Gear ratio of snowmobiles

[KIVALO]

Good afternoon everyone.

There is a surprisingly polarizing debate within the snowmobiling community regarding the final drive ratio of snowmobiles as it relates to size of the lugs on the track. For the non-rider here the tracks have paddles that stick out from the track and they are called lugs. They extend into the snow and provide the traction to move the machine forward.

Assume you are on asphalt, will the final drive ratio be affected simply by changing the length/depth of the lug?

[Frank]

Hey KIVALO, nice diagram and explanation.

I say no.  But more stuff will get squeezed between the lugs and more stuff might get kicked up, which could slow things down.  Because the track speed is dependent on on the final gear moving the track along, the radius between the track and the "driver" gear sets the speed.  Making the lugs longer means the end speed of the lugs around the gear will be faster, but the lugs will also come together faster.  The only way it could go faster is if the track got pulled up under the gear height or the surface travelled on was curving up.  If the thought is the speed is proportional to the lug length, that doesn't hold IMHO.

 

Edited March 27, 2018 by Frank
I'm an idiot

[StringJunky]

I agree, I think the length of the lugs  and snow quality - will determine the efficiency of the traction and ,hence, speed. Any real change in speed would need a change in gear size..

[KIVALO]

I understand your points about snow type but that's why we need to assume you are on asphalt. Then snow is not a factor.

[StringJunky]

48 minutes ago, KIVALO said:

I understand your points about snow type but that's why we need to assume you are on asphalt. Then snow is not a factor.

I agree, I was just saying that, that's your variable, not the track.

[J.C.MacSwell]

The deeper and greater the number of lugs should increase the distance travelled during each complete cycle of the track, similar to how a thicker track belt would, unless they sink into the asphalt completely or there is some other compensating mechanism...so it should effect the final drive ratio.

 

Compare a new snow tire to one with the tread worn down and which gives you a wheel of greater diameter.

Edited March 27, 2018 by J.C.MacSwell

[Bender]

5 minutes ago, J.C.MacSwell said:

The deeper and greater the number of lugs should increase the distance travelled during each complete cycle of the track, similar to how a thicker track belt would, unless they sink into the asphalt completely or there is some other compensating mechanism...so it should effect the final drive ratio.

Not really. This would be the case if the belt was only on the wheels, but it is mostly in contact with the ground during the flat part, where belt thickness has no influence on outer belt speed. You would have more slip in front and at the back.

There could be some influence because the resistance changes. A higher load usually means the motor will run slower for the same power.

Allow me some nitpicking on the figure : those aren't gears, but sprockets or chain wheels. 

[J.C.MacSwell]

3 minutes ago, Bender said:

Not really. This would be the case if the belt was only on the wheels, but it is mostly in contact with the ground during the flat part, where belt thickness has no influence on outer belt speed. You would have more slip in front and at the back.

There could be some influence because the resistance changes. A higher load usually means the motor will run slower for the same power.

Allow me some nitpicking on the figure : those aren't gears, but sprockets or chain wheels. 

Slip would be one of the compensating mechanisms I alluded to. The flat part has no effect on the gear ratio if you assume no slip or deformation (the even bending of the belt where it turns notwithstanding). The extra distance effect is all at the radii.

[Bender]

4 minutes ago, J.C.MacSwell said:

Slip would be one of the compensating mechanisms I alluded to. The flat part has no effect on the gear ratio if you assume no slip or deformation (the even bending of the belt where it turns notwithstanding). The extra distance effect is all at the radii.

To travel extra distance, the entire flat part would need to slip. It seems unlikely that that would be significant. 

[J.C.MacSwell]

15 minutes ago, Bender said:

To travel extra distance, the entire flat part would need to slip. It seems unlikely that that would be significant. 

OK, picture a simple set up with 2 wheels in line. Add an infinitely thin belt and the distance a wheel travels in one turn with no slip, on ground or wheel, does not change...now keep adding thickness to the belt until you recognize how it changes the distance. None of the increase is on, or due to, the flat.

