# How fast could a Mini Cooper go in a vacuum?

Lord Evulz just stole the Earth's atmosphere. Our hero must race his trusty old Mini - which he had already prepared to be airtight, to ensure the tires do not explode, with pre-packaged oxygen to supply his fuel with, etcetera... - to the last escape rocket before his air supply runs out.

Assume regular Earth highway conditions - (with no traffic because everybody asphyxiated to death) - with the only difference that there is no air resistance. What are the limiting factors on the car's top speed? And what velocity might be attained?

If the specific model matters much, take the 1977 British Leyland Mini 1000 - because it is Mr Bean's car and I fully expect him to find a way to drive it into orbit.

• Disclaimer: I was having much difficulty deciding whether this question belongs in the Physics stack exchange, the Worldbuilding one, or this one. I went here because I expect more members of this SE to know how fast the different parts of the car can physically rotate - but if it's not that suitable for here, I'd like to know. Nov 16, 2019 at 13:05
• Most likely, the limiting factor will be the maximum engine RPM. Even a formula 1 race engine can only run up to about 15,000 RPM, compared with the red line speed of around 7,000 for your engine. Nov 16, 2019 at 13:52
• With no air resistance, then the force the engine is able to put out is only countered by static friction and then rolling friction. The complexity comes from the fact that all the moving pieces contribute some amount of friction. I don't understand the second question - are you asking what typical max speeds can be expected? Nov 16, 2019 at 16:11
• @blacksmith37 The OP says there is "pre-packaged oxygen to supply his fuel with, etcetera." Nov 16, 2019 at 16:37
• Engine cooling would be a problem. You'd manage about ten miles before overheating. Nov 16, 2019 at 16:52

TLDR: Top speed increases from 81 to 89 mph.

The air drag force is 0.5 x air density x drag area * speed^2. (https://en.wikipedia.org/wiki/Automobile_drag_coefficient). Therefore drag power is 0.5 x air density x drag area * speed^3. The cube term on speed is very important, i.e. doubling speed requires 8 times more power to overcome air resistance. At highway speeds, air resistance becomes dominant.

According to https://www.automobile-catalog.com/auta_details1.php, the 1977 Mini has an Estimated drag area of 0.788 m^2

Doing the math, this means that at the top speed of 81 mph, overcoming air drag requires about 31 HP. According to same website, the 1977 Mini has 39 net HP. Therefore, at top speed, 79% of the engine's power is being used to overcome air resistance.

So, in theory, removing air resistance would give a huge amount of extra available power. However, based on the same site again , max horsepower occurs at 4750 RPM, whereas the engine redline is 5200 rpm. Therefore, only a modest increase of 9% is possible. Top speed would be 89 mph.

To achieve a higher max speed, you would need to redesign the gearbox to take advantage of the reduced air drag. I.e. give a higher max velocity for the same engine speed by using a different gear ratio.

• A lot less than I was expecting, but thanks for providing the calculations :) Dec 29, 2019 at 10:58

In an atmosphere, the top speed is probably limited by air resistance more than anything, but in a vacuum it would be limited by other factors. Rolling resistance is a major effect that would definitely limit speed. As discussed in the comments, engine rpm would also be a limit if using stock gear ratios.

According to a quick google search, the top speed of the Mini is 81 mph stock- actually quite impressive for a British economy car from the 70s. Whether the limiting factor proves to be rolling resistance or engine redline, it won't increase much.

I would expect less than 100mph, probably like 95 before the decreased power at high rpms, rolling resistance, and internal friction(wheel bearings, CV joints, transmission) conspire to prevent you from reaching higher speeds. This, of course, assumes that your engine hasn't melted down yet from lack of cooling, but I trust Mr Bean to have installed a sufficient system(ice tank in the cabin?)