Locomotion

Animal locomotion

See the article on biorheology for a description of swimming and flight.

Locomotion in a general quadruped:

Three feet are positioned on the ground at all
times for maximum stability (tripodal support)
as seen in newts, lizards and tortoises:

For example, crawling in a newt. The feet are held
out to the sides of the body, but the trunk is
generally held above the ground. The fish-like
undulations of the body help increase stride-length
and is used particularly in running. (The body
waves differ from those in a fish, in that in the
amphibian they are standing waves, like the
vibrations of a plucked guitar string, whereas in the
fish they are traveling waves).

In animals that spend more time moving on land, such as many mammals, the efficiency of locomotion is improved
by bringing the limbs vertically in align with the body, acting like columns to better support the weight. When
walking, such quadrupeds still maintain a tripod of support. The canter is half-way between a trot and a gallop,
with one diagonally opposite pair of legs moving together, but the other pair moving independently. All these
modes are seen in horses and dogs as they speed-up they transition from walking to trot to canter to gallop.
Some animals will miss out one or more of these modes of locomotion. The diagram below illustrates which feet
are on the ground as circles, as the animal goes through a locomotion cycle from left to right:

Notice that as locomotion speeds up, only two feet are in contact with the ground at once, when trotting, and only one
when galloping. This is still dynamically (momentarily) stable since the animal's body has much horizontal velocity which
carries it as it literally falls from one foot to another during the gallop. Wildebeest omit the trot and mice (and other small
mammals) do not walk. Walking maintains maximum stability, whilst trotting and galloping are more efficient at high
speeds, since energy is stored in elastic recoil, rather like a bouncing ball. Indeed, watching a dog run or 'bound along'
is rather like watching a bouncing ball! Joints, bones and tendons store elastic energy which is reused as these
structures recoil, providing extra thrust at no extra cost. Much of the energy needed for running goes into swinging the
legs. Galloping minimises these energy costs. The trunk of a galloping mammal flexes vertically (contrast to the sideways
flexing of the amphibian trunk) and this helps swing the legs outwards when the back extends and inwards when the
back arches upwards and inwards. Additionally, the legs of mammals have most of their muscle mass toward the base
with more distal parts near the foot being more slender, reducing the weight that has to be swung (reducing the moment
of inertia strictly speaking). Dogs run on their toes, extending their legs and increasing stride-length whilst only slightly
increasing the moment of inertia. The hoofs of horses and the fact that the 'knee' is actually the wrist are further designs
to increase stride length whilst minimising moment of inertia. (Speed = stride-length x stride-rate).

Humans make good use of the bouncing ball principle too. About one-third of the thrust during sprinting is due to the elastic recoil of
tissues. Kangaroo jumping makes extensive use of this recoil and is one of the most efficient forms of animal locomotion on land, in
terms of energy economy (along with crawling in snakes for quite different reasons) being comparable to flight, which is more energy
economic than running or walking (a bird can fly further on less energy than an animal can walk or run, making some birds
particularly good at very long migrations).

For a large animal to support its weight on dry land is no easy task, especially when one thinks of an elephant reaching up to 10
000 kg, and many prehistoric animals being much heavier still. Let us look at some of the techniques human engineers use to
support heavy structures and see how animals use some of the same principles:

The braced cantilever improves on the simple cantilever by using a compressive strut, essentially a diagonal column that gets
squeezed by the weight, but is made of a material, like wood, which is good at resisting compression. The braced cantilever instead
uses a cable under tension, using a material good at resisting tension, such as rope or steel cable. Compression and tension may
be used together, as in trusses:

The use of tension and compression to support the bridges above, is strikingly similar to how animals support their weight. Tendons,
ligaments and muscles provide tension, whilst bones, like the vertebral column (with its cushioning intervertebral discs and vertebrae
with spongy bone) resist compression:

Notice how the tail can counterbalance the head. Some dinosaurs seem to have taken these principles to extremes, such as the giant
sauropods. These dinosaurs had very little vertebrae, which can act as compression-resisting cushions whilst minimising their own
weight (which must be carried) and very stiff tendons stretched between the vertebrae kept the spine rigid under tension. (I would not
go so far as to speculate how movable these rigid spines and tails were since that depends in part on the strength of the muscles
moving them). It is now thought that the tails of the sauropods were mostly held out rigid and horizontal, so as to counterbalance the
long neck characteristic of these animals. Nevertheless, the neck could presumably be raised and lowered to reach vegetation, with
the tail moving to balance this as appropriate. (I am not entirely convinced by many modern computer animations in which the
movements of these creatures look so awkward and unnatural!).

Vertebrae have large centrum, which forms the body of the column and contains mostly light, shock-absorbing, low-density,
honeycomb-like spongy bone. The various muscles, ligaments and tendons, providing tension and movement, attach to prominent
bony processes - the neural spine and various apophyses. Various facets allow adjacent vertebrae to articulate with one-another: