The Dynamics of Hydroplaning

A hydroplane is pushed to the surface of the water by a good blast of air into its sail. There it scoots quickly across with little resistance from the water. In many ways, this motion of a hydroplane on the surface of the water is much like that of a block sliding down a ramp. But instead of a purely bulk force like gravity pushing the block down the ramp, blowing transfers a force to the sail and the motion is horizontal.

This makes for another difference, the force on the sail generally decreases as breath gives out so a hydroplane does not continue to accelerate as a sliding block might. Though small, the resisting friction at the surface is enough to make the boat travel near its terminal velocity, like many blocks. This is unlike a Grand Prix car that has wheels to reduce the friction even more. Their terminal velocities are almost always much faster than the fastest speeds they ever attain on the track.

Never-the-less, to make a useful model, we will assume that the force on the sail is constant and we will not attempt to model the transition from sitting in the water to hydroplaning when the race starts. We will assume the boat hydroplanes fast enough from the start not to make any difference in this race model.

We also make the big assumption that hydroplaning on the water can be reasonably well modeled by the simple friction expression F = nW where F is the friction force, n is the friction coefficient and W is the weight of the boat pushing down on the water.

What happens when the breath stops blowing? That part of the model is also derived but is of less value since the boat will abruptly stop when the surface tension of the water is no longer able to hold the boat's weight. The point where that happens is not explored on this page.

In the models, the equations of motion are used to derive the physical parameters; energy, speed, time and distance.

The Race Model

The simple race model derived is a constant breath-force approximation for an accelerating hydroplane. deceleration is handled as a zero-force conditioning of the same equations of motion. As you will see, the equations have the same form as those of the simple closed race model for the Grand Prix. In fact, replacing the mechanical car drag with the water surface drag; the car's aerodynamic constant with the boat's equivalent; and the car's gravitational force with the sail's breath force with a few adaptations of parameters to the regatta context, gives the boat's race equations.

However, using these equations is more difficult! They are not as deterministic for the boat race as for the car race. The assumptions made to derive the boat models "cheat" too much. So when they are used, they must be used carefully and in sequence for each breath taken.

In a 10 foot hydroplane race, the captain usually finds it sufficient to blow only two times, pausing only once to take a breath. Race times for 5th and 6th graders have been clocked better than 2.5 seconds! An adult friend of the author has been clocked in at 1.8 seconds!

So we have to at least model:

1. The Initial and Subsequent Breath Acceleration of the hydroplane
2. The Deceleration of the hydroplane

However, if the race you wish to model takes more breaths, then the final breath above must be followed by another deceleration, breath, deceleration, etc.. But we can also answer a lot of questions about blowing technique and boat limitations from just analyzing the acceleration equations and the deceleration ones.

Modeing Sail Drag

Sail drag for regatta boats is essentially the pressure drag of the air diverted around the sail. We know this because the Reynold's number for the fastest regatta hydroplane of raingutter size lies in the laminar range; there is no possibility of air turbulence.

A quick evaluation of the Reynolds number for a fast boat begins with,

RN = vLp/ug for p/ug = 43.10 s/in2

The fastest hydroplane regatta boat travels about 6 feet per second and that's probably generous. So let v = 72 in/s. By the usual rules, the hull length is 6 inches and that does nicely for the scale length, L. Put these factors together to get,

RN = 72*6*43.1 = 18,619 which is much less than 100,000, the upper limit for guaranteed smooth air flow.

Pressure drag is easy to model but not always easy to find the forces and constants in the expression. The general expression for any type of pressure drag operating through a center of pressure is,

Pressure Drag = cpAv2/2

In the models above for the motion of hydroplanes, you will see terms that look like this general one but they will use different symbols that relate more closely with the parts experiencing pressure drag.