Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-07-03T08:09:48.090Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimating the masses and centers of mass of extinct animals by 3-D mathematical slicing

Published online by Cambridge University Press:  20 May 2016

Donald M. Henderson
Donald M. Henderson*
Affiliation:
Department of Earth Sciences, University of Bristol, Bristol BS8 1RG United Kingdom
Get access Rights & Permissions [Opens in a new window]

Abstract

A mathematical-computational method for determining the volume, mass, and center of mass of any bilaterally symmetric organism is presented. Cavities within the body of an organism such as lungs are easily accommodated by this method. Sagittal and frontal profiles, obtained from tracings of “fleshed-out” skeletal reconstructions, are used to provide limits for defining transverse slices of the body. Any internal cavities are defined by their own sagittal and frontal profiles. The computations consist of mathematically slicing the body and any cavities into independent sets of transverse laminae and computing their masses, centroids, and moments with respect to the three coordinate axes. Further calculations produce the masses and the (x,y,z) coordinates for the centers of mass of the body, any cavities, and the body + cavities. Predicted body masses of large, extant mammals (elephant, giraffe, hippopotamus, and rhinoceros) are in close agreement with actual body masses. New, lower estimates for body masses of selected large dinosaurs, based on modern skeletal reconstructions, are also presented, along with numerical estimates of their centers of mass. This method is an improvement over earlier ones that relied on measuring displaced volumes of water or sand by scale models to estimate the masses, and suspending models by threads to estimate their centers of mass.

Type
Articles
Information
Paleobiology , Volume 25 , Issue 1 , Winter 1999 , pp. 88 - 106
Copyright
Copyright © The Paleontological Society 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature Cited

Alexander, R. McN. 1983. Animal mechanics. 2d ed.Oxford University Press, Oxford.Google Scholar
Alexander, R. McN. 1985. Mechanics of posture and gait of some large dinosaurs. Zoological Journal of the Linnean Society 83: 1–25.Google Scholar
Anderson, J. F., Hall-Martin, A., and Russell, D. A. 1985. Long-bone circumference and weight in mammals, birds, and dinosaurs. Journal of Zoology 207: 53–61.Google Scholar
Bakker, R. T. 1987. The return of the dancing dinosaurs. Pp. 39–69. in Czerkas, S. J., Olsen, E. C. eds. Dinosaurs past and present I. Natural History Museum of Los Angeles County, Los Angeles.Google Scholar
Behrensmeyer, A. K. 1990. Bones. Pp. 232–235. in >Briggs, D. E. G., Crowther, P. R. eds. Paleobiology: a synthesis Blackwell Scientific, Oxford.Google Scholar
Bramwell, C. D. and Whitfield, G. R. 1974. Biomechanics of Pteranodon. Philosophical Transactions of the Royal Society of London B 267: 503–581.Google Scholar
Colbert, E. C. 1962. The weights of dinosaurs. American Museum Novitates. 2076: 1–16.Google Scholar
Czerkas, S. J., Olsen, E. C. 1987. Dinosaurs past and present I and II. Natural History Museum of Los Angeles County, Los Angeles.Google Scholar
Damuth, J., MacFadden, B. J. eds. 1990. Body size in mammalian paleobiology: estimation and biological implications. Cambridge University Press, Cambridge.Google Scholar
Dodson, P. 1996. The horned dinosaurs. Princeton University Press, Princeton, N.J.Google Scholar
Farlow, J. O. 1990. Speculations about the diet and digestive physiology of herbivorous dinosaurs. Paleobiology 13: 60–72.Google Scholar
Farlow, J. O., Smith, M. B., and Robinson, J. M. 1995. Body mass, bone “strength indicator”, and cursorial potential of Tyrannosaurus rex. Journal of Vertebrate Paleontology 15: 713–725.Google Scholar
Gatesy, S. M. and Biewener, A. A. 1991. Bipedal locomotion: effects of speed, size and limb posture in birds and humans. Journal of Zoology 224: 127–147.Google Scholar
Gregory, W. K. 1905. The weight of the Brontosaurus. Science, new series 22(566): 572.Google Scholar
Hildebrand, M. 1982. Analysis of vertebrate structure. 2d ed.Wiley, New York.Google Scholar
Kingdon, J. 1997. The Kingdon field guide to African mammals. Academic Press, London.Google Scholar
McIntosh, J. S., Brett-Surman, M. K., and Farlow, J. O. 1997. Sauropods. Pp. 264–290. in Farlow, J. O., Brett-Surman, M. K. eds. The complete dinosaur. Indiana University Press, Bloomington.Google Scholar
Norman, D. B. and Weishampel, D. B. 1990. Iguanodontidae and related ornithopods. Pp. 510–533. in Weishampel, D. B., Dodson, P., Osmólska, H. eds. The Dinosauria University of California Press, Berkeley, Los Angeles.Google Scholar
O'Neil, P. V. 1983. Advanced engineering mathematics. 3d ed.Wadsworth, Belmont, Calif.Google Scholar
Paul, G. S. 1987. The science and art of restoring the life appearance of dinosaurs and their relatives. Pp. 4–49. in Czerkas, S. J., Olsen, E. C. eds. Dinosaurs past and present I Natural History Museum of Los Angeles County, Los Angeles.Google Scholar
Paul, G. S. 1988. Predatory dinosaurs of the world. Simon and Schuster, New York.Google Scholar
Romer, A. S. 1923. The pelvic musculature of saurischian dinosaurs. Bulletin of the American Museum of Natural History 48: 605–617.Google Scholar
Weishampel, D. B. 1995. Fossils, function, and phylogeny. Pp. 34–54. in Thomason, J. ed. Functional morphology in vertebrate paleontology Cambridge University Press, Cambridge.Google Scholar