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Coriolis diagram not drawn for effect

Jan 1, 2003

I want to comment on an error in an otherwise interesting and informative article on the Gulf Stream ("Origins of the Stream," Issue No. 62).

The article gives a good description of the mechanics of the Gulf Stream. However, the diagram in the article that attempts to describe the Coriolis effect using two locomotives is not accurate; it does not describe the relative motion of the ball and the locomotives properly, and does not correctly explain the apparent curvature due to the Coriolis effect. Proper understanding of relative motion should be the stock-in-trade of any mariner.

Referring to the diagram, the ball thrown from the fast locomotive will indeed cross the track ahead of the slow locomotive, as stated in the caption. However, contrary to what the caption says, the ball will appear to follow a straight path, not a curved path, to the observers in the two locomotives, as well as the observer in a plane flying overhead. The reason it is a straight path is because in the frames of reference of each of those observers, the horizontal velocity of the ball is unchanging (neglecting air resistance). The frames of reference of these observers are in uniform, straight-line motion relative to each other. (Note: The ball does follow a curved path downward because of the acceleration of gravity. But we're concerned with motion measured in the horizontal plane.)

For example, in the frame of reference of the fast locomotive, the ball travels directly out at 90° to the axis of the locomotive and crosses the adjacent track exactly abreast of the position of the fast locomotive at that instant. Meanwhile, in that same frame of reference, both the ground and the slow locomotive appear to travel backwardsthe ground more rapidly than the slow locomotive. Therefore, the ball crosses the track ahead of the slow locomotive. Similar arguments can be made to show the straight-line motion of the ball in all other frames of reference mentioned.

This is just a mirror-image of the familiar "constant, bearing, decreasing range" rule regarding risk of collision. Imagine, a movie being made from the fast locomotive. The movie shows the ball leaving the locomotive and traveling outward. Now, run the movie backwards: the ball collides with the fast locomotive. To collide with the fast locomotive, the ball must have a constant true bearing as seen from the fast locomotive; hence, it travels in a straight line as seen from the fast locomotive.

We could use a maneuvering board to determine the course and speed of the ball over the ground, its course and speed relative to either locomotive, the closest point of approach of the ball to the slow locomotive, etc.

The description above is accurate, but it doesn't directly explain why an object acting under the Coriolis effect appears to follow a curved path. A better analogy would be to describe locomotives traveling on curved trackstracks that are each circular paths, with the two circles having the same center but different radiiand with the two locomotives traveling at such speeds that they are always abreast of each other. That is, the locomotives on the inner and outer tracks are always directly in line with the common center of the two circles. The locomotive on the outer track will be going faster than the locomotive on the inner track. This is analogous to points on the same longitude, but at different latitudes, projected onto the plane of the equator. Now when the ball is thrown from the fast locomotive on the outer track toward the slow locomotive on the inner track, the ball will travel in a straight line in relation to a stationary observer. However, the picture will be different to the observers in the two locomotives. The ball will again cross the track of the slow locomotive ahead of the slow locomotive, but now it will appear to travel on a curved path relative to the frames of reference of the two locomotives. The reason for the apparent curved path is that the frames of reference of the two locomotives are rotating, because the locomotives are traveling on curves, not straight, tracks. If the locomotives are going counter-clockwise around the circle (which is how the earth rotates as seen from above the north pole), the ball would appear to curve in the opposite direction, that is clockwise or toward its own right. That is just what currents, winds, and long-range gun projectiles do in the northern hemisphere.

An even better analogy would be of a ball thrown between two people riding on a merry-go-round. The whole merry-go-round is rotating, just like the earth. The ball follows a straight path relative to a non-rotating frame of reference, but a curved path relative to the rotating frame of reference of the merry-go-round.

William G. Collins, Jr. is a retired naval officer who lives in Aiken, S.C.