motion.test.ts

1	import { describe, expect, it } from 'vitest'
2	import { G0, OMEGA_RAD_S } from '../src/canon/constants.js'
3	import {
4	RAINDROP_TERMINAL_M_S, freeFallDriftM, freeFallLeanRad, freeFallPathLeanRad,
5	freeFallTimeS, steadyFallLeanRad,
6	} from '../src/canon/motion.js'
7
8	const deg = (r: number): number => (r * 180) / Math.PI
9
10	/**
11	* These two numbers are the entire visible evidence that Tower spins, so they are
12	* worth pinning: the hull is sealed, there are no stars, and everything that does
13	* not fall is co-rotating and therefore perfectly still.
14	*/
15	describe('falling in the rotating frame', () => {
16	it('leaves rain very nearly vertical', () => {
17	expect(deg(steadyFallLeanRad(RAINDROP_TERMINAL_M_S))).toBeCloseTo(1.5, 1)
18	})
19
20	it('leans a waterfall enough to read as a compass', () => {
21	// A 1 km drop: eight times the lean of rain, and unmistakable.
22	expect(deg(freeFallLeanRad(1000))).toBeCloseTo(11.3, 1)
23	})
24
25	it('drifts an object dropped from 1 km by over a hundred metres', () => {
26	expect(freeFallDriftM(1000)).toBeCloseTo(133, 0)
27	})
28
29	/**
30	* design.md §1.9.2 tabulates 7.6° for a kilometre and this view reports 11.3°.
31	* Both are correct and they are not the same angle, so pin the relation that
32	* makes that true rather than quietly letting the two documents disagree.
33	*/
34	it('separates the lean of the path from the lean of the velocity', () => {
35	expect(deg(freeFallPathLeanRad(1000))).toBeCloseTo(7.6, 1)
36	for (const h of [100, 500, 1000, 2000]) {
37	expect(Math.tan(freeFallLeanRad(h))).toBeCloseTo(1.5 * Math.tan(freeFallPathLeanRad(h)), 9)
38	}
39	})
40
41	it('grows the lean with the drop, which is why the waterfall wins', () => {
42	const heights = [10, 100, 1000, 4000]
43	const leans = heights.map(freeFallLeanRad)
44	for (let i = 1; i < leans.length; i++) expect(leans[i]!).toBeGreaterThan(leans[i - 1]!)
45	// Rain does not: at terminal velocity the angle is fixed whatever the cloud.
46	expect(steadyFallLeanRad(RAINDROP_TERMINAL_M_S))
47	.toBe(steadyFallLeanRad(RAINDROP_TERMINAL_M_S))
48	})
49
50	it('agrees with the closed forms it is derived from', () => {
51	const h = 2500
52	const t = freeFallTimeS(h)
53	expect(t).toBeCloseTo(Math.sqrt((2 * h) / G0), 9)
54	expect(freeFallLeanRad(h)).toBeCloseTo(Math.atan(OMEGA_RAD_S * t), 9)
55	expect(freeFallDriftM(h)).toBeCloseTo((OMEGA_RAD_S * G0 * t ** 3) / 3, 6)
56	})
57
58	it('leans everything the same way — antispinward, always', () => {
59	expect(steadyFallLeanRad(1)).toBeGreaterThan(0)
60	expect(freeFallLeanRad(1)).toBeGreaterThan(0)
61	})
62	})