Rocket Ascents... Can divers breach like a fish (split from Accident in Mich)

[MXGratefulDiver]

Whoops, missed the decimal point. 83 feet in 10 seconds, or 8.3 ft/s, is the random number NWGratefulDiver came up with and Rec Diver used to get 6 mph.

Errrt ... what I was saying is that even if you were going that fast ... which really, REALLY FAST for a diver ... you wouldn't be able to breach.

The rest was someone else's creativity.

Now go fill out y'er profile ...

... Bob (Grateful Diver)

 

[roakey]

BTW the noise you hear is the sound of reality intruding into this thread...

Well, I introduced the same calculations as you a hundred replies before (reply #55 vs your #155) so you can see how much reality helped this thread...

Roak

 

[mccabejc]

Okay, we've been dancing around having to figure out the maximum speed that might be achieved underwater when the diver goes ballistic, so let me give it a shot:

First, assume that at depth (say 90ft. or so) the diver’s wetsuit is completely compressed, so he has to add air to his BC to make himself neutral. Suddenly his BC inflates completely, and overpressurizes so the safety valve blows.

So at that point he has a net positive buoyancy force on him and he starts to ascend. Let’s say that the net force is something like 50lbs. positive, which is probably kinda typical for the lifting force of a typical BC (measured at the surface). As he accelerates, the water starts to counteract his motion with a drag force, which increases exponentially with his speed. At some point the buoyancy force and the drag force become equal, and the diver ascends at a constant (“terminal”) velocity. To complicate this a bit, as he ascends his wetsuit decompresses, and maybe the buoyancy of his filled BC increases, and therefore the net buoyancy force will increase. But to simplify for now, lets assume there’s a constant positive buoyancy force of 50 lbs all the way up. We can play with the numbers later to see how much the answer changes. So the challenge is to figure out what this constant terminal velocity will be.

Now, using our heads and doing a little bit of “reasonableness review”, we can imagine a fully suited diver in a pool (tank and all), and we tie a rope to him and try to drag him thru the pool with 50lbs of force. How fast do you think you can drag him? Just off the top of my head, I can’t imagine that 50lbs of force can get the guy moving very fast. Can 50lbs of force drag him thru a 30ft. pool in 1 second? No way. How about 15 feet in 1 second? Doubt it. Too much drag. My guess is that you could probably pull the guy less than 5 feet per second at best with 50 lbs of force.

So at least we have an idea of what a reasonable terminal velocity might be. Now we can put some numbers to it to get a better idea.

We’re assuming that the forces on the diver are a net positive buoyancy of 50 lbs, and a net negative drag which increases with velocity squared. There is an equation for terminal velocity (normally used for objects flying thru the air, but we can substitute water I think), which is:

velocity = sqrt (2*buoyancy force/drag coefficient*water density*frontal area)

I substituted “buoyancy force” and “water density” for the equivalent air values.

I did some checking on the internet and found some values for the drag coefficient (which is a function of shape of the travelling object) for different shapes. A bullet is around 0.3, and a flat plate is around 1.3. So let’s pick a number more than a bullet, but less than a flat plate. We’ll chose 0.5, since we look more like a bullet going thru the water than a flat plate. At least I do...

Regarding frontal area, if you look at a diver swimming at you (tank and all) the frontal area is something like 1 square foot. Ballpark.

Water density is a constant, about 1027 kg per cubic meter.

So we can convert to Kg and meters and solve. Buoyancy force is 50 lbs, or 22.7 kg. Water density is 1027 kg per cubic meter. Frontal area is 1 square foot, or 0.092 square meters. And drag coefficient is 0.5.

Plug in the numbers and we get a velocity of about 1 meter per second, or 3 feet per second. Makes sense. If we double the buoyant force, we get 1.39 meters/second, or 4.5 feet per second.

So from 100 ft, how long does it take to get to the surface? Using 3 feet per second it would take 33 seconds. Using 4.5 feet per second it would take 22 seconds, which sounds more reasonable to me. Takes into account the increase in buoyancy as you near the surface due to wetsuit decompression, etc.

And when he hits the surface going at 5 feet per second, and buoyancy goes to zero and gravity takes over against the 180 pound diver with 75 lbs of gear, can he clear the water? Doesn't seem likely, does it?

Does this sound reasonable to anyone?

 

[pilot fish]

Finally broke down and gave us a profile, eh pants!?

Sort of. What part of Denial?

 

[Firefyter]

Sort of. What part of Denial?

Who says the profile is accurate? :06:

 

[bradshsi]

Well, I introduced the same calculations as you a hundred replies before (reply #55 vs your #155) so you can see how much reality helped this thread...

Roak

All too true. Sorry I missed your calculations since I "only" read back to the 7th page or so... I should remind myself to be more thorough in future.

On the plus side at least our calculations agree

Now if only the other posters would use the 21/22 ft/second figure sanity might be possible if not enirely realized.

And when he hits the surface going at 5 feet per second, and buoyancy goes to zero and gravity takes over against the 180 pound diver with 75 lbs of gear, can he clear the water? Doesn't seem likely, does it?

