This generative design study examines how building shape and insulation level affect heat loss through the envelope, the cost of insulation and heating/cooling equipment, and daylighting potential.

The first interesting tradeoff is that as you spend more money on insulation, heat transfer through the envelope decreases, which decreases the cost of heating/cooling equipment. As you continue to add more insulation and “tunnel through the cost barrier”, you eventually reach a point where your envelope is so well insulated that you can completely eliminate heating and/or cooling equipment. This drives overall cost down significantly and will likely pay for the extra insulation.

The chart below illustrates this tradeoff quite well. As wall R-value increases, the cost of insulation increases, but summer heat gain and cost of cooling equipment both decrease. When heat grain reaches a minimum threshold, there is no longer a need for cooling equipment, and the cost drops to zero.

The second interesting tradeoff is that as building length increases, the percentage of daylit floor area increases. However, because a longer building length (for a constant floor area) will increase envelope surface area, a longer building length will also increase heat transfer. Therefore, there is a tradeoff between maximizing percentage of daylit floor area and minimizing heat transfer through the envelope.

The chart below attempts to illustrate this relationship. You can clearly see that percentage of daylit floor area increases with building length. However, the relationship between daylit floor area and heat transfer is less clear in this chart. There are a couple reasons for this.

First, heat transfer is more heavily influenced by R-value than it is by building shape. So a long and skinny building with R-90 insulation will have much lower heat transfer than a square building with R-13 insulation. If the R-values were kept constant during the study, only varying building length, there would be a much clearer relationship between daylit floor area and heat transfer.

Additionally, the chart would ideally show the total R-value instead of just the roof R-value. Certain points in the chart below display low heat transfer AND low roof R-value. This is only possible because the wall R-value is very high, but this not shown in the chart. In future versions of this generative design study, perhaps it would be worth adding “Total R-Value” as an output to allow for more illustrative charts.

One more minor tradeoff is that increasing roof pitch will increase roof surface area and, therefore, the cost of roof insulation.

Below is an overview of my Dynamo graph. I will explain the logic for each part of this graph in more detail below.

These are my four variable inputs, four constant inputs, and width calculation.

Here, I generate my building form and calculate wall and roof areas. To generate the form, I first specify the five corners of the building profile, and then I connect these points to form a pentagon. Next, I extrude the pentagon to form the completed building form. Then I use a custom node “BuildingForm_SelectWallAndRoofSurfaces” to select the wall and roof surfaces. After that, I calculate the wall and roof areas using a simple Surface.Area node.

Here is the logic to my custom node “BuildingForm_SelectWallAndRoofSurfaces”. I first input the lofted solid and select every face. Then, I identify and eliminate the ground surface by calculating the normals to every surface and filtering out the surface with a normal containing a z-value of -1. Next, I identify and select the roof surface by calculating the normals again and filtering the surfaces with a normal containing a z-value of more than 0. After filtering the roof surfaces, I can then output both the roof surfaces and the remaining wall surfaces.

Next, I calculate the maximum winter heat loss and summer heat gain rates. I use the simple q = U * A * delta T equation. I calculate q_max for the walls and q_max for the roof and add these two values together to get a total q_max value.

Here, I calculate the cost of the heating and cooling equipment. For the heating equipment, I assume that if the winter heat loss rate (heating demand) is less than 3500 Btu/hr (the equivalent of one hair dryer), then no heating equipment is needed (cost = $0). For cooling equipment, I assume a minimum threshold of 2500 Btu/hr. This is lower than the heating threshold to allow for additional heat gain from occupants, lights, and plug loads. I also assume that heating and cooling equipment costs $0.75 for every Btu/hr of its capacity. This is a gross assumption, but serves the intended purpose of the design study.

Here, I calculate material cost of insulation and the percentage of floor area that can be effectively daylit. For the material cost of insulation, I assume insulation costs $0.05 per R-value per ft^2. I then multiply this unit cost by the wall and roof R-values and areas and sum the two costs together. For the percentage of daylit floor area, I assume that daylight can travel 12.5 ft into a room. I then calculate the area of a 12.5 ft border around the interior of the exterior walls. I have an “if” statement at the end to say that if the building width is less than or equal to 25 ft, then the percentage is automatically 100%, since daylight traveling 12.5 ft from either side of a building skinnier than 25 ft will cover the entire interior.

Below is a list of my six outputs.