# Principles of Animal Locomotion > Why does a horse switch from a trot to a gallop, and why does a dog do it at half the speed? R. McNeill Alexander’s classic book explains the mechanics and energy costs of how animals walk, run, jump, crawl, fly and swim. Along the way it covers the physics behind stride length, gait changes and footprint patterns that trackers read every day. Summary by Kersey Lawrence, Original Wisdom. Updated 9 November 2026. Page: https://www.originalwisdom.com/tracking-literature/2003-alexander-principles-animal-locomotion/ ## Citation and access - **Authors:** R. McNeill Alexander - **Year published:** 2003 - **Journal or source:** Princeton University Press (book) - **Full citation:** Alexander, R. M. 2003. Principles of animal locomotion. Princeton University Press, Princeton, New Jersey. - **DOI:** 10.2307/j.ctt4cg9j1 - **Access status:** Publisher link only - **Where to find it:** https://doi.org/10.2307/j.ctt4cg9j1 ## Tags - **Species:** Amphibians; Birds; Fish; Invertebrates; Mammals; Reptiles - **Tracking:** Gaits - **Behaviour and ecology:** Behaviour; Hunting; Migration; Movement; Predator avoidance - **Methods and technology:** Literature review; Telemetry - **Data type:** Modelling or theoretical; Review - **Observer qualification:** Not needed - **Discipline:** Behaviour and ecology - **Year published:** 2003 ## Detailed keywords - **Species:** A textbook covering many animals, mostly vertebrates, arthropods and molluscs. Examples include humans, horses, dogs, greyhounds, cheetah (Acinonyx jubatus), lion (Panthera leo), Thomson’s gazelle (Gazella thomsoni), African hunting dogs (Lycaon), pronghorn (Antilocapra), white rhinoceros (Ceratotherium simum), kangaroos and wallabies (Macropus eugenii), ostrich (Struthio camelus), crows, albatrosses, penguins, seals, dolphins, tunas and other fishes, lizards (Dipsosaurus dorsalis, Cnemidophorus, basilisk lizards), snakes, frogs, cockroaches (Periplaneta americana), ghost crabs (Ocypode quadrata), fisher spiders, earthworms, snails, squids and jellyfish (medusae). Fox, deer, weasel and rodent tracks are mentioned as examples of footprint patterns, and fossil dinosaur footprints as evidence of how dinosaurs walked. - **Location and habitat:** Not a field study. Mostly laboratory and treadmill research, with some field examples (such as lions hunting, a cheetah timed over a 200 m course, gray seals off the west coast of Scotland, albatrosses in the South Atlantic, footpaths in the Alps and Himalayas). Movement on land, through the air, and on and under water. - **Topics:** mechanics and energy cost of animal movement; muscle as the motor; speed, acceleration, swerving and endurance in predator and prey chases; gaits and gait changes (walk, trot, pace, amble, gallop, hop); stride length and duty factor; dynamic similarity and the Froude number; effects of body size; elastic energy saving in tendons; metabolic cost of transport; soft ground, hills, loads and route choice; stability and maneuverability; crawling and burrowing; climbing and jumping; gliding, soaring, hovering and flapping flight; swimming by oars, hydrofoils, undulation and jet propulsion; buoyancy; shoes, bicycles, scuba, boats and gliders; priorities for research. - **Statistics or models:** Simple mathematical and physical models (optimization theory, minimal models of walking and hopping, spring and mass models of running); dynamic similarity (Froude, Reynolds and Strouhal numbers); allometric (body mass scaling) equations for speed and cost of transport; aerodynamic and hydrodynamic calculations. - **Data type:** Review and synthesis of published research, including the author’s own experiments, with theoretical models. No new field data. Copyright 2003, paperback 2006 (the PDF is the 2006 second printing); the DOI is for the 2013 JSTOR digital edition. ## Synopsis ### 1. What they did This book by zoologist R. McNeill Alexander explains how animals move on land, in water and through the air, and what that movement costs them in energy. It focuses on understanding and principles rather than detailed description, and uses rough calculations and simple mathematics to test explanations. It covers only muscle-powered movement, and was written mainly for advanced students, researchers and university teachers of biology. The book is in 19 chapters: - Foundations (Chapters 1 to 4). What natural selection might favour in movement (speed, acceleration, maneuverability, endurance, energy economy, stability), how muscles work, where the energy goes, and how body size changes things. - Methods (Chapter 5). Filming, treadmills and wind or water tunnels, measuring oxygen use, force plates, recording muscle activity, and transmitters and data loggers on free-ranging animals. - Land (Chapters 6 to 9). Simple models of crawling, hopping, walking and running, then walking, running and hopping in real animals, climbing and jumping, and crawling and burrowing. - Air (Chapters 10 to 12). Gliding and soaring, hovering, and flapping flight. - Water (Chapters 13 to 17). Moving on the water’s surface, swimming with oars and hydrofoils, swimming by undulation and by jet propulsion, and buoyancy. - People and summary (Chapters 18 and 19). Shoes, bicycles, scuba, boats and gliders, then a short epilogue comparing running, swimming and flight. ### 2. What they found Speed and chases - Acceleration can matter more than top speed in a short chase. In films of lions hunting Thomson’s gazelles, the lions’ initial acceleration averaged 9.5 metres per second squared and the gazelles’ only 4.5. - Prey that turn more tightly than their predator can escape even if they are slower, but only if they swerve at the last moment. - Over long distances, a predator with better endurance, such as African hunting dogs chasing antelopes over several kilometres, can