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Trying To Understand Gear Ratios

Old 12-12-19, 12:57 PM
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GAtkins
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Trying To Understand Gear Ratios

All else being equal, are lower gear ratios easier to climb versus higher gear ratios?

Suppose I have two bikes set up as follows:

Bike 1
Cog/Cassette 30/27
Gear ratio = 1.1111
Roll out = 94.25 inches
Cadence = 60
Speed = 5.35 mph

Bike 2
Cog/Cassette 34/34
Gear ratio = 1.0000
Roll out = 84.82 inches
Cadence = 60
Speed = 4.82 mph

Which setup will be easier to climb with? I think it would be Bike 2, but I want to make sure I'm evaluating this correctly.

Thanks much for the help.
Glenn
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Old 12-12-19, 01:18 PM
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I use gear inches. from https://www.sheldonbrown.com/gear-calc.html.
That is the distance a bike rolls/moves forward with i revolution of the pedals. So, the shorter distance is your easier gear. Bike 1= 30 gear inches, Bike 2= 27 gear inches.
Hope this helps KB
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Old 12-12-19, 01:32 PM
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Originally Posted by kcblair View Post
I use gear inches. from https://www.sheldonbrown.com/gear-calc.html.
That is the distance a bike rolls/moves forward with i revolution of the pedals. So, the shorter distance is your easier gear. Bike 1= 30 gear inches, Bike 2= 27 gear inches.
Hope this helps KB
To understand gear inches you have to go back into the history of the bicycle.
In the penny farthing days, a bigger front wheel meant you could pedal faster. The limiting factor was your crotch to pedal distance. When chain drive safety bikes were invented, riders were interested in comparing their drive ratios to the high wheeler bikes that they were used to. Gear inches is the factor they came up with and it persists to this day. A 100 gear inches would be equal to a high wheeler with a 100 inch front wheel.

Gear inches = chainring teeth divided by rear cog teeth times wheel diameter. To get how far you will travel with one turn of the pedals you have to multiply gear inches times pi.
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Old 12-12-19, 01:54 PM
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Yes, bike two would be easier to peddle. The lower speed at the same cadence confirms this.
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Old 12-12-19, 02:16 PM
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Originally Posted by GAtkins View Post
All else being equal, are lower gear ratios easier to climb versus higher gear ratios?

Suppose I have two bikes set up as follows:

Bike 1
Cog/Cassette 30/27
Gear ratio = 1.1111
Roll out = 94.25 inches
Cadence = 60
Speed = 5.35 mph

Bike 2
Cog/Cassette 34/34
Gear ratio = 1.0000
Roll out = 84.82 inches
Cadence = 60
Speed = 4.82 mph

Which setup will be easier to climb with? I think it would be Bike 2, but I want to make sure I'm evaluating this correctly.

Thanks much for the help.
Glenn
I guess the chain inches makes sense if you are comparing bikes but for me i deal in the ratios only since it is what makes sense to me. you are right about which will be easier to go up hill. essentially...big chain ring/small cassette gear is easier going down hill, small chain ring/big cassette gear easier going up hill.

-scott
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Old 12-12-19, 03:16 PM
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Originally Posted by spelger View Post
I guess the chain inches makes sense if you are comparing bikes but for me i deal in the ratios only since it is what makes sense to me. you are right about which will be easier to go up hill. essentially...big chain ring/small cassette gear is easier going down hill, small chain ring/big cassette gear easier going up hill.

-scott

These ratios are so small that on anything but the smallest down hill, pedaling on either bike is likely to be useless.
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Old 12-12-19, 07:53 PM
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Originally Posted by livedarklions View Post
These ratios are so small that on anything but the smallest down hill, pedaling on either bike is likely to be useless.
i took those ratios to be hypothetical.
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Old 12-12-19, 08:05 PM
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Originally Posted by MattTheHat View Post
Yes, bike two would be easier to peddle. The lower speed at the same cadence confirms this.
I meant pedal. I donít think the OP is interesting is selling the bikes.
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Old 12-12-19, 08:10 PM
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Originally Posted by spelger View Post
i took those ratios to be hypothetical.

OK, but I think the hypothetical ratios make a good point--that there has to be a bigger difference in ratios to have a practical effect on riding downhill than uphill.
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Old 12-12-19, 09:24 PM
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Originally Posted by GAtkins View Post
All else being equal, are lower gear ratios easier to climb versus higher gear ratios?

