Watch walk, trot, canter and gallop (footfall diagram, duty factor, stride frequency) and keep the horse fed: its digestible-energy (DE) need depends on speed, gait, load, slope and hours of work.
Re-computes the gait kinematics step by step (planted feet, stride length, ground contacts), the Froude transition speeds, the minima of the cost curves, a hand-calculated ration and the gut absorption against closed-form results.
The science
Gaits and footfalls. Each foot is on the ground for a fraction β of the stride (the duty factor) and in the air for 1−β. Walk: β>0.5, four beats, never airborne. Trot: two diagonal pairs, β≈0.35–0.45. Canter: three beats with a suspension phase. Gallop: β≈0.15–0.2, four beats. Speed is stride length times stride frequency:
v = L · f (stance: foot moves back relative to the body by βL)
The model keeps each stance foot exactly planted: the foot moves backwards under the hip at speed v while the leg swings through ±βL/2.
Froude number and gait transitions. Dynamically similar animals change gait at the same Froude number:
Fr = v² / (g · h), h = hip height (here 1.2 m)
Auto mode switches walk→trot at Fr ≈ 0.5 (2.4 m/s), trot→canter at Fr ≈ 2 (4.9 m/s) and canter→gallop at Fr ≈ 4.5 (7.3 m/s). The first value is the classic Alexander result; the others are illustrative round numbers placed near the speeds where the cost curves cross — real horses vary with breed, ground and rider.
Cost of transport. Net metabolic energy per kilogram per metre is U-shaped within each gait (Hoyt & Taylor 1981): too slow wastes energy holding the body up, too fast wastes it on stride frequency. Each gait has its own minimum and the horse switches gait where the cheaper gait changes. The curves here are fitted shapes CoT = c·(1+((v−vopt)/w)²) with c ≈ 3.2–3.8 J/(kg·m); they follow the published trend but the numbers are illustrative, not data. Grade adds the external work of lifting the body at 25 % muscle efficiency:
P = CoT·m·v + m·g·v·grade / 0.25 [W]
Feeding. Maintenance digestible energy is taken as DE = 0.0333·BW Mcal/day (about 16.7 Mcal for 500 kg, a commonly quoted NRC-type figure for an average horse). Work DE = P·t / (4.184×106 J/Mcal · 0.65), with 0.65 an assumed efficiency of using DE for work. Feeds (as fed): grass hay 1.9, alfalfa 2.2, oats 2.9, apples 0.5 Mcal DE/kg. Forage is absorbed with a time constant of 8 h, concentrates 3 h (first-order, a stand-in for gut passage). One kilogram of body weight is booked as 8 Mcal.
Honest simplifications: the gait generator is kinematic (it does not solve muscle forces); timing parameters are typical values, not one horse; no protein, minerals, water or fibre quality; the DE categories are approximate; the horse refuses more concentrate as its gut load rises, but real colic/laminitis risk is not modelled. Educational only, not feeding advice for a real horse — ask a vet or equine nutritionist.
Baked 3D scene. The horse (jointed named parts), fence, manger, stable and trees were modelled in Blender 5.2 with Cycles-baked albedo, normal maps and per-vertex ambient occlusion; Three.js r160 animates and renders it.