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If We Built A Building On The Moon...


JT!

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...and the building had the same air pressure as earth, what would be a humans terminal velocity? Would we be able to skydive with no parachoot and land on the ground safe? Or would we be able to dive into water after reaching terminal velocity?

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Assuming a human has a terminal velocity on earth of 125mph (a quick google said it was 117-125) and weighs 80kg (guesstimate) then I make their terminal velocity on the moon with the same air density to be 51mph.

I make 51mph the speed you'd get up to in falling 52.9m on earth. That's a lot higher than I think a human would survive (equivalent of falling from the 16th floor!), so I'd have to say no, you couldn't land on your feet from terminal velocity on the moon.

I'm not sure where 20mph came from, but even that would be debatable, I make it that you'd reach 20mph after 19.5m on earth, which is still a hell of a long way to fall, (equivalent of the 6th floor) but I'd guess could be just about be borderline survivable if you were seriously lucky and had immediate medical attention.

Edited by RobinJI
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51mph terminal velocity? Wow I thought it would have been much less with such low gravity.

Yeah, the thing is that wind resistance isn't directly proportional to the objects velocity, it's a square function, so the results can be a little counter-intuitive at first glance.

It's like a 100bhp car might have a top speed of 120mph, but if the same car had 50bhp, it wouldn't be maxed out at 60mph, it could probably still manage something like 90. It's not a direct relationship. (That's a pure guess, not calculated, but hopefully it seems less counter-intuitive. With the moon situation, just think of the gravity as the cars power, it doesn't make as big difference as you'd initially expect.)

Edited by RobinJI
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... so it should be pretty easy to work out.

Yeah, the thing is that wind resistance isn't directly proportional to the objects velocity, it's a square function, so the results can be a little counter-intuitive at first glance.

You lied to me Danny!

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40mph is pretty damn fast to hit the ground. I make that the equivalent of falling from 32.7m up on earth, so about 10 stories up. I'd say the survival rate from that sort of a drop would be pretty damn low just hitting the floor with nothing to cushion you.

According to a random google, 30 feet (9.14 meters, or about 3 stories) is the cutoff where you're more likely to die than survive. I guess that's with a random unexpected fall, and I'd guess it's relatively easy to survive that sort of fall if you're fit, healthy and expecting it. I bet it'd hurt like hell, but be survivable.

Edit, out of interest, it looks like the reason we ended up with different terminal velocities is that I calculated the humans CdA to be 0.41 from a terminal velocity of 125mph in 9.81m/s^2 gravity and an air-mass-density of 1.225 (air at 15deg C), while you're using a given CdA of 0.581 and an air-mass-density of 1.29 (air at 0deg C). They're both in the same sort of ball park though, we're both equally right, just starting from different data.

Edited by RobinJI
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I had it in my head terminal V would be so low you'd be able to jump from anything and just land safely on your feet.

So how about landing it water, safe at 40-50mph?

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well if gravity is 1/6th that of earths, then you would be able to jump from 6 times higher and land fine, as that is a proportional relationship. So you'd be able to walk away from some pretty epic falls. That 30 foot cut-off I mentioned would become 55 meters, so you'd be able to survive falls from the 18th floor fairly easily, especially considering how much longer you'd get to prepare for impact.

Although the terminal velocity's still relatively high, if you assumed it was 45mph, it'd take you 245 meters to get up to that speed, and take 12.3 seconds. Plus I bet you could get that velocity down a fair bit by spreading your self out, you might even be able to get it down to speeds that are survivable with a decent landing technique, which would make you right.

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Assuming a human has a terminal velocity on earth of 125mph (a quick google said it was 117-125) and weighs 80kg (guesstimate) then I make their terminal velocity on the moon with the same air density to be 51mph.

That's a rather large assumption, given that there isn't really an atmosphere on the moon. For all intents there's a vacuum so no atmosphere to slow you down. I think this means acceleration would be virtually linear, no terminal velocity. It also means your parachutes would be rather useless.

EDIT: Oh wait, we've got an artificial atmosphere within the building? Ignore me...

I'm not sure where 20mph came from, but even that would be debatable, I make it that you'd reach 20mph after 19.5m on earth

20mph seemed a bit slow, I think you mean 20m/s ;)

v^2 = u^2 + 2as

v^2 = 0 + (2 * 9.8m/s/s * 19.5m) = 382

v = approximately 19.5 m/s = approximately 43.5 mph.

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I'm not sure what I did there, but I got 20mph from what JT said in his post above mine. When I said it would be debatable I meant you surviving hitting the ground at that speed, I was just calculating what height it was equivalent to falling from on earth, from JT's 20mph. Looking at it again I make it 8.144m to reach that speed falling on earth, not 19.2.

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Can you skydive inside a building?

Can you skydive OFF a building. The moons graivty is low so that makes for building really easy for building.

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