Gear inches are still beyond my comprehension.
Dave
Gear inches first arrived with the original "penny-farthing" bike Dave. It was the diameter of the large wheel which, because the pedals and cranks were directly on that wheel, gave an indirect indication of how far the wheel would go for a single turn, though that needed to be multiplied by Pi (3.14) to give the actual number of inches travelled.
Of course that inch measure's real use was that it represented the gear ratio, since a larger wheel went further for a single pedal stroke than a smaller wheel, it was a higher gear and needed more effort than a smaller wheel turn.
When the "safety bicycle" (our modern type) was invented, the gear inches of the wheel needed to be multiplied by the up-gearing of the front to rear chain sprocket to give the same indication for comparison with the penny-farthings still in use. For example, if the bike had 25 inch wheels and the chainwheel had 45 teeth and the rear one 15 teeth, each turn of the pedals turned the wheel three times. Therefore the wheel diameter of 25" had to be multiplied by three to give the 75 inch gear that it had. In other words, it was like a penny-farthing with a 75 inch front wheel.
So to work out the gear inches on a particular gear of a derailleur bike, its just necessary to divide the chainwheel teeth by a particular rear sprocket number of teeth and multiply the result by the overall wheel diameter.
To do the same for a hub gear bike, one must first find the ratio comparisons of that hub gear. For example, the Nexus/Alfine 8 speed hub gears have these ratio steps up and down for the eight gears, fifth gear being direct drive:
1.615
1.419
1.223
1.000
0.851
0.748
0.622
0.527
To get the gear inches for a particular gear, just divide the chainwheel number of teeth by the rear sprocket number of teeth, multiply the result by the wheel overall diameter and then multiply that result by the ratio of the gear from that list for your hub gear.
For example, a Nexus 8 equipped 26" wheel bike with a 48 tooth chainwheel and 16 tooth rear sprocket would be this gear inch ratio in fourth gear:
48 divided by 16 = 3, then that 3 times the 26" wheel = 78, then that 78 times the 0.851 for the fourth gear = 66.378, a 66 inch gear.
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