strength.ts

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`6216d5cb` 2026-10-09 Pavel Safronov	1	/**
	2	* How much ice it takes to hold a skater up.
	3	*
	4	* Gold's formula, from the record of what did and did not go through the ice roads of
	5	* Canada: a sheet `h` cm thick carries a load of `A · h²` kg, where `A` says how much
	6	* risk is being run. L. W. Gold, "Use of ice covers for transportation", Canadian
	7	* Geotechnical Journal 8, 170–181 (1971).
	8	*/
	9
	10	/** Gold's `A`, kg/cm²: safe, failure unlikely. */
	11	export const A_SAFE = 3.5
	12	/** The upper limit for ordinary use: beyond it the ice is being asked a lot. */
	13	export const A_LIMIT = 7
	14	/** Beyond this, failure should be expected. */
	15	export const A_FAILURE = 17
	16
	17	/** A skater with clothes, skates and a pack, kg. */
	18	export const SKATER_MASS = 80
	19
	20	/** Thickness of ice, metres, that carries `mass` kg at risk `a`. */
	21	export function bearingThickness(mass: number, a: number): number {
	22	return Math.sqrt(mass / a) / 100
	23	}
	24
	25	/**
	26	* The three thicknesses that matter to one skater, metres. They are the zones of the
	27	* lake, and nothing about them is chosen: they are Gold's three values of `A`.
	28	*
	29	* - Thinner than `BREAKING` (2.2 cm) the ice gives way.
	30	* - Up to `CRACKING` (3.4 cm) it holds, and cracks under the skater as it does.
	31	* - Up to `SAFE` (4.8 cm) it is sound ice run close to its limit: the ice of the film,
	32	* at 4.1 cm, and the ice that sings best.
	33	* - Beyond that it is safe, and sings lower the thicker it gets.
	34	*/
	35	export const BREAKING_THICKNESS = bearingThickness(SKATER_MASS, A_FAILURE)
	36	export const CRACKING_THICKNESS = bearingThickness(SKATER_MASS, A_LIMIT)
	37	export const SAFE_THICKNESS = bearingThickness(SKATER_MASS, A_SAFE)