I don't know the physics of skipping in detail,
but I can make a guess based on my knowledge of
fluid mechanics. You probably know that water
(and other fluids) has a "surface tension."
Basically, the surface tension means that it costs
energy to create new surface area. This fact
means that the water likes to minimize its surface
area. A consequence of this is that some objects
that are denser than water (and would ordinarily
sink) will rest on top of the surface of the water
if they are placed there carefully. By placing the
object carefully on the surface without disturbing
the surface too much, the object must overcome an
energy barrier in order to sink. The origin of
this barrier is the need to create additional
water surface area.
So, back to skipping.
If an object impacts upon the surface of water
with a small enough vertical velocity, then it may
be the case that it does not have the energy
(momentum) needed to break through the surface of
the water (overcome the surface tension). The
surface may act like a spring as the object hits,
and eject it back into the air. A flat object
would work best because the force of impact would
be spread over the largest area possible. I think
that the larger the contact area of the impacting
object, the more surface area must be created for
the object to pierce the surface,
and thus the
easier it is to skip.
Lastly, I think that the
horizontal velocity plays some role also. Namely,
I think that if the object is moving too slowly
horizontally, the friction during impact will
cause the object to "stick." That is it will come
to rest and will sink.
I can't find anything
about skipping in the books on my shelf, but you
have made me interested in this topic, and I will
see if I can find anything elsewhere. I will give
a warning to your student that I suspect that this
is a very complicated fluid mechanics problem (I
could be wrong). The theory is probably very
difficult, but experiments can probably be
The important variables would of course
be object shape, object size and density,
(possibly) object surface roughness, object
velocities (horizontal and vertical), and the
surface tension of the water or fluid being used.
Skipping stones is a tough one.This is closely
related to the 'slamming' problem that probably
first arose with seaplanes during WWII and has
continued in understanding slamming associated
with ships in heavy seas when the bow may come out
of the water altogether ad then slam back down.
The are conditions for which most ships are not
designed so there has been a lot of interest, but
not so many solutions.
Large forces are exerted
by the water on the body seeking to enter it.
Basically the density of the fluid and the density
of the body are not so different so it is not
unlike two billiard balls colliding. In the case
of the skipping stone it approaches the water at a
low grazing angle and so it rebounds much like two
billiard balls. If the angle is too low though,
the viscous losses associated with the fluid
resisting the motion will probably slow it down
enough that it may not escape the surface. If the
angle is too high the fluid swallows the object;
there is too much enrgy loss in the inelastic
nature of the 'collision'. Much of the kinetic
energy is lost to dissipation and the object can
One of our former graduate
students worked a great deal on this problem and
has written several technical papers on this
problem, but these are highly mathematical papers
that seek to solve for the fluid motion around the
object entering the water surface. In this case,
if my memory serves me,he looked at a cylinder
slamming into a fluin at rest. There are many
subtlties associated with this problem especially
related to the point where, water, solid and gas
all meet. This point migrates. The bottom line
is that very large faorces arise due to the need
for fluid to move out of the way of the object,
these forces are of short duration and difficult
to measure and/or model.
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