tower / files / src / canon / atmosphere.ts
atmosphere.ts
| 1 | /** |
| 2 | * Tower's atmosphere. See design.md §1.5 and §1.8. |
| 3 | * |
| 4 | * Gravity falls linearly to zero on the axis, so the air is far deeper than Earth's |
| 5 | * and the density profile is set by the rotational potential rather than by a |
| 6 | * constant g. This is what makes a sightline across the interior clearer than one |
| 7 | * of the same length along the floor — the defining optical fact about Tower. |
| 8 | */ |
| 9 | import { |
| 10 | OMEGA_RAD_S, RADIUS_M, SPECIFIC_GAS_CONSTANT, TEMPERATURE_K, |
| 11 | FLOOR_PRESSURE_PA, RAYLEIGH_FLOOR_PER_M, |
| 12 | } from './constants.js' |
| 13 | |
| 14 | /** Rotational potential per unit mass between the floor and radius `s`. */ |
| 15 | export function potentialAtRadius(s: number): number { |
| 16 | return (OMEGA_RAD_S ** 2 * (RADIUS_M ** 2 - s ** 2)) / 2 |
| 17 | } |
| 18 | |
| 19 | /** Air density at radius `s` from the axis, relative to floor density. */ |
| 20 | export function relativeDensityAtRadius(s: number): number { |
| 21 | return Math.exp(-potentialAtRadius(s) / (SPECIFIC_GAS_CONSTANT * TEMPERATURE_K)) |
| 22 | } |
| 23 | |
| 24 | /** Absolute pressure (Pa) at radius `s`. 5.2 kPa on the axis — thin, but real air. */ |
| 25 | export function pressureAtRadius(s: number): number { |
| 26 | return FLOOR_PRESSURE_PA * relativeDensityAtRadius(s) |
| 27 | } |
| 28 | |
| 29 | export const relativeDensityAtHeight = (h: number) => relativeDensityAtRadius(RADIUS_M - h) |
| 30 | export const pressureAtHeight = (h: number) => pressureAtRadius(RADIUS_M - h) |
| 31 | |
| 32 | /** Rayleigh extinction coefficient (per metre) at radius `s`. */ |
| 33 | export function extinctionAtRadius(s: number): number { |
| 34 | return RAYLEIGH_FLOOR_PER_M * relativeDensityAtRadius(s) |
| 35 | } |