The orientation of a submerged body is determined by the positions of its centre of buoyancy and centre of mass. The centre of buoyancy is effectively the pivot point about which the shell rotates. Since the centre of mass will, at rest, lie directly below this point, deducing its location is critical to identifying shell orientation. To demonstrate the effect of moving a small, heavy body within a freely floating shell it is thus necessary to locate the centre of buoyancy and the centre of mass.
The centre of buoyancy is the centre of gravity of the displaced fluid in which the body is immersed. In the models proposed by Trueman (1941) and Kakabadzé & Sharikadzé (1983), the water displaced is approximately equal to the volume of the phragmocone and the living chamber, since both are filled (the phragmocone with gas and cameral fluids, the living chamber with the animal). In contrast, our model reduces the size of the animal such that most of the living chamber is empty. Thus most of the water is displaced by the phragmocone.
The centre of mass is the point at which, from a gravitational point of view, the total mass may be considered to be concentrated. For Trueman, the heaviest part of the ammonite was the body, which filled most of the living chamber. Kakabadzé & Sharikadzé also considered the fluids within the phragmocone. We have concentrated the mass of the animal in a smaller volume.
The centre of buoyancy were found by producing a Plasticene model of that part of the ammonite which displaces water and identifying its centre of mass. Since the density of the Plasticene is uniform, its centre of mass will lie at the same point as a similarly-shaped mass of water. The Plasticene models were suspended from an arbitrary point by a light thread and allowed to come to rest. A vertical line was drawn from the point of suspension downwards. This was repeated for a number of different suspension points. The lines cross at the centre of mass of the Plasticene shape. In this way the centre of buoyancy of the ammonite can be estimated.
The centre of mass is more difficult to deduce since we know nothing about the density or mass distribution of the ammonite soft body parts or how much fluid was within the shell. We follow Trueman’s assumption that it lay close to the centre of mass of the body, the most massive part of the animal, which is taken to be of uniform density.