# Swimming

> An in-browser simulation of competitive pool swimming, built on the one mechanism that separates
> swimming from every other water sport: whether the body is on the free surface or under it.

## What it is

A race game for all four strokes, the individual medley and the relays, long course and short
course, with stroke legality and disqualification adjudicated against the World Aquatics
Competition Regulations in force from February 2026, Part Two. The hydrodynamics are calibrated on
published towing measurements. Everything runs client-side; no model, server or API is called.

## The mechanism

A body at the free surface drags a system of gravity waves along with it, and the energy in that
wave train is drag. A body deep enough makes no waves. The size of the escape is Havelock's result,
derived on the page rather than quoted: wave resistance falls as exp(-2gh/U^2), so the e-folding
depth is U^2/2g — which GROWS with speed. At 2.0 m/s, 24.0% of a surface swimmer's drag is
wave-making; at one metre down it is 0.55%.

## The headline finding

Fifteen metres is NOT where the underwater advantage runs out. The best breakout distance is
either well short of fifteen metres or right at the limit, and almost never in between: in the
full-race model a four per cent change in underwater kick power moves it from 8.5 m to 13.3 m, and
10-13 m is never the answer at any setting tested. The time saved by staying under
is stationary exactly where the underwater and surface speeds are equal — and if the underwater
steady speed exceeds the surface one, they are never equal, the integral never turns over, and
there is no interior optimum to find. The rule is a cap on an unbounded optimum.

## Corrections this app makes

- There is no 0.03 second relay take-over tolerance. Art. 10.4.5 is binary and carries none; the
  only nearby number is the equipment's 1/100 s resolution (Art. 15.16.6.3).
- Ties are not broken by a thousandth. Art. 11.2.3.1 discards thousandths; Art. 11.1.2 lets equal
  times stand as equal placings.
- The single butterfly kick in a breaststroke pull-down is now permitted at ANY time before the
  first breaststroke kick (Art. 7.1), not only during the first arm stroke as the old FINA rule and
  most coaching material still say.
- Arts. 5.4, 6.5 and 8.6 permit full submersion again once the head has passed the 5 m mark before
  the finish wall. Almost every summary omits it.
- Citing swimming rules as "SW 5.3" quotes a retired edition. The letter prefixes are gone.

## Where the model fails, stated on the page

Its drag exponent is 2.18 against a measured 1.90, and no allocation between friction and pressure
can fix it. It needs 535 W at the economical cadence and 858 W in a sprint, which is two to three
times what swimming energetics supports — because the passive-drag and active-drag literatures are
mutually inconsistent. It makes short course 10% SLOWER than long course, where reality has it two
to three per cent faster. And it does not reproduce the "1.8 to 2.8 chest depths" figure attributed
to Vennell et al. (2006), a paper that is closed access and could not be opened.

## Files

- /            the app
- /CREDITS.txt every source, marked full text, abstract only, secondary or could-not-open
- /LICENSE.txt MIT

Independent work. Not affiliated with World Aquatics or any federation.