Running On Water...

[sanctus]

I read often updates from a fb-groub (in German) called "useless" knowledge, where I read amongst other that if you go 45000 km/h the a red-street light would be shifted to appear green. That would be easy to check. But another which I am wondering how it is calculated is: Jesus (or whoever) would have had to run at 75 km/h to "walk" on water.

 

Now I am wondering how one finds this result. Surface tension? Archimedes-force? And where comes the amount oftime spent in the same spot into the calculation?

[Qfwfq]

Now I am wondering how one finds this result.

IMO one does not find this result at all because I'd say it is hogwash. They must have reckoned it according to the dynamics of waterskiing, which can be done barefoot if you are expert enough, but it doesn't determine the velocity one must move over the water surface. You would need to make very fast running motions with your feet and in the right way, while moving forward little. This would give you some forward thrust and as you gain speed over the surface you would need to increase the rhythm of the limb motion.

 

Surface tension? Archimedes-force?

Neither. Only chance is the lift from skimming over the surface.

 

BTW do you know the joke about the physics prof. that was fined for going through a red light? That's probably the reason why some nerd took the time to work out the speed necessary for the Doppler shift.

[C1ay]

http://www.youtube.com/watch?v=Oe3St1GgoHQ

[Qfwfq]

Geez I wish I could afford to squander so much resources on something utterly useful like that! :lol:

 

I could however give them a few thoughts on how to improve their approach. They don't seem to get what counts more and what less. Most of all, unless you aim to reach the other side of the lake, increasing forward speed isn't important and doesn't help in keeping above.

[sanctus]

Neither. Only chance is the lift from skimming over the surface.

 

But isn't that Archimede? Or is it due to the inertia of water? I mean you don't sink because the water has to move away which is not instantaneous...in other words which forces (a part from the obvious one: gravity) are involved when you just skim the surface?

[modest]

Not sure where this would get us (probably nowhere) but it shouldn't be too hard to solve how fast a foot must move through water in order to support the weight of a person. I would assume that the ability to run across water involves feet plunging a few inches into the water and using the resistance that water provides against the foot to support the weight of the person... meaning that the water's drag force is the key element.

 

Drag force is:

 

[math]F_D = \frac{1}{2} \rho v^2 C_D A[/math]

 

for a foot moving through water: rho (density) is 997 kg m^-3, v is velocity, C_D (the drag coefficient) is roughly 1.0 and A (area) is roughly .02 m².

 

To hold a typical person against gravity requires roughly 590 Newtons making the velocity,

 

[math]590_{Kg \ m \ s^{-2}} = \frac{1}{2} \cdot 997_{Kg \ m^{-3}} \cdot v^2 \cdot 1 \cdot 0.02_{m^{2}}[/math]

 

solved for v... 7.7 meters per second or just about 28 km/h.

 

Of course, while one foot is pushing down in the water the other foot is pulling up out of it. If the upward-moving foot requires half the force of the downward-moving foot at the same velocity (a very first order approximation) then the relationship would be:

 

[math]590 = (\frac{1}{2} \cdot 997 \cdot v^2 \cdot 1 \cdot 0.02) - \frac{1}{2}(\frac{1}{2} \cdot 997 \cdot v^2 \cdot 1 \cdot 0.02)[/math]

 

which makes v out to be 'bout 40 km/h.

 

On land a foot speed of 40 km/h is not unreasonable, but moving feet through water is quite a bit harder, so... :shrug:

 

~modest

EDIT--->

 

I should add that I agree with Q that the question is sort of hogwash. I don't see any reason the velocity along the surface of the water has to be related to the ability to stay above the water.

 

A person who could move their feet fast enough to run across water could likewise run in place and keep from sinking without moving across the water at all. So, I don't think any relationship could be set up between speed and the ability to stay on the water.

[sanctus]

But the surface tension exists no? So why does it not come into play?

 

A guy in office also asked why cheetah can not run on water? Because although the feet are smaller it runs much faster... he said that as an argument that he thinks 75km/h is not enough..

[Qfwfq]

I would assume that the ability to run across water involves feet plunging a few inches into the water and using the resistance that water provides against the foot to support the weight of the person... meaning that the water's drag force is the key element.

I noticed those dudes are doing this, but it helps to defeat them because, as you say, they've gotta pull the foot back out too.

 

What I suggested is skimming each foot backwards across the surface. The idea is just like making a flat stone plane over the water. There's even a shot of this in the video so they must be musing on it, but without understanding the physics of it. :doh:

 

On land a foot speed of 40 km/h is not unreasonable, but moving feet through water is quite a bit harder, so... :shrug:

But your computations regard vertical velocity; try maintaining such a speed upwards, even without the drag of pulling feet back up.

 

I should add that I agree with Q that the question is sort of hogwash. I don't see any reason the velocity along the surface of the water has to be related to the ability to stay above the water.

 

A person who could move their feet fast enough to run across water could likewise run in place and keep from sinking without moving across the water at all. So, I don't think any relationship could be set up between speed and the ability to stay on the water.

Actually, I voted more for a compromise, so as to avoid the already disrupted surface, but as your forward speed increases it gets harder to have each foot skimming backwards fast enough. If you could keep it up long enough, you'd need to prevent speed from increasing too much, due to the forward propulsion that the skimming would give; you'd need a surface to give drag in the air. It would quickly become a tricky balancing act in any case, almost like those guys at the rodeo.