= Bank angle
{title2=$\phi$}
The \b[bank angle] measures an <aircraft>'s lateral tilt relative to a local horizontal reference. In the ideal <fixed-wing aircraft> turning model, the <lift> vector tilts with the vehicle. For more general motion, vehicle attitude, flight-path direction and aerodynamic force direction must be distinguished; a banked vehicle need not follow a level circle.<Aircraft Rotations by NASA Glenn Research Center>[Roll axis, wing-tip motion and attitude-control discussion]{ref}
For steady horizontal circular motion with negligible vertical <thrust> and <lift> tilted by $\phi$, the <force balance> developed in <fixed-wing aircraft> gives the <aerodynamic load factor>
$$
n=\frac LW=\frac1{\cos\phi}.
$$
At $\phi=60\,{}^\circ$, \b[the required lift is twice the gravitational weight]. If the maximum usable <lift coefficient> is held fixed, $L=\rho V^2SC_L/2$ implies the model's limiting <airspeed> scales as
$$
V_{\rm limit}(\phi)=V_{\rm limit}(0)\sqrt n.
$$
A stipulated wings-level limit of $20\,\mathrm{m/s}$ therefore becomes $28.28\,\mathrm{m/s}$ at this loading. This is a comparison at fixed configuration and air <mass density>, not a claim that a particular <aircraft> can sustain the required condition. <Aerodynamic stall> and structural limits constrain the accessible turn.
A banked <glider (aircraft)> also needs a different loading balance from the shallow straight-glide model used to define <minimum sink speed>. Increasing <bank angle> cannot be analyzed merely by rotating a drawing of its still-air trajectory. Measured performance must specify the turn condition as well as <airspeed>; the FAA's performance discussion illustrates how bank and loading affect glider operation.<Glider Flying Handbook by Federal Aviation Administration>[Chapter 5, Effects of Weight and Figure 5-8, turn-radius comparison at fixed bank]{ref}
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