# Bicycle Mechanics - Gears, easier climbs, gear math

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View Full Version : Gears, easier climbs, gear math

angelaharms
08-25-08, 01:43 PM
I want to understand gears better. Anybody want to help?

Current bike has 38T crank, and 7 gears in back, ranging from 13-34T. Considering a bike with three gears in front, 28/38/48T, and the back is 8 gears, 11-34T.

I know that the tires and geometry will make a difference, but what I'm after now is to understand the math here. Clearly, I have approximately the same gear range on the old bike as on the new one in second. But I'd like to be able to understand it in more detail.

How can I tell what specific set of gears will match another specific set? Anybody know a formula?

Angela

croscoe
08-25-08, 01:56 PM
http://sheldonbrown.com/gears/

angelaharms
08-25-08, 02:00 PM
Been studying that... it took me a while to make any sense of it. But I think I have gear inches figured out:

Diameter * (front TPI) / (rearTPI)

A lower number here is "easier" pedaling, or more climbing. Is that right?

croscoe
08-25-08, 02:19 PM
That' right. The lower the number of gear inches, the "easier" the gear is to pedal.

Mr. Underbridge
08-25-08, 02:25 PM
Been studying that... it took me a while to make any sense of it. But I think I have gear inches figured out:

Diameter * (front TPI) / (rearTPI)

A lower number here is "easier" pedaling, or more climbing. Is that right?

Yep. But it doesn't take the cranks into account. Sheldon's best metric is "gain ratio", which divides what you have above by the length of the crank. This has some more useful benefits, including:

*gets rid of effects due to varying crank lengths
*makes the result an actual ratio
*is very conceptual - the result ends up being the distance traveled by your wheel divided by the distance traveled by your foot.

So if a certain gear combination has a gain ratio of 5, that means that the wheel travels 5 times as much distance as your foot. This number can be compared between any two bikes.

HillRider
08-25-08, 02:30 PM
Right, lower is slower and easier. The formula is

Gear inches = (Wheel Diameter)*Chainring teeth/cog teeth

For you case in the 38T chainring and 34T cog with a 700c or 27" wheel the gear inch would be:

GI = 27*38/34 = 30.2 gear-inches

For 700c or 27" wheels, the diameter is usually assumed to be 27" which is pertty close for most tire sizes. For MTB wheels the diameter is taken as 26".

Use the same calculation for each combination of chairring and cog.

BTW, Sheldon Brown's web site has a calcualtor for the gear table for any cassette/chainring set-up. Look here: http://www.sheldonbrown.com/gears/

ascend
08-25-08, 04:20 PM
http://www.kenkifer.com/bikepages/touring/gears.htm -- Another big long article about gears. This one is less about the basics than it is about the geekery though.

angelaharms
08-25-08, 04:31 PM
I couldn't figure out what the results meant, when I tried Sheldon's calculator. It was a list of percentages. Sorry to be such a n00b.

Bill Kapaun
08-25-08, 05:35 PM
Gear Inches are based on the old high wheel bikes A 60" diameter wheel was 60 GI. It was "direct drive", meaning every rotation of the crank was one rotation of the wheel,
With chain rings and cogs, you have gear multiplication/division.
A 48T ring driving a 24T cog means you get 2 rotations of the wheel for every rotation of the crank, or with the 60" wheel, you would have 120 GI.
A 48T ring & 24T cog will have EXACTLY the same GI as a 38T ring and a 19T cog or a 28T ring and a 14T cog. ALL are 2:1, and thus 120 GI with our 60" wheel. A 48:16 would be 3:1 or 180 GI.
It's just simple arithmetic, really.
Ring teeth/ cog teeth X tire diameter.

red_hook
08-25-08, 05:50 PM
I couldn't figure out what the results meant, when I tried Sheldon's calculator. It was a list of percentages. Sorry to be such a n00b.

The percentages between the gears are just the amount of change between one gear and the next at that end of the bike. The percentages are only between the numbers along the top or along the leftmost column (the yellow boxes, the gears themselves).

The numbers in the white boxes are either the gain ratios or the gear inches, depending on which option you set on the first page.

08-25-08, 06:24 PM
I want to understand gears better. Anybody want to help?

