Library / Automotive and vehicle dynamics / VEH-33
Automotive and vehicle dynamics
Aerodynamic downforce
Downward aerodynamic load on a vehicle, using a lift coefficient defined as positive for downforce.
- Ref
- VEH-33
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- Da [kN]
ρ is the air density, CL the downforce coefficient, defined here as positive when the force points down, A the reference area that the coefficient is based on, and Va the speed of the air relative to the vehicle. The force is the dynamic pressure ½ρVa² times CLA. The reference area must be stated with the coefficient, because CL values quoted for different areas are not comparable. The coefficient also changes with ride height, pitch and yaw.
Downward aerodynamic load on a vehicle, using a lift coefficient defined as positive for downforce. It rises with the square of airspeed, so it matters most at high speed.
Calculator
- Dynamic pressure, ½ρVa²1.5 kPa
- Mass equivalent of the downforce, Da / g305.8 kg
- Downforce at twice the speed12 kN
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.
- At 50 m/s (180 km/h) the aerodynamics press the car down with 3 kN, equal to the weight of 305.8 kg, without adding any mass. At 25 m/s it would be only 0.75 kN.
- Downforce raises tyre grip but it comes with drag. A wing usually adds drag as well, so race teams choose the wing angle to match each circuit: high downforce for twisty tracks and low for long straights.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kN) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Va Airspeed | 10 to 110 m/s | 0.12 | 14.52 | 14.4 | +10% | +21 % |
| A Reference area | 0.3 to 3 m² | 1.125 | 11.25 | 10.13 | +10% | +10 % |
| CL Downforce coefficient (positive = downward) | 0.5 to 5 | 0.6 | 6 | 5.4 | +10% | +10 % |
| ρ Air density | 0.8 to 1.3 kg/m³ | 2 | 3.25 | 1.25 | +10% | +10 % |
Sweep of Airspeed
| Airspeed (m/s) | Downforce (kN) |
|---|---|
| 10 | 0.12 |
| 22.5 | 0.6075 |
| 35 | 1.47 |
| 47.5 | 2.708 |
| 60 | 4.32 |
| 72.5 | 6.308 |
| 85 | 8.67 |
| 97.5 | 11.41 |
| 110 | 14.52 |
Sweep one variable
Variables and how each one contributes
Downforce
What the equation gives you. Everything else feeds it.
Air density
The air density, in kg/m³: 1.2 at sea level at 20 °C, and lower at altitude or in hot weather. Directly proportional: thin air at altitude gives less downforce (and less drag). Raising it by 10 % (to 1.32) moves the result by +10 %, from 3 to 3.3 kN.
Downforce coefficient (positive = downward)
The downforce coefficient (positive means downwards). A road car has about 0 to 0.3; a racing car with wings can reach 3 to 4 on the stated reference area. Directly proportional: wing angle and ground effect set this. Raising it by 10 % (to 2.75) moves the result by +10 %, from 3 to 3.3 kN.
Reference area
The reference area on which the coefficient is based, in m²: usually the frontal area or the plan area of the wing. Directly proportional, but only meaningful together with the coefficient quoted for that area. Raising it by 10 % (to 0.88) moves the result by +10 %, from 3 to 3.3 kN.
Airspeed
The air speed relative to the vehicle, in m/s. With no wind it equals the vehicle speed. The force grows with the square of the speed, so doubling the speed gives four times the downforce. Raising it by 10 % (to 55) moves the result by +21 %, from 3 to 3.63 kN.
Worked example with the values above
- Dynamic pressure: ½ρVa² = 0.5 × 1.2 × 50² = 1,500 Pa.
- Multiply by the coefficient and area: CLA = 2.5 × 0.8 = 2 m².
- Da = 1,500 × 2 = 3,000 N = 3 kN.
Assumptions and limits
- A coefficient that stays constant with speed, ride height and yaw, and air treated as incompressible.
- Va is the air speed relative to the vehicle and the force acts through the aerodynamic centre, so the front-to-rear split must be treated separately.
Common mistakes
- Comparing downforce coefficients that refer to different areas.
- Using the ground speed in a strong wind in place of the air speed.
Statistics and uncertainty
Aerodynamic coefficients from wind tunnel and track tests are typically good to ±3 to 5 %, but they change with ride height and pitch by 10 % or more as the car moves. The square of the speed amplifies any speed error, so a 2 % error in the air speed gives a 4 % error in the downforce, and wind (a headwind raises Va) matters significantly.
Where it is used
- Race car and high-speed vehicle design.
- Estimating the extra tyre load, and so extra grip, available at speed.
Maths you need
- Dynamic pressure: ½ρV²
- Coefficients and reference areas: how force coefficients are defined