This strike
Strike log
The swing has a closed form, so it is settled before anything can break
A conker on a lace of length L, drawn back to θ₀ and released,
arrives at the bottom at
and the mass does not appear. A heavy conker and a light one released from the same angle arrive at the same speed. That is where any argument about size has to start — and it means a big conker gets no free energy from being big. It only gets some if you do work on it with your arm, and then being heavy is a handicap, not a help.
Period against amplitude
Exactly T = 4√(L/g) K(sin(θ₀/2)), with the complete
elliptic integral K computed by the arithmetic-geometric mean. The
small-angle 2π√(L/g) is drawn alongside; it is wrong by
at 30° and at 90°.
Arrival speed
Free swing against a swing with arm work added, for a light conker and a heavy one. The free-swing curves lie exactly on top of one another.
What the harness checked
One contact, two jobs
Two conkers meet. Hertzian contact gives every quantity in closed form, and it produces two tensile fields that do different things:
The contact field is intense but tiny, and both bodies see exactly the same value of it because they share one contact. It takes a chip out of the shell. A duel decided by chipping alone is a coin flip and size never enters.
The bulk field is weak but covers the whole nut, concentrated by the drilled hole — and it is divided by each body's own cross-section. It is what splits a conker, and it is the only place in the whole problem where the two bodies differ at all.
The impact duration constant
Energy conservation on m*δ″ = −kδ^(3/2)
turns the contact time into one definite integral, and that integral is a Beta function.
Three methods, which share no code:
Mismatched conkers hit each other more gently
The peak contact pressure carries a factor
f(s) = (1+s)²/(1−s+s²) with s = R₁/R₂.
It is maximised at s = 1, so two equal conkers hit each other harder
than any mismatched pair does.
Nothing in a Hertz impact knows how big it is
At a fixed impact speed the only quantities available are a modulus, a density and a
speed — and none of them contains a length. So every stress is size-independent
exactly, while every size scales as R and every force as R².
Change the conkers' size and the numbers below do not move at all.
“A bigger conker wins because it’s stronger”
Half right, and for the opposite reason to the one people give. A bigger conker is weaker. It only wins because in a duel it is not being tested on its own.
Bigger is weaker: the size effect, recovered not assumed
A bigger body holds more flaws, so its weakest flaw is weaker. Weakest-link
statistics make that exact: σ ∝ V^(−1/m). The simulation below
was never told that law. It scatters flaws through a volume, gives each one a critical
stress, takes the smallest, and the law falls out.
Bigger is safer: the duel exponent, and where it changes sign
One transmitted force, two cross-sections. The bigger body divides the same
force by more area, and the risk of rupture goes as R^(3−2m), so the
odds it outlives the other are (R₁/R₂)^(2m−3). Positive only
when m > 3/2.
What the advantage is actually worth
The exponent is 2m − 3, so the whole strength of the folk rule rests on
m — the Weibull modulus of horse-chestnut seed, which nobody has ever
measured. Biological brittle solids run from about 1.8 to 4.5, and across that band the
answer changes from “barely matters” to “decides the match”.
The crossover is real, and it was tested where it flips
The control that could have failed
A size effect has to be removable. Keep the flaw count fixed instead of the flaw density and the size effect must vanish entirely — if any part of the simulation tied strength to volume by some other route, this is where it would show.
Try it yourself
What this is
Conkers is the British playground game: a horse chestnut drilled, threaded on a lace, and swung at somebody else's until one of them breaks. This is an independent reimplementation of it as a physics simulation. It is not affiliated with the World Conker Championships, the Ashton Conker Club, or anyone else.
There is no published physics of conkers. None — OpenAlex returns ten works with “conkers” in the title and they are sound art, pet toxicology, theology and a risk editorial; arXiv returns zero. Nobody has measured the strength, stiffness, toughness or Weibull modulus of a horse chestnut seed. So everything here is built from first principles, and every number on the page is tagged with where it came from.
The rules, as the World Conker Championships publish them
Paraphrased from the ten current rules at worldconkerchampionships.com/compete/rules/. Founded 1965 by a group of anglers at the Chequered Skipper in Ashton, Northamptonshire; now at the Shuckburgh Arms, Southwick. Over £485,000 raised for causes supporting the visually impaired.
Hardening: the clean negative
Bake it, soak it in vinegar, leave it in a drawer for a year, paint it with nail varnish, pass it through a pig. None of it has ever been measured. Not once, anywhere: Europe PMC, OpenAlex, Crossref and arXiv return nothing, and the one “experiment” online has one conker per condition, no control, and never publishes its numbers.
There is also no rule against it. Rule 1 makes it impossible instead — every conker is supplied by the organisers and drawn blind from a bag.
The seasoning settings in this app are RECONSTRUCTED. They say what each method would have to do to the flaw population for the folklore to be right. They are not evidence that it does.