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Instantaneous synchronisation of vessel’s roll period to ocean wave frequency, efficiently harvesting wave energy for vessel’s propulsion




Poor efficiency of harvesting ocean wave energy happens when the inertia of the free floating wave energy converter is in opposition with the inertia of the wave, thus cancelling out the energy of both. This could be rectified by ensuring that the natural roll period of the wave energy converter synchronises with the wave frequency, but until now, instantaneously controlling the roll period of a wave energy converter has not been possible.

On a ship, the natural roll period of a vessel can be altered by adjusting the height of the transverse centre of gravity.

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For example, if we move a container from the hatch (top of hold) to the tank top (bottom of hold), the centre of gravity for the vessel (C of G) moves from G to G1. A vessel with a lower C of G has a shorter natural rolling period. Obviously, it would be hugely impractical and energy intensive if we were to try and synchronise the roll period with the wave period (frequency) by changing the vertical position of containers stored in the hold. However, now consider the container in the above diagram being suspended one millimeter above the tank top by suspending it from the top of the hold. The C of G would return from G1 to G, despite the container only increasing its vertical position by one millimeter. Here lies the secret to instantaneously changing a vessel’s roll period.

Category of the action

Building efficiency: Physical Action

What actions do you propose?

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Consider a vessel rolling at sea with heavy containers suspended one centimeter above the tank top by suspending them from the top of the hold, and controlling how much the containers were allowed to swing by altering the oil pressure in rams attached to the cargo (as in the above diagram).

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A high oil pressure would stop the containers from swinging, imitating that the containers were resting on the tank top, so the C of G of the vessel would move down to G1. If the oil pressure was reduced to zero, the containers would swing freely again, suspended from the top of the hold, and the C of G of the vessel move back up to G.

By controlling the pressure in the rams, the vertical position of the C of G could be instantaneously controlled, giving instantaneous control of the roll period, allowing the vessel to stay synchronized with the wave period even if the wave period changes.

We now have a way of efficiently harvesting energy from ocean waves.

The pressure in the rams will be controlled by five variables:


1. The mechanical advantage between the hydraulic rams and the hydraulic engines.

2. Variable pressure regulators.

3. Compressed air accumulators.

4. The workload on the generators.

5. The workload on the vessel’s propulsion system.

The workload on the generators will be proportional to the amount of electricity they generate. The workload on the propulsion system will be controlled by the propeller's pitch and how much work the propellor is doing driving the vessel through the water.

In effect the hydraulic rams will be doing two things. Controlling the rolling period of the vessel and converting the movement of the ship to hydraulic energy (pressure).

Through computer algorithms carefully controlling the five variables, it should be possible to optimise the amount of power generated (from hydraulic pressure) for propulsion and electricity generation while keeping the vessel’s rolling movement synchronised to the waves.

Ocean waves contain far more energy than coastal waves, but until now, it has not been possible to harvest that energy and put the energy to immediate use.

Till now, no real alternatives have been found to fossil fuels powering heavy cargo ships.


The Energy Calculation.


To calculate the energy generated, consider the containers suspended from the top of the hold like a pendulum. “ h “ will be the height the containers will rise vertically. From this, calculate the potential energy for “ h “. Then calculate the power for half a wave period. ( Download Sheet 01 of spreadsheet model ). Finally, apply efficiency factor.

Example 1 - m.v. Baltic Tern.
A feeder vessel, 125 meters in length, suspending 2200 tonnes of containers 8 meters from the top of the hold. The angle of roll is 30 degrees (due to synchronous rolling motion). Rolling period 10 seconds. At 50% efficiency, this would produce about 2.2 MW of power. This would be enough to propel a ship of this size at a speed of about 10 knots.

So far, so good. Now we need to calculate the energy in the waves.

Annual average wave-power density flux (kW/m at deep water)
( Ref: )

The same feeder vessel traversing great circle from the UK to New York in the winter months, would probably experience an average wave energy of 60 kW per meter of wave crest. If the effective length of the vessel ( affected by waves ) is 100 meters, at 50% efficiency, this would be 3 MW of power, more than enough to propel the vessel at a speed of 10 knots.


Example 2 - APL Argentina.
A container ship, 270 meters in length, suspending 20000 tonnes of containers 11 meters on two levels.
bay plan.png
The angle of roll is 20 degrees (due to synchronous rolling motion). Rolling period 10 seconds. At 50% efficiency, this would produce about 12 MW of power. This would be enough to propel a ship of this size at a speed of about 8 knots.

