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| Fig. 1: CV Hyundai Ambition Pictured (Source: Wikimedia Commons) |
Maritime transport moves over 80% of all traded goods worldwide. [1] Decarbonizing overseas shipping has proven to be a significant challenge, as available clean fuels and battery storage options lack the stability, cost, and energy density of diesel. One proposed decarbonization strategy is powering ships using solar energy. In this study, we use rough approximations to assess the practicality of powering container ships using solar energy.
We consider the CV Hyundai Ambition, as shown in Fig. 1, is a 2012 New Panamax class container ship known for its relatively high fuel efficiency. This ship measures 366 m in length and 51.25 m in beam, and carries 13,082 TEU (Twenty-foot Equivalent Units) at maximum capacity. [2] Container ship fuel consumption varies by speed, quantitative speed fuel relations for 10000+ TEU ships are shown in the Table 1.
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| Table 1: CV Hyundai Speed vs Fuel Consumption. [2] |
The sun irradiates 1361 W/m2 onto earth, but when averaged over the Earth's entire surface area, this drops to 340 W/m2. [3] Gas and aerosol absorption in the atmosphere reduce irradiance by approximately 25%. [4] According to a study by the Earth surveying satellite MODIS, at any given moment roughly 72% of the ocean is covered with clouds. While solar energy transmission through clouds varies heavily with cloud thickness, for this estimate, we'll approximate cloud cover losses as a general reduction in light transmission by 20%. [5,6] With today's highest performing solar panels only capturing about 25% of available light energy, this gives an average sustained energy flux of [7]
| Φ | = | 1361 W/m2 4 |
× 0.75 × (1 - 0.20 × 0.72) × 0.25 = 54.6 W/m2 |
If we approximate the CV Hyundai's deck as rectangular, the area available for solar array is
This produces power
or 1.024 MW. This is 2.0% of the power necessary to operate the CV Ambition at 18 kts.
Modern solar panels are typically around 22% efficient and are based on the p-n junction solar cell, which have an upper solar efficiency limit of 26%.[8] However, the thermodynamic limit for solar power production of any kind is the Carnot efficiency
| η | = | 1 - | TEarth TSun |
= | 1 - | 300°K 6000°K |
= | 0.95 |
or 95%. If we consider an optimized shipping route with 95% efficient solar panels, along the equator, and under cloudless skies the maximum solar power generation is
| Φmax | = | 1361 W/m2 π |
× 0.75 × 0.95 | = | 308.7 W/m2 |
With maximally efficient solar panels and 100% solar transmission through the atmosphere, an 18,757 m2 array could maintain a maximum wattage of 5789 kW, approximately 11.7% of the 18 kts required output, and about 3.98% of the 25 kts cruising speed power requirement. Even operating at the theoretical solar power production limit solar power alone could not sustain the extreme energy demands of traditional cargo ships.
The vast majority of energy consumed by a ship is consumed counteracting hydrodynamic drag forces on the ship hull. This drag can be split into two categories: wave drag and skin friction. Wave drag is caused by the forced displacement of water by the ship hull and associated turbulent losses, while frictional drag is caused by the viscous drag of water along the surface of the ship. For cargo ships, skin friction drag accounts for over 90% of the total drag and generally follows the equation: [9]
where C is a resistance coefficient, A is the hull surface area, and V is speed.
On cargo ships, the energy consumption per container tends to decrease with larger ships in accordance with scaling laws. The number of containers a ship can carry is proportional to the volume (L3), while drag scales with surface area (L2). Given this relation, doubling ship dimensions can increase capacity by a factor of eight, while only increasing drag by four times.
For a solar powered ship however, the deck surface area available for solar panels scales similarly to the hull surface area. Thus increasing the size of the ship increases both solar power production and drag, cancelling potential gains.
Two strategies to reduce drag and shrink the energy gap are to decrease the ship speed, and reduce the drag coefficient. Since drag is proportional to the speed squared, reducing the speed by half could reduce energy requirements by four times. Likewise, recent technological advancements in superhydrophobic surfaces, which use specially engineered surface geometries to reduce friction, have been proven in small scale to reduce the skin friction coefficient by orders of magnitude in controlled experiments. [10] While superhydrophobic surfaces are currently impractical at scale, future advancements in this technology could provide an outlet to drastically reduce drag losses and the energy costs of large cargo ships.
In its current state, powering large container ships via solar energy alone is not practical due to the insufficient solar energy flux, relative to the ships' available deck area and energy demand. Significant technological advancements in solar panel efficiency and drag reduction would be necessary for solar powered cargo shipping to become practical at any scale.
© Atticus Cummings. 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.
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[8] W. Shockley and H. J. Queisser, "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells," J. Appl. Phys. 32, 510 (1961).
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