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I'm planning a randonneur-like bike with drop bars, STI shifters, and nevertheless some low gears. The crankset could be a "compact plus" (I guess from Sugino), 44 and 28 teeths, and the cassette a normal Shimano 105 11-32.

With this setup, the second lowest gear ratio would be 28/28 = one.

I can imagine that this could add some particular mechanical stress on the the entire rear wheel, from the cassette to the spokes. But on the other hand, given that it's not the lowest gear, I probably won't use it for more than a few minutes in a row. Should an exact gear ratio of 1/1 be strictly avoided ?

Edit: imagine a cyclist pushing from side to side as she/he stands to climb up a mountain road. As long as the 1:1 gear stays in, the rear wheel always get flexed in the same way.

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Maybe the air pressure is distributing the stress between all the spokes almost the same. – Alexander Jan 25 at 16:40
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Gidday and welcome to SE Bicycles. Good first question. – Criggie Jan 25 at 19:28
    
A 1:1 gear ratio is exactly what a penny farthing has. Fixies avoid this because otherwise they're braking on the same part of the rim all the time, and they tend to skid-stop resulting in more-focused wear. I've not seen an exact 1:1 combination on a bike, closest I have is 26/24, which will slowly "rotate" the rim WRT the cranks, over12 rotations. – Criggie Jan 25 at 19:32
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There is a slight theoretical issue, in terms of the repeated stress on the same point of the wheel. (Would also be present, to a degree, for 2:1, 3:2, etc ratios.) A bike that is designed to take mountain riding, however, should have wheels built to a level that it would not be a big concern, especially if only used intermittently. – Daniel R Hicks Jan 25 at 22:44
up vote 6 down vote accepted

I have a half-decent hybrid with the option of 28/28 from stock, and there are places where I used to use it quite a lot with no trouble.

More importantly though, I'm not sure what you think is special about 1:1 gearing. The load is spread over a good (large) number of teeth front and rear. There are no sharp bends or cross-chaining effects to worry about. If you're concerned about some sort of resonance, it would be small compared to resonant effects of stomping on the pedals a couple of times a second, or riding over cobbles. Both of these are normal and handled sensibly by ordinary frames.

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Thanks! Yes, it's the resonance I'm concerned about. With a 1:1 gearing, at each pedal stroke, it's the same spokes / the same side of the freewheel / etc that get the maximum stress. – mtewes Jan 25 at 12:46
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The stress on the spokes caused by the chain pulling are evenly distributed on the spokes -- otherwise the wheel would flex appreciably and unacceptably. The innards of the freewheel also distribute the forces: this is the point of bearings and multiple pawls in the ratchet (you can see this in youtube.com/watch?v=y7liTvGkNlg) – Chris H Jan 25 at 13:05
    
Chris H: I agree that the stress from the chain pulling should be ok. But the weight of the cyclist, thrashing from side to side as she/he stands in the pedals to climb up a mountain road (exagerating a bit here) ? As long as the 1:1 gear stays in, the rear wheel always get flexed in the same way. – mtewes Jan 25 at 13:19
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@mtewes so you might need to check/true the wheel a little more often in the absolute worst case. Even a road bike can take some pretty serious hits (I'm not recommending riding off kerbs on the best road carbon but for a look at what it will survive: youtube.com/watch?v=5z1fSpZNXhU). Repeated stresses are of course a little different, but they're also much less. And if this wasn't your only gear the back wheel would get repositioned from using the other gears anyway. 1:1 would be very low for a single speed. – Chris H Jan 25 at 13:31

1:1 and similar ratios are considered bad in automotive gearboxes. If there is one bad tooth it will soon take others with it, if it is always meshing with the same teeth. Automotive gearboxes tend to use coprime ratios (where the 2 gears have no common multiple) to avoid this.

There really isn't a similar issue on a bike. I suppose it might be a good idea to have a prime number of links on the chain to even out wear in case of a bad tooth, but the sprockets never come into direct contact, so that shouldn't be an issue.

Resonance shouldn't be an issue. the resonant frequency of the bike is going to be way higher than your pedalling frequency. It'll be in the audio range. Just give it a tap and you may hear it ring.

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Thanks! In my comment to @Chris H, I didn't mean the natural resonant frequency, but the repeated stress occurring in sync with the pedal strokes. I agree that resonance is not a good term to describe this. – mtewes Jan 26 at 8:39

I think that 1:1 is only a problem if you forget that you will end up coasting a bit. Any amount of coasting, or even switching gears for a few seconds will end up making a different part or the wheel undergo the stress. Unless you are climbing for a long period of time without any changes in gradient that would require changing gears, then I really don't think it's something that will have any real effects. I don't think that 1:1 would be particularly worse than 2:1 (42:21), or 3:1 (48:16).

