# Walking on Water

1. Dec 17, 2007

### wysard

How fast does a 100kg person with feet 300 cm^2 feet have to move to avoid sinking in water? ( assuming the water is 1 gram per cm^2 at STP )

Or does it not matter, the person will eventually sink, it's just a matter of how far out they get before the inevitable happens?

2. Dec 17, 2007

### mgb_phys

Last edited by a moderator: Apr 23, 2017
3. Dec 17, 2007

### wysard

Nice link, but let us assume that unlike a stone the trajectory of a human does not "flatten" with time. ie, you do not lift your feet less and less with each impact.

Secondly, I don't spin very well and can't imagine trying to run while performing some high speed piroutte.

Also, they have done measurements with differing thickness of stone, but do not incorporate (that I saw) the thickness and it's attendant alteration in mass and pressure footprint into the calculations given.

But a good starting point none the less.

4. Dec 17, 2007

### wysard

I apologize if my reply was somewhat obtuse or argumanatative. It was most certainly not ment to be so.

I realize that a hypothetical 100kg person must displace 100kg of water over the unit interval of time it would take for water to fill that space to remain "bouyant".

I just have no idea what that time interval would be. How long does it take water to fill a footprint say 1 cm deep? What is the coefficeint of pressure presented to the surface in the area given that gets lost in "slippage" around the edge of the foot?

These are the niggelling bits that confuse me and stop me from coming up with a general answer. ( I completely realize a specific answer depends on waay to many details, but just want an idea of how to get a good SWAG number for it)

5. Dec 17, 2007

### mgb_phys

The model just assumes that the stone bounces because of an elastic ollision with the water, the spinning is only necessay to stabilise the stone and the flattening only tells you when it will run out of energy.

The first part still works.
Work out how much momentum the body has when it hits the water, work out how much water you have to force out of the way to balance this momentum and how fats you have to do it.

6. Dec 17, 2007

### wysard

mgb, you mean the pU^2S bit?

where:
p = 1gm/cm^2
S = 300 cm^2

so U^2 = 1/PS => 1/300 gm cm^2 must balance 100kg * 9.8 m/s^2

Is that what you mean? (Think I'm following you)

7. Dec 17, 2007

### wysard

The way I figured it...

Take Senor Gomez. He weighs 100kg.

Now, to run across the water not sinking more than 1 cm he must displace his own weight in water. So...

100kg of weight / 300 cm of footprint yeilds 333.333 footprints of 1 cm depth

Given a human stride of 1 meter (yeah I'm reaching, but it makes the math nice)

means Senor Gomez can walk on water at about 333.333 m/s or about 1,200 km/h.