The Physics Behind Tesla’s Flying Roadster

The upside-down Roadster 2 makes for a compelling sales pitch, but the suction actually has a strong use case when it’s driving right side up. Frictional force is the thing that makes a car accelerate. More frictional force, better performance. Pushing the car down means you can accelerate faster and brake faster and make sharper turns. (Performance automakers have harnessed this principle for decades, though not to the degree of Tesla’s new prototype.)

0–60 in 1 second

The Roadster 2 also boasts an acceleration of 0 to 60 mph in less than a second. For a traditional car, this is impossible. Since a normal car uses the frictional force between the tires and road to accelerate, it’s limited by the coefficient of friction. Using a coefficient of friction at 0.6 (reasonable), the best you can do is 0 to 60 mph in 4.56 seconds. Yes, you can get better tires and you can also increase the frictional force once the car moves faster and interacts with the air (pushing it down)—but those improvements still won’t get you to 60 mph in a second.

The Roadster 2 relies on another form of force: compressed air shooting out the back. This is how rockets work. Since most of us don’t have rockets handy, consider the simple experiment of a toy car propelled by an inflated balloon.

Once the balloon is released, the stretched rubber acts as a force that pushes the air out of the balloon and through an attached tube. But since this air has mass, it will take a force to accelerate it from rest to its exhaust velocity. Here’s the cool thing about forces—they are an interaction between two things (like the balloon and the air). That means that when the balloon’s walls push on the air, the air pushes back with an equal force in the opposite direction—an example of Newton’s third law. This push-back force on the balloon is what makes the toy car accelerate. Instead of a wheezing balloon, the Roadster 2 relies on a tank of compressed air.

Flying Cars (Sort Of)

Now, we get to the flying car part. The Roadster 2 uses the same compressed-air method to push up on the car and get it off the ground. That’s stretching the limits of the term “flying,” especially because there’s only a few seconds of thrust that it can get from the tank before the pressure drops. With a lower tank pressure, the air comes out with a lower velocity and less thrust. If I was going to have a flying car, I would hope it could at least fly for 10 minutes of air time.

There’s a second issue—acceleration. Since the rockets only last for a short time, they need to apply a large force to get a change in velocity and get the car to leapfrog over a truck or some other obstacle. But with a large force, you also get a large acceleration, and large accelerations are generally bad for humans. We can estimate this acceleration using video analysis. I’m going to use Tracker Video Analysis to mark the location of the car in each frame as it jumps over a Tesla Semi truck. Because we know the truck is about 4 meters tall, we can get the position of the car as a function of time. Here is the vertical position of the Roadster 2 during this jump.