Designing with Earthbags
Earthbag construction, popularized under the term Superadobe, uses long sandbags filled with soil to form durable, low-cost structures. Domes are particularly strong because compressive forces flow along the curved surface, eliminating the need for additional support. Estimating the quantity of soil, bags, and barbed wire before breaking ground helps builders budget, schedule, and minimize waste. This calculator models a hemispherical dome shell and uses geometric relationships to approximate material requirements.
The wall volume \(V_w\) of a dome is the difference between outer and inner hemispheres. Given interior diameter \(D\) and wall thickness \(t\), the inner radius is \(r = D/2\) and outer radius \(R = r + t\). The volume formula for a hemisphere is \(V = \frac{2}{3} \pi r^3\); thus the wall volume is \(V_w = \frac{2}{3} \pi (R^3 - r^3)\). The script converts thickness from centimeters to meters before applying this equation. Soil mass is simply \(m = V_w \rho\), where density \(\rho\) is taken as 1,700 kg/m³, a typical value for moist subsoil used in bag filling.
Bag count depends on the volume of a single filled bag. Assuming a rectangular cross-section defined by width \(w\) and height \(h\), the bag volume is \(V_b = w h L\), where \(L\) is average length. Dividing wall volume by bag volume approximates the number of bags required: \(N = V_w / V_b\). In practice, bags are often continuous tubes cut to length, and overlap reduces effective volume slightly. Still, the estimate provides a useful starting point for ordering rolls of polypropylene tubing or individual bags.
Barbed wire is laid between courses to enhance friction and seismic resistance. Each course usually receives two strands. Calculating length begins with approximating the number of courses: \(n = H / h\), where \(H\) is dome height (approximated by the inner radius for a hemisphere) and \(h\) is bag height. The circumference varies from base to apex, but using the mean of base and top circumferences simplifies the process. The average circumference is \(C_{avg} = \pi (D + t)\). Total wire length is \(L_w = 2 C_{avg} n\). Builders may add extra for door and window openings.
Consider a 4-meter interior diameter dome with 40 cm thick walls. Using 35 cm wide bags filled to 15 cm height and cut to 1.2 m lengths, the outer radius is 2 + 0.4 = 2.4 m. The wall volume becomes \(\frac{2}{3} \pi (2.4^3 - 2^3) ≈ 11.5\) m³. At 1,700 kg/m³, soil mass totals about 19,500 kg. Each bag holds 0.35×0.15×1.2 = 0.063 m³, implying roughly 183 bags. The inner radius provides a height of 2 m; dividing by bag height 0.15 m gives 13 courses. With an average circumference of \(\pi (4 + 0.4) ≈ 13.8\) m, barbed wire length is \(2 × 13 × 13.8 ≈ 359\) m.
The table summarizes material needs for common dome sizes with 40 cm walls and the bag dimensions above.
| Interior Diameter (m) | Soil Volume (m³) | Bag Count | Wire Length (m) |
|---|---|---|---|
| 3 | 5.2 | 83 | 210 |
| 4 | 11.5 | 183 | 359 |
| 5 | 21.5 | 343 | 561 |
Because domes taper, upper courses have shorter circumferences and may require fewer or shorter bags, but the conservative estimate above ensures adequate materials. When designing openings, subtract their volumes and wire segments. For example, a doorway might remove several bags and a few meters of wire from the total. Rain protection and plaster coatings also add thickness, but they are not included here. Builders should plan for additional soil for earthen plasters and to account for compaction.
The script’s mathematics can be summarized in MathML as:
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Earthbag domes resonate with natural building enthusiasts because they transform abundant soil into sculptural shelters with excellent thermal mass. By precomputing materials, builders can streamline logistics, reduce waste, and focus on craftsmanship. The calculator serves as an open-source starting point; users are encouraged to adapt it for different geometries, such as elliptical domes or hybrid structures with vertical walls and vaulted roofs.