Tire Overtreads--A Needed Invention
- Thread starter glennmac
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head on down to ya friendly NH man......get some of that wide belt stuff out of an old or new round baler (apparently they use wide belts now?.....
cut to length..........vulcanise with a big over lap together in a circle.........
jack the tractor up.......deflate the tire..........slip the belt over........inflate.......
strap with packing tape, or dog collars to the rim to stop them sliding side ways
the end
pudding
ps. this pic showed up at ytmag a while back............worth posting again
OI you! Get back to work
cut to length..........vulcanise with a big over lap together in a circle.........
jack the tractor up.......deflate the tire..........slip the belt over........inflate.......
strap with packing tape, or dog collars to the rim to stop them sliding side ways
the end
pudding
ps. this pic showed up at ytmag a while back............worth posting again
OI you! Get back to work
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jdkid
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Hi ya
well there ya go ,can be done i do notic all are 2 wheel drive tho but with tracks 4wd kinda comes useless
gives people a few ideas if doing a heap of snow work tracks for winter back to tires for summer best of both worlds
thanks for the pics pudding i'll spring ya a beer or two once i get up your way
catch ya
JD Kid
well there ya go ,can be done i do notic all are 2 wheel drive tho but with tracks 4wd kinda comes useless
gives people a few ideas if doing a heap of snow work tracks for winter back to tires for summer best of both worlds
thanks for the pics pudding i'll spring ya a beer or two once i get up your way
catch ya
JD Kid
hayden
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Hi Patrick,
I just read this more closely and what you are saying I think is completely correct, but is not the point I think we are debating. Maybe this is why we still don't see eye to eye.
My original comment to Glenn, restated hopefully more clearly, is: Take a 4x4 tractor with properly geared front and rear wheels for operating on flat ground just like many of us have today. The front and rear wheels are predominantly different sized, but things work without violance because the drive gearing is matched to the wheel size difference. This is your pully analogy and I think we agree on the need for proper gearing and we agree that the front and rear wheels will turn at different rotational speeds just like the pullies.
The point I was trying to make is that if you then wrap a track around those same drive wheels with that same gearing it will work just fine without slippage or skidding. Further more, it doesn't matter if the track is 1"" thick or 1' foot think, the tractor drive gearing and drive wheel sizes will still be correct and will propel the track without slippage.
Hopefully we are debating the same point. I've seen some lively conversations where in the end you discover the people are debating two different issues or points.
I just read this more closely and what you are saying I think is completely correct, but is not the point I think we are debating. Maybe this is why we still don't see eye to eye.
My original comment to Glenn, restated hopefully more clearly, is: Take a 4x4 tractor with properly geared front and rear wheels for operating on flat ground just like many of us have today. The front and rear wheels are predominantly different sized, but things work without violance because the drive gearing is matched to the wheel size difference. This is your pully analogy and I think we agree on the need for proper gearing and we agree that the front and rear wheels will turn at different rotational speeds just like the pullies.
The point I was trying to make is that if you then wrap a track around those same drive wheels with that same gearing it will work just fine without slippage or skidding. Further more, it doesn't matter if the track is 1"" thick or 1' foot think, the tractor drive gearing and drive wheel sizes will still be correct and will propel the track without slippage.
Hopefully we are debating the same point. I've seen some lively conversations where in the end you discover the people are debating two different issues or points.
StoneHeartFarm
Veteran Member
Hayden,
My gut is voting with you. Fuzzy math says it doesn't matter what the thickness of the belt is. The tires would be running on the inside of the belt, not on the outside. The effective diameters of the pulleys would be changed, which would result in different speeds of rotation (RPM), however, the distance the belt travels along its inside surface would be the same, irregardless of the belt's thickness. (It's very important we get this figured out, or every automobile ever built may be in danger of blowing its belts.) Assuming your track has an inside diameter of 10', and an outside diameter of 14' due to the added thickness. (The inside of a pipe is not the same diameter as the outside). So, for every rotation of the inside, the tractor will think it has gone 10'. But, actually, it will have gone 14'. No matter what, the outside of that track will go around once for every one time the inside goes around.
The third wheel you are seeing in the pictures is an idler, which basically helps to take the pressure off the top of the drive tires and reduces tire scrubbing. It also keeps the distance between centers shorter to prevent the track from jumping. The better you can hold the track the less likely it is to jump off.
Now for a question. I understood that on 4x4 trucks (at least), the front wheels are designed to turn at a slightly slower rate than the rears. This is to ensure you can maintain steering. Since the rear wheels are always pushing the fronts, there is always a slight drag, which allows the front tires to steer. This explains two things. A. Why 4x4's are lousy on ice (I've seen a lot of em with their rears trying to pass their fronts.) B. Why the maunfacturers always add a warning label saying something like :"Do not operate on dry pavement."
Does anyone know if this rotational difference also applies to 4x4 tractors?
SHF
PS: Patrick,
42? 42? I believe the correct response is: "So long, and thanks for all the fish" /w3tcompact/icons/wink.gif
My gut is voting with you. Fuzzy math says it doesn't matter what the thickness of the belt is. The tires would be running on the inside of the belt, not on the outside. The effective diameters of the pulleys would be changed, which would result in different speeds of rotation (RPM), however, the distance the belt travels along its inside surface would be the same, irregardless of the belt's thickness. (It's very important we get this figured out, or every automobile ever built may be in danger of blowing its belts.) Assuming your track has an inside diameter of 10', and an outside diameter of 14' due to the added thickness. (The inside of a pipe is not the same diameter as the outside). So, for every rotation of the inside, the tractor will think it has gone 10'. But, actually, it will have gone 14'. No matter what, the outside of that track will go around once for every one time the inside goes around.