Suppose I have two bikes set up as follows:

Bike 1
Cog/Cassette 30/27
Gear ratio = 1.1111
Roll out = 94.25 inches
Cadence = 60
Speed = 5.35 mph

Bike 2
Cog/Cassette 34/34
Gear ratio = 1.0000
Roll out = 84.82 inches
Cadence = 60
Speed = 4.82 mph

Which setup will be easier to climb with? I think it would be Bike 2, but I want to make sure I'm evaluating this correctly.

Thanks much for the help.
Glenn
Yes, you are right. Bike 2 is easier to climb on...but not by much. The difference in your gears is pretty small as shown by the speed.

Gear ratios, development, gear inches, etc are all the same. Gear ratios are just the simplest to calculate because you arenít multiplying by anything. The way to make whatever you use to make sense is to realize that the smaller the number, the easier the gear. . You can also see that the smaller the gear ratio, the more times the crank goes around in relation to the wheel. For example, with your 1.0 ratio, the crank goes once around and the wheel goes once around. With the other one, the wheel goes around more times than the crank does.
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Old 12-13-19, 05:27 AM
  #11  
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Gatkins - you are correct on the basic concept: the gear ratio is the number of teeth on the front chainring divided by the number of teeth on the cog in use in the rear. The lower that ratio, the more times you will have to turn the pedals to move a given distance or maintain a given speed. When climbing hills, that translates to easier

How much easier you need is related to your fitness, the weight of you plus the bike and anything you are carrying, and how steep a hill you plan on climbing. Most touring bikes have a very low gear (under 1:1) because even if the rider is a skinny balink, the bike and the luggage is going to be pretty heavy and the fitness level of the rider may be really pretty low. Most racing bikes don't have such low gears because the rider is supposed to be skinny balink, have high cycling fitness, and the bike is lightweight and carrying nearly zero weight other than the rider. Yet, both are used to climb very steep hills, just at very different speeds!

Someone else pointed out the another consideration: how high a cadence and how fast you want to go on level ground and downhill. On a multi gear bike, the rear cassette and derailleur limit how wide a range you can cover in gear ratios and the largest front chainring determines if you will have to pedal like a Tasmanian devil to maintain your desired speed when not climbing.
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Old 12-13-19, 06:02 AM
  #12  
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Originally Posted by jpescatore View Post
and the fitness level of the rider may be really pretty low.


The last day of my four month, 6,000 mile, fully-loaded, cross country+ tour was a large (thousands of people) 75 mile, supported charity ride. Despite their being luggage transport, I rode my bike with all my gear. I dropped countless people and even had people drafting me.

Having toured with people and encountered many other people while out touring alone, I would bet my left front pannier that, on average, most of the self-contained touring population is fitter than the much of the general riding public.

Last edited by indyfabz; 12-13-19 at 01:00 PM.
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Old 12-13-19, 07:54 AM
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Originally Posted by spelger View Post
essentially...big chain ring/small cassette gear is easier going down hill, small chain ring/big cassette gear easier going up hill.

-scott
This isn't entirely accurate. Lower gear ratio (chainring:cog) will always mean easier pedalling, no matter up hill or down hill. It's just that you are far more likely to spin out going down hill.

There is one other nuance: if the climb is short and you speed up before it, the momentum will make more difference than the gear you are in - i.e., the effort you will put in using, say, 48/16 or 38/16 will be very similar, but the speed in the latter case will be lower.
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Old 12-13-19, 10:32 AM
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Originally Posted by subgrade View Post

There is one other nuance: if the climb is short and you speed up before it, the momentum will make more difference than the gear you are in - i.e., the effort you will put in using, say, 48/16 or 38/16 will be very similar, but the speed in the latter case will be lower.
Spending energy on a climb itself will always be faster than trying to carry speed into it.

Speed up a climb is almost linear with power. Pedal 20% harder, go 20% faster. 90% of your energy goes into hauling your carcass up to the summit.

Speed on flat ground is almost proportional to its cube root. Pedal 20% harder, go 6% faster. Even at low speed the overwhelming majority of your effort goes into overcoming aerodynamic drag.

Most of the energy you put in will be lost overcoming aerodynamic drag. Assuming a good position on the drops - 15 MPH on flat ground 74% of your power is wasted on aerodynamic drag, 83% at 20 MPH, 89% at 25 MPH, 92% at 30 MPH.

You might have more fun accelerating before a hill, but won't be faster than using your energy more efficiently.

