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Sturmey-Archer AC[1]
  Number of gear teeth         Number of gear teeth            
Gear Sun Gear 1 Pinion to Sun 1 Pinion to Ring 1 Ring gear 1 1=R to P, P to S 2=Direct, 3=P to R   Gear Drive Ratio Stage 1 drive ratio as fraction Gear drive ratio modified Sun Gear  2 Pinion to Sun 2 Pinion to Ring 2 Ring gear 2 Path: 1=R to P, 2=Direct, 3=P to R Gear Drive Ratio Stage 2 drive ratio as fraction Total Drive Ratio Total drive ratio as fraction Ratio incre- ment
1 20 20 20 60 1 0.750    3/4  -0.250 20 20 20 60 1 0.750    3/4  0.923[2]   12/13  
2 20 20 20 60 2 1.000 1          20 20 20 60 2 1.000 1        1.000 1        1.083
3 20 20 20 60 1 0.750    3/4  -0.188[3] 20 20 20 60 3 1.333 1   1/3  1.067[4] 1   1/15 1.067
[1]
John Allen:
Tooth counts verified:
https://hadland.files.wordpress.com/2012/07/1theory.pdf
https://hadland.files.wordpress.com/2012/07/2tables.pdf
[2]
John Allen:
This is the final gear ratio after the second stage, reflecting the rotation of its sun gear by the first stage.
[3]
John Allen:
This is the decrease in the rate of rotation of the stage 2 gear ring due to the rotation of the stage 2 sun gear. It is the first-stage gear ratio, multiplied by the ratio of the second stage sun gear to the second-stage ring gear and accounting for the reversal of direction due to the second-stage planet gears.
[4]
John Allen:
This is the final gear ratio after the second stage, reflecting the rotation of its sun gear by the first stage.