Note - You need to have the Tcl plugin installed. It can be downloaded from the Tcl Developer Xchange website .
This application computes the effect of different gear combinations. One way to visualize this is to think of replacing your modern bicycle with an old fashioned "ordinary" bike that has a large diameter front wheel and the pedals connected right to the front axel. In those bikes, the mechanical advantage comes from the wheel diameter. The larger the wheel the more power, but the harder it is to pedal.
The graph displays the effective wheel diameter for each gear combination. The horizontal lines correspond to the different gears up front (at the pedals). The points on each line correspond to each gear in the gear cluster at the back wheel. The values are the effective wheel diameter.
To use the application, just enter numbers and press the Recompute button. Just pressing Return in a text entry causes the graph to update, too. If you move the mouse over the graph, the specific values for the point under the mouse cursor are displayed.
The graph tells you the shift sequence that lets you use your gears effectively. As you ride along, if a hill becomes steeper, you want to know the derailleur positions for the next lower gear. Similarly, if the hill starts to level out, you want to know the positions for the next higher gear. In the initial chart displayed when you load (or reload) this page, the combination of the middle front sprocket and the smallest rear gear gives you an effective wheel diameter of 69 inches (move the mouse cursor over the rightmost point on the middle line to check this out). The next lower gear is 64 inches, which you get by using the large front sprocket and the fourth smallest rear gear. The next lower gear doesn't use the middle sprocket!
The gear ratio graph also makes it easy to tell how well spaced out your gears are. Notice in the initial chart that several derailleur positions have the same or nearly the same gearing. This 27-speed bike really has about 25 gears. Of these 25 gears, only about 18 should be used on a regular basis so as to avoid cross-gearing which laterally flexes the chain at extreme angles causing premature drivetrain wear. As a rule-of-thumb, you should avoid using the lower half of the rear cassette/cluster when in the inner ring (front sprocket) and the upper half when in the outer ring. You can buy real gear clusters and front sprockets to space out the gears more evenly. The gear chart application makes it easy for you to experiment with different gear combinations.