TABLE 1. Instructions for replicating the whorl section and septa used to digitally construct each 3D model. Each of these components are translated, rotated, and scaled down (with respect to the center of the aperture as a datum) to build a shell from the aperture toward the apex. These instructions are necessary for the array generation tool in Blender 2.76 (computer graphics software; Blender Online Community, 2017).
Translation (mm) | Rotation | Scale | ||
Nautilida - Nautilus pompilius | x | 0.0000 | -1.600 | 0.995 |
y | -0.3600 | 0.000 | 0.995 | |
z | -1.5300 | 0.000 | 0.995 | |
Ellesmerocerida - Plectronoceras | x | 0.0000 | 0.410 | 0.991 |
y | 0.0000 | 0.000 | 0.991 | |
z | 0.9350 | 0.000 | 0.991 | |
Adoral poriton of Orthocerid, Endocerid (Circular), Endocerid (Depressed) |
x | 0.0000 | 0.000 | 0.996 |
y | 0.0000 | 0.000 | 0.996 | |
z | 3.0000 | 0.000 | 0.996 | |
Adapical poriton of Orthocerid, Endocerid (Circular), Endocerid (Depressed) |
x | 0.0000 | 0.000 | 0.986 |
y | 0.0000 | 0.000 | 0.986 | |
z | 8.0000 | 0.000 | 0.986 | |
Oncocerida - Oonoceras | x | -0.0550 | 0.000 | 0.995 |
y | 0.0000 | -0.031 | 0.995 | |
z | 0.4400 | 0.000 | 0.995 | |
Oncocerida - Euryrizocerina | x | 0.0358 | 0.000 | 0.996 |
y | 0.0000 | -0.490 | 0.996 | |
z | 0.4550 | 0.000 | 0.996 | |
Discosorida - Phragmoceras (Early) |
x | -0.5500 | 0.000 | 0.993 |
y | 0.0000 | 1.000 | 0.993 | |
z | 1.0400 | 0.000 | 0.993 | |
Discosorida - Phragmoceras (Middle) |
x | -0.5200 | 0.000 | 0.993 |
y | 0.0000 | 1.060 | 0.993 | |
z | 1.1000 | 0.000 | 0.993 | |
Discosorida - Phragmoceras (Late) |
x | -0.4600 | 0.000 | 0.995 |
y | 0.0000 | 1.100 | 0.995 | |
z | 1.4500 | 0.000 | 0.995 |
TABLE 2. Centers of buoyancy, total centers of gravity (y component ignored due to model symmetry), masses and volumes of each component of unique density; sh = shell; sb = soft body; cg = cameral gas; cl = cameral liquid; dep = cameral or endosiphuncular deposits; ct = camerae total; wd = water displaced, separation between centers of buoyancy and gravity (BG), and stability index (St) for each hydrostatic experiment. Experiment (Exp.) numbers correspond to figured hydrostatic models: 2.4 – Nautilus pompilius with soft body flush at aperture; 2.5 – Nautilus pompilius with extended soft body; 2.6 – Nautilus pompilius CT-scanned model; 3.1 – the ellesmerocerid Plectronoceras with a minimum estimate of body chamber ratio (40% body chamber length to total length); 3.2 – the ellesmerocerid Plectronoceras with the body chamber ratio (35% body chamber length to total length) required for near neutral buoyancy; 4.1 – orthocerid model with adapically distributed gas; 4.2 – orthocerid model with adorally distributed gas; 4.3 – evenly distributed Φgas within each camera; 5.1 – orthocerid, larger body chamber, adapical gas; 5.2 – orthocerid, larger body chamber, adoral gas; 5.3 – orthocerid, larger body chamber evenly distributed Φgas; 6.1 – evenly distributed cameral deposits among all camerae; 6.2 – adapical cameral deposits; 6.3 – ventrally displaced cameral deposits; 7.1 – endocerid, central siphuncle; 7.2 – Endoceras; 8.1 – oncocerid, Oonoceras; 8.2 – oncocerid, Euryrizocerina; 9.1 – Phragmoceras, adapical cameral gas; 9.2 – Phragmoceras, adoral cameral gas; 9.3 – Phragmoceras, cameral gas evenly distributed.
