Lift Coefficient
Non-dimensional lift, obtained by rearranging the lift equation.
Formula
Variables
Example
Deploying flaps raises the lift coefficient, letting an aircraft fly slower on approach.
How it works
The lift coefficient measures how effectively a wing generates lift relative to the air conditions, speed, and wing size. Because lift itself increases with air density, the square of speed, and wing area, dividing by those factors produces a dimensionless number that lets engineers compare different wings, flap settings, or flight conditions on a common basis. It is especially useful in aerodynamics because the same wing can have very different lift forces at different altitudes or speeds, even though its lift coefficient may stay similar for a given angle of attack and configuration.
When to use it
Use this formula when you know the lift force and want to determine how aerodynamically “loaded” a wing is under a specific flight condition. It is also used in aircraft performance analysis, wind-tunnel testing, and comparing lift behavior across different aircraft or wing configurations.
Worked example, step by step
An aircraft wing produces a lift force of 48,000 N in level flight. Air density is 1.18 kg/m^3, the true airspeed is 72 m/s, and the wing area is 24 m^2. Use C_L = 2L / (ρv^2S). Substitute the values: C_L = 2(48,000) / (1.18 × 72^2 × 24) Compute the speed term: 72^2 = 5184 Compute the denominator: 1.18 × 5184 × 24 = 146,908.8 Compute the numerator: 2 × 48,000 = 96,000 So C_L = 96,000 / 146,908.8 ≈ 0.653 Final answer: the lift coefficient is about 0.65.
Common mistakes to avoid
- Forgetting that speed is squared, which causes a large error in the result
- Using wing span instead of wing area S
- Mixing units, such as using knots or pounds without converting to SI-compatible quantities
Did You Know?
The lift coefficient captures a wing's shape and angle in a single dimensionless number.
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