Logarithmic Spiral

The Logarithmic Spiral refers to a spiral with polar equation r(α) = r₀ exp(bα), where r₀ is the starting radius (r at α = 0), b = p/(2πr₀) and p is the starting pitch, that is, the derivative 2πdr/dα at α = 0 (starting growth rate of the spiral radius r(α) per turn). The first two terms of the Taylor expansion r(α) = r₀ + p/(2π) α + r₀(bα)²/2 + … give the polar equation of an Archimedean spiral.

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

The Logarithmic Spiral page

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

The logarithmic spiral is entered by giving the Start Point, Start Radius r₀, Start Pitch p (positive or negative) and Number of Turns (complete turns and fractions of a turn can be defined). 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 Logarithmic 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.