Geodesic Dome Chord Factors

Chords

• Chords are to geodesic domes as studs are to walls. They are structural members, which are subsequently sheathed to form an exterior surface. In a typical home, an exterior wall stud may be identical to just about every other wall stud. The same is true of geodesic domes: most chords are identical. What is different is that the angles of dome chords where they join are far more complex than the simple perpendicular ends of a stud. You can imagine that the math to cut a rafter, which planes perpendicularly into a roof's valley, is a little more complex. With dome chords, you may have three, five or more chords coming together in a single compound joint.

Sphere Types

• Before you can calculate chord dimensions (or strength), you have to determine what kind of dome you're building. There is an infinite number of possible geodesic sphere configurations. These patterns are called spherical tessellations. A tessellation is a shape that can be repeated and fill another shape without overlapping. In this case, the tessellation shapes are arranged to form a sphere without gaps or overlaps.

Tessellations

• The repeating patterns of tessellations can be found in the artwork of M.C. Escher. Mathematically, tessellation has its roots in trigonometry --- the language of triangles. Each plane in a tessellated sphere is a triangle --- or it can be divided into a set of equal triangles, such as a pentagram. The type of spherical tessellation pattern is used, along with the size of the structure, to determine the length and joint-angles of each chord.

Calculating Dimensions

• A commonly used chord factor formula, as seen on the Soul Visuals website, is "chord factor = 2 Sin (θ / 2) where θ is the corresponding angle of arc for the given chord; that is, the 'central angle' spanned by the chord with respect to the center of the circumscribing sphere." If you want more help making these calculations yourself, consider Hugh Kenner's "Geodesic Math and How to Use It" or consult Rick Bono's software, "Dome," which can handle the calculations for you and translate them into a 3-D graphic.