Stall Speed
Minimum speed to maintain lift.
Formula
Variables
Example
Below this, the wing stalls
How it works
Stall speed is the lowest airspeed at which the wing can produce enough lift to balance the aircraft’s weight without exceeding its maximum lift capability. It comes from the lift equation, L = 1/2 \rho V^2 S C_L, by setting lift equal to weight and using the largest achievable lift coefficient, C_{L,max}. The square-root form shows that heavier aircraft, thinner air, or smaller wings all require a higher speed to stay flying.
When to use it
Use this formula when estimating the minimum steady speed for a given aircraft configuration, especially for takeoff, landing, or low-speed maneuvering analysis. It is also useful for comparing how changes in altitude, weight, flap setting, or wing loading affect stall characteristics.
Worked example, step by step
Given: W = 18,000 N, \rho = 1.10 kg/m^3, S = 24 m^2, C_{L,max} = 1.8 Step 1: Substitute into the formula V_s = \sqrt{\frac{2W}{\rho S C_{L,max}}} V_s = \sqrt{\frac{2(18,000)}{(1.10)(24)(1.8)}} Step 2: Calculate the denominator (1.10)(24)(1.8) = 47.52 Step 3: Calculate the fraction 2(18,000) / 47.52 = 36,000 / 47.52 \approx 757.58 Step 4: Take the square root V_s = \sqrt{757.58} \approx 27.5 m/s Final answer: The stall speed is about 27.5 m/s.
Common mistakes to avoid
- Using mass instead of weight in the formula without multiplying by g
- Forgetting that air density changes with altitude and temperature
- Treating stall speed as a fixed aircraft constant even though it varies with configuration and load factor
Did You Know?
Stall speed rises in a turn, a hidden danger that has caught many pilots banking too hard near the ground.
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