As buildings evolve and grow we often intuit ideal adjacencies. In the age of computational design, we need quantifiable metrics to evaluate buildings. Evaluating adjacencies is a simple step in that direction.
What, Why and How: Applications of Pathfinding
Over the past few weeks we’ve spent time identifying rooms and finding paths between them. Now it is time to apply that knowledge on a larger scale. Once we have identified different locations within the building and the walking distances between them, we can start to analyze the relationships between spaces.
In large buildings, especially those that expand over time and undergo multiple major renovations, it is important to assess how the building evolves over time. In doing so, we can see how expansions and renovations impact adjacencies that may have been ideal when the building was constructed.
Take for instance a medium sized hospital. When the hospital was originally constructed, it was sized to accommodate the needs of the community. 10 years later, however, the surrounding community grew, and now the hospital needs to expand it’s services in key areas. Imaging equipment may have been moved as additional resources were needed, and a new surgery suite may have been built in a less than ideal location. On a day-to-day basis, walking the extra distance may not mean a lot, but as thousands of patients are moved through the facility, non-optimal adjacencies can have a big impact. From an operational perspective non-optimal adjacencies occupy staff time for transfers and in critical cases, like stroke cases, lost time can impact clinical outcomes.
I should note, that this evaluation is not ideal when you are trying to control the experience through adjacencies. This process for buildings where function takes precedent over form in buildings like hospitals, manufacturing facilities, etc.
Designing the Metric
To create our optimal adjacency score we’ll only need two variables. The first variable, will be the walking distance between two destinations. The second will be the number of times people travel between those two destinations. To create an analysis across an entire building, we’ll create a list of destination pairs so that we can analyze the entire building.
For our example, we’ll keep things simple, and using just 3 destinations, and walking distances that may not be realistic. Doing this will keep our list of destination pairs short, and allow us to work with walking distances are easier to comprehend.
Below we’ve set up three hospital destinations: an emergency department, an inpatient tower, and a surgery suite. We’ve assigned walking distances between the three destinations, and a count of the number of times people walk between the two departments. You can multiply the two variables to find the total distance people walk.
From an operational perspective, destinations that people frequently walk between should be closer together. Destinations that people rarely walk between can be further apart. Translating this to a mathematical perspective, optimizing the relationship between walking distances and times traveled means that as one variable increases, the other should decrease. Therefore, we need a way to evaluate whether there is an inverse or negative relationship between the two variables.
To evaluate the relationship we’ll use something called the correlation coefficient. This measures whether a set of variables have grow in tandem, or if one variable shrinks as the other grows. We’ll feed the formula two sets of variables, one of the walking distances, and the other of times traveled. To make the calculation easy, Excel provides the =CORREL() function.
The results of the calculation range from -1 to 1, with the negative indicating an inverse relationship (which we want), and positive indicating that travel distance increases with times traveled (which we don’t want).
To make the metric more score-like, I’m recommending that you used the following formula:
Adjacency Score = (1-[Correlation Coefficient]) * 5
This will shift the results of the correlation coefficient so that the highest score (indicating an inverse relationship) will be 10, and a positive relationship will be 0. A score from 0 to 10 makes the numbers easier to interpret, especially helpful in presentations when you don’t have time to explain the statistical measure.
To add an additional layer of approachability to the score, we can also assign stoplight colors, making the score even easier to digest. To do this, we’ll translate the strength of the correlation into green, yellow and red.
- Since a -0.7 correlation coefficient indicates a negative relationship, we’ll use that score as the lowest possible score for green. Using the adjacency score formula above, that means an green or “good” adjacency score would be from 8 to 10.
- Moving on to yellow, we want to highlight adjacency conditions that may be causing issues, but aren’t quite problematic. In correlation coefficient terms that means the coefficient is -.69 to 0, indicating moderate to no correlation. This mean that we want to pay attention to buildings with adjacency scores of 5 to 7.
- Finally, red, buildings where the places people travel most are the furthest away from each other. Using our metric, that means any building where the adjacency score is lower than 5. These are buildings where we need to dig deeper to understand why resources are laid out in a particular way, and if there are opportunities to move resources closer to one another.
Now we have a simple metric to evaluate building adjacencies, and can translate the statistical measure into a score that is easy to present and interpret.
Next Steps
With the metric created, we’ve only touched the surface of how adjacencies can be created. Depending on the needs of the evaluation, we could add additional variables into the formula. With additional variables such as daylight exposure, critical adjacencies, etc. we can bring more sophistication into formula while also identifying situations where non-optimal adjacencies (according to our simple metric) are the right solution.