Table of Contents
Geodesic Domes: Currently, in a world of uncertain times, it is important to maintain and manage current assets, but more so understand the reasons why your assets evolved to what you have today. Geodesic aluminium domes are one of the assets within the oil and gas industry that protects the product but more so improves the reduction in emissions in the aboveground storage tank (AST). It has a service life of at least half a century if maintained well.
In a nutshell, a geodesic dome is a site-specific, structurally engineered, above-ground storage tank roof. It is made from an aluminium structure of interlocking panels, extruded struts, gusset plates, batten bars, and hubs that requires no welding.
“For the technically or mathematically minded, a geodesic dome is a spherical structure composed of triangular elements forming part of a network of circles, or ‘geodesics’, on the surface of a given sphere.” – Jonathan Glancey
1 Geodesic Domes History – Architecture
Dome roof building structures are with us for centuries. Ancient Civilizations such as the Romans applied their masonry skills — and their Architectural knowledge of the arch — to create massive arched domes. Those concrete style domes needed equally large supporting walls to keep the entire structure from crashing to the ground. In short, huge old domes were heavy and bound to fail at some point and it took years to complete.
In 1926, the world’s first geodesic dome opened in Jena, Germany, as a planetarium funded by optics manufacturer Zeiss. The planetarium’s construction was the brainchild of Zeiss engineer Walter Bauersfeld.
In the 1950s in the United States, Buckminster Fuller was credited for popularized something as futuristic as geodesic domes. It was Fuller who titled these buildings with the term “geodesic,” even though he neglected to cite Bauersfeld. Prior designs in his patent application, Fuller was awarded a U.S. patent for his design in 1954, although Bauersfeld designed and built his dome 26 years earlier in Germany.
Fuller took his dome design inspiration from the world around him, he was intrigued at the structure uniformity of things like snowflakes, seed pods, flowers, and crystals and was determined that humans should mimic those simple, strong, and noticeably spherical arrangements [source: The Futurist Nov-Dec 1989 v23 n6 p14(5)].
The geodesic dome was appealing because it was extraordinary strength for its weight, and it is all over “triangulated” surface provided an inherently stable structure, and because a sphere encloses the greatest volume for the least surface area. He began construction on his first dome in 1948. That dome immediately failed due to the weak and thin Venetian-blind slats he used. Subsequent (and much more successful) models introduced strong, lightweight materials such as aluminium aircraft tubing. Fuller, helped spread and commercialize polyhedral constructions throughout the country, which he saw as an economical, efficient way to address the post-World War II housing shortage.
His geodesic domes were successful in part thanks to a structural principle that Fuller coined – tensegrity. Fuller said, “For twenty-one years, before meeting Kenneth Snelson, I had been ransacking the Tensegrity concepts. I had used the multiple rimmed, parallel or concentric wire wheel phases of Tensegrity, since 1927.” (Fuller, 1961)
Tensegrity is a word made of two others – tensional and integrity — and refers to the relationship and equilibrium between tension (Stretching force) and compression (a force shortens or crushing something) in a structure. Unlike arches that need buttresses to prevent them from spreading due to outward forces, the modern dome makes use of tension to keep them from spreading.
The low quantity of materials required for geodesic domes, matched with their durability, good appearance, and ease of construction, means they have found their way into various structures and applications all over the world.
Figure 1 -Amundsen-Scott South Pole Station in Antarctica
In 1971, the Amundsen-Scott South Pole Station in Antarctica installed a structurally supported aluminum dome, the dome was intended to last for only 10 years, a maximum of 15 years, but in the end, was in use for about 35 years. It resisted winds of around 322 kilometers per hour and heavy snow loads. The dome was designed and built by a California company that was co-founded by Donald Richter, who learned geodesic dome design from the inventor himself, Buckminster Fuller.
The South Pole dome was one of the first structures to make use of a multi-frame system, since then it has been used in thousands of domes designs around the world. It was said that it was one of the first of that kind, and that was kind of a pioneer dome. The South Pole dome was also the first to be analyzed by a computer. (Source: The Antarctic Sun, pg15, November 25, 2001)
Figure 2-© Archives de la Ville de Montréal, VM94-EX136-779
The most impressive of all was the eye-catching US Pavilion at Expo ‘67, the World Fair held that year in Montreal. It caught the focus of futuristic
architects around the world and especially the young architect Norman Foster who employed Fuller as a consultant to his successful London studio until Fuller died in 1983.
