The Physics of a Tesla Model X Towing a Boeing 787



This is pretty cool—an electric car pulling a full size commercial aircraft, apparently for the first time ever. In particular, it is a Tesla Model X pulling a Quantas Boeing 787. There are a million reasons this is cool, but I think we should just jump to the coolest ones: the physics questions.

Does the mass of the plane matter?

The Boeing 787-9 Dreamliner has a maximum takeoff weight of 254,000 kg—but this one was empty and had a mass of 130,000 kg. Yes, that's pretty massive—but it doesn't matter. In fact, a human could even pull a full-sized aircraft. Don't believe me? How about this guy:

Brent Winstone for Qantas

Mass doesn't matter. If there is only one force on an object, that object will accelerate. Here's an example you can try yourself (maybe). Go down to the dock and place one foot on a large boat and the other foot on the wooden dock. Now push. Guess what? It moves (assuming it's not tied down). That small force from your foot does indeed cause the boat to increase in speed at least for a little bit. Once it starts moving, there is a force from the water that prevents it from speeding up.

Forces cause objects to change velocity. If the object has a large mass, that just means the change in velocity is smaller—but it's still a change. So the mass of the plane doesn't really matter. If there were no other forces, I could push an aircraft carrier. But there are other forces. There is friction.

Why is there a frictional force on the plane?

We can think of most frictional forces as a force parallel to the ground and acting in the opposite direction as the motion of the object. There are really two types of friction that come into play when pulling a plane. There is the frictional force between wheel and the axle as they rub together and then there is rolling friction. If you look at a tire closely, you will get a good sense of how rolling friction works. Although it looks round, it's not. The bottom of the tire is flatter than the rest of the tire because it's pushed against the ground. As the wheel rolls over, a new part of the tire has to be flatter—and it takes a force to deform this tire. That's the basic idea of rolling friction.

Brent Winstone for Qantas

Both of these frictional forces (normal and rolling) increase with the force that the ground pushes on the plane, so in a sense the weight of the object matters. But once you have a frictional force on the object, a puny force won't get the plane to accelerate. You need a net force that is greater than zero and that's what makes this difficult. Of course you can reduce the friction some by decreasing the mass of the object (it's an empty plane) and increasing the pressure in the tires (decreases rolling friction)—but it's still going to be tough.

Could any car pull a giant plane like this?

If you get your big sport utility vehicle, it might not be able to pull this aircraft. Although the Tesla Model X is an SUV, it's different from internal combustion vehicles as it's electric powered. The big difference between electric and gasoline powered cars is the torque. Torque is sort of like a rotational force. It's a measure how how the engine can rotate the tires and in turn push the car forward. The Tesla Model X can produce a torque of 660 Newton-meters but a Ford Explorer has only 346 Newton-meters. Less torque means a lower forward pushing force from the tires. But wait! You could cheat. If you put smaller tires on the gasoline car, you can get a greater force with the same torque (but then your speedometer will be off).

Does the mass of the Tesla matter?

Let's imagine that you had the most powerful engine in the whole world. Could you pull anything you want with this monster vehicle? No, not quite. The problem is friction. You need a frictional force between the tires and the road in order to pull some object.

How about an example? Suppose there is a giant block of wood that requires a force of 1,000 Newtons to overcome the frictional force and get it speeding up. You run a cable from the block to your super SUV so that the car can pull this 1,000 Newtons. But the vehicle also has to have a net force greater than zero. That means it must have a frictional force pushing forward that is greater than the 1,000 Newtons pulling back.

But there is a problem. In order to get a large frictional force from the vehicle tires, you need a large force pushing the tires to the road. If there are no other vertical forces interacting in this case that means the weight of the car is equal to the force between the road and tires. If this weight is too small you won't get enough friction and the tires will just spin out—and that's not going to help pull that giant block.

The same is true for this Tesla X. If it's too light, it just won't have enough friction to pull anything. Fortunately the Tesla X does indeed have a significant mass—at around 2,400 kg. That's not crazy high, but it's not crazy low either.

So yes, the Tesla does a great job pulling this Boeing aircraft. It's impressive, but it's not impossible for other vehicles. What would be impressive? What about pulling a smaller plane on a runway such that it gets up to takeoff speed? That would be cool.

Also, this whole thing reminds of one of my earliest blog posts. It was an analysis of a Ford commercial in which a truck rolls out the back of a landing plane and the truck then proceeds to stop the plane. Here is that analysis (warning—it's a super old post).

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