Warning: more math inside

General Discussion
1

I friend emailed me this over the weekend. I understand it well enough to understand it, but not well enough to prove or disprove it. Well, the water part.

The computer stuff I don’t get at all because I have no idea what he’s talking about.

Any comments?

Quote:
Check this out. An oceanographer named Willard Bascom presented a wave energy equation as

E=wLH^2

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   8

Where w = weight of cubic foot of water ~64 pounds, L = wave length, and H = height.

So a 4 foot swell with 10 second period (translates to 512 feet between crests) contains 65,536 foot pounds of energy per linear foot.

If the period remains the same but wave height doubles to 8 feet, energy increases fourfold to about 262,000 foot pounds.

And a 27 foot swell at 20 seconds (2,048 feet btwn crests) = 11.9 million foot pounds in a 12 inch wide vertical slice of one wave.

Besides that monster generating enough power to light a city for a week, the mind blowing thing for me is that first equation since I’m a computer guy.

64x512x4^2 = 524,288/8 = 65,536 or 2^64th, the same number of processors in the first massively parallel supercomputer I worked on at Thinking Machines.

I find the synchronicity between 10 base 2 and these wave dynamics mind blowing. A four foot wave measures the same energy as the mathematical model for computer storage and memory.

Geeky wave energy indeed.

Shows why Hydro power has been so prevalent; think of Niagara as a 177 foot wave with a period of 60 seconds (water velocity is about 3 feet per second).

The original wave height/energy analysis was actually published in Book II of Newton’s Principia where he related it to the wind blowing over a distance of water.

The wind of course is a result of the solar energy hitting the earth. As impressive as the 20 foot wave is, it contains less than 10% of total solar energy driving the wave over the unit of time assuming noon at the equator.

2

E=wLH^2

8

Hey Benny,

if you use all the units of meas you get E= pounds x ft^3 = lb*ft^3

doesnt make sense to me…

maybe there’s something missing…

seems like a potential E analysis based on the height of a cubic segment above the water line…seems very complicated when you take all variables into account

interesting

3

If I may

the units get a skosh more interesting - the energy per foot is equal to the density per cubic foot multiplied by the wavelength ( in feet ) multiplied by the height ( in feet) squared .

E/ft= (lbs/ft^3)ftft*ft

Which becomes E/ft=(lbs*ft^3)/ft^3

cancel some units - kill the green guys

E/ft=lbs

and then we ask how many feet are we talking about the energy of? Multiply that unit in on both sides and its

ftE/ft = ftlbs

again, units cancel, so

E=ft*lbs

an answer in ft-lbs, a perfectly reasonable unit of energy.

hope that’s of use

doc…

4

The wave length for a 10 sec period swell is WAY off, it should be 262 ft for one wave period. Some geeky forecaster put up a page about this in your hometown, benny, mainly because he was interested in water depth and refraction of different period waves.

http://www.blakestah.com/surf/oldprediction.html

5

Well, thanks, guys. Doc, thanks for distilling the formula.

Blake, I agree that the first thing that raised my suspicion was the wavelength. I’ve surfed plenty of 10 second windswell and there’s no way its over 500 feet between crests! How did you get the 262 number?

How well do you know that geeky forecaster? :slight_smile:

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Was that reef, sand, open ocean or wrapping into a bay?

Who cares, just catch it!!! Well, at least catch one for me!

7
Quote:
Well, thanks, guys. Doc, thanks for distilling the formula.

Blake, I agree that the first thing that raised my suspicion was the wavelength. I’ve surfed plenty of 10 second windswell and there’s no way its over 500 feet between crests! How did you get the 262 number?

The 262 number is from the swell and wave velocity, and period.

Roughly like this…and come to think of it, I may have not been quite right at 262…

17 second period swell travels at 26.52 nautical miles per hour. Or 761 feet in 17 seconds (do the conversion).

A 10 second period swell travels proportionally slower, or 15.6 nautical miles per hour. That converts to 263 feet in 10 seconds.

But wait, there’s an error. Waves actually travel TWICE as fast as swells, so those numbers are off by a factor of two…or 526 feet for a 10 second period swell. Waves travel in wavelets, and the phase constantly advancees, waves move exactly twice as fast as swells.

