Bicycle gears

When you're riding - what's the best sequence for shifting gears?

Preamble, for the grown ups

No one will tell you that you don't need to exercise!  Exercise helps you feel better, makes you more alert, keeps you more active!  Your thinking machine, which you use especially when working robotics challenges, works better when there is lots of oxygen rich blood fueling it.  How does that blood get to your brain?  Good cardio-vascular conditioning!  Even geeky, nerdy robotic scientists need good exercise!

I have just rediscovered one of my favorite workouts - cycling!  I like swimming, skiiing, running, rollerblading, etc, but cycling is an old love from my high school days before Lance Armstrong was a household name and before bike trails were part of C-DOTs standard practices.

But, let's face it, any of these kind of exercise regamins can get a little monotonous!  How do I counter it?  Excerise my brain with arithmetic problems - how many laps in 25 yard pool to make a quarter mile or a kilometer?  How many vertical feet skied; and today's exercise - what is the most efficient gearing combination sequence for the smoothest ride?

This problem has been on my mind since the old days, and I was always troubled by the fact that, to obtain the most precise answer, I had to count the teeth on the sprockets / cluster and then determine the ratios and then order the ratios and then determine the gear combinations that would give me the best ordered sequence of gear changes for the smoothest ride.  And I have always been too lazy or preoccupied to count the teeth on the clusters.

But finally, today, I realized the obvious!  I don't really HAVE to count the teeth - I already have the ratios simply by which chain ring or cluster gear I was using at the time - that is to say...

Hey kids, what are we really talking about?

...which combination of front gear and rear gear gives the smoothest ride?

My bike has 3 gears in front (chain rings) and 6 in back (cluster gears).  Bicycle gearing works like this: 

• The larger the chain ring in combination with the smaller the cluster gear means a harder but greater distance per stroke.   This is the higher gear numbers on both chain rings and clusters.
• The smaller the chain ring in combination with the lartger cluster gear means the easier, but shorter distance traveled per stroke.  This is lower gear numbers on both chain ring and cluster.

The math!

So who want to take a stab at organizing the gearing sequence with just gear numbers?  Let me try it, and you tell me if you agree:

The green pattern is where I might choose to shift: 

1. I would start out, reasonably, in the lowest possible gear, 1X1 (i.e. cluster gear x chain ring).
2. I'd then shift my to cluster gear 2
3. slip up to the middle chain ring now, for a ratio of 2x2=4
4. then move to cluster gear 3, for a ratio of 3x2=6
5. again up the cluster to gear 4: 4x2=8
6. I'm cruising now, so I'll skip the cluster 10 combination and ratchet up to the third chain ring: 4x3=12
7. I'm on the highest chain ring now, so the only place to go is the next cluster gear 5x3=15
8. and finally the smallest (highest) cluster gear: 6x3 = 18

You try it!

You can see that there would be several different combinations that the rider could choose, depending on the size of the hill and the convenience of shifting. 

What other factors would you consider?  What if you wanted a truly linear progression through the gears, hitting every possible combination in order?

Is this truly the best riding combination set?  Are these approximate ratios actually the same as the actual ratios of the teeth on each of the gears?  What would be the easiest way to find out?

Please post your interpretations in feedback on the blog.  And hey, how would you use this understanding of your bicycle gears to build your next robot?

And hey - Don't forget about traffic if you're riding along trying to figure all this out in your head!  And ALWAYS WEAR A HELMET!

Thanks,

Ross Parrent
Operational Partner
FIRST LEGO League in Colorado
Twitter @RossP_FLL