Exactly since roakley (post #55) and belatedly myself in post #155 confirmed that you need about 21 ft/second

 

[rockjock3]

For those of you that can not exceed 2 feet of clearnace from the water, I would suggest that you consider losing some of your extra weight before continuing to dive. Hell, I have seen whales clear more than that at the zoo.

First, whales are much more streamlined than ANY diver wearing gear or being butt-naked.

Secondly, have you ever felt a whale's or dolphin's skin? Much smoother than ours and not all the pores to increase surface friction.

Thirdly, how fast to you think whales and dolphins swim when they clear the water? They are not swimming along at the 5-10 mph (being very generous here) that you MIGHT attain with runaway ascent. Killer whales, the ones jumping at seaworld, have a max swim speed to about 30mph and dolphins have one of about 22mph. Both use about all of that, along with all the other benifits that they have such as a streamlined body, to clear the water.

Another thing, I am a new diver but still know a lot of information and a little bit of physics also.

A breach based on a runaway ascent will not let you clear the water due to common sense. A person swimming up with this purpose can possibly swim 3-5 miles an hour with fins. A person doing this would not have any gear on and be as streamlined as possible.

Herein lies the problem. A person on an uncontrolled ascent is ascending from air in somekind of device. Again, unless that device is a solid plastic hull that is shaped like a rocket and has an open bottom for air to escape it will expand. Being that the flotation devices most likely to be in question are either a BC or a drysuit here is the problem.

If your are on an uncontrolled ascent with a poor fitting drysuit (to get as much air as possible then you will notice that you don't ascend faster than your suit, or BC for that matter. Well, as the air in the suit expands one of two things is going to happen. First you suit or BC, if it starts as being filled all the way, will expand to the point of either exhausting air or splitting at a seam. The second thing that might happen, if the device is filled less than full capacity, the air will expand put it will also flatten out at the top. Your feet will not fill with more air and streamline you. Your suit will carry most of the air at the top and flatten along the topmost parts as you ascent. This is due to the friction of the water pressing down on your suit and the air bubble pushing up on your suit.

Remember, the air no longer reacts the same if it isn't floating free in the water, where it will maintain a round shape. In your suit on an uncontrolled ascent it will flatten at the top, to some degree, and increase drag.

I would say if you can sand down your skin, coat it with some kind of supermooth lubricant, ascend from 100 feet with no gear that you might clear the water if you can swim at 35mph or so to the surface at 2200fpm then you might have a chance of clearing to your waist or knees.

****By the way, did anybody every do the math on RecDiver's supposition?******

Here is the funny part.

100 feet in 10 seconds. That equals 600fpm which comes out to 36000 feet per hour. Now take that old standards 5280 feet per pile and divide to come up with a mind-bending 6.818181818...mph. Now I know the reason that the DPVs only go 3-5 MPH. If they went the magic speed of 6.8 they could rip you out of the water and put you back into the boat. Sorry recdiver, you couldn't jump as high as your head, in air, at 7mph. Nobody EVER cleared the water with their fins ascending 100 feet in 10 seconds.

To give you an idea of the difference. A whale or dolphin, only swimming 20mph, will ascend 1760 fpm or 30 feet per second. A person would have to ascend 880fpm to attain a speed of 10mph (100feet in 6.5 seconds), 1320fpm for 15mph (100feet in 4.5 seconds), and 1760fpm for 20mph (100feet in 2.4 seconds). None of which are fast enough to get a poorly streamlined, not meant for swimming in water, human, even halfway out of the water.

 

[derwoodwithasherwood]

Too bad we have all these physicists but no rocket scientists. So many have come so close to the real answer and yet allowed it to slither through their fingers.

As the diver ascends with the stuck inflator air in the BC is expanding. Where do you think all this air (stuck inflator button + expansion) is going? Out the bottom dump valve of course! Now it's not just a BC, it's Flash Gordon's rocket pack! And since the rate of expansion and therefore the rate of discharge will vary inversely with depth, the diver will actually accelerate continuously with maximum acceleration occuring in that critical last 30 feet. All these calculations of negative acceleration due to gravity once the surface has been reached neglect to account for the continued thrust caused by the stuck inflator button blasting the ascendee well beyond the surface of the water.

:rofl:

 

[grouchyturtle]

Sorry I didn't read the whole thread. Waaaaaaaaaay to long.

What if the seas were really snotty, and in addition to a malfunctioning inflator, the diver was going up on the line, then just as they reached the surface they grabbed the line and at the same time a nice 5 footer rolled under the boat?

 

[do it easy]

i was so tired of all these asssumptions, that i finally tried this in open water...

just to give myself all the advantage, i greased myself up with vasaline, then put on my wetsuit, zeagle ranger bc, al80, and DIR snorkel. i dove down to 100ft and looked up at the glowing light above. i peed in my wetsuit and farted to appease the scubaboard gods, and started kicking like heck. i could feel my blood boiling and my lungs burning from the embolism as i rocketed past 40', but i really kicked hard with my twin jets and by the time i broke the surface i was unconscious. my buddy was videotaping, and he said i breached the surface with plenty of room to spare. i'll have to get him to post the video some time...