Gravity and Diving

[puternut]

I have been wondering about the following problem and can't seem to get an answer.

When we go off a diving board into the pool we go under the surface so far before returning to the top

Now lets assume a pilot has had to jump out of his plane at 1,000 feet. Assuming he makes a good entry into the water (feet first will probably increase his life expectancy) and his RAF issue boots protect him from the actual impact, how far under the surface would he go and would he be able to easily swim back up

Like wise at 10,000 feet 30,000 feet? Would he go so far down that he would have difficulty getting back up.

I believe there is a finite speed that we travel through the air when we are descending in freefall so at his speed can we expect to survive the dunking assuming we survive the water entry

[ChuckFickens]

Falling from much over 1000ft would make no difference as you would have reached terminal velocity so you would just fall for longer and not get any faster, depending on the position you took while falling terminal velocity would be anywhere from about 120MPH to about 200MPH.

How hard you hit the water (so how far down you'd go and what chance you had of surviving hitting the water) would largely depend on what the surface of the water was like at the time. hitting a perfectly smooth body of water at even 125MPH would almost certainly kill you straight away. if the surface of the water was very choppy there would be far less surface tension which would increase the chances of surviving the fall considerably.

As for how deep you'd go, I have no idea from 1000ft, but I know if you want to dive from 65ft (20M) the minimum recommended depth of water by the world diving federation is 15M and you'd be hitting the water at about 25MPH, assuming that they have allowed 5 meters extra for safety on that I'd work out that water would be decelerating you at about 6m/s2.

Now working that the other way and taking an impact speed of 150MPH (and assuming you did keep arrow straight all the way down) it seems to indicate that you would get to about 370meters under the water (!!)

(I'm hoping somebody can come and disprove that figure, as that seems really rather too deep!)

[Hopkirk]

Reading Chucks answer about how far under you would go, I suggest that the shape of your feet would act as a sort of rudder.

This would turn you in the water, and stop you continuing in a straight line downwards.

Mind you at 150 mph, this turning action would no doubt snap something.

[ChuckFickens]

You are quite correct hopkirk, in reality hitting the water feet first it's actually really hard not to rotate as you are going through the water (I can vouch for this having done a few cliff jumps/dives in my younger days), also just as a side point, when hitting water from any decent height feet first you really need to be clenching your bum cheeks hard together for fairly obvious reasons!

Hitting the water head first (which is done with arms locked straight above your head and fingers tightly clenched together) gives a much straighter path down through the water and a smoother entry into the water if you get it right, but does increase the chances of breaking your neck if you get it wrong.

(an interesting question puternut)

[Toureman]

I have done many dives from a ten metre board, this is the highest in competitions.

If you are only a few inches out of alignment when you hit the water it really hurts though no injuries.


You have a high likelihood of being killed by any impact with the water when jumping or diving from over 1000 meres !

[Toureman]

metres !

[puternut]

My initial idea came from hearing of these people who fall x thousand feet and survive. Now if you hit land then you may put a decent size 'crater' but won't go that far further down.

However with water, be it feet or head first, and assuming you are still alive after the actual water entry, I wondered if you would go so deep as to be unable to return up (even if you could hold your breath for that long). I have heard of submariners coming up from great depths but that is only one-way. In my scenario you would need to have sufficient air for both the down 'cycle' as well as the up 'cycle'.

[Hopkirk]

You need to fill your lungs as full as possible before impact, so your chest acts as a buoyancy aid.

If your lungs are empty, you have to work very hard just swimming upwards.

[Vagrant]

I don't agree with Chuck's figures - dropping from 20 metres, final speed is 20 metres per second (45 mph as opposed to 25).
Decelleration in 10 metres is therefore 20 as opposed to 6.
This would give 112 metres at 150 mph as opposed to 370 - still seems far too deep though.

[ChuckFickens]

Thanks for the correction Vagrant, I was looking at it and thinking something didn't seem correct about my figures (it was late, that's my excuse :))

I agree that even 112meters still seems very deep, but it's far more believable than over a 1/3 of a KM!

[bednobs]

but hang on, you wouldn't just stay in an arms and legs locked together position once you'd hit the water, would you?

[Vagrant]

Another way of looking at it - decelleration at 20 metres per second is 2g. If you turned horizontal (with buttocks very firmly clenched) as soon as you were submerged, you might incur enough g to kill you.
If you got into such a position to increase the drag to 5g (about as much as normal people can tolerate) you would descend 44 metres.

[DaveKeene]

I can't do the maths but I can explain why your figures are too high,

The pilot has an intial force of mass x velocity-squared (say 80kg x 10m/s x 10m/s = 8000N)

The deceleration that occurs as he enters the water is due to the displacement of water (i.e. accelerating it out of the way). Obviously, for the pilot to survive, the water has to get out of the way pretty quickly (actually it doesn't, which is why it's like hitting concrete!).

In the time it takes him to enter the water (2m @ 10m/s = 0.2s) an equivalent _volume_ of water has to be shifted (say 100Kg since water is denser than the human body).

Ignoring many things, and assuming the water is shifted 50cms on average, then the energy lost is 100Kg x 0.5m/0.2s x 0.5m/0.2s = 100Kg x 2.5m/s x 2.5m/s = 625N.

So now the pilot has a residual force of 8000-625 Newtons = 7375N and hence a velocity of 9.6m/s.

Each subsequent 2m has a similar calculation with the energy lost decreasing at each step. If it were 625N at each step, there would be about 13 steps and a total depth of 26m.

Only when you get toward the end of his final journey does he reach a similar velocity to a diver which is why the earlier comparisons don't work.

And the 625N force applied to the pilot is enough to make his buttock clenching pretty pointless :(

People survive by falling from great heights by dropping into snow (air filled, not compact), or flexible tree branches - none of which have that initial massive deccelaration.

[factor-fiction]

Is that right DaveKeene- I wasn't aware that force= mv². I thought it was= ma. It was a long time ago though since I did science at school.