Chloe Leung

Chloe Leung

2 Units Part 1:

To begin, a conceptual mass was created in Revit using the Parametric Tower – Twisting Rounded Triangular Mass (Shanghai Tower Proportions) template. This massing model includes adjustable parameters such as top height, top rotation, top radius, mid radius, mid height, base rotation, and base radius. By default, the mid rotation and mid radius are governed by the formulas:

• mid rotation = (top rotation - base rotation) / 2
• mid radius = top radius + (base radius - top radius) / 2

To ensure a more symmetrical design, an additional constraint was applied:

• top radius = ½ × base radius

Floors were added at 15-foot intervals along the building’s height.

To evaluate how different parameters impact the gross floor area, gross surface area, and gross volume, the top rotation was varied from 100° to 160° in 10° increments, while keeping the remaining parameters constant:

• top height = 750'
• base radius = 190'
• base rotation = 0°

All other dependent parameters were calculated based on these fixed inputs. The two images below illustrate how changes in top rotation affect the overall geometry. The first image shows the tower with 100° of rotation, while the second image shows the same form with 160° of rotation.

Although the visual difference is subtle, the 160° rotation model exhibits greater overall twisting. A parametric study was conducted to evaluate how this increase in rotation impacts key performance metrics. As shown in the summary table, increasing the top rotation generally leads to a decrease in gross floor area, gross surface area, and gross volume, helping inform design decisions related to building efficiency and form optimization.

2 Units Part 2:

Next, a custom building form was developed using two square profiles with adjustable side lengths and a circular profile with an adjustable radii, which were lofted to create the tower geometry. Parameters that can be flexed include the base, top square lengths, middle profile circle radii, as well as the heights of the middle and top profiles. For this parametric study, the middle radius was tested in 5’ increments, ranging from 115’ to 140’. Images of the building at 115’ radii and 140’ radii are shown below.

As expected, the summary table below shows that gross floor area, gross surface area, and gross volume all increase with a greater mid tower radius.

Points to Ponder: Exporting the results to Excel provides several advantages. It ensures that results are automatically updated with each parameter change, making it an efficient tool for iterative design. Metrics can be quickly sorted and filtered to identify maximum and minimum values, allowing designers and clients to easily pinpoint the most optimal parameters for an efficient building. Additionally, exporting to Excel provides clear documentation of all test cases and results, and enables easy visualization through charts and graphs—supporting both technical evaluation and communication with stakeholders.

3 Units:

For this stage, a custom building form was created in Dynamo. The bottom and top profiles are equilateral triangles, while the middle profile is circular. There was no specific design precedent for this form—it was developed out of curiosity to explore how the geometry would respond as parameters varied. Input parameters include the size of both equilateral triangles, the radius of the middle circle, the rotation of each triangle, and the middle and top heights of the structure. To allow flexibility in the form, the top and bottom triangles were intentionally not constrained to be dimensionally symmetrical.

For the parametric study, all parameters were held constant except for the mid-height circle radius and top height. The circle radius was varied from 135’ to 150’ in 5’ increments, while the top height ranged from 690’ to 720’ in 10’ increments. The first image below shows the structure with a circle radius of 135’ and height of 690’, while the second shows a radius of 150’ and height of 720’.

Again, the outcome of the study aligns with expectations, as all performance metrics—gross floor area, surface area, and volume—increase with larger circle radii and greater building heights. Notably, the final two trials clearly exceed the allowable gross floor area, immediately indicating that these parameter combinations are unsuitable for the building design. This further illustrates the value of exporting results to Excel, where such violations can be quickly identified and analyzed to allow informed decision-making.

Points to Ponder: The performance metrics are more sensitive to changes in the circle radius than to changes in the top height. For example, when the top height is held constant at 690’, increasing the circle radius from 135’ to 140’ results in an increase in gross floor area of approximately 160,136 SF. In contrast, when the circle radius is fixed at 135’, increasing the top height from 690’ to 720’ results in a smaller increase of about 111,668 SF in gross floor area. This suggests that modifying the circle radius has a greater effect on building performance than altering the building height. To further validate these observations, results can be graphed or statistically analyzed to ensure that these trends are consistent for a larger testing range.

4 Units:

An additional performance metric used to assess building efficiency in the 3-Unit model is the ratio of Gross Floor Area to Gross Surface Area. This ratio provides insight into how effectively the envelope encloses usable space. For example, when the structure has a circular radius of 135 feet and a height of 690 feet, the efficiency is 4.56. In comparison, increasing the radius to 150 feet and the height to 720 feet results in a slightly higher efficiency of 5.02.

Points to Ponder: If the primary design objective is to maximize efficiency, then a circular radius of 150’ and a building height of 720’ would lead to the most desirable result. However, it’s important to acknowledge that this configuration would likely lead to higher construction costs. Therefore, determining the “best” structure ultimately depends on the developer’s priorities. If efficiency is the main concern, this combination would be the recommended option.