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Servo Torque Calculator

Formula

Calculate Required Servo Torque

MeasurementImperial unitsMetric units
Max Speed mph kph
Control Surface Chord (front to back) inches mm
Control Surface Length inches mm
Control Surface Max Deflection (from center) degrees
Servo Max Deflection (from center) degrees
Servo Torque required oz-in Ncm
Control Deflection at max torque degrees

(NOTE: Graphing does not work with Internet Explorer)

Formula used

The maximum torque requirement does not always occur at full deflection. This calculator determines the torque at every control position, from 1 degree to the max. deflection specified.

The result is the max torque found, and the position of the control surface when the max torque was reached.

The formula used to calculate the torque is as follows :

Torque(oz-in) = 8.5E-6 * ( C2 V2 L sin(S1) tan(S1) / tan(S2)]

    Where:
  • C = Control surface chord in cm
  • L = Control surface length in cm
  • V = Speed in MPH
  • S1 = Max control surface deflection in degrees
  • S2 = Max servo deflection in degrees

This servo torque formula was taken from Craig Tenney. His website features excel spreadsheets to do detailed analysis of servo torque, and control linkage calculations. You can reach his website at http://web.egr.msu.edu/~tenneycr/. You can also find a very detailed page there that shows the derivation of this model.

Reducing the servo deflection from the default 60 degrees is similar to using ATV / Dual Rates to reduce the control throws. If you vary the servo deflection from the normal 60 degrees, you will see that using "Dual rates / ATV" to set the proper control surface deflection greatly increases the load on the servo.

Note that the numbers do not always match those generated by another servo calculator on the web, at www.multiplex-rc.com/calcservo.htm. That calculator uses different methods, and the formulas and derivations were not available to me at the time this was created. The Multiplex calculator factors in wing area, but does not include servo deflection.

Note the following assumptions:
  1. The angle of incidence of the wing, stab, or fuse is zero (relative to the airflow).
  2. Angular velocity and acceleration of the aircraft is zero.
  3. Air flow may be modelled using Bernoulli's equation for dynamic pressure.
  4. Conditions are: sea level, zero humidity, moderate (~55 F) temperature.
  5. Control linkages have zero offset at hingeline and are perpendicular to horns at neutral.
  6. Control mechanisms are frictionless and surfaces are mass-balanced.
  7. The wing, stab, fuse, and control surfaces are thin, flat slabs.
  8. No aerodynamic counterbalances are used. (Account for these manually, if desired.)
  9. The pushrods are significantly longer than the servo and control horns.

Please note:

  • The calculations are completely theoretical. No empirical "tweaking" has been done.
  • The assumptions (except #6) should generally yield conservative (high) predicted torques.
  • Extreme control throws are probably not practical at high speeds.
  • This model is best used for comparisons. No guarantees are made of its validity.
  • Maximum required servo torque may occur at LESS than maximum throw.