How a wing holds an aircraft up
A wing moving through the air turns the airflow downward. By Newton’s third law, the air pushes the wing up. The same effect shows up as lower pressure above the wing and higher pressure below it. Engineers sum all of this in one compact formula, the lift equation, which works for airplane wings, helicopter blades, sails, hydrofoils and even race car wings that push down instead of up.
The lift equation
L = ½ × ρ × v² × S × CL
- ρ is the air density, 1.225 kg/m³ at sea level in the standard atmosphere, lower at altitude.
- v is the true airspeed.
- S is the wing area, seen from above.
- CL is the lift coefficient, which depends on the shape of the airfoil and on the angle of attack.
The product ½ρv² is the dynamic pressure. Lift grows with the square of speed: double the speed and the lift is four times higher at the same angle of attack.
Level flight and stall speed
In steady level flight, lift equals weight. Rearranging the equation gives:
- CL needed = W ÷ (½ρv²S), which rises as the aircraft slows down.
- Stall speed = √(2W ÷ (ρ × S × CLmax)), the speed at which even the maximum lift coefficient cannot carry the weight.
Example
A light four-seat aircraft with a 174 sq ft wing, weighing 2,300 lb, at 100 knots at sea level:
- Dynamic pressure: about 33.8 lb/ft² (1,621 Pa)
- Lift at CL 0.4: about 2,356 lbf, slightly more than the weight
- CL needed for level flight: 0.390
- Stall speed with CLmax 1.6: about 49 knots
- Wing loading: 13.2 lb/ft²
At 8,000 ft, the air density is about 22% lower, so the true stall speed rises by about 13%.
What changes the lift coefficient
- Angle of attack: CL rises roughly in a straight line, by about 0.1 per degree for a typical wing, until the airflow separates and the wing stalls, usually around 15 to 18 degrees.
- Flaps and slats change the shape of the wing and raise CLmax, which lets aircraft fly slowly for takeoff and landing.
- Contamination: frost, ice or even insects on the leading edge can lower CLmax noticeably, which is why wings must be clean before takeoff.
Limits
The calculator uses the International Standard Atmosphere up to 36,089 ft (11,000 m) and assumes incompressible flow, which is accurate below about Mach 0.3. Real aircraft performance comes from the flight manual, which accounts for weight, flaps, bank angle and center of gravity.