Gear Ratios Question
 

I've been pondering gear ratios lately in an effort to tweak gears without having to go to the trouble of finding say a rare 7 tooth sprocket, and being able to effectively ratio the tooth to something as low as say 5, by increasing the teeth on the chainring. Is their such a ratio?

What I'm looking for is a ratio that correponds the number of additional teeth on the back cog to the X variable of that number on the front chain ring.(i;e 3 cog teeth = 5 chainring teeth)

(Bare in mind these are for fixed-gear)Using the junior velo gear chart(http://www.juniorvelo.com/?p=4090) I found that 42/10 equals 111.5 gear inches almost equaling 54/13 at 110.2. gear inches. Does that mean that 42/10 is the same mechanical advantage of 54/13? I found that where in this latter equation 3 back cog teeth = 1/4 ratio, in others the cog teeth it's 1/6. Does anyone know if this is correct? I can't seem to find anything directly pertaining to swapping gears like this

Thanks in advance,
Tinkerer

There is no answer that is as simple as you are thinking. 1 tooth on the rear can be the same difference as 2, 3, or 4 up front depending on what your ratio is to start with. Just think in gear inches or gain ratios. Wichever you prefer.

No, don't get me wrong, this is complicated stuff. A formula would be needed to adjust to the varying ratio's.

So, I'd be right thinking two gear ratios with the same or almost same gear inches are identifical? Or am I missing something still.

Correct.

Rear cogs below 13 teeth compromise efficiency and wear out extremely quickly...it is always preferable to use the largest chain ring and cog to get your desired gear.

The drive using the larger combination will run smoother and have better chain engagement.

Righteous, thanks everyone for the info. It's much appreciated

Just calculate the gear ratios in inches: front sprocket ÷ rear cog x wheel size in inches = "gear inches" (i.e. the inches the bike will move forward for each revolution of the cranks).

if you think about that formula for a second, you can see that a one tooth change of the rear cog is a much bigger effect than a one tooth change on the chainring.

just use the formula and turn it around however you want to get the variable you're looking for. for example, if you want to change the chainring, and want to know what rear cog would still leave you with the same gear ratio (same feel at pedals), you can just mix the formula around and solve for the cog size.

There was a question a few days ago, and one answer referred to this page, giving advantages/disadvantages of using larger or smaller gears for the same ratio:
http://www.sheldonbrown.com/fixed.html#bigsmall

Another consideration for fixed gear is the number of skid patches. Say if you have a 48:16 gearing, every time your cranks go around once, the wheel goes around exactly 3 times. So if you lock your leg up at the same place in the stroke each time, then the wheel will always be at more or less the same spot, so you wear that one spot more. Of course, there's no law that says you have to go skidding around. On a coaster bike, that makes no difference, and my cruiser has 2:1 gearing with no ill effects.

Of course. That's what it is...and it's not complicated

(number of teeth front)/(number of teeth rear) = gear ratio

(gear ratio)*(tire diameter in inches) = gear inches

http://en.wikipedia.org/wiki/Gear_inches

Sorry, but this is a common mistake. It was actually derived from the slightly deranged English way of working out what size penny farthing front wheel the gear is equivalent to.

If you place a mark on the ground, place a crank vertically above it and wheel the bike backwards in a straight line, until the crank has made one full revolution, that will tell you how far the bike will travel forward for each crank revolution. You will find that it is much more than the gear inches given by the traditional formula.

Europeans have always used the above system for measuring the gear and it is much more sensible.

Gear-inches is based on the old penny-farthing bike (like the one in my avatar). It was a way to compare the gearing of the new-fangled "safety" bikes (with sprockets and chains) to the "ordinary" bicycles. It's the diameter of the big wheel on an "ordinary" that would take you as far in one turn of the crank. Multiply gear-inches by pi (3.1416) to get the distance you'll travel in one turn of the crank...close to it, anyway.

An example:

I have two fixed gear mtb / tourers that are almost identical as far as wheels and tyres go and one runs a 48 tooth ring with a 17/19 in the rear for a 62.8 / 70.2 gearing and the other runs a 42 with a 15/17 combo that has a 61.5 / 69.6 gearing.

This is a perfect gearing for bikes that tend to be loaded up with gear and get ridden longer distances...the slightly lower geared bike tends to carry more (it has front and rear paniers), has slicker higher psi tyres, and gets taken on many longer rides.

One could use the physical method of measuring gear inches but for practical purposes, Sheldon Brown's Gear inch calculator is a perfect tool to help you figure things out... an inch one way or the other isn't a big deal.

http://www.sheldonbrown.com/gears/

thanks atbman and deraltekluge for the correction on gear inches vs. crank revolution.

I doubt most riders can tell the difference between two gears that are one or two gear inches apart. So think of a gear inch as the smallest unit. In other words, if one chainring/sprocket combination gives you 65 inches and another gives you 66 inches, consider them equivalent.

Once again, Sheldon Brown's articles are succinct and complete. To my mind, looking at his chart of pluses and minuses of bigger and smaller sprockets/chainwheels, I favor bigger. They're slightly heavier but have less friction and are more durable.

I've read that smaller chainrings/sprockets give slightly better acceleration, but I do not know at all if this is true.

As for sprockets smaller than 11, I wasn't even sure they were made except for BMX and folding bikes. The angle the chain has to travel on such tiny sprockets is ridiculous. I think even the 11 tooth sprocket is more for mountain bike compact gearing. I wouldn't use anything smaller than a 12 tooth, and actually prefer 13.

I'm a pretty strong rider and my tallest gear on my road bike is 50/13 - not even a 4:1 ratio (it is somewhere around 100 gear inches).

I know a fellow who bike commutes on a fixed gear with 53/19 gearing, which to me seems pretty ridiculous considering there are a lot of hills here. I always blow past him in a lower gear when there is wind.

My road bike (fixed) uses a 52:18 for 75 gear inches and not too many folks blow by me regardless of grade or wind.

Using this larger combination of chain ring and cog makes for a very smooth drive and a smoother drive is a more efficient drive.

Based on test information published by Berto and Kyle in the IHPVA Journal some years ago larger sprockets are measurably more efficient. Also per information on motorcycle chain drives I read 20+ years ago larger sprockets increase chain life. As I recall the article indicated that a decrease in engine output sprocket teeth from 16T to 13T about doubled chain wear, halfing life.

The modern tendency on bicycles to use 11 or 12 tooth casette sprockets and smaller chainrings is fine if the point is to minimize weight but is poor practice from both geartrain efficiency and wear standpoints IMO.

tatfiend - That is excellent.

Yeah, 3.14 times more! Sup wit dat? :rolleyes::lol: