Runs 40 chases per point for gaps of 20–100 m, once with a prey that only runs straight and once with the current zig-zag setting, using the settings above. Shows the success rate and the share of chases that ended in overheating.
The science
Muscle-limited acceleration. A muscle's force falls as it shortens faster (Hill's force–velocity relation). A linear version per unit mass gives the propulsive acceleration
a_prop(v) = a₀ (1 − v / v₀)
m dv/dt = m a_prop − ½ ρ CdA v² P_muscle = m a_prop v
Power peaks at v = v₀/2 with Pmax = m a₀ v₀ / 4 (3.3 kW for the defaults, about 80 W/kg). The cat therefore accelerates hardest at the start and creeps towards a terminal speed where propulsion equals drag: for a₀ = 10.5 m/s², v₀ = 31 m/s and CdA = 0.12 m² that is 27 m/s (98 km/h), close to measured top speeds of about 29 m/s.
Turning costs speed. Tyre-like grip is shared between steering and driving (friction circle): alat² + along² ≤ agrip², and the turning radius is R = v²/alat. At 25 m/s a cat limited to 10.5 m/s² needs a 60 m radius; a lighter gazelle at 20 m/s and 13.5 m/s² turns in 30 m. Every sharp jink makes the pursuer brake or run wide.
Heat budget. Only about 25 % of the metabolic energy becomes muscle work; the rest warms the body (which has a heat capacity of about 3.5 kJ/(kg K)):
Q = P(1/η − 1) + m qbasal + m krun v
m c dT/dt = Q − k(T − Tair) (k larger when panting at rest)
With η = 0.25, qbasal = 4 W/kg and a leg-cycling overhead krun = 7 J/(kg m) the body goes from 38.5 to about 40.5 °C in a flat-out chase of 600–700 m, after which the cat abandons the hunt. krun and the 40.5 °C limit are illustrative calibrations, not measurements of a particular animal.
Prey. The gazelle-like runner grazes until the gap shrinks below the flight-initiation distance (the slider), then flees at its own force–velocity limit and makes random sharp turns (a straight-running prey is the “0 % zig-zag” case). A catch is declared when the gap falls below 1.2 m; no contact is simulated.
Honest simplifications. Point masses in a plane (no gait cycle physics: the leg animation is driven by speed only), flat ground, constant air density, no wind, no terrain or vegetation obstacles, perfectly informed predator guidance and prey that does not tire. Success rates are emergent properties of this toy model, not field statistics (real cheetah hunts succeed roughly half the time, depending on the study). All animal parameters are typical values to be spot-checked.
Independent educational model. Made with Blender and Three.js.