Lift Equation
Aerodynamic lift produced by a wing depends on air density, speed squared, area and lift coefficient.
Formula
Variables
Example
Because lift grows with v², an aircraft at 200 kt makes four times the lift it does at 100 kt.
How it works
This equation estimates the aerodynamic force that a wing generates perpendicular to the airflow. It shows that lift increases with denser air, faster motion, larger wing area, and a higher lift coefficient, which bundles together effects like wing shape, angle of attack, and flap setting. The v² term appears because the energy and momentum carried by the airflow rise rapidly with speed, so small speed changes have a big effect on lift.
When to use it
Use this formula when you want to estimate or compare wing lift in steady flight, such as during takeoff, climb, cruise, or stall analysis. It is also useful for understanding how changing speed, altitude, wing area, or configuration affects the lift available to support an aircraft.
Worked example, step by step
Given: ρ = 1.225 kg/m³ v = 60 m/s S = 16 m² C_L = 1.2 Step 1: Write the lift equation L = 1/2 × ρ × v² × S × C_L Step 2: Square the speed v² = 60² = 3600 Step 3: Substitute the values L = 1/2 × 1.225 × 3600 × 16 × 1.2 Step 4: Calculate the result 1/2 × 1.225 = 0.6125 0.6125 × 3600 = 2205 2205 × 16 = 35280 35280 × 1.2 = 42336 Final answer: L = 42,336 N
Common mistakes to avoid
- Using indicated airspeed instead of true airspeed when density has changed
- Forgetting that speed is squared, which makes the effect of velocity much larger than a linear estimate
- Mixing up wing area and surface area of the whole aircraft, or using the wrong units for density and speed
Did You Know?
Lift grows with the square of speed, so doubling airspeed quadruples the lift a wing can produce.
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