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sophiecentaur
Science Advisor
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"no", what?S pump said:No!
"no", what?S pump said:No!
This description is hard for me to understand. Measuring what the track does round the top is not very relevant. What counts is the distances traveled by the vehicle for one rev of a wheel, with and without the track (or with different thicknesses of track. From your description, you have not done this. You seem to have been measuring distances on the track (or something) which is just an added confusion. The result you get will depend, as has been pointed out, by the detailed way in which the drive distorts the belt as it goes round the drive wheel. We have assumed that the drive is transferred to the contact surface of the belt and that the layers of the belt will stretch differentially as it goes round the wheel. (The belt has to distort in some way as it goes from straight to curved and back again.) But you can rely on the fact that there is no permanent 'creep' of one surface of the belt over the other surface. A given difference in the circumferences of the inner and outer surfaces on the curved section must disappear when that section becomes straight along the ground.OldYat47 said:A hand's on experiment? Take some car and truck toys with wheels of different diameters (toys are a great source). Choose some that you can "track" with a large rubber band (no interference from bodywork and stuff). Put the "tracked" toy on the ground. Where one wheel touches the ground mark the ground and the wheel (both marks line up). Now roll the toy forward one wheel revolution. Record the distance. Now put the vehicle in its starting position and mark the rubber band at the top of the "back" wheel. Now roll the vehicle forward until the rubber band mark is at the top of the "front" wheel (the axle to axle distance or wheelbase). Record the distance the vehicle travels.
Here's what you will find: The forward distance rolled for any vehicle will be pi*(diameter of the wheel plus the rubber band). This is sensitive enough that you can see the change if you stack two rubber bands together (adding a small amount of diameter). When the top section moves one wheelbase distance the vehicle will move 1/2 the wheelbase distance. The forward motion is defined by the wheel diameter. The top of the belt moves forward twice as fast as the vehicle moves forward. That's how tracked vehicles work, you can look it up.
sophiecentaur said:You could give us the reference where your idea is supported; that's the way things work on forums.
That reference contemplates rigid rotation. A track does not rigidly rotate. It flexes.OldYat47 said:
That has already been done repeatedly by various posters.OldYat47 said:OK, it flexes. So what? Relate that to changes in velocity and/or distance traveled per revolution.
OldYat47 said:So according you your post, the inner and outer surfaces of the track are moving at the same speed where the track is on the ground and stationary.
OldYat47 said:There are two points on the drive gear where the inner and outer surfaces of the track are moving at the same speed, though not the same direction. Those points are where the track is tangent to the drive wheel. No bend, no curvature, no distortion. What is the speed of the surface of the track at those points? (angular velocity) X (2*pi) X (radius from center of axle rotation to outer surface of the track).
The speed of the track is not a single number. Since it has a non-negligible thickness, its speed varies from inner surface to outer surface as it passes over the drive wheel.OldYat47 said:Sheesh. No, there won't be a "jump discontinuity" at that point or at any other point on the track.
In the simplest model, there will, indeed, be a jump discontinuity. In reality, there will be a change in speed from the section going round the wheel and the straight section (this applies to all the wheels and all the straight sections around the track). If you do not believe that the track flexes then take a rubber belt and stick some non-stretch tape along inner and outer faces and then bend it around a cylinder. You will, of course, notice that the outside paper will split and in inner paper may actually bunch up. You have two different distances around the wheels, traveled by inner and outer faces of the track / belt. That means two different speeds.OldYat47 said:Sheesh. No, there won't be a "jump discontinuity" at that point or at any other point on the track. I'm just trying to establish some common ground, which is beginning to look like an impossible task.
OK, looking at the frame of reference of the snowmobile, all points of the track make the same number of circuits around the track for a given number of rotations of the drive gear. How would you calculate the forward speed of the vehicle at any given RPM of the drive gear? Equations, please.
There is, in the simple model, a sharp boundary between the stretched and unstretched state on the outside of the belt or, conversely, between the compressed and uncompressed state on the inside of the belt.OldYat47 said:There is no jump discontinuity because the belt doesn't suddenly change thickness, it changes thickness at some finite rate.
