Question

Consider a building located near \(40^{\circ} \mathrm{N}\) latitude that has equal window areas on all four sides. The building owner is considering coating the south-facing windows with reflective film to reduce the solar heat gain and thus the cooling load. But someone suggests that the owner will reduce the cooling load even more if she coats the west-facing windows instead. What do you think?

Short answer

Answer: The south-facing windows should have the reflective film to minimize solar heat gain and cooling load, as they receive the highest solar heat gain throughout the day, particularly at solar noon.

Step-by-step solution

Determining the solar path at \(40^{\circ} \mathrm{N}\) latitude

First, we need to determine the solar path at the given latitude. In general, the solar path is higher in the sky and more directly overhead in the summer months. At \(40^{\circ} \mathrm{N}\) latitude, the solar path will be approximately highest at solar noon, where the sun is directly south. Throughout the day, the sun will rise from the east, move to its highest point in the south, and then set in the west.

Considering Solar Heat Gain on South and West facing windows

Let's consider the solar heat gain on the south and west-facing windows throughout the day. In the morning, the sun will be low in the sky and rising from the east, so there will be little solar heat gain on both south and west-facing windows. At solar noon, the sun will be directly south, and there will be maximum solar heat gain on the south-facing windows while the west-facing windows will still receive little solar heat gain. In the afternoon/evening, the sun will be moving towards the west, so the south-facing windows will receive less solar heat gain while the west-facing windows will start to see an increase in solar heat gain. However, the angle at which the sun hits the west-facing windows will be quite low, so the solar heat gain will not be as high as the south-facing windows at solar noon.

Comparing Solar Heat Gain on South and West facing windows

Since the solar path at \(40^{\circ} \mathrm{N}\) latitude is highest at solar noon (south), the south-facing windows will receive more direct sunlight and therefore will have the highest solar heat gain during the day. While the west-facing windows will receive some solar heat gain during the afternoon and evening, it will not be as significant due to the low angle of the sun.

Summary and recommendation

Based on our analysis of the solar path and comparing the solar heat gain on south and west-facing windows, we would recommend coating the south-facing windows with reflective film to reduce solar heat gain and the cooling load. This is because the south-facing windows receive the highest solar heat gain throughout the day, particularly at solar noon when the sun is at its highest point in the sky and directly south.

Key concepts

Understanding the Solar Path

The solar path is crucial in determining how sunlight travels across the sky depending on the location's latitude. At a latitude of approximately 40 degrees North, we can observe distinct patterns in the solar trajectory. During summer days, for instance, the sun takes a higher arc through the sky, peaking around solar noon, which means it is positioned in the southern part of the sky.

This elevation angle of the sun is essential for understanding which parts of a building will receive the most sunlight. Early in the morning and late afternoon, solar radiation is less intense since the sun is lower in the sky. However, near solar noon, when the sun's rays strike Earth at a more direct angle, areas facing the sun will experience significant solar heat gain. This is precisely the time when south-facing windows encounter the most solar heat, thereby contributing substantially to the building's cooling load.

Cooling Load Considerations

The cooling load of a building refers to the amount of energy required to maintain a comfortable indoor temperature. Factors influencing this include external temperature, the building's insulation, and, importantly, solar heat gain through windows.

Since the sun's intensity is greatest around solar noon, particularly at a latitude of 40 degrees North, it causes a significant increase in the cooling load for south-facing parts of the building. By mid-afternoon to early evening, the west-facing windows experience increased solar heat gain as the sun shifts westward. However, due to the lower angle of the sun at these times, the heat gain is not as potent when compared to solar noon. Subsequently, south-facing windows are typically the most influential in terms of adding to the overall cooling load.

Benefits of Reflective Window Film

Reflective window film is designed to reduce solar heat gain by reflecting the sun's rays away from the building. This type of film can be particularly effective in mitigating the impact of direct sunlight entering through windows.

Applying this film to south-facing windows can minimize the substantial solar heat gain occurring around solar noon, which is the most intense. This mitigation is a key factor in reducing the building's cooling load. In contrast, while coating west-facing windows will lessen the afternoon heat gain, the lower solar angle and the generally less intense heat during that time mean that the potential reduction in cooling load is less significant than it would be for south-facing windows.

Latitude Impact on Solar Exposure

Latitude plays a pivotal role in solar exposure as it affects both the sun's intensity and duration of daylight. Buildings at a latitude of 40 degrees North experience a significant variation in the sun's path and intensity across seasons.

In this case, understanding the influence of latitude is vital when choosing which windows to coat with reflective film. Since the sun is higher in the sky during the peak cooling season (summer), and directly south at solar noon, south-facing windows are exposed to more direct sunlight compared to west-facing windows. Therefore, in terms of reducing the building's cooling load, focusing on the latitude's impact directs us to prioritize south-facing windows for applying reflective films.