Oof -- this is a tough, but interesting one.
Typically, when faced with such a problem --
you do the experiment (which I don't recommend) or
scale it down to where you can. However,
introduces problems as well as where do you get
the models, what medium do you use as the water
density cannot be scaled... I'd suggest asking a
simpler problem -- does the tire pattern make a
difference in hydroplaning? You could make a
test setup with a bicycle where you can measure
the normal force to the tire slippage as a
function of the weight against a rotating, wet
surface with drag. (i.e. a rubber or nylon wheel,
with a continuous water drip, or with the lower
wheel in a bucket. Then you can determine if the
tire is hydroplaning by measuring how easy it is
to move normal to the motion and to the normal
force as a function of how fast the bicycle is
being pumped. In this case the round wheel is
approximating a flat road, while the weight of the
bicycle could provide the downward (normal) force.
If you had a few different tire patterns,you could
test how well they hold up. -- you will get wet
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