581 lines
33 KiB
JavaScript
581 lines
33 KiB
JavaScript
// ════════════════════════════════════════════════════════════════════════
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// physics.js — Physical constants and meteorological calculations.
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//
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// All numbers are peer-reviewed constants or coefficients. Nothing in
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// here should need editing unless the underlying science changes.
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//
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// Exports (in order of appearance):
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// SIGMA, EPSILON_P, A_K, ALBEDO_GRASS, ALBEDO_CONCRETE (radiation constants)
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// calcConcreteTemp(Ta, globalRad, windSpeed) urban surface temp
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// calcIndoorTempPass(TaArr, globArr, elevArr, buildingType) passive indoor temp
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// calcManagedIndoorTempPass(TaArr, globArr, elevArr, buildingType) managed indoor temp
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// calcVehicleInteriorTemp(Ta, globalRad, solElev, vehicleType, ventilated)
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// vaporPressureHpa(Ta, RH) Magnus formula → hPa
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// solarElevationDeg(lat, lon, dateUTC) NOAA simplified solar position (°)
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// calcTmrt(Ta, dirRad, diffRad, globalRad, solElev) Mean radiant temperature
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// utciApprox(Ta, Tmrt, va10, ehPa) Bröde et al. 2012 UTCI polynomial
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// ════════════════════════════════════════════════════════════════════════
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import { VEHICLE_TYPES, BUILDING_TYPES } from './utils.js';
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// ═══════════════════════════════════════════════════════════════════
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// PHYSICAL CONSTANTS
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// ───────────────────────────────────────────────────────────────────
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// These are real-world physics values — don't change them unless you
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// have a peer-reviewed reason. They're used by calcTmrt() below to
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// work out how much heat your skin actually absorbs from the sun.
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// SIGMA — Stefan–Boltzmann constant (radiates heat)
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// EPSILON_P — emissivity of human skin (~0.97)
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// A_K — short-wave absorption coefficient for clothing
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// ALBEDO_GRASS — how much sun grass reflects back at you (23%)
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// ALBEDO_CONCRETE — how much sun concrete reflects back (30%)
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// Concrete absorbs more net solar than grass and has
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// no evaporative cooling, so its surface runs hot.
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// ═══════════════════════════════════════════════════════════════════
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export const SIGMA = 5.670374419e-8;
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export const EPSILON_P = 0.97;
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export const A_K = 0.7;
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export const ALBEDO_GRASS = 0.23;
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export const ALBEDO_CONCRETE = 0.30;
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// ═══════════════════════════════════════════════════════════════════
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// CONCRETE SURFACE TEMPERATURE (Urban profile)
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// ───────────────────────────────────────────────────────────────────
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// Estimates the surface temperature of exposed concrete using a
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// simplified energy-balance approach:
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// • Absorbed solar = globalRad × (1 − albedo)
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// • No latent heat (no evaporation — concrete is dry)
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// • Convective loss to air proportional to wind speed
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// • Result is clamped to a physically plausible range
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//
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// This is what matters for contact heat stress in cities — the UTCI
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// standard uses grass, which runs ~5–15 °C cooler than urban concrete
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// on a sunny day because grass sweats (transpires).
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// ═══════════════════════════════════════════════════════════════════
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export function calcConcreteTemp(Ta, globalRad, windSpeed) {
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if (globalRad == null || Ta == null) return null;
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const absorbed = globalRad * (1 - ALBEDO_CONCRETE); // W/m²
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// Convective heat transfer coefficient: ~10 W/m²K still air, rises with wind
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// (10 reflects realistic natural convection; 5 was too low and ran too hot)
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const hc = 10 + 4.5 * Math.sqrt(Math.max(windSpeed || 0, 0));
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// Surface temp: Ta + solar gain / convective loss
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const Ts = Ta + absorbed / hc;
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// Clamp: can't be cooler than air, cap at 85 °C (melting asphalt territory)
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return Math.max(Ta, Math.min(Ts, 85));
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}
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// ═══════════════════════════════════════════════════════════════════
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// UK HOUSE INDOOR TEMPERATURE (windows closed, no active cooling)
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// ───────────────────────────────────────────────────────────────────
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// Estimates the ambient indoor air temperature of a typical UK brick
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// house with windows closed and no air conditioning.
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//
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// Two heat pathways are modelled:
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//
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// 1. WALL CONDUCTION
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// Heat conducts through brick cavity walls and roof. UK Part L
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// compliant walls have a U-value around 0.28–0.45 W/m²K; older
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// solid-brick stock runs higher. A representative mid-stock value
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// is used. This drives a slow, steady heat transfer proportional
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// to the difference between outdoor and indoor air temperature.
