# Co-ordinate system and Angles#

In module 3, four distinct axes sets will be utilised; body, wind, stability, and earth axes. For this module, aircraft body axes is the only one required. Hopefully aircraft body axes have been covered in previous courses but a bit of revision never hurts.

## Aircraft Body Axes#

Aircraft body axes is a right-handed Cartesian axis set, centred at the aircraft centre of gravity. $$x$$ is defined positive along the aircraft longitudinal axis, positive forward. $$y$$ is positive over the starboard wing. $$z$$ is positive down, in accordance with the right hand rule.

Along each of the $$x, y, z$$ axes the forces, moments, and velocities can be summarised:

Direction

Force

Linear Velocity

Description

Moment

Moment Coefficient

Angular Displacement

Angular Velocity

Nondimensional angular rate

Description

$$x$$

$$X$$

$$U$$

Fore/aft

$$L$$

$$C_\ell$$

$$\phi$$

$$P$$

$$\bar{p}$$

Roll

$$y$$

$$Y$$

$$V$$

Sideward

$$M$$

$$C_m$$

$$\theta$$

$$Q$$

$$\bar{q}$$

Pitch

$$z$$

$$Z$$

$$W$$

Heave

$$N$$

$$C_n$$

$$\psi$$

$$R$$

$$\bar{r}$$

Yaw

The direction of positive rotations is defined in accordance with the right-hand screw rule - see the interactive figure below, which enables you to rotate an aircraft model, and click on the legend to show/hide different components.