Re: What is the acceleration required to flip a jet ski backward 180 degrees?

Chris,

This is another one of those questions that is easy to ask, but to actually
solve it we'd need a lot more detail in the problem description. Let me try
to explain why. 

First, what keeps a boat from tipping over in the first place? When a boat
is sitting in water in an imaginary perfect world with no wind or waves, it
has a force pushing it down (gravity), and a force holding it up
(buoyancy). In this perfect world, the center of buoyancy could be directly
below or above the center of gravity in order for the boat to be in
equilibrium (ie not moving). But the world is not perfect, and when the
boat encounters a force that pushes it out of equilibrium (what someone
working on stability would call a "perturbation"), the location of the
center of buoyancy relative to the center of gravity changes. Basically the
force causes more of the boat to submerge on one side and less on the
other. Now that the center of gravity and center of buoyancy are not on the
same vertical line, those two forces create a couple (also called a moment
or torque). If this couple is in a direction that opposes the perturbation,
it will tend to bring the boat back to equilibrium, and if not, it will
push the boat farther out of equilibrium. In the first case, the boat is
stable, but in the second case it is unstable and it will quickly tip over
if even a small force bumps it slightly out of equilibrium. As a useful
thought exercise, you can draw a simple boat hull (as if you were looking
from the front or back) with a center of gravity well above or well below
the center of buoyancy, and then imagine it tilted slightly to one side.
Which way will the resulting couple act? What is the effect of lowering or
raising the center of gravity? Obviously, boats are designed to be stable,
but I haven't given you all of the complexity of how they are designed that
way. In fact the subject is quite complicated so I'll leave it to you to
explore it on your own (or with the help of a friendly physics
teacher/professor, perhaps). 

So what would we need to determine if a jetski would tip over in a given
direction due to the application of a given force? Obviously we'd need to
know the strength and location of the force, but we'd also need to have a
good understanding of the overall stability of the jetski. For that, we'd
need to know the shape of the hull so we could calculate the center of
buoyancy for any given displacement and angle of tilt (you might see this
called "heel"). We'd also need to know where the center of gravity is, and
this gets really complicated since the boat is small and we cannot neglect
the rider's mass. If the rider moves, so does the center of gravity. When
the perturbation occurs, the center of buoyancy will move some amount based
on the shape of the hull. The center of gravity may also move (if the rider
leans, for example). The new location of these two points will determine
what direction and how strong the "righting moment" is, and if it is in the
right direction (it should be for any real boat, since it will have been
designed to be stable), and also strong enough to overcome the moment
created by the perturbing force, then the boat will not tip over. Your
question basically amounts to "how much force do I need to overcome the
righting moment" and that obviously depends on the jetski design, the
rider's mass, and the rider's location. Life just isn't simple when you get
right down to it.

I'm sorry that I couldn't answer your question precisely, but I hope the
discussion of boat stability (even though it's a very brief one) has helped
you. The bottom line is that the jetski designer(s) would probably have
designed it so that it wouldn't tip backwards in normal use, so you'd
probably have to do a combination of things to get it to tip. I'm not
recommending you try it, but if you hit full throttle, stand up, lean
backwards, and maybe hit a wave at the same time, it would probably go. If
they laugh at you as you're climbing back on the jetski, just tell them you
did it in the name of science. 

David Coit
Aerospace Engineer
Naval Air Warfare Center - Weapons Division

References:
Google "boat stability"