Aircraft yaw axis

The aircraft yaw axis is the body-fixed axis about which the nose rotates from side to side. In a right-handed body coordinate system with $x$ forward and $y$ toward the right wing, it is the $z$ axis directed downward through the centre of mass. It completes the orthogonal set with the aircraft roll axis and aircraft pitch axis. The rudder can generate a side force aft of the centre of mass, producing a yawing torque.^[ref]

For a force $\mathbf{F}$ acting at displacement $\mathbf{r}$ from the reference point, the yaw component of $\mathbf{\tau }=\mathbf{r}\times \mathbf{F}$ isIn an original example, a rightward $80\mathrm{N}$ tail force at $\mathbf{r}=(-3,0,0)\mathrm{m}$ gives ${\tau }_z=-240\mathrm{N}\mathrm{m}$. With positive yaw defined nose-right, this force turns the nose left. If the axis is a principal axis with moment of inertia $I_z=1200\mathrm{kg}{\mathrm{m}}^2$ and the initial motion is pure yaw, the instantaneous angular acceleration is $\dot{r}={\tau }_z/I_z=-0.20rad/{\mathrm{s}}^2$. A tail's displacement matters as well as the force magnitude.

The aircraft yaw rate $r$ is a component of body angular velocity; it is not always the rate of change of aircraft heading. A banked vehicle projects its rotation onto several body axes, and its ground track also depends on wind. General coupled motion uses Euler's equations, rather than three independent scalar torque laws. Measuring a heading change alone therefore cannot establish the applied yawing moment.