Archimedean Spiral

The Archimedean Spiral refers to the Archimedes’ spiral with polar equation r(α) = r₀ + p/(2π) α, where r₀ is the starting radius and p is the pitch. For a spiral with an integer number of turns, M, we have α = 2πM at its end point, so r_end = r₀ + pM, the pitch p being the separation between turns. Besides, we have that the pitch equals the constant growth rate of the spiral radius r(α) per turn, that is p = 2πdr/dα.

Go to Draw > Archimedean Spiral in the main menu to display the Draw dialog box for the Archimedean Spiral. This dialog box has three pages: Archimedean Spiral, Attributes, and Materials.

The Archimedean Spiral page

In the Archimedean Spiral page, the geometrical parameters for the Archimedean Spiral can be set, Fig. 1.

The Archimedean spiral is entered by giving the Start Point, Start Radius r₀, Pitch p (positive or negative) and Number of Turns M (complete turns and fractions of a turn can be set). The spiral lies on a plane given by the Orientation Angles Theta and Phi (normal to the plane in spherical coordinates) and can be rotated by setting a Rotation Angle, Fig. 2.

Once the geometrical parameters in the Archimedean Spiral page have been set, the Attributes > page can be selected, where the number of segments and cross-section can be set. The wire resistivity and coating can be set in the Materials > page.