Stilts

Every figure in this strip is computed live from the sliders by js/theory.js, the same module the harness checks against the engine.

The claim, and what is actually true

“The longer the stilts, the harder they are to balance.”

That sentence names no mechanism, so it can be tested. Treat the walker as a uniform rod of height L standing on its end. It topples at rate ω = √(3g/2L), which falls as the stilts get taller: a — walker takes — to go from a 0.01 rad lean to 0.25 rad, and a — walker takes —. Longer stilts buy time. So where does the difficulty come from?

1 · The uncontrolled fall, against its closed form

Line: t = (1/ω) arccosh(θ_f/θ₀), exact for the linearised rod. Dots: the integrator, crossing time recovered by Hermite interpolation. Worst relative disagreement over the whole gate, —; against the nonlinear pendulum's elliptic quadrature, —. Fall time scales as L^—.

2 · The delay wall

Feed the lean back with gains p and d but only after a reaction delay τ: θ″(t) = ω²θ(t) − p θ(t−τ) − d θ′(t−τ) The stable set of gains is a wedge above p = ω², and the wedge closes completely once σ = ωτ reaches √2. Below that a walker can be balanced; above it, no gain whatsoever will do.

Each curve is the Hopf boundary at one value of σ; the stable gains lie between it and the line p/ω² = 1. Located numerically by counting unstable characteristic roots with the argument principle, the wall sits at σ = — against the analytic √2 = —. Of a —-point gain sweep past the wall, — stabilise; the same sweep inside the wall finds —. Rearranged, the wall says a walker of height L can be balanced only if τ < √(4L/3g), i.e. only if L > 3gτ²/4.

3 · The support limit

The other margin is the base of support. The centre of pressure cannot leave the stilt, so the corrective angular acceleration is capped at 3gb/L² for a pad of half-width b. The largest lean that can be held is 2b/L, and under a saturated correction the exact recovery boundary is the straight line θ′ = ω (2b/L − θ) so the kick you can absorb standing straight is ω·2b/L, which falls as L^−3/2. The engine, told none of this, returns an exponent of —; in impulse rather than angle it returns —, and in pad width —. Worst relative error against the separatrix, —.

4 · Both margins together

The largest sideways kick a walker can absorb, maximised over every gain the argument principle certifies as stable, with the pad limit switched on and the full nonlinear equation integrated. At — the delay wall bites and nothing is recoverable. The impulse frontier peaks at — — — times the wall height over — delay-and-pad combinations — and then decays with measured exponent —, the L^−1/2 the support limit predicts.

Over every height a person actually walks on, the two margins point in opposite directions: the delay margin grows as L^— and the support margin shrinks as L^—. A — walker is left with a critical delay of — — several times any human reaction time — so the loop is never close to closing. Nothing about tall stilts is hard because you cannot react in time.

Try it on your own numbers

How the equation was integrated

Classical RK4 on a fixed grid with the delay pinned to an exact whole number of steps, so no step ever straddles one of the propagated derivative breaks at t = 0, τ, 2τ, … The half-step value of the history comes from the cubic Hermite interpolant of the two surrounding grid points. Measured order on a smooth right-hand side, —; with a zero-order-hold player command instead, the same integrator drops to —, which is how you know the number is measuring the scheme and not itself. Energy drift of the undriven pendulum over 20 000 steps, —.

What this is

Stilt-walking is not one person's invention and has no author, no year and no publisher. It is a worldwide folk technique, attested in China, Japan, West Africa and the Caribbean, the Low Countries and Gascony. This app is an original piece of work built around that tradition, not a copy of anyone's game: an independent implementation of the physics, an original renderer, and an original set of measurements. Nothing here is taken from any existing stilts game, any existing simulation code, or any third-party library. The people and institutions whose documented facts and published results the app relies on are credited below and in CREDITS.txt.

