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🏠 Core Concepts: Layman's Guide

Why does $21^{\circ}\text{C}$ in the winter feel cold, while $21^{\circ}\text{C}$ in the summer feels warm?

The answer is Radiant Heat. Your standard thermostat is lying to you because it only measures the air. Humans feel the temperature of the objects around them.

The Two Temperatures

  1. Mean Radiant Temperature (MRT): The average surface temperature of the walls, windows, floor, and ceiling. This acts like a "thermal battery" for the room.
  2. Operative Temperature ($T_{op}$): What you actually feel. It is a weighted average of the Air Temperature and the MRT. This is the metric you should use to trigger your heating and cooling.

Note

Example: In winter, your room air might be $21^{\circ}\text{C}$, but if your windows and walls are cold, the MRT might only be $16^{\circ}\text{C}$. The resulting Operative Temperature ($T_{op}$) will be $18.5^{\circ}\text{C}$. You feel cold.

🏗️ The 4 Room Physical Constants

To accurately calculate your room's thermal battery, the integration needs to know how the room is built.

You do not need to guess these! The integration includes Default Profiles (like "Top Floor Attic", "Basement", "Interior Room") which pre-fill these values. However, you can fine-tune them using the four numeric inputs below.

1. Exterior Envelope Ratio ($f_{out}$)

What percentage of the room's total interior surface area touches the outside?

  • $0.0 - 0.2$: An interior hallway or closet (surrounded by warm rooms).
  • $0.4 - 0.5$: A standard room with one exterior wall.
  • $0.7 - 0.8$: A corner room with two exterior walls.
  • $0.9 - 1.0$: A top-floor attic room where the ceiling and walls are all exposed to the cold.

2. Window Share ($f_{win}$)

What percentage of the exterior wall area is made of glass?

  • $0.0 - 0.1$: A basement with no windows, or tiny egress windows.
  • $0.2 - 0.3$: A standard bedroom with one normal window.
  • $0.4 - 0.5$: A living room with a large picture window or sliding glass door.
  • $0.8 - 1.0$: A sunroom or conservatory made entirely of glass.

3. Insulation Loss Factor ($k_{loss}$)

How poorly insulated is the room? (Higher = worse insulation).

  • $0.08 - 0.10$: Passive house, extremely well insulated (R-40+ walls, triple pane windows).
  • $0.14 - 0.16$: Modern standard home built to code (R-20 walls, double pane).
  • $0.20 - 0.25$: Old 1950's home with uninsulated walls and drafty single-pane windows.

4. Solar Gain Factor ($k_{solar}$)

How much solar energy penetrates the windows to heat up the room?

  • $0.4 - 0.6$: Basement windows or heavily shaded windows.
  • $0.8 - 1.0$: Standard clear double-pane windows.
  • $1.2 - 1.4$: Large, unshaded south-facing windows.
  • $1.5+$: Tilted skylights or solariums that receive direct perpendicular sunlight.

🧱 Thermal Mass (Smoothing Factor $\alpha$)

Heavy buildings (brick, concrete) take a long time to heat up and cool down. Light buildings (wood frames) change temperature quickly.

The Thermal Smoothing Factor ($\alpha$) controls this behavior in the calculation:

  • High $\alpha$ (0.50 - 0.95): Fast reacting. Use for standard wooden structures or mobile homes.
  • Low $\alpha$ (0.05 - 0.20): Slow reacting. Use for heavy masonry, concrete block homes, or earth-sheltered homes.

Important

When you change the $\alpha$ setting, the formula updates instantly, but the sensor reading will take time to adapt because it is simulating physical thermal lag.