Wow this got way too long, but what the heck, I’ll post it (I get about a 1 cubic mile float to extract 1 GW from tidal power).

There is a lot of power in waves, but one thing to keep in mind is that the amount of extractable energy is proportional to the head (height difference):

https://en.wikipedia.org/wiki/Hydroelectricity

http://www.reuk.co.uk/Calculation-of-Hydro-Power.htm

https://en.wikipedia.org/wiki/Low_head_hydro_power

https://en.wikipedia.org/wiki/Tides#Example_calculation

http://www.infoplease.com/encyclopedia/science/tide-the-magn...

So a dam uses a high head/low flow rate, and tidal or wave power uses a low head/high flow rate.

I’ve seen a few dams built around coves that work like a lock, filling up at high tide and draining during low tide, running a turbine to generate electricity. But if there is only a 1 or 2 meter head, it takes a huge water current to make more than a few MW.

I’ve also seen these snake-like creations that are big floating drums with hydraulics between them, that bend with the waves. So the head is about the same, but the period is a few seconds instead of a day, so a lower current is needed. However, the amount of current they capture is so small compared to a dam that they only generate on the order of a few kW.

The idea of using a large float is certainly compelling. Off the top of my head, maybe it could work similarly to having a bag at the bottom of the ocean with a pipe connected to an artificial floating island on the surface. It would pull on the bag as the tide rises to inhale air into the bag, and then let it exhale as the tide falls. A turbine in the tube would generate electricity in both directions. Water weighs 1000 kg per cubic meter (62.5 pounds per cubic foot), so if we use the dam formula for 1 cubic meter and +/- 1 meter of tide, the float would travel 1 m up, 1 m back down, then 1 m down and 1 m back up, for a total distance of 4 meters every 24 hours. So I think we can use the dam formula:

power P = phrgk

density p = 1000

height h = 4

flow rate = volume/time = r = 1/(60 * 60 * 24) = 1.16e-5

gravity g = 9.8

efficiency k = .6

so:

P = 1000 * 4 * 1.16e-5 * 9.8 * .6 = 0.27 W/m3

As a sanity check, the amount of energy required to raise 1000 kg of water 4 meters is:

E = mgh = 1000 * 9.8 * 4 = 39200 J

So power is energy over time, so:

P = E/t = 39200/(60 * 60 * 24) = 0.45 W/m3

So at 60% efficiency, power = 0.27 W/m3

This is one of the reasons why the head is so important, because it takes remarkably little energy to raise a ton of water, literally.

So if we want a 1 MW plant, we’d need a float about 3.7 million cubic meters, which would be a sphere with a radius of about 100 meters by V = (4 * pi * r^3)/3, or about 600 feet across. It would also need a bag of similar volume anchored to the bottom of the ocean.

Since the pressure is reversed for the bottom balloon, it would take on the shape of a tetrahedron, so would need strong anchors holding 3 corners to the ocean floor, with one of the corners connected to the float by a tube. The 3 edges touching the floor would need to be sealed against water leaking in. A bit of an engineering feat..

To make it worth our while, we’d probably want a float 1000 times bigger, or 6000 feet across to generate 1 GW. I have a little trouble picturing a mile wide float, its surface area would be:

Area = 4 * pi * r^2 = 4 * pi * 1000^2 = 12.6 million square meters

Although this doesn’t seem that bad, even at a cost of $10 per square meter.

Now that I write this, maybe a better alternative to the bottom bag would be a steel cable connected by a pulley to the ocean floor, that comes up on land and moves a meter or two forward and back each day. It could either be connected to a hydraulic system with a thin (high flow rate) tube, or perhaps a high gear reduction transmission that converts the motion to say, 60 Hz or something.

Unfortunately we’re talking 4 trillion kg of tension (4 billion m3 * 1000 kg per m) for a 1 GW plant, and a steel cable to carry that tension is infeasible, at 7500 kg per square cm (75 million kg per square m) of cross sectional area, which I calculated from the 11.5 mm cable which works out to a 1 cm2 cross section at 16540 lb (7500 kg):

http://www.engineeringtoolbox.com/wire-rope-strength-d_1518....

So when it’s all said and done, it’s possible to build the float but I don’t know how the power could be extracted practically.