Help Settle Argument (Physics, Mechanics, Gear Ratios, etc)

Question posted on another forum (see link).

 

http://www.ahooga.com/wwwboard/messages/273952.shtml

Model A snowmobile quiz:  Mac has a Model A with tracks made of a flat rubber belt. The distance around the outside of the track is 150 inches. Joe comes over and tells Mac that he replaced the 30 inch diameter tires on his Model A with 33 inch diameter tires and this increased his speed by 10%, so he could now drive 44 MPH at the same engine RPM where he used to drive only 40 MPH. This gives Mac the idea to bolt a bunch of wood blocks to his flat rubber track. After adding the wood blocks the track now measures 165 inches around the outside of the track. At the same engine RPM, how has the speed been affected by adding the wood blocks to the track?

We can't seem to agree on correct answer.

There are a lot of variables being ignored. Things like sink in the snow, slip and ability to turn max revs at a particular effective gearing. But being you give none of that data and are using a car tire for comparision, we will assume the snow mobile is being driven on the same surface as the car  lets say hard ice, unlimited running room so slip is not an issue and has plenty of Hp,. Therefore, the blocked track is 10% larger diameter and therefore travels 10% further for every rev.

 

 

BTW, a dirt bike will travel slower on a dirt road than it will on asphalt. Same bike, same rpm, nothing changed.

 

Two tires, identical inflated OD, zero tire growth at speed,a street tire will travel faster than a knobby.

William - I disagree!

 

Imagine if you cut the track and laid it flat.  Vehicle would move at same speed.  Only height above ground would change.

 

All the "extra" length is on the curved ends of the track. Since they are not touching ground, they do not contribute to speed.  If it was doing a wheelie, then it would move faster.

(::::::::: )  'the track' is going to be equivalent to (: ) 'a wheel', => O when you remove the center track part. If you assume the same angular velocity at both ends of the track, you get a wheel with the same angular velocity. The increase in width of the track would increase the radius of either end, or the radius of the wheel. Increase the radius results in higher speed.

 

 

it's not the distance around the track that matters, it's the combine radius of the drive wheels and belt. Thicker belt, larger radius, larger velocity at same rpm.

 

 

edit: i'm wrong. the tracks are in contact with the ground, not moving relative to the ground so the wheel is rolling along on the track like a train on a train track essentially, the tracks aren't adding to the radius of the wheels.

Edited by Die_trying

Ground contact (for the sake of this discussion) means nothing. It only matters the OD/over all effective gearing.

 

For simplicity, say you had an engine that had total gearing of 2/1. You have a wheel/tire/track, 3' circumference. You change the gearing to be 4/1 and increase the wheel to 6' circumference. Effective gearing is the same.

 

One wheel or two (or six) on the ground, does not effect speed (assuming all else is constant).

If you ignore variables such as weight of the track and the traction coefficient then it sounds like it is an angular velocity problem. The final speed of the machine is proportional to the radius of the track. The radius would have to be measure from the center of the oblong circle to the bottom of the track and the center to the back of the track, then divided by 2. This radius would become greater with wood blocks attached to the bottom of the track. The larger radius would therefore cause a greater velocity.     

Try this:

Get some rope. Make a pieces 2' long. Tie it together to make a circle. Mark the ground. Place the rope around your ankles so when you step, you step at about 1' with each step. Use a stop watch, step once a second for ten seconds. Repeat the experiment with a rope 3' long (50% longer). Ignoring the part going around your ankle, you'll of walked 50% further at the same 'rpm'. Try it again with MX boots then high heels. The results will be the same (except for the embarrassment).

AH ha ah Die_trying you beat me!

The snowmobile is moving the same speed with or without the tracks, the extra "OD" from the blocks only contributes at the radius at either end of the track. Think of this, when the blocks go around the radius end of the track they will spread apart and have big gaps between them, this space is where all the extra od went, but when they hit the ground they would be back together and their edges are parallel, same speed with or without blocks

The snowmobile is moving the same speed with or without the tracks, the extra "OD" from the blocks only contributes at the radius at either end of the track. Think of this, when the blocks go around the radius end of the track they will spread apart and have big gaps between them, this space is where all the extra od went, but when they hit the ground they would be back together and their edges are parallel, same speed with or without blocks

The blocks spreading apart on the ends has no effect on the outside diameter of the track. Think of it this way, if you have two identical dirt bike tires, ones brand new and ones completely worn flat... Which ones going to have a greater outside diameter? It doesn't matter if the lugs aren't touching all the time, a track is nothing more than an oval tire.

William - I disagree!

 

Imagine if you cut the track and laid it flat.  Vehicle would move at same speed.  Only height above ground would change.

 

All the "extra" length is on the curved ends of the track. Since they are not touching ground, they do not contribute to speed.  If it was doing a wheelie, then it would move faster.

