Performative analysis and design of a responsive gyroid shading system for façades

Abstract

The design of building envelopes, which are the structural elements that passively affect the energy performance of buildings, is important for reducing energy consumption and carbon emissions. The building skin makes up a significant portion of construction costs and can have a significant impact on operating costs. Solar control systems can be incorporated into building envelope design to make use of natural daylight source and improve the energy efficiency of buildings. This is particularly important in light and thermal energy concerns and the high energy consumption of buildings. Natural light from the sun, or daylight, can be used to reduce the need for artificial lighting in buildings. The windows in an architectural façade allow natural light to enter, which can help to lower energy consumption for heating, cooling, and lighting. The amount of daylight a building receives can depend on its location, the time of year, and the weather. The facade is the front of a building and serves as a protective barrier against natural elements like heat, cold, wind, and rain. It is a transition zone between the interior and exterior and allows natural light to enter the interior spaces. The facade is visible from the street and has aesthetic value. It also supports the weight of its own and other building components. Its main function is to protect the building from environmental factors and provide visual communication between the indoor and outdoor spaces. As a result of the relation between daylight and architectural façade, sun shading systems, a sub element of façade, have emerged. When the direct natural daylight coming from the outside of the facade is uncontrolled, it can cause overheating and glare problems of the interior. However, in cases where it is less than necessary, it also causes problems in indoor use quality. For this reason, the existing sunshade types have been examined and a sunshade form that can be used instead of the traditionally used horizontal and vertical louvers, which has features from both, has been studied. The main problem to be solved in this study is that the traditionally used horizontal louvers on the south façade and the vertical louvers positioned on the east and west façade do not provide the necessary shading when used interchangeably. Instead, a solution to this problem was found by proposing a responsive facade system by using the Gyroid surface, which contains both cross sections at the same time. Thus, by using a single form on the façade, providing protection both in the south and in the east and west has been the main goal. Therefore, in this study, this parametric sunshade produced for the facade was requested to work responsively with certain contexts. Since the main target is shading, the sun position was chosen as this attractor context in the study. The study began by reviewing examples and design criteria for shading systems used to meet the need for indoor shading. The research focused on daylighting, including the positive and negative effects of uncontrolled daylighting. The architectural façade was then defined and its main role, the importance of energy efficiency, and the design parameters of an energy efficient façade were discussed. At the end of first part, the study looked at various classifications of sun shading elements and proposed a new classification by combining elements from different systems. This classification divided shading systems into natural and artificial elements, with artificial elements further divided into fixed and adjustable. The different types of sun shading elements were then examined as individually. In the second phase of the study, the parametric modeling method was employed to design a responsive Gyroid sunshade system using the Grasshopper environment. Three different geometries obtained by repeating a basic unit at three different angles among triply periodic minimal surfaces are discussed. These geometries considered are Schwarz D, Gyroid and Schwarz P surfaces, respectively. Bonnet angle values of 0, 38.01 and 90 degrees, respectively, were used in the formation of these surfaces. In Grasshopper software, the mathematical equations of these geometries are produced as geometric surfaces. Then, the cross-section of these three surfaces was taken and the work was continued with the Gyroid surface, which gives both vertical and horizontal sections. The tessellation system, which allows for the periodic repetition of the Gyroid surface, was also introduced. Among the two dimensional and three dimensional tessellation methods introduced, the bounding box of the Gyroid surface, which is a unit cube, is taken into account and the three dimensional cube tessellation form is used. With this chosen form, a structural system has been proposed in which responsive Gyroid surfaces will be placed. The edge length of each unit cube of the structural system is defined as a parameter under the Grid Size. In this way, it is planned to construct a grid system with an appropriate repetition in the dimensions of the façade. This system will be included in the facade from the outside and will perform the deformation from the corner points of the Gyroid surface with the rings it contains. An attractor point for deformation