# Tidal Energy

## Wenshi Chen October, 2010

### Submitted as coursework for Physics 240, Stanford University, Fall 2010

 Fig. 1: Tidal relationship amongthe Sun, Moon and Earth. Top: Neap tide. Bottom: Spring Tide. (Source: Wikimedia Commons.

## Mechanism of the Tides

Tides are periodic changes in sea level caused by gravitational effects of the sun and moon in conjunction with the rotation of the earth. As a basic principle, when the moon or sun is overhead of a specific portion of the ocean, the water is attracted from elsewhere due to the gravitational force and thus the sea level rises up in that region and drops down elsewhere. When the moon or sun is right underfoot, the situation is similar. So, there are high tides when moon is overhead or under foot. Since the distance between moon and earth is much closer than between sun and earth, the gravitational effect of moon is much more significant than that of sun on earth, despite their tremendous contrast in mass. Therefore, there are generally two high tides and two low tides per day, due to the rotation of earth.

The difference between highest and lowest water levels within half a day is termed semidiurnal range. This range varies in a two weeks cycle. As shown in Fig. 1, around the full moon and new moon, sun, moon and earth form a straight line, and thus the gravitational effect of sun will increase the tidal range to the maximum. This is called spring tide. When the angle between moon and sun viewed from earth is 90°, the presence of sun reduces the difference of tide level so that the tidal range reaches minimum.

In most cases, the moon is the dominant factor in tides. Fig. 2 demonstrates the global distribution of tidal range contributed by the moon. The amplitude of the tidal range is represented by different colors. The white solid curve represents the so-called cotidal line along which the tidal phase is constant. Cotidal lines join at several points where the tidal range is zero, called amphidromic points. The curved arcs around the amphidromic points indicate the direction tidal current. The amplitude of tidal range is an important indicator of the density of the tidal energy.

 Fig. 2: The lunar tidal component as measured by the U.S./French satellite TOPEX/Poseidon. [6-8] (Courtesy of NASA.)

## Tidal Energy and its Application

Tidal energy is derived from the motion of the Earth-Moon system. Due to the rotation of earth, the bulges of tides are always ahead of the position on earth right under the moon. The gravitational force between this portion of water and moon generates a torque that decelerates the rotation of earth. On the other hand, this force helps to accelerate the orbital movement of moon around earth. As a consequence, without other interference, the rotational period of earth will finally be equal to the orbital period of moon. The utilization of tidal energy, which will inevitably reduce the tidal currents, takes advantage of the angular dynamic energy of earth in the similar way. However, the process of tidal acceleration is extremely slow, and the phenomena of tide can be expected to last until the vaporization of the ocean on earth billions of yeas later. Therefore, the tidal energy can be classified as renewable energy.

 Fig. 3: The Tidal Turbines of SeaGen. (Source: Wikimedia Commons)

Tidal energy has two forms: the dynamic energy of the sea currents and the potential energy due to the change of water levels. The dynamic energy can be made used by turbines in the tidal stream system analogous to wind turbines. Due to the high density of water compared to air, the density of dynamics energy of water flow is much higher than air flow. Therefore, the tidal turbine is usually smaller than wind turbine and can work at a lower flow velocity. Like wind turbines, tidal turbines can be divided into two major types. The first one, axial turbines, have rotary blades with axis parallel to the flow direction. Fig. 3 demonstrates the currently most powerful tidal generator SeaGen. [1] Developed by Marine Current Turbines, it has the capacity of 1.2 MW and was installed in the sea near Stranford, Northern Ireland. The second type is termed cross-turbines. It consists of foils. The axis of the turbine is usually vertical and the turbine can be driven by horizontal flow in all directions. This design is derived from the famous Darrieus wind turbines. An award-winning design of cross-flow turbine has been proposed by Prof. Gorlov in 2001. [2] Similar design can be found in the wind turbine "Turby" shown in Fig. 4. The cross-flow turbines have the advantage over axial turbines that they can efficiently make use of flow in all directions without adjustment of the axis of the turbine and have been gaining popularity. Pilot and practical projects have been launched around the world.

In order to utilize the potential energy of tides, dams are generally required. These are called barrages. A barrage is usually built at the estuary to separate the fresh water from the sea with sluices and turbines installed. Though varied, the basic principle of barrage tidal generation systems are similar. The basin formed by the barrage is filled during high tides. The water head difference between the basin and lower water table is used to drive the turbines to generate. This barrage method is probably the oldest attempt to make use of tidal energy, which can be dated back to Roman times. [3] However, it suffers from high construction cost to build the dam and potential damage to the estuarine ecosystem. Nowadays, the only large-scale barrage power plant is the Rance Tidal Energy Plant in France.

 Fig. 4: A Prototype of Turby. (Source: Wikimedia Commons)

In 1997, two Dutch engineers proposed a new method to utilize tidal energy, called Tidal Dynamic Power (TDP). [4,5] The method involves building a large dam extended to the ocean and a long perpendicular barrier at its far end, forming a T-shape. Since the tidal current is parallel to the coastlines near the coast, this system can accumulate large difference in water head on both sides of the dam twice per day. The difference of water head can be used to generate, as in the barrage system. The estimated installed capacity of the dam can reach over 8 GW with less influence on the ecosystem than barrage. Another benefit of this method is that it does not require a high natural tidal range, and can be applied in more sites than other methods.

## Conclusion

Tidal energy is a kind of renewable energy with large potential. It has many advantages over solar and wind energy. For example, the availability of tidal energy is highly predictable and not subject to the impact of weather condition. The energy density of tides is also higher than solar and wind energy. However, the high demand in technology and capital investment has hindered the development of tidal energy so that the tidal energy projects are much less than those of solar and wind energy. With the development of innovative tidal turbine system and coastal infrastructure, the popularization of tidal energy worldwide can be expected.

© 2010 Wenshi Chen. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] C. A. Douglas, G. P. Harrison and J. P. Chick, "Life Cycle Assessment of the Seagen Marine Current Turbine,", Proc. Instit. Mech. Eng., Part M: J. Eng. Maritime Environ 222, 1 (2008).

[2] A. M. Gorlov, "Helical Turbines for the Gulf Stream," Marine Technol. 35, 175 (1998).

[3] R. Spain, "A Possible Roman Tide Mill," Paper 005, Kent Archaeological Society (2002).

[5] J. M. B. Ilzarbe and J. A. Teixeira, "Recent Patents on Tidal Power Extraction Devices," Recent Patents on Engineering 3, 178 (2009).

[6] R. D. Ray, "A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99.2," U.S. National Aeronautics and Space Administration, TM-1999-209478, September 1999.

[7] Y. Accad and C. L. Perkins, "Solution of the Tidal Equations for the M2 and S2 Tides in the World Oceans from a Knowledge of the Tidal Potential Alone," Phil. Trans. Roy. Soc. A 290, 235 (1978).

[8] M. Starobin, "TOPEX/Posidon: Revealing Hidden Tidal Energy," U.S. National Aeronautics and Space Administration, 30 Mar 07.