The third wheel you are seeing in the pictures is an idler, which basically helps to take the pressure off the top of the drive tires and reduces tire scrubbing. It also keeps the distance between centers shorter to prevent the track from jumping. The better you can hold the track the less likely it is to jump off.
Now for a question. I understood that on 4x4 trucks (at least), the front wheels are designed to turn at a slightly slower rate than the rears. This is to ensure you can maintain steering. Since the rear wheels are always pushing the fronts, there is always a slight drag, which allows the front tires to steer. This explains two things. A. Why 4x4's are lousy on ice (I've seen a lot of em with their rears trying to pass their fronts.) B. Why the maunfacturers always add a warning label saying something like :"Do not operate on dry pavement."
Does anyone know if this rotational difference also applies to 4x4 tractors?
SHF
PS: Patrick,
42? 42? I believe the correct response is: "So long, and thanks for all the fish" /w3tcompact/icons/wink.gif
patrickg
Veteran Member
Haydn, I'm sorry to be the cause of any "thinking pains" or frustration, well almost.
You said: In fact, spacing the wheels farther apart in a track device will slow it down even more for the
same 2.27 rotations of the drive wheels.
I'm sorry but I'm losing it... I guess I'm just not smart enough to have your view explained to me so that I "believe".
I just can't imagine how the "wheelbase" would slow ground speed. D O E S N O T C O M P U T E for me.
I keep thinking that it the track doesnt slip, compress, or stretch a huge amount, the linear feet of track passing by a drive wheel is a linear function of the circumference of the drive wheel times the rotational rate of the drive wheel (RPM). I believe this is invariant with changing track lengths. How does the wheel know how long the track is? Sure the time required to rotate the track one time changes linearly in direct proportion to the change in track length but the length per unit time of the track (sans slippage, compression, or stretching) that goes by is invariant.
If this goes on much longer I may recommend binding arbitration or I may have to sue for peace separately with the various litigants (combatants). Of course these options would be like voting on the laws of physics and the various universal constants. I'm reminded of the school board member who wanted pi made three so kids wouldn't have such a hard time with it in math.
Ahh, my all time hero Galileo Galilei when his friends persuaded him to go before the pope to recant his heretical notions. He had to "take it back" to have his life spared B U T was heard to mutter under his breath as he withdrew "respectfully" from the pope's prescence, "It moves."
Patrick
P.S. Could you give me just a little more detail on the "goes slower if the tracks are longer" thing.
You said: In fact, spacing the wheels farther apart in a track device will slow it down even more for the
same 2.27 rotations of the drive wheels.
I'm sorry but I'm losing it... I guess I'm just not smart enough to have your view explained to me so that I "believe".
I just can't imagine how the "wheelbase" would slow ground speed. D O E S N O T C O M P U T E for me.
I keep thinking that it the track doesnt slip, compress, or stretch a huge amount, the linear feet of track passing by a drive wheel is a linear function of the circumference of the drive wheel times the rotational rate of the drive wheel (RPM). I believe this is invariant with changing track lengths. How does the wheel know how long the track is? Sure the time required to rotate the track one time changes linearly in direct proportion to the change in track length but the length per unit time of the track (sans slippage, compression, or stretching) that goes by is invariant.
If this goes on much longer I may recommend binding arbitration or I may have to sue for peace separately with the various litigants (combatants). Of course these options would be like voting on the laws of physics and the various universal constants. I'm reminded of the school board member who wanted pi made three so kids wouldn't have such a hard time with it in math.
Ahh, my all time hero Galileo Galilei when his friends persuaded him to go before the pope to recant his heretical notions. He had to "take it back" to have his life spared B U T was heard to mutter under his breath as he withdrew "respectfully" from the pope's prescence, "It moves."
Patrick
P.S. Could you give me just a little more detail on the "goes slower if the tracks are longer" thing.
hayden
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I agree, it doesn't make sense and I think now I've REALLY figured this out, but first....
Glenn, my appologies for taking this discussion off course, but it's too puzzling a question for me to resist. I guess we've gotten "side tracked" - yuk, yuk, yuk. But all jokes aside, this would in fact make a great extra credit question for a Mechanical Engineering exam.
Now back to the problem. I now believe that not only is the "It's a Bigger Wheel" model incorrect, but I believe my "It's two ovals" model is ALSO incorrect. The real answer comes from looking more closely at the problem and seeing that it's neither circles nor ovals, but that a track changes shape as it goes around.
Let's look at the same example where we have two equal sized drive wheels of 1' diameter, spaced 2' center to center, with a 1' thick track wrapped around. Now let's look at the track's shape and distances around the inner and outer surfaces.
The track can be broken into two parts, that which is in contact with the wheel, and that which is running straight between the wheels. The sections in contact with the wheels are two half circles, one forward of the front axle, and the other rearward or the rear axle. In these sections, the inner track surface length is 1/2 of the wheel circumference, or 1.57'. The outer track surface is 1/2 of the wheel circumference plus 2x the track thickness, or 9.41/2 => 4.71'. The outer length is considerably longer than the inner length.
Now look at the sections of track between the axles where the track is not in contact with the wheels. Each of these sections (one top and one bottom) is 2' long, and for both of these sections the inner track surface is exactly the same length as the outer track surface.