Last edited by Drew Eckhardt; 12-13-19 at 10:40 AM.
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Old 12-13-19, 10:56 AM
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Originally Posted by Drew Eckhardt View Post
Spending energy on a climb itself will always be faster than trying to carry speed into it.

Speed up a climb is almost linear with power. Pedal 20% harder, go 20% faster. 90% of your energy goes into hauling your carcass up to the summit.

Speed on flat ground is almost proportional to its cube root. Pedal 20% harder, go 6% faster. Even at low speed the overwhelming majority of your effort goes into overcoming aerodynamic drag.

Most of the energy you put in will be lost overcoming aerodynamic drag. Assuming a good position on the drops - 15 MPH on flat ground 74% of your power is wasted on aerodynamic drag, 83% at 20 MPH, 89% at 25 MPH, 92% at 30 MPH.

You might have more fun accelerating before a hill, but won't be faster than using your energy more efficiently.

That last sentence is very context dependent. If you have enough energy to pedal hard on the downhill and the uphill, you will be marginally faster than if you only pedal hard on the uphill. You're only correct if shifts in the the amount of energy between the two are zero sum. On short climbs in short rides where you're not testing limits of endurance, efficiency isn't all that important.
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Old 12-13-19, 12:31 PM
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Originally Posted by Drew Eckhardt View Post
Spending energy on a climb itself will always be faster than trying to carry speed into it.

...
Not true on the right rollers on a fix gear. When I hit those, I go easy on the descent until just before the bottom, then spin as fast as I can, hit the hill with all the speed I can and basically go crazy to keep that speed as far up the hill as I can. When I finally lose the speed, I settle in to grunting up the rest in that big gear. it's hard. Enough rollers and I hit the point where I cannot do this any longer. The remaining miles are forgettable (yeah I wish!).

Now the much bigger "rollers" of the Oregon coast highway are simply not fun. My approach above gets me about 20% up the hill. I rode Reedsport to Brookings on the 2016 Cycle Oregon. Wasn't fun. Had the option to return on Highway 1 or go inland, climbing several thousand feet, then descending back to the highway just short of Gold Beach, our camp. I had gears (flip-flop hub and a cog wrench) but stopping to change meant a from-a-standstill climb, then having to stop at the top to flip the wheel back. But on the inland climb, I only had to do this three times in 20+ miles. That was some of the nicest riding of the week

I won't argue your point that it may be more energy efficient to take your approach, but riding fix gear, there are other concerns. We have to look at the big picture of resources. Calorie reserves, muscle reserves; both aerobic and anaerobic, and other details like our crotches (if we do not stop and change gears for downhills). If we do stop, that comes with costs also. Lost time, cool down and usually the need to do this again when that hill (up or down) is over.

The roller hill approach I described above is wonderful for all the changes in types of effort. While it works, it is fast and fun. High RPM, high power and full deep breathing is wonderfully cleansing. And it's a blast flying past the geared riders who are selecting the proper gear for the sensible climb.

Ben
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Old 12-13-19, 12:50 PM
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Anyway, yes, bike two would be the bike that is easier to pedal uphill.
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Old 12-13-19, 02:12 PM
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Thanks to all who responded. Much appreciated. I thought I was correct, but wanted to make sure.

I currently have a bike with a triple (yeah, I know ) on the front at 30-40-50 and a 12-27 on the back.

I'm considering getting a new bike with a 50-34 chain ring and a 11-34 cassette. I'm not in the best shape, but getting there. I wanted to make sure I wasn't loosing anything on the low end. Looks like I will have a lower low-end and a higher-high end, but just slightly.

Thanks again.
Glenn
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Old 12-13-19, 03:06 PM
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Originally Posted by GAtkins View Post
Thanks to all who responded. Much appreciated. I thought I was correct, but wanted to make sure.

I currently have a bike with a triple (yeah, I know ) on the front at 30-40-50 and a 12-27 on the back.

I'm considering getting a new bike with a 50-34 chain ring and a 11-34 cassette. I'm not in the best shape, but getting there. I wanted to make sure I wasn't loosing anything on the low end. Looks like I will have a lower low-end and a higher-high end, but just slightly.

Thanks again.
Glenn
Frankly, going from a triple to a compact double isnít an improvement in my opinion. You are trading a system with a pretty good arrangement for gears for one with lots of holes. This is a comparison of your current triple with your proposed compact double. Look at the 17 gear and how it shifts across the two systems. The difference from the higher gear to the middle on the triple results in a 5 mph shift in speed. Your cadence wonít have to change much to keep up with the change in speed. The difference in the double is almost 10 mph. More importantly, youíll have to increase your cadence to keep up with the speed change from about 90 rpm to nearly 120. It feels like you have lost a chain.

