Ryan Fruehwirth

2 or More Units: Create Two New Evaluator Nodes

Evaluator Node # 1: Net Solar Score

The Net Solar Score (NSS) reframes the goal to “maximize cumulative insolation potential” as a directional economic tradeoff. Solar exposure on the facade is treated as a cost (cooling penalty), while solar exposure on the roof is treated as a benefit (rooftop solar panel potential). The two effects are computed separately using Ladybug Tools’ annual incident radiation analysis with EPW data from Dubai Intl Airport. To translate into monetary value, the following assumptions were made:

• Roof Solar Panel Value: $0.0128/kWh

= (Solar panel efficiency 20%) * (system derate 0.80) * (DEWA feed-in tariff $0.08/kWh)

• Facade Cooling Cost: $0.0071/kWh

= (curtain wall SHGC 0.25) * (1/chiller COP 3.5) * (DEWA commercial rate $0.10/kWh)

• 40 year building lifetime

Higher NSS = better liftetime economic outcome from solar exposure decisions. The metric is signed; negative values indicate that cooling penalty exceeds solar panel benefits.

Evaluator Node #2: Burj View Score

In Dubai’s luxury real estate market, unobstructed views of the Burj Khalifa command rent premiums often exceeding $200 per sf per year compared to obstructed units in the same building. The Burj View Score (BVS) quantifies how effectively a given form converts its envelope into Burj-facing real estate. The logic proceeds in four steps:

1. Sample 16 viewer points per floor distributed evenly around each floor’s perimeter.
2. Define three target points stacked vertically above the Burj base: the observation deck (1,483 feet), the Sky Lounge (1,820 feet), and the spire tip (2,717 feet). These represent the visible upper portion of the Burj that constitutes the actual amenity. It is assumed that the lower towers are obstructed by intermediate buildings.
3. Cast sight lines from every viewer to every target, producing 3,024 candidate views (63 floors * 16 viewers * 3 targets).
4. Test each line for view quality by counting Brep-line intersections against the tower’s own envelope. A clean unobsructed line crosses the facade once at its starting point, a blocked line crosses both the starting face and the opposing face it would have to pass through. The threshold of fewer than three intersections separates the two cases.

The aggregate score is the sum of unobstructed view counts across all viewer-target pairs. Higher BVS = more total view-amenity value preserved by the design.

Point to Ponder: Do the new evaluation metrics that you’ve designed capture the meaningful differences between the building form alternatives? The Net Solar Score (NSS) discriminates primarily on building size rather than form efficiency. Across the 50-case sweep, absolute NSS ranges from $757,418 (Twist = 10 deg, Sides = 4) to $1,194,200 (Twist = 20 deg, Sides = 12), a 58% spread. Once normalized by GFA, this spread collapses to just 0.375-0.401, a 7% range. In Dubai’s solar regime, form contributes around 7% to per sq. ft. economics while size drives the rest.

The Burj View Score (BVS) discriminates primarily on form alignment with site context. Sides = 4 and sides = 6 forms saturate at BVS = 1,490 because their few large facades easily orient toward the Burj. Sides = 8, 10, and 12 forms never saturate since their tighter polygonal symmetry forces some viewers to face away from the target. Sides = 12 shows a 30% BVS swing across twist values, meaning that for highly-faceted shapes, panel-to-target alignment dominates view quality.

Together, the two metrics demonstrate that maximizing NSS tends to minimize BVS, and vice versa.

Point to Ponder: What other metrics would be useful to compute to help understand and make the case for which alternatives are truly better than others?

Most importantly, the current metrics fail to capture architectural distinction. Distinctive forms in markets like Dubai command commercially meaningful premiums. Visual identity can drive leasing velocity and rent. Beyond that, three additional quantitative metrics would strengthen the analysis:

2) View-Premium-Weighted Floor Area

The current BVS counts units that either have a view of the Burj or not. A more market-realistic metric would compute the rentable area that can charge a Burj view premium for each floor. Then it would weight by floor height with premium scales for higher elevations. Lower floors would likely be hampered by buildings in between the site and the Burj that were not modeled in this analysis.

3) Floor Plate Efficiency

The current GFA metric counts every square foot the same; however, deep tapered or distorted forms produce dead corners (interior space too far from the perimeter for natural light or operable windows). Twisted forms tend to have floor plates with awkward angled corners that lease poorly.

