From time immemorial until roughly the 19th century, boats have been powered by either muscle power or the wind. Galleys were driven by oars and everything else raised sails to be propelled across the seas and oceans. The advent of steam changed that. First boilers were fired by wood and coal, and then by oil as ships got bigger and faster with greater and greater range. Oil, as the densest form of energy available, was essential to both effective military ships and competitive commercial ships. Some large military ships and submarines are now nuclear, and coal retains a sliver of the market in antique vessels - the SS Badger which ferries cars from Muskegon to Manitowoc is an example - but the vast majority of all shipping is still powered by bunker fuel feeding boilers or diesels.
Alternative energy has made some small inroads on e.g. pleasure craft for auxiliary electrical power, but major vessels are still running on oil both in and between ports. This shows strong signs of changing; the high cost of oil is rekindling interest in sail. Modern materials and automation have reduced the labor requirements to use it. Roller-furling jibs are one thing, but computer-controlled parafoil kites are a whole new game. Flying well above the waves, these kites can capture more power than even the highest topsail of a clipper ship. With favorable winds, even large cargo ships can see substantial fuel savings, greater speeds or both.
All of this begs the questions (I'm sure you're anticipating me by now):
Solar energy isn't going to manage. A large container ship might be over 350 meters long and 48 meters wide, for a footprint of 16800 m2. Even if all of this area could be covered with PV cells at 20% efficiency (yielding ~200 W/m2 in full sun) the total power output would be a mere 3.36 MW. Large container ships have engines as powerful as 80 megawatts; even if a deck-full of containers could be covered by PV, this is clearly too great a demand to be satisfied by direct sunlight.
Sky WindPower Corporation is attempting to commercialize the "gyromill" concept invented by the Australian professor Bryan Roberts. The gyromill or flying electric generator (FEG) is an autogyro kite with an electric generator attached; it can be sent aloft by powering its rotors with electricity supplied through its tether, and then return power to the ground when it reaches an altitude where the wind is strong.
Sky Windpower claims a power capability of 1.5 MW from rotors totalling 24329 ft2 (2660 m2) in swept area. The current wind-power champ is a 5 MW ground-based turbine with a single rotor of roughly 124 meters diameter (12080 m2 area); if a single-rotor FEG could return the same power per unit area, it would generate up to 6.8 MW. One or two of these would be able to supply a substantial fraction of even a large ship's propulsive power demands.
One thing that's not used in the FEG concept is the tension in the tether. What good is pulling the Earth around? It won't go anywhere... but a ship does. A wind turbine generating 6.8 MW of power from a stream of air moving at 15 m/sec requires a minimum force of 454 kilo-Newtons (~102,000 pounds) just to hold it in place; a flying generator would need even more to compensate for aerodynamic drag caused by lift (induced drag). A force of 102,000 pounds pulling forward on a ship moving at 15 knots supplies 4700 horsepower, or 3.5 megawatts of tractive power; as the speed of the ship goes up, so does the power per unit of force. (This force could be increased by flying back and forth across the wind, perhaps at some cost in electric generation.) The combined electric and tractive power supplied by a 124-meter marine FEG might be 12 megawatts or more.
Two such units on a ship could supply 24 MW. They would even be able to supply net power when the ship was sailing directly upwind, though the ability to fly the FEG's at different altitudes with different winds would allow the operator to pick the most favorable. This would allow the ship to shut down its diesel engines and operate on wind power alone. It would not run fast, but a ship capable of 27 knots on 80 MW would still manage at least 18 knots on 24 MW. On a route of 5000 nm, the difference in trip time would be about 3 days 21 hours (7.7 days vs. 11.6 days) with the best winds. A ship generating 80 MW by burning residual oil at 18,830 BTU/lbm1 and 50% efficiency would burn 29,000 pounds per hour; at this rate, a 5000 nm voyage at 27 knots would consume 2540 m3 (671,000 gallons) of fuel. If this fuel costs $300/tonne, the FEG system could save $731,000 in fuel at the cost of less than 4 days at sea. If the ship's (and cargo's) time costs less than about $180,000 per day, this looks like a profitable tradeoff. It will only get more so as petroleum prices rise.
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