Current bike has 38T crank, and 7 gears in back, ranging from 13-34T. Considering a bike with three gears in front, 28/38/48T, and the back is 8 gears, 11-34T.

I know that the tires and geometry will make a difference, but what I'm after now is to understand the math here. Clearly, I have approximately the same gear range on the old bike as on the new one in second. But I'd like to be able to understand it in more detail.

How can I tell what specific set of gears will match another specific set? Anybody know a formula?

Angela

There are many interpretations of gearing, but I think gear inches is as useful as any. Bill gave you a great 5-minute lesson. In setting up the gearing for a particular bike, the first questions are, how high and how low do I need? Your bike under consideration will go as low as almost any bike and similarly as high, so you shouldn't need any easier or harder gears.

JanMM
08-25-08, 06:31 PM
Most folks never consider the actual math involved but, rather, just look at the charts or calculators that give you the gear inches for the various combinations of cogs, chainrings and wheel sizes.

angelaharms
08-25-08, 06:33 PM
So how does 29.1 gear inches compare with 22.5? The old bike goes down to 29.1, and I am hoping I'll be a little stronger on hills on the new one, which goes down to 22.6 (27*28/34). Is that a significant difference, do you think?

I honestly couldn't tell subjectively, when I tested the bike. I was pretty tired from testing all of them. (On the other hand, I did climb up a particular bridge three times in one day.) :D

Anyway, I'm a bit of a crip. If it's possible to customize to get better climbing, it might be worth doing.

KevinF
08-25-08, 06:38 PM
So how does 29.1 gear inches compare with 22.5? The old bike goes down to 29.1, and I am hoping I'll be a little stronger on hills on the new one, which goes down to 22.6 (27*28/34). Is that a significant difference, do you think?

29.1 to 22.5 is a big drop in gearing.

Al1943
08-25-08, 06:58 PM
22.5 is really low. You should be able to climb a tree with that.:)

Al

angelaharms
08-25-08, 10:27 PM
That's terrific news. Thanks, guys. I'm heavy and also have muscle issues, so I doubt I'll climb a tree, but maybe overpasses will be easier, and occasional hills will be *possible* :D

Bill Kapaun
08-26-08, 12:58 AM
I see you're just about 40 miles down the road from me!
You always want 1 ger lower than you think you need.
IF you could "almost" manage with 29 GI, just a couple less will make a significant difference.
There are other factors involved also. A longer crank arm gives you more leverage, thus you can get by with a slightly greater GI, or the opposite with a shorter arm.
Bike weight. More weight going uphill requires lower GI.

On your current bike, do you have the tires aired up to the max pressure printed on the sidewall?
Are they knobbies? SMOOTH street type tires weigh less and roll easier.
Is your seat adjusted properly? A little too low and you don't develop all the power from your stroke. See-
http://bikenhike.com/page.cfm?pageid=23&FAQid=25

angelaharms
08-26-08, 08:11 AM
40 miles... Corvallis? I have tweaked my current bike, except for replacing the very fat (2.125) 26" street tires with only slightly fat ones (1.75). Potential bike has thinner tires, 700c. When I rode the potential bike, it seemed like it was just as hard to get up the test hill as with my old bike, but that might have been just me. I definitely needed to go down to 1-1, though.

Old bike is crank-forward though. It might also just have to do with getting used to it.

I'ma go ride the new one again this morning. :D

dit
08-26-08, 12:12 PM
There are folks out there running gears down around 17-19 gi. Sometimes it is just easier to walk up the hill but it sure hurts the ego.

DannoXYZ
08-26-08, 12:40 PM
There's another website somewhere that gives a final number of "development" for gearing. That's the distance the bike travels per turn of the crank. Much easier to understand.

To answer Angela's original question, NO, the lowest gearing on those two bikes are not the same:

current bike - MTB
38f/34r = 1.118 gear-ratio * (26in*3.14/12in/ft) wheel-circumference = 7.60 ft per crank-revolution

28f/34r = 0.824 gear-ratio * (27in*3.14/12in/ft) = 5.82 ft per crank-revolution

The new bike will be MUCH easier to pedal up hills in its lowest gear compared to the current one. But you have to get into the 28t granny-ring instead of staying in the middle 38t chainring.

