Helicopter Lateral Trim Calculator

Gross Weight		\( lb \)
Torque		\( lb*ft \)
Lateral Mast Tilt (positive when pilot sees right side of the rotor down, normally negative)		\( deg \)
Main Rotor Flap Stiffness		\( lb*ft/deg \)
Main Rotor Hub Y-Displacement (from CG, positive right from pilot's POV)		\( ft \)
Main Rotor Hub Z-Displacement (from CG, positive up)		\( ft \)
Tail Rotor X-Displacement (from CG, positive aft)		\( ft \)
Tail Rotor Z-Displacement (from CG, positive up)		\( ft \)

Main Rotor Thrust	13500	\( lb \)
Tail Rotor Thrust	1000	\( lb \)
Roll Angle	-2.83	\( deg \)
Lateral Flapping	0.59	\( deg \)

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 body-lateral 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 y-displacement from CG (see notes in input section)
\(M_z\)	main rotor z-displacement from CG (see notes in input section)
\(T_T\)	tail rotor thrust
\(T_x\)	tail rotor x-displacement from CG (see notes in input section)
\(T_z\)	tail rotor z-displacement 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 \( \cos ( \beta + \gamma ) \approx 1 \).

\[ N=0 \Rightarrow Q_{mp} = T_x T_T \] \[ Z=0 \Rightarrow GW \cos \phi = M_T \cos (\beta + \gamma )\] \[ L=0 \Rightarrow T_T T_z = M_T M_y \cos ( \beta + \gamma ) - k\beta - M_T M_z \sin ( \beta + \gamma ) \] \[ Y=0 \Rightarrow GW \sin \phi + T_T + M_T \sin (\beta + \gamma ) = 0 \]

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