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Terminal velocity

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CB27
1390060.  Thu Sep 16, 2021 9:59 am Reply with quote

Years ago there were several claims about squirrels possibly being amongst the few non flying mammals who will be able to survive an impact from any fall because they have a low terminal velocity due to their stretchy body, fluffy tail and relatively light body (of course some conditions could cause squirrels to die on impact from short distances, but we're talking about perfect conditions).

However, it seems some clever bods out there came up with a height from which squirrels certainly won't survive at impact, and that height is... 4,800 miles! The argument being that (ignoring the lack of air, freezing temperatures and perhaps accidentally headbutting an eagle), the fall from that height would take so long that the average squirrel will have starved to death shortly before impacting on the ground.

However, another set of clever bods have managed to calculate that at great heights the pull of gravity is lower, hence the squirrel will have a lower terminal velocity, and that perhaps the true figure is closer to 3,080 miles.

So next time you find yourself with a spare set of juggling squirrels while standing at a great height, remember what your safety height is for health and safety measures...

 
Alexander Howard
1390071.  Thu Sep 16, 2021 11:30 am Reply with quote

'For a brazen anvil falling down from heaven nine nights and days would reach the earth upon the tenth: and again, a brazen anvil falling from earth nine nights and days would reach Tartarus upon the tenth.'

That gives us a location of heaven according to Hesiod. Ignoring the effect of other heavenly bodies, with F = GmM/rē, and s=ut+1/2atē, the force of gravity increasing with a reduction in r, our differential equation is, erm - help!

 
PDR
1390080.  Thu Sep 16, 2021 12:14 pm Reply with quote

Even if we ignore the lack of air, the radiation and the various temperature issues (cold and hot) it's much more involved than that, and I suspect the gravity variation would have a pretty negligible effect.

The "terminal velocity" concept only starts to come into play once the falling object encounters air which is actually thick enough to present significant air drag. A fag-packet number for that would be about 100,000 feet or 20 miles.

Even at this altitude the air is very thin so the terminal velocity is likely to be a thousand miles an hour or more, and its only when you get down to the last 20,000 feet or so that the air will be thick enough to reduce the terminal velocity below 100mph or so. The oft-cited terminal velocity of a squirrel* (usually stated as 23mph) only really applies for altitudes below about 5,000 feet (1 mile).

But the whole question (like the conveyor-belt runway one) is something of a non-sequitur because it's just too selective about which real-world aspects it ignores.

Drop a squirrel from 1,000 feet it will almost certainly live.

Drop it from 20,000 feet and it might live, but if it falls through cloud and icing layers it's likely to accrete a lot of ice that would increase it's density to the point where it's terminal velocity could rise to over 100mph so the fall would probably kill it.

Drop it from 40,000 feet and it would die. Whether through asphyxiation or hypothermia is something of a moot point, but its furry cadaver would then probably accrete ice and accelerate anyway.

Drop it from 100,000 feet and it would die. Initially it would asphyxiate and perhaps explode before freezing, but soon the shock-heating of its supersonic fall through the upper atmosphere would then probably cook it. Passing through 40,000 feet the cooked squirrel would then be frozen, so if someone was quick with the packaging this could form the basis of a gourmet frozen-meal enterprise.

Above that things become rather more speculative. There would be as near zero pressure & oxygen as makes no difference, so the asphyxiate/explode options are likely to dominate. But the initial acceleration (in vacuum) would be unfettered, so it could get to velocities of over 10,000mph (assuming zero lateral velocity). This would definitely super-heat the squirrel's carcass when it entered the atmosphere. How hot it would get depends on the actual velocity and thus the actual height it was dropped from so we have a range of outcomes from complete vaporisation to a "well-done" option on the gourmet food enterprise menu.

Now we are told in the question, which is one of the frequently-distributed popular-sci ones (like the conveyor-belt runway) that infest the internet, that we should ignore the problems of the squirrel freezing or suffocating and just focus on the time it takes to descend. So presumably the assumption is that the squirrel has equipped itself with a thermally-controlled, heat-resistant pressure-suit.

The suggestion is that the squirrel would then starve to death before touch-down, but I have to point out that any squirrel with the intellectual and financial wherewithal to obtain and use suitable PPE would surely also have thought of bringing a packed lunch?

PDR

* not to be confused with that of a swallow which (as evry fule knwo) depends on whether it's african or european and how many coconuts it may or may not be carrying


Last edited by PDR on Thu Sep 16, 2021 2:49 pm; edited 1 time in total

 
CB27
1390082.  Thu Sep 16, 2021 12:38 pm Reply with quote

I seem to recall it was claimed that space smelled a bit like burned sulphur, but I now wonder if it's overcooked squirrel smell from all those squirrels getting cooked on re-entry from numerous tests on their terminal velocity...

 
AlmondFacialBar
1390089.  Thu Sep 16, 2021 1:18 pm Reply with quote

If we assume a spherical, frictionless squirrel, on the other hand...

https://twitter.com/profbriancox/status/1142962082155024386

:-)

AlmondFacialBar

 

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