We investigated the hydrodynamic properties of cephalopod shell sculpture in two ways: 1) flow visualization experiments with sculptured shells; and 2) application of drag coefficient data for simple geometric bodies to cephalopod shells. Results of this work suggest:
1) the hydrodynamic effect of shell sculpture depends primarily on the size of the sculptural elements relative to the size of the shell and on the positions of sculpture elements on the shell and relative to each other.
2) sculpture is detrimental to swimming (reduces hydrodynamic efficiency) if it exceeds the height of the lower part of the shell's boundary layer.
3) sculpture is advantageous to swimming (increases efficiency) if it remains immersed in the boundary layer and induces premature conversion to turbulent boundary layer flow. To be hydrodynamically optimal, small shells (diam ≈ 10 cm) must have rough (sculptured) surfaces, whereas large shells (diam ≈ 100 cm) require smooth surfaces. Thus, in order to maintain maximum efficiency throughout life, the ontogeny of small individuals, or species, should be characterized by progressive roughening of the shell, while large forms should become increasingly smooth. Such allometries are observed among many ammonoids.
4) sculpture always has an effect on the flow around a cephalopod shell. In some species this effect was probably negligible, while in others, those with compressed shells especially, it was probably of major importance. In these species, sculpture appears to have functioned primarily to increase swimming ability.