Now we need to calculate the energy in the waves.

The same container ship traversing great circle from the UK to New York in the winter months, would probably experience an average wave energy of 60 kW per meter of wave crest. If the effective length of the vessel ( affected by waves ) is 230 meters, at 50% efficiency, this would be 14 MW of power, more than enough to propel the vessel at a speed of 8 knots.

A large drawback of using the container vessel to extract the wave energy is the loss of container capacity. This would be the case for both the examples above, and can be clearly seen on the bay plan of the APL Argentina. In the hold, the containers take up a lot of space due to their swinging movement. Further, it would be very difficult to load on the deck because the swinging containers would have already made the vessel less stable. As the calculations show below (see costs) despite the large savings in fuel costs, the freight rate would still have to double to make up for the loss in vessel capacity. Wave energy powered vessels would still have difficulty competing with oil powered vessels even with a considerable price on carbon.

Wave Powered Towing Vessels.

A way around this would be to construct wave powered towing vessels. The towing vessels would carry something heavy in their swinging containers, like fine sand. They would still create propulsion in the same way, but they would be used to tow enclosed barges, loaded with the cargo of containers. Because the propulsion would be driving two vessels, the speed of the vessels would only be 3 or 4 knots. New York to London would take about 45 days.

While many cargoes require tight schedules (such as electronic goods for Christmas), there is definitely a market for goods which could arrive months later than normal. For example, in Amsterdam, cocoa beans are discharged from ocean going vessels into storage barges. These beans can stay in storage for years. Bilbao, Spain, imports huge quantities of steel swarf which lies under tarpaulins for months until processed. Quite often ships slow steam around the Horn of Africa, rather than take the Suez to Europe.

Like any new technology, it’s impossible to predict how markets will change, but what with the savings in marine fuel oil costs, for certain new markets will open up.


CO2 Emissions Allowances

The biggest changes will come about when vessels are asked to cut their CO2 emissions. To date, the authorities have been reluctant to demand this because it just hasn’t been possible. With Ship Roll Propulsion, authorities will be able to introduce tradable CO2 emissions allowances for sea trade. Vessels with zero carbon emissions will be able to create additional income streams through selling their allowances.

What Now

The first action to undertake at this stage would be plausibility and feasibility research. Despite back of envelope calculations suggesting that during winter months, vessels propulsion systems could be powered by wave energy, there are still too many unknowns.

The fields of research will require computer modeling to determine what the maximum propeller thrust could be, for differing sea states, roll angles and inertia, if all processes were optimised - an intellectual challenge perfect for MIT scientists. This research would include the following:

1. Determining the efficiency of each stage of power conversion. These stages are:
    a) Wave energy to turning moment of the vessel (rolling).
    b) Turning moment of the vessel to potential energy stored in the containers (lift).
    c) Potential energy stored in the containers to hydraulic pressure (ram compression).
    d) Hydraulic pressure to torque in the hydraulic rotary engine (rotary energy).
    e) Rotary energy to thrust created by the propellor.

In the two examples above, when calculating the wave power, the sum efficiency of stages a, b, c and d were assumed to be 50%. Is this plausible?

2. How significant the buoyant forces are compared to the righting moment. The above calculation assumes that only the vessel’s ‘righting lever’ is returning the ship to an upright position, however, the buoyant forces as the wave passes under the vessel also play significantly in bringing the vessel upright. This could result in as much as twice the power calculated.

3. Consider delaying the swing of the containers to optimise power output. The maximum potential energy will be disproportionately greater at the ends of the arc, i.e. the amount of energy produced along a 10 degree arc between 20 and 30 degrees would be greater than the energy produced along a 10 degree arc between 10 and 20 degrees.


Therefore, if oil flow in the rams were closed off at the end of the arc so that the ram would neither contract or extend, as the vessel lists the other way, the containers would be pushed even higher, increasing their potential energy. However, forcing the containers higher would reduce the angle of roll and change the rolling period.

4. Determine the roll angles relative to the energy in the waves for differing relative directions of the waves, and determine the increase in roll angles when vessel synchronises with the relative wave period.

5. Consider other phenomena.
All four phenomena listed in the table increase the roll angle and should be considered as a way to increase power output. Note also that synchronous rolling motion can happen when the waves are coming from any direction. What is important is the wave encounter period (relative wave period).

6. Consideration should be given to the shape of the hull. Container vessels are built with vertical sides for practical reasons.

More flare would reduce rolling, but increase the righting moment.