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Yes, this is why I would be more worried if 1:1 would be the lowest gear of the road bike, gear which one might actually use for an entire climb (and without coasting, of course). – mtewes Jan 26 at 8:46
    
I guess if it's the easiest gear, you might spend some time in that gear, but I personally wouldn't set up a bike such that I would be in the easiest gear for a significant amount of time. The most extreme gear on either end should not be something you use a lot in most cases because it means that you should probably have a gear or two beyond that one in case the riding gets a little tougher or easier than you would usually encounter. – Kibbee Jan 26 at 15:57

There is very little to no side to side stress in the wheel. The side to flex is from the bar to the crank via the frame and headset.

My single speed mounting bike is 32 x 16 so it gets repeated stress and zero problem. 32 x 16 is a pretty common SS mountain set up. Some SS cyclocross racers go with with that. In loose gravel/dirt at my max torque if the wheel spins it does not spin to the side.

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The 2:1 ratio isn't the same at all. That means at 1:1 the "x" point on the wheel get stress when you push the right pedal. The opposite point "y" get stress from the other side after half of pedal turn, and then again point "x" get stress in the same way. While on 2:1 point "x" get stress in one direction, then after half of pedals turn point "x" is again in the same place and get the stress in opposite direction. – Alexander Jan 25 at 16:33
    
@Alexander In two pedals it repeats and that is the gear 100%. And you don't think one direction then the other is not more wear than same every time. If you are trying to loosen a post from the ground would you just pull in one direction? – Paparazzi Jan 25 at 16:36

I have a cheap Walmart mountain bike and my 2nd lowest gear is also exactly 1:1 (24/24). Why would you avoid a gear that is very useful? I am setting up my bike so it has multiple underdrive gears instead of just 1 so I can better control my speed and cadence in low bike speed situations. Having just 1 low gear is not as good as having several. If all goes well with my conversion, I should have 3 underdrive gears.

So my answer is no a 1:1 gear should not be avoided since many bikes already use it even cheap $100 bikes like mine. So the logic is if a cheap bike can handle the stress, pretty much any bike should. Also I will be going much lower than 1:1. My goal is 0.59 lowest gear ratio (20/34) so I should be more worried than you, however, I would say avoid a 0.5:1 ratio because that is both a very low gear and an exact submultiple of a direct 1:1 ratio so that is one reason I am not going below a 0.59:1 target lowest gear.

My $100 Walmart mountain bike

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Thanks! I fully agree that low gears are useful, and on my current bike I have in fact 4 gears with a ratio below 1. No worries about low gear ratio, it's really about the 1:1. It could be that the designers of very cheap bikes just didn't bother about potential issues with an exact 1:1 ratio. – mtewes Jan 25 at 12:43
    
I find that a 1:1 gear is useful in some situations even on pavement like when I am riding lakeside on a sidewalk and want a very slow ride so I can enjoy the scenery. It is also good as you are transitioning from flat ground with some speed into a decent upgrade. I am not sure why you are worried about 1:1 but you didn't mention anything about 2:1 and 3:1. My bike has 42/14 = 3:1. Just out of curiosity what is your lowest gear? Mine currently is 24/28 with 26" tires so that is about 22.3 gear inches but if my double reduction mod works I will have 15.3 and will also have 3 underdrive gears. – David Jan 25 at 12:52
    
David: on my travel bike the lowest gear is 22/34 (17.7 gear inches), and I love this, with a trailer. But on the 28''-tire randonneur-bike I'm planning (drop bars, STI shifters), it would be 28/32 (24 gear inches). 2:1 or 3:1 should be less stressful to the bike than 1:1. – mtewes Jan 25 at 13:02
    
A 1:1 gear on pavement at very low speeds (perhaps 5 MPH or even slower) requires so little watts to maintain and is wonderful if you just want some exercise without exerting yourself (good for older people for example). Sometimes on my lunchbreak at work (at WalMart of course), I like to go for a leisurely ride around a lake that has a walking path. I generally like to use my 1:1 (2nd) gear as it is so easy to pedal and a nice slow pace that I can enjoy the scenery/nature. So relaxing and so easy. If someone has a wattmeter I would like to know at say 5 MPH if it is 25 watts or so. – David Jan 25 at 13:19
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I would say the opposite: the cheap bikes are poorly equipped and can have bad gear ratios. (Thou I don't really think that it's a bad ratio.) – Alexander Jan 25 at 16:21

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