Chapter 6 Sustainabilty and Engineering: Windown Transmittance

Chapter 6 Sustainabilty and Engineering: Windown Transmittance#

  1. Introduction: Window Transmittance

  2. Simulation: Window Transmittance

  3. Self-Assessment

1. Introduction#

Descriptive alt text for accessibility

Fig. 41 **Figure 6.8 **: Glass Transmittance#

Window Transmittance Analysis: Theoretical Overview#

1. Solar Heat Gain Coefficient (SHGC)#

Definition:
The Solar Heat Gain Coefficient (SHGC) is the fraction of incident solar radiation that passes through a window and contributes to indoor heat gain.

Range:

  • SHGC values range from 0 to 1.

  • A higher SHGC means more solar heat enters the building.

Application:
Used to calculate heat transmitted through the window:

image.png

2. Visible Transmittance (VT)#

Definition:
Visible Transmittance (VT) is the fraction of visible light that passes through a window.

Range:

  • VT values range from 0 to 1.

  • A higher VT means more daylight enters the space.

Application:
Used to calculate light transmitted through the window:

3. Cooling Cost Estimation#

Objective:
Estimate the energy cost associated with cooling the indoor space due to solar heat gain.

Assumptions:

  • 1 W/m² over 1 hour ≈ 0.001 kWh/m²

  • Cooling cost rate = $0.12 per kWh

Formula:

4. Room-Specific Recommendations#

Based on Light Transmittance:

  • >600 lumens/m² → Ideal for sunrooms, studios, or high daylight spaces

  • 400–600 lumens/m² → Suitable for living rooms, kitchens, or general use

  • <400 lumens/m² → Best for bedrooms, storage, or low-light areas

Based on Heat Transmittance:

  • <300 W/m² → Energy-efficient, minimal cooling load

  • 300–500 W/m² → Moderate heat gain, may need shading

  • >500 W/m² → High heat gain, increased cooling costs

5. Comparative Analysis#

The calculator compares all window types under the same input conditions to help users select the most efficient option for their climate and room type.

Output Table Includes:

  • Window type

  • Heat transmitted (W/m²)

  • Light transmitted (lumens/m²)

🔍 Summary#

This method provides a simplified yet effective way to evaluate window performance in terms of:

  • Thermal comfort

  • Daylight availability

  • Energy cost implications

It supports informed decision-making for residential window selection based on climate, orientation, and room function.

2. Simulation#

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from ipywidgets import interact, FloatSlider, Dropdown

# 📋 Window types and properties
window_types = {
    "Clear Glass": {"SHGC": 0.85, "VT": 0.90},
    "Tinted Glass": {"SHGC": 0.40, "VT": 0.60},
    "Low-E Glass": {"SHGC": 0.30, "VT": 0.70},
    "Double Pane": {"SHGC": 0.55, "VT": 0.75},
    "Triple Pane": {"SHGC": 0.35, "VT": 0.65}
}

# ⚙️ Constants
cooling_cost_per_kwh = 0.12  # USD per kWh

# 📊 Interactive function
def transmittance_calculator(window, solar, visible):
    data = window_types[window]
    heat = solar * data["SHGC"]
    light = visible * data["VT"]
    cost = (heat / 1000) * cooling_cost_per_kwh

    print(f"\n🔍 Results for {window}:")
    print(f"🔆 Heat Transmitted: {heat:.2f} W/m²")
    print(f"💡 Light Transmitted: {light:.2f} lumens/m²")
    print(f"💰 Cooling Cost (1 hr): ${cost:.2f}/m²")

    # 🧠 Interpretation
    interpretation = []
    interpretation.append("📘 Interpretation:")
    if heat < 300:
        interpretation.append("✅ Low heat gain — good for cooling efficiency.")
    elif heat < 500:
        interpretation.append("⚠️ Moderate heat gain — may require shading.")
    else:
        interpretation.append("❌ High heat gain — could increase cooling costs.")

    if light > 600:
        interpretation.append("✅ High daylight — ideal for sunrooms or studios.")
    elif light > 400:
        interpretation.append("⚠️ Moderate daylight — suitable for living rooms.")
    else:
        interpretation.append("❌ Low daylight — better for bedrooms or storage.")

    print("\n" + "\n".join(interpretation))

    # 📊 Comparison table
    print("\n📊 Comparison of All Window Types:")
    print(f"{'Window':<15} {'Heat (W/m²)':>15} {'Light (lumens/m²)':>25}")
    print("-" * 55)
    for name, props in window_types.items():
        h = solar * props["SHGC"]
        l = visible * props["VT"]
        print(f"{name:<15} {h:>15.2f} {l:>25.2f}")

# 🧪 UI sliders and dropdown
interact(
    transmittance_calculator,
    window=Dropdown(options=list(window_types.keys()), description="Window Type"),
    solar=FloatSlider(value=800, min=100, max=1200, step=50, description="Solar (W/m²)"),
    visible=FloatSlider(value=750, min=100, max=1200, step=50, description="Visible (lumens/m²)")
)

<function __main__.transmittance_calculator(window, solar, visible)>

3. Self-Assessment#

📘 Conceptual Questions#

These questions explore the physical principles and modeling logic behind the calculator.

Solar Heat Gain Coefficient (SHGC)#

  • What does the SHGC represent in terms of energy transmission through windows?

  • How does SHGC affect indoor temperature and cooling load?

  • Why is SHGC multiplied by solar radiation to estimate transmitted heat?

Visible Transmittance (VT)#

  • What does VT measure in the context of window performance?

  • How does VT influence natural lighting and visual comfort?

  • Why might a window with high VT be desirable in certain rooms but not others?

Energy Cost Estimation#

  • How is the cooling cost estimated from transmitted heat?

  • What assumptions are made about energy pricing and cooling duration?

  • Why is the heat value converted to kilowatt-hours before calculating cost?

🔍 Reflective Questions#

These questions encourage critical thinking and application to real-world building design.

  • Which window type would you choose for a sunroom in a hot climate, and why?

  • How would the results change if the solar radiation input were based on seasonal averages?

  • What trade-offs exist between maximizing daylight and minimizing heat gain?

  • How could this model be extended to include window orientation or shading devices?

  • How might energy cost estimates vary across regions with different electricity rates?

❓ Quiz Questions#

Multiple Choice#

  1. Which window type has the highest SHGC value?
    A. Tinted Glass
    B. Low-E Glass
    C. Clear Glass
    D. Triple Pane
    Answer: C

  2. If solar radiation is 800 W/m² and SHGC is 0.40, what is the transmitted heat?
    A. 320 W/m²
    B. 400 W/m²
    C. 480 W/m²
    D. 640 W/m²
    Answer: A

  3. Which factor most directly affects the amount of daylight entering a room?
    A. SHGC
    B. Cooling cost
    C. VT
    D. Solar radiation
    Answer: C

True/False#

  1. A window with low SHGC and high VT is ideal for reducing cooling costs while maintaining daylight.
    Answer: True

  2. The calculator assumes a constant cooling cost per kilowatt-hour.
    Answer: True

  3. Visible transmittance affects the thermal load of a building.
    Answer: False

Short Answer#

  1. Explain why a window with high SHGC might be problematic in a warm climate.
    Answer: It allows more solar heat to enter, increasing indoor temperatures and cooling demand.

  2. What physical factors might cause actual heat gain to differ from the model’s estimate?
    Answer: Window orientation, shading, frame material, and air leakage can all influence real-world performance.

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