Shape, Drag, and Power in Ammonoid Swimming

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Abstract
This study assesses swimming potential in a variety of ammonoid shell shapes on the basis of coefficients of drag (Cd) and the power needed to maintain a constant velocity. Reynolds numbers (Re) relevant to swimming ammonoids, and lower than those previously studied, were examined. Power consumption was scaled to a range of sizes and swimming velocities. Estimates of power available derived from studies of oxygen consumption in modern cephalopods and fish were used to calculate maximum sustainable swimming velocities (MSV).Laterally compressed, small thickness ratio (t. r.) ammonoids, previously assumed to be the most efficient swimmers, do not experience the lowest drag or power consumption at all sizes and velocities. At low values of size and velocity associated with Reynolds numbers below 104, less compressed forms have smaller drag coefficients and reduced power requirements. At hatching a roughly spherical shell shape would have minimized drag in ammonoids; with increasing size, hydrodynamic optima shift toward compressed morphologies.The high energetic cost of ammonoid locomotion may have limited dispersal and excluded ammonoids from high current velocity environments.