Tumblehome would allow more rolling but reduce the righting moment.

It may be more practical to use old tonnage, in which case the vessel would have to be strengthened to withstand the extra transverse forces due to the swinging of the heavy containers. Suspending tens of thousands of tonnes from the top of a vessel’s hold or a specially constructed tween-deck will be a daunting engineering challenge.


No accommodation block would be required, The vessel would have to be unmanned due to the constant heavy rolling.

Some companies may choose hybrid versions, where main engines are used during calm weather, when rolling isn’t possible.

Obviously, there are many other practical considerations to take into account, for example:

  • Will the fuel savings make it financially viable for such vessels to be transferred to operate in the southern winter oceans when calmer weather arrives during the northern ocean summers?

  • Will the fuel savings compare favourably with the increase in freight rates because of lower container capacity?

  • How will regulatory policy change with the introduction of unmanned vessels?

  • Will the short turnaround in ports be long enough to carry out the ship maintenance which normally takes place at sea?

  • What will be the increase in risk of capsizing due to synchronous rolling and how will this affect regulations pertaining to dangerous cargoes?

  • Would it be more practical to have such vessels permanently carrying containers full of fine sand, and then use these vessels to tow cargo ships and passenger vessels across the winter oceans? Such wave powered towing vessels could be hooked up to one another much like train engines pulling a heavy load.


Who will take these actions?

At this stage, this is primarily a research project for mathematicians and computer modelers. Back of the envelope calculations show that if the wave power is extracted by the cargo vessels, it will still be difficult for these vessels to commercially compete with fossil fuel powered vessels even with a price on carbon, (see costs below). However, if the wave energy was extracted by towing vessels, these towing vessels could then tow the cargo, slowly but steadily, across the oceans, with no fossil fuel costs.

Researchers will need to demonstrate to the shipping industry that at a scientific level, ocean waves could power commercial shipping. Only then would the shipping industry be forthcoming with finance for prototype research.

Over here in Europe, the E.U. is very generous with supplying finance, especially for renewable energy projects. This is precisely the sort of project which will attract such funding, however, there are some administrative loops to jump through first.

The first criteria which the E.U. demand before funding renewable energy projects is viability.

The feasibility and viability of a project has to be proven by a respected and established authority, such as an educational and research institute like MIT. I would be able to demonstrate the environmental and financial benefits of such a project, but do not have the facilities or intellectual capacity to carry out the research needed to optimise the power output of such a wave energy converter, as discussed above.

I do have access to the Polish navy’s 2 dimensional wave pool, so limited physical modeling could take place there.

I also have access to Gdansk shipyard, who would gladly accept any E.U. funded proposal to convert an old vessel into a full size test prototype.

To summarize, what I really need is a published paper demonstrating proof of concept.

Where will these actions be taken?

In leading educational research institutions, like MIT.


Small scale modelling would have to happen at research establishments equipped with modern scientific wave pools.

If the prototype was an old converted container vessel, the conversion could take place in Gdansk Shipyard.

Gdansk Shipyard.jpg

Ever since the end of communism in Eastern Europe, Gdansk shipyard has been in financial difficulty. Any other shipyard would have been converted into a housing complex, but because the end of communism was triggered by the Solidarity Movement which started at this shipyard, both the E.U. and Poland are determined to keep it in business. That means generous loans and finance from the E.U. and favourable tax status for any companies investing in the shipyard.

How much will emissions be reduced or sequestered vs. business as usual levels?

According to the IMO, shipping emitted 870 million tonnes of CO2 in 2007. By 2050, those emissions could grow by a factor of 2 to 3.

Wave powered vessels will primarily be used in northern winter oceans, perhaps for three months per year.

Frequency of shipping traffic

It might be possible to build transportable wave powered warehouses, storing commodities when there is a natural annual glut, and discharging the commodities when there is higher demand perhaps six months later. Such vessels would only need to travel at a speed of 1 knot across the oceans to reach their destination in time. Such wave powered warehouses would be able to operate in oceans which have lower wave energies, all year round.

Assuming this, perhaps 10% of the global sea trade could be delivered by wave powered vessels, saving 90 million tonnes of CO2 emissions per year at todays trade levels, and  200 million tonnes per year by mid century.

What are other key benefits?

Old ships could be given a new lease of life, instead of being sent to be scrapped in countries which do little to prevent marine pollution during the breaking process.

