// WIRED US/UK — FINANZA
The Physics Behind Tesla’s Flying Roadster
We’ve been promised flying cars for decades. We finally have one. Well, sort of.
Last week, Elon Musk revealed Tesla’s long-delayed Roadster 2 with a few bells and whistles. The car flies—but not for very long—and the prototype also did a few other things normal cars can’t, like driving up a vertical wall and jumping over Tesla’s entire lineup of vehicles.
This raises two questions: Should we let humans drive up walls and into the air? Given their trouble navigating two-dimensional roads, this seems like an obvious no. But that’s one for lawyers and the Federal Aviation Administration to figure out. The other question is, how did the Roadster 2 prototype do this stuff? We can answer that ourselves, with physics.
Let’s start with how the car drove up a circular ramp and then stayed glued to it Spider-Man–style, completely upside down. I don't think you should ever do this, but this feature of the Roadster 2 can actually improve performance on normal roads. It has to do with friction.
When two surfaces interact—like rubber tires and a road—there can be a force that prevents the surfaces from sliding relative to one another. This interaction is called static friction. We have a simple model for this static friction force where the magnitude (Ff) depends on how hard the two surfaces are pushed together (FN) and the two types of surfaces (μ).
The force pushing the surfaces together is often called the “normal” force, since it's perpendicular to both surfaces. The coefficient of static friction (μ) describes the types of materials interacting. The practical maximum coefficient of friction is 1, and for rubber on asphalt, the value is somewhere around 0.6. What about that ≤ sign? This is because static friction is a “force of constraint.” It applies the force needed to prevent sliding—up to some maximum value.
Suppose a mere mortal car tries to drive up an incline. Here's a force diagram showing the three important forces: friction, normal force, and gravity (the product of mass and the gravitational field).
As the angle (θ) of the incline increases, the gravitational force (mg) has less of a component in the direction perpendicular to the surface. This means the normal force (FN) also decreases, as does the maximum frictional force. If this frictional force is less than the component of the gravitational force pulling down the incline, the car will slip. With a coefficient of 0.6, this maximum angle is about 31 degrees. That's not vertical. It's not even close to vertical. Even with a coefficient of friction at 0.9, you still only get to an incline of 42 degrees.
So how can a car drive up a vertical wall? The answer is to increase the normal force—and, by extension, the frictional force. For a vertical wall, this friction force must be equal to the gravitational force to prevent the car from slipping.
Here's where the Roadster 2 does its first trick. It uses fans to blow air out from under the car. With some side flaps, this lowers the air pressure under the car, akin to how a vacuum cleaner works.