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Re: [Phys-l] surfing



On 07/09/2009 12:50 PM, Carl Mungan wrote:

But I don't really get it - surfers don't seem to change altitude
much as they surf. Thus, the kinetic energy they acquire doesn't seem
to come from (direct) change in gravitational PE.

During the steady state, i.e. excluding things like the start-up
transient, they don't need to change altitude at all, which is
consistent with the fact that they're not changing KE at all.

In the frame comoving with the surfer, which is also the frame
comoving with the wave, the KE remains zero during the steady
state.

The force exerted by gravity in concert with the slope of the
wavefront can be calculated by the principle of virtual work.
Keep in mind that only /virtual/ work is involved; the water
is effectively a constraint, nonmoving in our chosen frame, and
there's a famous theorem that says a nonmoving constraint never
does any work. Similarly the drag force of the water does no
work. Drag is very dynamic from the point of view of the water,
but in the surfer frame, we are talking about (force) times (zero
distance) which is zero work.

You (the surfer) can modulate (reduce) the gravity/slope force
by surfing across the face of the wave, rather than straight
down the gradient. Again the principle of virtual work applies.
Such modulation is important because you want to keep the
gravity/slope force in balance with the hydrodynamic drag force.

I don't see a problem here.

I assume they "suck
it" out of the water wave somehow (presumably at the expense of the
wave losing some amplitude or speed, or more likely both as they're
probably connected to each other).

Switching attention now to the start-up transient, you need to
be careful about what reference frame you are using.
1-) Using the frame comoving with the surfer is possible ... but
it's tricky, because you're talking about an accelerated reference
frame.
2-) Using the beach-bunny frame of reference is also tricky,
because then you have a huge moving constraint, and the
aforementioned theorem does *not* apply to moving constraints.
(Hint: a bat changes the energy of the batted ball.)
3+) Therefore I recommend the frame comoving with the wave. In
this frame, the surfer starts out with some KE and /loses/ it as
he moves up the slope of the wavefront. Nice and simple. I
don't see a problem here.

As always, you can have all sorts of problems if you analyze the
motion partly in one frame and partly in another.

==============

The _stability analysis_ is also interesting. What happens if you
get fast and outrun your wave? What happens if you get slow and
get overtaken by your wave?