Calculating Fluke: Subtract A or R?

Edwardy · Apr 13, 2023

I need to calculate fluke.
Why do I in the first picture, when calculating the height, subract a from r, while in the other one, I subract r from a?
What does that depend on?
*I didn't translate the text because it is long and would take me a lot of time to do, but I will do it if it's neceserry.

Printed diagram of a toroid cross-section with two materials, labelled μ1 and μ2, and dimensions r, a, h, dr and 2a, followed by a red-boxed equation h/2a = (r-2a)/a, so h = 2(r-2a).

Cross-section of a toroid with a triangular cross-section, showing labels N, I, mu1, mu2, dr, r, a and 2a, with a dashed-line triangle and the equation y/2a = (2a - r)/a, y = 2(2a - r).

TSny · Apr 13, 2023

Edwardy said:

Why do I in the first picture, when calculating the height, subract a from r, while in the other one, I subract r from a?
What does that depend on?

In one case, ##\mathbf{2}a## is subtracted from ##r##. In the other case, ##r## is subtracted from ##\mathbf{2}a##.

The reason for the difference is that the geometry is different for the two cases. But, in each case you use similar triangles to set up the relations.

For the first case you have the figure

Two side-by-side diagrams: left shows a magnetic circuit with H1 and H2 and permeabilities mu1 and mu2; right shows a geometry sketch with points A, B, C, D, E, F, dimensions r, dr, 2a and a.

The triangles ABC and DEC are similar. Note that the length of red segment CF is ##r - 2a##.

For the second case you have the figure

Diagram of a toroid with a winding labelled N, I and two regions marked mu 1 and mu 2, with an inset cross-section showing points A, B, C, D, E, a width a and height 2a.

The triangles ABC and DEC are similar. Note that the length of EC is ##2a - r##.

Calculating Fluke: Subtract A or R?

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