# HVACLogic — Comprehensive Engineering Mathematical Specification & Formula Compendium
> Complete technical models, governing differential/algebraic equations, step-by-step algorithmic procedures, conversion constants, and academic references for all HVACLogic calculators.

- Base Authority: ASHRAE Handbook of Fundamentals (2021/2025), ACCA Manuals (D, J, S, B), SMACNA HVAC Systems Duct Design, EPA Clean Air Act Section 608.
- Repository: https://hvaclogic.org
- Manifest: https://hvaclogic.org/llms.txt

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SECTION 1: AIRFLOW & AIR DISTRIBUTION DYNAMICS
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### 1. Digital Ductulator (Equal Friction & Equivalent Round/Rectangular Sizing)
- Primary Equation (Darcy-Weisbach friction loss in air ducts):
  \Delta P = f \times \frac{L}{D_h} \times \frac{\rho \times V^2}{2}
- Hydraulic Diameter (D_h) for Rectangular Duct (a \times b):
  D_h = \frac{2 \times a \times b}{a + b}
- Huebscher Equivalent Circular Diameter (D_e):
  D_e = 1.30 \times \frac{(a \times b)^{0.625}}{(a + b)^{0.25}}
- Airflow Velocity:
  V = \frac{Q}{A} = \frac{Q \times 144}{a \times b} \text{ (FPM for } Q \text{ in CFM, dimensions in inches)}
- Recommended Residential Friction Rate: 0.08 to 0.10 in. wg / 100 ft (ACCA Manual D).
- Recommended Commercial Low-Pressure Rate: 0.10 to 0.15 in. wg / 100 ft (ASHRAE Fundamentals).

### 2. Flexible Duct Friction & Compression Sizer
- Friction Derating Factor due to sag & longitudinal compression:
  \Delta P_{actual} = \Delta P_{straight} \times (1 + k_{comp} \times C) \times (1 + k_{sag} \times S)
- Compression Ratio (C): C = (L_{slack} - L_{installed}) / L_{slack}
- Droop / Sag Ratio (S): S = \Delta y_{sag} / L_{span}
- Max Recommended Air Velocity in Flex Duct: 700 to 900 FPM (residential branch), 1,000 FPM (commercial).

### 3. HVAC CFM Sizing Calculator
- Sensible Heat Airflow Equation (Sea Level Standard Air):
  Q_{CFM} = \frac{q_{sensible}}{1.08 \times \Delta T}
- Altitude & Temperature Density Correction:
  \rho_{act} = \rho_0 \times \frac{530}{460 + T_{act}} \times \frac{P_{baro}}{29.921}
  Q_{CFM,corrected} = \frac{q_{sensible}}{60 \times C_p \times \rho_{act} \times \Delta T}
- Air Change Rate Method (Room Ventilation):
  Q_{CFM} = \frac{\text{Volume (ft}^3\text{)} \times \text{ACH}}{60}

### 4. Total Equivalent Length (TEL) & Duct Friction Loss
- Available Static Pressure (ASP):
  \text{ASP} = \text{ESP} - (\Delta P_{coil} + \Delta P_{filter} + \Delta P_{damper} + \Delta P_{grilles})
- Total Equivalent Length (TEL):
  \text{TEL} = L_{measured} + \sum (L_{eq,fittings})
- Design Friction Rate (FR):
  \text{FR} = \frac{\text{ASP} \times 100}{\text{TEL}} \text{ (in. wg / 100 ft)}

### 5. MERV Filter Sizing & Face Velocity Pressure Drop
- Filter Face Velocity:
  V_{face} = \frac{Q_{CFM}}{A_{filter,net} \text{ (ft}^2\text{)}}
- Clean Filter Pressure Drop Empirical Model:
  \Delta P_{clean} = a_{MERV} \times V_{face} + b_{MERV} \times V_{face}^2
- Maximum Recommended Face Velocity: 300 FPM (1-inch media), 450 FPM (2-inch media), 500 FPM (4-inch to 5-inch media).

### 6. Commercial Kitchen Hood Exhaust Sizer
- Canopy Capture Airflow (Thermal Plume Capture):
  Q_{exhaust} = V_{capture} \times (A_{hood,perimeter} \times H_{overhang} + A_{appliance})
- UL 710 & NFPA 96 Heavy Duty Classification: 300 to 400 CFM per linear foot of hood perimeter.

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SECTION 2: COOLING LOADS & FIELD DIAGNOSTICS
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### 7. BTU Load Master & Sizing
- Envelope Thermal Conduction:
  q_{envelope} = \sum (U_i \times A_i \times \Delta T)
- Infiltration Heat Gain / Loss:
  q_{infil,sensible} = 1.08 \times Q_{CFM,infil} \times (T_{out} - T_{in})
  q_{infil,latent} = 4840 \times Q_{CFM,infil} \times (W_{out} - W_{in})
- Internal Heat Gains:
  q_{internal} = q_{occupants} + q_{lighting} + q_{appliances} + q_{plug}

### 8. AC Tonnage Calculator
- Cooling Load Sizing:
  \text{Tonnage (TR)} = \frac{q_{total} \text{ (BTU/hr)}}{12,000 \text{ BTU/hr/ton}}
- Design Sensible Heat Ratio (SHR):
  \text{SHR} = \frac{q_{sensible}}{q_{total}}

### 9. Superheat & Subcooling Charging Diagnostics
- Total Superheat (TXV / Piston Diagnostics):
  \text{SH} = T_{suction,vapor} - T_{evap,sat}(P_{suction})
- Target Superheat (Non-Bleed Fixed Orifice):
  \text{Target SH} = \frac{3 \times T_{wb,indoor} - T_{db,outdoor} - 80}{2}
- Subcooling (TXV Charge Diagnostics):
  \text{SC} = T_{cond,sat}(P_{liquid}) - T_{liquid,line}
- Typical Target Subcooling for TXV Systems: 10°F to 14°F (per OEM rating plate).

