3D MODELING OF AMMONITE HYDRODYNAMICS

We explore the hydrodynamic efficiency of a wide range of planispiral shell shapes belonging to extinct ammonoid cephalopods, and demonstrate trade-offs in growth trajectories and swimming potential. We produce three dimensional models of ammonite shells in Blender, including: replicas of specific fossils; synthetic forms based on ideal shapes or literature examples; and hybrid models that change real forms in idealized ways. These models are printed in medical grade resin for water flume experiments, and rendered in ZBrush as dynameshed models for inclusion in ANSYS Fluent hydrodynamics modeling software. Flow simulations treat ammonoids of average size (5-10 cm) at stable water speeds ranging from 1-50 cm/s, with particular focus on speeds of one shell-length per second. We measure drag force at different velocities, and calculate coefficients of drag across a large range of Reynolds numbers. We use surface area and volume in these calculations, to easily compare hydrodynamic consequences to shell growth trajectories. This also allows common estimates of drag coefficients for larger ranges of shell morphospace. In several cases, serpenticones, spherocones, and ammonoids of average shape share a shallow decrease of drag coefficient with increasing size (and speed), which allows a small discount to their increased drag force. Oxycones, in contrast, have a steep drop in drag coefficient which provides a much greater discount to their drag increase with size. We further evaluate the consequences of ornament (ribs and venter details) and extent of soft body extrusion. Results, including drag forces, rankings of shell morphotypes, and trends in forces over variations in shape and speed, are consistent with some previous published studies and with new water channel flume experiments. The synthetic models and emerging 3D printing technologies allow advantages over past methods. First, idealized and altered fossil forms are easy to construct. Second, morphological variables are easier to isolate and assess (for example, instant measurement of surface area). Third, matching models make physical experiments easier to match to computational solutions. Together these methods are powerful tools to illuminate functional morphology in extinct life, with ammonites as an ideal case study.