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Up: Table of contents Description of reverse-engineering procedure
Sturmey Sprinter 7 assuming simple planetary in 2 and 6[1]
  Number of gear teeth Drive path Ratios  
Shifter Position Sun Gear 1 Pinion meshing with sun  Pinion meshing with ring Ring gear 1=R to P, 2=Direct, 3=P to R Drive ratio as fraction Drive ratio from bro- chure Ratio incre- ment
1 30 12 16 60 1    3/5  0.600 0.600  
2 27 16 16 60 1   20/29 0.690 0.690 1.149
3 21 23 16 60 1  115/143 0.804 0.804 1.166
4 21 23 16 60 2 1        1.000 1.000 1.243
5 21 23 16 60 3 1  28/115 1.243 1.243 1.243
6 27 16 16 60 3 1   9/20 1.450 1.450 1.166
7 30 12 16 60 3 1   2/3  1.667 1.667 1.149
Tooth counts for this hub were reverse-engineered. See description for the Torpedo 7-speed to see how this is done. Only tooth counts shown in red in the table here were entered manually for the reverse engineering. The formula used in this process is in the cell in the top row for the 12-tooth planet gear, in the Excel version of this page, This formula solves for the planet gear when the hub's highest ratio is known. Because of rounding of the decimal ratio from the product brochure, calculation for the 23-tooth planet gear did not come out exact. I revised the result, and so, in the Excel file, you will find no formula for the 23-tooth gear. The surprise in this worksheet is the exact ratio of 115/143 rather than 37/46. Both round to the same decimal numbers.

[1]
John Allen:
Calculated but almost certainlly correct, as planet gears fit -- 27+16+16=59, 27+16=43, 30+12=42, 21+23=44.