## 2 Materials and Methods
### UHI Direct Impact Evaluation  
#### 2.2.1 Sun Ray Trace Analysis Studies--Component and Facade Level  
The first explorations of the initial geometry concept were based on the proportions of the component and how these relate to their environmental performance in terms of solar radiation, to receive a first indication on the impact of the self-shading effect and how the proportions affect the overall scale and performance, as seen on the figure below (Figure 6). However, since the most important factor to evaluate the direct impact was the reflectivity of the sun rays back to the atmosphere, a first round of sun ray trace analyses on a segment of the facade was realized. The first results already showed that the original geometry reflected only about 10% of the rays. This was mostly due to the rays reflected from the top pyramid downwards, and led to a geometry refinement, having a more flattened pyramid on top. Apart from that, the rotation of the bottom pyramid was optimized to have the top surface perpendicular to the sun rays from June to December as a first case (Figure 7).  
Figure 5: Close-up views of the facade component and mechanism during the summer and winter situation.  
During the ray trace analysis, a backward ray-tracing method was followed using a combination of a forward ray trace analysis and the \"Bounce from Surface\" component of the Honeybee plug-in. The advantage of the latter method is that it also enables the  
Figure 6: Overview of the various geometry alternatives based on proportions and sizes and a first solar radiation study.  
Figure 7: Overview of the various geometry alternatives based on proportions and sizes and a first solar radiation study.  
visualization of the sun rays after several bounces, considering the rays reflected from the neighboring surfaces before bouncing off to the atmosphere or the urban environment. In this study, the analysis considered 2-3 bounces and evaluated the reflectance both between the different proportions and between a horizontal and a diagonal arrangement. A summary of the results can be found in Figure 8, where it was concluded that Option 2 showed a good enough performance with both a larger rotational range with a starting angle between 45\({}^{\circ}\)-50\({}^{\circ}\) and a strain ratio within allowable limits of 3-5% strain. Some further observations were the existence of a \"blind\" angle, which corresponds to the rays being reflected from the top pyramid downwards through the in-between geometry gaps in certain time periods, as also seen in the diagram below. The analyses showed that the bottom pyramid's size and arrangement had the most impact on obstructing the sun rays from the top ones with a wider geometry being more efficient towards this goal. In this respect, the diagonal facade arrangement exhibited a better performance as well, because those rays were reflected back to the atmosphere by the neighboring components and the ones below, as a result of the more scattered component distribution, while the horizontal one had a negligible impact. These observations led to the final refinement set of component proportions for each pyramid to be used for the next studies, which were length-to-height: 1/0.5 and base-length-to-pyramid-height: 1/0.5, with an overall component proportion of 1/1.  
Figure 8: **Top**: Summary of the sun ray trace analysis studies and in comparison to the facade arrangement. **Bottom**: The impact of the “blind” angle impact and the difference between the horizontal and diagonal arrangement.