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Here's a question simple at face value but for the math nerds feel free to dig in. Do all ratios of similar proportion (eg. 1:1, 1.5:1) etc feel the same. As in require the same work? Is the bottom end of a 2x (52/34 x 11-34) Exactly the same as a 1x (42 x11-42)?

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    Don't forget that tire diameter is a factor as well. – Daniel R Hicks May 7 '20 at 0:51
  • The diameter of the cogs and rings makes that there is probably no 17 but a 25 on a cassette used together with a 50-34 crank. since both are 1:2 and the 50/25 combination is better. – Carel May 7 '20 at 9:27
  • One thing I always asked myself: Doesn't the chain run faster if I run 50/25 than on 34/17, and what difference does that make? – NoirDesir May 7 '20 at 16:22
  • GOAT Sheldon Brown had a great explanation of how to compare gear ratios across bikes on his website – sam May 8 '20 at 2:43
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The answer is that yes, a 34t cog and 34t chainring would be the same gear ratio as a 50t cog and 50t chainring. However, the difference would be in drivetrain friction, as this Velonews article demonstrates. Larger cogs and chainrings make the chain articulate less, and these have lower friction than combinations where the chain articulates more. This would be true even if we are considering single-speed or track bikes where the chain is totally straight. Otherwise, the more the chain is angled, the more friction is produced.

Now, would you notice the difference? The testing facility in the Velonews article I linked estimated the the average friction difference between a 2x setup, 53/39 chainrings and 11-34 cassette and the equivalent 1x setup with a 48t chainring was about 3 watts at 250W total input power; 1x systems often have smaller cogs or larger chainrings than the equivalent and optimal 2x gear. The 1x system has the greatest friction in the 48t ring and 10t cog, and this combination has the biggest friction disadvantage to the 2x system's equivalent gear (53x11) at about 6 watts. The next two biggest gears are about a 4-5W deficit to a 2x system. Note that this is all at 250W, and riders operating at lower power would see less of a differential.

Is this difference perceptible or important? In this Cyclingtips review of the Ceramicspeed oversized pulley wheel system, which should be about a 1-2 watt saving, the reviewer claimed he did not consistently perceive a friction difference. In many gears, the 1x system is within 2 watts of the 2x system, so you would be unlikely to notice the difference. In the top 3-4 gears, the 1x system is at a bit more of a disadvantage to the 2x. Nonetheless, the difference even then may not be that noticeable to many riders.

Also, 1x setups lack a front derailleur, which reduces the bicycle’s aerodynamic drag slightly. The Velonews article pegs this at about 3W at 30 miles/hr. This would partially offset the increased drivetrain friction for many users, even those not cycling at 30 mph.

(Edit: note that a previous version of the answer mis-stated the Ceramicspeed system's claimed savings. I remembered that it was 2.4W from somewhere. CS actually claims greater potential savings, but the Cyclingtips article reminds readers that if you are diligent on drivetrain maintenance, you are likely to see only about 1-2W of friction savings from the Ceramicspeed system. If you are not diligent about drivetrain maintenance, then you should be, as it's cheaper than a Ceramicspeed oversize pulley wheel system. Moreover, if you still chose to get one, you would make it last longer with better maintenance - and at the asking price, this would be a really, really good thing!)

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No, because chains lose efficiency and smoothness the tighter of a gear they're wrapped around. All other factors equal, physically larger gears on bikes tend to be more efficient.

Technically the extra weight of bigger gears counteracts this some amount.

Larger gears also wear slower.

In your example, chainline effects would also likely make a difference.

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