Archimedean Spiral

An Archimedean Spiral represents an Archimedes’ spiral in AN-SOF.

The Archimedean spiral is a planar spiral defined by the polar equation:

$\displaystyle r(\alpha) \,=\, r_0 \,+\, \frac{p}{2\pi} \; \alpha$

where $r_0$ is the starting radius, $p$ is the pitch, and $\alpha$ is the angle in the plane of the spiral, ranging from $0$ to $2\pi M$, with $M$ representing the number of turns.

The spiral’s starting radius is $r(0) = r_0$ and its ending radius is $r(2\pi M) = r_0 + pM$. Consequently, the pitch $p$ represents the constant spacing between consecutive turns. Additionally, the pitch is equal to the constant growth rate of the spiral radius $r(\alpha)$ per turn, expressed as:

$\displaystyle p \,=\, 2\pi \frac{dr}{d\alpha}$

Accessing the Archimedean Spiral Dialog Box

To open the Archimedean Spiral dialog box:

1. Navigate to Draw > Archimedean Spiral in the main menu.
2. The dialog box contains three tabs: Archimedean Spiral, Attributes, and Materials (Fig. 1).

Archimedean Spiral Tab: Setting Geometrical Parameters

Define the Archimedean spiral by specifying the following (Fig. 1):

• Start Point: Starting coordinates (X1, Y1, Z1).
• Start Radius: The initial radius of the spiral.
• Pitch: The constant spacing between turns (can be positive or negative).
• Number of Turns: This value does not need to be an integer, allowing for fractional turns.
• Orientation Angles: Sets the direction of the spiral axis using spherical angles (Theta, Phi).
• Rotation Angle: Rotates the spiral around its axis.

Attributes Tab

• Specify the Number of Segments and Cross-Section properties (refer to Wire Attributes).

Materials Tab

• Set the Resistivity and Coating properties of the wire (refer to Wire Materials).