Torque and gearing

[LanceT]

I was just having a discussion with one of the engineers at the show, and we were debating on whether or not having a smaller gear in the front is going to give the drivetrain more torque or leaverage. I did a little experiment a while ago where I calculated out the same gearing I was running on the trials bike, (like 22-19) but using a 29 tooth chainring in front. It was mathematically the same, yet felt totally different. I noticed that many riders are using a much smaller (20 or 18 tooth) gear in the front than I am used to. It actually reminded me of this observation when I was reading Aaron Lutze's post about trying to use a 26 tooth gear on the front of his new control.
So, without extensive rambling, my question is: with the same gear ratio, is using a smaller cog or freewheel in the front going to give the drivetrain more mechanical advantage? Has anyone experienced this and can give an explanation, technical or otherwise?

Thanks

[Cory]

Hi Lance, the mechanical advantage will be identical. Imagine connecting each of the front gear teeth with straight lines all around and you would obtain a polygon. For a larger front gear you will have a much shallower angle between each line. As the number of teeth approaches infinity you would get a circle becuase the line lenght would become zero and the lines would be tangent to each other.

In a nutshell what you are probably noticing with the larger gear is a much smoother power transfer becuase a larger gear better approximates a circle than a small one does,

Cory

[[BMF]Andy]

The simple answer is no, as long as you run the same gear ratio your hub will experience the same amount of torque from your drivetrain as long as the force you put on ur pedals is constant.

The other side of this is that your chain actually sees more force attempting to pull it apart as the gears you are using become smaller.

Torque=Force*distance. So we know that the force on the chain increases as you use a smaller gear. But by using a smaller gear the distance from where the force is applied, i.e. the tooth of your rear cog, to the center of rotation, i.e. the axle of your rear hub, decreases. This increase and decrease cancel each other out and that is why the torque is the same no matter what size gears you use, as long as they result in the same ratio.

[KeepRollin]

I'm curious what you mean by felt totally different. Would what cory suggested that it was a smoother power transfer explain what you felt?

[airfruit]

well, it is mathmatically the same, but how the drivetrain feels to u depence on the friction within the drivetrain, length of chain that wraps around ur cog and tension of ur chain, and maybe a few other factors, like freehub/freewheel flex..... anyhow

Mechanically, if u have the same amount of chain wrap and tension in the driventrain, the smaller the gears, the more brutal it is on ur drivetrain. The force exerted by ur leg turns into a moment/torque around the bb. this torque is distributed among the teeth of ur front chainring. The less the teeth, the more force per teeth the chainring has to withstand. Moment/Torque is the force applied times the moment arm which are perpendicular. easy highschool physics, so to find the tension in the chain you have to take the torque applied and divide by the radius of the chainring. You can see then, the smaller the chainring in front, the more force the chain has to sustain.

so, bigger front chainring/freewheel will be easier on the driventrain. You can get into how the larger chainring has more moment of inertia and all that crap, but it's not very significant. only thing is that u have alittle more friction force in the drivetrain due to more chain rubbing against more teeth.

Therefore, mechanically, a driventrain with smaller cog/chainring/freewheel is worse than a drivetrain with larger cogs. :) that was enough physics, lol. but if u are uci, then smaller chainring has physical clearance advantage

[Elan]

hgypothetical- if you run a 9t rear cog, and a 20t front, you chain is going to have to be made out of god material or its going to break, but if you run a 18-40 gearing, you arent going to have much trouble. the torque on the hub is hte same, but hte torque on the chain is diferent methinks

[trialsrider50]

the torque is the same at each central location, rear, front, all that stays the same, but the force at each link point obviously is more. so yes, elan

[Cryo-Cube]

Andy']The simple answer is no, as long as you run the same gear ratio your hub will experience the same amount of torque from your drivetrain as long as the force you put on ur pedals is constant.

The other side of this is that your chain actually sees more force attempting to pull it apart as the gears you are using become smaller.

Torque=Force*distance. So we know that the force on the chain increases as you use a smaller gear. But by using a smaller gear the distance from where the force is applied, i.e. the tooth of your rear cog, to the center of rotation, i.e. the axle of your rear hub, decreases. This increase and decrease cancel each other out and that is why the torque is the same no matter what size gears you use, as long as they result in the same ratio.
Your right when the rear wheel can freely move
but arent you forgetting the situations where the rear wheel is in a positon where its stuck/cant move for a split second or even longer (wedge, stuck between a pallet..., standing on one pedal with brakes locked)?

Also arent you forgetting the physical inertia?
The whole weight on the rear wheel + gear ration makes the spinning of the rear wheel even more inert as it is. Meaning it takes some time till the force applied on the crank is able to rotate the rear wheel. In this slip scond where you are already applying the full torque but the wheel is not yet moving becaue of its inert, you are applying more torque to the chain/drivetrain than you would on a bigger front cog.

Im not saying its a drasticall effect. Just that in lets say 6 month of trial abuse this 2 things (wheel inertia & situation where the wheel is stuck/cant rotate imidiately) will effect your chain and drivetrain (more fatigue/wear)

[LanceT]

Thanks everyone. What I experienced still remains a little elusive to me, but I certaintly accept the scientific explanations. The only thing that I would offer as a further consideration is that, when testing full suspension bikes for cannondale I noticed a similar effect. With a fully active design that would compress the suspension slightly under pedal force, when we used a comparable gear ratio but put it in the middle or large chainring as opposed to the small, it "bobbed" the rear suspension much less. Again, the gear ratio was the same or similar, but the feeling was different. i will have to admit though, that I am in over my head on the principles behind what I am trying to explain. Back to the trials bike though, there was no wayI could have done the same moves with the 26 tooth front chainring as I was doing with the 22. Maybe I was just fooling myself. Anyway, thanks again.