This comparison shows what you would get if you changed the 12-27 to an 11-34. Youíll get a lower low and it will probably be cheaper. For the double, youíll need the cassette, crank, a new chain, probably a new derailer, and perhaps new shifters. If you keep the triple, youíll need only the cassette and chain. You might need a new derailer as well but I would see if your current derailer works with an 11-34.

By the way, the gear calculator is one of the best Iíve ever used. Itís very easy to use and the comparison feature is really nice.
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Old 12-14-19, 10:59 PM
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cyccommute Thank you. I had seen that gear calculator before, and I'm still trying to wrap my head around what I'm looking at on that site, and others, particularly as it relates to the 17 gear steps between the two comparisons you did for me.

In the spring I'm seriously considering getting either a TREK Domane SL 7 or a Specialized Rubaix Expert. I currently have a Specialied Allez Comp with a 105 group set, the triple I mentioned and a 12-27 cassette.

Both the new Trek Domane SL 7 and the Rubaix Expert come with that 50-34 chain ring in the front and the same 11 speed 11-34 cassette on the back. In either case the bike will come with a Shimano Di2 group set.

Is it practical to make the changes you suggest as far a triple in front and a wider cassette in the back on a Di2 stock group without further breaking the bank on a $6k bike?

Thanks again for your help and any further information you might have.

Glenn
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Old 12-14-19, 11:27 PM
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Originally Posted by GAtkins View Post
All else being equal, are lower gear ratios easier to climb versus higher gear ratios?

Bike 1
Speed = 5.35 mph

Bike 2
Speed = 4.82 mph
Hill climbing is complex, and hard to break down into simple numbers.

If you look at raw horsepower to go up the hill, Bike 1 takes more horsepower to go up the hill than Bike 2 at a slower pace.

But, say you alter your cadence sufficient to hit 5 MPH on both bikes. Then you're using the exact same amount of power.

Yep throw it into say 50/25 gearing, and slow down your cadence a bit to hit 5 MPH... still the same amount of power (although perhaps more stressful on the body with standing, pulling up on the bars, pedals, etc, on some hills).

The other factor related to effort is duration. So, I can do pretty well with any effort sustained less than say 1 minute. Beyond that minute, I start slowing down rapidly.

So, I may well be better off climbing a short hill at 10 MPH in 1 minute than climbing the same hill at 5 MPH in 2 minutes.

Extend that to a longer hill...
Say you can climb the hill at 7.5 MPH for 1/2 hour, vs 5 MPH for 45 minutes. You're over the hill and coasting down in the first example long before you get to the top in the second example. Yes, a lot more work for that extra 2.5 MPH, but it is over quicker.

Beyond gearing, you can look at things such as crank length. So, say you're comparing cranks from 165/170/175/180mm. In a sense, your cadence is related to the circumference of the crank stroke (2*pi*radius). So, longer cranks give more leverage, but slower cadence. No free power. But, it may also impact your overall gearing choice.
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Old 12-17-19, 11:35 AM
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I would simply say that any new bike you buy has ALL the gears you'll ever need. That being said do you NEED all those gears. The joke in the ten speed days was every bike you'd see on the street was in the small chainring and small rear cog. And I still see that today on a lot of hibreds. Push both levers forward or click the gear levers all the way and the gear you're left in is the small/small.

i've ridden a lot of miles. And I'm a flatlander. So my basic riding gear is a 67in gear, feeling speedy 78" gear, out on Sunday group ride 88" gear. Thats really all I need. The others come in handy when I find a hill or do some off road stuff.
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Old 12-17-19, 12:35 PM
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Originally Posted by MattTheHat View Post
Yes, bike two would be easier to peddle. The lower speed at the same cadence confirms this.
Oh, I don't know. Maybe something like frame color, available options or price might make one easier to peddle than the other...
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Old 12-17-19, 12:52 PM
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Originally Posted by Phil_gretz View Post
Oh, I don't know. Maybe something like frame color, available options or price might make one easier to peddle than the other...
I already chastised myself in post #8 . This was exactly the kind of thing I was trying to avoid.
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Old 12-17-19, 01:06 PM
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Originally Posted by MattTheHat View Post
I already chastised myself in post #8 . This was exactly the kind of thing I was trying to avoid.
I would've told Phil_gretz to go pedal his papers.

I'm kidding, Phil!
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