That expression doesn’t look nice, but at least now the energy calculation is in terms of things that we actually know or can estimate. All we need to do is convert our estimates from imperial units to metric and we are all set. Using a wave traveling at 20 miles per hour, with these estimations I get a wave energy of 16 million joules.
Is this a lot of energy? Here are some quick numbers for comparison. Suppose you pick up a textbook from the floor and put it on a table. This takes roughly 10 joules. Your smartphone’s battery stores about 10,000 joules. A full tank of gasoline, or 12 gallons, is about 1.5 billion joules.
OK, now that we know the energy it takes to make a wave, we have some options for how to create this thing. Suppose you use an electric motor to pull the hydrofoil. If the motor is 85 percent efficient, then you will actually need to put 19 million joules into it in order to get 16 million joules into the wave.
The average price of electricity in the US is 23 cents per kilowatt-hour. Power is a measure of how fast you use energy, and we can calculate that as P = E/ΔT, where T is time. If energy is in joules and time is in seconds, then the power would be in watts. So 1 kilowatt-hour is the energy you would get running 1,000 watts for 1 hour (3,600 seconds), or 3.6 million joules. That’s how much energy you get for just 23 cents. If you want 19 million joules, it would cost you $1.23.
What about a gasoline-powered hydrofoil? In the US, you normally buy gasoline by the gallon; in other parts of the world, it’s sold by the liter. Gasoline stores about 34 million joules per liter (or 128 million joules per gallon).
However, a gasoline engine has a much lower efficiency than an electric motor. At best, it would be 40 percent efficient. That means we would need to use 40.9 million joules, or 1.2 liters (0.32 gallons) of gasoline. Assuming you pay $3 per gallon (which is a bit lower than the US average in July 2023), that would cost close to $1, or about the same price as an electric-generated wave.
Now, suppose you are really off the grid and wanted to make waves with human power. Obviously you can’t pull a hydrofoil by yourself. But maybe you could pedal a bike to raise some large mass using pulleys, and once the mass had enough energy, you’d let it fall and pull the hydrofoil. Let’s say this whole system is 50 percent efficient, so that you would need to produce enough energy to store 32 million joules.
Let’s suppose that you can output 100 watts of power. How long would it take you to get that much energy stored for your wave? Let’s calculate this: