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Posted by Ed Hahn on September 13, 2000 at
06:21:29:
In Reply to: No, no... not quite my meaning... posted by Mike
Bilow on September 13, 2000 at 04:47:15:
Posted from Host: webproxy3.mitre.org (128.29.4.1)
You are correct when you say that the deceleration is caused by the increase in pressure in moving between air and water. BUT, this is still governed by the laws of hydrodynamics - and you have a fundamental mistake in your assertions - the PRESSURE caused by the motion in water is constant, NOT THE FORCE. Therefore, the actual force will vary greatly for a large surface area object vs. a small surface area object.
In my example, the pressure associated with entering the water from 40mph (my example) is constant - 3.4 atmospheres worth.
Given a human body with (say) 4 square feet of surface area, this leads to a deceleration FORCE of 28,788 lbs. For a 200lb man, this is an instantaneous deceleration of 144 times the force of gravity.
HOWEVER - note that the factor which is most important here is the SURFACE AREA affected by the pressure - pressure by definition is force per unit area.
Since a watch is a small object, the force, therefore, is going to be much smaller - by orders of magnitude. If we assume that the watch's vulnerable area is 0.01 square inches (this seems more than reasonable - the actual AREA between the caseback and case is pretty tiny because the junction is very thin), this is a half-pound of force that needs to be held back.
To repeat, it's the pressure that remains constant in this scenario, not the forces involved.
Finally, I will disagree with one of your main sentences here: a human body is not going to survive a sudden depth change of 100m - while I honestly believe that a properly designed watch will survive without even noticing.
Ed Hahn
Aeronautical Engineer
: Obviously, if you hit the water with enough force to kill you, you don't care about your watch. My point, however, is that it is possible to enter water with enormous forces. The force necessary to compromise a seal on a watch is probably a great deal smaller, by orders of magnitude, than it would take to kill a person.
: When you enter the water aggressively, say in a hands-first dive, the water must exert force on your in order to decelerate you fairly rapidly. This force is, by definition, distributed over some area as pressure. In an extreme case, of course, this could crush the watch and kill the diver, but it takes nowhere near that amount of force to compromise the seals. The area of impact is therefore critical: if you distribute the force over a wider area, then the pressure at any point is much less.
: -- Mike
:
: : Some very good points here. I suppose a small bit of elastomer would probably provide
hysteresis for even a simple depth guage such as that in a watch, so you could be correct
about watch depth guages working like other diving depth guages. But we don't really know
for sure. Ludwig did say that his seemed to be quite responsive with some sort of test
rig, so that may counter your argument for his particular watch.
: : You don't seriously think that anyone is concerned about his watch after a fatal impact with the water surface do you? ;-) Basically, I'm pretty sure that if you survive an impact, your watch will probably only barely have noticed it -- remember we're trying to reach levels of forces that threaten the watch yet don't kill the human. The most extreme way to enter the water would seem to be in a hands first dive, with maximum velocity water rushing by and around the crown/pushers. But Ed (I think) showed the math for the terminal velocity of a human in freefall and the uninteresting results on a watch. Does anyone know a Venezuelan cliff diver? Perhaps we could get some real world results. Anyway, it seems highly unlikely to me that swishing water around the crown/pushers at these pressures and velocities is a big deal.
: : And water is very different than a wall. It's only sort of like a wall to a belly flopping human because a human in that conformation is also sort of like a wall, and of some appreciable extent. A watch is a much smaller, much less flat thing. The biological effects on a big flat soft human smacking the water are very different from the mechanical effects on a small lumpy hard watch in the same situation.
: : Oh, and BTW, I don't need crumple zones in my '76 Lincoln Continental four door sedan -- because all you folks have them in your newer cars! ;-) I just better not run into another beast like mine. ;-(
: : --cn
: : Conrad C. Nobili Conrad_Nobili@Harvard.EDU Harvard University NDTL/NOC
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