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| Fig. 1: The tidal bulge due to gravity is shown on the side of Earth facing the moon, while the tidal bulge due to inertia emerges on the side of Earth facing away from the Earth. (Source: B. Cantrall) |
The ever increasing demand of global energy necessarily brings with it the increase in demand for energy sources. Currently, the generation of energy is reliant on fossil fuels, with over 80% of energy consumed in 2021 coming from oil, natural gas, and coal worldwide. [1] A major consequence of this reliance is the heavy contribution to climate change and air contamination. In an attempt to offset the effect that burning fossil fuels has on the environment, many alternative energy sources have been proposed and implemented, such as solar, wind, and hydropower. Tidal energy is another promising alternative to carbon-based energy sources considering the dependability and predictability of the motion of the tides. Several tidal power stations are currently producing energy; however, these stations do not have capacities that make them major competitors to conventional energy plants. This report analyzes the harnessable energy stored in the tides and compares this with global energy demand. Current tidal power stations are also discussed, including their economic costs and technological hindrances.
The tides are caused by the gravitational interaction of the Earth, sun, and moon. This report will focus solely on the interaction of the Earth and moon to explain the tides. To begin, note that the rocky Earth is not perfectly rigid, such that as the Moon's gravity acts on the Earth, the shape of the Earth is distorted, becoming elongated at the equator and shortened at the poles. While this effect is detectable by scientific instruments, one can see this much more dramatically from the more fluid ocean water. The moons gravity acts the strongest on the area of Earth facing the moon, causing a tidal bulge to occur on this "near side" of the Earth. On the far side, the gravitational effect of the moon is dominated by inertia generated from the Earth itself circling the moon. This causes the second tidal bulge on the "far side", as shown in Fig. 1. As the Earth spins beneath these tidal bulges, one sees what are known as low and high tides. For a more comprehensive explanation of the mechanics of the tides, as well as the role that the sun plays in their formation, see Butikov. [2]
As the Earth spins beneath these tidal bulges, it attempts to drag the bulges along with it. The friction generated from this motion slows down the Earth's spin in addition to enlarging the orbit of the moon. This spin-down rate has been proven analytically as well as measured, showing that the day lengthens by 1.5 ms/century. [3] One can use this value to calculate the power contained in the tides.
First, note that this spin-down rate corresponds to a change in the period of the Earth T as it rotates about its axis per unit time, such that
| dT dt |
= | 0.0015 sec century-1 100 y century-1 × 365 d y-1 × 24 h d-1 × 3600 sec h-1 |
| = | 4.756 × 10-13 seconds/second. |
With this value in mind, we observe that the earth's rotational kinetic energy is
| E | = | I 2 |
( | 2π T |
)2. |
The moment of inertia I is given in terms of earth's mass M and radius R by
| I | = | 2 5 |
M R2 |
| = | 2 5 |
× 5.972 × 1024 kg × (6.378 × 106 m )2 | |
| = | 9.717 × 1037 kg m2. | ||
Differentiating the energy with respect to time gives
| P | = | dE dt |
= |
|
||||
| = |
|
|||||||
| = | - 2.83 × 1012 Watts. |
This number gives the energy loss in Joules per second of the Earth as it rotates beneath the tidal bulges. If the sign is flipped, this value can instead be interpreted as the amount of energy transferred to the tidal motion from the Earth's rotation. In the steady state this must equal the energy lost by the tides to tidal friction. The energy dissipated by the tides over a calendar year is then
| 2.83 × 1012 J sec-1 × 3600 sec h-1 × 24 h d-1 × 365 d y-1 | = | 8.925 × 1019 J y-1 |
This value gives a theoretical maximum amount of harnessable tidal energy over one calendar year. Note that the energy consumption of civilization in 2021 was 5.95 × 1020 J. [1] While there is an immense amount of energy contained in the tides, viable locations for tidal power stations and the efficiency of these stations makes harnessing all of this energy exceedingly difficult, if not unfeasible. The next section explores current capacities of tidal power stations, as well as discusses technological and economic limitations.
