The Tesla CEO’s latest claim looks iffy under the microscope
The second-generation Tesla Roadster is back in the news after Elon Musk announced that the car would hit 60 miles an hour in less than a second. This is nearly a full second faster than the current record-holder, which got me wondering: Is it actually possible? I crunched some numbers to get the answer: It’s technically doable, but it would be so inconvenient as to make the whole endeavor not worth it. Let’s run down what I found.
Back in 2021, when Musk was claiming that the Roadster would go zero to 60 in a lumbering 1.1 seconds, we checked his work and found that it could theoretically happen — if Tesla replaced the rear seats with a massive pressurized air tank and a compressor. With this new claim, though, I went back to update those numbers and see if they still held up.
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I always show my work, but I’ll explain it tooPhoto: Steve DaSilva / Jalopnik
First, we’ll lay down the facts we know. The Roadster can hit 60 in “less than one second,” which definitionally means a max of 0.99 seconds. Out of the generosity of my heart, this is the number we’ll work off, for an acceleration figure of 2.763 gs. We know from the spec sheet that the Roadster claims 10,000 newton-meters of wheel torque, but we crucially don’t know the car’s weight. We do know the battery weighs about 1,800 pounds on its own, while estimates for the car’s weight range from 3,500 pounds to 4,100. I went with 3,900, as it’s both within that range and the approximate weight of a Nissan GT-R — a solid benchmark for acceleration.
First up, we need to calculate how much force the car can provide from its own electric drivetrain. Using that 10,000 Nm figure and the size of the tires (visible in some of the press photos, if you really zoom in) we can calculate out that the electric drive provides 27,435 newtons of force — enough thrust to bless a 3,900 pound car with 1.58 g of acceleration. That’s nothing to scoff at on its own, but it’s not enough to hit that 0.99-second goal. That’ll require an additional 1.183 g, provided by Musk’s other other other other company: SpaceX, with its compressed-air tanks cold air thrusters. For that, we’re going to look back at Dr. Stephen Granade’s work from 2021:
How effective are cold air thrusters, though? The rocket equivalent of fuel efficiency is called “specific impulse”. The higher a rocket engine’s specific impulse, the more efficient it is. Specific impulse is measured in seconds, which sounds weird until you realize that specific impulse is the answer to the question, “How many seconds can a specific engine, using a specific fuel, accelerate its own mass at one g?” The Falcon 9’s first stage uses engines with a specific impulse of 280 seconds at sea level.
A cold air thruster using air? Since air’s mostly nitrogen, I’ll use the specific impulse for a nitrogen thruster: about 70 seconds.
That’s…not very fuel efficient. But is it enough? To figure that out, we need to see how much thrust we need and, based on that, how much air the thrusters will use up pushing the car with that amount of thrust.Another word for “thrust” is “force”, and force is equal to mass times acceleration. I’ll assume the Roadster speeds up at a constant acceleration, which probably isn’t true but is close enough for my purposes. To get to 60 MPH in 1.1 seconds, the car needs an acceleration of a touch over 24 meters per second squared, or nearly 2.5 g. Going back to high school physics, we know that the force required will be that acceleration times the car’s mass. The battery pack may be around 800 kg, so I’ll assume that the car will be around 1600 kg. That means the car needs nearly 39,000 newtons of thrust to reach that speed.
However, the thrusters aren’t the only thing pushing the car. The wheels and powertrain can supposedly get the car to 60 MPH in 2.1 seconds. To do that, they must provide around 20,000 newtons of force. Assuming the thrusters don’t make the tires lose their grip, that leaves 19,000 newtons of force for the thrusters to provide.
Stephen and I differ in our early math (things like the car’s weight, and the amount of force provided by the electric drive) but those differences actually roughly balance out. His calculations led to a 19,000 newton deficit, while my 1.183 g deficit requires 20,254 newtons — close enough that the rest of the math barely changes. So, let’s take a look at what that looks like in real life:
A rocket’s thrust equals its specific impulse times g times how fast the rocket engine expels mass. To produce the amount of thrust we need, the thruster has to throw out nearly 27 kilograms of air every second. The Roadster will supposedly use 10 thrusters instead of just one, but that just means that each thruster will throw out 2.7 kilograms of air each second. The total required air per second stays the same.
(By the way, the air will come out of the thrusters at some 1,500 mph. Don’t change lanes too close in front of another car when you’re firing those thrusters!)If you’re only going to use the thrusters to get to 60 MPH over the 1.1 seconds, you’ll need 30 kg of air. At normal air pressure, you’d need a tank the size of a shipping container. But Tesla is using compressed air stored in a SpaceX pressurized vessel, known as a COPV. The SpaceX COPVs hold nitrogen at 6,000 psi. At that pressure, you can get the air you need into a 55 liter container.
55 liters is equivalent to 15 gallons. That’s not bad! A COPV the size of a small home water heater would hold that much. Tesla plans on taking out the two back seats to make room for the COPV (), which I estimate would leave room for about 140-150 L tank.
However, being in the neighborhood of plausible isn’t the same thing as being practical. The pressure inside the COPV will drop as air goes out of the thruster, so you’d want more than 55 L of air. Worse, though, will be refilling the tanks. Tesla has suggested that they’ll use an electric pump to re-fill the tanks:
The trick is to find a portable electric air compressor that can refill the tanks to their pressure of 6,000 psi. Worse, the higher the output pressure, the slower it fills a tank. You find these high pressures in SCUBA tanks, so I too a look at SCUBA tank air compressors. HPDMC makes one that has a working pressure of 4,500 psi. It would take two and a half hours to fill our 55 L tank. It also sucks down 3,000 watts. That’s a lot of power, but you could swap it out with one from BEAMNOVA or Orion. They only use 1,800 watts. Of course, now it would take four hours to refill the tank.
You may think of compressors like those found in garages and workshops — loud, rattly, and inconvenient — but don’t worry, the compressor needed here isn’t the same situation. Most garage air compressors only pack air down to about 150 to 200 psi, far below the 6,000 that Roadster owners will be shuttling around directly behind their heads.
This is all the kind of theoretically possible but realistically absurd thinking that Musk seems to love — promising to bring science fiction into reality, regardless of whether or not it’s actually a good idea. The Roadster may, in theory, if it ever releases, hit 60 miles an hour in under one second, but the costs of doing so are so great that it would never be worth it.
A version of this article originally appeared on Jalopnik.
