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Aerospace
Dynamic pressure and lift
Lift on a wing from air density, speed, area and lift coefficient.
- Ref
- AER-01
- Rev
- v1
- Field
- Aerospace
- Result
- L [kN]
L in newtons, ρ air density in kg/m³, V true airspeed in m/s, S the reference area in m² and CL the lift coefficient. The dynamic pressure is q = ½ρV² in pascals. Drag has the same form, D = q S CD.
Moving air presses on a wing with a pressure that grows with the square of the speed. Multiply by the wing area and a coefficient describing how well the shape and angle make lift, and you have the lift force.
Calculator
- Dynamic pressure q1,500 Pa
- Wing loading L/S900 N/m²
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Speed is squared, so it is the biggest lever. Slowing to 70% of the speed cuts lift by half unless CL is raised.
- In steady level flight lift equals weight, so this formula sets the speed needed to stay airborne at a given CL.
- The same q gives the drag force with CD in place of CL, so a rise in q increases both.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kN) | Local step | Change in result |
|---|---|---|---|---|---|---|
| V True airspeed | 20 to 250 m/s | 1.44 | 225 | 223.6 | +10% | +21 % |
| S Reference area | 1 to 100 m² | 0.9 | 90 | 89.1 | +10% | +10 % |
| CL Lift coefficient | 0.1 to 1.6 | 1.5 | 24 | 22.5 | +undefined% | — |
| ρ Air density | 0.2 to 1.3 kg/m³ | 1.5 | 9.75 | 8.25 | +10% | +10 % |
Sweep of True airspeed
| True airspeed (m/s) | Lift (kN) |
|---|---|
| 20 | 1.44 |
| 27.42 | 2.708 |
| 37.61 | 5.091 |
| 51.57 | 9.573 |
| 70.71 | 18 |
| 96.96 | 33.85 |
| 133 | 63.64 |
| 182.3 | 119.7 |
| 250 | 225 |
Sweep one variable
Variables and how each one contributes
Lift
What the equation gives you. Everything else feeds it.
Air density
1.225 at sea level, about 0.41 at 10 km altitude. Directly proportional: thin air at altitude means less lift at the same speed.
True airspeed
Speed relative to the surrounding air. The dominant driver: lift grows with V², so +10% speed gives about +21% lift.
Reference area
Wing planform area used in the coefficient definition. Directly proportional.
Lift coefficient
Dimensionless measure of the wing’s lift at its current angle of attack and flap setting. Directly proportional, up to the stall.
Worked example with the values above
- Dynamic pressure: q = ½ρV² = 0.5 × 1.2 × 50² = 1,500 Pa.
- Lift: L = qSCL = 1,500 × 10 × 0.6 = 9,000 N.
- In kilonewtons, 9 kN.
Assumptions and limits
- Airspeed measured relative to the air, not the ground.
- Coefficient defined for the same reference area S.
- Subsonic, attached flow.
Common mistakes
- Using ground speed instead of airspeed.
- Using sea-level density at altitude.
- Using a CL defined with a different reference area.
Statistics and uncertainty
Relative errors combine as δL/L ≈ √[(δρ/ρ)² + (2δV/V)² + (δS/S)² + (δCL/CL)²]. The factor of two on speed matters: an airspeed error of 3% (typical for pitot-static systems) becomes 6% in lift. Wind tunnel CL values carry 2–5% uncertainty.
Where it is used
- Wing sizing and take-off performance.
- Missile and UAV control surface loads.
- Estimating aerodynamic loads on structures.
Maths you need
- Pressure: force per unit area
- Squares: q depends on V²