Overview
I am very interested in energy efficient residential construction, and one major consideration in the design process is how much insulation to install in the walls and roof. I am in Amory Lovins’ class right now, and he has discussed the concept of “tunneling through the cost barrier”. He says that most people will install as much insulation as will pay for itself through saved heat loss and gain. However, they fail to account for the cost of the heating and cooling equipment. If you hit the “breakeven” level of insulation and keep going, your cost will continue to rise until your insulation is good enough to eliminate any active heating and cooling systems. At that crucial point after “tunneling through the cost barrier”, your cost falls back down to reasonable and often profitable levels. This is a very interesting concept to me, and I would like to take this opportunity to model this interaction between insulation cost and heating/cooling equipment cost.
Building shape will, of course, affect surface area and, therefore, square footage of insulation required. However, building shape also affects the ability to effectively daylight the interior. Daylight can only travel so far into a space, so a long, skinny building has better daylighting potential than a square building. I will include daylighting potential in the model as well because this pulls the building shape in an opposite direction. A square building would be best to minimize insulation cost, but a long, skinny building would be best to maximize daylighting potential. I think this makes for an interesting model to study.
I will build off my Module 7 generative design study. This already has many of the core concepts built into it, but I will expand on this model in ways I will explain further down.
Intended users
This tool is intended for designers or conscientious owners of single family residential buildings, although certain modifications to the range of building sizes and shapes could allow this tool to be applied to larger residential and commercial projects.
Need you’re trying to provide a solution or support for
By creating this tool, I am trying to provide designers with an easy way to explore how building shape and insulation level affect insulation cost, heat transfer through the envelope, the need to purchase active heating and cooling equipment, and daylighting potential.
Inputs
Variable Inputs - inputs that will be varied during the generative design study
- Building length
- R-value of the walls
- R-value of the roof
- Roof pitch - this is an addition from Module 7. Module 7 assumed a flat roof for simplicity, but not many homes actually have a flat roof. I will set a range of allowable roof pitches from 4/12 to 9/12, assuming a basic gable roof. This will make the model more realistic and useful.
Constant Inputs - inputs that will remain constant during the generative design study
- Floor area
- Wall/ceiling height
- Design winter temperature
- Design summer temperature - design summer and winter temperature are also an addition to Module 7. In Module 7, I only had a single maximum delta T value, but splitting it up into summer and winter allows me to analyze heating and cooling equipment separately.
Underlying logic of the model you’ll implement
To begin with, I will just say that I recognize this is a very complex problem, and in the interest of time, I will need to make a lot of simplifying assumptions. To name just a few, I am not including windows, effects of solar radiation, heat transfer through the floor slab, thermal mass, and internal gains from occupants, lighting, and plug loads. Despite these simplifications, I will still try to produce valuable results, but if nothing else, this can serve as a framework for a more robust and accurate model in the future. I will highlight the logic for calculating each of my outputs listed below.
- Maximum summer heat gain
- Fairly simple calculation using the formula q = U * A * delta T. I will calculate q_walls and q_roof and sum them together to produce a maximum summer heat gain rate.
- Maximum winter heat loss
- Same method as maximum summer heat gain
- Cost of heating equipment
- This will require significant assumptions. I will do some research to find the cost of heating equipment for a standard home. I will then associate this with a standard maximum heat loss rate, and create a linear relationship between these two variables. In other words, as the maximum heat loss rate decreases, so will the cost of the heating equipment. I will then specify a critical heat loss rate, below which you would theoretically be able to avoid purchasing heating equipment (cost = $0).
- Cost of cooling equipment
- Same method as cost of heating equipment.
- Material cost of insulation
- As I did in Module 7, I will specify a unit cost for insulation of $0.05 per R-value per ft^2. I will then multiply this by wall R-value and area and roof R-value and area, summing these two numbers to produce my total material cost of insulation.
- Percentage of floor area that can be effectively daylit
- As I did in Module 7, I am assuming daylight can travel 12.5 ft into a room. Through fairly simple geometric equations, I will calculate the area of a 12.5 ft border around the interior of the walls. I will then divide this area by the total floor area.
Outputs
- Maximum summer heat gain
- Maximum winter heat loss
- Cost of heating equipment
- Cost of cooling equipment
- Material cost of insulation
- Percentage of floor area that can be effectively daylit