Now, how is this so? Well, as the track goes around, the outer surface expands as it goes around the wheel, and the expanded outer surface is indeed moving faster than the inner surface, BUT IT"S NOT IN CONTACT WITH THE GROUND! Ground contact occurs only between the two axels, and in that section the inner and outer lengths are exactly the same.
So, I now believe that a trackless vehicle (just drive wheels) will travel EXACTLY the same distance per drive wheel revolution as a tracked vehicle with the same drive wheels, and it will do this regardless of the track thickness. This is because the section of track in contact with the ground is always the same length as the inner track section covered by the drive wheel rotation.
The "Bigger wheel" model does not work because the bigger wheel is never in contact with the ground. The "concentric Oval" model is wrong too because the longer part of the outer surface is also never in contact with the ground.
To summarize, as a track goes around, the length in contact with the ground is exactly the same as the length that came in contact with the drive wheels. As the track leaves contact with the ground at the exact same time that is makes contact with the wheel, and for the whole time it's in contact with the wheel the outer surface of the track expands, either by stretching in the case of a belt, or "fanning out" as in the case of a metal track. The outer surface is moving much faster as it goes around the wheel, then slows back down to the drive wheel speed once it leaves contact with the wheel. If you watch a track you can clearly see this speed change.
A track is exactly like having a person walking in front of the vehicle doing just-in-time road construction (of any thickness) while someone else is walking behind doing just-in-time road destruction and passing the removed material forward to the road builder guy. The tractor speed and leverage is completely unchanged with the addition of tracks, just as the thickness of a road surface does not alter speed or leverage.
I also retract my assertion that wider wheel spacing changes things. It changes nothing.
I think this now makes sense. Does anyone else agree (or care)?
Glenn, my appologies for taking this discussion off course, but it's too puzzling a question for me to resist. I guess we've gotten "side tracked" - yuk, yuk, yuk. But all jokes aside, this would in fact make a great extra credit question for a Mechanical Engineering exam.
Now back to the problem. I now believe that not only is the "It's a Bigger Wheel" model incorrect, but I believe my "It's two ovals" model is ALSO incorrect. The real answer comes from looking more closely at the problem and seeing that it's neither circles nor ovals, but that a track changes shape as it goes around.
Let's look at the same example where we have two equal sized drive wheels of 1' diameter, spaced 2' center to center, with a 1' thick track wrapped around. Now let's look at the track's shape and distances around the inner and outer surfaces.
The track can be broken into two parts, that which is in contact with the wheel, and that which is running straight between the wheels. The sections in contact with the wheels are two half circles, one forward of the front axle, and the other rearward or the rear axle. In these sections, the inner track surface length is 1/2 of the wheel circumference, or 1.57'. The outer track surface is 1/2 of the wheel circumference plus 2x the track thickness, or 9.41/2 => 4.71'. The outer length is considerably longer than the inner length.
Now look at the sections of track between the axles where the track is not in contact with the wheels. Each of these sections (one top and one bottom) is 2' long, and for both of these sections the inner track surface is exactly the same length as the outer track surface.
Now, how is this so? Well, as the track goes around, the outer surface expands as it goes around the wheel, and the expanded outer surface is indeed moving faster than the inner surface, BUT IT"S NOT IN CONTACT WITH THE GROUND! Ground contact occurs only between the two axels, and in that section the inner and outer lengths are exactly the same.
So, I now believe that a trackless vehicle (just drive wheels) will travel EXACTLY the same distance per drive wheel revolution as a tracked vehicle with the same drive wheels, and it will do this regardless of the track thickness. This is because the section of track in contact with the ground is always the same length as the inner track section covered by the drive wheel rotation.
The "Bigger wheel" model does not work because the bigger wheel is never in contact with the ground. The "concentric Oval" model is wrong too because the longer part of the outer surface is also never in contact with the ground.
To summarize, as a track goes around, the length in contact with the ground is exactly the same as the length that came in contact with the drive wheels. As the track leaves contact with the ground at the exact same time that is makes contact with the wheel, and for the whole time it's in contact with the wheel the outer surface of the track expands, either by stretching in the case of a belt, or "fanning out" as in the case of a metal track. The outer surface is moving much faster as it goes around the wheel, then slows back down to the drive wheel speed once it leaves contact with the wheel. If you watch a track you can clearly see this speed change.
A track is exactly like having a person walking in front of the vehicle doing just-in-time road construction (of any thickness) while someone else is walking behind doing just-in-time road destruction and passing the removed material forward to the road builder guy. The tractor speed and leverage is completely unchanged with the addition of tracks, just as the thickness of a road surface does not alter speed or leverage.
I also retract my assertion that wider wheel spacing changes things. It changes nothing.
I think this now makes sense. Does anyone else agree (or care)?
Peter,
You dont have to apologize to me. This thread started with a hypothetical product. You are solving a problem for an actual product.
Your analysis makes sense to be. But, then again, so did all the prior ones as they were argued. Does it make any difference if the wheels are different sized. Then the upper length between wheels is longer than the length on the ground. Or is it only the one on the ground that counts.
You dont have to apologize to me. This thread started with a hypothetical product. You are solving a problem for an actual product.
