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# Stone skipping. Was: Re: bending of object thrown into pool

"Yes. In particular, wouldn't an object thrown into a pool also tend
to "bounce" off the surface and hence might be expected to bend away
not toward the surface, assuming it penetrates at all? Again, someone
should actually try this, I bet the book writer did not!"

http://news.nationalgeographic.com/news/2004/01/0107_040108_stoneskipping.html

[first appropriate I found]

Some time ago (fifties or sixties?) Sci. Am. had an article on stone skipping, including I think, on sand.

bc

I found it: Yes (sand) August 68 [C. L. Strong] Koths used the "Edgerton" method.

Carl E. Mungan wrote:

This is a response to all of the excellent comments in last night's

What if you shoot the arrow upward from below the water surface? Does
it speed up? (Robert Cohen)

Good point, it wouldn't. That seems a pretty damning argument against
a Snell's law analog.

I saw references to "throwing" and "launching" and other
highly dynamic verbs.

If you actually _throw_ a stick into a pool, you must
first worry about how it *behaves* in absolute terms,
before you worry about how it appears.

The behavior will be verrry complicated. In addition
to plain old buoyancy there will be hydrodynamic
forces such as lift and drag, which in turn depend on
the angle of attack and the sideslip angle etc., not
to mention dependence on Reynolds number etc. etc. etc.

In contrast if you have a static stick just sticking
into a quiet pool, it is straightforward to determine
the appearance by ray-tracing. The result is a
combination of Snell's law and projective geometry. (John Denker)

I did in fact mean the object is *moving*, crossing the boundary from
one fluid to another. But focus on the bending as it crosses the
interface, not the longer term effects of drag and so on. Perhaps

I'm assuming that it's the object's trajectory, and not the object
itself, that is bending. Think of a toy car with wheels that don't
turn. If you roll the car from a tile floor onto a carpet, at an
oblique angle to the boundary, the car will turn. This is because
the wheels on one side are traveling at a different speed than the
wheels on the other side. You might get the same effect by sliding
a piece of two-by-four across the tile floor. It'll tend to spin
around when it hits the carpet.

Nice examples!

A ball, on the other hand, has only one contact point and so would
be less likely to turn as it crosses the boundary.

Agreed, size and shape of the object are important.

Should "would be less likely to" be replaced by the more categoric
"would not" in this sentence?

All of the above assumes that there is no lip or crack or other
place that causes bouncing at the interface.

Yes. In particular, wouldn't an object thrown into a pool also tend
to "bounce" off the surface and hence might be expected to bend away
not toward the surface, assuming it penetrates at all? Again, someone
should actually try this, I bet the book writer did not!

In the case of tossing stuff into a pool, the trajectory will be
altered by the water resistance.

This is not obvious to me. What about your above example of the ball?
Is a difference in fluid viscosities *alone* enough to bend the

cut