Math Is Hard

CNN is correct that it would be theoretically possible to convert modern cargo ships to sailing vessels, but would it be practical.Let’s do some math.

As a first approximation, let’s assume that the amount of force necessary to move the ship roughly varies in proportion to its displacement, the mass of water it pushes aside as it moves. The Cutty Sark clipper ship displaced about 900 tonnes when loaded and underway and carried just over 2,900 square metres of sails supported by over 17 km of rigging rope. The typical medium-sized oil tanker displaces 1,200,000 tonnes unloaded. That’s over 130 times greater displacement. Thus, we might expect that an unloaded tanker would need at least 380,00 square metres of sail area to achieve the performance of a sailing ship that was obsolescent in the mid-19th-century. Thousands of cargo ships are this large or larger. [Opps, see Update 3.]

BTW, 380,000 square metres is about 94 acres. It will take a lot of cotton (or, more likely, dead dinosaurs to make the kevlar) to make the sails for one ship. Thousands of sets of sails would be necessary to keep world commerce alive.

UPDATE—Where would the energy to run the motors needed to control such sails come from? They would be too heavy to be operated by human muscle power.

Also, how would such a ship maneuver in the confines of a harbor?


UPDATE 3—Math is hard indeed. I slipped a digit. The mass ratio is 1,300:1 rather than 130:1, so the sail area required is 10X larger—940 acres!

Thanks to @WitCoHE_Bak for catching my error.

3 thoughts on “Math Is Hard

  1. To be fair though, I think the idea is to launch the sails as a supplement to regular power. Not as a complete replacement. One of those things you’d only deploy when conditions are safe and boring. In those conditions I suppose it might reduce fuel requirements by two or three percent maybe.

  2. Notice that the ship in the image is local freighter of rated for 10s of TEUs probably in coastal or inter-island service, not a Maersk colossus that transports 1,000s of containers between continents.

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