# Energy of the Oscillating Legs of a Fast-moving Cheetah, Pronghorn, Jackrabbit, and Elephant

> Why does a cheetah give up after a short sprint while an impala runs on? By turning films of a cheetah, pronghorn, jackrabbit and elephant at full speed into energy models of their swinging legs, the authors found that the cat’s legs carry far more energy than the pronghorn’s, even after adjusting for timing, weight and leg length. They suggest this may help explain why dash-hunting carnivores have less staying power than their hoofed prey.

Summary by Kersey Lawrence, Original Wisdom. Updated 9 November 2026. Page: https://www.originalwisdom.com/tracking-literature/1985-hildebrand-hurley-energy-oscillating-legs-fast/

## Citation and access

- **Authors:** Milton Hildebrand and James P. Hurley
- **Year published:** 1985
- **Journal or source:** Journal of Morphology
- **Full citation:** Hildebrand, M. and Hurley, J. P. 1985. Energy of the oscillating legs of a fast-moving cheetah, pronghorn, jackrabbit, and elephant. Journal of Morphology 184(1): 23–31.
- **DOI:** 10.1002/jmor.1051840103
- **Access status:** Publisher link only
- **Where to find it:** https://doi.org/10.1002/jmor.1051840103

## Tags

- **Species:** Mammals > Asian elephant; Mammals > Black-tailed jackrabbit; Mammals > Cheetah; Mammals > Pronghorn
- **Behaviour and ecology:** Behaviour; Movement
- **Data type:** Existing data; Modelling or theoretical
- **Observer qualification:** Not needed
- **Discipline:** Behaviour and ecology
- **Year published:** 1985

## Detailed keywords

- **Species:** Studied (as leg models built from film and limb measurements): cheetah (Acinonyx jubatus), American pronghorn antelope (Antilocapra americana), black-tailed jackrabbit (Lepus californicus) and Asian elephant (Elephas maximus). Mentioned for comparison: gazelle and goat (from Taylor and colleagues 1974), impala, deer, small antelope, cursorial reptiles and dinosaurs.
- **Location and habitat:** Not reported. The animals were filmed running unrestrained, not on a treadmill; the paper does not say where. The authors worked at the University of California, Davis, United States.
- **Topics:** running and locomotion at near top speed; gaits (rotary gallop in cheetah and jackrabbit, rotary and transverse gallop in pronghorn, lateral-sequence singlefoot in elephant); limb segment movements and joint angles; kinetic and potential energy of the swinging legs; forward swing and backward swing of the leg; follow-through and down-swing; distribution of mass along the leg (digitigrade cat versus unguligrade hoofed animal); leg proportions of cursorial (running-adapted) animals; endurance versus short sprints; cost of transport; internal and external energy of running; evolution of limb shape in predators and prey. Possible inconsistency: the text gives pronghorn bone lengths as percentages of leg length (femur 31%, hindfoot 31%, humerus 28%, forefoot 39%) that do not match the functional segment lengths in the Appendix (which work out to roughly 27%, 40%, 20% and 50%), and the text says the cheetah foreleg is 84% as long as the pronghorn’s, while the Appendix lengths give about 87%. The cheetah figures do match. The text may be using different length measurements; this is not explained.
- **Statistics or models:** Three-segment leg models (the foot treated as one rigid unit), motion in the side-on (sagittal) plane only; Lagrangian equations to calculate kinetic energy (translational plus rotational) and potential energy for 19 positions per stride; moment of inertia calculated by treating each segment as a uniformly tapered rod; models adjusted to give the cheetah the pronghorn’s time interval, leg mass, leg length or joint angles; sensitivity check (an error of plus or minus 5% in the mass of the upper leg segment changes kinetic energy by plus or minus 7%); published equations from Harvard studies relating internal and external energy to body mass and ground speed. No statistical tests.
- **Data type:** Existing data and modelling: the best available films of very fast runs, found in the authors’ earlier work on locomotion (64, 80, 200 and 24 frames per second for cheetah, pronghorn, jackrabbit and elephant). Limb masses and mass centres measured from carcasses (pronghorn, jackrabbit), freeze-dried limbs plus data from other cats (cheetah), and estimates from photographs, skeletons and models (elephant). Dates not given.

## Synopsis

### 1. What they did

Running animals spend energy swinging their legs back and forth. Biologists have long assumed that fast runners save energy by keeping the heavy, fleshy part of the leg close to the body and having long, slender lower legs. But a 1974 treadmill study of cheetahs, gazelles and goats had concluded that leg shape makes little difference to the energy cost of running. The authors set out to test this with animals running far faster than any treadmill.

- Choosing the animals. The cheetah, because they are the fastest land animal; the pronghorn, because they may be as fast as any hoofed mammal; the black-tailed jackrabbit, one of the smallest and most limber fast runners; and the Asian elephant, whose bulk forces stiff, simple leg movements.

- Reading the films. They used the best films available of each animal running near top speed (roughly 25 metres per second for the cheetah). Each stride was standardised to 19 positions equally spaced in time, and the angle of each leg segment was measured at each position. The cheetah film was barely adequate, so many strides were averaged.

