# Circular slide rule

I explained the basics of how a slide rule works in the previous post. But how does a circular slide rule work?

Apparently the prop Mr. Spock is holding is an E6B aircraft slide rule. It includes a circular slide rule and more functionality.

Start with an ordinary straight slide rule, with each bar labeled 1 on the left and 10 on the right end. Now imagine bending this into a circle so that you now have two concentric circles. For x between 1 and 10, the label for x is located at

log10 x × 360°.

Suppose you want to multiply x and y, and xy is less than 10, i.e. log10 x + log10 y < 1. Then the multiplication procedure works exactly analogously to how it would have with a straight slide rule. Line up the 1 of the inner ring with the position of x on the outer ring. The position of y on the inner ring lines up with xy on the outer ring because it is at position

log10 x × 360° + log10 y × 360° = log10 xy × 360°.

But what if xy > 10, i.e. log10 x + log10 y > 1? In that case the y on the inner ring is at position

(log10 x + log10 y) × 360°− 360° = (log10 x + log10 y − 1) × 360°

which is equal to

(log10 x + log10 y − log10 10) × 360° = log10 (xy/10) × 360°

and so the y on the inner ring is aligned with the position labeled xy/10. As we noted in the previous post, slide rules only give you the significand (mantissa) of the result, so a slide rule doesn’t know the difference between xy and xy/10. That’s up to you to keep up with.

## E6B Flight Computer

Update: After first posting this article, I bought an E6B flight computer from Amazon for about \$14. I bought the paper version because I’m certainly not going to wear it out. But if you’d like a nicer one, they make the same product in metal.

Here’s a photo of mine:

You can slide the horizontal piece out and essentially have a circular slide rule with some extra markings.

## 2 thoughts on “Circular slide rule”

1. John S.

The writers obviously thought it would make Spock look intelligent to TV viewers of the era, but how strangely anachronistic it seems now for a 23rd-century science officer to be using a slide rule.