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//
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// 2. WINDOW SOLAR GAIN
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// A typical UK semi has ~15–18% glazing ratio. Solar energy
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// transmits through glass, is absorbed by floors and furniture,
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// and heats the indoor air. Gain is averaged across orientations
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// (not all windows face south). Diffuse radiation contributes
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// regardless of sun angle.
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//
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// THERMAL LAG
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// Brick and concrete have high thermal mass — the house responds
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// slowly to outdoor temperature swings. Each hour builds a realistic
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// target temperature from outdoor air, window solar gain, retained
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// warmth, and internal gains, then the room temperature lags toward
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// that target. This avoids runaway accumulation while still giving
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// the characteristic late-day indoor peak.
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// Call calcIndoorTempPass() on the full hourly arrays after
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// building rows — it returns a per-hour indoor temp array.
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//
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// No mechanical cooling. Minimal infiltration (windows closed).
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// Internal heat gains (people, appliances) are not modelled.
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//
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// Colour thresholds:
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// < 20 °C — cool, may need heating
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// 20–26 °C — comfortable
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// 26–32 °C — warm; WHO heatwave advisory threshold for sleeping
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// > 32 °C — hot; risk for elderly and vulnerable occupants
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// ═══════════════════════════════════════════════════════════════════
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// Two-pass function: call with the full arrays of hourly Ta and globalRad.
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// Returns an array of indoor temperatures, one per hour.
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// buildingType must be a key of BUILDING_TYPES; defaults to 'brick'.
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export function calcIndoorTempPass(TaArr, globArr, elevArr, buildingType = 'brick') {
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const preset = BUILDING_TYPES[buildingType] || BUILDING_TYPES.brick;
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const { lagHours, glazingRatio, gValue, orientFactor, solarScale, baseTemp, internalGain, retainedScale } = preset;
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const n = TaArr.length;
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const result = new Array(n);
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const alpha = 1 - Math.exp(-1 / lagHours); // per-hour blending weight
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// Seed to a plausible occupied indoor baseline rather than outdoor air.
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let Ti = Math.max(TaArr[0] ?? 15, baseTemp ?? 16);
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for (let i = 0; i < n; i++) {
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const Ta = TaArr[i] ?? Ti;
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const glob = globArr[i] ?? 0;
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// Solar gain through windows (W/m² effective)
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const solarGain = glob * glazingRatio * gValue * orientFactor;
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const retainedWarmth = Math.max(0, (baseTemp ?? 16) - Ta) * (retainedScale ?? 0.35);
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const target = Ta + solarGain * (solarScale ?? 0.1) + retainedWarmth + (internalGain ?? 0.7);
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// Apply thermal lag: blend toward the hour's target instead of adding
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// solar gain repeatedly onto the previous indoor temperature.
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Ti = Ti + alpha * (target - Ti);
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// Can't be colder than outdoor (house doesn't actively cool)
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result[i] = Math.max(Math.min(Ti, 55), Math.min(Ta, Ti));
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}
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return result;
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}
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// ═══════════════════════════════════════════════════════════════════
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// UK HOUSE INDOOR TEMPERATURE — MANAGED (curtains closed, windows open)
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// ───────────────────────────────────────────────────────────────────
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// Models the same UK brick house as calcIndoorTempPass but with two
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// behavioural interventions that reflect standard heatwave advice:
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//
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// 1. CURTAINS CLOSED
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// Thick curtains block ~80% of window solar gain before it enters
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// the room. The small remaining fraction is diffuse light through
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// the curtain fabric. Wall conduction is unchanged.
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//
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// 2. WINDOWS OPEN (smart ventilation)
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// When outdoor air is cooler than the indoor air, windows are open
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// and a ventilation heat exchange pulls the indoor temp toward
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// outdoor. When outdoor is hotter than indoor, windows are kept
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// shut — so this strategy never makes things worse, only better.
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// Ventilation rate ~2 air changes/hour for a well-opened house.
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//
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// Same thermal lag model as calcIndoorTempPass (4 h brick time constant).
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// ═══════════════════════════════════════════════════════════════════
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// buildingType must be a key of BUILDING_TYPES; defaults to 'brick'.