Since then it is well known that geodesic domes withstood natural disasters like hurricanes, earthquakes, and fires better than rectangle-based structures
2 Geodesic Domes History – Bulk Liquid Storage Tanks
Aluminium dome roof Aboveground Storage Tanks (AST) are used globally today. Although it dates back almost a century, the reasons for their use of petroleum tanks evolved over the past 40 years.
The first Aluminum Dome was installed for a water storage tank in 1968, for a wastewater tank in 1969, and a petroleum tank in 1977 all by the same company. It was only in 1989, that API produced API 650 Annex G: “Structurally-Supported Aluminum Dome Roofs.”
The initial purpose of the Aluminum Dome Roof Tanks (ADRTs) for petroleum in the US were as weather covers to keep snow and ice off the decks of external floating roofs (EFRs). Other reasons were for the strength-to-span-ratio and their lightweight that made it very desirable to use and retrofit existing tanks.
An example of this is in the early 1960s, when Colonial, a tank farm owner in the US only had steel EFR’s in their tank farms. By 1978 they had evaluated several roof replacement options and decided on ADRT with an aluminum internal floating roofs (IFRS) deck. This was adopted as the company’s standard roof design for roof replacements and new tanks.
By 1980, some tank owners began to cover tanks, replacing EFRs with lower-profile internal floating roofs (IFRS). This increased the working capacity, reduced emissions, reduce product vapor loss due to evaporation, and stopped the wind-induced VOCs associated with an EFR due to design. Studies proofed that the ADRT was identified to improve fire safety, and over 70 percent of large diameter AST fires occur with EFRs. While writing this document, a fire broke out on 22 May 2020 and damaged a crude oil AST with an EFR in Hengyuan Refining Company in Berhad, Port Dickson, Malaysia.
ADRTs are structurally supported and it avoids Internal steel roof pillars or columns and thus avoids column penetrations, corrosion, and coating cost associated with steel roofs. AST operators reported lower internal tank temperature with tanks fitted with geodesic domes thus reduces product evaporation due to lower product temperature. By 1982, geodesic dome installations spread south to Brownsville, Texas. By 1985, gasoline additives and water disposal drove more conversion of EFRTs to domed EFRs or replacement of EFR with IFR altogether and retrofit it with a geodesic dome.
The API Committee on Evaporation Loss Estimation (CELE) produced the Manual of Petroleum Measurement Standards (MPMS) Chapter 19. This has emission factors for various AST configurations. Sample emission calculations in MPMS Chapter 19.2, Section 5 — using a 30,48 Meter (100-foot) -diameter EFR as a baseline — indicate emissions are reduced to 35 percent for an IFR and 10 percent for a domed EFR.
In 2006, API CELE research collected thermal data on geodesic domed ASTs and EFR tanks located in Dammam, Saudi Arabia, and Edmonton, Alberta. EFR tanks had slightly lower “average bulk temperature” — EFRs lose heat rapidly at night, whereas ADRTs do not, but diurnal daylight surface liquid temperature peaks. This resulted in lower overall reduced emissions for domed EFR tanks.
API MPMS 19.4 includes thermal research information in Annex I and a table comparing superior reflective properties for mill-finish aluminium versus steel-painted white (or other colours).
In the US, the states and local jurisdictions issue air permits, the goal is to further reduce VOCs. Considering wind reduction factors alone, before thermal benefits from high reflectivity and low emissivity of aluminum, to reduce emissions inventory, the South Coast Air Quality District of Southern California in 2001 issued SCAMD Rule 1178. It states that the vapors around stored product storage tanks must be contained and regulated, and it considers the aluminum geodesic dome as the ‘perfect’ solution, thus requiring the conversion of EFR tanks to domed ASTs.
Initially, the factors that drove the industry to cover the tanks were due to snow and rain and possible sandstorms conditions. However, an additional benefit resulted in reduced vapor loss and lower product temperatures and lower emissions. Currently, lower VOCs and clean air requirements are the driving force behind improving the ADRTs.
Overall, the Genuity, engineering, and design of the geodesic dome and benefits it brought to the tank industry as a long-term asset was so timely. So now let us dive deeper into the theory behind the Geodesic Dome.
