To determine which sprocket should be used to achieve the most distance in one pedal stroke, we need to consider the gear ratio of each combination and calculate the distance covered by each.
First, let's calculate the gear ratio for each sprocket:
Gear ratio = Number of teeth on the front crankshaft / Number of teeth on the rear sprocket
For the 20-tooth rear sprocket:
Gear ratio = 40 teeth / 20 teeth = 2
For the 16-tooth rear sprocket:
Gear ratio = 40 teeth / 16 teeth = 2.5
For the 12-tooth rear sprocket:
Gear ratio = 40 teeth / 12 teeth = 3.33 (rounded to two decimal places)
The gear ratio represents the number of wheel rotations for one full rotation of the crankshaft. To calculate the distance covered in one pedal stroke, we need to consider the circumference of the rear wheel.
Circumference of the wheel = π * diameter
Circumference = 3.14 * 60 cm = 188.4 cm (rounded to one decimal place)
Now, suppose one full rotation of the crankshaft is performed, we need to calculate how much distance is covered for each sprocket:
Distance covered = Gear ratio * Circumference
For the 20-tooth rear sprocket:
Distance covered = 2 * 188.4 cm = 376.8 cm or 3.77 meters
For the 16-tooth rear sprocket:
Distance covered = 2.5 * 188.4 cm = 471 cm or 4.71 meters
For the 12-tooth rear sprocket:
Distance covered = 3.33 * 188.4 cm = 627.012 cm or 6.27 meters (rounded to two decimal places)
Therefore, the sprocket with 12 teeth should be used to achieve the most distance in one pedal stroke, covering approximately 6.27 meters.