Stall Speed

A wing stalls when the flow separates from its upper surface and the lift coefficient stops rising with angle of attack and starts falling. Set $C_L$ to that maximum in the lift equation, set lift equal to weight, and solve for speed, and you have the stall speed: $V_s = \sqrt{2W/(\rho S C_{L,max})}$.

The most important thing on this page is that a stall speed is not a number an aeroplane has. It is a number an aeroplane has at ONE weight, ONE load factor, ONE configuration and ONE density, and treating the placard figure as fixed is the classic mistake in low-speed flying. Everything under the square root moves.

Weight moves it: the speed follows the square root of the weight, so an aircraft 20% over its reference weight stalls about 10% faster. Load factor moves it the same way, because the wing is carrying $n$ times the weight in a manoeuvre — in a 60° banked level turn the wing carries 2g and the stall speed rises by $\sqrt{2}$, about 41%. That is the accelerated stall, and it is why the base-to-final turn, flown slow and steepened to avoid overshooting the runway centreline, has killed more pilots than any other single manoeuvre in light aviation. Configuration moves it through $C_{L,max}$: full flap might raise $C_{L,max}$ from 1.5 to 2.3, which drops the stall speed by about 20%.

Density is the interesting one, because it is the term that mostly does not matter. A stall speed computed as a TRUE airspeed does climb with altitude, exactly as $1/\sqrt{\rho}$. But the airspeed indicator is itself a $q$ gauge calibrated at sea-level density, so it under-reads by precisely the same factor, and the two errors cancel. The result is that the INDICATED stall speed is the same at every altitude — which is why placards are written in indicated airspeed, and why one number can serve from sea level to the service ceiling.

Two footnotes. The wing does not stall at a speed at all; it stalls at an ANGLE OF ATTACK, and it will do so at any airspeed and any attitude if the angle is exceeded — which is what makes the high-speed stall possible and why angle-of-attack indicators are worth having. And the certified $V_{S0}$ and $V_{S1}$ figures in a flight manual are measured under a defined test procedure at a defined weight, usually with the engine at idle and a specified deceleration rate; a real stall entered with power on, in a turn, or out of trim will happen somewhere else.