# Can Bernoulli fly a car?

I need to settle an argument. How much influence, if any, does the Bernoulli principle have in sending a stock car traveling at 200 MPH sailing through the air when the air pressure unexpectedly increases underneath the car by, say, getting bumped from behind by another car? I say that just because of the shape of the top of the car roughly approximates the shape of an airplane wing, the Bernoulli principle could never generate enough force to lift the car, but rather the car is sent through the air by a huge gust of wind from underneath.

• Stock car? They have devices that actively prevent cars from becoming airborne (but fail, a la Austin Dillon in the 2nd Daytona race this year). If you look at open-wheel racing, there were 2 (maybe 3?) airborne cars in the practice for the Indy 500 alone -- so clearly the aerodynamics can make a car flip. But they work really hard to design aerodynamic kits to prevent that from happening. – tpg2114 Oct 22 '15 at 3:52
• See What really allows airplanes to fly. At 200MPH relative airspeed, almost any object the shape, size and weight of a car will fly. Only specially designed objects do so stably, meaning that either they are aeroplanes or they are upside-down aeroplanes, harnessing the lift needfully produced to keep them stably on the ground. So there is definite aerodynamic design needed. The Bernoulli principle simply follows from conservation of momentum given certain approximations and is accurate when they hold. – Selene Routley Oct 22 '15 at 6:55

As tpg2114 partly mentioned, there are two implicit assumptions in the question that aren't quite right:

1. The Bernoulli principle is just an idealized or simplified description of the relationships between the air speed and pressure. In more complex situations, we can't work with a simple relationship between one pressure value and one value of the speed. We need a much more complicated, space-dependent analysis, and the Bernoulli formula gets more complex and is enhanced into the whole business of "aerodynamics". The Bernoulli principle is still among the most important principles or effects behind all of aerodynamics but a much more complex analysis than the simple Bernoulli equation is needed to predict what happens.

2. We don't really want the car to "fly". When it flies, it loses the contact with the road, the grip, which prevents the wheels from controlling the speeds. That's why the goal of the carmakers and racing teams is exactly the opposite. They need to increase the downforce. This is done by the "reverse wings". The formula for the magnitude of the downforce is completely analogous to the drag of the "ordinary wing": $$D = \frac 12 (WS) H \alpha F \rho V^2$$ The symbols are explained on the Wikipedia "downforce" page. In the SI units, all factors are of order one with the exception of $V^2$ which is $8,000~{\rm m}^2 / {\rm s}^2$ for the speed 200 MPH. In effect, the downforce is comparable to thousands of newtons, enough to add a ton (or slightly less) to the apparent weight of the car.

In real-world situations during the races, it is indeed often needed to increase the apparent weight of the car by up to one ton or so – the "Bernoulli forces" (or their generalizations) may want to make the car "fly" and reduce the weight by this much. And the car designers and mechanics need and can indeed achieve such an effect whenever they want.

At speeds below the speed of sound, the Bernoulli principle, which is just $F=ma$ for fluids, totally governs what is happening. Even bricks can fly. I bet you are thinking the Bernoulli principle is the wrong explanation you were probably taught, the equal time fallacy.

I would simply point out that in other cars, as speed increases, the amount of rubber on the road decreases. This helps to provide a dampening effect, to keep the car from going airborne. It isn't perfect, but in most instances, your average commuter driving a Ford Escape doesn't reach the necessary velocity to become airborne.

On a tenuously-related topic, have you read the alleged complete tale of the rocket car?

http://www.wired.com/2000/08/rocketcar/