Your analysis makes sense to be. But, then again, so did all the prior ones as they were argued. Does it make any difference if the wheels are different sized. Then the upper length between wheels is longer than the length on the ground. Or is it only the one on the ground that counts.
jdkid
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hay hayden
read "hang on gugs think about it" my last posting the light bulb goes on in there
catch ya
JD Kid
read "hang on gugs think about it" my last posting the light bulb goes on in there
catch ya
JD Kid
patrickg
Veteran Member
Haydn, I'm most plesed that you recant the aberant "speed varies with wheel base" nonsense. That is another step in the direction of our becoming more congruent in our thinking or expressing our thinking. If our discussion, coming under Glenn's Subject title is an embarassment or annoyance to him we could move to "Of topic, and just for blood, uh er ah I mean fun".
If you put this on a mechanical engineering exam the incidence of school shootings would skyrocket.
I agree with your surmise that the oval model is incorrect however, I would like to hear a cogent explanation of why the lever arm extending from the center of the axle and terminating at the ground's surface under the tread isn't the correct one to use in determining torque and other forces, speeds, and lengths in the system. Please strive to make this explanation NOT rely on rolling wheels along on unrolled tracks. Why this restriction? Because it seems too close to the idea that a thick tire, thin tire or no tire at all makes no difference and that taking the tire off and unrolling it under the car would achieve the same forces, torques, distances per revolution, etc. as driving the car with the tires on. I have some reservations with that. Succeed in this and my model will begin to crumble. I'm not being pig headed and this isn't a negotiation. Laws of physics don't secumb to political solutions. I believe all either of us wants (besides being right) is to find the truth, whether we are personally upheld or proven erroneous is secondary to the truth and its pursuit. Mental gymnastics are a noble employment of our faculties and win, loose, or draw all participants should profit from playing the game. Hope the rest aren't too upset with us.
Oh, by the way, it would sure help put a stake through the heart of my contention if in your cogent explanation you could explain the difference between two wheels without tracks running around them and a set of wheels with tracks running around them in the following areas:
With the exception of increased footprint (reason for the tracks in the first place but that isn't the issue in the is microcosm just now) what is the difference between a wheel of diameter x with a tire thickness of y and a track covered wheel of diameter x with a track thickness of y as the wheel base (inter axle distance decreases, degenerating the hypothetical example into a wheel of thickness x with a tire of thicknes y? You, I am sure recall some of the theory of calculus. Stuff like smoothly differentiable curves vs discontinuous curves like say a tangent (not our personal tangent but the math thingy)? So as the excess track is mentally shrunk and the two axles get closer and closer together until the two axles are one, at what point do we encounter the massive discontinuity. To uphold your view, there must be one. There must be someplace along the smooth transition where a non-linear transformation must suddenly occur as in the case of the tangent curve which suddenly with only an infintesimal change in the horizontal axis has the value of the vertical axis jump from negative to positive infinity.
I know some out there say, "but the front tires and back tires will rub on each other before the axles get too close." Remember we ain't a builldin' one of these to see what it does, we is a cussin and discussin the theory of operation.
Go get a beer while the grownups talk big people talk.
Ok, I'm back. Yup, you would have me down a queen and a rook if you could point out that inflection point or great discontinuity that we should discover following your model if we slowly "morph" the tracked version into the wheels only version with equal wheel diameters and tire size equal to tread thickness.
Ok, the above verbage contains a challenge which if taken and won could mortally wound my assertions and conjectures offered so far, I F you pick up the gauntlet and unhorse the challenger.
I'll just take two Excedrin and stay here in the shade a while...
Patrick
If you put this on a mechanical engineering exam the incidence of school shootings would skyrocket.
I agree with your surmise that the oval model is incorrect however, I would like to hear a cogent explanation of why the lever arm extending from the center of the axle and terminating at the ground's surface under the tread isn't the correct one to use in determining torque and other forces, speeds, and lengths in the system. Please strive to make this explanation NOT rely on rolling wheels along on unrolled tracks. Why this restriction? Because it seems too close to the idea that a thick tire, thin tire or no tire at all makes no difference and that taking the tire off and unrolling it under the car would achieve the same forces, torques, distances per revolution, etc. as driving the car with the tires on. I have some reservations with that. Succeed in this and my model will begin to crumble. I'm not being pig headed and this isn't a negotiation. Laws of physics don't secumb to political solutions. I believe all either of us wants (besides being right) is to find the truth, whether we are personally upheld or proven erroneous is secondary to the truth and its pursuit. Mental gymnastics are a noble employment of our faculties and win, loose, or draw all participants should profit from playing the game. Hope the rest aren't too upset with us.
Oh, by the way, it would sure help put a stake through the heart of my contention if in your cogent explanation you could explain the difference between two wheels without tracks running around them and a set of wheels with tracks running around them in the following areas:
With the exception of increased footprint (reason for the tracks in the first place but that isn't the issue in the is microcosm just now) what is the difference between a wheel of diameter x with a tire thickness of y and a track covered wheel of diameter x with a track thickness of y as the wheel base (inter axle distance decreases, degenerating the hypothetical example into a wheel of thickness x with a tire of thicknes y? You, I am sure recall some of the theory of calculus. Stuff like smoothly differentiable curves vs discontinuous curves like say a tangent (not our personal tangent but the math thingy)? So as the excess track is mentally shrunk and the two axles get closer and closer together until the two axles are one, at what point do we encounter the massive discontinuity. To uphold your view, there must be one. There must be someplace along the smooth transition where a non-linear transformation must suddenly occur as in the case of the tangent curve which suddenly with only an infintesimal change in the horizontal axis has the value of the vertical axis jump from negative to positive infinity.
I know some out there say, "but the front tires and back tires will rub on each other before the axles get too close." Remember we ain't a builldin' one of these to see what it does, we is a cussin and discussin the theory of operation.
