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# Rear Wheel Torque Values

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## Rear Wheel Torque Values

(OP)
I found some differing equations on the internet than what I thought on how to arrive at the rear wheel torque value for motorcycles, so I thought I had better ask here to make sure.
One site said Rear Wheel Torque = Chain Tension X Tooth Count Ratio (front & rear sprockets)

I was under the impression that the formula was:
Rear Wheel Torque = Chain Tension X (Rear Sprocket Pitch Radius/Front Sprocket Pitch Radius)

At first I thought both would work out the same but after measuring some things & doing the numbers there is quite a difference in the final outcome.

Not sure now what to think?

Thanks

### RE: Rear Wheel Torque Values

Both formulas are wrong.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Rear Wheel Torque Values

(OP)
Hi Mike,
Maybe that's why nothing seems to make sense, can you help me with the correct formula's please.
I have found many different so called formula's on the net that don't seem to be correct either.
Basically I want to see if the pitch radius of both sprockets has an influence on the output, among some other things.

Thanks

### RE: Rear Wheel Torque Values

Basically I want to see if the pitch radius of both sprockets has an influence on the output, among some other things.

uh, yes. that is the reason for transmission and sprocket gearing changes.

Torque is force acting at a radius around an axle or shaft centerline. so torque = force x radius, or force = toque divided by radius.

Engine torque is multiplied by the primary ratio (before clutch), then multiplied again by whatever transmission gear ratio are involved. Lower gear ratios = more reduction = more rear wheel torque and less speed. Lower sprocket ratios = more reduction = more torque and less speed.

Torque at the transmission output shaft can be either:
1. multiplied again by the sprocket ratio, which gives torque at the rear axle, then divided by loaded wheel radius to get force at the ground. Chain tension is not determined in this method.

2. output torque divided by sprocket radius = chain tension. Then chain tension times radius of rear sprocket gives torque at rear wheel. That torque divided by rear tire loaded radius is force at the ground.

Both are the same results, method 1 just cancels out the chain tension and does the two steps of calculations together. If you write out the math you will see it cancels out.

Larger sprockets on both front and rear, with the same ratio, will give the same wheel torque obviously. The chain tension will be less but chain speed will be higher. Force in the chain x chain speed is hp, and since that is a fixed number, chain speed and chain tension vary inversely.

### RE: Rear Wheel Torque Values

(OP)
Thanks kcj,
Yes I am aware of the torque gain or reduction of different diameter sprockets. I am looking more at how the pitch radius affects the Chordal action & it's effect on various things.

Thanks for helping out.

### RE: Rear Wheel Torque Values

The smaller sprocket has more chordal action. The centerline of the roller goes upward approaching TDC if you will, then drops downward as it comes off the sprocket, then the next tooth coming upward picks the chain back up again. The amount of that vertical motion relates to the cosine of the angle between the teeth, which relates to sprocket diameter.

Even changing by several teeth, I don't think the difference would be even noticeable because it is such a small percentage change. BUT, if the change in diamaeter meant a change in frequency which just happened to then match a natural freqency of the chain span it could be noticeable. The chain 'sing' that comes and goes in a narrow band is this.

There are also torque ripples caused by the chain action but that is complicated and usuallynot significant.

At very high speeds these issues might be important, but I can't comment there. I got off the street in the late 80's so my current knowledge is minimal. Now I ride observed trials motorcycles, at pretty low in the skill classes, over logs and ledges like countertops, and even the loop speeeds between sections are under 50 mph.

### RE: Rear Wheel Torque Values

I should have been clearer: for front, it drops downwards once on the sprocket, not upwards. driven rear sprocket action direction is as I stated, but rear diameter is so larger that chordal action is usually ignored.

### RE: Rear Wheel Torque Values

(OP)
Thanks kcj,
Yes it is at high speed I am interested in, much testing to do.
I am building a 500cc motorcycle for a land speed record, if I can get the power I want out of this thing, a class record that is.

Trials Bike riding is a skill on it's own, I remember when I was younger I used to race motocross bikes & sit back & watch the Trials guys do their thing, their is plenty of skill involved even at low speeds.

Thanks again

### RE: Rear Wheel Torque Values

Ah, you are at very high chain speeds. I understand your concerns about oscillations and natural frequency and chain motions, I just can't contribute anything there.
Have you thought about timing/tooth belts drive?

Bonneville is cool, there is a class for everything. I would love to watch it someday.

Trials is totally different than in the 70's and 80's. Higher levels are insane. My level is very low. I am 62, only started at age 46, so I will never be any good, but I love it.
www.trialscentral.com has good modern info.

best of luck on the salt.

kcj

### RE: Rear Wheel Torque Values

I think chain manufacturers publish limits for, among other things, maximum pitch line velocity. Like belts, the added force when rounding a high speed sprocket can be more than significant. Not that any motorcycle was ever designed so as to remain within industrial chain standards

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