  # Helicopter longitudinal trim calculator

 Gross Weight $$lb$$ Forward Mast Tilt $$deg$$ Main Rotor Flap Stiffness $$lb*ft/deg$$ Main Rotor Hub X-Displacement, Forward From CG $$ft$$ Main Rotor Hub Z-Displacement, Up From CG $$ft$$ Main Rotor Thrust 13500.0 $$lb$$ Pitch Angle, Positive Nose Up -0.00 $$deg$$ Longitudinal Flapping , Positive Front of Rotor Up 2.00 $$deg$$

## 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 x-displacement, forward from CG $$M_z$$ main rotor z-displacement, 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.

$M=0 \Rightarrow -T \sin (\gamma - \beta )M_z + T\cos (\gamma - \beta ) M_x + k\beta = 0$ $X=0 \Rightarrow T\sin (\gamma - \beta ) - GW\sin \theta = 0$ $Z=0 \Rightarrow T\cos (\gamma - \beta ) - GW\cos \theta$

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