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Sachs Elan[1]                                        
          Number of gear teeth                                
Gear Sun Gear  1 Pinion to Sun 1 Pinion to Ring 1 Ring gear 1 Sun Gear 2 Pinion to Sun 2 Pinion to Ring 2 Ring gear 2 Path: 2=Direct, 3=P to R Stage 2 Gear Drive Ratio Stage 2 drive ratio as fraction Sun Gear  3 Pinion to Sun 3 Pinion to Ring 3 Ring gear 3 Path: 2=Direct, 3=P to R Stage 3 Gear Drive Ratio Stage 3 drive ratio as fraction Total Drive Ratio[2] Total drive ratio as fraction Ratio incre- ment Mfr ratio Num denom check
1 88 13 13 114         2 1.000 1           38 29 29 97 3 1.392 1  38/97 0.698  203/291      0.697
2 88 13 13 114         2 1.000 1           27 42 29 97 3 1.192 1  64/333 0.852  10987/12901  1.221 0.851
3 88 13 13 114         2 1.000 1                   2 1.000 1        1.000  1/1      1.174 1.000
4 88 13 13 114 36 32 21 87 3 1.272 1   63/232  38 29 29 97 3 1.392 1  38/97 1.179  1512035/1282728 1.179 1.179 1512035[3] 1282728[4] 0.000000000000000
5 88 13 13 114 36 32 21 87 3 1.272 1   63/232  27 42 29 97 3 1.192 1  64/333 1.333  3989143/2993032 1.131 1.333 3989143[5] 2993032[6] 0.000000000000000
6 88 13 13 114 36 32 21 87 3 1.272 1   63/232          2 1.000 1        1.481  6529/4408   1.111 1.481 6529[7] 4408[8] 0.000000000000000
7 88 13 13 114 45 21 21 87 3 1.517 1   15/29   38 29 29 97 3 1.392 1  38/97 1.614  258808/160341 1.090 1.612 258808[9] 160341[10] 0.000000000000000
8 88 13 13 114 45 21 21 87 3 1.517 1   15/29   27 42 29 97 3 1.192 1  64/333 1.768  661518/374129 1.095 1.766 661518[11] 374129[12] 0.000000000000000
9 88 13 13 114 45 21 21 87 3 1.517 1   15/29           2 1.000 1        1.917  1056/551    1.084 1.915
10 88 13 13 114 51 16 21 87 3 1.769 1  357/464  38 29 29 97 3 1.392 1  38/97 2.061  5287177/2565456 1.075 2.061 5287177[13] 2565456[14] 0.000000000000000
11 88 13 13 114 51 16 21 87 3 1.769 1  357/464  27 42 29 97 3 1.192 1  64/333 2.215  13258869/5986064 1.075 2.217 13258869[15]  5986064[16] 0.000000000000000
12 88 13 13 114 51 16 21 87 3 1.769 1  357/464          2 1.000 1        2.363  20835/8816   1.067 2.364 20835[17] 8816[18] 0.000000000000000
Step Ratio Formula
1 0.698 decrease, simple
1 0.698 decrease, simple as compound
2 0.852 decrease, compound
9 1.917 increase, simple
12 2.363 increase, compound
10 2.061 mixed
11 2.215 total
2.215 total, with refs
[1]
John Allen:
This is the most complicated internal-gear hub I know of.
[2]
John Allen:
This is the final drive ratio, the product of the ratios of all three stages.
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