[trialsrider50]

the physical inertia doesn't matter because no matter what the size of the cog the torque is transferred to the center. so no matter what size rear cog, its the same force transferred. as long as the front gear increases as well and holds the same ratio. so the total torgue remains the same. the torque in the center of the cog(the hub) never changes, only the distribution on the chain, it only feels smoother because of chain being angled less.

[tybikes]

Total guess here, and very likely wrong, but I think it has to do with how far your foot moves to get the same "power" or "kick" out of the bike. You'd have the same gear ratio, but your foot moves, say, 1/8th of a full pedal revolution versus 1/6, or something like that. Similarly, how far your foot has to move before the hub engages. Just a thought.

I just switched to an 18t ffw/track cog setup in the front, and dropped from a 22-19 to an 18-15. The new setup should feel slightly harder, but actually feels easier.

[trialsrider50]

a lot of this "feels easier" has more to do with the quality of the parts in use rather than the gear size. and you're on the right track tybikes but having a different portion of the rotation would mean a different gear ratio. that's not at discussion here, but having a different length crank, say 158 vs. 170 means the linear movement is more on a 170(you cover more area even though the degree of turn is the same), but it feels easier. so the degree of turn correllates directly with the gear ratio. in this thread the ratio is remaining the same, the crank size would make a difference though.

back on the "feels easier" thing. basically, if you run a regular ole, shimano 18t freewheel in back and a 22 tooth cog in front. if you switch to a 16 tooth fixed in front and a 13t chris king hub. (the ratios are like .008 off) the size and tension of the pressure on each link of the chain is so minimul in comparison to the different in quality of the parts.

[jmkimmel]

nerds

[vaughn]

I've got something to say about this....because i totally feel it too.


I think it has to do with the flexyness of the frame. Imagine that the chain were around a gear as big as your crank, so that when you pedaled your foot was right next to the chain ring...if you preload to do a side hop or something, your frame will twist much less, i think because in essence you are pushing directly to the chain ring...

But when you have a much smaller front chainring your foot is away from the point of pull to the rear and this allows more sideways torquring to occur....which twists the frame of the bike, maybe this allows you to spring more giving you more jive in the moves you're doing.

if our feet were directly inline with the chain and not a few inches out on a pedal then everything we've been saying would map directly to a bike world, but thankfully we live in a world of three dimensions. Like that picture on trialsrider50's, she looks good in 2D but just imagine how much different it would be in 3D

[rush]

nerds.

Interesting nonetheless.

[BrettM]

Some goofy bmx racers ride the biggest front ring possible, but keep the same gear ratio as they would on a normal setup. It's more efficient somehow. Not sure if thats anywhere near what you are after.

There is also something aboots odd number rear cogs being harsher on your drivetrain as it stresses the chain unevenly.

Just some weird, pretty much useless info.

[CoppellStereo]

well the chain is longer :D

[Cryo-Cube]

the physical inertia doesn't matter because no matter what the size of the cog the torque is transferred to the center. so no matter what size rear cog, its the same force transferred. as long as the front gear increases as well and holds the same ratio. so the total torgue remains the same. the torque in the center of the cog(the hub) never changes, only the distribution on the chain, it only feels smoother because of chain being angled less.
nooo, my point was, if the rear cant move, you are applying more torque to the chain if you run 18t instead of 22t front cog. The force applyed to the hub, the rear cog and the ratio is irrelevant when the backwheel is locked/cant move. And yes the inertia matters

[such]

I think it has to do with the flexyness of the frame. Imagine that the chain were around a gear as big as your crank, so that when you pedaled your foot was right next to the chain ring...if you preload to do a side hop or something, your frame will twist much less, i think because in essence you are pushing directly to the chain ring...

But when you have a much smaller front chainring your foot is away from the point of pull to the rear and this allows more sideways torquring to occur....which twists the frame of the bike, maybe this allows you to spring more giving you more jive in the moves you're doing.

if our feet were directly inline with the chain and not a few inches out on a pedal then everything we've been saying would map directly to a bike world, but thankfully we live in a world of three dimensions. Like that picture on trialsrider50's, she looks good in 2D but just imagine how much different it would be in 3D

Dude - only your post makes sense here

[Cryo-Cube]

i have no idea what he is talking about

[such]

omg

[smudge]

There is also something about odd number rear cogs being harsher on your drivetrain as it stresses the chain unevenly.

Just some weird, pretty much useless info.
I'd be interested to hear more about that. I've always thought that using an odd number of teeth was beneficial for the drivetrain. Since the chain is always going to have an even number of teeth, the inner plates will sit on a cog tooth once per two revolutions, as opposed to once per rev when using even gears. It should help prevent tooth wear and the gears *should* last longer

[xxxfr]

lol, wow......i never thought this would go that far, and most of it makes sense, i used to run 26/25 on my woodman, more of an urban bike, i wanted the 26/11 for crusin, ANYWAY, i pedal kicked it around, it worked, but when i got the STP i went to 22/21 and i cant say i noticed any difference, same ratio, well close, but it felt the same to me

[AndyT]

my elbow hurts, how did this come about- the torque or chain length?

[eXtreme_one]

interesting indeed but i have a question...
the torque on the chain is a bit different when using a biger chainring or a smaller cog but what about the freewheel and rear hub (let's say a C.king). Would it be more torque on a freewheel or on a chris king hub ??