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# 6th Order Point Mass Forces (Coordinated Flight)

Calculate forces used by sixth-order point mass in coordinated flight

## Library

Equations of Motion/Point Mass

## Description

The 6th Order Point Mass Forces (Coordinated Flight) block calculates the applied forces for a single point mass or multiple point masses.

The applied forces [Fx Fy Fh]T are in a system is defined by x-axis in the direction of vehicle velocity relative to air, z-axis is upwards and y-axis completes the right-handed frame and are functions of lift (L), drag (D), thrust (T), weight (W), flight path angle (γ), angle of attack (α), and bank angle (μ).

`$\begin{array}{l}{F}_{x}=T\mathrm{cos}\alpha -D-W\mathrm{sin}\gamma \\ F\gamma =\left(L+T\mathrm{sin}\alpha \right)\mathrm{sin}\mu \\ {F}_{z}=\left(L+T\mathrm{sin}\alpha \right)\mathrm{cos}\mu -W\mathrm{cos}\gamma \end{array}$`

## Inputs and Outputs

InputDimension TypeDescription

First

Contains the lift in units of force.

Second

Contains the drag in units of force.

Third

Contains the weight in units of force.

Fourth

Contains the thrust in units of force.

Fifth

Contains the flight path angle in radians.

Sixth

Contains the bank angle in radians.

Seventh

Contains the angle of attack in radians.
OutputDimension TypeDescription

First

Contains the force in x-axis in units of force.

Second

Contains the force in y-axis in units of force.

Third

Contains the force in z-axis in units of force.

## Assumptions and Limitations

The block assumes that there is fully coordinated flight, i.e., there is no side force (wind axes) and sideslip is always zero.

The flat Earth reference frame is considered inertial, an excellent approximation that allows the forces due to the Earth's motion relative to the “fixed stars” to be neglected.

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