The secondgeneration Tesla Roadster is back in the news after Elon Musk introduced that the automotive would hit 60 miles an hour in lower than a second. That is practically a full second sooner than the current record-holder, which received me questioning: Is it really attainable? I crunched some numbers to get the reply: It’s technically doable, however it will be so inconvenient as to make the entire endeavor not value it. Let’s run down what I discovered.

Again 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 located that it may theoretically occur — if Tesla changed the rear seats with an enormous pressurized air tank and a compressor. With this new declare, although, I went again to replace these numbers and see in the event that they nonetheless held up.

I always show my work, but I’ll explain it too

I all the time present my work, however I’ll clarify it too
Photograph: Steve DaSilva / Jalopnik

First, we’ll lay down the info we all know. The Roadster can hit 60 in “lower than one second,” which definitionally means a max of 0.99 seconds. Out of the generosity of my coronary heart, that is the quantity we’ll work off, for an acceleration determine of two.763 gs. We all know from the spec sheet that the Roadster claims 10,000 newton-meters of wheel torque, however we crucially don’t know the automotive’s weight. We do know the battery weighs about 1,800 pounds by itself, whereas estimates for the automotive’s weight vary from 3,500 pounds to 4,100. I went with 3,900, because it’s each inside that vary and the approximate weight of a Nissan GT-R — a stable benchmark for acceleration.

First up, we have to calculate how a lot drive the automotive can present from its personal electrical drivetrain. Utilizing that 10,000 Nm determine and the dimensions of the tires (seen in a number of the press pictures, if you happen to actually zoom in) we are able to calculate out that the electrical drive gives 27,435 newtons of drive — sufficient thrust to bless a 3,900 pound automotive with 1.58 g of acceleration. That’s nothing to scoff at by itself, however it’s not sufficient to hit that 0.99-second objective. That’ll require a further 1.183 g, supplied by Musk’s other other other other company: SpaceX, with its compressed-air tanks chilly air thrusters. For that, we’re going to look again at Dr. Stephen Granade’s work from 2021:

How efficient are chilly air thrusters, although? The rocket equal of gasoline effectivity is known as “particular impulse”. The upper a rocket engine’s particular impulse, the extra environment friendly it’s. Particular impulse is measured in seconds, which sounds bizarre till you notice that particular impulse is the reply to the query, “What number of seconds can a selected engine, utilizing a selected gasoline, speed up its personal mass at one g?” The Falcon 9’s first stage makes use of engines with a selected impulse of 280 seconds at sea degree.

A chilly air thruster utilizing air? Since air’s principally nitrogen, I’ll use the precise impulse for a nitrogen thruster: about 70 seconds.

That’s…not very gasoline environment friendly. However is it sufficient? To determine that out, we have to see how a lot thrust we want and, primarily based on that, how a lot air the thrusters will dissipate pushing the automotive with that quantity of thrust.

One other phrase for “thrust” is “drive”, and drive is the same as mass occasions acceleration. I’ll assume the Roadster quickens at a relentless acceleration, which most likely isn’t true however is shut sufficient for my functions. To get to 60 MPH in 1.1 seconds, the automotive wants an acceleration of a contact over 24 meters per second squared, or practically 2.5 g. Going again to highschool physics, we all know that the drive required will likely be that acceleration occasions the automotive’s mass. The battery pack may be around 800 kg, so I’ll assume that the automotive will likely be round 1600 kg. Meaning the automotive wants practically 39,000 newtons of thrust to succeed in that velocity.

Nonetheless, the thrusters aren’t the one factor pushing the automotive. The wheels and powertrain can supposedly get the automotive to 60 MPH in 2.1 seconds. To try this, they need to present round 20,000 newtons of drive. Assuming the thrusters don’t make the tires lose their grip, that leaves 19,000 newtons of drive for the thrusters to supply.

Stephen and I differ in our early math (issues just like the automotive’s weight, and the quantity of drive supplied by the electrical drive) however these variations really roughly steadiness out. His calculations led to a 19,000 newton deficit, whereas my 1.183 g deficit requires 20,254 newtons — shut sufficient that the remainder of the maths barely adjustments. So, let’s check out what that appears like in actual life:

A rocket’s thrust equals its particular impulse occasions g occasions how briskly the rocket engine expels mass. To provide the quantity of thrust we want, the thruster has to throw out practically 27 kilograms of air each second. The Roadster will supposedly use 10 thrusters instead of just one, however that simply signifies that every thruster will throw out 2.7 kilograms of air every second. The full required air per second stays the identical.

(By the way in which, the air will come out of the thrusters at some 1,500 mph. Don’t change lanes too shut in entrance of one other automotive while you’re firing these thrusters!)

If you happen to’re solely going to make use of the thrusters to get to 60 MPH over the 1.1 seconds, you’ll want 30 kg of air. At regular air stress, you’d want a tank the dimensions of a transport container. However Tesla is utilizing compressed air saved in a SpaceX pressurized vessel, generally known as a COPV. The SpaceX COPVs hold nitrogen at 6,000 psi. At that stress, you may get the air you want right into a 55 liter container.

55 liters is equal to fifteen gallons. That’s not unhealthy! A COPV the dimensions of a small residence water heater would maintain that a lot. Tesla plans on taking out the 2 again seats to make room for the COPV (), which I estimate would depart room for about 140-150 L tank.

Nonetheless, being within the neighborhood of believable isn’t the identical factor as being sensible. The stress contained in the COPV will drop as air goes out of the thruster, so that you’d need greater than 55 L of air. Worse, although, will likely be refilling the tanks. Tesla has instructed that they’ll use an electrical pump to re-fill the tanks:

The trick is to discover a transportable electrical air compressor that may refill the tanks to their stress of 6,000 psi. Worse, the upper the output stress, the slower it fills a tank. You discover these excessive pressures in SCUBA tanks, so I too a have a look at SCUBA tank air compressors. HPDMC makes one that has a working pressure of 4,500 psi. It will take two and a half hours to fill our 55 L tank. It additionally sucks down 3,000 watts. That’s numerous energy, however you could swap it out with one from BEAMNOVA or Orion. They solely use 1,800 watts. In fact, now it will take 4 hours to refill the tank.

It’s possible you’ll consider compressors like these present in garages and workshops — loud, rattly, and inconvenient — however don’t fear, the compressor wanted right here isn’t the identical scenario. Most storage air compressors solely pack air right down to about 150 to 200 psi, far under the 6,000 that Roadster homeowners will likely be shuttling round immediately behind their heads.

That is all of the sort of theoretically attainable however realistically absurd pondering that Musk appears to like — promising to deliver science fiction into actuality, no matter whether or not or not it’s really a good suggestion. The Roadster might, in principle, if it ever releases, hit 60 miles an hour in underneath one second, however the prices of doing so are so nice that it will by no means be value it.

A version of this article originally appeared on Jalopnik.


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