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Sturmey-Archer AR[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 15 20 20 54 1 0.783   18/23 -0.261 20 20 20 60 1 0.750    3/4  0.932[2]   69/74  
2 15 20 20 54 2 1.000 1          20 20 20 60 2 1.000 1        1.000 1        1.072
3 15 20 20 54 1 0.783   18/23 -0.196[3] 20 20 20 60 3 1.333 1   1/3  1.072 1   5/69 1.072
[1]
John Allen:
Tooth counts verified:
http://www.users.globalnet.co.uk/~hadland/1theory.pdf
http://www.users.globalnet.co.uk/~hadland/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.