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Dinosaur Speed Calculator
On Line Calculator for Estimating Dinosaur Speed and Gait
Dinosaur footprint diagram

Introduction
The key to deriving estimates of dinosaur gait and speed from trackways was provided by the zoologist R. McNeill Alexander (1976). From observations of modern animals he derived a general relationship between an animal's speed of locomotion (v) and its hip height (h) and its stride length (SL), which is

v = 0.25*g0.5*SL1.67*h-1.17

Alexander also pointed out that this formula could be applied to dinosaur trackways since the stride length can be measured directly and the hip height could be estimated from the size of the foot print.

The stride length is the distance between successive prints of the same foot.

Alexander estimated from a range of dinosaur skeletons that the hip height ranged from 3.6 to 4.3 times the foot length and h=4*foot print length has become widely used as a convenient and easily remembered rule of thumb.


The On-line Calculator
The on-line dinosaur speed calculator saves you having to work out Alexander’s rather complex formula for yourself and allows you to input the trackway parameters of stride length and foot size (measured in metres) together with the conversion factor, that you want to use, to relate foot size to hip height. From these it will give estimates of the gait and speed of the animal including speed estimates using another formula recommended by Thulborn (1990).

You can use the calculator with your own data or with the data given elsewhere in this web site. Try using different conversion factors to see what effect this could have on the speed estimate. The calculator can also be used to predict how fast different sized dinosaurs would be moving when they broke into a trot and then accelerated to a run.

Input Foot Length: Input Conversion Factor:

Input Stride Length:

The relative stride length (SL/h) is used to determine whether the animal is walking (SL/h<= 2.0), trotting (SL/h>2.0 and <2.9) or running (SL/h>=2.9)

Alexander's formula
Thulborn's formula
Mean

Recalculate Values


Hip Height Conversion Factors
(The On-line Calculator)
Several workers have pointed out that different types of dinosaur had slightly different relationships between foot length and hip height and Thulborn (1990) has suggested that the following approximations could be used for bipedal dinosaurs

FL less than 0.25m
small theropods
small ornithopods
small bipedal dinosaurs in general

h=4.5*FL
h=4.8*FL
h=4.6*FL
FL greater than 0.25m
large theropods
large ornithopods
large bipedal dinosaurs in general

h=4.9*FL
h=5.9*FL
h=5.7*FL

Recommendations for quadrupedal dinosaurs are less clear because in many groups the hind foot or pes has a large padded area. For sauropods Thulborn (1990) has suggested that h=5.9*FL while Lockley et al. (1986) used h=4*the foot width (FW) but a better general estimate may be h=4.6*FL. Published reconstructions and other lines of evidence also suggest the following conversion factors for other groups

Ceratopsians h=4.2*FW
Ankylosaurs h=3.7*FW
Stegosaurs h=6.0*FW or h=5.0*FL

In the stegosaurs there is a very large difference between the height at the hips and the height at the shoulder and the latter, which may be more important in determining speed of movement, can be estimated from the width of the front foot or manus as 3.5*FW.

Gaits and Speed (The On-line Calculator)
From his studies Alexander (1976) showed that the relative stride length, the ratio SL/h, is an indicator of gait. Where the SL/h ratio is less than 2.0 the animal is walking and where it is greater than 2.9 it is running, while intermediate values indicate that the animal is trotting (Thulborn, 1990).

Thulborn (1990) has suggested that for running gaits a better estimate of speed is given by the formula

v= [gh(SL/1.8h)2.56]0.5

He has also recommended that for trotting gaits the mean of his and Alexander’s formulae should be used.

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