How do you define distance traveled for a belt that has finite thickness?Suppose belt A is 1/2" thick and belt B is 4' thick. Their elastic design is such that they actually work. For one rotation of the drive gear which belt will travel farther?
Will what component of that setup travel further per rotation? Will any component of that setup travel more rapidly than any other component over the flats?So here's another. Suppose the drive track is a total of 10' long. What if you install 20 flexible lugs, 1/4" thick, each lug 10' "tall" (standing up from the belt). Will that setup travel further per drive gear rotation than the original smooth belt?
A.T. said:Actually, the OP should clear up what is meant by "changing the lug height" with a diagram, that shows:
- Where the drive sprocket teeth attack
- Where the track links are connected
- What part is being changed / extended
We here and the people in the original thread might have different ideas on this, and thus might be talking past each other.
A.T. said:The speed of the vehicle on hard surface would be ωr and is not affected by the lug length.
The tip speed... is not affected by thelugblade length.*
If that's supposed to be my quote, please quote in full context. I was talking about the lugs on the straight part, which are not rotating.OCR said:Note: My modifications to quote...
A.T. said:If that's supposed to be my quote, please quote in full context.
OldYat47 is correct...[COLOR=#black]..[/COLOR]OldYat47 said:http://physics.info/rolling/
There you go. To convert all this to tracked vehicles just put two of the wheel drawings together, one behind the other, and imagine them tracked such that the outer surface of the track is at radius "r". Anything that changes that radius will change tangential velocity (pure translation) or forward velocity (pure rolling).
Any counter statements should be made with appropriate equations and calculations.
OldYat does not contemplate tracks of non-zero thickness.OCR said:OldYat47 is correct...[COLOR=#black]..[/COLOR]![]()
Of course not. They do not have tracks.OCR said:Would you say the same thing about an airplane propeller, or a helicopter rotor blade?
jbriggs444 said:OldYat does not contemplate tracks of non-zero thickness.
sophiecentaur said:Of course not. They do not have tracks.
Even that idea introduces problems because the rollers on chains bear on different parts of the sprocket teeth as the chain enters or leaves so the effective radius of the drive changes. This would suggest that there is a change in speed as the non-stretchable chain transitions but, in addition to having a different radius of rotation, the rollers actually move forward and backward, tangentially to compensate because of the profile of the teeth. Putting it another way, there is a radial component as well as a tangential component of roller velocity as it feeds onto and off the chain. So nothing is easy.Tom.G said:Hey guys. Can you all settle on a simplification of considering the 'Track' to be a chain and the 'Lugs' retaining the same attachment as in the OP?
That might bypass getting tangled up in side issues.
The simple model being described contemplates a belt that stretches without thinning [or compresses without thickening]. That model requires a sudden change in density and in speed. However, that is much ado about nothing. Even if we apply a realistic condition of thinning, it is still the case that the outer surface of the belt moves more rapidly than the inner surface in the region where it is wrapped around the drive wheel. Accordingly, it is a simple fact of the matter that the speed of at least one of the two surfaces will change speed during the transition from flat to curved and back to flat.OldYat47 said:A couple of comments: First, if the belt stretches elastically there is no "sudden change" in thickness. It tapers as it is stretched. On the top section and all the way to where it is in contact with the ground it would be stretched along its entire length by the effects of the drive gear pulling it. Second, I have definitely been trying to describe belts of non-zero thickness. Lastly, I am out of here. This thread is hopeless.
Do the math.OldYat47 said:You guys are a laugh. From very early on I have been talking about forward speed being the same as the tangential velocity of the outer surface of the track. "Requires a sudden change in density and speed"? Sheesh.
OldYat47 said:From very early on I have been talking about forward speed being the same as the tangential velocity of the outer surface of the track.
When track links reach the sprocket they transition from linear motion to rotational motion. This means the outer lug tips change speed and get further apart. When the track leaves the sprocket the reverse happens.OldYat47 said:"Requires a sudden change in density and speed"? Sheesh.
And "sheesh" is supposed to be a valid argument against it? If you do not understand it then don't try to argue against it.OldYat47 said:"Requires a sudden change in density and speed"? Sheesh.