Aircraft yaw axis
= Aircraft yaw axis
The \b[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>.<Aircraft Rotations by NASA Glenn Research Center>[Yaw axis and final control-surface discussion]{ref}
For a <force> $\mathbf F$ acting at displacement $\mathbf r$ from the reference point, the yaw component of $\boldsymbol\tau=\mathbf r\times\mathbf F$ is
$$
\tau_z=r_xF_y-r_yF_x.
$$
In an original example, a rightward $80\,\mathrm N$ tail force at $\mathbf r=(-3,0,0)\,\mathrm m$ gives $\tau_z=-240\,\mathrm{N\,m}$. With positive yaw defined nose-right, this force turns the nose left. If the axis is a principal axis with <moment of inertia> $I_z=1200\,\mathrm{kg\,m^2}$ and the initial motion is pure yaw, the instantaneous <angular acceleration> is $\dot r=\tau_z/I_z=-0.20\,\mathrm{rad/s^2}$. 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 (rigid body dynamics)>, rather than three independent scalar torque laws. Measuring a heading change alone therefore cannot establish the applied yawing moment.