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export function calcManagedIndoorTempPass(TaArr, globArr, elevArr, buildingType = 'brick') {
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const preset = BUILDING_TYPES[buildingType] || BUILDING_TYPES.brick;
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const { lagHours, glazingRatio, gValue, orientFactor, curtainBlock, ventAlpha, solarScale, baseTemp, internalGain, retainedScale } = preset;
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const n = TaArr.length;
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const result = new Array(n);
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const alpha = 1 - Math.exp(-1 / lagHours);
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let Ti = Math.max(TaArr[0] ?? 15, baseTemp ?? 16);
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for (let i = 0; i < n; i++) {
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const Ta = TaArr[i] ?? Ti;
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const glob = globArr[i] ?? 0;
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// Solar gain — curtains block curtainBlock fraction
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const solarGain = glob * glazingRatio * gValue * orientFactor * (1 - curtainBlock);
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const retainedWarmth = Math.max(0, (baseTemp ?? 16) - Ta) * (retainedScale ?? 0.35);
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const target = Ta + solarGain * (solarScale ?? 0.1) + retainedWarmth + (internalGain ?? 0.7);
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// Apply thermal lag toward the managed target.
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Ti = Ti + alpha * (target - Ti);
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// Smart ventilation: only open windows when outside is cooler
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if (Ta < Ti) {
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Ti = Ti + ventAlpha * (Ta - Ti);
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}
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result[i] = Math.max(Math.min(Ti, 55), Math.min(Ta, Ti));
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}
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return result;
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}
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// ═══════════════════════════════════════════════════════════════════
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// VEHICLE INTERIOR CABIN TEMPERATURE (seated occupant, not in sunbeam)
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// ───────────────────────────────────────────────────────────────────
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// Models the ambient cabin air temperature experienced by an occupant
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// seated out of direct sunlight inside a sealed, parked vehicle.
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// Two heat sources are combined:
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//
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// 1. PANEL CONDUCTION
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// Aluminium body panels absorb solar radiation and conduct heat
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// into the cabin. Albedo ~0.25 (mid-point for typical mixed-colour
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// fleet; dark paint ~0.10, silver/white ~0.40).
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// Panel surface temp → conductive gain into cabin air.
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//
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// 2. SIDE-WINDOW GLAZING GAIN (sun-angle dependent)
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// When solar elevation is between ~10° and ~60°, the sun's rays
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// cut through the side glass at an angle that allows significant
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// transmission into the cabin (rather than hitting the roof or
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// reflecting off at a shallow angle). This warms the cabin air
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// but the occupant is modelled as NOT sitting in the beam —
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// so it adds to ambient cabin temp, not direct radiant load.
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// Above 60° the sun mostly hits the roof; below 10° it reflects.
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//
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// Wind is ignored unless ventilation is enabled. No evaporative cooling.
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// Cars warm quickly; motorhomes and caravans are treated as insulated living
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// spaces with 25–35 mm sandwich panels, so panel heat gain is much smaller
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// and the interior response is slower than a car cabin. Because they are
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// occupied living spaces, they also retain warmth from previous hours, people,
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// appliances, and background heating; without that, cool sunny days are
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// under-estimated badly.
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//
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// Colour thresholds in the table:
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// < 35 °C — warm but tolerable for short periods
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// 35–45 °C — dangerous for children/pets (hyperthermia risk)
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// > 45 °C — potentially fatal within minutes
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// ═══════════════════════════════════════════════════════════════════
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export function calcVehicleInteriorTemp(Ta, globalRad, solElev, vehicleType = 'car', ventilated = false) {
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if (globalRad == null || Ta == null) return null;
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// Look up vehicle preset; fall back to a standard car if key unknown.
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const preset = VEHICLE_TYPES[vehicleType] || VEHICLE_TYPES.car;
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// ── 1. Panel conduction ──────────────────────────────────────────
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const panelAbsorbed = globalRad * (1 - preset.albedo); // W/m² absorbed by bodywork
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// Panel surface temp: absorbed solar / convective loss to outside air
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// hOut ~10 W/m²K (light breeze over panel surface even when parked)
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const hOut = 10;
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const panelSurfaceTemp = Ta + panelAbsorbed / hOut;
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// Conductive gain into cabin. Cars are thin metal + trim; motorhomes and
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// caravans use insulated sandwich panels, so their bodyU is much lower.
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const hCabin = preset.bodyU ?? 4;
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const conductionGain = hCabin * (panelSurfaceTemp - Ta); // W/m²
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// ── 2. Side-window glazing gain (angle-dependent) ─────────────────
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// Glazing transmission for auto glass ~0.70; scaled by vehicle glazing area.
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const tau = 0.70 * preset.glazingArea;
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let glazingGain = 0;
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if (solElev != null && solElev > 10 && solElev < 60) {
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// Scale factor: peaks around 30–40° elevation (sun cuts squarely
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// through side glass), tapers off toward 10° (shallow/reflected)
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// and 60° (sun increasingly hitting roof not side glass).
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// Use a simple tent function peaking at 35°.
