Homework Help: precalc

Posted by syd on Tuesday, January 20, 2009 at 10:52pm.

a 21-speed bike has varying top speeds dependent on the gear it's in. the bike's tire diameter is 26 inches. the bike can pedal at a maximum of 130 revolutions per minute. the front chain wheel has sprokets of 24, 32, and 40 teeth. the rear cassette sprokets have 28, 24, 21, 18, 16, 14, 12 teeth. the bike's gears are labeled 1-21. gears 1-7 associated with the smallest front chain wheel's sproket. clearly communicate the top speed (in miles per hour) in each gear.

precalc - drwls, Wednesday, January 21, 2009 at 7:09am
The fastest speed of the bike at a fixed pedal speed is achieved at the highest front/back sprocket or "gear" ratio of 40/12. Multiply that by 120 rev/min and pi*Diameter to get the top speed
(130 rev/min)*(40/12)*pi*(26/12 feet) = 2949.6 ft/min = 49.2 ft/s = 33.5 miles/h

Speeds with other gear combinations can be calculated similarly. The lowest speed is
(130 rev/min)*(24/28)*pi*(26/12 ft) = 758.5 ft/min = 8.6 mph at the same pedal speed. The actual speed will be slower still if the rider reduces the pedal rpm, as most riders do in the lowest gear

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