single curve
A three-dimensional shape into which a thin flat sheet of material, e.g. metal, can be formed by bending alone, without stretching or compression.
single curve: the shape you get from bending, not stretching
A single curve is a three-dimensional surface that can be created by bending a flat sheet of material in one direction only, without any stretching, compression, or tearing. Think of rolling a sheet of paper into a cylinder: the paper stays the same size, but gains curvature along one axis. In metalworking, this matters because single-curved shapes can be formed by simple bending operations on sheet stock, making them economical to produce at scale.
Mathematically, a single-curved surface has zero Gaussian curvature. The surface can be "unrolled" back to a flat pattern without distortion. Common examples include cylindrical shapes (like pipes, drums, or curved panels), conical sections (like tapered sleeves or funnels), and some helical forms. A hemisphere or sphere, by contrast, cannot be flattened without stretching, so these are double-curved surfaces.
Single-curved shapes are formed using simple machines: rolls, presses, or manual bending equipment. A three-roll bender gradually curves sheet metal into a cylinder; a cone brake or press brake can create angular or curved tapers. Because the material flows in one direction only, thinner gauges remain feasible even in stiffer metals. Thicker material requires more force but stays within the capability of standard shop equipment.
The constraint is real: if a designer specifies double curvature (like a domed roof or a car body panel), the sheet must be stretched or compressed locally. This demands stamping presses, hydraulic forming, or stretch-forming equipment, all far more expensive than simple bending. Shops quoting work often distinguish single-curved parts sharply from complex forms because the tooling and skill required differ dramatically.
In layout and pattern development, the single-curved rule is foundational. Before cutting and forming, a pattern maker calculates the flat blank size by "developing" the surface, accounting only for bend deductions and material spring-back. Double-curved surfaces require empirical testing or finite-element simulation because the strains distribute unpredictably.