3 or More Units: Develop a Single-Objective Optimization Scheme

The single-objective optimization scheme combines five evaluation metrics into a weighted composite score. Each metric is first normalized by dividing by the dataset maximum to put values on a common 0-1 scale, preventing metrics with large absolute magnitudes from drowning out metrics with small magnitudes. The normalized values are then combined as a weighted sum:

Optimization Score = 0.35 * (BVS/max BVS) + 0.30 * (GFA/max GFA) + 0.20 * (NSS / max NSS) + 0.10 * (NSS per GFA / max NSS per GFA) + 0.05 * (GFA per SA/max GFA per SA)

1. Burj View Score (BVS):
1. This should be the primary rent driver in the Dubai market. Unobstructed views of the Burj command substantial premium especially across upper floors.
2. Gross Floor Area (GFA):
1. More rentable area = more lucrative
3. Net Solar Score (NSS):
1. Solar dollars saved are much smaller than the view-driven rent on a per-floor basis
4. NSS per GFA
1. Secondary check on solar form efficiency decoupled from size
5. GFA per SA
1. Penalizes envelope-inefficient forms which may waste unnecessary material

The weights were chosen based on the relative magnitude of each metric’s commercial impact in the Dubai luxury real estate market, anchored by what actually drives rent on this lot. BVS received the highest weight at 35% because view amenity is the single largest rent differentiator on sites adjacent to the Burj Khalifa. This can translate to tens of thousands of dollars per unit per year extra. GFA received 30% as the second-tier driver as more rentable area means more total revenue. However, GFA on its own delivers ordinary rent at ordinary rates, so it should not eclipse view amenity. NSS received 20% because while $1M of lifetime operating economics is significant, it amortizes to roughly $25,000 per year, equivalent to a single luxury 1-bedroom unit’s annual rent, and is therefore meaningfully smaller than the BVS-driven view premium captured across hundreds of units. The two efficiency metrics received the smallest weights because they measure form quality rather than absolute commercial outcomes. They should influence the ranking as tiebreakers between similarly performing designs, but not dominate the results. The 5% gap between NSS/GFA and GFA/SA reflects that solar form efficiency is more directly tied to long-term operating cost in Dubai’s climate than envelope efficiency, which is more of a short-term construction cost. In fairness, these weights were not derived through a formal market analysis (which is outside the scope of this assignment) but that could/would certainly be done in the field.

All 50 candidate designs were filtered against the assignment’s GFA constraint (between 2.5M and 3.0M square feet). This eliminated nearly all 10-sided and 12-sided combinations.

The 30 surviving designs were then sorted by composite score and the three best options are highlighted below (yellow is the recommended choice).

Point to Ponder: What propelled the recommended alternative to the top of the list? Explain your reasoning -- include a brief analysis of why this alternative rose to the top of the list and why you consider it to be the best option. Are there important nuances or tradeoffs that got lost is the single evaluation?

After filtering out all options that did not provide between 2.5 and 3 million SF of GFA, the clear winner according to my optimization score is the 8-sided structure with a 70 degree twist.

• Burj View Score: 1,458.82 (top quartile)
• Net Solar Score: $1,109,300 (strong)
• GFA: 2,835,500 ft^2 (94% of cap)
• NSS/GFA: 0.391 (high)
• GFA/SA: 3.52 (efficient)

The 8-sided polygon is large enough to capture meaningful GFA without hitting the GFA cap, and circular enough that envelope efficiency stays high. There are also few enough sides that the tower retains discrete facade panels capable of orienting strongly toward the Burj.

The 70 degree twist is the max aggressive twist before BVS starts to degrade. At 80 and 90 degrees, BVS drops slightly.

While 4-sided polygons perform well on BVS, they lose badly on GFA and NSS. The 12-sided polygon wins on GFA but loses on BVS due to polygonal symmetry. 8-sided polygons with a strong twist angle threads the needle where it is strong in every metric.

Perhaps surprisingly, the 8-sided 70 degree twist is also an architecturally compelling form as opposed to the four-sided 0 degree twist building for example (see below).

There are two significant tradeoffs that got lost in the single evaluation. First, per-square-foot solar economics are nearly flat across all 50 designs. The composite hides this by weighting both raw NSS and NSS/GFA. In other words, large designs win on absolute NSS even though they offer essentially the same per sf economics as smaller designs. The single evaluation rewards size as if it were a form-quality signal, when in reality form efficiency on solar is a near non-issue in Dubai’s economy. Building bigger is what produces more dollars, not building more cleverly.

Second, and perhaps most importantly, the BVS implementation in this analysis weighs all unobstructed view lines equally regardless of floor elevation. However, real-world rent premium scales don’t work like that and scale sharply with height (penthouse view-units in Dubai command rents several times larger than equivalent low-floor units). A future refinement weighting each view line by viewer elevation would amplify the discriminating power of BVS. This is particularly true for taller forms with more upper-floor view exposure. Under that refined metric, the recommendation might shift toward configurations that maximize upper-floor Burj exposure specifically, rather than total view-availability across all floors.

4 Units: Visualize the Recommended Alternative

The colored panel pattern visualizes the per-panel directness of each curtain wall element to the Burj Khalifa observation deck. This is computed as the dot product of panel normal vector and panel-to-Burj direction. Red panels face the Burj directly while blue panels face away. The diagonal red band that spirals up the tower demonstrates the architectural value of the 70 degree twist. It distributes Burj-facing exposure across all floors rather than concentrating it on one elevation. Every floor offers premium-view units, supporting the developer’s ability to charge view premiums consistently throughout the tower’s leasable area.