### Spherical Geometry

Geodesic domes are geometric structures designed by American architect and inventor Buckminster Fuller. They are semi-spherical in shape and distinguished by their ability to be constructed using easily producible flat geometric components that form a curved sphere surface. The image below illustrates the general structure of a geodesic dome.

One of the most important features of these domes is their ability to distribute the load and tension evenly throughout the entire surface (via connection points). This allows the domes to be scaled up to the extent permitted by material science without the need for external supporting structures.

The structure’s spherical geometry enables it to be constructed using the minimum amount of building materials over a specific land area.

A geodesic dome can be manufactured and constructed quickly using various materials. The main skeleton of the structure is created by joining straight bars or tubes cut to specific lengths.

The surface of the dome can be covered later with different materials, or the dome structure can be directly achieved by cutting and assembling triangular blocks of appropriate dimensions.

One of the most appealing aspects of such a structure is that it can be built by anyone without requiring any professional construction or assembly knowledge. For instance, it can be set up in a backyard, on a university campus, or at an outdoor event with just a few people and basic equipment.

The modularity of the structure allows for easy disassembly after use, making it possible to reuse it in different locations.

Geodesic domes can serve various purposes, but in this article, we will focus on their use as greenhouses in hydroponic farming applications, considering their geometric design and cost-effectiveness.

A geodesic dome is a structure that covers the largest volume with the least surface area. This feature enables it to retain the trapped heat inside for an extended period compared to other greenhouses with different geometric shapes.

Maintaining proper heat balance is crucial for greenhouse cultivation. If the dome’s surface is covered with a light-transmitting material like greenhouse polyethylene, it can lead to significant energy savings, particularly in cold climate conditions.

Another advantage offered by spherical geometry is that as the circular base radius of the dome increases, the cost of constructing the structure per square meter decreases. Below is the connection diagram of the struts used in a geodesic dome with a frequency of 3.

Let’s explain with another example. Let’s say we want to build a geodesic dome with a total area of 20 square meters on a circular plot. That means when we complete the dome, the interior area will be a total of 20 square meters. In this case, we would need:

• 50 Pieces of 1.04 meters (blue),

• 40 Pieces of 1.00 meters (yellow),

• 30 Pieces of 0.88 meters (red)

struts. When these struts are interconnected as shown in the visual, they form a geodesic dome with a height of 5 meters.

Therefore, for building a geodesic dome with a base area of 20 square meters, we used a total length of 119 meters for 120 struts.

Now, let’s double the total area to 40 square meters. In this case, we would need:

• 50 Pieces of 1.47 meters (blue),

• 40 Pieces of 1.44 meters (yellow),

• 30 Pieces of 1.24 meters (red)

struts. This corresponds to a total length of 168.5 meters for 120 struts. As seen, even though we increased the total area by 100 percent, the number of struts used only increased by 41 percent.

Let’s go a bit further and assume we want to produce on an 80-square-meter area. The required struts would be:

• 50 Pieces of 2.08 meters (blue),

• 40 Pieces of 2.03 meters (yellow),

• 30 Pieces of 1.76 meters (red).

Again, using only 41 percent more of the number of struts we used for a 40-square-meter greenhouse, we have doubled our production area to 80 square meters.

Let’s talk about the concept of “frequency” a bit. The frequency of a geodesic dome can be thought of as its surface density. As the frequency increases, the number of struts used in the dome also increases. In other words, there are more triangular shapes on the dome’s surface. As shown below, each increase in frequency indicates how many equal segments one side of the main triangle on the dome’s surface will be divided into.

For example, in a dome with a frequency of 2, each side of the main triangle is divided into two equal segments. In a dome with a frequency of 3, each side is divided into three equal segments, and so on. As the frequency increases, the dome’s surface becomes smoother and more curved, allowing for a more efficient use of materials and reducing the number of struts required for construction.

In the examples above, we used a 3-frequency dome. The 3-frequency of this dome means that there are 3 struts used on each side of the largest triangular pattern (or the main triangle) present on the dome’s surface.

The frequency number is important for geodesic domes for two reasons. Firstly, as the frequency increases, the structure’s geometry becomes more similar to a sphere. Secondly, as the frequency increases, the structural strength of the dome improves.

For a dome intended for greenhouse purposes, a frequency value of 2 or 3 can be chosen. However, for larger domes intended for residential or commercial purposes, which need to withstand loads such as wind and snow accumulation, a frequency of 5 or 6 may be required.

The number of struts used is fixed and determined based on the selected frequency value. For a 3-frequency 3/8 dome, we used a total of 120 struts. For a different variation, such as a 3-frequency 5/8 dome, 160 struts are required. If a 4-frequency dome is to be constructed, a total of 250 struts are needed. For a 3-frequency 3/8 dome (as used in our example), regardless of criteria such as the base area and height of the dome, 120 struts should be used. The length of the struts becomes decisive for the volume and height of the dome.

Applying these structures as an alternative to existing greenhouses used for hydroponic farming can be a very innovative and reasonable approach. The geodesic domes’ low installation costs compared to traditional greenhouses used for under-cover cultivation, energy-saving capabilities, and long-term durability requiring less maintenance, may make them an excellent option for large-scale sustainable farming applications in the near future.

### Other Parts Of The Article Series

- The Future of Agriculture: Designing Tomorrow-1
- The Future of Agriculture: Soilless Agriculture-2
- The Future Of Agriculture: Mars Greenhouses-4

**References**

- Tarım ve Orman Bakanlığı. (2020). “Bitkisel Üretim Verileri”.
- Euronews.com (Mayıs 2020). “Türkiye’de son 12 yılda çiftçi sayısı yüzde 48 düştü, tarım alanları da azalıyor”. (Erişim tarihi: 2 Mayıs 2023)
- Anaç, D. (Ed.). (2020). “Topraksız Tarım ve Bitki Besleme Teknikleri.” Nobel Akademi Yayıncılık.
- ziptiedomes.com. (2023). “Geodesic Dome Kits that are Easy to Build!”. (Erişim tarihi: 2 Mayıs 2023)