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.