Fish propel themselves forward by wiggling their tail fin, pushing the water back with each semiwiggle.
The double-tailed dragonfish (dracula bicauda excogitata) does the same thing with two tail fins. Since power is proportional to the square of force, the total propelling power is four times that of each of the two tail fins.
The little known centifin (centipinna impudico ficta) resembles the centipede in that it has much fewer than a hundred tail fins, just like the centipede has fewer than a hundred feet (and certainly fewer than the thousand that the German Tausendfubler would imply). But if it has n tail fins, the propelling force is n times that of a single tail fin, and therefore the power is increased by a factor of n^2.
But this of course assumes that the fish is in good health and wiggles its tail fins in phase
¾all of them to the left or to the right at the same time. What would happen if they each wiggled at random¾at the same rate or frequency, but without coordination of the moments when the wiggling cycles start?For the double-tailed dragonfish, the result would lie between two extremes. If the two tail fins wiggled in antiphase
¾one going left just as the other goes right¾the total forward propelling power would be zero, for the water between the fins would be pushed out when they move toward each other, but would then be sucked back in as they part, leaving the fish osculating forward and backward in the same place. The other extreme is that of perfect coordination or movement in phase, which yields four times the power of a single tail fin.Quite similarly, the power of a centifin with totally independent tail fins wiggling in random phases would lie between zero and n^2 times the power of a single fin. However, both of these extremes are most highly improbable. Clearly the chances of n randomly wiggling fins just happening to be all aligned in phase are hopelessly slim, and the chances of them all just happening to be such that the end effect cancels are (as can be shown) even smaller. But when one considers what happens on the average
¾the average of very many lobotomized centifins with randomly wiggling tail fins¾it works out to n times the power of a single fin. Note that they all swim forward: the minimum is zero, not negative¾there is no way in which a centifin, however neurotic, can phase its fins to swim backward. Some swim a little faster, some a little slower, but the average swims with n times the power of a single fin.Although it is only incidental to our story, some readers may be interested about the habitat of these fish. They are an extremely endangered species, for they can be found in only one place in the world
¾the pink pages of Access to Energy (excogitata means "thought up" and impudico ficta "shamelessly contrived").I invented them to illustrate the coherent fight of a laser.
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Vol. 14, No. 6
Newsletter: Access to Energy Newsletter Archive Volume: Issues Issue/No.: Vol. 14, No. 6 Date: November 30, 2004 08:41 AM Title: "The same thing"
Copyright © 2004 - Access to Energy Newsletter Archive
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