# Tidal Power and Conservation of Energy

1. May 18, 2010

### lachy89

This is something that I have wondered about for a while now which is related to how tidal power stations work and the law of conservation of energy.

Scenario:

As far as I am aware the tidal variations all around the world are primarily caused by the gravitational force of the moon on the vast oceans.

To simplify the scenario, tidal variation in a certain area is 2m - that is at low tide height = 0, high tide height = 2m.

If a Bucket suspended on a rope at a height of 1m at low tide, and then left for an entire cycle, that same bucket will now be filled with water. The gravitational potential energy has now been increased, as the mass inside the bucket has increased.

The bucket is to represent a visual model of water being moved via the high and low tide variation. Using Dams instead of buckets, and using turbines electricity can be produced.

My Query:
My understanding is that the energy transformations go like this

Gravitational potential energy from the moon oribitting the Earth transfers into kinetic energy in the waves around the world, this kinetic energy transfers into potential energy in the dam and then is transfered into electical energy via the turbines.

What I don't understand is where the energy loss is.

My understanding is that the energy ultimately is sourced by the moon orbitting the Earth, and if the orbitting radius stays constant and the Mass's of Earth and Moon stay constant. Where is the energy loss?

The only solutions that I can think of is that either the moon is slowing collapsing into the earth, the masses of the Earth and Moon are increasing or that the conservation of energy laws need to be explained to me further.

If anyone can explain to me this scenario I would be most thankful.

(Also I apologise if this is not posted in the right thread).

2. May 18, 2010

### sophiecentaur

The Earth is rotating. It has rotational KE. The mass of the Moon is 'dragging' the oceans so that they are lagging behind a bit and this is constantly slowing the Earth down and the Earth is 'pulling' the Moon into a higher orbit*. This happens because the total angular momentum of the Earth Moon system remains constant. Some of the energy involved in this transfer is in the huge tide wave that travels around the Earth as it rotates under the Moon. Tidal Schemes can just extract a tiny fraction of this wave energy by intercepting the rising and falling water.

*This may be counter intuitive but think about whirling a conker round on a string. As you pull on the string (your hand is going in a small circle), the tension increases and the string would stretch if it were weak enough. You have 'given' energy to the conker. Eventually, and in total isolation from the Sun and other masses, the Earth would rotate at the same rate as the Moon's (much increased) orbit - which is the condition of minimum energy. (No more tidal power then!)

3. May 18, 2010

### D H

Staff Emeritus
The Moon is slowly moving away from the Earth as a result of tidal interactions.

The total mechanical energy of the Earth-Moon system is the potential energy due to gravitation plus the kinetic energy due to the Earth and Moon orbiting about one another plus the kinetic energy due to the Earth and Moon rotating about their axes. This mechanical energy is not conserved. Some of the energy is lost due to tidal friction.

What is conserved is angular momentum. There is angular momentum from the rotation of the Earth and Moon about their axes and angular momentum from these bodies orbiting one another. Tidal friction slowly reduces the Earth's rotation rate. Conservation of angular momentum requires that this be balanced elsewhere, and this elsewhere is the orbit. The Moon is slowly receding from the Earth.

4. May 18, 2010

### Studiot

One other point is worth making.

Your proposed mechanism for extracting energy from tides uses the vertical movement of the water.

It is often forgotten that associated with the vertical movement there is horizontal movement. This movement is called a tidal stream.

I mention this because placing turbines directly in the path of tidal streams offers far greater opportunity to extract energy thanusing the vertical component of the movement. Most of the tidal energy that is extracted is likely to come from this source in the future.

5. May 18, 2010

### sophiecentaur

Spot on there.
You can see many square km of wind turbines which are at the mercy of the weather. Compare that with the possibility of large underwater turbines with tides in both directions four times a day. They would, obviously, affect the flow to some extent and could also modify sediment drift and would have to be sited in narrow channels to get the appropriate speed of current. (Tidal flow in oceans is very small compared with the effect in the shallow seas). The good thing about this method is that there is much less structure involved and the turbines could be re-sited, if things changed.

Something also struck me. Why not use large floats (really large, like old tankers for instance) and use the 4 or 5m tidal range to provide a lot of Nm of energy as the tide ebbs and flows, lifting them up and down and moving them from side to side?

6. May 18, 2010

### skeptic2

No doubt it's a lot easier to extract energy from the rotation of the earth than to put it back.

