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, scaling 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 doing this!