= Aircraft roll axis
The \b[aircraft roll axis] is the longitudinal body axis through the <centre of mass>, conventionally directed toward the nose. Positive rotation around that forward axis lowers the right wing in the right-handed system with $y$ right and $z$ down. An <aileron> changes the aerodynamic loading of a wing; unequal loads on opposite sides can generate a rolling <torque>.<Aircraft Rotations by NASA Glenn Research Center>[Roll axis and control-surface moments]{ref}
The roll component of $\boldsymbol\tau=\mathbf r\times\mathbf F$ is
$$
\tau_x=r_yF_z-r_zF_y.
$$
An original pure-couple example places an upward incremental force of $50\,\mathrm N$ at $y=+3\,\mathrm m$ and a downward incremental force of the same magnitude at $y=-3\,\mathrm m$. With both application points at $z=0$, their total incremental <force> vanishes but
$$
\tau_x=3(-50)+(-3)(50)=-300\,\mathrm{N\,m}.
$$
The negative sign means right-wing-up rotation. For an initially pure roll about a principal axis with <moment of inertia> $I_x=600\,\mathrm{kg\,m^2}$, the instantaneous <angular acceleration> is $\dot p=-0.50\,\mathrm{rad/s^2}$. This is a stipulated force couple, not an aileron-performance prediction.
The <aircraft roll rate> $p$ describes rotation, while <bank angle> describes attitude relative to a local horizontal reference. A vehicle held at a constant <bank angle> can have zero change of that angle while its flight direction turns. Conversely, a rolling <aircraft> need not already have the steady centripetal <force> required by the <fixed-wing aircraft> turning model. Attitude, <angular velocity> and trajectory are separate measured quantities.
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