American Scientist

To the Editors:

The passive engulfment model for lunge feeding in “The Ultimate Mouthful” by Jeremy Goldbogen (March–April) appears to violate the law of conservation of momentum because it shows the whale’s speed dropping to zero. As a most basic first approximation of the process, if an average whale engulfs a mass of water equal to its own mass, the velocity after engulfment should be one half the velocity before engulfment. Factoring in active swimming and changes in drag during engulfment will modify that result, but any model that stops a whale dead in its tracks should have been stopped dead in its tracks.

Peter Kaiteris
West Hempstead, NY

Dr. Goldbogen responds:

Peter Kaiteris is correct. The “passive engulfment” scenario of Figure 9 indeed shows a whale that is suddenly decelerating to a zero speed at the moment of complete buccal cavity filling—clearly an unrealistic sequence of events. But this never occurred in our simulations because they were instructed to automatically terminate whenever the cavity filled up. Such an instantaneous drop in speed was included to show that “passive engulfment” fails. Our computer model did account for the momentum transfer between whale and engulfed mass, as can be seen in the “active engulfment” graph shown in that same figure. In this case, the whale’s and engulfed water’s final speeds (that is, by the time the mouth closes) are indeed at about half the whale’s initial speed. That is to be expected because most of the force sustained by the whale comes from the reaction to its forward push of the engulfed water.