Edited March 27, 2018 by J.C.MacSwell

[Bender]

Now, instead of adding thickness, add lugs of increasing length until you recognise that the speed does not change. 

[J.C.MacSwell]

2 minutes ago, Bender said:

Now, instead of adding thickness, add lugs of increasing length until you recognise that the speed does not change. 

Did you miss the "unless they sink into the asphalt completely", or can you not really picture the difference increasing the length of the lugs would make?

[Bender]

I cannot. In a thicker belt, the outer part compresses the inner part of the belt, resulting in a different speed between the inner part of the belt and the reference plane (middle of the belt if it is homogeneous). This difference only happens at the wheels, and at the flat part, the entire belt moves at the speed of the reference plane, which is the speed of the vehicle. The increase in speed depends thus on the increased diameter of the reference plane.

In the case of lugs, sunk into the asphalt or otherwise, no such compression of the inner belt happens, because the lugs are not connected and are free to move away from each other. The radius of the reference plane does not change, and neither does the speed of the reference plane, the speed of the flat part, or the speed of the vehicle.   

[J.C.MacSwell]

17 minutes ago, Bender said:

I cannot. In a thicker belt, the outer part compresses the inner part of the belt, resulting in a different speed between the inner part of the belt and the reference plane (middle of the belt if it is homogeneous). This difference only happens at the wheels, and at the flat part, the entire belt moves at the speed of the reference plane, which is the speed of the vehicle. The increase in speed depends thus on the increased diameter of the reference plane.

In the case of lugs, sunk into the asphalt or otherwise, no such compression of the inner belt happens, because the lugs are not connected and are free to move away from each other. The radius of the reference plane does not change, and neither does the speed of the reference plane, the speed of the flat part, or the speed of the vehicle.   

Would you see it if there were enough lugs that the main belt never touched the asphalt, just the lugs?

Edited March 27, 2018 by J.C.MacSwell

[Bender]

No. The lugs could be touching and still would not be compressing the inner belt because there cannot be tension between them.

Are you even considering my answers? I am happy to clarify if you don't understand. 

[arc]

    If we were to increase the red drive sprocket's diameter (the number of teeth would need to increase to properly engage the track belt) the new larger outside surface diameter of the sprocket would rotate at the same RPM as the old diameter did. It would however cover more contact area of the track belt in the same amount of time as the old diameter sprocket did. The track belt would thus move faster. This means that by adding any extensions to the track belt you would be doing the same thing as you did to the sprocket. You are making the now longer outside contact area of the track belt change its speed or "surface contact area covered in one revolution" . When you extend the contact surface OUTWARD whether by tread or spikes or lugs you are increasing its surface area and by that its speed respectively. This is very similar to the effects that occur when tire sizes are changed slightly and will thus change the speedometer reading in proportion to the tire size difference.

[arc]

I've been thinking on this for the last hour and believe that animation is not a good representation of the situation. The frame and assembly shown above is more rigid and would give the expected result. But the snow mobile track belt is likely very flexible with little chance that an increase in the track belt's profile could add up to some effect. Right now I would say it would have no effect on the speed ratio. Will be pondering this for now. 

[Bender]

12 hours ago, arc said:

    If we were to increase the red drive sprocket's diameter (the number of teeth would need to increase to properly engage the track belt) the new larger outside surface diameter of the sprocket would rotate at the same RPM as the old diameter did. It would however cover more contact area of the track belt in the same amount of time as the old diameter sprocket did. The track belt would thus move faster. This means that by adding any extensions to the track belt you would be doing the same thing as you did to the sprocket. You are making the now longer outside contact area of the track belt change its speed or "surface contact area covered in one revolution" . When you extend the contact surface OUTWARD whether by tread or spikes or lugs you are increasing its surface area and by that its speed respectively. This is very similar to the effects that occur when tire sizes are changed slightly and will thus change the speedometer reading in proportion to the tire size difference.

