Stage 1: Create Two New Evaluator Nodes
Building off of last week’s tower, I used the same hourglass form to generate five total metrics for 12 tower options. First, I developed a series of nodes which calculated the Gross Floor Area, Gross Surface Area, and Volume, and then merged all the fields to export as a csv to my local drive. I then implemented my two primary metrics: construction cost and solar irradiance.
First, I created nodes that mapped construction costs linearly from $500/SF at grade to $1000/SF at 755’. I did this by using a Remap Number component which translated floor elevations (Z) into specific unit costs. I then set a Source Domain to [0, 755] and Target Domain to [500, 1000]. These results were multiplied by their corresponding floor area and aggregated via Mass Addition.
Second, I used Ladybug to measure annual solar radiation. I sourced a Dubai EPW files from ladybug tools and used the Import EW node to channel weather data into a Cumulative Sky Matrix. The technical integration on macOS was the most significant challenge. The Sky Matrix initially failed because Ladybug couldn’t located the Radiance rayinit.cal dependency. I resolved this by hard-coding the bin and lib paths into the Python environment variables. Furthermore, a ‘library identity crisis’ caused components to reject valid data collecitons due to conflicting library paths. I fixed this by implementing a global path-setter script that synchronized the sys.path across the entire document. Finally, I optimized the grid size to 3.0 to ensure calculations remained under 20 seconds.
Stage 2: Develop a Single-Objective Optimization Scheme
I developed an overall scoring metric that aggregates the relative ranks of each metric and selects the option with the highest rank (lowest value) as the most optimal choice. My equation evaluates three forces: Financial Constraint (Cost), Performance Value (Size: GFA, V, SI), and Envelope Size (GSA). For instance, when optimizing for construction cost, the lowest construction cost is ranked as 1 and the highest is ranked 12; for envelope size, the lowest GSA is ranked as 1 and the highest is ranked as 12. Since GFA, Volume, and Solar Irradiance all move in the same direction as the the tower enlarges, I decided to create one variable, Size, which receives a rank of 1 for greater values and a rank of 12 for smaller values. To evaluate the importance of each metric, I implement a weighted scale whereby each of the three variables are tweaked by a ‘weight’ value. I chose these weights myself, but they are subject to change depending on the client’s needs.
The result is a 3 variable equation. Our goal is to minimize the equation in order to determine the most optimally-ranked design option.
where C = Cost, S = Size, and E = Envelope Size.
See the following table for the resulting scores:
The top 3 choices end up being tower 10 (score = 5.6), tower 7 (score = 6.2), and tower 11 (score = 6.2). The reason why each option ranked highest differs depending on how cost and size ranked. Tower 10 received a relatively row rank for both cost and size (6 and 4, respectively), which brought down the overall score. Tower 7 succeeded by having a cost rank and envelope size rank that were low (4, and 5), but it was outweighed by a high size rank of 8. Meanwhile, tower 11 received a very high rank for cost and envelope, but a very low rank for size, which outperformed the other two variables, and bringing this option to the top 3.
Ultimately, I believe the best option is Tower 10 because it ranks very well for cost, and in-between for size. Using our optimization equation, it is the best choice when considering the tradeoffs between cost and size. It avoids the extremes of both cost and scale, capturing the sweet spot where the client can get the best possible performance-to-budget ratio. Visually, it represents a tower that conforms to the hourglass form I was interested in (see below).
There are a few nuances that got lost in this evaluation. First, is the consideration of the variables. Treating Solar Irradiance as a pure performance benefit creates a severe thermal paradox in the Dubai context. While maximizing solar capture is beneficial for potential photovoltaic energy generation, it simultaneously introduces extreme radiant heat gain on the building envelope. In this desert climate, that exposure translates directly into massive mechanical HVAC cooling loads, creating a cost that is hidden from our current equation, which only considers construction cost. Second, the structural complexity of the hourglass form is masked by the linear cost model. Because the economic metric calculates cost strictly as a function of floor height, it assumes a straight vertical tower and an undulating tower are fiscally identical if they share the same elevation. In reality, Tower 10’s pinched waist requires complex structural load transfer. This introduces heavy structural premiums that a flat, height-weighted formula cannot capturrtte.