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.
I will do one of the combinations for you
front: 40 teeth
back wheel: 12 teeth
(this will be the gear that can produce the highest speed)
for each turn of the front sprocket the back wheel will turn 40/12 or 10/3 or 3 1/3 times
each revolution of the back wheel covers
2(26)pi inches or 163.3628 inches
so at 130 rpm of the front sprocket, the back will will cover
130(10/3)163.3628 inches/minute
= 1.117275 miles/min (I divided by 5280*12)
~= 67 mph (I multiplied by 60)
you do the rest,
can you see the only part that would change ???
I think Reiny used the rire diameter for the radius, so the speed is two tiomes too high.
This question was posted and answered previously
See your other post at http://www.jiskha.com/display.cgi?id=1232509956
To calculate the top speed in each gear of a 21-speed bike, we need to consider the gear ratio, tire diameter, and pedal revolutions per minute (RPM). The gear ratio is the ratio of the number of teeth on the front chain wheel to the number of teeth on the corresponding rear cassette sprocket.
First, we need to calculate the gear ratios for each gear. Let's start by calculating the gear ratios for gears 1-7, associated with the smallest front chain wheel's sprocket.
Gear 1: Front sprocket = 24 teeth, Rear sprocket = 28 teeth
Gear Ratio = Front Teeth / Rear Teeth = 24 / 28 = 0.857
Gear 2: Front sprocket = 24 teeth, Rear sprocket = 24 teeth
Gear Ratio = Front Teeth / Rear Teeth = 24 / 24 = 1.0
Gear 3: Front sprocket = 24 teeth, Rear sprocket = 21 teeth
Gear Ratio = Front Teeth / Rear Teeth = 24 / 21 = 1.143
Gear 4: Front sprocket = 24 teeth, Rear sprocket = 18 teeth
Gear Ratio = Front Teeth / Rear Teeth = 24 / 18 = 1.333
Gear 5: Front sprocket = 24 teeth, Rear sprocket = 16 teeth
Gear Ratio = Front Teeth / Rear Teeth = 24 / 16 = 1.5
Gear 6: Front sprocket = 24 teeth, Rear sprocket = 14 teeth
Gear Ratio = Front Teeth / Rear Teeth = 24 / 14 = 1.714
Gear 7: Front sprocket = 24 teeth, Rear sprocket = 12 teeth
Gear Ratio = Front Teeth / Rear Teeth = 24 / 12 = 2.0
Now that we have the gear ratios, we can calculate the top speed (in revolutions per minute) for each gear. To do this, we multiply the gear ratio by the pedal RPM.
Top Speed (RPM) in Gear 1 = Gear Ratio * Pedal RPM = 0.857 * 130 = 111.41 RPM
Top Speed (RPM) in Gear 2 = Gear Ratio * Pedal RPM = 1.0 * 130 = 130 RPM
Top Speed (RPM) in Gear 3 = Gear Ratio * Pedal RPM = 1.143 * 130 = 148.59 RPM
Top Speed (RPM) in Gear 4 = Gear Ratio * Pedal RPM = 1.333 * 130 = 173.33 RPM
Top Speed (RPM) in Gear 5 = Gear Ratio * Pedal RPM = 1.5 * 130 = 195 RPM
Top Speed (RPM) in Gear 6 = Gear Ratio * Pedal RPM = 1.714 * 130 = 222.82 RPM
Top Speed (RPM) in Gear 7 = Gear Ratio * Pedal RPM = 2.0 * 130 = 260 RPM
To convert the top speeds from RPM to miles per hour, we need to know the circumference of the tire. Assuming the tire diameter is 26 inches, we can calculate the circumference using the formula: Circumference = π * Diameter.
Circumference = 3.14 * 26 inches = 81.64 inches
Now we can convert the top speeds from RPM to miles per hour. The formula for this conversion is: Speed (mph) = (Circumference * Top Speed) / (12 * 5280)
Top Speed (mph) in Gear 1 = (81.64 * 111.41) / (12 * 5280) = 7.59 mph
Top Speed (mph) in Gear 2 = (81.64 * 130) / (12 * 5280) = 8.88 mph
Top Speed (mph) in Gear 3 = (81.64 * 148.59) / (12 * 5280) = 10.10 mph
Top Speed (mph) in Gear 4 = (81.64 * 173.33) / (12 * 5280) = 11.84 mph
Top Speed (mph) in Gear 5 = (81.64 * 195) / (12 * 5280) = 13.32 mph
Top Speed (mph) in Gear 6 = (81.64 * 222.82) / (12 * 5280) = 15.16 mph
Top Speed (mph) in Gear 7 = (81.64 * 260) / (12 * 5280) = 17.72 mph
Therefore, the top speed in each gear of a 21-speed bike with a 26-inch tire diameter and a maximum pedal RPM of 130 is as follows:
Gear 1: 7.59 mph
Gear 2: 8.88 mph
Gear 3: 10.10 mph
Gear 4: 11.84 mph
Gear 5: 13.32 mph
Gear 6: 15.16 mph
Gear 7: 17.72 mph