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Of the many shell morphologies produced by ammonoid cephalopods, the helical torticone shape appears poorly-suited to rapid locomotion. We investigate torticone hydrostatics and hydrodynamics through virtual modeling, computational fluid dynamics simulations, and water-chamber experiments, using the Cenomanian (Cretaceous) turrilitid Mariella brazoensis (Roemer, 1852) as a test case. Our hydrostatic model suggests that M. brazoensis, and other torticones, could attain neutral buoyancy. This morphotype is highly stable compared to planispiral cephalopods with a slightly tilted, apex-upward orientation. The corresponding mass distribution, relative to the source of jet propulsion at the hyponome, suggests that jet thrust would be more efficiently transmitted into upwards movement than horizontal movement. Most directions of thrust would send the shell spinning about its vertical axis. We 3D printed shell models to have either surpluses or deficiencies in buoyancy that imparted estimated thrusts of extant cephalopod analogues in the vertical directions within a water chamber. The models consistently rotate aperture-backwards during upward movement, and aperture-forwards during downward movement. A neutrally buoyant model was used to assess rotational aptitude during active locomotion. The model required low torques to sustain rotation. Simulations of water flow around the shell support the movement directions observed in the physical experiments and demonstrate that hydrodynamic drag is lower in the vertical directions than the horizontal directions. These results show that the animal within a torticone shell could spin about its vertical axis easily; perhaps even simple respiration could have allowed rotation at ~20 degrees per second. Hydrostatic and hydrodynamic properties of torticones suggest that rotation and vertical movement potential constrained the behavior of these helically-coiled cephalopods. We interpret that torticone ammonoids, prominent throughout neritic and epeiric seas during the Albian and Cenomanian (Cretaceous), may have used passive spiral motions to feed upon small food items through the water column, and may have had low metabolic demands compared to modern-day coleoids.