Helicopter Lateral Trim Calculator
Description
This calculator estimates a lateral trim condition for a hovering helicopter.
Outputs include the roll angle, lateral main rotor flapping and thrust.
It's assumed that the tail rotor thrusts in the bodylateral direction only;
tail rotor flapping and cant are neglected.
Equations
The following equations are used to estimate the output values.
These equations come from setting the net yaw moment (N), vertical force (Z),
roll moment (L) and lateral force (Y) to zero.
Many symbols used below are defined in
Helicopter Abbreviations and Symbols.
In addition, we use the following symbols here.
\(M_T\) 
main rotor thrust 
\(k\) 
main rotor flap stiffness 
\(\gamma\) 
main rotor lateral mast tilt 
\(M_y\) 
main rotor ydisplacement from CG (see notes in input section) 
\(M_z\) 
main rotor zdisplacement from CG (see notes in input section) 
\(T_T\) 
tail rotor thrust 
\(T_x\) 
tail rotor xdisplacement from CG (see notes in input section) 
\(T_z\) 
tail rotor zdisplacement from CG (see notes in input section) 
Small angle approximations are used when solving for outputs. For example,
\( \sin ( \beta + \gamma ) \approx \beta + \gamma \)
and \( \cos ( \beta + \gamma ) \approx 1 \).
\[ N=0 \Rightarrow Q_{mp} = T_x T_T \]
\[ Z=0 \Rightarrow GW \cos \phi = M_T \cos (\beta + \gamma )\]
\[ L=0 \Rightarrow T_T T_z = M_T M_y \cos ( \beta + \gamma )  k\beta  M_T M_z \sin ( \beta + \gamma ) \]
\[ Y=0 \Rightarrow GW \sin \phi + T_T + M_T \sin (\beta + \gamma ) = 0 \]
