GolfAddict
Veteran Member
I'm reading these posts absolutely fascinated, head spinning a bit, and then I hit this. Just about laughed my ***** off.
Calculating Your Predicted Rollover Angle
- Thread starter Rhino35
- Start date
I'm reading these posts absolutely fascinated, head spinning a bit, and then I hit this. Just about laughed my ***** off.
CalG
Super Member
- Joined
- Sep 29, 2011
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- 5,105
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- vermont
- Tractor
- Hurlimann 435, Fordson E27n, Bolens HT-23, Kubota B7200
What Black Dark is describing is exactly true in any case where a rear wheel lifts from the ground prior to tipping over. We have all seen the "Joey Chitwood Stunt Show" trick of driving along with the vehicle tipped up on two wheels.
However, When evaluating the maximum slope that a stationary tractor can keep it's wheels on the ground, that description does not apply.
Simply, if the ground is tipped, the uphill rear wheel leaves the surface at precisely the same angle that causes the entire tractor to tip over. Which is when the CoG crosses over the line of support, which is the down hill contact point on a solid axle.
However, When evaluating the maximum slope that a stationary tractor can keep it's wheels on the ground, that description does not apply.
Simply, if the ground is tipped, the uphill rear wheel leaves the surface at precisely the same angle that causes the entire tractor to tip over. Which is when the CoG crosses over the line of support, which is the down hill contact point on a solid axle.
CalG (and DarkBlack),
CalG, I agree with you. I read an article by Chrysler this morning that discussed roll axis and while I admit I don't understand it all I saw nothing that directly related to the tip over angle of a static tractor (or one traveling very slow). All the roll axis depicted were very low - in most case below the axles of low sprung cars. And it was obvious that the concept of roll axis and how it relates to modern car handling is one that a lot of automotive people have trouble understanding.
DarkBlack, the line you pictured from the outside of the downhill rear tire to the center pivot point of the front axle seems fine - I agree that as long as the front axle pivots there is no force on the outside of the downhill front tire. It stays flat on the ground (if we're jacking up a tractor on level ground to find the rollover angle). So maybe the pivot - probably - the pivoting front axle is a design that assists stability - and in particular assist a four wheel drive tractor's traction on a hillside. But my point, and I think it marries up with CalG's, is that when the front axle hits the stops, just as you say, the roll axis shifts to the outside of the downhill front wheel and we're in a situation now - at whatever angle the axle hits the stops, where the front axle behaves like a fixed axle. I'm pretty sure the rollover angle based on the CG moving over the support base is greater than the pivot stop angle - so that pivoting axle won't make a difference to the eventual actual rollover angle.
I also think CalG makes a good point when he says you are talking about a tractor with an FEL loaded, or on a hill, in such a way that the front weight of the tractor lifts a rear wheel. I think I made the observation in my OP that if that happens the tractor might not only roll, but begin swapping ends in the process of the rollover.
Maybe we're talking past each other. Maybe someone has an old scrap tractor, with a pivoting front axle, and a front axle that is wide, not a triangle, who is willing to jack it up. How about we submit this to Mythbusters?
Best,
Rhino
CalG, I agree with you. I read an article by Chrysler this morning that discussed roll axis and while I admit I don't understand it all I saw nothing that directly related to the tip over angle of a static tractor (or one traveling very slow). All the roll axis depicted were very low - in most case below the axles of low sprung cars. And it was obvious that the concept of roll axis and how it relates to modern car handling is one that a lot of automotive people have trouble understanding.
DarkBlack, the line you pictured from the outside of the downhill rear tire to the center pivot point of the front axle seems fine - I agree that as long as the front axle pivots there is no force on the outside of the downhill front tire. It stays flat on the ground (if we're jacking up a tractor on level ground to find the rollover angle). So maybe the pivot - probably - the pivoting front axle is a design that assists stability - and in particular assist a four wheel drive tractor's traction on a hillside. But my point, and I think it marries up with CalG's, is that when the front axle hits the stops, just as you say, the roll axis shifts to the outside of the downhill front wheel and we're in a situation now - at whatever angle the axle hits the stops, where the front axle behaves like a fixed axle. I'm pretty sure the rollover angle based on the CG moving over the support base is greater than the pivot stop angle - so that pivoting axle won't make a difference to the eventual actual rollover angle.
