Could an F1 Car Drive Upside Down?
A Formula One car makes so much downforce that, past a certain speed, it could drive upside down on the roof of a tunnel.
A claim you have probably heard
The claim sounds like a myth. An F1 car with its driver weighs about 800 kg, as much as ten grown adults. On a ceiling, only the air rushing past could hold the car up. Yet on paper, the physics backs the claim.
So the real question is not whether the car could stick, but how fast the car has to go.
Make your guess. How fast must the car go before the air can hold the car on the ceiling?
- 80 km/h (50 mph)
- 200 km/h (125 mph)
- 400 km/h (250 mph)
- Never. Air can't hold up a car.
Show answer
B. 200 km/h (125 mph)
About 194 km/h (121 mph) with our numbers; other fair estimates give 180 to 220 km/h. An F1 car passes 300 km/h on a long straight, so the car has speed to spare. Test the claim yourself below.
Put the car on the ceiling
Your goal: press Flip it, then change the speed until you find the slowest speed where the car stays on the ceiling.
Somewhere just under 200 km/h, the air takes over. Below that speed the car drops; above that speed, moving air alone holds the car up. But air is thin, invisible stuff. How can air push down on a car at all?
How air pushes down
Start with a plane. A plane's wing is shaped and tilted so the passing air gets turned downward. The wing pushes the air down, so the air pushes the wing up, the way a wall pushes back on your hand. That upward push is called lift.
Flip the wing over, and the wing turns the air up instead. So the air pushes the wing down: a push called downforce. An F1 car carries upside-down wings at the front and back, and the car's shaped floor does the same job underneath.
An F1 car is a plane built to fly into the ground. Yet a parked F1 car makes no downforce, because no air flows past the wings. What changes as the car speeds up?
Twice as fast
The car doubles its speed, from 100 to 200 km/h. How much more downforce do the wings make?
- The same amount
- Twice as much
- Four times as much
- Eight times as much
Show answer
C. Four times as much
Four times as much. Speed counts twice: once for how much air hits the wings, and once for how hard each bit of air hits.
Your goal: press each speed and watch the blue downforce arrow. Count how many times longer the arrow gets.
Twice the air each second, each bit pushed twice as hard: four times the force. Downforce grows with the square of the speed, \(v^2\).
| Speed (km/h) | Downforce | Weight, 800 kg | They cross near 194 km/h |
|---|---|---|---|
| 0 | 0 | 7.85 | 7.85 |
| 10 | 0.02 | 7.85 | |
| 20 | 0.08 | ||
| 30 | 0.19 | ||
| 40 | 0.33 | ||
| 50 | 0.52 | ||
| 60 | 0.75 | ||
| 70 | 1.02 | ||
| 80 | 1.33 | ||
| 90 | 1.69 | ||
| 100 | 2.08 | ||
| 110 | 2.52 | ||
| 120 | 3 | ||
| 130 | 3.52 | ||
| 140 | 4.08 | ||
| 150 | 4.69 | ||
| 160 | 5.33 | ||
| 170 | 6.02 | ||
| 180 | 6.75 | ||
| 190 | 7.52 | ||
| 200 | 8.33 | ||
| 210 | 9.19 | ||
| 220 | 10.08 | ||
| 230 | 11.02 | ||
| 240 | 12 | ||
| 250 | 13.02 | ||
| 260 | 14.08 | ||
| 270 | 15.19 | ||
| 280 | 16.33 | ||
| 290 | 17.52 | ||
| 300 | 18.75 | ||
| 310 | 20.02 | ||
| 320 | 21.33 | ||
| 330 | 22.69 | ||
| 340 | 24.08 | ||
| 350 | 25.52 | ||
| 360 | 27 | ||
| 370 | 28.52 | ||
| 380 | 30.08 | ||
| 390 | 31.69 | ||
| 400 | 33.33 |
The weight line is flat: the car weighs the same at every speed. The downforce curve keeps climbing, so the two must cross. Past the crossing, near 194 km/h, the air pushes harder than gravity pulls.
On the road, downforce and weight both point down, into the road. So which way does downforce point when the car is upside down?
Hanging upside down
The car is upside down on a ceiling. Which way does downforce push the car?