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const peak = 35;
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const halfWidth = 25; // degrees either side
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const factor = Math.max(0, 1 - Math.abs(solElev - peak) / halfWidth);
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// Diffuse radiation also enters through glass regardless of angle
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glazingGain = tau * globalRad * factor * 0.5; // occupant not in beam → 50% ambient
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} else {
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// Outside the side-window zone: diffuse only (scattered sky light)
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glazingGain = tau * (globalRad * 0.15); // ~15% diffuse fraction
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}
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// ── Combine into cabin air temperature ───────────────────────────
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// Total heat input per m² of cabin surface
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const totalGain = conductionGain + glazingGain;
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// Cabin heat rejection: an effective blend of leakage, internal air volume,
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// and surfaces exchanging heat with the outside. With windows open it is
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// roughly 5× higher — air moves freely
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// through the cabin, flushing heat out and capping interior temperature much
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// closer to ambient. Cabin temp still rises a little due to panel/roof solar gain.
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const effectiveHLoss = ventilated ? preset.hCabinLoss * 5 : preset.hCabinLoss;
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const thermalMass = preset.thermalMass ?? 1;
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const solarRise = (totalGain / effectiveHLoss) * thermalMass;
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// Motorhomes/caravans behave more like small insulated rooms than parked
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// cars. This term captures retained living-space warmth: strongest on cool
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// days, tapering away as outdoor air warms, and reduced when ventilated.
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const retainedWarmth = preset.retainedWarmth
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? Math.max(0, 8 - 0.25 * Ta) * (ventilated ? 0.35 : 1)
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: 0;
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const internalGain = (preset.internalGain ?? 0) * (ventilated ? 0.35 : 1);
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const Ti = Ta + solarRise + retainedWarmth + internalGain;
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// Clamp: can't be cooler than outside air; physical cap at 90 °C
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return Math.max(Ta, Math.min(Ti, 90));
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}
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// ── FUTURE FEATURE v2: Pets Profile — Fur Temperature & Heat Stress ──────────
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// Dogs and cats experience heat very differently from humans:
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//
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// FUR SURFACE TEMPERATURE
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// Dark/thick fur absorbs solar radiation and can run significantly hotter
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// than air temperature — similar in principle to calcConcreteTemp() but
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// with fur-specific albedo values:
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// Black fur: albedo ~0.05 (almost all radiation absorbed)
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// Brown fur: albedo ~0.15
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// Golden fur: albedo ~0.25
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// White fur: albedo ~0.40
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// Add a calcFurSurfaceTemp(Ta, globalRad, windSpeed, furAlbedo) function
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// mirroring calcConcreteTemp but with appropriate convective coefficients
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// for fur (lower hc than concrete — fur insulates).
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//
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// PAW BURN RISK
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// Paw pads are highly sensitive to surface temperature. Use calcConcreteTemp()
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// output directly — the existing concrete surface temp is already the right
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// number. Threshold guidance:
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// < 40 °C — safe
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// 40–52 °C — discomfort / possible burn (hold-your-hand-for-7-seconds test)
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// > 52 °C — burns within 60 seconds
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// Display as a simple traffic-light column in the Pets profile.
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//
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// BREED-SPECIFIC HEAT STRESS
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// Brachycephalic breeds (Bulldogs, Pugs, French Bulldogs, Persians) have
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// severely impaired thermoregulation — their safe UTCI ceiling is much lower.
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// A breed selector (Normal / Brachycephalic / Senior) applies a risk multiplier
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// to the UTCI thresholds, similar to the planned activity modifier.
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//
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// SUGGESTED COLUMNS FOR PETS PROFILE
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// Hour | Air Temp | UTCI+P | Fur Surface Temp | Paw Burn Risk | Shade Advised
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//
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// ─────────────────────────────────────────────────────────────────────────────
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// ── FUTURE FEATURE: Vehicle-at-speed thermal model ────────────────────────────
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// Idea: extend calcVehicleInteriorTemp (or add a companion function) to model
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// cabin temperature for a vehicle travelling at speed, not just parked.
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//
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// Key physics differences from the static model:
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// • Forced convection over the shell scales with vehicle speed (v²), so
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// hOut rises significantly — shell cools much faster than when parked.
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// • Above ~30 mph the vehicle's own forward motion dominates airflow, so
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// ambient wind direction becomes largely irrelevant (simplifies the model).
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// • Speed classes to model: urban (~20 mph), dual carriageway (~50 mph),
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// motorway (~70 mph) — each with a derived hOut multiplier.
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// • Windows-open behaviour changes completely at speed: at 70 mph open
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// windows create high-velocity through-flow, dramatically cutting cabin
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// temp vs. the sealed-car case (but much less pleasant than AC!).