Go get a beer while the grownups talk big people talk.
Ok, I'm back. Yup, you would have me down a queen and a rook if you could point out that inflection point or great discontinuity that we should discover following your model if we slowly "morph" the tracked version into the wheels only version with equal wheel diameters and tire size equal to tread thickness.
Ok, the above verbage contains a challenge which if taken and won could mortally wound my assertions and conjectures offered so far, I F you pick up the gauntlet and unhorse the challenger.
I'll just take two Excedrin and stay here in the shade a while...
Patrick
patrickg,
Nice challenge - will need some diagramming I do believe.
Of course, there can be no discontinuity as you state - the challenge is in clearing up some of the murky language so far used to describe the problem. I'll have a crack at a diagram tomorrow and see where it takes us.
It's always the small, unaccounted for variables that control these problems. They never simplify well - unless you want thrown tracks and snapped belts!! The difference between a bright idea in the bathtub and a 'I didn't expect that' in the field ...
Patrick
Nice challenge - will need some diagramming I do believe.
Of course, there can be no discontinuity as you state - the challenge is in clearing up some of the murky language so far used to describe the problem. I'll have a crack at a diagram tomorrow and see where it takes us.
It's always the small, unaccounted for variables that control these problems. They never simplify well - unless you want thrown tracks and snapped belts!! The difference between a bright idea in the bathtub and a 'I didn't expect that' in the field ...
Patrick
hayden
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Look at this in the time domain. Assume in our example that the drive wheel is rotating at 1 revolution per minute.
Every minute the following happens.
1) 3.14 ft of track travels over the contact area between the drive wheel and track inner surface. (rotating wheel in contact with a surface)
2) 3.14 ft of track travels along the two ft span between the wheels on the inner surface directly over the road surface contact area. (inner track is fixed length without contraction or compression hence movement at one point in contact with drive wheel has corresponding movement of another point anywhere else on same surface)
3) 3.14 ft of track travels in contact with the road (straight section of track is a rectangular solid without compression or expansion, so all points - inner surface and outer surface - are moving in the same straight line at the same speed.
4) 9.42 ft of track travels around the half circle forming the outer track surface on the same radius as the wheel-track contact area. (This is the distance around that path - basic geometry) The track achieves this by expanding on it's outer surfaces as it rounds the wheel.
5) The area where the track contacts the ground causes forward movement. 3.14 ft of track traverses this contact point so vehicle moves 3.14 ft.
6) A drive wheel in direct contact with the ground rotating at the same 1 revolution per minute will also move the vehicle 3.14 ft.
At this point hopefully we agree the tracked vehicle moves at the same speed as the untracked vehicle. If not, let me know which step above is off or missing.
7) If the ground contact point were on either of the two end half circles, 9.42 ft would move in contact with the ground. This is the only way to get speed and leverage the same as a 3 ft wheel.
Conclusion: The track propels the vehicle at the same speed as the wheels alone when the contact point is on the straight part of the track. If the contact point is on the half circle part of the track then propulsion will be equivalent to a wheel with diameter equal to the sum of the drive wheel plus 2x the track thickness.
As for the moment arm, it runs down vertically from the axle to the point on the wheel where the track departs the wheel. These are the end points of the moment arm so it's length is the wheel radius. Why doesn't it extend through the track to the ground? Because the line extending through the track is passing through a solid in flat contact with the ground and it's incapable of pivoting. Same reason the moment arm of a tire doesn't extend through the solid surface of a road. In contrast if you tip the track on end and place the half circle end in contact with the ground, the track is no longer a solid flat on the ground but rather a solid in full contact with the wheel such that it must be pivoting as part of the wheel radius, so the moment arm includes the track thickness in that case.
The discontinuity is in the transition between being on the circumference of a circle to being on it's tangent. When the ground contact is on the tangent, the world looks one way, and when it's on the circumference it looks another way. As the two drive wheels come closer together until they are concentric, the drive contact area makes an institaneous transition from being a tangent to being on the circle. The solid surface that the wheel moment arm is pushing against instantaneously disappears and the moment arm extends the full distance.
Every minute the following happens.
1) 3.14 ft of track travels over the contact area between the drive wheel and track inner surface. (rotating wheel in contact with a surface)
2) 3.14 ft of track travels along the two ft span between the wheels on the inner surface directly over the road surface contact area. (inner track is fixed length without contraction or compression hence movement at one point in contact with drive wheel has corresponding movement of another point anywhere else on same surface)
3) 3.14 ft of track travels in contact with the road (straight section of track is a rectangular solid without compression or expansion, so all points - inner surface and outer surface - are moving in the same straight line at the same speed.
4) 9.42 ft of track travels around the half circle forming the outer track surface on the same radius as the wheel-track contact area. (This is the distance around that path - basic geometry) The track achieves this by expanding on it's outer surfaces as it rounds the wheel.
5) The area where the track contacts the ground causes forward movement. 3.14 ft of track traverses this contact point so vehicle moves 3.14 ft.
6) A drive wheel in direct contact with the ground rotating at the same 1 revolution per minute will also move the vehicle 3.14 ft.
At this point hopefully we agree the tracked vehicle moves at the same speed as the untracked vehicle. If not, let me know which step above is off or missing.
7) If the ground contact point were on either of the two end half circles, 9.42 ft would move in contact with the ground. This is the only way to get speed and leverage the same as a 3 ft wheel.
