Helicopter longitudinal trim calculator
Description
This calculator estimates a longitudinal trim condition for a hovering helicopter.
Outputs include the pitch angle, longitudinal main rotor flapping and thrust.
Equations
The following equations are used to estimate the output values.
These equations come from setting the net pitch moment (M), vertical force (Z),
and longitudinal force (X) to zero.
Many symbols used below are defined in
Helicopter Abbreviations and Symbols.
In addition, we use the following symbols here.
\(k\) 
main rotor flap stiffness 
\(\gamma\) 
main rotor forward mast tilt 
\(M_x\) 
main rotor xdisplacement, forward from CG 
\(M_z\) 
main rotor zdisplacement, up from CG 
Small angle approximations are used when solving for outputs. For example,
\( \sin ( \gamma  \beta ) \approx \gamma  \beta \)
and \( \cos ( \gamma  \beta ) \approx 1 \).
The flap angle \( \beta \) is considered positive here when the front of the rotor is flapped up.
\[ M=0 \Rightarrow T \sin (\gamma  \beta )M_z + T\cos (\gamma  \beta ) M_x + k\beta = 0 \]
\[ X=0 \Rightarrow T\sin (\gamma  \beta )  GW\sin \theta = 0 \]
\[ Z=0 \Rightarrow T\cos (\gamma  \beta )  GW\cos \theta \]
