Liquid mountaineering physics

Now, I realise the liquid mountaineering guys are just having a bit of fun, keeping us on our toes, on tenter hooks, hanging by a thread, wondering whether or not they’re nothing more than a viral ad campaign for sports apparel or headbands. But, aside from some hippy dude a couple of thousand years ago with a penchant for loaves and fishes there has been no other serious claim to walking, if not running on water.

Anyway, I asked a physicist friend what he thought about the liquid mountaineering video (watch it here). And he was just as skeptical as I about its veracity. He pointed out that riding atop water is certainly possible, but only if you have a big enough and steady enough thrust:

Water skiing is possible because the combination of the high density of water, low density of air, and the forward thrust provided by a powerful outboard motor provides enough lift at the boundary between air and water to keep a person above the water. If one shortens the skis to the length of a shoe, skiing is still possible albeit more difficult. This has definitely been done. (Barefoot waterskiing is even possible, but you have to go even faster than in conventional water skiing).

In “liquid mountaineering”, the lift is intermittent rather than continuous, and the lift mechanism relies on the difference in density between the fluids as opposed to using Bernoulli lift as well. My hunch is that it will require more power to sustain a person on the surface in “liquid mountaineering” mode than in “water skiing” mode. A human can deliver about 1 horsepower peak and 1/4 hp of sustained power output. That doesn’t sound like it’s anywhere near enough to run any great distance on the surface of the water, given that skiing normally calls for tens of horsepower.

There is another factor to consider in the physics of liquid mountaineering, and that is viscosity. Water’s higher viscosity compared to air means that, if you ease into it very slowly, it behaves like the liquid you expect, but if you hit it at very high speed, it might as well be a brick wall.

It should be possible to construct a simple physical model of liquid mountaineering by approximating the runner’s feet as a pair of two pistons acting at the boundary against an infinite sea of dense viscous fluid. Assuming a realistic stroke speed, is the resulting force sufficient to buoy the human? The underlying modelling must already have been done by fluid mechanics people to study automotive shock absorbers and similar devices. I believe such modelling will show that a human runner does not have anywhere near the necessary power to sustain himself on the surface. If the deficit were only a few percent or even tens of percent, one could argue that improved physique, technique, and equipment might overcome the deficit. However, the power shortfall is likely to be orders of magnitude. Increasing the footprint would help, but at the cost of some increase in awkwardness and atmospheric drag. In any case, I would recommend the liquid mountaineers try the water equivalent of Canada’s snowshoes (invented by natives to walk over snow) if they are to have any hope at all. (And I bet they will fail anyway.)

There are ample demonstrations that hitting water at truly high speed is like hitting a wall. Perhaps the most spectacular example is British, the crash and death of daredevil Donald Campbell on Coniston Water in the lake district. In January 1967 he lost control of his racing boat “Bluebird” at over 500 km/h while attempting to set a new water speed record. The Bluebird was powered by a turbojet with 16 kN sustained thrust. The video is on Youtube: http://www.youtube.com/watch?v=fL3Vi6iyHOU

The physics of liquid mountaineering, it seems, just doesn’t add up. The physics of a submerged platform or gangway and a decent pair of grippy running shoes on the other hand…or supernatural powers and a flowing robe and beard…or perhaps golfer’s charm? That’s another story…