catch faster prey. - Most published speeds of large wild mammals are unreliable estimates. A cheetah timed at 29 metres per second is the most reliable record for the fastest runner. Mammal sprint speeds roughly increase with body size, but the very largest mammals are relatively slow. Gaits - A gait is a pattern of movement used over a limited range of speeds, which changes abruptly at the switch to another gait. People walk to go slowly and run to go fast; horses walk, trot and gallop. - Animals of different sizes tend to change gait at the same Froude number (speed squared divided by hip height times gravity). Quadrupeds change from trotting to galloping at a Froude number of about 2 to 3, and from walking to trotting (or people from walking to running) at about 0.3 to 0.8. So bigger animals change gait at higher speeds: dogs at about half the speeds of horses with legs four times as long. - Animals speed up by taking longer strides, faster strides, or both. Galloping mammals mostly lengthen their strides. Feet stay on the ground for a smaller part of each stride as speed rises: in four-legged mammals, from about 70% in slow walking to 20% to 30% in fast galloping. - In cursorial (running-adapted) mammals and birds, the feet pass beneath the hips and shoulders, so the lines of left and right footprints are close together. In noncursorial mammals, such as weasels and rodents, the lines are farther apart for their stride length. Fossil footprints show that dinosaurs walked more like birds and mammals than like modern reptiles. - Each gait seems to be the most energy-saving one over the speeds at which it is used, at least in horses and people. Energy - Tendons act as springs. In hopping wallabies, elastic recoil of the ankle tendons did about 20 times as much work as the muscle fibres, and cut the work needed from the leg muscles by 45% at 6 metres per second. - Per kilogram and per metre, larger animals move more cheaply. Running is the most costly way to travel, flapping flight moderate, and swimming by fish the cheapest. - Walking on soft sand cost people up to 2.5 times as much as walking on concrete, and deep snow up to five times as much as a treadmill. To save energy, a walker may detour around soft ground, a zigzag path saves energy on steep hills, and a path around the shoulder of a hill can save energy over climbing it. Old mountain footpaths seem to fit these predictions. Other modes of travel The book shows how the same principles (gaits, size effects, elastic energy saving and energy costs) apply to jumping, climbing, crawling, burrowing, gliding, soaring, hovering and flapping flight, and to many styles of swimming. Flying is generally much faster than running or swimming; most birds fly at 9 to 19 metres per second over distances of a few hundred metres or more. ### 3. What they concluded - The cost of transport scales in a similar way with body mass for running, swimming and flight, though at very different levels. Why the muscles of small runners and fliers seem to work less efficiently than those of large ones is not yet explained. - Gait changes are found in runners, swimmers and fliers. For legged animals, the prediction that gaits change at equal Froude numbers works reasonably well, but gait changes in flying and swimming animals are still poorly understood. - The role of elastic energy saving in running is well established; its role in flight and swimming is much less clear. - Most research has studied animals moving at steady speed in laboratories. Much less is known about accelerating, slowing down, turning and staying stable, and about how animals move, how fast, and at what energy cost in their natural environments. - The author expects that some of the explanations in the book will be shown to be wrong, but cannot say which. ### 4. How tracking was or was not used Tracking was not used. The book touches on footprints in its discussion of gaits: the spacing between the lines of left and right footprints differs between cursorial and noncursorial mammals (citing fox, deer, weasel and rodent tracks in Lawrence and Brown 1974), and fossil footprints show how dinosaurs walked. ### 6. Other technologies, skills or innovations - Film and video recording, treadmills, and wind and water tunnels. - Force plates that record the forces feet exert on the ground. - Measurement of oxygen consumption to estimate energy use. - Electromyography (recording muscle activity), tendon buckles to measure tendon forces, and sonomicrometry crystals to measure muscle length changes. - Radio and ultrasonic transmitters and data loggers carried by free-ranging animals, such as gray seals and black-browed albatrosses. ### 8. Implications for tracking (Original Wisdom's observations) _These are Original Wisdom's observations, not the authors'._ - The book gives the mechanics behind what trackers read in a trail: stride length, the switch between walk, trot and gallop, and how both change with speed and body size. - Because gait changes happen at similar Froude numbers, trackers may find that a trail’s stride length and gait, together with the animal’s leg length, give a rough sense of how fast the animal was moving. - The narrow or wide separation between left and right footprint lines reflects how an animal holds its legs, which may help trackers understand why trails of running-adapted animals and of small, bent-legged animals look different. - The findings on soft ground, slopes and route choice may help trackers think about why animals and people detour around soft patches, zigzag up steep slopes, or skirt the shoulders of hills. ## Cite this summary Lawrence, K. 2026. Summary of: Principles of Animal Locomotion (Alexander, 2003). Original Wisdom, Tracking Literature. https://www.originalwisdom.com/tracking-literature/2003-alexander-principles-animal-locomotion/