was determined. First of all, the location of this attractor point is the back surface of the facade. From this position, a deformation is defined that pulls the front surface of the façade. This defines a deformation with a radius of 2m and reducing the facade thickness to 5cm at the center of the deformation. The goal was to define an attractor point that would adjust the thickness of the facade based on the position of the sun but it has also been studied that there may be different contexts. These other contexts can be listed as follows. By providing a point deformation, deformation can be achieved with a point centered circle. Here, the main effect can be briefly summarized as a complete deformation in the center of the circle, while it is approximately zero at the edges and zeroing at the edges. A Curve positioned on the façade can be considered as another attractor. Again, by determining an offset value from the curve center, the area to be deformed can be defined. Also in here, the deformation will be reset gradually from the center to the offset edges. While determining the context, user defined or natural data can be used. With an interactive screen to be set up indoor space, the deformation of the facade is left to the user's definition, and the interior user can decide on the point or curve position that affects the facade. Or this system can be connected to an external factor that provides a constant data. For example, the sun position used in this study can provide daily and annual data, and the movement of this deformation point on the facade may vary according to the sun position. Again, if there is a landmark outside, the point on the façade can be selected accordingly in order to direct the view of those inside to this landmark. In the third stage of the study, the responsive Gyroid sunshade system, which had been developed using the Grasshopper environment, was subjected to various constraints and analyzed for annual sun exposure and outdoor views. The system was limited to be tested on a rectangular facade surface of 360cm in height and 720cm in width, which is the common measurement for the grid dimensions of 30cm x 30cm, 60cm x 60cm, 90cm x 90cm, and 120cm x 120cm. The thickness of the three dimensional Gyroid surfaces within the grids was varied between 10cm and 30cm. Although it has any value in this range, it has been restricted in terms of operation and has been tested at the extreme and middle values as 10cm, 20cm and 30cm. The facade was tested in five different configurations: undeformed, deformed, with different room typologies, with traditional horizontal louvers, and with traditional vertical louvers. The analysis was conducted on the south and west facing facade only, resulting in a total of 120 different scenarios. The annual sun exposure analysis produced the following results. In the undeformed facade without a responsive system, increasing the thickness from 10cm to 30cm resulted in more shading to indoor space. On the other hand, increasing the size of the grid structure on the facade led to more daylight entering the interior by the gaps from the Gyroid unit and reduced shading. The deformed, responsive facade system showed an increase in direct daylight entering the interior as the facade thickness decreased. This indicates that the responsive system achieved shading within LEED standards while also allowing for more daylight to reach the interior space. The Gyroid sunshade design performed better than traditional horizontal and vertical elements at the same facade thickness, especially when compared to horizontal louvers, which are recommended for south facing facades. The gyroid sunshades provided the best shading in all dimension values and façade direction. The results of the analysis of different types of test rooms showed that changing the space geometry at constant facade thickness and grid size values resulted in varying levels of annual sun exposure. It was found that increasing the indoor height resulted in more annual sun exposure. Moreover, adding a mezzanine with a height of two floors to the interior space resulted in more direct daylight exposure. Overall, it is important to consider the impact of space geometry on annual sun exposure when designing a building, as well as the use of responsive systems and other techniques to control the amount of light and heat entering the interior. The view analysis results indicated that the responsive system using the undeformed gyroid shading geometry resulted in a lower quality view percentage when compared to traditional horizontal and vertical louvers. Specifically, the quality view percentage increased as the grid size and facade thickness increased, ranging from 1.54% to 16.67%. In contrast, traditional horizontal and vertical louvers almost always provided a quality view close to 100% in the same grid and thickness values. The responsive gyroid sun shading system had a lower quality view range instead of traditional horizontal and vertical louvers, with values ranging from 11.28% to 53.49%. These findings suggest that the responsive system using the deformed gyroid shading geometry may be a suitable choice for balancing the need for shading and preserving views, while traditional horizontal and vertical louvers may provide a higher level of view but potentially obstruct shading.