Russ Roth

I'm moving my daughter from a 24" (520) wheeled bike to a 650c track bike and need to figure out the new gearing. The "bike" is a frame/fork/wheels type of deal with no crank. Currently she runs a 42/15 which is 62.39 gear inches, though admittedly I have no idea what that means; I do know the higher the number the faster the bike goes for a given cadence the lower the number the slower/easier and don't know how gear inches are even calculated. When measuring rollout, she is a junior and they do that, it rolls out 187" which does seem to be about 3x what the gear inches are.
A 44/17 with a 650c is the easiest to get close approximation with a 62.91, should I expect this gearing to feel about the same to her and for it to allow the bike to travel roughly 189". Either way I will be pushing her up a little harder but I'm trying to figure out the whole gearing thing to begin with. If the gearing is close I may push her to a 44/16 since I think she can push a little harder then what she's currently doing though maybe something in between like a 46/17 would be better.

Also tossed on crankset, currently looking at a Crupi Rhythm Mini crank which is a 5x110. I've seen her on a cheap trek MTB with 145mm cranks and I've seen how much her hips rock when pedaling on it which has me leaning towards the 135, any more affordable, decent cranks in that length? A typical search for 130mm or 135mm cranks typically nets me a lot of Campy or Shimano due to chainring BCD while 140 gets me things like the Origin 8 cranks but they start at 140mm.

DrIsotope

To my understanding, the current gear inches is actually something like 75-80, because you have to take the tire into account, unless you're riding directly on the rim.

mihlbach

"Gear inches" refers to the hypothetical wheel diameter that you would need to get the same mechanical advantage (or, distance traveled per crank rotation) if your cranks were attached directly to the wheel, like a tricycle, so that 1 rotation of the cranks equals one rotation of the wheel.

Gear inches can be easily calculated by multiplying your gear ratio times your wheel diameter (the whole wheel, including rim and tire).

If you want to know the actual distance traveled for each revolution of the cranks, multiply the gear inches by pi (~3.14).

For example, a bike with 62 gear inches will travel 194.7 inches per crank rotation. 63 gear inches will travel 197.8. Thats a very small difference. For an average rider, changes of one gear inch or less are going to feel basically the same, and aren't going to significantly alter the top speed, cadence, or the perceived effort of the rider.

TugaDude

Try Sheldon Brown's online calculator. I plugged in the 110mm cranks and a 650 x 23c wheel/tire combo with 42/15 and got 68.1 gear inches. When you know all of the component values, it is more accurate to go ahead and enter their values.

https://sheldonbrown.com/gear-calc.html

mihlbach

While Sheldon Brown's calculator does have a box for inputing crank length, crank length does not factor into calculations of gear inches. You can vary the crank length and see that it does not change the results.
Crank length DOES factor into the calculation of "gain ratio". The gain ratio is the crank length/wheel radius times the gear ratio. This ratio is a more wholistic measurement of mechanical advantage that describes the relative distance moved by your foot (on the pedal) and the bicycle itself. Gain ratio factors all the variables that matter (crank length, gear ratio, wheel size) and is worth considering if you are changing crank lengths, but if you are just re-gearing your bicycle without changing cranks, gear inches are good enough.

Mikefule

It's simple if you look at it methodically.

Back in the time of the penny farthing, the cranks were connected directly to the hub. The wheel went round exactly one for every revolution of the cranks.

A penny farthing was therefore described by its wheel size. A 56 inch penny farthing had a 56 inch diameter wheel and would be faster than a 54 inch penny farthing, but slightly harder to ride up hill.

When they introduced bikes with chain drives and different sized cogs at the front and back, they were able to reduce the size of the wheels to make the bikes safer to ride. However, people who did not understand gear ratios saw the small wheels and did not know how they compared in "performance" to a penny farthing.

Therefore, they started the tradition of quoting gear sizes in "inches" to make the comparison with the penny farthing easier.

Imagine a 26 inch wheel that goes round twice for every revolution of the pedals. It has a 2:1 ratio. This is the same if the cogs are 40:20, or 50:25 or any other combination that gives a 2:1 ratio.

Therefore, if the wheel goes round twice for every revolution of the pedals, it works as if it is "twice as big". The 26 inch wheel gives you the same "performance" as a 52 inch penny farthing. (2 x 26 = 52)

So they would say that that bike had a "52 inch gear".

The ratio is always worked out as "front cog divided by back cog". So with a 48t chainring (front cog) and a 24t sprocket (back cog) the ratio is 48 divided by 24. That is the same as 2 divided by 1, so the answer is 2.

The gear inches is this number multiplied by the wheel diameter.

So 48 divided by 24 then times 26 (wheel size) would give you:
48 divided by 24 = 2. Then 2 x 26 = 52.