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// • Roof and bonnet solar gain stays the same; side-glass gain is unchanged.
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// • AC-off vs AC-on would be the primary user toggle alongside speed class.
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//
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// Suggested signature:
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// calcVehicleInteriorTempAtSpeed(Ta, globalRad, solElev, vehicleType, speedMph, windowsOpen)
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//
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// This would be a useful companion output column (e.g. "Vehicle (moving)")
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// for road-trip planning, dog-in-car safety at a rest stop vs. motorway, etc.
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//
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// ── CYCLIST AT SPEED (companion to the above) ────────────────────────────────
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// A cyclist generates their own headwind, so the felt temperature (UTCI) is
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// very different from a stationary person — even without ambient wind.
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// Could share the same speed-class approach as the vehicle model:
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// Slow (10 mph) / Moderate (15 mph) / Fast (25 mph)
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//
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// Key differences from the vehicle model:
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// • The cyclist IS the exposed person — use the UTCI polynomial directly
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// with va = max(ambientWind, cyclingSpeed * conversionFactor)
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// • No cabin heating effect — the cyclist gets wind chill, not solar entrapment
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// • High metabolic heat generation raises core temp (links to the activity
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// modifier planned in compute.js — cycling at speed is a combined effect)
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// • UVA/UVB exposure is unchanged — still fully exposed to the sun
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//
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// Could be a sub-option within the existing Cycling activity variant rather
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// than a separate column — e.g. a speed picker in the variant controls.
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// ─────────────────────────────────────────────────────────────────────────────
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// ═══════════════════════════════════════════════════════════════════
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// VAPOUR PRESSURE — Magnus formula.
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// ───────────────────────────────────────────────────────────────────
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// Converts air temperature (°C) and relative humidity (%) to vapour
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// pressure in hPa. Used as the humidity input to utciApprox().
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// ═══════════════════════════════════════════════════════════════════
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export function vaporPressureHpa(Ta, RH) {
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const es = 6.105 * Math.exp((17.27 * Ta) / (237.7 + Ta));
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return es * (RH / 100);
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}
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// ═══════════════════════════════════════════════════════════════════
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// SOLAR ELEVATION — NOAA simplified algorithm (degrees above horizon).
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// ───────────────────────────────────────────────────────────────────
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||
// Accurate to within ~0.01° for most practical purposes. Returns a
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// negative value when the sun is below the horizon (civil twilight
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// starts at −6°, nautical at −12°, astronomical at −18°).
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// ═══════════════════════════════════════════════════════════════════
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export function solarElevationDeg(lat, lon, dateUTC) {
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const start = Date.UTC(dateUTC.getUTCFullYear(), 0, 0);
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const diff = dateUTC - start;
|
||
const DOY = Math.floor(diff / 86400000);
|
||
const hourUTC =
|
||
dateUTC.getUTCHours() +
|
||
dateUTC.getUTCMinutes() / 60 +
|
||
dateUTC.getUTCSeconds() / 3600;
|
||
const gamma = ((2 * Math.PI) / 365) * (DOY - 1 + (hourUTC - 12) / 24);
|
||
const eqtime =
|
||
229.18 *
|
||
(0.000075 +
|
||
0.001868 * Math.cos(gamma) -
|
||
0.032077 * Math.sin(gamma) -
|
||
0.014615 * Math.cos(2 * gamma) -
|
||
0.040849 * Math.sin(2 * gamma));
|
||
const decl =
|
||
0.006918 -
|
||
0.399912 * Math.cos(gamma) +
|
||
0.070257 * Math.sin(gamma) -
|
||
0.006758 * Math.cos(2 * gamma) +
|
||
0.000907 * Math.sin(2 * gamma) -
|
||
0.002697 * Math.cos(3 * gamma) +
|
||
0.00148 * Math.sin(3 * gamma);
|
||
const timeOffset = eqtime + 4 * lon;
|
||
const tst = hourUTC * 60 + timeOffset;
|
||
const ha = (((tst / 4) - 180) * Math.PI) / 180;
|
||
const latRad = (lat * Math.PI) / 180;
|
||
const cosZenith =
|
||
Math.sin(latRad) * Math.sin(decl) +
|
||
Math.cos(latRad) * Math.cos(decl) * Math.cos(ha);
|
||
const zenith = Math.acos(Math.max(-1, Math.min(1, cosZenith)));
|
||
return (Math.PI / 2 - zenith) * (180 / Math.PI);
|
||
}
|
||
|
||
// ═══════════════════════════════════════════════════════════════════
|
||
// MEAN RADIANT TEMPERATURE (Tmrt)
|
||
// ───────────────────────────────────────────────────────────────────
|
||
// Tmrt is the uniform temperature of an imaginary enclosure that would
|
||
// cause the same net radiation exchange as the actual environment.
