Design Decision #1 – The optimal shape and level of insulation in a building

Design Decision #2 – Optimal sizing of lots in a neighborhood

Design Decision #3 – Optimal number of square skylights on a roof

I chose design decision #1 for my generative design study. I will walk through my Dynamo graph as I explain the details of my analysis.

My general organizational structure is fairly simple, made up of 4 groups. I have inputs on the far left. In the top left, I specify and/or compute dimensions and areas of my building and generate a structure for visualization purposes. In the bottom right, I calculate my three outputs. On the far right, I display my three outputs.

My three inputs are building length, wall R-value, and roof R-value. The ranges for both wall and roof R-values are 13-90. This was chosen because 13 is a fairly standard minimum insulation value, and R-90 is approaching the highest value you would ever see in construction. Floor/roof area is set at a constant 2500 ft^2, and width is calculated by dividing floor area by length. The range of possible lengths is 50-100 ft. This was chosen because a length of 50 generates a square building, while a length of 100 generates an elongated building with a 4:1 ratio of length to width. Building height is set a constant 10 ft, and wall area is calculated following a standard formula. Next, a visualization of the building form is generated using Cuboid.ByCorners.

Next, the three outputs are calculated, starting with maximum total heat transfer rate. I chose this output because it heavily influences the sizing of the HVAC system. I did not specify whether this was a winter or summer design condition, which was mainly because I could only have 3 outputs. A summer design condition would help size the cooling system, while a winter design condition would help size the heating system. However, simply calculating an absolute maximum heat transfer rate (regardless of the direction of flow) gives a fairly good idea of the effectiveness of the insulation, which is the overall goal. I specified a maximum delta t value of 35, and then I used the standard q = U*A*deltaT equation to calculate heat transfer through the walls and roof, summing these two values to arrive at my final output value.

After that, I calculated the material cost of insulation. I did this by specifying a unit cost of insulation ($ per R-value per ft^2). After some research, I found that insulation usually costs anywhere from $0.65 - $5.00 per ft^2. I then divided my minimum R-value of 13 by $0.65 to get a unit cost of $0.05 / R-value - ft^2. With a maximum R-value of 90, the insulation cost per ft^2 in my model ranges from $0.65 - $4.50, which is very close to the numbers I found online. I then calculated the cost of insulation for the walls and roof, summing these two values to arrive at my final output value.

Lastly, I calculated the percentage of floor area that can be effectively daylit. This was the last output I thought of, and I chose this for a very specific reason. All else being equal, both of my first two outputs would be minimized by a square building shape (minimum length value). This happens because heat transfer rate and material cost of insulation depend on wall area, and wall area is minimized by a square building shape. Therefore, just looking at these first two outputs, the most desirable building shape would clearly be a square. Because of this, I wanted to think of a third output that would pull the building shape in a different direction (literally). Natural daylight can only reach so far into a building, so a long and skinny building is able to experience the most natural daylight. To calculate the percentage of daylit area, I first needed to specify a constant distance that daylight could travel into a building. I chose 12.5 ft for two reasons. First, this is actually a reasonable value, since I found values ranging from 10 -15 ft online. Second, since my minimum building width is 25 ft, 12.5 ft works nicely for calculations because light traveling 12.5 ft from both sides would perfectly cover 100% of the area at this minimum building width. Through basic geometric equations, I completed the calculation for percentage of daylit floor area. At the two building shape extremes (skinny and long vs. square), the percentage of daylit floor area ranges from 100 - 75% respectively.

I then ran my generative design study. The chart below shows the interactions between all inputs and outputs. For example, it is clear to see that heat transfer rate and cost of insulation are inversely proportional.

The scatterplot below illustrates one main tradeoff, that as the cost of insulation increases, the heat transfer rate decreases. The cost of insulation depends on the wall R-value (the thickness of insulation) and the length of the building (corresponding to the wall surface area). As seen in the chart, there is a general trend that high wall R-values (large dots) correspond to low heat transfer rates. Additionally, since a square building minimizes wall surface area, there is a general trend that shorter building lengths (approaching a square shape and represented by increasingly yellow dots) correspond to lower heat transfer rates and lower insulation costs. As a decision maker, you need to decide between saving money by buying less insulation or minimizing heat transfer by spending more money on insulation.

The scatterplot below illustrates another tradeoff. As the building shape becomes more elongated, the percentage of daylit floor area increases. However, a more elongated building shape also increases the wall surface area, which increases the heat transfer rate. As a decision maker, you need to decide between prioritizing a daylighting or minimizing heat transfer.