氷 · KŌRI
How much ice does a cold plunge actually need?
Almost every answer to this is a number somebody used once, quoted with no volume and no starting temperature attached, which makes it useless. The arithmetic is not difficult. It is below, in full, and you can check it.
It matters because the number it produces decides whether a twelve-week protocol is affordable on bagged ice or not — and the answer changes partway through, which is why people stop around week nine and think they lost their nerve.
| Weeks | Target | Duration | Ice | Bags | Per session | Per week |
|---|---|---|---|---|---|---|
| 1–2 | 15–18°C | 30–45 sec | none | — | — | — |
| 3–4 | 12–15°C | 60–90 sec | 1.3 kg | 1 | £2.50 | £7.50×3 |
| 5–6 | 10–12°C | 90 sec – 2 min | 4.0 kg | 2 | £5 | £20×4 |
| 7–8 | 8–10°C | 2–3 min | 6.8 kg | 4 | £10 | £40×4 |
| 9–10 | 5–8°C | 3 min | 9.8 kg | 5 | £12.50 | £50×4 |
| 11–12 | 5°C or below | 3–4 min | 11.3 kg | 6 | £15 | £60×4 |
Twelve weeks, on bagged ice
£355
Spent on water, and gone. A second-hand chest freezer, a liner and a timer plug cost less than the weeks shown in crimson — which is the arithmetic that decides the build, and the reason people stop at week nine believing they lost their nerve.
Why the melt is the machine.
Ice does not cool water by being cold. Almost all of the work is the melt itself. Turning one kilogram of ice at 0°C into one kilogram of water at 0°C absorbs 334 kilojoules — roughly eighty times what it takes to warm that same kilogram by a single degree. The coldness of the ice is a rounding error beside it.
The whole of it
m = V × 4.18 × (T₁ − T₂) ÷ (334 + 4.18 × T₂)
m kilograms of ice, V litres of water, T₁ what comes out of the tap, T₂ what you want. The denominator carries the melt plus warming the meltwater to the final temperature, which is why colder targets cost disproportionately more rather than proportionally more.
The season decides the first eight weeks.
Mains water in a temperate climate runs roughly 6–12°C in winter and 16–20°C in summer. Set the calculator to midwinter and the first eight weeks need no ice at all — the cold tap is already colder than the schedule asks for.
Which is worth knowing before you start, because the first eight weeks are exactly the ones in which this either becomes a habit or does not, and they are free for half the year.
What this does not account for.
Heat leaking in from the room, from the tub itself, and from you. Water left standing drifts back up. Treat the figure as the floor — what it takes at the moment of entry, under ideal conditions — and expect to want a little more in a warm room. It is stated here rather than buried, because a number presented as exact that a reader finds to be approximate costs more than the approximation was ever worth.
This is the whole of the arithmetic and there is nothing held back in it. What it does not tell you is what to do about the number it produces — which build, bought in which order, and which of the things commonly sold to people starting this are worth anything. That is 支度, and it is paid work. I will not pretend otherwise.
Take the table with you
The twelve weeks, as one page.
Every week's temperature, duration and frequency with the ice beside it. Printable, for the wall by the tap. Sent once. What follows it is where the schedule comes from — Takuan Sōhō, the 1630s, and the mind this was ever meant to train.
The build itself — which apparatus, bought in which order, heat without a sauna, and the five things commonly sold to people starting this that no week of the protocol requires — is inside 不動心 Fudōshin, $297, one payment. It does not renew.