Conclusion: The track propels the vehicle at the same speed as the wheels alone when the contact point is on the straight part of the track. If the contact point is on the half circle part of the track then propulsion will be equivalent to a wheel with diameter equal to the sum of the drive wheel plus 2x the track thickness.
As for the moment arm, it runs down vertically from the axle to the point on the wheel where the track departs the wheel. These are the end points of the moment arm so it's length is the wheel radius. Why doesn't it extend through the track to the ground? Because the line extending through the track is passing through a solid in flat contact with the ground and it's incapable of pivoting. Same reason the moment arm of a tire doesn't extend through the solid surface of a road. In contrast if you tip the track on end and place the half circle end in contact with the ground, the track is no longer a solid flat on the ground but rather a solid in full contact with the wheel such that it must be pivoting as part of the wheel radius, so the moment arm includes the track thickness in that case.
The discontinuity is in the transition between being on the circumference of a circle to being on it's tangent. When the ground contact is on the tangent, the world looks one way, and when it's on the circumference it looks another way. As the two drive wheels come closer together until they are concentric, the drive contact area makes an institaneous transition from being a tangent to being on the circle. The solid surface that the wheel moment arm is pushing against instantaneously disappears and the moment arm extends the full distance.
jdkid
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- 8350 valmet with 980SL FEL duels had a 150 Hp deutz just sold it 10 NOV 01
Hi ya's
hey i may have nutted something out Hayden ya right it's what i've been trying to say BUT in a patrickg is right too (ya both got to say how so !!!)hayden me and you have been looking at it like a dozer track (hinges in side out ie opens like this < ,while going around a driver.)that is right but if you take a "V" belt (one of them coged ones)the inside changes becouse it contracts on the pulley so the out side runs the same speed all the time but is faster than the inside .but in this case we are talking about tracks so inside speed remanes the same all the time
catch ya
JD Kid
hey i may have nutted something out Hayden ya right it's what i've been trying to say BUT in a patrickg is right too (ya both got to say how so !!!)hayden me and you have been looking at it like a dozer track (hinges in side out ie opens like this < ,while going around a driver.)that is right but if you take a "V" belt (one of them coged ones)the inside changes becouse it contracts on the pulley so the out side runs the same speed all the time but is faster than the inside .but in this case we are talking about tracks so inside speed remanes the same all the time
catch ya
JD Kid
jdkid
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Hi ya's
better way of putting it take 10 foot of flat rubber now cut V's every 2 inchs so there is just a strip holding it all together now make 2track shapes 1 with V's in ,one with V's out the one with V's out is a dozer track the inside stays the same ie10 foot..the one like a belt is 10 foot on the outside ie the in side is less .now if we made both tracks the same inside diamater the belt type would drive the tractor faster as the outside dosenot change but the track would drive the same speed as the driveing wheel .but back to the story, if all drivers were timed with each other it could be done, just that the belt type would in crease ya speed
catch ya
JD Kid
better way of putting it take 10 foot of flat rubber now cut V's every 2 inchs so there is just a strip holding it all together now make 2track shapes 1 with V's in ,one with V's out the one with V's out is a dozer track the inside stays the same ie10 foot..the one like a belt is 10 foot on the outside ie the in side is less .now if we made both tracks the same inside diamater the belt type would drive the tractor faster as the outside dosenot change but the track would drive the same speed as the driveing wheel .but back to the story, if all drivers were timed with each other it could be done, just that the belt type would in crease ya speed
catch ya
JD Kid
hayden
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Yes, you have a very good point. The track, or belt, or whatever can be designed such that the outter surface expands to go around the wheels, or the inner surface could contract to go around the wheel. In all my examples I've assumed the outer surface expands which is the case in drive tracks that I've seen, and I think is the case with a fan belt. In the case of a cogged fan belt it's not clear to me how much the coggs collaps when rounding the wheel verses simply provide an interlocking mechanism. Maybe it's a combination. Either way, at any point in time the distance around the inner path and outer path is the same regardless of HOW the track was formed into that shape. The "do you stretch it or do you compress it" question I think only affects the length of the track if you lay it out flat on the ground. An "expansion" track would lay out flat and measure the length of the inner path, where a "compression" track woudl lay out flat and measure the length of the outer track. With either track design I think the model still holds true and travel speed and leverage is the same.
Either way I think we've been able to show why you can't model a tracked vehicle as a wheeled vehicle with bigger wheels. My description I'm sure is far from a rigorous proof but I think it does answer the questions. Maybe if there's someone with more current and practiced acedemic skills they can help formalize it a bit. I haven't done calculus in close to 25 years and probably couldn't remember how to solve the simplest integral or differential. Also, the circle to tangent transition may be improperly called a discontinuity - I don't know. It clearly is an instantaneous transition point that appears to be fundamental in the mechanics of a track. Which side of that point you are one determines if you have a short moment arm pushing against a solid object, or a longer moment arm pushing against a single point of road contact and causing rolling action.
Anyway - got to get to work now.
Peter
Either way I think we've been able to show why you can't model a tracked vehicle as a wheeled vehicle with bigger wheels. My description I'm sure is far from a rigorous proof but I think it does answer the questions. Maybe if there's someone with more current and practiced acedemic skills they can help formalize it a bit. I haven't done calculus in close to 25 years and probably couldn't remember how to solve the simplest integral or differential. Also, the circle to tangent transition may be improperly called a discontinuity - I don't know. It clearly is an instantaneous transition point that appears to be fundamental in the mechanics of a track. Which side of that point you are one determines if you have a short moment arm pushing against a solid object, or a longer moment arm pushing against a single point of road contact and causing rolling action.
