Aircraft pitch axis

The aircraft pitch axis is the transverse body axis about which the nose rotates upward or downward. In the convention used by NASA Glenn Research Center, it passes through the centre of mass and points toward the right wing tip; the aircraft roll axis points toward the nose and the aircraft yaw axis toward the underside. These are body-fixed directions, so their orientation relative to the ground changes with the aircraft.^[ref]

Choose right-handed body coordinates $x$ forward, $y$ right and $z$ down. A force $\mathbf{F}$ acting at displacement $\mathbf{r}$ from the centre of mass produces torque $\mathbf{\tau }=\mathbf{r}\times \mathbf{F}$. Its pitching moment isFor an original tail-load example, $\mathbf{r}=(-4,0,0)\mathrm{m}$ and $\mathbf{F}=(0,0,100)\mathrm{N}$ give ${\tau }_y=+400\mathrm{N}\mathrm{m}$. The downward tail load lifts the nose in this convention. If the aircraft pitch axis is a principal axis, the motion is initially pure pitch and the corresponding moment of inertia is $I_y=2000\mathrm{kg}{\mathrm{m}}^2$, then the instantaneous angular acceleration is $\dot{q}={\tau }_y/I_y=0.20rad/{\mathrm{s}}^2$. Coupled three-axis rotation requires the full Euler's equations.

The axis is a geometrical reference, not necessarily a physical hinge. Changing a control-surface load changes both forces and torques; a zero net translational force does not establish zero pitching moment. A balance measurement therefore needs the reference point and sign convention alongside its reported moment.^[ref]