- Measuring the legs. For each of three leg segments (upper, middle and foot) they found length, mass and centre of mass, from carcasses, freeze-dried limbs or estimates.

- Calculating energy. With these data, J.P. Hurley calculated the kinetic energy (energy of motion) and potential energy (energy of height) of each foreleg and hindleg through the stride.

- Adjusting the models. To separate the effect of leg shape from other differences, they altered the cheetah model so that it had the pronghorn’s timing, leg mass, leg length or joint angles, and compared again.

The authors stress that they modelled legs closely resembling those of their animals in typical fast motion, not the exact motion of any one animal, and that they did not know the animals’ actual speeds.

### 2. What they found

The energy curves

- Kinetic energy peaked once on the forward swing of the leg and once on the backward swing, closely following the leg movements.

- For the elephant the forward swing was a little faster and had the higher peak. For the other three animals the backward swing was much faster, with a much higher peak.

- For all four animals the hindleg had more kinetic energy than the lighter foreleg, though least so for the elephant, whose foreleg was estimated to be nearly as heavy.

- The elephant had almost no follow-through after the foot left the ground and no down-swing before it landed, so the foot lifted and landed when kinetic energy was lowest. This was not so for the other animals.

- Potential energy was much lower than kinetic energy (for the cheetah it is shown magnified ten times).

Cheetah compared with pronghorn

- Leg proportions: the cheetah’s thigh bone is 39% of hindleg length and the hindfoot 24%; the text gives 31% and 31% for the pronghorn.

- Forward swing, peak kinetic energy: the cheetah’s hindleg and foreleg had 171% and 260% of the pronghorn’s.

- Giving the cheetah model the pronghorn’s slightly longer time between positions cut this to 127% and 194%.

- The cheetah’s legs are also heavier (106% and 120% of the pronghorn’s). Giving the model both the pronghorn’s timing and mass cut the figures to 116% and 147%, but this also shrank the cheetah’s legs, which are already shorter (79% and 84% of the pronghorn’s).

- Lengthening the cheetah’s legs to match the pronghorn’s added so much mass that energy rose beyond reasonable comparison.

- The comparison the authors thought best, a cheetah model given the pronghorn’s joint angles, still had 152% and 176% of the pronghorn’s peak kinetic energy.

- Backward swing (approximate figures): the cheetah had 750% and 430% of the pronghorn’s peak; with the pronghorn’s joint angles, still 128% and 169%.

- Potential energy gave similar results.

Internal and external energy

Using published equations, the authors worked out that at high speed the energy needed to move the body parts relative to the body’s centre (internal energy) is 2.3 times the energy needed to move the body as a whole at about 10 metres per second (roughly the elephant model’s speed) and 3.8 times at about 25 metres per second (roughly the cheetah’s). Most internal energy goes into swinging the legs.

### 3. What they concluded

- By every comparison, the legs of the fast-running cheetah model carry considerably more kinetic energy than those of the pronghorn.

- Relating energy use to leg shape is more complicated than had been thought.

- Because most energy at high speed is internal, and most of that is in swinging the legs, the authors believe that, contrary to the 1974 treadmill study, the cheetah’s leg shape and way of running are significantly more costly than those of slender hoofed animals. They note that the effects of wind resistance and of energy stored and released by springy tissues were not yet known.

- Carnivore-type legs that cycle fast may help explain why carnivores that hunt with a high-speed dash usually have less endurance. The impala or gazelle that escapes the cheetah’s dash (successful chases average about 200 m) runs on to safety as the cat gives up.

- Heavy upper legs with very long, slender lower legs are not needed for bursts of top speed, but do go with the ability to keep up great speed. The authors suggest that perhaps no running dinosaur had the leg proportions of hoofed mammals because none escaped predators by outlasting them in an open chase.

### 6. Other technologies, skills or innovations

- Frame-by-frame analysis of high-speed film (24 to 200 frames per second), with skeletal measurements used to find hidden joints such as the shoulder and hip from the more visible elbow and heel (hock).

- Adjustable leg models that let one variable at a time (timing, mass, length, joint angles) be changed to see its effect on energy.

- The authors list the limits of the method: arbitrary amounts of flesh left at the shoulder and hip when limbs are cut from carcasses, side-on motion only, feet treated as rigid (ignoring flexing at the pronghorn’s fetlock and the cheetah’s and jackrabbit’s foot pads), and time intervals taken from camera speeds that may be off.

### 8. Implications for tracking (Original Wisdom's observations)

_These are Original Wisdom's observations, not the authors'._

- The paper is a reminder of how differently a cat and a hoofed animal swing their legs at full speed: the cheetah’s long follow-through and high knee lift, and the elephant’s stiff, simple stride with almost no follow-through. These limb movements are what produce the gaits and track patterns trackers read on the ground.

## Cite this summary

Lawrence, K. 2026. Summary of: Energy of the Oscillating Legs of a Fast-moving Cheetah, Pronghorn, Jackrabbit, and Elephant (Hildebrand and Hurley, 1985). Original Wisdom, Tracking Literature. https://www.originalwisdom.com/tracking-literature/1985-hildebrand-hurley-energy-oscillating-legs-fast/