At Hoffman Laboratories, we were manufacturing some of our own inductors. These coils were basket-wound. Basket winding presents an interesting trigonometric problem.
For n (actually n + delta) revolutions, there are m cycles (to and fro) of linear-throw of the wire, thread, or rope, etc. Let R be the radius of the basket. Let w be the width of the basket (actually, the altitude of the cylinder). Let d be the diameter of the wire -- measure it very carefully with a micrometer. The delta is positive for an over-thrown basket or negative for an under-thrown basket. This delta is small, in magnitude, compared to one.
Then, the slope-angle theta is given by
tan(theta) = (n + delta) 2 pi R / (2 m w)
We may draw a pair of small triangles, with a common side u. Then
sin(theta) = d / u
and
tan(theta) = 2 pi R delta / u
Division yields
cos(theta) = d / (2 pi R delta)
Now, the solution proceeds as follows
Begin with delta = 0.
Iterate
tan(theta) = (n + delta) pi R / (m w)
sec(theta) = sqrt(1 + (tan(theta))^2)
delta = +- (d / 2 pi R) sec(theta)
for two or three cycles -- until delta stabilizes to a reasonable precision. Then express the ratio
(n + delta) / m
as a fraction. This is the required gear-ratio for the winding lath.
An extreme example of a basket weave -- called bobbin weave -- is a bobbin of thread. It has n very large and m equal to one. A bobbin weave is not self-supporting -- it requires flanges. Spools of twine or string usually are wound with a basket weave. So are inductor coils. To be self-supporting (that is, to be stable without any flanges), neither n nor m may be one. The n should be greater or equal to m/2. Any pair of small natural numbers may be used for n and m. An over-throw is more stable than an under-throw. Ratios of 2/3 or 3/2 are popular. 3/5 or 5/3 are more stable. 5/7 or 7/5 look elegant. The greater the ratio of R/d, the larger the natural numbers for n and m may be. As you see, it is very much an art.
copyright 1999 by R. I. 'Scibor-Marchocki
last revised on Monday 22-nd November 1999.