So the formula is "teeth on chain ring, divided by teeth on sprocket, then multiplied by diameter of the wheel."

A standard 700c wheel including tyre is about 28 inches diameter.


The ratio alone is not enough, because you could have the same chain ring and sprocket on a Moulton small wheeler, or a BMX, or a 29 inch mountain bike, and get very different performance.

If you want to know how far you actually travel per pedal revolution, it is the gear inches, x Pi. Pi is roughly 3.14.

There are of course many other factors to take into account including the length of your cranks, the position of the seat relative to the pedals, and the rider's ability, confidence and physiology. Gear inches is only part of the story.

For a fit adult who is not racing, a gear around 65 inches is a good all round gear. If you want to know how much difference there is between two gears, just look at it as a fraction or as a percentage. So a 70 inch gear is 70/65 as big as a 65 inch gear.

70/65 is the same as 14/13, so it's about 1/13 bigger, which is less than 10%. It will be a little bit faster when the riding is easy, and a little bit harder on a climb.

Russ Roth

Thank you for all the answers, I've been using bikecalc to get gear inches which does input tire and wheel size though I didn't know how it got the results. When I did the basic math of gear inches to distance traveled and came up with the distance traveled being roughly 3x gear inches I should have realized it was a multiplication of Pi and feel a touch dumb for not seeing it. Thanks for clearing it all up.

Mikefule

It may be an urban legend, but many years ago I heard of an "iron curtain country" where the authorities were so tired of contractors fiddling the figures when calculating requirements for concrete when making pipelines/sewerage (or other civil engineering projects involving circles or arches?) that they passed a law saying that Pi must be treated as exactly 3.

I don't know if it's true, but I can see how an official standard that is wrong, but is near enough, simple to understand, and rigidly enforced, is better than allowing people to fudge the figures rounding up or down depending on whether they were charging or paying.

For your purposes, calculating how far you travel per revolution of the cranks, Pi is only 4.7% more than 3, so that means that your rough calculation makes about as much difference as HALF a tooth on the rear sprocket. It's a negligible difference.

natloz

I went with 66.7 for hybrid road bike with 27" rim, seems good around town with no major climbs. Not too tough to pedal but can go a decent speed without spinning out. 42T x 17T

IAmSam

Congrats on posting your way to 10...posts - now post some pics...

I wasn't planning to post in this thread 'cos online calculators work fine for me...
but I had to respond to someone riding the exact gear configuration as I have on my sw8 phiksie. I was a bigger ring & cog user for a long time at about the same G/I, it was fine, but for ****zngigglz switched to 42/17 last year. It works fine too in my flat locale. Have thought about doing a 43T ring but...you know...

natloz

Thanks, the forum limits are kinda strange I gotta say, but I made it to 10 yay for me!

I am new to single speed so I don't have much in terms of comparisons, but I went with the science and the range suggested between 65 and 75 GI, so I decided to go on the lower end of the spectrum (as I like it somewhat leisurely to bike around with the kids in the city). Haven't tackled any steeper hills yet, but strategically avoiding them! May some day I will play around more, but cash is a premium these days!

Russ Roth

Played around with my gearing since I'm trying to do the Pink Rhino race at Kissena, went to a 53/16 on my bike which inproved my 1000m speed by 7 sec and still left me in dead last at 1:47.67. I'm thinking I'll spend the money on a 54t which will get me 1.9 more gear inches, not a lot but I'm not certain how much taller a gear I can or can't handle so it seems like a safe step.

For my daughter I went with a redline Microline 2 piece crank which are on clearance in spots right now and did settle on a 46/17 for her, the crank and chainring should show up tomorrow and we'll get to test it out wed I hope. Even without the larger bike or different gearing she managed to drop 12 sec off her time and got down to 2:24.81 on the 1000m and did a respectable 26.53, (I also think the wind was a little worse today too) although it doesn't rank her high I can't imagine that at 9 I'd have been doing 16.7mph with no brakes and it was nice to see her crush her personal best.

My older son will be taking over the 24" for this year and just received his first pair of clipless, he's excited though disappointed he won't be able to use them at the BMX track since you now need to be 13 or 14 to run clipless. He's asked for a taller gear so I'm moving him from a 42t to a 44t and we'll see how he goes from there.

fietsbob

(tooth count F , \ ' tooth count rear, a ratio) x diameter (inches) .. how far you go is circumference of the wheel.







...

DiabloScott

Engineering: for any belt drive or chain drive or direct gear
drive circumference / driven circumference = drive rpm / driven rpm

the tooth count works for bikes because the pitch is one tooth per half inch, so tooth count is proportional to circumference.
so if you have a 48x24 your wheel goes around twice for every crank revolution... no matter what your wheel size.