Let's try a different approach. I might have been too concise for those not familiar with belt design.

A belt has a neutral line, which does not change length as the belt goes around a wheel. The length of this neutral line is called the reference length or datum length of the belt. Belt pulleys also have a reference diameter, which is where the reference plane of the belt passes. It is this reference diameter that determines the speed of the belt, and any belt geometry or structure that does not affect the reference diameter, does not affect the belt speed.

Adding lugs eg does not alter the reference length of the belt. Regardless of how long the lugs are, the same length of belt is going to pass the belt pulley in a given time. The outer rim of the lugs will move faster, but the belt itself won't.

The example given in the animation is a chain. In that case, only the amount of teeth of the sprocket counts and any geometry of the belt is irrelevant.

In retrospect, the belt in a snowmobile is most likely a timing belt (synchronous belt or toothed belt), which works like a chain. This means even increasing the thickness does not affect speed. At worst a thick belt would compress the teeth of the belt to the point where they no longer fit the pulley.

(Note: tension on the belt will change the length of the reference plane somewhat, but lugs have no influence on this stretching, so no reason to overcomplicate this discussion) 

Edited March 28, 2018 by Bender

[J.C.MacSwell]

21 hours ago, arc said:

    If we were to increase the red drive sprocket's diameter (the number of teeth would need to increase to properly engage the track belt) the new larger outside surface diameter of the sprocket would rotate at the same RPM as the old diameter did. It would however cover more contact area of the track belt in the same amount of time as the old diameter sprocket did. The track belt would thus move faster. This means that by adding any extensions to the track belt you would be doing the same thing as you did to the sprocket. You are making the now longer outside contact area of the track belt change its speed or "surface contact area covered in one revolution" . When you extend the contact surface OUTWARD whether by tread or spikes or lugs you are increasing its surface area and by that its speed respectively. This is very similar to the effects that occur when tire sizes are changed slightly and will thus change the speedometer reading in proportion to the tire size difference.

This, the bolded, was my thinking but since there is no ground contact in way of the sprocket I think Benders interpretation is correct. There may be a (very) small effect, but it really doesn't work like my "simple setup" I described earlier. +1 to Bender and Arc also for the animation, it may not be an exact representation but sufficient  for me to see where I was wrong.

Edited March 29, 2018 by J.C.MacSwell

[arc]

25 minutes ago, J.C.MacSwell said:

This, the bolded, was my thinking but since there is no ground contact in way of the sprocket I think Benders interpretation is correct. There may be a (very) small effect, but it really doesn't work like my "simple setup" I described earlier. +1 to Bender and Arc also for the animation

    Yes, that was my realization too, after I had considered the way changing the circumference on a car tire would change speed ratios yet changing the length of a track belt in any direction would have no effect on the vehicle's speed rather busted the whole argument for me. The whole thing is dependent on the radial distance from the shaft center and the track belt is not round or centered on that very obvious detail.  +1 to Bender for the breakdown.

[Bender]

I'll take some credit for changing your viewpoints but I give you at least as much for actually changing it and even more for admitting it.

[J.C.MacSwell]

12 hours ago, Bender said:

I'll take some credit for changing your viewpoints but I give you at least as much for actually changing it and even more for admitting it.

I had thought you were complicating it unnecessarily but you actually had the significant factor. It is easy to see by Arc's animation that the extra distance due to the lugs is having almost no effect. It is (mostly) created and disappears above the ground, and any grip it might have would be negated by the much greater contact of the flat area gripping the ground. (essentially what you said in your second post)

 

Edited March 29, 2018 by J.C.MacSwell

[Bender]

In a way I was overcomplicating by first discussing a flat belt instead of a timing belt.

Edited March 29, 2018 by Bender

[KIVALO]

Interesting discussion, thanks folks!