7. May 18, 2010

### mgb_phys

The size is limited by the fact that you have to anchor them, you need an anchor much bigger than the float or your would simply lift the anchor.
But the basic idea is called Salter's ducks

The most efficient way to use tidal rise is a barrier, you open the gates to let the water flow in, then let it run back out through turbines. This way you use the mass of the entire river * tide height, with a float you only use the mass of water displaced by the float.

Last edited: May 18, 2010
8. May 18, 2010

### Studiot

I think it's a great deal more complicated that that.

Have you ever seen the installation at Strangford Loch?

9. May 18, 2010

### mgb_phys

A tide flow turbine only extracts a tiny amount of energy and suitable sites are very limited.
A barrier is a bigger (but relatively simple) structure that can generate a lot more power - and with the current examples at Rance pretty cheaply.

Although a barrier has a bigger environmental impact (silting / species migration etc)

10. May 18, 2010

### sophiecentaur

An anchor could be concret / rock based - just like permanent moorings. It wouldn't need to be more than the displacement of the vessel used - use another old ship and sink it, then fill it with rocks - cheap.
Salters ducks use wave energy to tilt the duck- reciprocating rotation not a large displacement due to changing tidal height.

@mgb_phys
A wind turbine doesn't use all the energy of the passing wind (no pun here ;) ) but they are still used. A suitable free standing tidal turbine wouldn't be of the same design as in a barrage scheme. It would be a large diameter and operated at a reasonable depth to remove it from the worst effects of sea state.
As far as I remember, the coast at Rance (north Brittany) is essentially rocky and the river doesn't appear to carry a lot of silt. This contrasts to the Severn, which is a massive (by UK standards) river and has a very different (sandy / muddy) estuary. I think that many of the sites which have large tidal ranges are of this kind. I can foresee serious dredging problems arising not long after any of the Severn schemes is commissioned.

11. May 18, 2010

### Studiot

I can't agree with your analysis.

For water to rise vertically, the same amount of water must flow horizontally. Conservation of matter requires horizontal and vertical flows to be equal.

The difference is that the horizontal flow takes place over a longer time, so the ability to generate is spread out over more of the tidal cycle. Further generation is unavailable with the vertical scheme for half the time as you cannot generate whilst the gates are open and the water flows in. You can impound water behind a dam extend the generation time whilst the time height is low.
However a tidal flow turbine can be made to operate on both the inflow and outflow.

I would say that there are few suitable locations for using the vertical movement since this movement is almost zero for large parts of the ocean, particularly in tropical and sub tropical waters for example the Mediterranean tides are a few centres in height.
However the tidal streams encompass the entire world ocean.
I understand, for instance, that enough water is horizontally exchanged twice a day between the Atlantic and the Irish Sea to power the whole of Europe, were a sufficient number of turbines appropriately placed on the sea bed.

Incidentally no tide turbine will be 'efficient'. Conventional hydro-electricity is base on low flow high head high speed generation. Tidal generation is high flow low head low speed generation.

Last edited: May 18, 2010
12. May 18, 2010

### mgb_phys

There are issues for both schemes.
Tidal barriers block a major river, so not exactly low-impact, but you do get to extract a lot of energy if you have a large tidal height difference. They often also serve as flood control so you get back some of the construction costs.

I think the main limitation of tidal flow turbines is that, like wind turbines, the power is a strong function of flow speed. So you need somewhere with not only a large tidal difference but also somewhere that it is funneled through a narrow gap like Strangford Loch or the Bay of Fundi, or possibly Gibralter?
You also need to anchor the turbine to the sea bed, so you need relatively shallow and rocky, although presumably this goes together with fast flow.

Obviously a small (few x10m diameters) turbine only extracts a tiny amount of the energy in an ocean current, just like a wind turbine only gets a fraction of the energy in the wind. If your source of energy is almost infinite, like the gulf stream this isn't an issue, but if you have a limited number of sites, such as a few river estuaries then a barrage will extract a lot more of it.

Either way wave/tidal looks like a better bet than wind in terms of availability and energy cost.

13. May 18, 2010

### lachy89

Well thanks guys - Turned into a reasonable discussion too :)

Just something I have wondered about and obviously areas of 'green' energy are being researched thoroughly at the moment.

14. May 18, 2010

### Integral

Staff Emeritus
Google Wave power, you will find that there are already several different systems in production to do this. Though they are facing many difficulites actually getting them into production.

Last edited: May 18, 2010