I also think CalG makes a good point when he says you are talking about a tractor with an FEL loaded, or on a hill, in such a way that the front weight of the tractor lifts a rear wheel. I think I made the observation in my OP that if that happens the tractor might not only roll, but begin swapping ends in the process of the rollover.
Maybe we're talking past each other. Maybe someone has an old scrap tractor, with a pivoting front axle, and a front axle that is wide, not a triangle, who is willing to jack it up. How about we submit this to Mythbusters?
Best,
Rhino
DKCDKC
Platinum Member
As a physics major many years ago, I find the discussion interesting, if a bit esoteric. Knowing the slope that a stationary tractor could endure without rolling is interesting, but of little value. After all, that stationary tractor would have had to get to that position by moving.
In any event, the real world is marked by slopes with depressions and rises in them. Effective slope angles essentially change constantly. Add to that the various weights attached to the tractor, and you get a rather vague flip factor. Most of us have endured the agony of finding ourselves on a slope where we are not sure how much more the tractor will take. I am particularly sensitive because I have one of those narrow CUTs and have lifted the rear wheel a few times in the past year. I didn't have to change my underwear, but it is not something I want to do often. To me the secret is to be cautious and slow. By going slow on any significant slope, I give myself time to react. I have found that dropping the FEL and implement seem to immediately halt the roll and pull wheels on the ground. That gives you time to decide on your next action. Usually I have been able to lift stuff a tad and back off the problem slope without difficulty. Turning downhill can be problematic. A friend actually got off and dug some dirt from behind the uphill tires and was able to back out comfortably.
But going slow and wearing your seatbelt is the key. Although I think a spring-loaded outrigger that would pop to your downhill side and lock would be helpful now and again. I just don't have time to invent it.
In any event, the real world is marked by slopes with depressions and rises in them. Effective slope angles essentially change constantly. Add to that the various weights attached to the tractor, and you get a rather vague flip factor. Most of us have endured the agony of finding ourselves on a slope where we are not sure how much more the tractor will take. I am particularly sensitive because I have one of those narrow CUTs and have lifted the rear wheel a few times in the past year. I didn't have to change my underwear, but it is not something I want to do often. To me the secret is to be cautious and slow. By going slow on any significant slope, I give myself time to react. I have found that dropping the FEL and implement seem to immediately halt the roll and pull wheels on the ground. That gives you time to decide on your next action. Usually I have been able to lift stuff a tad and back off the problem slope without difficulty. Turning downhill can be problematic. A friend actually got off and dug some dirt from behind the uphill tires and was able to back out comfortably.
But going slow and wearing your seatbelt is the key. Although I think a spring-loaded outrigger that would pop to your downhill side and lock would be helpful now and again. I just don't have time to invent it.
IslandTractor
Super Star Member
- Joined
- Sep 15, 2005
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- 17,101
- Location
- Prudence Island, RI
- Tractor
- 2007 Kioti DK40se HST, Woods BH
I agree with your points. The practical challenge is how to work safely on slopes.
One question I have pondered is whether it makes more sense to turn the wheels uphill or downhill if you feel the tractor starting to tip when moving across a slope. I would guess downhill but wonder if any of you Newtonian physicists can shed some light on the mechanics of such a dynamic scenario.
IslandTractor,
If you're moving then turn downhill (unless it is into a pond, etc.). If you turn downhill then centripetal force will offset gravity and might keep you from rolling over. If you turn uphill you'll add centripetal force to gravity and increase the likelihood of a rollover.
Rhino
If you're moving then turn downhill (unless it is into a pond, etc.). If you turn downhill then centripetal force will offset gravity and might keep you from rolling over. If you turn uphill you'll add centripetal force to gravity and increase the likelihood of a rollover.
Rhino
DarkBlack
Veteran Member
I'd be a concerned about that 5"? thru-bolt design. You might be luck and It might last forever for you , it might not. Normally you short bolt a spacer from the back to an axle hub and then short bolt the wheel to the front of the spacer, it's a much stronger design. Hitting a jarring bump, could put heavy racking force on those long bolts. Lets us know how it holds up.
DarkBlack,
Thanks for pointing out that long bolts would not be as strong. I hadn't given it any real thought. From the beginning of my negotiations with Motorsport-Tech I was informed they would send me all the bolt hardware. When it got here I didn't have an intuitive understanding of how it would all go together. A phone call to Lenny the owner and he explained it to me.
