The idea is that you could put a large water displacing structure in the ocean, tie it to the seafloor, and when it came time for the tide to rise the force exerted by the rising water could be used to generate energy.

This Coda doc is dedicated to exploring the feasibility of that idea.

The claim in this paper is that using tidal energy to provide 1% of the earth’s power requirements will result in the earth ceasing to spin in as little as 1000 years.

But other sources (the guy who runs the Real Engineering youtube channel) claims that this is hogwash. So maybe don’t trust things just because they have stanford affixed to them.

This is to model a cone shaped water displacer

000

13

height

0000

19

radius

4,914

volume (cubic meters)

4,914,498

liters

set a target

4875750

off by

38,748

liters

Save Setting in Combinations Table

This is to compare the effects of certain parameters on power generation, earnings, and structure cost.

standard assumptions

alaska assumptions

000

2

steel thickness (cm)

000

100

tidal range (meters)

0000

0.3

earnings per KWh ($)

7850

steel kg per m^3

603

steel cost per metric ton ($)

124

cement cost per metric ton ($)

1.025

salt water mass per liter (kg)

2

cycles per day

0.1

delta (meters) - step size used when calculating depth pressure

Combinations and consequences

Combinations and consequences

0

Created with Highcharts 9.2.1r (m)years to payoff1002003004005006007008009001000020406080100

I'm pretty sure I'm doing many things wrong

Or else this is completely infeasible

As a point of comparison, a 1 MW solar farm supposedly costs about $1 million to build (though I've seen that number as high as 3 million) and generates on average four megawatt hours per day (it depends on the amount of sunshine). The

@best combination

I found generates about 1 MWh per cycle. With two cycles a day that comes out to 2 MWh per day (half of the output of the solar farm). That means that for this to be competitive with solar it should ideally cost about .5 to $1.5 million to deploy.

That

@best combination

, however, is about

130

times more expensive than a solar farm just in terms of steel cost. But there is good reason to think that I'm dramatically overestimating the cost to build it.

Hopefully my assumptions are somehow extremely incorrect or I made an error in the math (both highly likely).

Possible things that I could be wrong about:

Maybe a cone is the wrong shape (would a cylindrical shape be better? sphere?)

Maybe you could use cement instead of steel (or steel reinforced cement)

Maybe you could use some much cheaper material like plastic

Maybe internally pressurizing the structure would allow you to use significantly less material

I'm also pretty sure that the way I model the forces is incorrect. In particular, I need to model the fact that the deeper you pull the water displacing structure the more forces are exerted on it due to depth pressure. I tried to estimate the total forces acting on the structure in

depth pressure force (bar m^2)

but I would guess I'm doing it wrong. The results I’m getting are on the order of 200 large blue whales worth of force

Manufacturing is definitely a concern, since these things are enormous, but could perhaps be overcome with in situ additive manufacturing. I.e. put the base in the water, then pump water into the base until it falls to a height that can be serviced from the deck of a boat, then add an additional layer of material, pump in more water, add another layer, etc.

if you know where I'm wrong or to tell me why this won’t work

Comparison with the tallest buildings in the world and their costs to build

By BurjKhalifaHeight.svg: *BurjDubaiHeight.svg: Ramaderivative work: Astronaut (talk)derivative work: WelcometoJurassicPark (talk), Scaling and drawings from https://commons.wikimedia.org/wiki/File:BurjKhalifaHeight.svg and http://www.skyscrapercenter.com All rights reserved. - File:BurjKhalifaHeight.svg http://www.skyscrapercenter.com, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=54960521

Somehow it only cost 1.5 billion to build the burj, and 700 million to build empire state building, $675 million for hoover dam (

volume of cylinder: 4875.75 m^3 which is 4,875,750 liters

which at these parameters:

4 tidal range (meters)

0.3 earnings per KWh ($)

generates this output:

If we straight up used a submarine

If we straight up used a submarine

0

KWh per cycle

MWh per year

annual earnings

1

1371.2814859029384

1001.0354847091451

$300,311

There are no rows in this table

Subs can withstand up to 300 bar pressure, so clearly these are way over engineered for what we need. If we were to just naïvely scale the cost of the sub to hit 1000 kWh per cycle then we would multiply the $4 billion cost by 18, which is 72 billion dollars.

I've read that Australia’s subs are more than double the cost that most people expect to pay for subs, but reducing our cost down to only 36 billion still doesn't get us close to our $3 million goal, nor is it close to the 500 billion estimate above. Naturally, there is a lot more in a submarine than there would be in one of these structures (a nuclear reactor for one thing), but even as a gut check I’m not sure I’ve made any progress in improving my estimate.

What else can I use as an estimate of the cost to manufacture a highly external pressure resistant structure?

It needs to be able to withstand 10 to 15 bar at most. It would be nice to know how manufacturing costs scale with respect to the ability to withstand pressure

found this (thank you Google recommendation algorithm). The creators claim 25 tons over 15 m generates 250 kWh. Costs $1,385 million to build. We would expect that the idealized output of that sort of system would be (assuming metric tons):

3,675,000

joules gravitational potential energy

1

kWh gravitational potential energy

uh.. that’s not 250 kWh, do they mean per year or do they expect to do this 250 times a day?

Chile has pretty good tidal ranges and high prices

Europe also ranks pretty high and would also have decent prices + likely subsidies thanks to carbon markets

New zealand too

The battery approach

There's an alternative way to use this, which is as a massive battery, storing energy when prices are low and releasing it when prices are high

Japan would be a great place to model that approach since it has decently high energy prices and, if you look at the title range map, it has almost 0 tidal range:

This is important because if you store energy when the prices are low and the tide high, and then you want to release energy while the tide is low you’ll have less potential energy than you previously stored

select the height and radius combination you want to model this with

Set tidal range to 100

Press this button to set the tidal range to 100 m. Of course, there's nowhere in the world with a tidal range of 100 m, but we are using energy from the grid to pull the water displacers deeper. So, in theory we could pull them all the way to the seafloor (engineering permitted). At 100 m there are 10 bar of pressure which is 1/3 of what a submarine can handle, so it seemed like a reasonable estimate.

Add Spreads

This button populated the table below with what would happen if we were to perfectly arbitrage the 2020 Japan energy market with the water displacement energy storage solution. This is pretty unrealistic, but it gives us an idea of the maximum market opportunity. In other words,

we are buying energy for the day at the lowest price and selling the energy that same day at the highest price

Japan Daily Max Spread

Japan Daily Max Spread

0

0.0093

dollars per yen

0.9

work conversion efficiency

$4,794,109.41

estimated annual earnings

This estimate is almost definitely wrong due to the depth pressure modeling errors in my calculation. I'll fix it eventually