Michael McCormick On Dam-Atoll And Ocean Wave Energy

Excerpt from Ocean Wave Energy Conversion by Michael McCormick

Note: What follows is an excerpt from Michael McCormick's book OCEAN WAVE ENERGY CONVERSION (Mineola, NY, Dover Publications, Inc., 2007, pp. 124-133), in which he discusses Dam-Atoll. This extract is made with the kind permission of Professor McCormick.


Refraction Focusing—"DAM-ATOLL"


In 1946 Robert S. Arthur presented a paper in which he desribed the refraction of water waves by idealized islands having circular bottom contours. By the proper choice of bottom profile, Arthur (1946) showed that the power from that portion of the wave front directly influenced by the island is focused on the center of the island, as illustrated in Figure 4.39a. He studied the focusing phenomenon by analyzing the changes in the directions of the wave orthogonal or rays as the wave refracts on the island.


Using the results of the Arthur (1946) study, Wirt (1976) of the Lockheed California Company showed that the most suitable island profile for wave energy conversion is the one that yields logarithmic spiral orthogonals, that is, those described by


r = r0exp[ ( &theta - &theta0 ) cot ( &theta0 ) ] (4.124)


where r0 is the radius of the first shoaling contour and &theta0 the angle of the nonrefracting orthogonal. Referring to Figure 4.39b, the profile of the island is given by the equation


d1 = λ0 ∕ 2&pi ( rr0 )tanh-1( r ∕ r0) (4.125)


The waves refract in the pattern shown in Figure 4.39a until they break. The broken waves then become surges and are guided tinto a vertical shaft by vanes, as illustrated in Figure 4.40. The entrance of the guide vanes are positioned just before the breaking point of the waves. The vanes are designed to give the surge a tangential velocity as the water enters the veritcal shaft, as illustrated in Figure 4.40. The water then descends as a water column with a rotational motion and thus acts as a fluid flywheel. At the bottom of the shaft is a vertical axis turbine, which is illustrated in the cross-sectional sketch in Figure 4.41. The turbine, in turn, drives an electrical generator. After [exiting] this turbine, the water then passes through a radial diffuser and returns to the ocean.


The system described by Wirt (1976), called the "DAM-ATOLL," is designed to adjust its vertical position as the mean water level changes with the tides. This is accomplished by giving the system a relatively small amount of positive boyancy and by using an adjustable mooring, as illustrated in Figure 4.41. The island, or atoll, can be compliant walled and water filled. This design feature allows for ease in both transportation to the site and positioning. After the system is placed in the water, it floats as a result of flotation chambers located in the rigid central portion of the system. The flexible chambered walls of the atoll are then filled with water tht is pumped in at a high pressure to maintain the desired profile [given by the equation (4.125)]. These design features should keep the costs of the DAM-ATOLL system to a minimum. A sketch of an operational system is presented in Figure 4.42.


Example 4.21
Assume that the wave conditions of Examples 4.19 and 4.20 [discussed earlier in McCormick's chapter] are experienced by DAM-ATOLL, that is, H0 = 3 ft (0.914 m) and T = 3.50 sec. Furthermore, the depth of the water surrounding the wave energy converter is greater than half of the length of the incident waves; thus


h > &lambda0 ∕ 2 = 31.3 ft ( 9.55 m )


Therefore the incident waves are deep water waves. The atoll is assumed to have a diameter of 200 ft (61.0 m) at its first refracting contour; thus


r0 = 200 ft (61.0 m)


d0 = 31.3 ft (9.55 m)


The wave power available to the DAM-ATOLL is obtained from equation (4.112), where b in that equation [is] replaced by 2r0. Thus in deep water, where the group velocity is



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The Patent for Dam-Atoll is now in the public domain

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An Atoll Bends And Refracts The Approaching Wave

Wave Velocity

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When the submerged atoll is dome-shaped, it refracts the wave path to its center

The exact shape of the atoll's dome is critical

the atoll acts as a kind of lense concentrating the wave energy

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A wave is nothing but energy

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A deep-water ocean wave is always half potential and half kinetic energy

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Vortex is a fluid flywheel

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This in sum is how Dam-Atoll works

Smoothing out the succession of wave pulses

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Dam-Atoll has only one moving part

Thus Dam-Atoll loses no energy in monkey motion

Monkey motion

Competing Ocean Wave Energy Extraction Devices are monkey motion machines

Energy Efficiency

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Mathematically Optimal Shape Of Dome Crucial To Energy Efficiency

A Future So Bright For Ocean Systems You Will Need Sunglasses

The Patent for Dam-Atoll is now in the public domain

The Opportunity

Leslie Wirt is available for lectures

Leslie Wirt offers consulting services

Video of working scale model of Dam-Atoll

Dam-Atoll Patent

Michael McCormick's Comments On Dam-Atoll

John Isaac's Comments On Dam-Atoll

Links To Books, Articles, And Web Sites Mentioning Dam-Atoll

Excerpts From Scattering And Absorption Of Surface Waves By Arthur's Island

Future Prospects For Dam-Atoll

Dam-Atoll Humor


About the inventor of Dam-Atoll, Leslie S. Wirt

Contact Leslie Wirt


Next: John Isaac's Commentary On Dam-Atoll


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