Psychrometrics in Code: Implementing ASHRAE Hyland-Wexler Moist Air Formulations in TypeScript

Most HVAC and building simulation software still relies on archaic Fortran or compiled C dynamic libraries to evaluate moist air thermodynamic properties. If you inspect typical web calculators, you will usually find crude quadratic curve fits or linear approximations that deviate by more than 8% at non-standard barometric pressures or elevated humidity ratios.

When building HVACLogic, our goal was to run all thermodynamic and building science calculations 100% client-side in the browser with zero external dependencies, zero backend roundtrips, and zero database tracking.

To calculate thermodynamic air properties with laboratory-grade precision, we implemented the governing ASHRAE Fundamentals (Chapter 1) Hyland-Wexler formulations in pure TypeScript.

Here is an architectural walkthrough of how these thermodynamic equations work and how to solve moist air state points deterministically in modern JavaScript engines.

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1. The Physics of Moist Air: Dalton's Law & Hyland-Wexler

Atmospheric air is a binary mixture of dry air and water vapor. Under Dalton's Law of Partial Pressures, total barometric pressure P_atm is the sum of partial pressure exerted by dry air P_da and partial pressure of water vapor P_w:

P_atm = P_da + P_w

At sea level, standard atmospheric pressure is 14.696 psia (101.325 kPa). When evaluating high-altitude structures (such as Denver at 5,280 ft), barometric pressure drops to 12.15 psia. Calculating moist air without adjusting for altitude produces severe sizing errors.

The barometric pressure as a function of elevation h (in feet) is governed by the ASHRAE Standard Atmosphere:

export function getBarometricPressurePsia(altitudeFeet: number = 0): number {
  const h = Math.max(-1000, Math.min(15000, altitudeFeet));
  return 14.696 * Math.pow(1 - 6.8754e-6 * h, 5.2559);
}

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2. Saturation Vapor Pressure: The Hyland-Wexler Formulation

The core thermodynamic anchor of psychrometrics is the saturation vapor pressure P_ws, which defines the maximum partial pressure water vapor can exert at a given temperature before condensing into liquid or sublimating into frost.

ASHRAE endorses the Hyland-Wexler equations. These polynomials evaluate saturation pressure over absolute temperature T in degrees Rankine (°R = °F + 459.67).

Crucially, the physics of phase change require two distinct formulations depending on whether the temperature is above or below the triple point of water (32°F / 0°C):

Over Liquid Water (32°F <= T <= 392°F):
ln(P_ws) = C8/T + C9 + C10*T + C11*T^2 + C12*T^3 + C13*ln(T)

Over Ice (-148°F <= T < 32°F):
ln(P_ws) = C1/T + C2 + C3*T + C4*T^2 + C5*T^3 + C6*T^4 + C7*ln(T)

Here is the deterministic TypeScript implementation:

export function getSaturationVaporPressurePsia(tempF: number): number {
  const tRankine = tempF + 459.67;

  if (tempF >= 32) {
    // Coefficients over liquid water (ASHRAE Fundamentals)
    const c8 = -1.0440397e4;
    const c9 = -1.129465e1;
    const c10 = -2.7022355e-2;
    const c11 = 1.289036e-5;
    const c12 = -2.4780681e-9;
    const c13 = 6.5459673;

    const lnPws =
      c8 / tRankine +
      c9 +
      c10 * tRankine +
      c11 * Math.pow(tRankine, 2) +
      c12 * Math.pow(tRankine, 3) +
      c13 * Math.log(tRankine);

    return Math.exp(lnPws);
  } else {
    // Coefficients over ice
    const c1 = -1.0214165e4;
    const c2 = -4.8932428;
    const c3 = -5.3765794e-3;
    const c4 = 1.9202377e-7;
    const c5 = 3.5575832e-10;
    const c6 = -9.0344688e-14;
    const c7 = 4.1635019;

    const lnPws =
      c1 / tRankine +
      c2 +
      c3 * tRankine +
      c4 * Math.pow(tRankine, 2) +
      c5 * Math.pow(tRankine, 3) +
      c6 * Math.pow(tRankine, 4) +
      c7 * Math.log(tRankine);

    return Math.exp(lnPws);
  }
}

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3. Humidity Ratio and Grains of Moisture

Once we know the actual partial vapor pressure P_w, we can calculate the humidity ratio W, defined as the mass of water vapor per unit mass of dry air:

W = 0.621945 * [ P_w / (P_atm - P_w) ]

The constant 0.621945 represents the ratio of the molecular weight of water (18.01528 g/mol) to the molecular weight of dry air (28.966 g/mol).

In residential building science and dehumidification equipment sizing, humidity ratio in pounds of water per pound of dry air is an unwieldy decimal (e.g. 0.00928 lb/lb). The trade uses grains of moisture per pound of dry air, where 1 pound contains exactly 7,000 grains:

const humidityRatioLbPerLb = (0.621945 * pw) / (patm - pw);
const humidityRatioGrainsPerLb = humidityRatioLbPerLb * 7000;

For instance, at standard indoor design conditions (75°F dry bulb, 50% relative humidity), air contains approximately 65 grains per pound (gr/lb). If indoor air exceeds 70 gr/lb, mold spore germination acceleration occurs regardless of dry-bulb thermostat settings.

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4. Dew Point Inversion via ASHRAE Logarithmic Polynomials

The dew point temperature T_dp is the temperature at which moist air must be cooled at constant barometric pressure and moisture content to reach 100% saturation.