Center of Buoyancy | Center of Gravity | ||||||||||||
Exp | x (mm) | z (mm) | x (mm) | z (mm) | Vsh (cm3) | msh (g) | Vsb (cm3) | msb (g) | Vcg (cm3) | mcg (g) | Vcl (cm3) | mcl (g) | Vdep (cm3) |
2.4 | -38.794 | -22.716 | -35.923 | -27.601 | 53.802 | 140.961 | 505.602 | 538.466 | 96.851 | 0.117 | 33.674 | 34.516 | NA |
2.5 | -30.715 | -13.577 | -27.331 | -17.378 | 53.802 | 140.961 | 695.690 | 740.910 | 109.053 | 0.131 | 21.471 | 22.008 | NA |
2.6 | -32.391 | -13.926 | -29.408 | -17.862 | 69.881 | 183.088 | 778.307 | 828.897 | 132.897 | 0.160 | 0.000 | 0.000 | NA |
3.1 | -4.306 | 25.116 | -2.717 | 21.140 | 4.093 | 10.725 | 22.327 | 23.778 | 5.470 | 0.007 | 0.000 | 0.000 | NA |
3.2 | -4.306 | 25.116 | -2.617 | 20.498 | 4.260 | 11.162 | 20.775 | 22.125 | 6.855 | 0.008 | 0.000 | 0.000 | NA |
4.1 | -0.001 | 176.815 | -0.001 | 137.841 | 62.483 | 163.705 | 277.763 | 295.817 | 108.352 | 0.130 | 54.086 | 55.438 | NA |
4.2 | -0.001 | 176.815 | -0.001 | 159.402 | 62.483 | 163.705 | 277.763 | 295.817 | 108.051 | 0.130 | 54.293 | 55.651 | NA |
4.3 | -0.001 | 176.815 | -0.001 | 147.522 | 62.483 | 163.705 | 277.763 | 295.817 | 108.357 | 0.130 | 54.278 | 55.635 | NA |
5.1 | -0.001 | 176.815 | -0.001 | 138.644 | 60.015 | 157.240 | 328.454 | 349.804 | 106.383 | 0.128 | 7.938 | 8.136 | NA |
5.2 | -0.001 | 176.815 | -0.001 | 141.841 | 60.015 | 157.240 | 328.454 | 349.804 | 106.271 | 0.128 | 7.941 | 8.139 | NA |
5.3 | -0.001 | 176.815 | -0.001 | 140.054 | 60.015 | 157.240 | 328.454 | 349.804 | 106.055 | 0.128 | 7.928 | 8.126 | NA |
6.1 | -0.001 | 176.815 | -0.052 | 147.899 | 62.483 | 163.705 | 277.763 | 295.817 | 162.473 | 0.196 | 0.000 | 0.000 | 21.298 |
6.2 | -0.001 | 176.815 | -0.001 | 165.130 | 62.483 | 163.705 | 277.763 | 295.817 | 162.473 | 0.196 | 0.000 | 0.000 | 21.258 |
6.3 | -0.001 | 176.815 | -0.840 | 147.948 | 62.552 | 163.887 | 277.756 | 295.810 | 162.410 | 0.196 | 0.000 | 0.000 | 21.285 |
7.1 | -0.001 | 176.815 | -0.001 | 149.511 | 61.683 | 161.610 | 278.727 | 296.844 | 162.410 | 0.196 | 0.000 | 0.000 | 21.692 |
7.2 | -0.001 | 176.816 | 0.348 | 150.683 | 82.767 | 216.851 | 346.129 | 368.627 | 154.905 | 0.161 | 0.000 | 0.000 | 8.098 |
8.1 | -7.484 | 19.929 | -6.454 | 18.152 | 2.130 | 5.581 | 9.182 | 9.779 | 3.666 | 0.004 | 3.204 | 3.284 | NA |
8.2 | -9.234 | 23.448 | -7.123 | 21.424 | 2.356 | 6.173 | 14.448 | 15.387 | 4.241 | 0.005 | 2.403 | 2.463 | NA |
9.1 | 9.911 | 50.859 | 5.023 | 47.644 | 15.963 | 41.824 | 71.255 | 75.887 | 27.096 | 0.033 | 10.151 | 10.405 | NA |
9.2 | 9.911 | 50.859 | 8.451 | 46.676 | 15.963 | 41.824 | 71.255 | 75.887 | 27.673 | 0.033 | 9.892 | 10.139 | NA |
9.3 | 9.911 | 50.859 | 6.572 | 47.500 | 15.963 | 41.824 | 71.255 | 75.887 | 27.337 | 0.033 | 10.076 | 10.328 | NA |
TABLE 2 (continued).