I threw the pictures up in a hurry today. I should have explained how the bolts provided by Motorsport-Tech work. They gave me six stainless steel bolts per wheel to attach the spacer to the hub through drilled out holes big enough for the bolt heads to fit, and six of the black bolts in the photo per wheel to attach the wheel to the spacer. So all the bolts are pretty much the original length of the stock set up. Here they are painted before installation.
And here is me and some of the hardware the day the spacers arrived! The weeds on the hillside have no chance against me now! A close examination shows there are some scratches in the anodizing layer on one of the spacers - in fact there photos were sent to Lenny to show him how they were scratched. This unusual slight damage was from a few of the bolts getting loose in the box - they were in plastic bags which must have torn during shipping. When I mentioned this to Lenny he immediately offered to make me another spacer, which I declined as I was always going to paint them. I was in high obsessive compulsive mode regarding combating any future corrosion, but the small scratches were not going to make a difference to my tractor - which I'm lucky enough to keep in a detached garage. They painted perfectly. I mentioned it in my OP, but Motorsport-Tech impressed me totally with their eagerness to stand behind their workmanship.
DKCDKC (and all),
I reread the thread and I also think the comments are interesting. Esoteric knowledge is by definition difficult for most people to understand and we've had posters make valid points, but not always talking about the same situation. It is impossible to confine a discussion of tractor rollover angles to a static situation - and we really shouldn't because they are moving - but you have to start somewhere. With the static angles in mind, then it makes sense to back way off from them because of the variables. My goal here was to enhance safety awareness, not empower folks to take greater risks.
DarkBlack and CalG, methinks, kind of got into a talking past each other discussion. My point, and CalG's, was that for a FLAT hillside - in other words the front and rear tires are on a constant, flat, inclined surface, the roll axis will, by virtue of the tractor tip over angle being greater than the pivot stop angle not be an important factor. The tractor will behave irrespective of the roll axis point for a pivoting front axle.
In my example I talked about (and envisioned without thinking about the pivoting front axle) jacking the tractor up on one side on level ground to see the angle at which the CG would move outside the support base and tip over. And if we did that I now realize, thanks to DarkBlack and CalG, that the front axle would pivot and keep the front wheels flat while one rear wheel went up in the air. So DarkBlack's explanation about drawing an imaginary roll axis is correct. It would initially be the line from the "downhill" rear tire to the center of the front axle, but when the axle hits the stops that roll axis moves downward and "downhill" towards the outside of the "downhill" front wheel. That would be a dynamic effect, but I also don't see it as a catastrophic rollover inducing moment. If the tractor is stable at, say a maximum front axle pivot angle of 20 degrees, and we keep jacking it up to 21 degrees the tractor doesn't roll over. All that happens on a level floor is the "uphill" front tire moves up 1 degree. Now with the front axle is behaving like a rigid rear axle so if we keep jacking up the same side the only variable (ignoring tire deformation, if any, and lack of friction so the tractor slides) affecting rollover is where is the CG? The instant vertical CG exceeds the lateral boundary of the support wheel base the tractor will roll over. And as the math shows, even with a wide variety of vertical CG's, it's pretty high.
I'll even make an additional point about the pivoting front axle now that I've given it more thought. The practical effect of the pivoting action is to lower the tractor's CG by lowering the front of the tractor with respect to where it would remain with a fixed axle. This shouldn't be too hard to imagine - picture two identical tractors except that one has the pivoting front axle. Put them side by side and observe them from the front while one side is jacked up. The fixed axle tractor's front end goes up evenly with the rear end. But the pivoting axle tractor's front end remains level side to side, and lower to the ground, until the pivot stops are reached. At that point front end movement to the side keeps pace with the rear end's upward motion as the jacking up continues. If we kept jacking I think the fixed front axle tractor would tip over before the pivoting front axle tractor would tip over - simply because the pivot has allowed the overall tractor's vertical CG to remain below the fixed axle's CG. If this is a practical effect of a pivoting front axle, which my tractor is probably equipped with because it is four wheel drive and a pivoting front axle allows the front tires to grip better across uneven terrain, then it is an aid to preventing side rollovers.