Rather than running an iterative search on getSaturationVaporPressurePsia, ASHRAE provides an explicit inverse logarithmic polynomial using alpha = ln(P_w):

export function getDewPointTempF(vaporPressurePsia: number): number {
  const p = Math.max(0.0001, vaporPressurePsia);
  const alpha = Math.log(p);

  if (p >= 0.08865) {
    // Tdp >= 32°F
    return (
      100.45 +
      33.193 * alpha +
      2.319 * Math.pow(alpha, 2) +
      0.17074 * Math.pow(alpha, 3) +
      1.2063 * Math.pow(p, 0.1984)
    );
  } else {
    // Tdp < 32°F
    return 90.12 + 26.142 * alpha + 0.8927 * Math.pow(alpha, 2);
  }
}

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5. Solving Wet Bulb Temperature via Numerical Energy Balance

Unlike dew point, wet bulb temperature T_wb does not possess a direct, closed-form algebraic inverse across broad atmospheric ranges.

Wet bulb temperature reflects dynamic thermodynamic equilibrium reached when evaporative cooling of a wetted wick balances convective heat transfer from passing air.

The governing ASHRAE energy balance equation is:

W = [ (1093 - 0.556 * T_wb) * W_s_wb - 0.24 * (T_db - T_wb) ] / 
    [ 1093 + 0.444 * T_db - T_wb ]

Where:

• T_db is the dry bulb temperature in °F.
• T_wb is the wet bulb temperature to solve for.
• W_s_wb is the saturation humidity ratio evaluated strictly at T_wb.
• W is the known humidity ratio of the state point.

Because T_wb is strictly bounded between -20°F and T_db, we can use a bisection solver (or 1D Newton solver) that converges to within 0.01°F in under 25 iterations:

export function getWetBulbTempF(
  dryBulbF: number,
  humidityRatio: number,
  patm: number
): number {
  let low = -20;
  let high = dryBulbF;
  let wetBulb = dryBulbF;

  for (let i = 0; i < 30; i++) {
    wetBulb = (low + high) / 2;
    const pwsWb = getSaturationVaporPressurePsia(wetBulb);
    const wsWb = 0.621945 * (pwsWb / (patm - pwsWb));

    // ASHRAE psychrometric wet bulb energy balance
    const calcW =
      ((1093 - 0.556 * wetBulb) * wsWb - 0.24 * (dryBulbF - wetBulb)) /
      (1093 + 0.444 * dryBulbF - wetBulb);

    if (calcW < humidityRatio) {
      low = wetBulb;
    } else {
      high = wetBulb;
    }
  }

  return Math.round(wetBulb * 10) / 10;
}

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6. Evaluating Specific Enthalpy, Volume, and Density

With the state point fully resolved, we evaluate the thermodynamic energy content and volumetric properties:

Specific Enthalpy (h, in BTU/lb dry air)

Total enthalpy represents sensible heat of dry air plus latent heat of water vapor:

const specificEnthalpyBtuPerLb = 
  0.24 * tdb + humidityRatioLbPerLb * (1061 + 0.444 * tdb);

Specific Volume (v, in cu ft/lb dry air)

Accounting for molecular expansion:

const tRankine = tdb + 459.67;
const specificVolumeCuFtPerLb =
  (53.352 * tRankine * (1 + 1.607858 * humidityRatioLbPerLb)) / (patm * 144);

Air Density (rho, in lb/cu ft)

const airDensityLbPerCuFt = (1 + humidityRatioLbPerLb) / specificVolumeCuFtPerLb;

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7. Interactive State Verification: The State Point Matrix

Here is how our TypeScript engine solves standard atmospheric air across common operational states:

State Condition	Dry Bulb (°F)	Relative Humidity	Wet Bulb (°F)	Dew Point (°F)	Humidity Ratio (gr/lb)	Enthalpy (BTU/lb)
Standard Indoor (Comfort)	75.0°F	50.0%	62.5°F	55.1°F	64.9 gr/lb	28.14 BTU/lb
Cooling Coil Discharge	55.0°F	90.0%	53.6°F	52.2°F	58.1 gr/lb	22.42 BTU/lb
Summer Peak Design	95.0°F	40.0%	75.2°F	67.2°F	98.4 gr/lb	38.61 BTU/lb
Dry High-Altitude (Denver)	85.0°F	20.0%	58.4°F	38.8°F	40.6 gr/lb	26.83 BTU/lb

You can test these state transitions interactively in our open-access Psychrometric State Point Calculator, which runs these exact TypeScript functions with live reactive SVG state plotting.

For a deeper dive into how moist air enthalpy governs sensible-to-latent load splitting and building envelope vapor barriers, read our complete Building Science & Psychrometrics Engineering Guide.

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Conclusion: Zero-DB Deterministic Engineering

Building thermodynamic simulation software in TypeScript does not require sacrificing mathematical rigor for performance.

By implementing exact ASHRAE Hyland-Wexler formulations in pure functions:

1. Zero Latency: Calculations execute in microseconds directly in the browser.
2. Offline Resilience: Field technicians on job sites can diagnose evaporator coils and moisture problems without cell coverage.
3. 100% Privacy: Client psychrometric submittals and facility environmental parameters never leave the user's browser.

If you are developing building science tools, HVAC modeling engines, or smart thermostat algorithms, treating moist air as a non-ideal mixture governed by rigorous thermodynamic equations eliminates hidden 5% to 10% errors in sensible and latent load calculations.