# Wind Angular Rates

Calculate wind angular rates from body angular rates, angle of attack, sideslip angle, rate of change of angle of attack, and rate of change of sideslip

## Library

Flight Parameters

## Description

The Wind Angular Rates block supports the equations of motion in wind-fixed frame models by calculating the wind-fixed angular rates (pw, qw, rw). The body-fixed angular rates (pb, qb, rb), angle of attack $\left(\alpha \right)$, sideslip angle (β), rate of change of angle of attack $\left(\stackrel{˙}{\alpha }\right)$, and rate of change of sideslip $\left(\stackrel{˙}{\beta }\right)$are related to the wind-fixed angular rate by the following equation.

`$\left[\begin{array}{c}{p}_{w}\\ {q}_{w}\\ {r}_{w}\end{array}\right]=\left[\begin{array}{ccc}\mathrm{cos}\alpha \mathrm{cos}\beta & \mathrm{sin}\beta & \mathrm{sin}\alpha \mathrm{cos}\beta \\ -\mathrm{cos}\alpha \mathrm{sin}\beta & \mathrm{cos}\beta & -\mathrm{sin}\alpha \mathrm{sin}\beta \\ -\mathrm{sin}\alpha & 0& \mathrm{cos}\alpha \end{array}\right]\left[\begin{array}{c}{p}_{b}-\stackrel{˙}{\beta }\mathrm{sin}\alpha \\ {q}_{b}-\stackrel{˙}{\alpha }\\ {r}_{b}+\stackrel{˙}{\beta }\mathrm{cos}\alpha \end{array}\right]$`

## Inputs and Outputs

InputDimension TypeDescription

First

2-by-1 vector Contains angle of attack and sideslip, in radians.

2-by-1 vector Contains rate of change of angle of attack and rate of change of sideslip, in radians per second.

Contains the body angular rates, in radians per second.

OutputDimension TypeDescription

First

Contains the wind angular rates, in radians per second.