of different materials are shown in the table below, where UTS is ultimate tensile strength, or the breaking load: Structural forms Air-supported structures are a form of tensile structures where the fabric envelope is supported by pressurised air only. The majority of fabric structures derive their strength from their doubly curved shape. By forcing the fabric to take on double-curvature the fabric gains sufficient stiffness to withstand the loads it is subjected to (for example wind and snow loads). In order to induce an adequately doubly curved form it is most often necessary to pretension or prestress the fabric or its supporting structure. Form-finding The behaviour of structures which depend upon prestress to attain their strength is non-linear, so anything other than a very simple cable has, until the 1990s, been very difficult to design. The most common way to design doubly curved fabric structures was to construct scale models of the final buildings in order to understand their behaviour and to conduct form-finding exercises. Such scale models often employed stocking material or tights, or soap film, as they behave in a very similar way to structural fabrics (they cannot carry shear). Soap films have uniform stress in every direction and require a closed boundary to form. They naturally form a minimal surface—the form with minimal area and embodying minimal energy. They are however very difficult to measure. For a large film, its weight can seriously affect its form. For a membrane with curvature in two directions, the basic equation of equilibrium is: where: R1 and R2 are the principal radii of curvature for soap films or the directions of the warp and weft for fabrics t1 and t2 are the tensions in the relevant directions w is the load per square metre Lines of principal curvature have no twist and intersect other lines of principal curvature at right angles. A geodesic or geodetic line is usually the shortest line between two points on the surface. These lines are typically used when defining the cutting pattern seam-lines. This is due to their relative straightness after the planar cloths have been generated, resulting in lower cloth wastage and closer alignment with the fabric weave. In a pre-stressed but unloaded surface w = 0, so . In a soap film surface tensions are uniform in both directions, so R1 = −R2. It is now possible to use powerful non-linear numerical analysis programs