Original Design
This assignment optimizes the above custom design made using Dynamo geometry from Module 5 for the following characteristics:
- Minimize surface area
- Maximize solar insolation potential
- Minimize energy intensity
- Minimize construction cost
Custom Nodes for Three New Evaluation Metrics
The custom node builds on Module 5. In addition to the base Dynamo geometry and functions to calculate gross volume, surface area and floor area, the node has been updated to include functions to measure solar insolation potential (as cumulative insolation available on building envelope surfaces throughout the year), average energy intensity, and total construction cost.
(1) Solar Insolation Potential
This first custom node within the solar analysis component captures non-ground surfaces by computing surface normals and identifying surfaces with normals that do not point to the ground.
This second custom node within the solar analysis component uses the Solar Analysis for Dynamo package. The grid spacing used is 8 to balance trade-offs — the more closely spaced the points are, the more accurate the estimation is, but the longer the model takes to run. The cumulative insolation total value is calculated with the formula:
The project location was set to San Francisco and the parameters were connected to the required input for the solar analysis component of the custom node.
(2) Average Energy Intensity
Based on literature review, the average energy intensity (kWh/sq ft) of a tall building is greater on the lower and higher floors and lower in the middle of the building. This is due to more common areas that consume greater energy on the lower floors of the building, and greater use of HVAC systems as a result of wind and other weather variables on the higher floors of the building.
Therefore, a simple mathematical representation of this relationship would be a quadratic equation. I fixed the minimum energy intensity of the building on the middle floor of the building and estimate the energy intensity of a respective floor using the following equation:
The energy intensity for each floor is then computed by multiplying its floor area (sq ft) and energy intensity (kWh/sq ft). Following this, the average building energy intensity is calculated — I chose not to use the total building energy intensity because taller buildings would unfairly fare worse in the subsequent optimization and this is
A number slider was used so the base energy intensity per square feet can be adjusted. I used 16 kWh/sq ft in this analysis, which is a respectable base minimum energy intensity that developers can work towards.
(3) Total Construction Cost
Based on the assignment brief, I assumed that the construction cost per sq ft will grow linearly from $700/sq ft at the ground level to $1500/sq ft at 750 ft above the ground.
As I am adjusting the top height of my Dynamo geometry, my input cost for the highest floor is therefore:
The construction cost per sq ft is calculated for each floor using a series node, and then the cost for each floor is calculated by multiplying its floor area (sq ft) with its construction cost ($/ sq ft). Following which, the total construction cost is calculated by summing the costs of all floors.
Designing a Single-Objective Optimization Scheme
The outputs from the custom node were combined into a list.
The maximum and minimum values are separated for each column in order to rescale them and compute a single weighted optimization score.
I gave average energy intensity and total construction cost higher weight in order to improve the cost-effectiveness of the project as average energy intensity contributes to reduced energy costs. Nonetheless, the four evaluators intersect in interesting relationships that warrant further thought on their ideal respective weightage for optimization as discussed below.
Solar Insolation Potential vs Average Energy Intensity: Although solar insolation potential is maximized, greater insolation can result in overheating during heatwaves or summer (which is likely in San Francisco) and therefore, increase HVAC costs. Conversely, it could decrease the heating load during cooler months.
Surface Area vs Construction Costs vs Solar Insolation Potential: Less building envelope surface can mean a lower facade construction cost as well as less surface area that is subject to conduction gains or losses (which could run counter to our other objective of maximizing solar insolation potential). However, the surface area could also be used for green walls and solar panels, which is a possibility on the lower floors of the building. This could reduce energy costs from heating and electricity consumption from the grid.
I decided to focus on construction costs for short-run cost savings (important for project finance) and average energy intensity for long-run cost savings. As the surface area and solar insolation potential can be further creatively optimized in various other ways, e.g. green wall, solar panel, better facade materials, they were given a lower weightage in this optimization.
This custom node unpacks the column values and normalizes them.
Importantly, in the blue group, I have flipped the normalization for indexes 3, 6 and 7, which are surface area, average energy intensity and total construction cost respectively, because these are evaluators that I want to minimize. In other words, a smaller surface area will now be rescaled to have a higher score on a 0 to 1 scale. This will be helpful for computing my optimization metric below, where I add the 4 scores and choose the test cases with the best scores.
Results
The lists were re-created, now with the addition of the evaluation score. The results are exported to excel and the top 3 designs are identified with another custom node as modeled after the module example. This custom node helps to find the maximum and/or minimum value of a certain metric, or sorts the data to find the top or bottom three items of the metric.
Discussion
The final ‘best’ design (dark green) is therefore a 650 ft-tall building with a 10-degree top rotation as it has the best overall optimization score.
The cells highlighted in light green are the top 3 recommended design alternatives: (1) 20 degree top rotation and 650 ft building, (2) 30 degree top rotation and 650 ft building, and (3) 40 degree top rotation and 650 ft building. The optimization of construction cost is highly dependent on tower height and has been weighted twice as heavily, so it is unsurprising that the shortest buildings tested fare better.
Interestingly, at taller heights (e.g. 750 ft), there are larger differences between the scores when the top rotation changes. This is unexpected at first thought because my Dynamo geometry defines a building form with a thin top so the marginal cost of construction should decrease. Instead, I notice a significant difference in the range of solar insolation potential between buildings with 20 degrees or less of top rotation and buildings with 30 degrees or more of top rotation.
Considering the insight that the twist of the building can have an important influence on the amount of sunlight received, the downstream impact could be that buildings with less twist may be more suitable for solar panels or green roofs, while buildings with more twist can consider building materials to improve heat retention from solar energy to minimize energy costs.
