AU Tiger

In the process of researching bikes, I became very interested in the concept of gear inches… probably because I’m a math teacher, and I’m always looking for practical examples of how to use math. So my question is more for that purpose than it is for the purpose of choosing a bike. (I’ve pretty much settled on the Giant Escape 2.)

My question is this: if you had to categorize gear inches into five categories, what would the boundaries between those categories be? The categories I’m thinking of are very low (going up a steep hill), low (going uphill), medium (relatively flat grade), high (going downhill), very high (going down a steep hill). Of course there are other purposes for those gearings, but I’m just throwing those out there as a guide. This is based on your opinion, anyway, so I’m not looking for a hard-and-fast rule here… just a reasonable idea so that when I use this example in class, it is somewhat realistic. Oh, and since this is the hybrid forum, think in terms of the type of riding you do on a hybrid bike. (I’m guessing I’d get different answers in the road bike or mountain bike forums.)

Thanks in advance!

AU Tiger

Not quite how I was thinking about it, but interesting anyway. This is all brand new to me, so it's no surprise that it doesn't quite fit into the box I had in mind.
Besides, I'll take what I can get. This forum doesn't seem to get quite as much activity as the photography forum I spend time on. Maybe because digital photography involves a good bit of time on the computer, whereas biking does not. Either way, thanks for the response.

FamilyMan007

I admire your objective of trying to teach math from a practical perspective that children can relate to.

I hesitate to provide input due to my limited experience, but here goes as a 'strawman' for more knowledgeable cyclists to shoot down:

Background:
~ my bike has an overall range of 28 - 111 inches;
~ I started my re-introduction to cycling with an upright stance and thus head wind makes a major difference to me (perhaps less so as gradient increases, not that my area has any really 'steep' hills);
~ my middle front crank provides a gear range of 37 - 87 inches, and with limited hills in my area I fancy I could restrict myself to that range for nearly all my riding)
~ degree to which one trades off cadence/muscular strength (at 67 yrs old, I am tending to increase emphasis on cadence);
~ speed one is aiming for (in my case my absolute max is about 50kph and I only hit that briefly going down a steeper stretch just for fun, otherwise rarely exceed 30kph; and average is in range 20-24kpm unless riding with better half when it is 15-20kph);
~ climbing style (biggest area for me to understand - normal routes provide very little exposure to hills)
~ how tired I am, including how long have I been riding that day.

Suggested ranges which could be a start point for your objective
Steep down hills 95+
Downhill 70 - 95
Flat 50 - 75
Uphill 40 - 55
Steep up hills 25 - 40 (no exposure to date, but even walking ? )

This website Mike Sherman's Bicycle Gear Calculator has great info on gear ratios, speed etc

Best wishes

Bill Kapaun

I'm 66 and simply don't sprint on the down hills. I rest for the uphills.
I get from point A to B quicker that way.

AU Tiger

Well, you're definitely more knowledgeable than I am, so I appreciate the input.
And thanks for the kind words regarding teaching. The way I see it, I have to spend too much time teaching them a lot of math they'll probably never really need... so it's nice whenever I can to show them the useful stuff.

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.


I spend almost all of my time in the middle and foresee occasionally needing the lower gears. I don' foresee much need for the higher end of the spectrum. In fact, I try my best to ride my bike as a single-speed, only shifting when absolutely necessary. I used to shift with every little change in elevation or wind but now I find it more satisfying to simply work a little more by spinning faster or mashing harder.

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.

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.

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.

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.

AU Tiger

Very helpful -- thanks! And I also like cruising better than medium.

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.

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.

Good idea.

Thanks for the tip. That looks like a great site for this type of math.

Wanderer

Where I actually started using math, was building motorbikes back in the 60s. Trying to figure out gear ratios, to calculate possible speeds........... Used it a lot, since that time.

You know, RPM with a given size pulley, to another given (variable) size pulley, driving a given size sprocket, which is driving another sprocket, on a wheel with a given circumference............. Just kept increasing until the motor was maxed out.

Real world, practical stuff.

Uphills, downhills, flats, wind direction, doesn't matter. Maxing out the motor is what matters.

It all converts to time.................... which is important.

Bravin Neff

1. Very low - teens to high 20s. Steep uphills on a mountain bike. Fat bike terrain crawling.
2. Low - high 20s to high 30s. Normal hills for normal people.
3. Medium - high 30s to mid 80s. Almost all flat riding is done here for most normal people.
4. High - high 80s to 105ish. Almost all flat high speed riding is done here for most normal people.
5. Very high - 110 - 150. Bursts of high speed for normal people. Elite athletes can live here in a triathlon. Racers. Greg Lemond.

AU Tiger

Thanks, Bravin!

fietsbob

Add carrying stuff , touring, utility , commuting with more than a thumbdrive in your pocket , and every thing gets bumped to a lower range.


Remove air resistance like wheel sucking behind Don Vesco on the Bonneville salt flats and you can gear way higher ..

AU Tiger

Ahhhh... graph transformations!!

Mike_Sherman

Re: Mike Sherman's gear calculator

Hello, I just wanted to spread the word that, because of ISP issues, I have moved the calculator to GitHub.
Because this account is new, I'm not allowed to post a link, but you can message me and I'll send the links.

I'm also working on a new version to try to make the program friendlier on small screens.

-Mike