chapter 7 the spirule

  Joined at the hip at the birth of root locus was a need for an aid to designers to sum angles and multiply the distances from a trial point “p” on the complex plane to other fixed points. Evans’ own classroom notes describe his initial approach: transparent overlays held together with a thumbtack: “Place a transparent sheet on top of the diagram, draw the red line for reference, stick a thumbtack through at the guess point to serve as a pivot.”

One of Evans’ colleagues (and a student in Evans’ servo class) was Jeff Schmidt. Schmidt’s assignment in the summer of 1948 was to design an analog autopilot for the NATIV missile. It had to work without adjustment throughout the changing mass and center of gravity during the launch phase. Schmidt (on right) was stymied until Evans presented root locus. In 2003, he recalled.

“When Walt first started discussing root locus in his class I saw a ray of hope. While the problem was still very difficult, I could at least get a feel for what I was trying. As more people started to use Walt’s method, many ideas for automating the plot were thought of. I was looking for something better than (Evans’) transparent paper to add angles. I went over to the engineering shop and made an “angle adder” out of a circle of plexiglass with a straight arm held on with a small bolt. This worked much better than the transparent paper for determining the locus, but I still had to measure lengths and multiply them to get loop gains. Walt and I were kicking this problem around one day and we came up with the idea of adding a logarithmic spiral to my angle adder. This worked well and became the first spirule. I applied for a patent but the company decided a copyright was more appropriate.” 

The Name: The spiral shaped curve was key to simultaneously using the principles of a linear slide rule (i.e., multiplication by addition of logarithms) and performing the addition with the circular protractor. DeWitt Lyon(left), colleague of Schmidt and Evans, looked at the spiral curve on Schmidt’s device and coined the name “Spirule” as a contraction of “spiral” and “slide rule”.