This spreadsheet predicts required servo torques using the following assumptions:
1 The angle of attack 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 the concept of 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.*
* This assumption dropped in "ServoPlus" worksheet.
** This assumption dropped in "Offset & Differential" and "ServoPlus" worksheets.
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.
The mathematical model: t = (AMPC2LV2) / (4RT) where
t = servo torque
A = sin(S) * tan(S) / tan(s)
S = control surface angle from neutral
s = servo arm angle from neutral
M = molecular weight of air (~28.6 g/mol)
P = air pressure (1 atm)
C = average chord length of control surface
L = average length of control surface
V = airspeed
T = air temperature (~290 K)
R = ideal gas constant (82.056 atm cm3 / mol K)
Feel free to share this spreadsheet and model with other individuals for nonprofit use.
Just be sure to give proper credit to its creator.