Bill Kapaun
08-26-08, 01:27 PM
"When I rode the potential bike, it seemed like it was just as hard to get up the test hill as with my old bike, but that might have been just me."

Did you verify the shift to the granny ring? Maybe it didn't shift? You should be able to nearly climb a wall with 28-34! Was the seat set at the right height? Too low and you can't develop 100% of your thrust.

What bike are you getting?

I'm on I-5 and it starts with Alban:)

angelaharms
08-26-08, 05:28 PM
Today I bought a Raleigh Detour 3.5, 24 speed, girly-girl frame. Here's Raleigh's pic. (Mine has the seat up and the handlebars down.)

I'll try it on some hills (bridges & overpasses, really) and get back to you about the easyness. Thanks to everybody for the help figuring out gears.

Angela

jamesd416
08-26-08, 09:07 PM
22.5 is really low. You should be able to climb a tree with that.:)

Al

Agreed. It's too late for the math but my new LHT bottom end is 26t front 34t rear and I think I could climb straight up the wall of our house.

James
http://onelessindenver.blogspot.com

JiveTurkey
08-26-08, 09:15 PM
The most intuitive output on the gear-calculator to me is MPH/KPH per given RPM; it's much easier for me to compare gears.

angelaharms
08-26-08, 09:54 PM
Agreed. It's too late for the math but my new LHT bottom end is 26t front 34t rear and I think I could climb straight up the wall of our house.

James
http://onelessindenver.blogspot.com

This is helping me, for sure. I just rode the new one more, and I know I ain't climbin' up no walls. What it's helping me with is getting a sort-of concrete way of comparing my ability with "normal" ability. I am generally too hard on myself. Like I think most people are in real pain doing normal things, but they don't mind, and I'm somehow just too weak to buck up and do it. But this sort of feedback helps me understand that I really do have a different experience, and maybe I should cut myself some slack! :eek:

Anyway, sorry to get so personal. Thanks again, and stuff. I'm enjoying experimenting with my new improved climbing ability. :)

Angela

Bill Kapaun
08-27-08, 03:30 AM
" Today I bought a Raleigh Detour 3.5, 24 speed"

The Raleigh site shows that as a 21 speed????

angelaharms
08-27-08, 09:07 AM
Oops. You are correct. The 24 speed I'd looked at was 11-34T, this one is 14-34. But the granny gear is the same.

Al1943
08-27-08, 11:41 AM
There's another website somewhere that gives a final number of "development" for gearing. That's the distance the bike travels per turn of the crank.

Develpement = (gear inches)(pi)

angelaharms
08-27-08, 11:44 AM
What's pi?

DannoXYZ
08-27-08, 03:37 PM
What's pi?Pi is the relationship between a circle's diameter vs. its circumference: http://en.wikipedia.org/wiki/Pi

What Al1943 did just above is convert the abstract gear-inches into actual rolling-distance of the gearing. Much more user-friendly and easy to understand. It's the distance your bike travels per crank-revolution. The shorter the distance, the less effort it takes and the easier it is to climb in that gear.

angelaharms
08-27-08, 04:43 PM
Oh, heh. I read it as P.I. I'm a super-genius. :thumb:

Wanderer
08-27-08, 05:17 PM
Right you are Mr Turkey! Easy to understand using RPM and MPH.

angelaharms
08-29-08, 11:22 AM
Hey, how cool is this? I finally rode my normal commute, and my normal overpass (Yes, I'm a wimp). I rode most of the way up in 1-3, then shifted to 1-2. The last bit, I really wanted 1-1, but 1-1 wasn't working (must visit LBS) so I ended up staying in 1-2. And I made it just fine! :D I think I'm gonna like this multi-gear life.:thumb: A seven-speed is great, but this is better.

(And I love understanding gears better. Thanks, again.)

Angela

Bill Kapaun
08-29-08, 11:59 AM
When you need a low gear, you NEED a low gear!
I never use my granny ring, but I'm not taking it off to save a few ounces. There might be that ONE time!

angelaharms
08-29-08, 01:36 PM
Raleigh Detour 3.5 Girly-girl has just been exchanged for a Raleigh Detour 4.5 manly-man in ugly green. Now I have 24. :)