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| Fig. 2: The left side depicts a tidal barrage with closed sluice gates when the ocean has reached low tide. The right side depicts the flow of water as the sluice gates are opened, allowing the tidal basin to empty into the ocean. As water flows through the barrage, the turbine spins and generated electricity. (Source: B. Cantrall) |
Current tidal power stations range in capacity from 500 kW at the Bluemull Sound Tidal Stream Array in the United Kingdom to 254 MW at the Shiwa Lake Tidal Power Station in South Korea, with only 9 tidal power stations operational worldwide as of 2023. [4,5] Many tidal power stations are built along tidal barrages that separate the ocean from a tidal basin or lake. When the tide is high, sluice gates are closed along the barrage so that as the ocean water level lowers, the level in the basin remains high. At low tide the sluice gates are opened, causing a turbine to spin and generate electricity as water flows from the tidal basin to the ocean, as shown in Fig. 2. Thus, viable locations for tidal power stations of this type must have large differences in tidal range. The Shiwa Lake Tidal Power Station takes advantage of this method, as well as the second largest tidal power station, the Rance Tidal Power Station in France. Another method of generating electricity from the tides is tidal stream energy, which takes advantage of locations with high ocean currents. These locations most often include places where tidal channels and waterways become narrow. Turbines are placed in strategic places in these locations and generate electricity from the water currents. As tidal stream generators are a fairly new technology, there is no industry standard for the design of these stations, such as turbine array spacing. This method is used in the Bluemull Sound Tidal Stream Array in the United Kingdom, which currently includes five 100 kW turbines.
Not only are these stations relatively expensive to deploy, the electricity production cost can be greater than that of conventional energy sources, as is the case for tidal stream energy. [6] However, high production cost can be mitigated by optimizing the layout of a tidal stream farm. [7] Technological advancement is thus crucial to achieve the necessary reduction in cost and deployment time that would make tidal energy a competitor to conventional energy sources. [5] In the case of the Bluemull Sound Tidal Stream Array, data taken on wake interactions and array spacing throughout the deployment of the turbines allows for restructuring of the array layout as new turbines are added. [8] Projects such as this are crucial to the development of tidal stream energy and tidal energy as a whole.
Interest in tidal energy as a renewable energy source has risen as global energy consumption increases, with a 13% growth in power produced from the ocean from 2018 to 2019. [5] This is due in part to the desire to move away from carbon-based energy sources, which are known to contribute heavily to air pollution and climate change. While the energy contained within the tides is immense, harnessing this energy is difficult due to available locations for tidal power stations, deployment costs, and technological limitations. For example, tidal power stations must produce hundreds of thousands of megawatts of power to compete with the production of conventional energy sources. [5] Major research and development must be done to reduce costs associated with deploying and maintaining a tidal power station, as well as increase the capacity of these stations.
© Brianna Cantrall. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. 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.
[1] "BP Statistical Review of World Energy2022," British Petroleum, June 2022.
[2] E. I. Butikov, "A Dynamical Picture of the Oceanic Tides," Am. J. Phys. 70, 1001 (2002).
[3] G. B. Arfken et al., International Edition University Physics (Academic Press, 1984), pp. 212-228.
[4] S. P. Neill et al., "The Wave and Tidal Resource of Scotland," Renew. Energy 114A, 3 (2017).
[5] M. S. Chowdhury et al., "Current Trends and Prospects of Tidal Energy technology," Environ. Dev. Sustain. 23, 8179 (2021).
[6] M. Melikoglu, "Current Status and Future of Ocean Energy Sources: A Global Review," Ocean Eng. 148, 563 (2018).
[7] A. Vazquez and G. Iglesias, "Device Interactions in Reducing the Cost of Tidal Stream Energy," Energy Convers. Manage. 97, 428 (2015).
[8] A. Macleod et al., "Tidal Resource, Turbine Wake and Performance Modelling on the EnFAIT Project," Nova Innovation, 2020.