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Old 02-11-2010   #1
Redpaddle's Avatar
Newport, Oregon
Paddling Since: 1989
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physics of waterproof cameras

I had a friendly back and forth with a paddler out here in Oregon about dropping waterfalls and forces/pressures on waterproof cameras. The question was: "How high of a waterfall is big enough to stress the seals on a waterproof camera?"

this is actually a tougher physics problem than you think at first. If the camera is rated to 10 feet in depth, how high would the waterfall have to be such that you hit the bottom pool with enough speed to submerge you 10 feet deep?

it takes math skills beyond mine, but I know there are a ton of braniac engineers here with nothing to do at work, no water to paddle and no snow to ski.

For my calculations i was using a total mass (boat+ paddler) of 90 kg and disregarding any friction or properties of aerated water. One calculation by a friend put it at 8 meters high. is that close?

"Paddle silently, boof loudly"
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Old 02-11-2010   #2
Denver, Colorado
Paddling Since: 2002
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Ok here goes:

1) I do not have the math skills it is a very difficult problem hydrdymaics of the entry will play a big role in the depth

2) But is not just the depth you need to worry about. The seals are rated to withstand a set static perssure - when you enter the water at speed that is a dynamic pressure and that dynamic pressure may well past the seals rating at even a shallow depth of .5 feet.

good luck in finding the exact numbers


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Old 02-11-2010   #3
Fort Collins, Colorado
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You would also have to assume a total volume of the kayak and person.
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Old 02-11-2010   #4
Arkansas during the off-season Nomadic during the summers! :), Arkansas & Colorado
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This problem is very difficult to put a number on!

It is simply how fast will the camera hit the water!

But how fast is dependent on alot which makes it difficult.

Because the boat will hit the water first and the water will exert a reaction on the boat due to the volume of air etc...So technique has alot to do with the forces exerted on the seal by the water..Also depending on where the camera is located...boat is easier to make assumptions about, person very difficult!

The landing after drops is always less dense due to the churning water where as seals I believe are rated in calm water.

Water type and temp will also play a role.

Beause its very interesting and I know you probably want a number on it I'll give you a very VERY simplified version.

Just dropping a camera off a diving board assuming the camera is rated at 10ft = approx 85 N/sq in

Assume the seal breakage occurs immediately after impact..(.01s) and the mass of my camera, then a drop of nearly 1 meter would elicit an impact force equal to that which would penetrate the seal in calm water.

Disclaimer::Any other engineers out there don't give me crap for me EXTREME over simplification of the problem! Just having fun!
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Old 02-11-2010   #5
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Fort Collins, Colorado
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ENGINEERS!?!?! You want a physicist!

And if you ignore enough factors, this becomes a really simple problem. The question then becomes: which factors are ignorable? But for now, let's go into a little more detail on that 8 meters estimate.

Let's use conservation of energy (meaning that we will ignore any energy loss on impact and any friction once in the water - pretend that the paddler makes an absolutely perfect oregon tuck to get maximum depth). The paddler's energy just as they enter the water will be mgh where h was the height of the waterfall. The buoyant force (which we'll approximate as constant) will be equal to the weight of the displaced water; rho V g, where V is the volume of the boat and paddler. The total force will be this buoyant force and gravity. Recall that work is the change in energy, and work is the integral of F dot dx. The dot product switches the sign, and when the paddler comes to a stop at the instant of greatest depth d, we will have:

mgh = (rho V g - mg) d

so that

h= (rho V / m - 1) d.

When I used a mass of paddler +boat of 100 kg (since it's a round number), and a volume of .4 m^3 (which is a little over 100 gallons, since it also includes the upper body of the paddler), and recalling that rho = 1000 kg/m^3, I got about 9 meters for h.

Is this the "real" answer? No, of course not. First, the time spent at that depth is very short, which I don't think gives the water time to work its way through the seals. Second, the impact with the surface would steal a lot of the energy that we assumed, meaning that taller waterfalls would be safer. On the other hand, there's not just buoyant force acting on you after you land, there is often water moving down (from that waterfall you just ran) that will pull you deeper than impact alone would. That factor would make the height of the waterfall mostly irrelevant.

I think the only solution is to turn to experiment. Run the brown. Fred Gnorquest had a helmetcam when he ran Metlako a little while back. We should ask him if the seals held.

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Old 02-11-2010   #6
Redpaddle's Avatar
Newport, Oregon
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Now THAT'S what I'm talkin about! thanks Leif, sorry I didn't ask for a physicist first!

that is fascinating actually that only a 9 Meter height would be required to submerge something that big to 3 meters deep.

What you're saying is that maybe we need cameras that are rated on "waterfall height" like "huckable up to 50 feet!" yeah, I'll call Canon this afternoon.

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Old 02-11-2010   #7
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The Ranch, Colorado
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I also have a level 68 Druid in World of Warcraft. Factor that!

(no seriously, this was one of the cooler discussions on the buzz, even if I only learned what a coefficient is last semester).
"self-aggrandizing jackass" - it says it right on the label
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Old 02-11-2010   #8
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x, x
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looks like someone has been in the forest killing boars.

and to think i put mine in a pelican case........ just a joke, you guys are smart.

but think about it, there is a good chance it is protected in your pfd some where, how does this factor?
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Old 02-11-2010   #9
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Edge o' the Dust Bowl, Oklahoma
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Very simple answer to this problem: Hand your camera to one of your boating buddies. You want them shooting you from every angle anyway.
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Old 02-12-2010   #10
Arkansas during the off-season Nomadic during the summers! :), Arkansas & Colorado
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Hey Leif,

Are you a physicist? I never knew if so.

SAD day for me...I just interviewed for a position in Mass near Boston. I am finishing my PhD in Biomechanics and will teach most likely in the East...Hoping for WV but who knows...Of course there is the chance I might bum around colorado another year I like the yakin here too much. Maybe we should write a grant to test this topic on some of the major brands!!

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camera, physics, waterproof camera

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