Searching for Geometric Ratios

The 13-31 block could have been exceeded, but at the expense of the evenness of the gearing. For example, compare the wider ratio 13-34 block:

sprkts ideal

13

16.532

21.024

26.736

34

sprkts integer

13

17

21

27

34

delta squared

0.0%

21.9%

0.1%

7.0%

0.0%

error =

0.54

to the one that I selected:

sprkts ideal

13

16.15

20.07

24.95

31

sprkts integer

13

16

20

25

31

delta squared

0.0%

2.4%

0.6%

0.3%

0.0%

error =

0.18

The root-mean-square error is three times larger with the 13-34 combination, so it will give much less even gearing,