There’s a science demonstration thing where a ping pong ball is accelerated to mach 1 speeds by the simple process of letting a vacuum rapidly re-pressurize.
If scaled up, how would the physics react? Would the ultimate speed be increased, stay much the same, decrease for some reason?
From the link:
Why yes, yes it is. It is also faster than anything else at low speeds.
Seriously, how did that sentence get by an editor?
The maximum speed of the projectile can’t be greater than the speed of the air behind it. That air speed can be modeled based on the pressure ratio between atmospheric pressure and the pressure in the vacuum chamber of the gun (and, in the case of the gun featured in your video, the geometry of the converging-diverging nozzle used to further accelerate the air jet).
The more massive your projectile (and/or the smaller the cross-sectional area), the longer the gun barrel needs to be in order for the projectile’s speed to more closely approach its theoretical maximum. A ping pong ball is pretty hard to beat in terms of having a large cross-sectional area and a low mass; that’s why the Purdue gun is able to achieve Ludicrous Speed with a reasonable barrel length.
IIRC, Mythbusters played with this and found that after a certain barrel length speed of the projectile started to drop off. It may have been that their vacuum source wasn’t large enough though.
Because it’s a quote.
It’s really no different than typical guns shooting bullets, or a BB gun. What matters is the pressure differential, and the vacuum ideally provides for the low pressure side to remain at low pressure unlike real guns that have to force air out of the barrel. Sufficient air pressure on the high pressure side will accelerate a projectile past Mach 1 if high enough. Pneumatic potato guns can do this, the potato is carefully located in the barrel with a volume of air behind it that gets rapidly compressed when the barrel is pressurized creating extremely high pressure. Doing the same thing with a vacuum on the low pressure side would get velocities several times the speed of sound. Another approach could use a shorter barrel on the low pressure side. The barrel on the high pressure side converges behind the projectile so that the high pressure air increases greatly in velocity before it meets the projectile.
Some aspects of the idea are used for real physics experiments. Not so much the accelerating of projectiles, but generating fast gas flows. Although there is only a tiny moment in the video, you can see them installing a rupture disk in the pressure chamber. Essentially what they have is a chamber of compressed air, that when the disk ruptures ejects into the vacuum side, and drives the ping-pong ball down the evacuated barrel, where it emerges through a second rupture disk. The tweak is to add the compressor/expander.
If you want to build a real system to test things at hypersonic velocities you can indeed just scale a lot of the ideas up. Queensland University have had a facility for decades that has a number of such devices. They get up to Mach 10. That is serious. Useful to test things like scram-jets. Well at least test a scale model for a few milliseconds, but that can lend significant understanding to the problem.
ETA - note in the UQ system, it is only the gas flow that is hypersonic - there is no projectile.
“919 miles an hour” is a quote. But the bit about a jet fighter at low speeds is not-- That’s down to the writer of the article. And is stupid.
Sorry, I typed the OP at like 5 am. I should have clarified that by “scaling up”, I meant something like a 3 meter tall tube over x kilometers, with a human capsule inside.
How fast/far could we launch our soon-to-be-flattened victims?
As in Hyperloop?
Funny, my nephew just accepted a job with them starting next week. 
I built a small version of one of these at home, with maybe a half-meter barrel. I didn’t measure the speed but the ball traveled “instantly” as far as my eye was concerned. Took me a while to find the ball.
When I first heard about the idea, I was a bit confused as to how you could break the sound barrier. Come close, sure, but break? But then I thought about it more and realized: the speed of the air particles isn’t exactly mach 1, but rather a distribution close to that value. Some particles will be slower; others faster. As the air accelerates down the vacuum, the fastest of the air particles will outrace the rest of them. The overall pressure will go down, but their average speed will go up. The ping-pong ball is so light that it’s not really limited by the pressure so much as the ability of the gas particles to catch up with it.
One experiment I wanted to try was to put a giant bag of hydrogen on the entrance end. No, not to ignite it, though that could be fun too. The hydrogen is still at one atmosphere (it’s just contained in a flimsy bag), but the average particle speed is much higher than with nitrogen or oxygen. It should enable much higher speeds.
Yes, but with a controlled, rapid pressurization.
Not just stupid, but F-16 Fighter Jet is like triple redundant.
You could put that fancy nozzle in a non-evacuated spud gun, pump the reservoir up to 15psi on the gauge (i.e., 1 Bar over chamber pressure), and get similar results (maybe a tiny bit slower, because of the input air dragging against the chamber air, but should be pretty close).
40mm grenades from the likes of the M79 and M203 use a similar principle, just using a bit more than atmospheric pressure to fill the vacuum.
Projectile speed always starts to drop off after a certain barrel length, because of friction. I remember an article in one of the firearms periodicals some years ago where they tested a wimpy little pistol round in barrels of various lengths, and it went faster as barrel length increased up to a certain point, and then started to slow down again – i.e., the same cartridge in a 3" pistol is slower than in a 7" pistol is slower than in a carbine is slower than in a rifle, but once you get beyond the standard rifle-barrel length of 30" or so, friction between bullet and barrel becomes a problem.