Formula & Calculator
Coefficient of Lift
Dimensionless lift coefficient relating generated lift to dynamic pressure and wing reference area.
Interpretation
Lift coefficient: C_L = L / (q·S), where L is lift, q is dynamic pressure, S is reference area. It is a dimensionless parameter measuring lifting efficiency. Example: L=10,000 N, q=5000 Pa, S=10 m² → C_L = 10000/(5000×10)=0.2.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| C_L | Lift coefficient | |
| L | Lift force | N |
| q | Dynamic pressure | Pa |
| S | Wing reference area | m2 |
What it means
The lift coefficient is the dimensionless factor that relates the lift generated by an airfoil or wing to the dynamic pressure and area. It depends on the angle of attack, airfoil shape, Reynolds number, and Mach number. C_L is obtained from experiments or CFD and is plotted in the lift curve (C_L vs α). The linear region (C_L = C_Lα · α) is used for small angles. The maximum C_L (C_Lmax) determines the stall speed. C_L is also used in performance calculations: cruise C_L is set for minimum drag, and high C_L for low‑speed flight. Understanding C_L is essential for designing wings that meet lift requirements at various flight conditions.
Worked example
Coefficient of Lift – Two Examples
Real‑World| Parameter | Value |
|---|---|
| L | 50,000 N |
| q | 3000 Pa |
| S | 20 m² |
| Parameter | Value |
|---|---|
| L | 15,000 N |
| q | 2000 Pa |
| S | 18 m² |
Common mistakes
- Coefficient of lift C_L: C_L = L / (q·S) – non‑dimensional.
- Lift L: In Newtons.
- Reference area S: Wing planform area (m²).
- C_L vs. angle of attack: C_L = C_Lα (α − α₀) for linear region; beyond stall, use experimental data.
- Units: All SI to get dimensionless C_L.
Applications
The coefficient of lift, C_L = L / (q·S), normalises the lift force by dynamic pressure and wing area, providing a dimensionless measure of lifting efficiency. It depends on angle of attack, airfoil shape, and Reynolds number. This coefficient is fundamental for plotting lift curves, determining stall angles, and designing high‑lift systems. Engineers use C_L to calculate the lift generated at a given flight condition, to compare aerodynamic performance of different wing designs, and to develop control laws. The maximum C_L (C_L,max) dictates stall speed. By using the lift coefficient, aerospace engineers can systematically analyse and optimise the lifting performance of aircraft, ensuring adequate lift at all flight stages.
- Wing aerodynamic performance assessment
- Stall speed determination and margin calculation
- Design and evaluation of high‑lift devices
- Airfoil selection and optimisation
- Flight control system development (based on C_L‑α relation)
Frequently Asked Questions
CL is a dimensionless parameter that relates the generated lift to the dynamic pressure and the wing reference area. It characterises the lifting efficiency of an airfoil or wing.
L = lift force (N)
q = dynamic pressure (Pa)
S = wing reference area (m²)
In the linear region, CL increases linearly with α: CL = CLα·(α − α₀). The slope CLα is about 2π per radian for a thin airfoil. At stall, CL reaches a maximum and then drops.
Wing aspect ratio, sweep, and taper affect the lift‑curve slope and maximum CL. High‑aspect‑ratio wings have higher CLα and lower induced drag.
Flaps increase CL,max and shift the lift curve upwards. Slats increase the stall angle, allowing higher CL before stall.
- Confusing wing planform area with wetted area.
- Using a CL value that does not correspond to the actual angle of attack.
- Applying 2D airfoil data to a 3D wing without span‑efficiency corrections.
At subsonic speeds, CLα increases with Mach number (Prandtl‑Glauert correction). Near Mach 1, CL behaviour is nonlinear due to shock waves.
An aircraft weighing 150,000 N has wing area S = 50 m² and flies at q = 3000 Pa. Required CL = L/(q·S) = 150000/(3000×50) = 1.0.
For a finite wing, the effective angle of attack is reduced by the downwash, so CL = CLα·(α − α₀) / (1 + CLα/(π·e·AR)).
Measure lift force L at a given q, then compute CL = L/(q·S). Corrections for tunnel boundary effects and model support interference may be applied.