### Re: A 20,000 ton ship sailing east at 20 knots weighs 3 tons less than the same

Date: Wed Apr 26 20:11:29 2000
Posted By: Ken Wharton, Post-doc, Laser/Plasma Physics
Area of science: Physics
ID: 956124804.Ph
Message:

Believe it or not!

Actually, on the equator, I calculated the weight difference should be more like 6 tons.

This is caused by a ficticious force called the Coriolis force . (It's called a ficticious force because it only appears when you're pretending that a rotating reference frame is still. We're on a rotating Earth, and since we think that we're not moving, we see ficticious forces like centrifigal force and the Coriolis force.)

The Coriolis force on a moving object creates an accleration that is proportional to the object's velocity. Ships at rest feel no such force. The direction of the force is in the direction that is both perpendicular to the Earth's axis and also perpendicular to the velocity of the object. For something moving east on the equator, the force is directly up. For something moving west, it's directly down. When you leave the equator, the coriolis force now is at an angle; it has an up-down component and a side- to-side component.

So at the equator, a 20,000 ton ship moving east at 20 knots has an extra 3 tons of coriolis force pulling up on it. A 20,000 ton ship moving west feels like it has an extra 3 tons pulling down. Leaving the equator, the effect drops off as the cosine of the latitude, so at 60 degrees north or south the effect has dropped in half, to the 1.5 ton level that was quoted in your question. If ships could sail near the poles, they would feel no up-down coriolis force at all; it would all be sideways and their weight would not change.

Unlike the oft-quoted effect of toilets spinning the other way in the southern hemisphere, the up-down coriolis force on an east-west moving ship does not depend on which hemisphere you are in; east is always better. (The sideways component of the coriolis force DOES change, though.)

So next time someone says that prevailing east-blowing winds are why east- bound airplane flights are faster than west-bound flights, mention that there's over a 1% difference in effective airplane weight between the two cases, and that might have something to do with it, too!

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