Stride Analysis of Two Extinct Bipedal Vertebrates
By Sue Ford
Here to see a walking dinosaur
Over the past hundred years much research has gone into studying
the motion of animals. One of the important variables measured in attempting
to understand animal motion is stride length. Stride length is defined
as the distance between any two successive prints of a single foot. A linear
relationship between stride length and speed has been well established;
as an animal moves faster their stride length increases. Using data collected
from studying the motion of many different animals a British biophysicist,
R. McNeill Alexander, has mathematically modeled the motion of animals
in order to calculate absolute speed using only a couple of simple variables:
stride length (S.L.), hip height (sum of the lengths of the femur, tibia,
and the longest metatarsal. Abbreviated “h”), and the acceleration due
to gravity (g). The equation is: Vabs = (0.25 g0.5)
. (SL1.67) . (H-1.17).
Our first hypothesis is that a bipedal dinosaur, the Allosaurus, should
have a greater absolute speed than a bipedal bird from more modern times,
the recently extinct Moa.
Alexander has also developed a way to compare the movement of organisms
that vary greatly in size. In order to do this he created two new quantities:
relative stride length and dimensionless speed. He calculated Relative
Stride Length (Srel) which is the Stride length/leg length (Relative Stride
Length: Srel = SL / LL) and dimensionless speed which is absolute
speed/ square root of leg length times the acceleration due to gravity
(Dimensionless Speed: Vdem = Vabs / (LL . g) 0.5).
By plotting these values he found that all animals fall on the same line.
Our second hypothesis is that the Allosaurus and Moa should both fall
on this line, despite the fact that they are both extinct animals.
Methods and Materials
metric tape measure
Allosaurus specimen at the Guyot Museum, Princeton University.
Two Moa skeletons at the Guyot Museum, Princeton University.
Gather data using metric tape to measure hip height (distance from hip
to ground), stride, femur, tibia, and fibula.
Record results in data table.
Use Alexander’s formulas to calculate relative stride length, absolute
speed, and dimensionless speed.
Compare the results of Allosaurus and Moa.
Plot relative stride length and dimensional speed on Alexander’s
graph to test hypotheses.
|Stride Length, SL
|Hip Joint to Ground, LL
|| 0.43 meters
|Relative Stride Length, Srel
|Dimensionless Speed, Vdem
Relative Stride Length: Srel = SL / LL
Absolute Speed: Vabs = (0.25 g0.5) .
(SL1.67) . (H-1.17)
Dimensionless Speed: Vdem = Vabs / (LL .
This experiment had two hypotheses. The data from this experiment
supported the hypotheses that Allosaurus has a faster absolute speed than
the Moas. The second hypothesis stated that the dimensionless speed
of the Allosaurus and the Moas would conform to Alexander’s predictions
was also confirmed.
The absolute speed of Allosaurus was 2.86m/s (meters per second.)
The absolute speed of Moas number one was 0.90 m/s. Moas number two
had an absolute speed of 0.66 m/s.
The dimensionless speed of Allosaurus was 0.70. Moas number one
registered a dimensionless speed of 0.33 while the speed of Moas numbers
two was 0.26.
The variable of size was viewed as another factor. Eliminating
the size variable did not alter the outcome. The Allosaurus remained
faster. Keep in mind that these animals are walking not running.
Pages by T. Mike Keesey
Trace Fossils by Anthony J. Martin