Anyway, my reply to you is a reply to all - and I'll close by mentioning that while I was in the process of lifting mounded FEL buckets of gravel on level ground my wife thought she saw my rear tire lift a tiny bit. I didn't notice. But I shook some of the gravel out so it wouldn't fall out on the way to the dump site and that lightened the load a bit. And then I carefully drove almost straight down a 10-15 degree grassy hill - FEL first - about 25 times. Slow and steady, and feeling like the loaded rear tires and bush hog back there were going to keep me from tipping forward. And keeping the bucket as low as I could without spilling gravel.
And ready to drop the FEL to the ground immediately if I felt the rear end lifting! The nightmare scenario!
Best,
Rhino
I reread the thread and I also think the comments are interesting. Esoteric knowledge is by definition difficult for most people to understand and we've had posters make valid points, but not always talking about the same situation. It is impossible to confine a discussion of tractor rollover angles to a static situation - and we really shouldn't because they are moving - but you have to start somewhere. With the static angles in mind, then it makes sense to back way off from them because of the variables. My goal here was to enhance safety awareness, not empower folks to take greater risks.
DarkBlack and CalG, methinks, kind of got into a talking past each other discussion. My point, and CalG's, was that for a FLAT hillside - in other words the front and rear tires are on a constant, flat, inclined surface, the roll axis will, by virtue of the tractor tip over angle being greater than the pivot stop angle not be an important factor. The tractor will behave irrespective of the roll axis point for a pivoting front axle.
In my example I talked about (and envisioned without thinking about the pivoting front axle) jacking the tractor up on one side on level ground to see the angle at which the CG would move outside the support base and tip over. And if we did that I now realize, thanks to DarkBlack and CalG, that the front axle would pivot and keep the front wheels flat while one rear wheel went up in the air. So DarkBlack's explanation about drawing an imaginary roll axis is correct. It would initially be the line from the "downhill" rear tire to the center of the front axle, but when the axle hits the stops that roll axis moves downward and "downhill" towards the outside of the "downhill" front wheel. That would be a dynamic effect, but I also don't see it as a catastrophic rollover inducing moment. If the tractor is stable at, say a maximum front axle pivot angle of 20 degrees, and we keep jacking it up to 21 degrees the tractor doesn't roll over. All that happens on a level floor is the "uphill" front tire moves up 1 degree. Now with the front axle is behaving like a rigid rear axle so if we keep jacking up the same side the only variable (ignoring tire deformation, if any, and lack of friction so the tractor slides) affecting rollover is where is the CG? The instant vertical CG exceeds the lateral boundary of the support wheel base the tractor will roll over. And as the math shows, even with a wide variety of vertical CG's, it's pretty high.
I'll even make an additional point about the pivoting front axle now that I've given it more thought. The practical effect of the pivoting action is to lower the tractor's CG by lowering the front of the tractor with respect to where it would remain with a fixed axle. This shouldn't be too hard to imagine - picture two identical tractors except that one has the pivoting front axle. Put them side by side and observe them from the front while one side is jacked up. The fixed axle tractor's front end goes up evenly with the rear end. But the pivoting axle tractor's front end remains level side to side, and lower to the ground, until the pivot stops are reached. At that point front end movement to the side keeps pace with the rear end's upward motion as the jacking up continues. If we kept jacking I think the fixed front axle tractor would tip over before the pivoting front axle tractor would tip over - simply because the pivot has allowed the overall tractor's vertical CG to remain below the fixed axle's CG. If this is a practical effect of a pivoting front axle, which my tractor is probably equipped with because it is four wheel drive and a pivoting front axle allows the front tires to grip better across uneven terrain, then it is an aid to preventing side rollovers.
Anyway, my reply to you is a reply to all - and I'll close by mentioning that while I was in the process of lifting mounded FEL buckets of gravel on level ground my wife thought she saw my rear tire lift a tiny bit. I didn't notice. But I shook some of the gravel out so it wouldn't fall out on the way to the dump site and that lightened the load a bit. And then I carefully drove almost straight down a 10-15 degree grassy hill - FEL first - about 25 times. Slow and steady, and feeling like the loaded rear tires and bush hog back there were going to keep me from tipping forward. And keeping the bucket as low as I could without spilling gravel.
And ready to drop the FEL to the ground immediately if I felt the rear end lifting! The nightmare scenario!
Best,
Rhino
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