Controls

• ← → — shift your weight across the base of support. Your command does not arrive instantly: the rig's lag delays it, and your own reaction time stacks on top of that.
• On a phone or tablet, press and hold the Lean left / Lean right buttons under the scene instead.
• Space or Set off — set off / pause. R or Restart — restart. 1 2 3 — Walk, Lab, Help.
• While both stilts are planted you can put the centre of pressure anywhere across your stance. The moment one stilt lifts you are standing on a pad a couple of centimetres wide, and for that fraction of every step you are very nearly uncontrolled. Watch the green dot under the walker.

The headline

The folk claim is right about tall stilts and wrong about why. Reaction time is the reason everybody gives, and it is exactly backwards: a taller walker is a slower inverted pendulum, the critical delay √(4L/3g) grows as √L, and at any height a person actually walks on, a human reaction delay is nowhere near the wall. What tall stilts really cost you is the disturbance you can absorb, because the pad under your foot does not get bigger as you get taller: the absorbable angular kick goes as L^−3/2 and the absorbable impulse as L^−1/2. Put both margins into one measurement and the frontier has an interior optimum at about — times the delay-wall height — around — for a human delay, far below any stilt anyone stands on. Above that, taller is monotonically worse, forever, at L^−1/2.

And the published biomechanics says the balance margin is not what limits a real stilt walker at all. Trunk kinematics stay near normal on stilts; what changes with practice is step length, step frequency and double-support time. That is consistent with what this app measures: the delay loop is never close to closing, while the support margin collapses precisely during the single-support phase of each step. Stilt-walking is a stepping problem wearing a balance problem's clothes.

What was replicated, and what is original

Credits

• The tradition. Chinese 高踭 gaoqiao; Japanese 竹馬 takeuma; the Moko Jumbies of Trinidad and Tobago and their West African antecedents; the échasseurs namurois of Namur; the échassiers landais of Gascony.
• Sylvain Dornon (1858–1900), baker of Arcachon, who founded the first stilt-dancing troupe in 1889 and walked from the Place de la Concorde to Moscow on 1.2 m stilts between 12 March and 10 May 1891.
• Doug Hunt (Canada), tallest stilts walked, 16.76 m, 17 October 2023. Saimaiti Yiming (China), 79.6 km in 24 hours on 73 cm stilts.
• B. A. Kovacs, J. Milton and T. Insperger, “Virtual stick balancing: sensorimotor uncertainties related to angular and linear displacements”, Royal Society Open Science 6 (2019) 191006 — the closed-form critical delay this app checks itself against.
• P. Morasso and colleagues for the stick-balancing limit, and Akram & Frank (2009), Singer (2011) and Vielemeyer et al. (2023) for the gait work that says stilt-walking is limited by stepping rather than by balance.

Full source URLs, provenance tags and every point where the sources disagree with each other are listed in CREDITS.txt, which ships with this page.

Still open

• Trademark clearance was not obtained. The EUIPO and USPTO search interfaces are JavaScript applications that could not be driven from the tools available when this app was made, and the WIPO Global Brand Database served a CAPTCHA. No register was actually queried. A clearance search on the term is still owed and is not claimed here.
• The optimum is measured, not derived. — Its location is a number this app measured over a handful of delay-and-pad combinations; no closed form for it is offered and none was found in the literature.
• The duty factor is invented. The fraction of the step cycle spent on one stilt is a modelling choice. Real stilt-gait duty factors exist in the biomechanics literature; this app did not obtain them.
• The reaction delay is borrowed. The default comes from fingertip stick balancing, which is pivot-acceleration control, not ankle torque. No measurement of the effective delay of a stilt walker was found.
• One source contradicts its own group. Milton et al., Chaos 19 (2009) 026110 is paywalled; its abstract describes the critical delay as proportional to pendulum length, where the same group's 2019 closed form makes it go as the square root. Only the abstract was read, so the app quotes the 2019 paper and not that one.

Gates

Every number on this page is produced by tools-harness.js and read out of js/figures.js; none of them is typed in by hand. The shipped build passed — engine assertions with — failures.