3 Geodesic Domes Design Theory Explained
Geodesic domes not only incorporate the strength of a strong sphere/arch shape, but they are also made up of many triangles. The success of the dome as a structure is a result of the natural integrity of its shape. The dome uses the same curved shape as to what gives the Arch its strength. The only difference is it is making use of tension to prevent it from spreading.
As it is well known the triangle is the strongest shape because it has fixed angles and it is the only configuration of artifact that is steady within itself without the need for added support at the intersection points to prevent distorting of the geometry.
Arches on the other hand are three-dimensional constructs using triangles resembling a sphere to create multiple load bearing paths from apex center to the point of structural support.
Pair Arches with Equilateral and Isosceles triangles and you have one extremely lasting formation, called the geodesic dome. Thus, if you apply pressure to one side of a triangle, and that force is equally spread to the other two sides, which then transfer the load force to adjacent triangles. Triangles are crucial to the design strength of a dome. This distribution of the force is how geodesic domes effectively spread stress along with the entire shape.
The design of geodesic domes is inward tilted pentagons or hexagons into a sphere shape. Both the hexagon and the Pentagon can be precisely be divided into triangles, so inherently they are also very strong.
Dome frequency is represented by the Letter “v”, e.g. 2v is a 2-frequency and 3v is a 3-frequency dome, etc. The higher the frequency the more triangles are there in a geodesic dome. Almost all geodesic domes are based on the Icosahedron (fig 3.) but could also be designed from other platonic solids; dodecahedron, octahedron or tetrahedron.
The Icosahedron is a geometric solid with 20 faces. Each face of the Icosahedron is made of an equilateral triangle. When the bottom of the Icosahedron is removed it becomes a 1- frequency or “1v” dome. All struts in a 1v geodesic dome are the same length, but 1v geodesic domes have several limitations in the optimal length vs strength of the struts. To design a geodesic dome with a larger area we need to break each of the 1v triangles into smaller triangles through “tessellation”.
So here is the secret of how the lengths of the tessellated triangles cause the vertices to be pushed out into a sphere. The edges or the struts on the outside of the tessellated triangles in higher frequency domes are always shorter than the middle of the triangle. (fig- 8)
Another reason is each corner of the original Icosahedron triangle is part of a 5-way connection, which if flattened, creates a 72-degree angle (fig.9).
The interior angles of the triangle are part of a 6-way connection, and normally the sum of the 3 angles of a Euclidian or “flat” triangle creates a 180-degree angle. However, this Geodesic Dome triangle is being applied to a positive curvature of a sphere, and so must follow the rules of “spherical geometry”, that every triangle applied to the positive curvature of a sphere must exceed 180-degrees.
This means that the 60-degree angles in this diagram are greater than 60 degrees. These 60+ degree angles, along with the 72-degree angles in the corners will cause the triangles to bend away from a flat plane so that the vertices will follow the curved surface of a sphere.
This combination of these 5-way and 6-way connections and their 72 degree and 60+ degree angles, along with the shorter edges on the outside of the Icosahedron triangle, that will bend each Icosahedron face into a 3-dimensional curved surface to create a portion of the Geodesic Dome.
4 Geodesic Domes Cone Roof vs Geodesic Dome.
Nature. Steel Cone Roofs and Aluminum geodesic domes are engineered for maximum weather-tightness and thus is there an ecological aspect combines with the economical benefit. To prevent the stored product contamination from the elements of nature like snow, rainwater, sand, and other foreign matters were and still is today an important factor. The question is what the long-term benefit and does the owner get a Return on Investment since this is a plant asset. Let us jump into it.
Roof Drains. Many open-top tanks with carbon steel EFRs have drainage issues with their roof drain system during the severe rainy season, hurricanes, and during severe snow season. With the spherical shape of the geodesic dome, a drainage system is not needed and the concern that your floating roof will sink into your product is dismissed.
Self Supporting clear span. Inherently geodesic domes have an excellent strength-to-span-ratio. It is self-supporting and this allows domes to span a large area without structural support columns. Over the years the increase in the demand for storage of oil & gas products has led to an increased in the size of the storage tanks. The benefit of a clear-span self-supported aluminum geodesic domes allows for the elimination of columns that would be required on a typical steel cone roof installation. Columns are emission risk points and by removing them your tanks gain emission credits by local government and international environmental agencies.
Columns and IFRs. No structural support columns mean that there are no columns that will pass through the IFR or decks, increasing the efficiency of the system. This advanced constructional design results in an important reduction of evaporation loss and emissions.