 

I disagree with you Still Bill!  The extra lenght would contribute to speed, but not proportionally 10% because when you increase the "countershaft" size, you increase the "rear sprocket" size too.  You would have to put pen to paper to figure out mathematically exactly how much bigger this thicker belt makes the "countershaft" and "sprocket," then you can get your answer. 

 

But it would take a lot of thinking, a lot of math.  I can easily calculate how much slower or faster a dirt bike will go if I know the top speed with a given sprocket set..

I am amazed at how much over analyzation is going on. A belt/wheel are all the same. A Biker Boy pointed out, the OD is the OD. The actual shape does not matter. You have the OD and a number of revolutions.

 

 

LORP, the math is simple, simply it is the Delta Percent change.

 

(New Value - Old Value) divided by Old Value

165-150 = 15

15 divided by 150 = 10 (a percentage) so it is a 10% change

Running on a track is no different whether you roll it out on the ground and drive across the top or in a conventional manner, because, like greg says, the angle between the cleats on the portion of track that you actually ride upon is zero. Increasing the height of the cleats only increases the length between the tips of the cleats where the track bends around the rollers, where the track is not in contact with the ground. On tracked vehicles you see some minor amounts of scrubbing at both ends where the cleats come in and out of contact with the ground. If you were to wrap a section of track around a wheel in order to maintain that angle between cleats, then yes, it would behave just like a larger diameter tire.

Running on a track is no different whether you roll it out on the ground and drive across the top or in a conventional manner, because, like greg says, the angle between the cleats on the portion of track that you actually ride upon is zero. Increasing the height of the cleats only increases the length between the tips of the cleats where the track bends around the rollers, where the track is not in contact with the ground. On tracked vehicles you see some minor amounts of scrubbing at both ends where the cleats come in and out of contact with the ground. If you were to wrap a section of track around a wheel in order to maintain that angle between cleats, then yes, it would behave just like a larger diameter tire.

Once again, THE SHAPE DOES NOT MATTER! You could have a round shape, a triangle shape, oval shape, any shape you want, the bottom line is that what ever the outside diameter is that's the distance it will travel in one revolution. Rolling it out flat and saying it just sits higher and isn't any "longer" is completely irrelevant because you are then still measuring the radius of the belt and not the added blocks.

Let me put it this way since everyone wants to lay things out flat and call it the diameter.

The original post states that the tire that was three inches bigger did indeed increase the speed, which we all can seem to agree on. Now let's assume he kept the same sized rim just the side wall got higher. If they were both on say a 25 inch rim and you cut them both and laid them flat they would both be 25 inches.

Edited by biker boy

The distance between the cleat ends increases as the track rolls over the front wheel an decreases back to the distance equal to the distance between link pins as the track flattens out. Overall length will increase but not over a section of track that actually matters.

 

This help any?

Track.png

The distance between the cleat ends increases as the track rolls over the front wheel an decreases back to the distance equal to the distance between link pins as the track flattens out. Overall length will increase but not over a section of track that actually matters.

 

This help any?

Track.png

Over a section that doesn't matter? So your saying that only part of the track ever touches the ground? You can't look at just the horizontal part and say that because it's the same length the speed will not change, you have to look at a complete revolution of the track.

I certainly can. Unless you have sufficient traction over a bent portion of track to cause the flat section to skid, or an A model can ride a wheelie you'll still cover a distance proportional to the diameter of the drive wheels. You're still moving the same linear amount of track because adding or lengthening the cleats doesn't change the actual length of the track. Actual length would be measured through the axes which the track pivots about. If Mac had gone with a thicker rubber track that had moved the rubber track's centroidal axis 10% farther away from the wheel center or had gone with 10% larger drive wheels then he would be moving faster.

I certainly can. Unless you have sufficient traction over a bent portion of track to cause the flat section to skid, or an A model can ride a wheelie you'll still cover a distance proportional to the diameter of the drive wheels. You're still moving the same linear amount of track because adding or lengthening the cleats doesn't change the actual length of the track. Actual length would be measured through the axes which the track pivots about. If Mac had gone with a thicker rubber track that had moved the rubber track's centroidal axis 10% farther away from the wheel center or had gone with 10% larger drive wheels then he would be moving faster.

Well if your therapy is right, draw a line around the outside of the tracks and it should be the same length as the original belt if the outside length of the track has not changed.

I give you all a D :devil:

You aren't hearing me. Roll a track out, add some taller cleats, the length will not change. That is my entire point.

 

Now if you installed that same track on a dozer, with the taller cleats, the distance measured around the outside of the cleats would increase, ONLY around the wheels. The drivers don't care how tall the cleats are and move the same length of track per rev regardless.

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