|
||
// It accounts for:
|
||
// • Direct solar beam (DNI), scaled by the projected-area factor fp
|
||
// • Diffuse sky radiation (scattered and cloud-reflected)
|
||
// • Ground-reflected shortwave (albedo × global radiation)
|
||
// • Longwave thermal emission from surrounding surfaces (≈ blackbody at Ta)
|
||
//
|
||
// The fabric index 0.308 (fp formula from ISO 7933) projects the sun
|
||
// onto a standing person's silhouette as a function of solar elevation.
|
||
// Output feeds directly into utciApprox() as the Tmrt argument.
|
||
// ═══════════════════════════════════════════════════════════════════
|
||
export function calcTmrt(Ta, dirRad, diffRad, globalRad, solElev) {
|
||
const TaK = Ta + 273.15;
|
||
let fp = 0;
|
||
if (solElev > 0) {
|
||
const h2 = solElev;
|
||
fp = 0.308 * Math.cos((Math.PI / 180) * h2 * (0.998 - (h2 * h2) / 50000));
|
||
}
|
||
let DNI = 0;
|
||
if (solElev > 1) {
|
||
DNI = dirRad / Math.sin((solElev * Math.PI) / 180);
|
||
DNI = Math.min(DNI, 1100);
|
||
}
|
||
const Sshort = A_K * (fp * DNI + 0.5 * diffRad + 0.5 * ALBEDO_GRASS * globalRad);
|
||
const Slong = EPSILON_P * SIGMA * Math.pow(TaK, 4);
|
||
const TmrtK = Math.pow((Sshort + Slong) / (EPSILON_P * SIGMA), 0.25);
|
||
return TmrtK - 273.15;
|
||
}
|
||
|
||
// ═══════════════════════════════════════════════════════════════════
|
||
// UTCI POLYNOMIAL — DO NOT EDIT (or be VERY careful if you do)
|
||
// ───────────────────────────────────────────────────────────────────
|
||
// This is the official 210-term Bröde et al. (2012) approximation.
|
||
// It takes air temp, mean radiant temp, wind, and humidity and returns
|
||
// the "felt" temperature. Every number is a peer-reviewed coefficient.
|
||
// Scroll past it — there's nothing here you'll want to change.
|
||
// ═══════════════════════════════════════════════════════════════════
|
||
export function utciApprox(Ta, Tmrt, va10, ehPa) {
|
||
const va = Math.max(0.5, Math.min(17, va10));
|
||
const D_Tmrt = Tmrt - Ta;
|
||
const Pa = ehPa / 10;
|
||
const T = Ta, V = va, D = D_Tmrt, P = Pa;
|
||
const T2=T*T, T3=T2*T, T4=T3*T, T5=T4*T, T6=T5*T;
|
||
const V2=V*V, V3=V2*V, V4=V3*V, V5=V4*V, V6=V5*V;
|
||
const D2=D*D, D3=D2*D, D4=D3*D, D5=D4*D, D6=D5*D;
|
||
const P2=P*P, P3=P2*P, P4=P3*P, P5=P4*P, P6=P5*P;
|
||
return T +
|
||
6.07562052e-1 +
|
||
-2.27712343e-2 * T + 8.06470249e-4 * T2 + -1.54271372e-4 * T3 +
|
||
-3.24651735e-6 * T4 + 7.32602852e-8 * T5 + 1.35959073e-9 * T6 +
|
||
-2.25836520e0 * V + 8.80326035e-2 * T*V + 2.16844454e-3 * T2*V +
|
||
-1.53347087e-5 * T3*V + -5.72983704e-7 * T4*V + -2.55090145e-9 * T5*V +
|
||
-7.51269505e-1 * V2 + -4.08350271e-3 * T*V2 + -5.21670675e-5 * T2*V2 +