Wind. As per API 2517, the evaporation losses are a function of the wind speed in EFRs., however, the geodesic dome prevents evaporation loss by deflection of the wind over the top of the dome, eliminating the vortex effect of wind passing over the top of an EFR. It also aids in odour control because of reduced emissions.
Loads. The dome’s design strength allows it to handle additional loads, suspending IFRs from the dome roof, this modification makes it possible to increase to the overall usable capacity of the storage tank. Any additional required loads are considered and calculated for during the design phase of the dome, as for snow, wind, and other possible loads. It also provides maintenance benefits.
Maintenance. The ability to suspending IFRs from the roof allows for the removal of the IFR legs that determine the lowest possible point inside the tank. By not having legs, you can set a reasonable maintenance roof level above the floor, this will ease the difficulty of access with equipment in/out of the tank during out-of-service work.
Corrosion. Geodesic domes usually require less maintenance than a steel cone roof. It is corrosion resistant and no corrosion dictates less debris that gets on your secondary seal system, and that can create holes causing emission leaks. No time-consuming repair process is required, of sandblasting and painting the underside of the steel cone roof during out-of-service maintenance. Besides, the top side of the steel cone roof must be sandblasted, repaired, and coated to prevent corrosion-based damage to the roof surface.
Painting. Geodesic domes do not need to be painted for corrosion protection, a natural oxidation process occurs, creating a thin layer of protection over time. This is a huge cost-saving and adds to the return-on-investment (ROI) over the life of the storage tank.
Thermal Effects. The Aluminum Geodesic domes have a superior reflective property for mill-finish aluminium, and it protects the stored product from UV and weather exposure allowing for a cooler product. Emission is reduced due to direct exposure to sunlight by covering an open-top EFR style tank, that resulted in lower overall product temperature. A dome installed over an EFR can cut emissions by over 90%.
Weight. The geodesic dome is a lightweight construction. The weight of a geodesic dome is about 1/3 in weight or less in comparison with a self-supporting steel cone roof. For new tanks, the lightweight allows cost savings on the foundations as well as the tank shell. Due to the lightweight of the dome, it is also suitable for the retrofitting of existing tanks, that are initially designed to operate without a roof. (Fig 11)
Installation. A Geodesic dome has the benefit of being installed while the tanks are in service. It could be built on the ground beside the tank or even on an EFR and lifted into place with a crane. The construction of the geodesic dome does not require any hot work. It takes less time to be done and the customer can have the tank in service much earlier than the time it will take to finish a steel cone roof that needs to be welded. An example indicated that for an ADRT with IFR a 68% lower labour requirement was needed – 6880 man-hours vs 21930 man-hours. Installation was done in approximately 40% of the time with a lower-skilled labour team. (Fig. 12)
Pressure. Unless specified the customer has a different request, the Internal design pressure shall not exceed the weight of the roof. The internal pressure of ADRTs is limited per API 650 G.4.3 to 9″ of water. There has been testing performed to 26″ of water and petroleum applications are in service to 17″ of water. The ability to contain pressure is specific to the design and manufacturer.
Gasket compatibility. A critically important aspect that needs to be considered with geodesic domes is the gasket compatibility with the product stored in a storage tank when NO floating roof is used.
Lightning. EFR tanks could potentially accumulate potential charges due to steel-to-steel contact and could be a potential source of ignition upon lightning strikes. It is the opinion of many manufacturers that the Aluminum Dome roof does serve to provide the Faraday Cage Effect, even though that metallic shell is very thin. If no combustible vapors are present in the atmosphere due to emissions, there should be little to no concern with lightning. There should be no reason to additionally protect a dome covered internal floating roof from exposure to lightning, as the Faraday Cage has proven effective, but bonding IS required per API 650-H for other purposes. Aluminum does not hold a static charge and will not spark it will dissipate atmospheric discharge.
The original objective for aluminium geodesic domes to cover tanks remains an efficient, cost-effective means to reduce maintenance and operating costs, but recent motivation and market drivers are to further reduce the emissions of VOCs associated with petroleum storage tanks.
There are plenty of manufacturers around the world and each has its unique propriety design features with specific benefits it offers the customer. As such customers should take a structured approach to ensure they select the correct Geodesic Dome that provides the best value for the application.
