By name: HVAC Formulas & Calculations description: Core physics and HVAC formulas used in the ThermoNeural application.
HVAC Formulas & Calculations
This skill contains the authoritative formulas used in the application. Refer to this when implementing new calculators or verifying existing logic.
1. Target Superheat (Fixed Orifice)
Used for charging fixed orifice systems (pistons/capillary tubes).
Formula:
Target SH = ((3 * IndoorWB) - 80 - OutdoorDB) / 2
Constraints:
- Indoor Wet Bulb (WB) must be between 32°F and 100°F.
- Outdoor Dry Bulb (DB) must be between 0°F and 130°F.
- Results are typically valid within ±5°F.
Source: standard industry formula (Emerson/Copeland approved method).
2. Air Density & Derating
Calculates the density of air at altitude to determine system capacity loss (derating).
Key Constants:
- Sea Level Pressure ($P_0$): 101325 Pa
- Sea Level Temp ($T_0$): 288.15 K
- Lapse Rate ($L$): 0.0065 K/m
- Gas Constant ($R$): 8.31447 J/(mol·K)
- Molar Mass ($M$): 0.0289644 kg/mol
Steps:
Pressure at Altitude (Barometric Formula): $$ P = P_0 \cdot (1 - \frac{L \cdot h}{T_0}) ^ \frac{g \cdot M}{R \cdot L} $$
Saturation Vapor Pressure ($E_s$) (Magnus Formula): $$ E_s = 6.112 \cdot e^{\frac{17.67 \cdot T_c}{T_c + 243.5}} \text{ (hPa)} $$
Density ($\rho$): Derived effectively using Partial Pressure of Dry Air ($P_d$) and Vapor ($P_v$).
Derating Impact: $$ \text{Impact %} = (1 - \frac{\rho_{actual}}{1.225}) \cdot 100 $$ (Where 1.225 kg/m³ is standard sea-level density).
3. Psychrometrics
Dew Point ($T_{dp}$): Calculated using the Magnus formula inversion involving Natural Log of Vapor Pressure.
Wet Bulb ($T_{wb}$): Uses the "Stull" formula (arctangent approximation) as it is computationally efficient for code:
Tw = T * atan(0.151977 * sqrt(RH + 8.313659)) + ...
4. A2L Safety (IEC 60335-2-40)
For calculating max charge of mildly flammable refrigerants (e.g., R32, R454B).
Primary Variables:
- $LFL$: Lower Flammability Limit (kg/m³)
- $h_{inst}$: Installation height (m) (Floor=0.6, Wall=1.8, Ceiling=2.2)
- $A$: Room Area (m²)
Logic: Max charge ($m_{max}$) is derived based on checking if the charge concentration would exceed safety factors of the LFL if leaked into the room volume.
Refer to lib/calculators/a2l.ts for the full specific implementation of the chart lookup/formula.