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What is the Torque at the rear wheel in this gear setup ?

  1. Apr 17, 2014 #1
    Dear Experts

    A bicycle has the following gear setup. I like to get your advice what is the effective gearing and torque at the rear wheel that is being turned by a electric motor that is turning the whole gear set using a chain.

    There are 2 gear sizes : small gear and large gear. Their gear ratio is about 5:1.

    A electric motor is mounted onto the bicycle. It has a pinion gear of the small gear size.
    This gear is connected to a large gear mounted on the bottom bracket shaft.

    There is another small gear connected to the other end of this shaft. This is same size as the motor's pinion gear. This gear is connected to another big gear mounted on the rear wheel shaft via another chain.

    I am not sure what is the gearing effect at the rear wheel.

    I suspect, its like this :

    1. when the motor turns, its pinion gear turns the bottom bracket large gear at a stepped-down ratio of 5:1 increasing the torque by 5 times.

    2. The small gear at the opposite end of this large gear rotates at this stepped-down speed with this same torque even though the gear is smaller.

    3. The Rear wheel rotates at a even slower rate because of the gearing ratio of a further 5:1 increasing the rear wheel torque to be more than the torque at the large gear mounted on the shaft in the bottom bracket.

    Thanks for reading my question and hope to hear your advice.

    Have a nice day.

  2. jcsd
  3. Apr 19, 2014 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    The gear ratio is: 25:1

    Work it out this way: if the small gear has T teeth, the big gear has 5T teeth. So when the small gear turns twenty five complete revolutions (i.e. 25T teeth), the first big gear turns 5 revolutions (i.e. 25T teeth = 5 (5T) teeth). This means that the small gear to which the first gear is fixed also turns 5 complete revolutions (5T teeth). When the small gear turns 5 revolutions (5T teeth) the second large gear turns 5T teeth = 1 revolution.

  4. Apr 23, 2014 #3
    Thanks AM

    for confirming that my assumption is correct.

    I wish you have a nice day.
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