A small evaluation has been made between manufacturers in the market and highlights the features and benefits required to decide. Evaluate these components and ask the right questions and factor in the variance and you could make your bid evaluation much easier.
The main components that are important to mention for evaluations are the beam, batten bars, nodes, support structures, and accessories available.
5 Geodesic Domes Technological Factors
Beams and Batten bars design (Fig 14 – Fig 18)
- The batten bar/gasket system should fully encapsulate panel edges to ensure a perfect seal to prevent any emissions.
- To prevent batten fasteners penetrating through and into the dome’s interior, the beams are designed with an extruded groove to receive fasteners. These grooves have a specific design that ensures that the fastener could be turned in and out into the same position several times.
- Gasketed stainless steel batten fasteners provide extra security for a water-tight connection
- Single web beam profiles reduce the overall weight of the structure without compromising structural performance.
- Double web beams allow for a heavier load-bearing ability, greater unsupported clear span, and possible lower profiling. The extruded box beam prevents buckling failure compared with I-Beams with less material.
- Both the required strength to carry the design loads and the weight-to-strength ratio must be considered. This results in different levels of material efficiencies and will impact the cost.
- The typical and most popular dome height is about 16% of the diameter of the tank. A low-profile dome is usually requested when there is a height restriction in the area, typical close to airports. Lower profile domes ensure more cost.
- The panels lock mechanically in place securely incorporating a seal with a fully engaged gasket. The mechanical sealing is either done by ridges located on the top flange engage with sheeting. Or torsional buckling requirements adopted by the Aluminum Design Manual and International Building Code (IBC 2012). These design features are the key to being able to provide effective water and gas-tight domes.
- The mechanical seals’ feature also protects gasket from product-side attack to prevent premature gasket failure
- Low profile or Flush Batten design, seal increases water shedding and eliminates ponding. A flush batten system eliminates ponding that could occur even on a low-profile design while providing a water-tight cover solution.
- Unique designs have the gasket is fully enclosed, non-exposed, and protected by the batten against ultra-violet exposure and seal degradation.
- Silicone is an inert material not affected by UV. Solid Silicone gaskets are preferred gasket material for sealing the nodes and batten bars. Silicone gaskets could last for 25-30 years.
- The exclusion in the integral tension ring will result in lower cost dome but the buyer will still need to install a steel tension ring on the tank shell and is still exposed to additional costs. It is easier to retrofit an existing tank with a Geodesic Dome that includes an integral tension ring, that in turn can save on installation costs. For new tank projects, for vapor tight domes, a fixed type dome with tension ring installed on the tank shell will provide an improved gas-tight design.
The Node
The Node is the point where the beams and plates meet and connected to upper and lower flanges to resist transverse deflection. These nodes need to be water and gas-tight and are thus fitted with the hubs that have a gasket sealing that allows for tight sealing and reduces emissions. A well-designed, manufactured, and installed dome, the top of the panels and battens are flush, which fixes the main dome leak risk point: the hubs.
The hub design must allow for easy removal of the cover for inspection and easy adjustment of internal floating roof support chains when it is fitted.
Support Connection details
The dome could either be free vented or Vapor tight depending on the application (fig. 21 & 22). In case of a standard water tank, a free vent eve will be good enough but when you dome a petrochemical tank and need to reduce emissions a vapor-tight design could be requested. A vapor tight ADR is more expensive due to larger load requirements and will increase material use.
The dome is also designed with either a Sliding support connection and a Fix support connection where the Beam and the tank wall meet each other. (Fig. 21-23)
Accessories. The ADR is shop fabricated and to reduce installation time and additional cost includes the complete list of additional accessories required on the ADR. This ensures that panes and accessories fit each other perfectly and now additional cutting and drilling onsite are required.
List of accessories could include
- PV Vents
- Emergency vent
- Centre Free Vent
- Triangular skylight
- Gauge hatch
- Manhole cover
- Door Section
- Nozzles
- Centre Safety line support
- Eyebolt at the apex
- Connectors for IFR Cables
- 24” Flame detector Flange
- Crane Lifting lugs
- Radial walkways
- Rolling ladder connections,
- Sprinkler support systems
6 Geodesic Domes Construction and Lifting Methods
Construction. The benefit of the Geodesic Dome is that it requires no hot work and is pre-manufactured and shipped to the site in parts where it only requires assembly. The Dome could be assembled INSIDE the tank, directly “In-Place” on the shell support structure of the tank or NEXT TO the tank. The latter method is preferred when the tank is kept in-service while the dome is assembled and installed on the tank. A typical application where the tank is kept in-service is during construction is for a wastewater tank.
