

How do you calculate the force on a control surface? I just bought some micro servos and I'm wondering what models they can be used in.

I imagine there are tons of complex mathematical procedures to analyze it properly. I'm interested in a simple relationship between air speed and force exerted on the deflected surface (non-calculus based aerodynamics for dummies). Assume the air flow is straight; model the deflected surface as the equivalent surface area that is perpendicular to the air flow: at x miles per hour, the air pressure is???

Thanks in advance,

[Ollie]

See:
http://www.giantscalerc.com/technical-servo-calc.htm

The torque on the control surface is roughly proportional to the square of the airspeed, the area of the control surface and, 1/2 the average chord of the control surface times the sine of the angle of deflection. The constant of proportionality depends on the mass density of the atmosphere and all the units of measurement. All these considerations are incorporated into the excel spread sheet at the above site.

You will find it very inconvenient to use MPH as your unit of velocity because then the area of the control surface will have to be expressed in square miles to be consistent. You will also find it harder to find the mass of a cubic mile of atmosphere.

Use either the English system of feet, pounds and seconds or the metric system of meters, kilograms and seconds.

[Bob Chiang]

Thanks Ollie,

I won't be able to look at the spreadsheet until Monday because I don't have Excell at home, but it sounds like just what I was hoping for.

Any suggestions for how to analyze the area on the other side of the hinge line for balanced surfaces? Use the same deflection angle and subtract the result? And any suggestions for what to use as a safety factor?

-Bob

[Ollie]

When the hinge line passes through the aerodynamic center of the control surface, the surface is said to be aerodynamically balanced. For simple shapes like rectangles and trapazoids, the aerodynamic center is very near 25% of the mean aerodynamic chord (MAC). The MAC is the control suurface chord that passes through the centroid of the control surface area. When the hinge line passes through the aerodynamic center, the load on the servo due to aerodynamic effects is zero. However, there may be inertial forces to cope with.

When the control surface outline isn't everywhere straight or convex, finding the MAC isn't so easy. Make a model of the control surface that allows you to change the position of the hinge or pivot line. Use the model control surface as a weather vane and adjust the pivot line untill it doesn't weather vane in a strong wind. The model of the control surface will then be aerodynamically balanced.

[dw1122]

Here's a site for on-line calculation, but you can click on the "formula" link to get to the what-make-it-ticks:

http://www.csd.net/~cgadd/eflight/calcs_servo.htm