Motions of the running horse and cheetah revisited: fundamental mechanics of the transverse and rotary gallop

1. What they did

Mammals use two kinds of gallop. In the transverse gallop, best known from the horse, the animal lands on one side and takes off from the opposite side. In the rotary gallop, best known from the cheetah, landing and take-off are on the same side. These two gaits were described in detail by Hildebrand in 1959, but why animals use them was still poorly understood.

The authors revisited the question with simple mechanics. Between leaps, each time the feet touch the ground the animal’s centre of mass (CoM) has to be turned from moving downward and forward to moving upward and forward. Each foot contact acts like a small collision, and some momentum and energy are lost. Using a model of the body as a point mass on stiff, weightless legs, they asked which limbs start this turn and which finish it. They tested the model against published force and movement data for horses and fast-galloping dogs (used in place of cheetahs, for which no force data exist), Muybridge’s photographs of dogs and other animals, greyhound timings, and video of jackrabbits.

2. What they found

How the turn is spread over the feet

• Energy lost in one contact rises with the square of the angle the path is turned through. Spreading the turn over several feet cuts the loss: over four feet, to about a quarter of the loss from a single foot.

The horse (hindlimb-initiated gallop)

• The horse lands on a hind foot, then the other hind foot, then the forefoot on the same side as that first hind foot, and takes off from the last forefoot (the “lead” leg).
• The first hind foot gives a net push forward; the lead forefoot gives a net braking push needed to send the body upward. As a result, the horse leaves the ground at a relatively low forward speed.
• This works like a stone skipping on water: the turn is spread over several contacts, and the gait does not seem to depend mainly on elastic energy storage.

The cheetah and fast dog (forelimb-initiated gallop)

• The cheetah lands on a forefoot after its main, stretched-out flight, then the other forefoot, then the hind foot on that same side, and takes off from the hind foot on the side it first landed on.
• The hind feet give a net forward push at the end of the contact sequence, so the animal enters its main flight at its highest forward speed of the stride. This probably helps the speed of cheetahs and dogs.
• The model predicts larger losses for this arrangement. The authors suggest the bending back and the limbs change length together, perhaps storing some energy in the spine, much as a human runner’s leg does.
• Greyhounds at their fastest showed little difference between the two flight phases, so their path flattens at top speed.

Footfall order is not what matters

• Dogs use both gallops: a cheetah-like gallop at high speed and a stiff-backed, horse-like gallop at moderate speed, and they can use the rotary footfall order for both.
• Jackrabbits use nearly the same footfall pattern (a half bound) for both a slow, stiff-backed, horse-like gait and the fast, arched-back, cheetah-like gait used when escaping an immediate threat.
• Horses sometimes use a rotary footfall order (common in turns), but the mechanics stay horse-like.

3. What they concluded

• The two gallops are best told apart by which pair of legs, front or hind, starts turning the body from downward to upward, not by the left and right order of the feet.
• The horse-like gallop saves energy mainly by using the legs as struts and spreading the turn, at the cost of slower forward speed during flight. The cheetah-like gallop probably relies on muscle work, a bending back and some elastic energy return, much like human running.
• The two gallops may be points on a continuum that reaches even symmetrical running gaits, such as the tölt of horses and the amble of elephants.
• Why many hoofed animals seem limited in using the forelimb-initiated gallop is not known. No survey yet shows which species use which type; Muybridge’s plates suggest deer may use the forelimb-initiated type.

6. Other technologies, skills or innovations

• A simple strut and collision model that explains gait mechanics without detailed muscle data.
• Centre of mass curves rebuilt by combining force and timing data from different studies and dogs, adjusted to be physically consistent.
• Use of Muybridge’s 1887 photographic sequences and high-speed video as evidence.