Originally Posted by
corwin1968
I would go with:
Extremely Low - This would be low 20's down into the teens. For steep hills and strong headwinds.
Low - This would be low enough to tackle modest hills and headwinds.
Cruising - This would be a small gear-inch range in which I can comfortably ride in relatively flat terrain with little wind. Probably in the 60-75 gear-inch range for me.
High - This would be for modest downhills or tailwinds. Probably high 70's to 80's.
Very High - This would be for significant downhills or tailwinds.
Very helpful -- thanks! And I also like
cruising better than
medium.
Originally Posted by
Little Darwin
Also, reasonable for a rider, and for mathematical illustration is that the shifting the front is mostly to get you into the right range of gears, and shifting the rear is to fine tune your ride. However, I wonder if it might be a better way to teach ratios than gear inches specifically... (you could actually use either one, or possibly both, depending on your needs). You could even go as far as computing wheel circumference and ratios to calculate gear inches for specific tire and gearing selections.
Oh yeah. There's a lot of fun math in there. The spreadsheet I put together looks at the ratios themselves, the gear-inches, and the distance traveled per crank-revolution. The reason I wanted category boundaries is for creating graphs to compare the gearings of different bikes -- to look at which bike is better suited for different styles of riding. Traditionally, high school mathematics has spent a lot of time teaching students to create graphs but not so much time teaching them to use and interpret graphs. Fortunately, that is improving these days.
For me, I spend most of my time in the middle chainring, and only use the large ring when riding at higher speed (down hill or with a good tail wind), and the small ring for significant climbs.
And that's something else I'm looking at with these categories -- which bikes more readily lend themselves to that practice by having a nice variety of gearings on that middle ring.
You could use this method to help demonstrate how to achieve different ratios/gearings, and the show that there may be more than one way to get a certain ratio/gear inch value. This could also be used to show the value of a Venn diagram.
Good idea.
You should check out Sheldon Brown's gear calculator for different things his calculator produces. This could show a few other ideas of things that are relevant to some riders, and could provide good ideas for math instruction.
Thanks for the tip. That looks like a great site for this type of math.