There are two methods of construction and one is from the centre cone/hub outwards (fig 25) and the second is from the outside to centre (fig 24). Usually, domes will be erected” In-Place”, directly on the support structure, when there are space constraints. The “In-Place” construction process consists of a dome being built directly on a tank shell from Outside towards the centre.
When the Dome is assembled inside the tank or next to the tank on the ground, the erection process makes use of tripods or quadpods to lift the dome at each tier make it convenient and safe to work at grade and limit the working at heights. After the construction of the dome is done it could be raised to the top of the support structure using winches or cranes. This method ensures a safer, quicker installation process.
Lifting. The dome lifting method will affect installation time and equipment cost (e.g. crane vs grip hoist). It needs to be clarified at the beginning which method would be possible since it has an implication on the timeline and the cost of the project.
When the Dome is assembled on the floor inside the tank, rigging of the dome will be required to fit it on the support structure. This lifting could be done utilizing two methods; one is using grip hoist winches and pulleys (fig 27) and the second is using cranes for rigging (fig 26 and 28).
A crane is a least-effective method, as an alternative. However, in certain situations, it requires the use of cranes when it is available. However, contingent factors such as light wind conditions cause the lightweight dome to sway too much to allow for a safe installation. In fig., 26 below four Cranes were used to lift this dome into place from inside of the tank.
Once the assembly process has been completed of the construction of the Dome inside the tank, the erection crew utilizes a system of grip hoist winches and pulleys to efficiently hoist it to the top of the shell. It requires several Grip Hoists (fig. 27) fitted around the top of the tanks shell so the dome could be lifted in place.
The Crane Erection process consists of a dome being assembled on the ground next to the tank and then lifted into place with a crane. This way the tank and the dome could be constructed simultaneously and will save valuable time.
The initial cost for a Steel Cone Roof is less than that of an Aluminium Dome Roof but the cost-saving could be realized of the lifetime of the dome.due to lower maintenance cost. The increased steel prices and high labour cost makes the Aluminium dome roof more attractive. Overall in the life cycle of the dome vs the life cycle of a stell cone roof the dome is more cost-effective.
About EPCM
7 Bibliography
Apex Dome by Tank Connections Retrieved 5 21, 2020, from
https://www.tankconnection.com/assets/pdf/Apex_Domes_web.pdf
Ateco dome roof Catalog Retrieved 5 21, 2020, from
https://drive.google.com/file/d/1f4CAm-HyXiL3ywEomvtTceSp_D7K64c0/view
Buckminster Fuller’s 50-foot “Fly’s Eye” Retrieved 5 21, 2020, from archpaper.com
https://archpaper.com/2017/01/fuller-flys-eye-dome-crytal-bridges/
CST Optidome Retrieved 5 21, 2020, from
Environmental Regulations Drive Changes In Floating-Roof Designs for Storage Tanks – Retrieved 5 21, 2020, from
Fuller, B. (1961). Tensegrity. Portfolio and Art News Annual(4), 112–127, 144, 148. Retrieved 5 21, 2020, from http://www.rwgrayprojects.com/rbfnotes/fpapers/tensegrity/tenseg01.html
Geodesic Dome. (n.d.). Retrieved 5 21, 2020, from Wikipedia: The Free Encyclopedia: http://en.wikipedia.org/wiki/Geodesic_dome
Geodesic Domes and Charts of the Heavens. (n.d.). Retrieved 5 21, 2020, from Telacommunications.com: http://www.telacommunications.com/geodome.htm
Buckminster Fuller. (n.d.). Retrieved 5 21, 2020, from Wikipedia: The Free Encyclopedia: http://en.wikipedia.org/wiki/Buckminster_Fuller
Superior Dome. (n.d.). Retrieved 5 21, 2020, from Webb.nmu.edu: http://webb.nmu.edu/SportsAthletics/SiteSections/Facilities/SuperiorDome.shtml
What is Geodesic Dome Frequency? An Explanation. Retrieved 5 21, 2020, from ziptiedomes.com
https://www.ziptiedomes.com/faq/What-Is-Geodesic-Dome-Frequency-Explained.htm