Anyway - got to get to work now.
Peter
jdkid
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Hi ya hayden
i think a fanbelt contracts as most i have seen have a stronger backing also fanbelt cracks on the inside from flexing ,most coged belts ya find on gear that has a pulley running off the back of the belt or a small pulley
i think a belt maybe faster tho and bigger would be faster still .
ok pic this 1 belt and 1 track both haveing 20 foot outside meserment (?)where they would touch the ground .both have 16 foot inside meserment (i don't know how thick etc etc ) now knowing the track expandes to go around wheels 1 full turn of the track = 16 foot (hell i hope i got this right) but cos the belt contracts 1 full turn =20 foot (of travel in both cases) meaning that patrickg's tractor would be faster on belts than ours on tracks
i know a heaps of maths would back this up but i'm a better driver than math's man
catch ya
JD Kid
i think a fanbelt contracts as most i have seen have a stronger backing also fanbelt cracks on the inside from flexing ,most coged belts ya find on gear that has a pulley running off the back of the belt or a small pulley
i think a belt maybe faster tho and bigger would be faster still .
ok pic this 1 belt and 1 track both haveing 20 foot outside meserment (?)where they would touch the ground .both have 16 foot inside meserment (i don't know how thick etc etc ) now knowing the track expandes to go around wheels 1 full turn of the track = 16 foot (hell i hope i got this right) but cos the belt contracts 1 full turn =20 foot (of travel in both cases) meaning that patrickg's tractor would be faster on belts than ours on tracks
i know a heaps of maths would back this up but i'm a better driver than math's man
catch ya
JD Kid
patrickg
Veteran Member
Patrick, I see we are converging. Usually do when everyone is patient and actually considers all points of view.
Now that you accept the NO_DISCONTINUTY concept, the implications of that is that you agree with my basic understanding of how it works pretty much in its entirety with the exception of some area(s)t you have called muddy language. Likely mine, yours, and everyone elses even peripherally involved. Or rephrased less egocentrically, our mutual ongoing understanding is approaching congruity.
Haydn, on the other hand is still out there holding onto the extreme and untenable idea that track thicknes doesn't equate to tire profile/thickness or effect the vehicle speed given the same RPM, assumining I recall his comments without reference to the written word.
I have difficulty with the delayed turnaround. I'm much more used to a fast paced give and take with a chalk or dryboard handy. Then usually diferences are either erased or solidified much more speedily and I come across much more better on a personal level when you can see me (no visible horns, tail, un-forked tongue).
If there are any residual REAL differences in our understanding of the physics, mechanics, or math beyond that masked with imprecise language, please point them out and I will try to agree with you, if able, or try to pose an example or question that I think will illuminate the issue.
If there are none, I'm ready to sign a separate peace with you and proceed to deal with Haydn. Or if we are in basic agreement perhaps you can have an exchange with Haydn, I may not have the requisite background experience to formulate communicative but definitive examples within the envelope of his personal experience base.
Patrick
Now that you accept the NO_DISCONTINUTY concept, the implications of that is that you agree with my basic understanding of how it works pretty much in its entirety with the exception of some area(s)t you have called muddy language. Likely mine, yours, and everyone elses even peripherally involved. Or rephrased less egocentrically, our mutual ongoing understanding is approaching congruity.
Haydn, on the other hand is still out there holding onto the extreme and untenable idea that track thicknes doesn't equate to tire profile/thickness or effect the vehicle speed given the same RPM, assumining I recall his comments without reference to the written word.
I have difficulty with the delayed turnaround. I'm much more used to a fast paced give and take with a chalk or dryboard handy. Then usually diferences are either erased or solidified much more speedily and I come across much more better on a personal level when you can see me (no visible horns, tail, un-forked tongue).
If there are any residual REAL differences in our understanding of the physics, mechanics, or math beyond that masked with imprecise language, please point them out and I will try to agree with you, if able, or try to pose an example or question that I think will illuminate the issue.
If there are none, I'm ready to sign a separate peace with you and proceed to deal with Haydn. Or if we are in basic agreement perhaps you can have an exchange with Haydn, I may not have the requisite background experience to formulate communicative but definitive examples within the envelope of his personal experience base.
Patrick
Assume the model with 2 equal size wheels with the tracks going around them. Now put a third wheel under the track. So the track goes under the front wheel, over the middle wheel, and under the back wheel. The track is now touching the ground only at the tangent points of the front and back wheels. What happens to the speed of the tractor? Is this like Peter's example of the tractor standing on its nose? Does this example affect anyone's viewpoint?
patrickg
Veteran Member
Hi Haydn, Finally got a chance to read your latest. Time domain? You got me all ready for fourier transforms or some sophisticated stuff and then nothing... back to rotating wheels with unstated error introducing assumptions.
OK a wheel rotates once a minute and goes 3.14 ft, assuming the wheel is 1 ft in diameter, which wasn't stated. Statement 1 is true. Statement 2 is conditionally true with the assumption that the track is infintesimally thin (at least much much thinner than the diameter of the wheel so that its thickness, which adds to the wheels radius, is not contributing significantly to the diameter of the wheel.
Not sure what this next part is trying to say...
3) 3.14 ft of track travels in contact with the road (straight section of track is a
rectangular solid without compression or expansion, so all points - inner surface and
outer surface - are moving in the same straight line at the same speed.
Unless this system is "laying rubber" i.e. spinning its wheels uh er ah "track", the part of the track in contact with the ground isn't moving. So, yes the top and bottom surfaces of this stationary track are going equal speeds, zero, the straight line part is mute.
