If a bicycle has a crankshaft of 40 teeth, and there are three rear sprockets attached to the rear wheel, 20 teeth, 16 teeth and 12 teeth. The diameter of the rear wheel is 60 cm. Which sprocket should be used to get the most distance in one paddle? What would the distance be?
To determine which sprocket will result in the most distance in one pedal stroke, we need to consider the gear ratios.
The gear ratio is calculated by dividing the number of teeth on the front crankshaft sprocket by the number of teeth on the selected rear sprocket.
Let's calculate the gear ratios for each of the three rear sprockets:
- For the 20-tooth sprocket: Gear ratio = 40 (teeth on crankshaft) / 20 (teeth on rear sprocket) = 2
- For the 16-tooth sprocket: Gear ratio = 40 / 16 = 2.5
- For the 12-tooth sprocket: Gear ratio = 40 / 12 = 3.33
As we can see, the 12-tooth sprocket has the highest gear ratio, meaning it will result in the most distance covered in one pedal stroke.
To calculate the distance traveled in one pedal stroke, we can use the formula:
Distance = Circumference of the wheel x Gear ratio.
The circumference of the wheel can be calculated as:
Circumference = π x Diameter
where π is a mathematical constant approximately equal to 3.14159.
Let's calculate the distance traveled using the 12-tooth sprocket:
Circumference = 3.14159 x 60 cm = 188.495 cm
Distance = 188.495 cm x 3.33 (gear ratio) = 627.25635 cm or approximately 6.27 meters.
Therefore, using the 12-tooth rear sprocket will result in covering the most distance in one pedal stroke - approximately 6.27 meters.