Thankyou so much I begin to understand now this relation, One last thing , if a I have an 11/30 ans 12/27. Whay´s the difference of having 11 or 12 teeth for the minimun and so. The 11 cog is smaller than the 12?

best regards

The 11 would be better for racing down a steep hill. The 30 would be better for climbing a very steep hill. The 12-27 has closer ratio spacing which will allow you to maintain an ideal cadence under a wide variety of situations. The 12-27 (or 12-25) mated with your crankset would be the better choice for most riders.

Al

But if I compare a cog with 11 teeth and a cog with 12 teeth, what´s the diffrence?, is the 11 going to be a little smaller? meaning is more difficult to peda than the 12. Sorry for all this questions , i am feeling very curiuous about leatnig this stuff

An 11 will cause the bike to travel a greater distance for each pedal stroke. If you can maintain the same cadence with the 11 that you can with the 12 you will be doing more work, requiring more energy spent, and yes it will probably feel harder. In reality you will probably not be able to go faster with an 11 than with a 12 unless you are going down a steep hill.

That is not correct. The amount of work will be the same. What changes is the mechanical advantage, so it is harder to turn the 11 tooth cog. In theory, you can go faster in an 11 tooth cog opposed to a 12 tooth cog. In reality, it is the rider that determines the top speed. The rider can only supply so much power, so he can only go so fast.

To OP, yes an 11 tooth cog will be smaller than a 12 tooth cog. The chains of bicycles are standardized at 1/2 inch. So, the cogs also need to be at 1/2 inch apart. The only way to do this in cogs is to change the circumference of the cogs depending on the number of teeth.

With bicycle gearing, we try to find the most efficient way to transfer power from ourselves to the rear wheel. The amount of work is the same. To ride a bicycle up a mountain will take the same amount of work if done in an 11 tooth cog or a 28 tooth cog. What we try to do is find a cog with the correct mechanical advantage that allows us to pedal at a cadence that is the most efficient, one that will allow us to continue to pedal for a long time.

Think of it in another way. Say you need to go to the store that is 1 mile away. You could sprint, jog or walk there. If you try to sprint, you will soon tire and not be able to make it. If you walk, you will make it there, but it will take you a long time. If you jog, you will make it there in the least amount of time. The amount of work is the same, but jogging is the most efficient way.

[QUOTE=SweetLou;5953884]That is not correct. The amount of work will be the same. What changes is the mechanical advantage, so it is harder to turn the 11 tooth cog. In theory, you can go faster in an 11 tooth cog opposed to a 12 tooth cog. In reality, it is the rider that determines the top speed. The rider can only supply so much power, so he can only go so fast.
/QUOTE]

I disagree. If you travel further for a single pedal rotation you have done more work, what I said.

Well, yes. One turn of the cranks would be more work done. But since we are talking about going from one place to another, then the amount of work does not change.

No, I did read your post. The amount of work is the same. You do more work in one revolution of the cranks in the 11 tooth cog than the 12 tooth cog, but you have to do more revolutions on the 12 tooth cog.

work=force x distance. Imagine you tie a rope onto your tire and climb the rope 10 meters. You and the bike weigh 90kg. Force = mass x acceleration. So, the force would be 90 x 9.8
(90 x 9.8) x 10 = work done
8820J or 8820 Newton meters of work was done. This does not matter how fast you do it or what gear you are in.

Now Power is different. Power = work / time. If you were in the 11 tooth cog and climbed the rope in 5 seconds the amount of power would be: 8820 N.m/5 seconds = 1764 watts. If the same person climbed the rope in the 12 tooth cog in 6 seconds then in would be 8820 N.m/6 seconds = 1470 watts. If the same person climbed the rope in the same time no matter what gear was used, the watts would be the same since the work would be the same.

Now back to the bike. The work done is the same no matter what gear you are in. The power used will be different. With a good cadence, you can maintain a higher wattage for a longer period of time.

How about friction loss due to wider tires, cheap bearings?

That wouldn't matter since it is on the same bike. One thing would make a difference though, that is wind resistance. Since the faster you go, the more wind resistance there is, so more force is needed. If you going faster, more work will be done because of this. But, if you are going the same speed, then no difference in work.

I apologize, I meant to say if you can maintain the same cadence (not speed) more work will be done. I have edited a change.

all right , I see the right cadence is the most important factor. A bike like mine with 11/38 8 speed opposed to a madone, 12/25 at 10 speed. So the firs gear is more oriented towards MTB, going hills up and down and the Madone is more limited in that way although it has 10 speed which is better fo find a right cadence in a road

Yeah, if I was you, I would work on my cadence and find the correct rate for me. Like said above about 90 - 100 for most people. Once that is done, if you feel like the big chainwheel/small cog is not enough (I doubt it) then we can talk about changing the cassette or chainwheels. Remember what was calculated on Sheldon Browns' website gear calculator, the set up you have now will get you to 35 mph if your cadence is at 100. That is mighty fast and I can only reach that while going downhill. But I am not that strong, pros can do that on flat land.

All right , thanks very much for your help