strength.ts

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)