|
||
1.94544667e-6 * T3*V2 + 1.14099531e-8 * T4*V2 +
|
||
1.58137256e-1 * V3 + -6.57263143e-5 * T*V3 + 2.22697524e-7 * T2*V3 +
|
||
-4.16117031e-8 * T3*V3 +
|
||
-1.27762753e-2 * V4 + 9.66891875e-6 * T*V4 + 2.52785852e-9 * T2*V4 +
|
||
4.56306672e-4 * V5 + -1.74202546e-7 * T*V5 +
|
||
-5.91491269e-6 * V6 +
|
||
3.98374029e-1 * D + 1.83945314e-4 * T*D + -1.73754510e-4 * T2*D +
|
||
-7.60781159e-7 * T3*D + 3.77830287e-8 * T4*D + 5.43079673e-10 * T5*D +
|
||
-2.00518269e-2 * V*D + 8.92859837e-4 * T*V*D + 3.45433048e-6 * T2*V*D +
|
||
-3.77925774e-7 * T3*V*D + -1.69699377e-9 * T4*V*D +
|
||
1.69992415e-4 * V2*D + -4.99204314e-5 * T*V2*D + 2.47417178e-7 * T2*V2*D +
|
||
1.07596466e-8 * T3*V2*D +
|
||
8.49242932e-5 * V3*D + 1.35191328e-6 * T*V3*D + -6.21531254e-9 * T2*V3*D +
|
||
-4.99410301e-6 * V4*D + -1.89489258e-8 * T*V4*D +
|
||
8.15300114e-8 * V5*D +
|
||
7.55043090e-4 * D2 + -5.65095215e-5 * T*D2 + -4.52166564e-7 * T2*D2 +
|
||
2.46688878e-8 * T3*D2 + 2.42674348e-10 * T4*D2 +
|
||
1.54547250e-4 * V*D2 + 5.24110970e-6 * T*V*D2 + -8.75874982e-8 * T2*V*D2 +
|
||
-1.50743064e-9 * T3*V*D2 +
|
||
-1.56236307e-5 * V2*D2 + -1.33895614e-7 * T*V2*D2 + 2.49709824e-9 * T2*V2*D2 +
|
||
6.51711721e-7 * V3*D2 + 1.94960053e-9 * T*V3*D2 +
|
||
-1.00361113e-8 * V4*D2 +
|
||
-1.21206673e-5 * D3 + -2.18203660e-7 * T*D3 + 7.51269482e-9 * T2*D3 +
|
||
9.79063848e-11 * T3*D3 +
|
||
1.25006734e-6 * V*D3 + -1.81584736e-9 * T*V*D3 + -3.52197671e-10 * T2*V*D3 +
|
||
-3.36514630e-8 * V2*D3 + 1.35908359e-10 * T*V2*D3 +
|
||
4.17032620e-10 * V3*D3 +
|
||
-1.30369025e-9 * D4 + 4.13908461e-10 * T*D4 + 9.22652254e-12 * T2*D4 +
|
||
-5.08220384e-9 * V*D4 + -2.24730961e-11 * T*V*D4 +
|
||
1.17139133e-10 * V2*D4 +
|
||
6.62154879e-10 * D5 + 4.03863260e-13 * T*D5 + 1.95087203e-12 * V*D5 +
|
||
-4.73602469e-12 * D6 +
|
||
5.12733497e0 * P + -3.12788561e-1 * T*P + -1.96701861e-2 * T2*P +
|
||
9.99690870e-4 * T3*P + 9.51738512e-6 * T4*P + -4.66426341e-7 * T5*P +
|
||
5.48050612e-1 * V*P + -3.30552823e-3 * T*V*P + -1.64119440e-3 * T2*V*P +
|
||
-5.16670694e-6 * T3*V*P + 9.52692432e-7 * T4*V*P +
|
||
-4.29223622e-2 * V2*P + 5.00845667e-3 * T*V2*P + 1.00601257e-6 * T2*V2*P +
|
||
-1.81748644e-6 * T3*V2*P +
|
||
-1.25813502e-3 * V3*P + -1.79330391e-4 * T*V3*P + 2.34994441e-6 * T2*V3*P +
|
||
1.29735808e-4 * V4*P + 1.29064870e-6 * T*V4*P +
|
||
-2.28558686e-6 * V5*P +
|
||
-3.69476348e-2 * D*P + 1.62325322e-3 * T*D*P + -3.14279680e-5 * T2*D*P +
|
||
2.59835559e-6 * T3*D*P + -4.77136523e-8 * T4*D*P +
|
||
8.64203390e-3 * V*D*P + -6.87405181e-4 * T*V*D*P + -9.13863872e-6 * T2*V*D*P +
|
||
5.15916806e-7 * T3*V*D*P +
|
||