Ship Breaking.jpg

Normally vessels come to the end of their working lives when they become too expensive to carry out the maintenance required to get them through stringent safety surveys. The surveys are so stringent to protect the crews working on the vessels. Because the wave energy powered vessels would be unmanned, they wouldn’t have to pass such stringent safety surveys, and would be able to carry on operating as wave powered tugs for a further ten years.

What are the proposal’s costs?

In the second example (APL Argentina), the vessel normally would be at 70% capacity carrying 2800 TEU from London to New York. However, the new container arrangement would mean a loss of 2300 TEU. At freight rates (excluding handling) of $340 per TEU, that’s a loss of 770 thousand USD.

However, with a consumption of 100 tonnes of intermediate fuel oil (IFO) per day, and a nine day passage, with IFO costing 600 USD per tonne, thats a potential saving of 540 thousand USD.

So overall, we are 230 thousand USD down per voyage, or nearly 440 USD loss per TEU. To break even, the freight rate (excluding handling) would need to increase to 770 USD per TEU. Without a price on carbon increasing the freight costs (including handling) by 200%, a container ship powered by wave energy would not be able to compete with a ship powered by fossil fuels. ( See costs - APL Argentina )

However, if the cargo was transported in enclosed barges, towed by wave powered tugs, there would be no loss of cargo space, but there would now be two vessels to power for each wave energy converter. Using the 1st example, where m.v. Baltic Tern is converted into a towing vessel, the passage speed would only be about 4 knots.

The cost of chartering a 2.2MW wave energy tug would be about 4000 USD per day. A 350 TEU barge would be about 3000 USD per day. So the total is 7000 USD per day.

If we compare this to an oil powered vessel:

The cost of chartering a 350 TEU vessel is about 4000 USD per day. Fuel consumption (at 12 tonnes per day) would be 7000 USD per day, so the total would be 11000 USD per day.

So the wave energy tug and tow would be operating at 4000 USD cheaper per day. However the wave energy tug and tow would need three times as long to get to it’s destination, so it’d nearly be twice as expensive per voyage.

Once again, we have an example of a low carbon technology, calling out for a price on carbon.

(See costs - m.v. Baltic Tern)

(Charter Costs)


Time line

2014 - 2024

A) Prepare a feasibility study into wave powered vessels. If, as back of envelope calculations suggest, such vessels could be cost competitive with a price on carbon, promulgate study for peer review.

B) Publish a study in shipping trade journals so that shipping companies understand that there is a real alternative.

C) Set up an international company to develop wave energy powered vessels.

D) Use the study to raise both public and private finance for model and prototype research.

E) Approach shipyards to convert an old vessel into a prototype wave energy powered vessel.

F) Carry out research on the oceans.

G) Approach shipping companies to build commercial wave powered vessels.

Related proposals



For landlubbers, how a vessel behaves when in a synchronous state with the waves is counter-intuitive. These misconceptions arise because rarely do landlubbers get the chance to experience what happens to a vessel when it’s rolling motion synchronises with the wave period. Even veteran seafarers might only experience this phenomena a few times in their sea going careers and yet understanding this concept is central to this proposal.


Misconception 1 - Roll Angles.

Ship roll propulsion uses a novel way to keep a vessel in a permanent synchronous state. This would result in moderate rolling in a light swell, and heavy rolling in a moderate sea and swell.

Sea Scale.pngSea Scale Tables.

This larger than expected rolling happens for two reasons.

1. The energy from one roll gets “carried over” to the next roll.

2. The buoyant forces from the waves add further energy to the carried “over energy”.

Misconception 2 - Wave Direction vs Approach Wave Period.

It is not intuitive that the amount a vessel in a synchronous state rolls, isn’t dependent on the direction of the waves, but dependent on the approach wave period.

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A vessel with a roll period of 13 seconds will roll very little in a moderate beam sea of wave period 8 seconds.

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However, if such a sea were to veer or back to become a following quarterly sea, the vessel would roll more heavily. This is because the waves would be chasing the vessel, and so the relative wave period would increase to nearer 13 seconds.

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A vessel in a synchronous state in a moderate sea will roll heavily no matter what the direction of the sea, provided it is not from directly aft or forward. Vessels in a synchronous state with a directly head or following sea could still roll heavily due to parametric forces, though this also depends on the length of the vessel.


Misconception 3 - Wind vs Sea State

In the winter North Atlantic, North Pacific and Southern Ocean, very rarely are the waves small. Even in calm weather, there is usually an ocean swell running. This is because, around every high pressure area, there are low pressure areas where the wind will whip up waves. These waves then propagate into the high pressure areas as ocean swells. See illustration.