eprintid: 192
rev_number: 4
eprint_status: archive
userid: 6
dir: disk0/00/00/01/92
datestamp: 2008-11-03
lastmod: 2015-05-29 19:49:05
status_changed: 2009-04-08 16:55:40
type: report
metadata_visibility: show
item_issues_count: 0
creators_name: Bohun, C. Sean
contributors_name: Henderson, Donald
contributors_name: Monthubert, Bernard
contributors_name: Westbrook, Rex
contributors_name: Mackenzie, Donald
contributors_name: Clysdale, Robin
contributors_name: David-Rus, Diana
contributors_name: Emmett, Matthew
contributors_name: Hogan, Chad
contributors_name: Hughes, Mark
contributors_name: Lushi, Enkeleida
contributors_name: Smith, Peter
contributors_name: Vaidya, Naveen
title: Mathematical Model of the Mechanics and Dynamics of the Tails in Dinosaurs
ispublished: pub
subjects: transport
subjects: other
studygroups: ipsw9
companyname: University of Calgary
full_text_status: public
abstract: In this paper, we investigate the effect of tails in the locomotion of dinosaurs. We begin with a survey of physical data for both bipedal and quadrupedal dinosaurs. The ratio of the tail to leg length is compared across many diverse species and a scaling law is developed that relates the tail length, leg length and tail radius. A continuous model for the tail is then developed, and by nondimensionalising a small parameter related to the thinness of the tail simplifies the resulting coupled nonlinear equations. It is shown that the resulting set of equations contain aspects of both beam dynamics and wave propagation.  Finally, a discrete version of the tail is derived with the assumption that the sections of the tail are coupled with a stiff joint that allows rotation but does not allow extension. In this model the stiffness of each joint is characterized by an effective spring constant $k_i$ for the $i$th joint and results in a discrete version of the Euler-Bernoulli expression for each of the tail segments. The paper finishes with some preliminary conclusions and directions for future work.
problem_statement: Unlike mammals which have very reduced tails, the tails of dinosaurs represented a substantial fraction of their body lengths and masses. The left and right sides of the tail base in all dinosaurs acted as the anchor points for large, powerful muscles that attached on the rearward side of the hind limbs. These muscles pulled on the legs, causing them to rotate backwards and under the body, with the result that the animals were propelled forward. As well as pulling on the legs, these muscles would have exerted a reciprocal pull on the tail. During locomotion the left and right hind limbs would be alternately pulled, and be out of phase with each other. These alternating tugs would have set up oscillations in the tail. It would seem that some sort of synchrony would have to arise between the rate at which the legs were swung back and forth and the natural frequencies of oscillations of the tail to allow efficient, stable walking and running. The extreme sizes of some dinosaurs—up to 30 tonnes in some cases — and the great range of body sizes - from a few hundred grams to many tonnes - gives dinosaurs the potential to be insightful models for the study of locomotory dynamics in terrestrial animals.
date: 2005
date_type: published
pages: 14
citation:   Bohun, C. Sean  (2005) Mathematical Model of the Mechanics and Dynamics of the Tails in Dinosaurs.  [Study Group Report]     
document_url: http://miis.maths.ox.ac.uk/miis/192/1/calgary.pdf