Published on January 15th, 2019 |
by Steve Hanley
January 15th, 2019 by Steve Hanley
When Elon Musk tweeted recently that the upcoming Tesla Roadster would be able to fly like the DeLorean from the movie Back To The Future, some people were skeptical. Marques Brownlee was one who wondered if Musk was joking.
The new Roadster will actually do something like this https://t.co/fIsTAYa4x8
— Elon Musk (@elonmusk) January 9, 2019
Musk was quick to point out he was not joking and offered an explanation of how he would pull off the levitating Roadster trick.
I’m not. Will use SpaceX cold gas thruster system with ultra high pressure air in a composite over-wrapped pressure vessel in place of the 2 rear seats.
— Elon Musk (@elonmusk) January 9, 2019
That got Wired contributor Rhett Allain thinking. “I’m not a rocket expert, but it seems like you would have to keep refueling the rockets. It would be a nice stunt, but not for everyday use.” Not to mention that ultra-high-pressure recharging infrastructure is seriously lacking in most parts of the world today.
He made a few calculations and decided a properly designed system of air thrusters could do the trick. The physics are not esoteric. It’s what makes helicopters and VTOL airplanes fly. “It doesn’t matter if you use some type of jet engine or a rotor, the physics is mostly the same,” he writes. “In order to hover, the flying car will take air from above the car and ‘throw’ it down. Since air has mass, a change in velocity of this air would mean it has a change in momentum.”
Here’s the physics part. “Momentum is the product of mass and velocity. According to the momentum principle, this change in momentum requires a force and it is this force that counteracts the gravitational force to make the car fly.”
To generate the needed volume of air, you could use a really big fan, but that would be hard to fit into the back seat area of the Roadster. “The other option is to have smaller rotors with lower mass air but moving down at a much faster speed. But faster air has a consequence. It turns out that the power required to speed up the air depends on air speed raised to the third power. In the end, the power to hover can be expressed as the following formula.”
To figure out how much energy is needed to get the Roadster off the ground, Allain makes two key assumptions. The first is that the Roadster weighs about the same as a Model 3 — 1800 kilograms. The second is that the fan will have a diameter of 20″ and an area of 0.81 square meters.
“Just to be clear,” Allain says, “the ρ symbol represents the density of the air (around 1.2 kilograms per cubic meter) and the A is the total cross-sectional area of the rotors (or jets or whatever).” The answer he gets is an air speed of 190 meters per second and a total energy required of 1.7 megawatts.
“So, if the car uses this much power to hover then how long could it stay off the ground? According to Wikipedia, the biggest Model 3 battery is 75 kWh (kilowatt-hours). Perhaps it would be better to write this as 0.075 megawatt-hours. So, if the hovering takes 1.7 MW, then it could fly for 0.044 hours or 2.64 minutes.”
Since we know the Roadster will have a 200 kWh battery, it should be able to stay aloft 267% longer, or 7 minutes, assuming the battery is fully charged and none of that stored energy is used to turn the wheels of the car. That leaves the question of what do you do with the car once the battery is fully discharged — put it on a flat bed and take it home to recharge in your garage?
Despite any potential hurdles, the exposure a flying car would garner Tesla would surely be worth it. And the owners of used Roadsters could advertise them for sale with a notation that they were only ever flown on Sundays.
The notion of a flying Tesla may not be entirely rational, but ask yourself this question — what other manufacturer can claim its cars fly? If the answer is “none,” perhaps that is all the reason Tesla needs for doing this.
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