Stall Speed

Stall speed: V_s = √(2·W/(ρ·S·C_L_max))

Stall speed V_s is the slowest you can fly before the wing stops carrying its weight at the maximum lift coefficient C_L_max. The relation is V_s = √(2·W/(ρ·S·C_L_max)), where W is weight in N, ρ is air density (about 1.225 kg/m³ at sea level) and S is wing area in m². Drop below V_s and the laminar flow over the wing separates; lift falls away suddenly and the aircraft sinks. Note that this can happen in any attitude once the angle of attack passes the critical value, somewhere around 15–18°. A few reference numbers: the Cessna 172 stalls at V_s0 ≈ 33 kt (61 km/h, full flaps) and V_s1 ≈ 44 kt clean, while a Boeing 737 sits near V_s ≈ 108 kt (200 km/h). Worked example: 1000 kg · 9.81, ρ=1.225, S=16 m², C_L_max=1.6 gives V_s ≈ 24.9 m/s (≈48 kt).

Applications

It shows up in ANAC private and commercial pilot training, where stall recovery is a required part of the PPA. Beyond that, it feeds flap planning for approach and landing, RBAC 91/121 compliance, flight envelope work, and short-field operations, where V_s is what sets the published V_REF, usually 1.3·V_s0.

FAQ

Why does V_s rise in a banked turn? Load factor n grows as 1/cos(φ). Since lift now has to equal n·W, stall speed scales with √n. Roll into a 60° bank and the load factor doubles, so V_s climbs by √2, roughly 41%.

Does V_s change with weight? Yes, and it tracks √W. Load the aircraft up and it stalls faster; fly it light and the stall speed comes down.

What is the difference between V_s0 and V_s1? V_s0 is the stall in landing configuration, full flaps and gear down, whereas V_s1 is the stall in clean configuration. V_s0 always comes out lower because the flaps raise C_L_max.