[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