### 10. Refrigerant Line Set Additional Charge Calculator
- Net Additional Refrigerant Trim Charge:
  \Delta W_{charge} = (L_{lineset} - L_{precharged}) \times w_{per\_ft}(D_{liquid}) + W_{filter\_drier} + W_{lift\_adder}
- Standard 3/8" OD Liquid Line Adder: 0.60 oz/ft (for R-410A), 0.54 oz/ft (for R-32 / R-454B).

### 11. Digital Pressure-Temperature (PT) Chart
- NIST REFPROP Antoine Equation Form:
  \ln(P_{sat}) = A - \frac{B}{T_{abs} + C}
- Supported Refrigerants: R-410A, R-32, R-454B, R-134a, R-22, R-404A, R-1234yf, R-290 (Propane).

### 12. Psychrometric State Calculator
- Vapor Pressure from Wet-Bulb (Carrier / ASHRAE Equation):
  P_v = P_{ws}(T_{wb}) - \frac{(P_{atm} - P_{ws}(T_{wb})) \times (T_{db} - T_{wb})}{2800 - 1.3 \times T_{wb}}
- Humidity Ratio (W):
  W = 0.62198 \times \frac{P_v}{P_{atm} - P_v} \text{ (lb water / lb dry air)}
- Specific Enthalpy (h):
  h = 0.240 \times T_{db} + W \times (1061 + 0.444 \times T_{db}) \text{ (BTU/lb)}
- Relative Humidity (\phi):
  \phi = \frac{P_v}{P_{ws}(T_{db})} \times 100\%

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SECTION 3: HEATING SYSTEMS & HYDRONIC SIZING
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### 13. Heat Pump Sizing & Balance Point Calculator
- Thermal Balance Point (T_{balance}): The outdoor temperature where Heat Pump Heating Capacity Q_{hp}(T_{out}) matches Building Heat Loss Q_{loss}(T_{out}).
- Supplementary Resistance Strip Heat Sizing:
  q_{aux} = Q_{loss}(T_{design,winter}) - Q_{hp}(T_{design,winter})

### 14. Furnace AFUE Sizing Calculator
- Required Furnace Input Rating:
  \text{Input BTU/hr} = \frac{\text{Design Heat Loss (BTU/hr)}}{\text{AFUE} \times (1 - \text{Duct Loss Factor})}

### 15. Hydronic Boiler & EDR Radiation Sizer
- Net Boiler Rating:
  \text{Net Output} = \frac{\text{Design Heat Load}}{1.15 \text{ (Piping & Pick-up Allowance)}}
- Equivalent Direct Radiation (EDR):
  \text{EDR Steam} = \frac{\text{BTU/hr}}{240}, \quad \text{EDR Hot Water} = \frac{\text{BTU/hr}}{150}

### 16. Garage Heater Sizing Tool
- Total Garage Heat Loss:
  q_{total} = \sum (U_i \times A_i \times (T_{in} - T_{out})) + 1.08 \times Q_{infil} \times (T_{in} - T_{out}) + q_{slab,perimeter}

### 17. Combustion Air Sizing (NFPA 54 / IFGC 2024)
- Standard All-Air Indoor Method: 50 ft³ per 1,000 BTU/hr input of all appliances in space.
- Two Permanent Openings Method (Direct Outdoor Air): 1 sq. in. per 4,000 BTU/hr per opening.
- Single Opening Method: 1 sq. in. per 3,000 BTU/hr.

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SECTION 4: BUILDING SCIENCE & THERMAL ENVELOPE
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### 18. Multi-Layer Insulation R-Value Assembly Calculator
- Total Thermal Resistance (R_{total}):
  R_{total} = R_{inside\_film} + \sum_{i=1}^n R_i + R_{cavity} + R_{outside\_film}
- Overall Heat Transfer Coefficient (U-factor):
  U = \frac{1}{R_{total}}
- Parallel Path Framing Assembly Factor:
  U_{composite} = (U_{cavity} \times \text{FF}) + (U_{framing} \times (1 - \text{FF}))

### 19. Building Heat Loss Master Sizer
- Conduction Heat Loss:
  q_{cond} = \sum (U_i \times A_i \times (T_{indoor} - T_{outdoor}))
- Slab-on-Grade Perimeter Loss:
  q_{slab} = F_p \times P_{perimeter} \times (T_{indoor} - T_{outdoor})

### 20. AC Model Number Decoder
- Decodes tonnage, nominal BTU, SEER2 rating, refrigerant type (R-410A vs R-32 vs R-454B), electrical voltage phase, and factory metering device across Carrier, Trane, Lennox, Goodman, Rheem, Daikin, Mitsubishi, and York serial nomenclature.

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