Most of the Spiral slide rule patents featured some features to support “turn counting” in their design.
With any calculation on a spiral slide rule, the user must have some means to determine which turn of the spiral the answer lies.
Conceptually, the problem is simple; just keep tabs on the radial distances of the numbers in the computation and add (subtract) them to obtain the location of the answer.
Suppose a multiplication: a*b is being performed on a slide rule with an Archimedean spiral scale.
One cursor "A" is set to 1, and the second cursor "B" is set to the number 'b'. This stores the logarithm of 'b' as a constant angle between the two cursors, with a radial distance R1 represented by the turns that 'b' is on.
Then the pair of cursors are locked and rotated until the value of 'a' is under cursor "A", at a radial distance R2 represented by the turn that the 'a' value is on.
Cursor B now points to the answer, which is on the turn that is located on the turn whose radial distance is equal to the sum of the original radial distances R1 and R2, or the sum of the turn counts of 'a' and 'b'.
As with any single cycle scale, this sum might be greater than the total number of turns on the spiral; the answer is 'off-scale', just as might happen with a linear slide rule. The operator must subtract the total number of turns to find the turn that the answer is on.
Hence, to find the correct answer on a spiral scale calculation, the operator needs the means to keep a tally of the radial distances of all numbers in a computation. I'm calling that concept "turn counting" in this section.