= Wing loading
{title2=$W/S$}
{wiki}
<Wing loading> is the <gravitational weight> of an <aircraft> divided by its reference <wing area>:
$$
w_S=\frac WS,\qquad W=mg.
$$
It is a whole-aircraft loading measure. In SI its units are $\mathrm{N/m^2}$, not $\mathrm{kg/m^2}$. The latter units describe mass per wing area, $m/S$, and require multiplication by gravitational acceleration to obtain $W/S$.
For an original unit check, $m=500\,\mathrm{kg}$, $S=10\,\mathrm{m^2}$ and $g=9.81\,\mathrm{m/s^2}$ give $m/S=50\,\mathrm{kg/m^2}$ but $W/S=490.5\,\mathrm{N/m^2}$. Although this has the units of <pressure>, it is not the local pressure distribution on the wing surface.
In straight level flight with negligible vertical thrust, <lift> balances <gravitational weight>.<Four Forces on an Airplane by NASA Glenn Research Center>[Weight and Lift, force directions]{ref} Combining this with the definition $L=\tfrac12\rho V^2SC_L$ of the whole-wing <lift coefficient> gives
$$
V=\sqrt{\frac{2(W/S)}{\rho C_L}}.
$$
At fixed air <mass density> and required coefficient, <airspeed> therefore scales as the square root of <wing loading>. For stipulated $W/S=600\,\mathrm{N/m^2}$, $\rho=1.2\,\mathrm{kg/m^3}$ and $C_L=1$, the result is $31.62\,\mathrm{m/s}$. Doubling only the loading gives $44.72\,\mathrm{m/s}$, a factor of $\sqrt2$.
If a model assumes a maximum attainable $C_{L,\max}$, the same equation gives a corresponding minimum speed for that straight-level condition. It is not a universal speed for every attitude or configuration: a turning condition can require $L>W$, and a changed <airfoil>, surface condition or <Reynolds number> can change the attainable coefficient.
A geometric and weighing check determines $m$, the relevant loading state and projected <wing area>. Those measurements establish $W/S$; a separate aerodynamic experiment is needed to establish the applicable <lift coefficient>. Equal <wing loading> does not establish equal <lift-to-drag ratio> or identical <aerodynamic stall> behavior.
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