-3.59217476e-5 * V2*D*P + 3.28696511e-5 * T*V2*D*P + -7.10542454e-7 * T2*V2*D*P +
|
||
-1.24382300e-5 * V3*D*P + -7.38584400e-9 * T*V3*D*P +
|
||
2.20609296e-7 * V4*D*P +
|
||
-7.32469180e-4 * D2*P + -1.87381964e-5 * T*D2*P + 4.80925239e-6 * T2*D2*P +
|
||
-8.75492040e-8 * T3*D2*P +
|
||
2.77862930e-5 * V*D2*P + -5.06004592e-6 * T*V*D2*P + 1.14325367e-7 * T2*V*D2*P +
|
||
2.53016723e-6 * V2*D2*P + -1.72857035e-8 * T*V2*D2*P +
|
||
-3.95079398e-8 * V3*D2*P +
|
||
-3.59413173e-7 * D3*P + 7.04388046e-7 * T*D3*P + -1.89309167e-8 * T2*D3*P +
|
||
-4.79768731e-7 * V*D3*P + 7.96079978e-9 * T*V*D3*P +
|
||
1.62897058e-9 * V2*D3*P +
|
||
3.94367674e-8 * D4*P + -1.18566247e-9 * T*D4*P +
|
||
3.34678041e-10 * V*D4*P +
|
||
-1.15606447e-10 * D5*P +
|
||
-2.80626406e0 * P2 + 5.48712484e-1 * T*P2 + -3.99428410e-3 * T2*P2 +
|
||
-9.54009191e-4 * T3*P2 + 1.93090978e-5 * T4*P2 +
|
||
-3.08806365e-1 * V*P2 + 1.16952364e-2 * T*V*P2 + 4.95271903e-4 * T2*V*P2 +
|
||
-1.90710882e-5 * T3*V*P2 +
|
||
2.10787756e-3 * V2*P2 + -6.98445738e-4 * T*V2*P2 + 2.30109073e-5 * T2*V2*P2 +
|
||
4.17856590e-4 * V3*P2 + -1.27043871e-5 * T*V3*P2 +
|
||
-3.04620472e-6 * V4*P2 +
|
||
5.14507424e-2 * D*P2 + -4.32510997e-3 * T*D*P2 + 8.99281156e-5 * T2*D*P2 +
|
||
-7.14663943e-7 * T3*D*P2 +
|
||
-2.66016305e-4 * V*D*P2 + 2.63789586e-4 * T*V*D*P2 + -7.01199003e-6 * T2*V*D*P2 +
|
||
-1.06823306e-4 * V2*D*P2 + 3.61341136e-6 * T*V2*D*P2 +
|
||
2.29748967e-7 * V3*D*P2 +
|
||
3.04788893e-4 * D2*P2 + -6.42070836e-5 * T*D2*P2 + 1.16257971e-6 * T2*D2*P2 +
|
||
7.68023384e-6 * V*D2*P2 + -5.47446896e-7 * T*V*D2*P2 +
|
||
-3.59937910e-8 * V2*D2*P2 +
|
||
-4.36497725e-6 * D3*P2 + 1.68737969e-7 * T*D3*P2 +
|
||
2.67489271e-8 * V*D3*P2 +
|
||
3.23926897e-9 * D4*P2 +
|
||
-3.53874123e-2 * P3 + -2.21201190e-1 * T*P3 + 1.55126038e-2 * T2*P3 +
|
||
-2.63917279e-4 * T3*P3 +
|
||
4.53433455e-2 * V*P3 + -4.32943862e-3 * T*V*P3 + 1.45389826e-4 * T2*V*P3 +
|
||
2.17508610e-4 * V2*P3 + -6.66724702e-5 * T*V2*P3 +
|
||
3.33217140e-5 * V3*P3 +
|
||
-2.26921615e-3 * D*P3 + 3.80261982e-4 * T*D*P3 + -5.45314314e-9 * T2*D*P3 +
|
||
-7.96355448e-4 * V*D*P3 + 2.53458034e-5 * T*V*D*P3 +
|
||
-6.31223658e-6 * V2*D*P3 +
|
||
3.02122035e-4 * D2*P3 + -4.77403547e-6 * T*D2*P3 +
|
||
1.73825715e-6 * V*D2*P3 +
|
||
-4.09087898e-7 * D3*P3 +
|
||
6.14155345e-1 * P4 + -6.16755931e-2 * T*P4 + 1.33374846e-3 * T2*P4 +
|
||
3.55375387e-3 * V*P4 + -5.13027851e-4 * T*V*P4 +
|
||
1.02449757e-4 * V2*P4 +
|
||
-1.48526421e-3 * D*P4 + -4.11469183e-5 * T*D*P4 +
|
||
-6.80434415e-6 * V*D*P4 +
|
||
-9.77675906e-6 * D2*P4 +
|
||
8.82773108e-2 * P5 + -3.01859306e-3 * T*P5 +
|
||
1.04452989e-3 * V*P5 +
|
||
2.47090539e-4 * D*P5 +
|
||
1.48348065e-3 * P6;
|
||
}
|