You're really starting to lose me on this next part.
4) 9.42 ft of track travels around the half circle forming the outer track surface on the
same radius as the wheel-track contact area. (This is the distance around that path -
basic geometry) The track achieves this by expanding on it's outer surfaces as it rounds
the wheel.
I don't get the part just before, "The track achieves this by expanding on it's outer surfaces as it rounds
the wheel."
Give me some more detail or an example illustrating this last statement. I'm not sure why this track that was, a moment ago, rectangular solid and apparently infinitely rigid but bendable (strong thin steel band or something) as it could neither be compressed or stretched, suddenly expands on its outer surface as it rounds the wheel. This disagrees with and is inconsistent as regards the "thin" assumption that was required to get past an earlier statement.
OK I'm hanging in there to read, analyze, and comment on the conclusion B U T it is not logically consistent to disagree with the premises and accept the conclusion. If it were a logically constructed argument calling any premise into question, inescapably questions the conclusion. Still, I'll have a look.
OK, had a look, ought to say, "no comment", I'd get into less trouble but lets try this, I don't buy it for now and don't think we were close enough in the earlier stuff (numbered section) that I could have a valid surmise on the conclusion, see paragraph above.
e.g. you said "The discontinuity is in the transition between being on the circumference
of a circle to being on it's tangent."
I don't understand what you mean. By definition all tangents are on the circumference at the point of tangency. If you refer to the flat part of the track on the ground as a tangent to the circle at the bottom of the wheel then I still don't know what you mean by discontinuity or how it figures in.
A. Maybe you could get it through my thick skull faster if you explained to me the difference between your "two wheels running on a track laid out on the ground" thingy (with real world thickness to track N O T thin") and taking the tire off of a wheel cuting it into in one place laying it out on the ground and driving over it with the tireless wheel.
B. I would also like your "take" on the thought experiment where we shorten the wheel base of a thick track using vehicle until the axels merge and we have a wheel with a tire the thickness of the original track. Where is the discontinuity in this? At what point does the behavior "know" to change from the Haydn-Track tracked model to just about everybody in the world's wheel-with-tire model.
If you can explain these last two things, A and B above, in a clear, concise, and communicable manner then I'll probably throw in the towel, and have a rootbeer float in your honor. Probably to the undying (for several seconds) appreciation of the viewers at home.
Patrick
OK a wheel rotates once a minute and goes 3.14 ft, assuming the wheel is 1 ft in diameter, which wasn't stated. Statement 1 is true. Statement 2 is conditionally true with the assumption that the track is infintesimally thin (at least much much thinner than the diameter of the wheel so that its thickness, which adds to the wheels radius, is not contributing significantly to the diameter of the wheel.
Not sure what this next part is trying to say...
3) 3.14 ft of track travels in contact with the road (straight section of track is a
rectangular solid without compression or expansion, so all points - inner surface and
outer surface - are moving in the same straight line at the same speed.
Unless this system is "laying rubber" i.e. spinning its wheels uh er ah "track", the part of the track in contact with the ground isn't moving. So, yes the top and bottom surfaces of this stationary track are going equal speeds, zero, the straight line part is mute.
You're really starting to lose me on this next part.
4) 9.42 ft of track travels around the half circle forming the outer track surface on the
same radius as the wheel-track contact area. (This is the distance around that path -
basic geometry) The track achieves this by expanding on it's outer surfaces as it rounds
the wheel.
I don't get the part just before, "The track achieves this by expanding on it's outer surfaces as it rounds
the wheel."
Give me some more detail or an example illustrating this last statement. I'm not sure why this track that was, a moment ago, rectangular solid and apparently infinitely rigid but bendable (strong thin steel band or something) as it could neither be compressed or stretched, suddenly expands on its outer surface as it rounds the wheel. This disagrees with and is inconsistent as regards the "thin" assumption that was required to get past an earlier statement.
OK I'm hanging in there to read, analyze, and comment on the conclusion B U T it is not logically consistent to disagree with the premises and accept the conclusion. If it were a logically constructed argument calling any premise into question, inescapably questions the conclusion. Still, I'll have a look.
OK, had a look, ought to say, "no comment", I'd get into less trouble but lets try this, I don't buy it for now and don't think we were close enough in the earlier stuff (numbered section) that I could have a valid surmise on the conclusion, see paragraph above.
e.g. you said "The discontinuity is in the transition between being on the circumference
of a circle to being on it's tangent."
I don't understand what you mean. By definition all tangents are on the circumference at the point of tangency. If you refer to the flat part of the track on the ground as a tangent to the circle at the bottom of the wheel then I still don't know what you mean by discontinuity or how it figures in.
A. Maybe you could get it through my thick skull faster if you explained to me the difference between your "two wheels running on a track laid out on the ground" thingy (with real world thickness to track N O T thin") and taking the tire off of a wheel cuting it into in one place laying it out on the ground and driving over it with the tireless wheel.
B. I would also like your "take" on the thought experiment where we shorten the wheel base of a thick track using vehicle until the axels merge and we have a wheel with a tire the thickness of the original track. Where is the discontinuity in this? At what point does the behavior "know" to change from the Haydn-Track tracked model to just about everybody in the world's wheel-with-tire model.
If you can explain these last two things, A and B above, in a clear, concise, and communicable manner then I'll probably throw in the towel, and have a rootbeer float in your honor. Probably to the undying (for several seconds) appreciation of the viewers at home.
Patrick
