Dimensions of a Stranded Wire

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A wire strand consists of a central core wire with a number of helical wires wrapped around it. Its principal characteristics are the helix (or winding) angle and the radius of the wires.


The perpendicular cross sections of the helical wires are kidney shaped. The total surface area of these cross sections is an important parameter influencing the strength, flexibility, and so on of a wire strand.

This Demonstration plots the cross section of a wire strand with between five and eight wires and computes the surface areas of the section of the outer wires. The wire diameters are computed to make a closest fit between the helical wires and maximize the surface area of the cross section for the given helical angle.

You can see that the circle passing through the centroids of the cross sections does not coincide with the circle passing through the points of tangency of the wires.

On the right, a 3D view of the core wire and one of the outer helical wires is shown.


Contributed by: Erik Mahieu (July 2015)
Open content licensed under CC BY-NC-SA



A helical cylinder with radius and helix angle can be described in parametric coordinates, as functions of and :

where is the helix radius, is the helix angle, and is the cylinder radius.

The cross section of a helical cylinder with the horizontal is given in terms of the parametric coordinate , with the helix radius taken to be 1:

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