- Down, toward the ground, like gravity
- Up, into the ceiling
- Nowhere. Downforce stops when the car flips.
Show answer
B. Up, into the ceiling
Up, into the ceiling. The wings flip with the car, so downforce always pushes the car toward the surface under the tyres.
Weight, \(mg\), pulls the car down. Downforce, \(F_D\), pushes the car up into the ceiling. When downforce wins, the ceiling pushes back down on the car, a push called the normal force, \(F_N\).
The car needs that push. Tyres only grip a surface they are pressed against, like a shoe on a floor. The harder the ceiling pushes, the more grip the tyres have to drive the car forward. So how hard does the ceiling push back?
On the road, the road pushes back against both: \(F_N = mg + F_D\). That extra push means extra grip in corners, which is why F1 cars have wings at all.
On the ceiling, the ceiling pushes back with only the difference: \(F_N = F_D - mg\). If \(F_D\) is smaller than \(mg\), the difference is negative. A ceiling can push but never pull, so the car falls.
So the whole trick is one rule: downforce must beat weight. Exactly how fast must the car go?
The math
Engineers write downforce the same way as lift on a plane's wing:
Each symbol is something you could measure. \(\rho\) (rho) is how dense the air is, in kilograms per cubic metre. \(v\) is the speed, squared just as the speed widget showed. \(C_L A\) is one number for how good the car's shape is at making downforce.
The car sticks once \(F_D = mg\). Solve for the speed, and call the answer \(v^{*}\):
Our numbers, step by step
Start where downforce equals weight: \(\tfrac12 \rho v^2 C_L A = mg\).
Multiply both sides by 2, then divide both sides by \(\rho\, C_L A\): \(v^2 = \dfrac{2mg}{\rho\, C_L A}\).
Find the weight: \(mg = (800\text{ kg})(9.81\text{ m/s}^2) = 7848\text{ N}\).
Put in the numbers (newtons, kg/m³ and m²): \(v^2 = \dfrac{2 \times 7848}{1.2 \times 4.5} \approx 2907\text{ m}^2/\text{s}^2\).
Take the square root: \(v^{*} \approx 53.9\text{ m/s}\).
Convert to km/h by multiplying by 3.6 (1000 m in a km, 3600 s in an hour): \(53.9 \times 3.6 \approx 194\text{ km/h}\).
Convert to mph by dividing by 0.447 (1 mph is 0.447 m/s): \(53.9 \div 0.447 \approx 121\text{ mph}\).
With our numbers, the car sticks above about 194 km/h (121 mph). But F1 teams keep \(C_L A\) secret, so that number is a guess. How far off could our answer be?
What if we're wrong?
Outside estimates of \(C_L A\) run from about 3.5 to 5 m², a spread of over 40%. Mass varies too, since fuel adds weight. Make one quick guess first.
Say the car is 10% heavier than we thought. How much faster must the car go to stick?
- About 20% faster
- 10% faster
- About 5% faster
- No faster. Mass doesn't matter.
Show answer
C. About 5% faster
About 5% faster. The speed goes as the square root of the mass, and \(\sqrt{1.1} \approx 1.05\). A square root roughly halves a small change.
Your goal: drag the mass to 880 kg, then drag the downforce slider end to end. Watch how little the big speed number moves.
The square root softens every error. The downforce estimates differ by over 40%, yet the speed only moves from about 184 to 220 km/h. That is why a question about a secret number still gets a useful answer.
Back to the tunnel
So the myth holds up, and now you can explain why. Upside-down wings turn the air up, so the air pushes the car into the ceiling. Twice the speed gives four times the push, while the weight never changes.
You worked out the line with a pencil: \(v^{*} = \sqrt{2mg/\rho C_L A}\), about 194 km/h, the same line you hunted for on the ceiling. Above that speed the push wins and the tyres can grip. And even if F1's secret numbers are off by 40%, the square root keeps the answer between 180 and 220 km/h.
Ask Phy
- Why does downforce grow with \(v^2\) and not just with \(v\)?
- How much faster can an F1 car take a corner when downforce adds to its grip?
- Could a car drive around a loop-the-loop slower than it could drive along a flat ceiling?