Bank angle ($\varphi$)

The 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.^[ref]

For steady horizontal circular motion with negligible vertical thrust and lift tilted by $\varphi$, the force balance developed in fixed-wing aircraft gives the aerodynamic load factorAt $\varphi =60{}^{\circ }$, the required lift is twice the gravitational weight. If the maximum usable lift coefficient is held fixed, $L=\rho V^{2}S{C}_L/2$ implies the model's limiting airspeed scales asA stipulated wings-level limit of $20m/s$ therefore becomes $28.28m/s$ 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 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.^[ref]

The aerodynamic load factor $n=L/W$ compares lift with gravitational weight. The stated convention takes $L$ along the chosen positive lift direction, so $n$ is a signed force ratio, not simply the magnitude of total acceleration divided by $g$. A steady level condition can have $n=1$ with zero inertial acceleration.^[ref]

A focused example is a wings-level pull-up at the bottom of a vertical curved path. Neglect other vertical forces and take upward normal acceleration as positive. The force balance givesFor stipulated true airspeed $V=50m/s$, curvature radius $R=500\mathrm{m}$ and $g=9.81m/{\mathrm{s}}^2$, the upward centripetal acceleration is $5m/{\mathrm{s}}^2$ and $n\simeq 1.510$. With $m=600\mathrm{kg}$, lift is $8886\mathrm{N}$, while the net upward force is $3000\mathrm{N}$. Neither is the other.

In the steady horizontal-turn model, the condition instead is $n=1/\cos \varphi$; bank angle derives that balance. It does not apply unchanged to the vertical pull-up. At fixed air mass density, wing area and usable maximum lift coefficient, the relation $L=\rho V^{2}S{C}_L/2$ gives limiting speed proportional to $\sqrt{n}$ for positive $n$. For this example, the factor is about $1.229$ relative to the corresponding one-load condition.

A force balance measures aerodynamic load; a trajectory measurement estimates inertial acceleration. Comparing them requires the gravitational weight term and correct directions. A reported load factor also needs its force-axis convention: thrust, side forces and coupled motion can matter to what an instrument actually records. The definition alone establishes neither structural capability nor available lift before aerodynamic stall.