The reason you think these are way off is because these are OPEN OCEAN numbers and not NEAR SHORE numbers. Near shore the speed is much slower, as the wave is scrubbing the ocean bottom.

OK, maybe they weren’t so far off…my bad, carry on.

8

someone’s been trying to build a hydroelectric power device out here in deep water. But funding has been a problem. The idea is to capture the energy between the peak and valley of these parge ocean swells heading here from up north.

The device would be submerged and generate energy by traveling the distance between the peak and valley.

But right now purified deep ocean freash water going to japan is all the rage here on the big island, There were some temperature gradient energy generation proposals out there as well but it’s all about funding. You think with our dependance on oil for power out here we’d be listening but that’s not the way of the “man”.

9

Ah - I suspect that an engineer looked at that floating ( barely) power generator and said ‘nope, Orville, this thing isn’t gonna fly’. Thing is, with petrochemicals becoming more expensive, there have been a lot of proposals around, many of which are smoke and mirrors.

The thing is, all that energy in a wave is, much as anything, tied up in the water it lifts above ‘sea level’, kinda like if you took an equivalent quantity of water and carried it up to a platform of a given height, then ran it through a water wheel or water turbine. There are actually backup power plants that work just like that, pumping water up when electricity is plentiful/cheap and then letting the water down through generators when needed.

But the power a buoy-type generator can produce hasn’t got much to do with that power in the wave itself, rather it involves the buoyancy of the buoy and the height it’s lifted and dropped by the waves or swells. For instance, take a boat, drop an anchor and tie the anchor line to a drum ( like a lawnmower starter cord is set up) and attach a generator to that.

Now, do the same thing with an empty freighter and a BIG generator… you see what I mean? The more buoyancy, the bigger the generator it can spin.

But if said buoy is just about submerged, the power available is pretty low. It won’t get lifted, especially, it’ll just sit there. There may be some other, smaller and less efficient ways to make power from it (like the pressure changes as a swell goes over), but we are not talking about revolutionising power generation.

On the other hand, thermoelectric generators are good stuff and improving fast. If you have hot water and cold water available, such as off Hawaii, then you can use that temperature difference to generate power, the main problems being pump efficiency and friction losses in your piping. There was a project out there ( I think in the '70s, but memory is a little vague ) to see what that could do which involved a buoy ( mostly submerged) something like 4-500 feet long/tall.

And the tech has improved since then: http://www.varmaraf.is/engl/prod.htm has some small ones.

hope that’s of use

doc…

10

I think Doc, that your view on the form of energy in a wave is not close enough to correct to be useful. Waves do not lift the ocean level any more than they decrease them. Under-water the motion is circular. So, if you were to submerge a big turbine (envision a paddlewheel), it would generate quite a bit of energy and stop swells in their tracks.

The problem is that swells come in all periods, and so you end up needing paddlewheels of different sizes, each tethered an needing a different buoyancy. Amd the paddlewheels need to be a few hundred feet in diameter.

There are approaches now producing energy from waves, though. There is a saltatory duck. It bobs back and forth, and produces energy from its tilting motion.

There is the Japanese whale. This is a floating platform with a beach. I’m sure you’ve noticed that beaches with gentle enough slopes do not generate backwash. The whale is a floating platform with a soft slope. It has air turbines on top. When a wave hits it, the air turbines release air and produce energy. And when the wave recedes, air is sucked in through the same turbines and produces energy.

If you’ve ever been underneath a swell, you know it yanks you up and forces you down when a wave passes. Some scientists in Norway made underwater pistons. These go up and down with the waves, and in doing so generate energy.

And then there are the guys making linked logs. These long pipe-like chains of logs rise and fall with the swell, and the links between them are geared to generate energy.

Honestly, I think the spatial scale required to harness the energy is the biggest problem…there’s a LOT of energy, but it is not so focussed, and sampling it effectively means operating on the same spatial scale as at least half the wave length, or several hundred feet min.

I’d love to see a wave generator that sampled selectively, taking out the short periods while not impacting the long periods. Like kelp does, only creating energy as well, and sitting well offshore and not getting wrapped around your fins and legs.

11

Here’s a link to what Oneula is talking about http://reslab.com.au/…les/tidal/text.html. Theres many variations on a theme, but some of them look intersting.