# How to properly gear compensate for short crank arms?

Is there a linear relationship between gearing and crank arm length? For example, on my multispeed bike, my favorite gearing is 34/20 which is 1.7 and with 26" tires, that is 44.2 gear inches but I have 170mm crank arms. For my wife to be, I want a similar "feel" (pedal effort) but her bike has 24" diameter tires and 140mm crank arms. So does that mean instead of shooting for 44.2 gear inches, I should also compensate for the shorter crank arms and instead go for (140/170) * 44.2 gear inches = 36.4 gear inches? If so, since they are 24" tires, I will need about a 1.5 gearing so something like 34/22 or 32/22 sprocket combination should be just about right.

Additional information (although not sure if relevant here) is I am 5' 9" tall and she is 4' 11" tall. With her shorter, weaker legs, I am thinking a little extra compensation is in order. The "shortest" gearing I can go with (using sprockets I already have), are 28/22 which is 1.27 which will be 30.5 gear inches.

• Please try to write in paragraphs. It makes your question much easier to read. Dec 5, 2016 at 14:56
• @WillVousden... fixed. Dec 5, 2016 at 15:23
• In terms of the force required to turn the wheels with a given headwind or uphill resistance, it will be in inverse proportion to the crank arm length. Basically calculate gear inches and divide by crank arm length to get a number you can compare to a similar number from another bike. Dec 5, 2016 at 18:21
• Ask the woman to ride around the block. When she comes back she will either say it's too hard, too easy, or just right. Dec 12, 2016 at 1:44
• @jqning - Well you win the simplest answer award, unfortunately it is not that simple because what would she be basing the "too hard, too easy, or just right" on? I have to consider other factors such as giving her enough gear to keep up with me at a reasonable pace. I also need to know what her comfortable cadence is. This takes more than just riding around the block to determine. I'll have her ride with me a few times 6 miles each way so we get a good mix of wind from multiple directions to help determine the optimal gear for her. To start, I will go with 34/22 which should match mine. Dec 12, 2016 at 12:20

Being able to easily compare gearing across bikes with different crank lengths is the main reason why Sheldon Brown advocated switching to the proposed Gain Ratios system for expressing bicycle gearing. Gain Ratios measure gearing in terms of movement of the pedal rather than rotation of the chainring. You can use his popular Gearing Calculator to check it out. The other systems are more or less racer-myopic and force you to do additional math when different length cranks are involved, but yes you've got it as far as how to do so.

• Ok that helps but it doesn't seem to take into account shorter legs. For example, if I ride my wifes bike, it is not the same "effective" gain ratio because her legs are shorter than mine and I can generate more power simply by raising the seat and generating more torque. It seems like the smaller cranks (140mm vs. 170mm) should be more than linearly weighted like maybe a fudge factor of 1.5 of the difference so instead of treating it like 30mm different crank lengths, treat it like a 45mm difference as far as computing the gain ratio. I am trying to match the pedaling "feel" (effort). Dec 5, 2016 at 17:16
• I think Sheldon's system is somewhat flawed in that it doesn't take shorter legs into account. It is useful for the same rider comparing different crank lengths but not for different riders. What I really need is a calculation tool that will allow me to match the "pedal effort" of my 26" mountain bike in my favorite gear (about 44 gear inches) to a woman's (actually girls) cruiser bike such that it feels the same as far as pedal effort. I have used many gears while riding on the sidewalks here in flat Florida and that gear seems best for me. Since her bike is 1 speed I want to get it right. Dec 5, 2016 at 17:20
• So I have 3 sprocket combinations I can use for her bike to get it so it is very easy to pedal but not excessively low gearing for her. My choices for sprockets (I already have) are 34/22, 32/22, or 28/22. Again this is on a 24" girls (my future wife is short) single cruiser bike to be ridden on mostly flat sidewalks, bikepaths, and streets. The "stock" gearing is 44/19 which is ridiculously high and I will make it almost half of that, which means it is about double what it should be ideally! Dec 5, 2016 at 17:39
• They should have instead called it something like effort ratio not gain ratio because what are you "gaining"? Force time distance. The higher the gear, the more force needed to turn it but the less distance you have to spin the cranks. Conversely, the lower the gearing the less force needed to turn the cranks but you have to spin them more to cover some set road distance (assuming you pedal the entire way). I think Sheldon had the right idea but slightly wrong execution (and naming) of it. It needs at least 1 more parameter, length of riders legs. Dec 5, 2016 at 18:02
• You're covering a lot of territory here but maybe think of it this way: the reason why her bike has shorter cranks in the first place is because different length cranks are what allow riders with different leg lengths (actually different femur lengths and overall leg length numbers, plus throw saddle setback in there) to achieve good pedaling efficiency. Between two riders with crank lengths and overall bike fitting that work well for them, gain ratios should be a way of comparing their gears. Also note that cyclists differ in ideal cadence. Dec 5, 2016 at 19:30

I went from 170 to 150mm, and surprisingly did not feel like I used much lower gears.

1. Maybe because it's just a 11.7% drop, less than a typical gear step.
2. Maybe because part of the leverage happens in the leg anyways, when you think about it.

My 2 cents.

• But imagine if you stand up on a set of 170s vs a set of 150s from a dead stop. Physics says the 170s should give you more torque for the same downforce applied to the pedal (from gravity and rider effort). They should have crank arms that are adjustable depending on what type of riding is being done. May 19, 2017 at 14:30