Superlesson
Project 3-2
Geometry
Chapter 3, Angles and Parallel Lines
Gears are a crucial component of many mechanical devices. One of these devices that you may be familiar with is the bicycle. The combination of gears on a bicycle determines whether you can easily climb a steep hill or speed along a level road. In this exercise, you will first examine the basic principles of bicycle gears. Next, you will learn how to determine the order of gears on a bicycle from the lowest gear (the one you use to ride up a steep hill) to the highest gear (the one you use on a level or downhill road).
Part C, Making Connections
1. First, let's get acquainted with the bicycle and its gear vocabulary. Either get your own bicycle or go to the Bicycle Web site to see a picture of a bicycle.
a. Sketch a picture of a bike, paying close attention to detail on the front and rear gears.
b. Explain how pedaling a bicycle results in the bicycle's wheels turning.
c. Based on your own bicycle and/or the bicycle you saw in the picture, are the gears in the front or the gears in the back of a bicycle generally larger?d. Why would this difference in size between the front and the rear gears make pedaling a bicycle more efficient?
e. If you were going to try to pedal up an extremely steep hill, how do you think you should position the chain on the front chain-rings and back cogs (the series of teeth on the edge of a gearwheel)? Why?
2. Now, go to the Gears Web site, and read some basic information about bicycle and other types of gears.
a. The gears on a bicycle are sometimes called chain-rings and cogs. On your sketch above, label the chain-rings and cogs.
b. In this article, the author describes how to make a gear chart for a bicycle. What is the purpose of making this gear chart?
c. Read through the author's example for creating a gear chart for a ten-speed bicycle. Note that "gear-inches" are a way to indicate how high or low a gear is. You calculate gear-inches by taking the gear ratio (number of front teeth divided by number of back teeth) and multiplying it by the wheel diameter. Does a large number of gear-inches mean it is easier or harder to pedal the bicycle?d. At one point in the article, the author says, "I essentially have only 6 different gears." (He may have made a slight mistake, and meant 7 different gears.) In any case, why does he say this?
e. Now, you get to create a gear chart for your own bike. Use the instructions at this web site to create your gear chart. First, make a chart showing gear-inches for each gear combination. Second, make a chart ranking the gears from 1 to 10 (or the number of gears you have on your bike), where first gear has the fewest gear-inches. Finally, make your gear chart listing the gear, the chain-ring for each gear, the cog for each gear, and a possible use for each gear.If you do not have a bike available, you can use the following data:
- -3 chain rings with 38, 44 and 50 teeth
- -5 cogs with 14, 18, 22, 26, and 32 teeth
- -wheel diameter: 26 inches
[Note that this bicycle has 15 gear combinations, so the first two tables will have five rows and three columns each.]
3. Now, go to Gear Inch & Shifting Pattern Web site. This site will give you some additional information about a bicycle's gears if you give it the number of teeth on each chain-ring and free-wheel (or cog) and the diameter of the wheel. Enter the data for your bicycle or the sample data given above onto this web page.
a. Which gear combination gives you the shortest distance traveled in a single pedal rotation?
b. Which gear combination gives you the longest distance traveled in a single pedal rotation?
c. Explain why the lowest gear on a bicycle gives the shortest distance traveled and the highest gear gives the largest distance traveled in a single rotation of the pedal.