Center of Buoyancy | Center of Gravity | ||||||||||||
Exp | x (mm) | z (mm) | x (mm) | z (mm) | mdep (g) | Vct (cm3) | Vwd (cm3) | mwd (g) | mtotal (g) | ɸgas (%) | ɸdep (%) | B͞͞͞͞G (mm) | St |
2.4 | -38.794 | -22.716 | -35.923 | -27.601 | NA | 139.438 | 698.842 | 716.313 | 714.059 | 74.3 | NA | 5.666 | 0.064 |
2.5 | -30.715 | -13.577 | -27.331 | -17.378 | NA | 139.438 | 882.227 | 904.283 | 904.010 | 83.6 | NA | 5.090 | 0.053 |
2.6 | -32.391 | -13.926 | -29.408 | -17.862 | NA | 132.897 | 986.400 | 1011.060 | 1011.060 | 100.8 | NA | 4.938 | 0.050 |
3.1 | -4.306 | 25.116 | -2.717 | 21.140 | NA | 5.470 | 31.891 | 32.688 | 34.503 | 133 | NA | 4.282 | 0.135 |
3.2 | -4.306 | 25.116 | -2.617 | 20.498 | NA | 6.855 | 31.891 | 32.688 | 33.287 | 108 | NA | 4.917 | 0.155 |
4.1 | -0.001 | 176.815 | -0.001 | 137.841 | NA | 162.473 | 502.718 | 515.286 | 515.091 | 66.6 | NA | 38.974 | 0.490 |
4.2 | -0.001 | 176.815 | -0.001 | 159.402 | NA | 162.473 | 502.718 | 515.286 | 515.303 | 66.6 | NA | 17.414 | 0.219 |
4.3 | -0.001 | 176.815 | -0.001 | 147.522 | NA | 162.473 | 502.718 | 515.286 | 515.287 | 66.6 | NA | 29.293 | 0.368 |
5.1 | -0.001 | 176.815 | -0.001 | 138.644 | NA | 114.249 | 502.718 | 515.286 | 515.307 | 93.1 | NA | 38.172 | 0.480 |
5.2 | -0.001 | 176.815 | -0.001 | 141.841 | NA | 114.249 | 502.718 | 515.286 | 515.310 | 93.1 | NA | 34.975 | 0.440 |
5.3 | -0.001 | 176.815 | -0.001 | 140.054 | NA | 114.249 | 502.718 | 515.286 | 515.297 | 93.1 | NA | 36.762 | 0.462 |
6.1 | -0.001 | 176.815 | -0.052 | 147.899 | 55.800 | 162.473 | 502.718 | 515.286 | 515.322 | 100 | 13.1 | 28.917 | 0.364 |
6.2 | -0.001 | 176.815 | -0.001 | 165.130 | 55.695 | 162.473 | 502.718 | 515.286 | 515.217 | 100 | 13.1 | 11.685 | 0.147 |
6.3 | -0.001 | 176.815 | -0.840 | 147.948 | 55.767 | 162.410 | 502.718 | 515.286 | 515.464 | 100 | 13.1 | 28.880 | 0.363 |
7.1 | -0.001 | 176.815 | -0.001 | 149.511 | 56.833 | 162.410 | 502.718 | 515.286 | 515.288 | 100 | 86.9 | 27.305 | 0.343 |
7.2 | -0.001 | 176.816 | 0.348 | 150.683 | 21.218 | 154.905 | 591.900 | 606.697 | 606.695 | 100 | 27.2 | 26.135 | 0.311 |
8.1 | -7.484 | 19.929 | -6.454 | 18.152 | NA | 6.873 | 18.185 | 18.640 | 18.648 | 53.5 | NA | 2.054 | 0.078 |
8.2 | -9.234 | 23.448 | -7.123 | 21.424 | NA | 6.650 | 23.454 | 24.041 | 24.029 | 63.7 | NA | 2.925 | 0.102 |
9.1 | 9.911 | 50.859 | 5.023 | 47.644 | NA | 37.688 | 124.906 | 128.029 | 128.148 | 73.4 | NA | 5.850 | 0.117 |
9.2 | 9.911 | 50.859 | 8.451 | 46.676 | NA | 37.688 | 124.906 | 128.029 | 127.883 | 73.4 | NA | 4.431 | 0.089 |
9.3 | 9.911 | 50.859 | 6.572 | 47.500 | NA | 37.688 | 124.906 | 128.029 | 128.071 | 73.4 | NA | 4.736 | 0.095 |
TABLE 3. Comparison of hydrostatic computations using different density estimates for the soft (ρsb) body and shell (ρsh) for the CT-scanned Nautilus pompilius model. Averaged ρ refers to the densities used in all other hydrostatic experiments in this study. Φgas = percent of phragmocone occupied by cameral gas at neutral buoyancy. St = stability index. The percent change from the averaged density values are denoted by %Δ.
ρsb (g/cm3) | ρsh (g/cm3) | Φgas (%) | St | %ΔΦgas | %ΔSt | |
High ρ (g/cm3) | 1.068 | 2.94 | 118.9 | 0.057 | 18.0 | 15.7 |
Low ρ (g/cm3) | 1.060 | 2.53 | 93.3 | 0.046 | -7.4 | -7.7 |
Averaged ρ (g/cm3) | 1.065 | 2.62 | 100.8 | 0.050 |