Speed, Stride Frequency and Energy Cost Per Stride: How Do They Change With Body Size and Gait?

1. What they did

Per gram of body, a small animal burns energy much faster than a large one when running. A 30 g mouse uses energy six times faster than a horse at the speed where each switches from a trot to a gallop, even though the mechanical work each gram of muscle does is about the same. The authors suspected that stride frequency (how many strides an animal takes each second) holds the answer.

They trained 16 species of wild and domestic four-legged mammals, from 29 g mice to a 680 kg horse, to run on a treadmill. Ten species came from Kenya (antelopes such as suni, dik-dik, Grant’s gazelle, wildebeest, waterbuck and eland, plus goats, sheep, zebu cattle and a donkey). Six came from the United States (mice, chipmunks, 13-lined ground squirrels, rats, dogs, ponies and a horse).

• Measuring strides. After at least several weeks of training, they timed 25 cycles of one foot at a steady treadmill speed, with a stopwatch for large animals and high-speed film (100 to 200 frames per second) for small ones.
• Finding “equivalent” speeds. For each animal they found five comparable speeds: the slowest trot, the preferred trot (the middle of the trotting range), the trot-gallop transition, the preferred gallop (the middle of the galloping range they measured) and the fastest sustained gallop.
• Scaling with body size. They worked out how these speeds and the stride frequencies used at them change with body mass.
• Energy cost per stride. They combined their results with published energy data for the same species to calculate the energy each kilogram of animal uses per stride.

Walking could not be analysed across body sizes: small animals would not walk steadily on the treadmill. Mice, chipmunks and rats ran to the front, stopped and rode to the back, over and over.

2. What they found

Trotting

• Small animals start trotting at much slower speeds. The slowest trot rose about nine-fold, from 0.19 m/s in a mouse to 1.8 m/s in a 170 kg horse.
• Every animal’s fastest trot was about 2.6 times its slowest trot, whatever its size.
• Stride frequency rose in a nearly straight line with speed, by about 1.55 times from the slowest trot to the trot-gallop transition, in all animals.
• Preferred trotting speed (in metres per second) is about 1.09 × body mass (kg) to the power 0.222. Stride frequency at that speed is about 3.35 × body mass to the power -0.130.

The trot-gallop transition

• At the transition speed, stride frequency was the same whether the animal trotted or galloped, so the transition can be found where the two lines meet.
• Transition speed rose with body mass to the power 0.216; stride frequency there fell with body mass to the power -0.150. A 30 g mouse began to gallop at 0.8 m/s, a 170 kg pony at 5 m/s.

Galloping

• The fastest sustained gallops were about 2.1 times the slowest gallops.
• Stride frequency barely changed with speed in a gallop: about 10% higher for double the speed. A mouse gallops at about 7 to 9 strides per second, a horse at about 2.
• Dogs and horses, built for endurance, gave much wider speed ranges than goats and cattle. Top speeds could not be measured, because only steady, aerobic running was studied.

Energy cost per stride

• All the preferred speeds rose with roughly the 0.21 power of body mass, and stride frequencies fell with roughly the -0.14 power.
• At four of the five equivalent speeds (all except the slowest trot), each kilogram of animal used about the same energy per stride, whatever its size. At the trot-gallop transition this was 5.34 ± 0.25 joules per kilogram per stride, from mice to horses.
• Cost per stride rose with speed: about 5.0 joules per kilogram at the preferred trot, 5.3 at the transition, 7.5 at the preferred gallop and 9.4 at the fastest sustained gallop (figures from the summary).
• At the slowest trot, cost per stride depended slightly on size: about 2.5 times higher in a 30 g mouse than in a 270 kg horse.

3. What they concluded

• Small animals are slower, have a narrower range of speeds and take more strides per second, but the relative changes in speed and stride frequency within each gait are similar from mice to horses.
• Because cost per kilogram per stride is about the same at equivalent speeds, the high energy cost of running in small animals is explained by their higher stride frequencies.
• The cost of running comes mainly from switching muscles on and off (activation, about 30% of muscle energy use) and from generating force over time (about 70%). Both should rise with stride frequency: muscles switch on and off once per stride, and faster strides need faster force generation.
• Cost per stride may rise with speed because longer strides change the leverage of the limb muscles, so they need more force for the same push on the ground. In a trot about three-quarters of the rise in cost can be explained by higher stride frequency; in a gallop, where speed rises almost entirely through longer strides, this leverage effect may matter more.

6. Other technologies, skills or innovations

• Treadmill running after weeks of training.
• High-speed cine cameras (Eclair GV-16 with a clock in view, and Photosonics 1PL with a clock mark on the film) to count strides in small animals.
• Defining “equivalent speeds” so animals of very different sizes can be compared fairly.