What method of pattern development is commonly used to layout a gored elbow?

The correct method of pattern development for laying out a gored elbow is the parallel line method. This technique is particularly effective for creating patterns that require consistent dimensions along parallel lines, which is essential for achieving the correct curvature and fit of the elbows within a sheet metal application.

When using the parallel line method, measurements are taken from the centerline, and lines are drawn in parallel to this reference. This helps in accurately transforming the three-dimensional curvature of the elbow into a two-dimensional flat pattern. The geometry involved requires precise alignment to ensure that the angles and lengths are maintained when the metal is formed into the elbow shape.

Though the other methods listed, such as triangulation, slope method, and radial line, are useful in various contexts of sheet metal pattern development, they do not provide the same level of control and accuracy needed for the specific curvature involved in a gored elbow. Triangulation is often used for irregular shapes, the slope method is more suited for sloped roofs or ductwork, and the radial line method is particularly valuable for circular or cylindrical forms. Thus, each of these methods has distinct applications but is not the best choice for developing the pattern for a gored elbow.