# Plotting the Logarithmic Scale

Slide rules, once figure out how to use them, have a near magical power to them. How can such a simple idea as two rulers become such a powerful calculating tool?

I knew that slide rules had a long history on pilots watches.  These are typically set up for specialized navigational calculations.  I wanted to create a general purpose slide rule that could help people discover the fascinating power of a slide rules.

To create the scales, I used Excel to calculate a set of values for the indexes that I then converted to degrees which I used to plot guide lines in AutoCAD.

For the whole number scale I used formulas like this: LOG(2)*360 = 108.37 degrees.  The mark for 2 is on a line rotated 108.37 degrees clockwise from the 12 position.

For the next set of markers, the first decimal place, I used formulas like this: (LOG(21)-1)*360=116.00 degrees. the mark for 2.1 is on a line rotated 116.00 degrees clockwise from the 12 position.

Similarly, I  could continue with finer graduations:(LOG(211)-2)*360=116.74 degrees.  The line for 2.11 is on a line rotated 116.74 degrees clockwise from the 12 position.

I then used these values to to plot the guides on my CAD file like this:

I’ve used software to design this device that pre-dates computers. In a future post, I will explore a way to create the scale using only pencil, paper and a drafting table!