Slopes and tractor tilt

[SPYDERLK]

This formula gives the limit of stability slope angle;
limiting slope angle = arctan (1/2 the rear wheel track/vertical height of the cg).
In this case, the limiting slope angle was 36.3ｰ assuming no other loads on the vehicle. If you hit a bump and it tips the tractor slightly down slope, you could tip over at a lower slope angle.

This gives you an upper limit on stability. Given that tractors often operate on a rough ground, you really wouldn't want to operate at this limiting angle. I would limit myself to oerating at a maximum of 80% of this angle and keep my speed down to preclude big tipping from rough spots. You can also increase the track of the rear wheels and gain some stability.
Iif you know the effect of the loader installation on the verticle height of the cg, you can compute the limit for a tractor with a loader installed.

Only if the CG is directly over the rear wheels on a tractor. -- An impossible situation since it would back flip. You have to allow for the longitudinal position of the CG as well, and since its well forward of the rear axle its going to reduce resistance to sidetip. A tractor always simulates a tricycle. No stability contribution from the front.
larry

The cg does not have to be over the rear wheels for this relationship to hold. It's just a simple static stability relationship. The assumption is that the rear track is the widest(and is rigid) and will react out tipping loads untill the line of action of the CG falls outside the rear track.(Front tractor axles usually pivot so they can't support a moment about the longitudinal axis.)

In parentheses you have given the reason your assertion is not correct. Think about it a bit. ... You have a triangle formed on the surface from the rear contacts and a vertical projection of the front pivot. The CG must stay within this triangle or you tip. The further forward the CG the less slope necessary to tip. ... However, a tip on a slight slope will be stopped on a 4 wheel tractor by the pivot stop on the front axle.
larry

 

[North Country]

In parentheses you have given the reason your assertion is not correct. Think about it a bit. ... You have a triangle formed on the surface from the rear contacts and a vertical projection of the front pivot. The CG must stay within this triangle or you tip. The further forward the CG the less slope necessary to tip. ... However, a tip on a slight slope will be stopped on a 4 wheel tractor by the pivot stop on the front axle.
larry

This would hold true in the lab, but in the real world you usually have enough angular momentum by the time you reach the pivot stop that the tractor keeps rolling.

 

[SPYDERLK]

This would hold true in the lab, but in the real world you usually have enough angular momentum by the time you reach the pivot stop that the tractor keeps rolling.

Yes. Note the word slight modifying slope however. Such tips happen in almost level situations in the real world with a loaded bucket, even held low, if the tractor rear is light enuf. With prudent bucket position on a non tricycle front tractor they are not likely to progress further than the limit of the front pivot if the slope is less than around 5 degrees. The transition up into double digits would certainly be a very real danger of full rollover with a light rear.
larry

 

[TripleR]

"In theory, there is no difference between theory and practice. But in practice, there is." - Yogi Berra

 

[North Country]

...if the slope is less than around 5 degrees...
larry

I wouldn't know; I don't have any of those. :laughing:

 

[SPYDERLK]

:thumbsup:Its a clever quip, but in actuality theory covers practice. Its only when assumptions are introduced in problem solution that theory seems to break down. The best Engineers will hilite their assumptions and justify their validity to the instant problem. Changing the variables just makes the solution more complex, but seldom unsolvable in practice.
larry

 

[SPYDERLK]

I wouldn't know; I don't have any of those. :laughing:

Yah. How do you define the slope of a hill with a hill.

 

[TripleR]

:thumbsup:Its a clever quip, but in actuality theory covers practice. Its only when assumptions are introduced in problem solution that theory seems to break down. The best Engineers will hilite their assumptions and justify their validity to the instant problem. Changing the variables just makes the solution more complex, but seldom unsolvable in practice.
larry

I guess it all depends on how you define or apply theory. My uncle was a Mechanical Engineer and I rarely understood him either.

 

[RoyJackson]

This would hold true in the lab, but in the real world you usually have enough angular momentum by the time you reach the pivot stop that the tractor keeps rolling.

Gotta disagree with you...
Once you start across a slope, the weight of the tractor is going to result in the front axle pivot hitting it's stops and that's as far as it (the axle) will go. Remember, this happens as soon as you start across.
The only effect that would have as you go across the slope is a bit more weight downslope (moving the tractor's CofG downslope a bit). That could result in a tractor slightly more prone to rolling on it's side. The upslope ballasted tire's weight would counteract that weight shift and provide resistance (inertia) to the tractor rolling over.
If you were correct in your statement I bolded (and I am correct in what I think you meant), everytime a tractor goes across a slope, it would roll over. Obviously not the case...
Read the full definition of inertia, as that's what's really being discussed here...

Now, an abrupt change (hole or rut on the downslope side of the tractor or something on the upslope side) is bad news and all bets are off (but I hope your ROPS is up and seatbelt nice and tight around your body).

 

[North Country]

Gotta disagree with you...
Once you start across a slope, the weight of the tractor is going to result in the front axle pivot hitting it's stops and that's as far as it (the axle) will go.
The only effect that would have as you go across the slope is a bit more weight downslope (moving the tractor's CofG downslope a bit).
If you were correct in your statement I bolded (and I am correct in what I think you meant), everytime a tractor goes across a slope, it would roll over.

I agree that we'll disagree.

The only way to hit the stop is to 1) drive across uneven ground or 2) start a roll. No matter how steep the slope, if the slope is flat (like a 1/2 open hardback book cover) then you'll be dead center on the front pivot - equidistant from both stops.

So no, you don't roll on every slope because you don't hit the stop on every slope. I was responding to someone earlier who talked about the front axle stop arresting a roll - and my point is that once a roll has started because of the usual reasons*, it's rare that the front stop arrests the roll.

*usual reasons include - hole, bump, sudden turn, load shift, etc. All of these things lead to a sudden change in the stability of the tractor. Rolling because you just flat out exceeded the tilt limitations without turning, hitting a low spot or high spot is pretty rare, IMHO.

 

[RoyJackson]

I agree that we'll disagree.

The only way to hit the stop is to 1) drive across uneven ground or 2) start a roll. No matter how steep the slope, if the slope is flat (like a 1/2 open hardback book cover) then you'll be dead center on the front pivot - equidistant from both stops.

So no, you don't roll on every slope because you don't hit the stop on every slope. I was responding to someone earlier who talked about the front axle stop arresting a roll - and my point is that once a roll has started because of the usual reasons*, it's rare that the front stop arrests the roll.

*usual reasons include - hole, bump, sudden turn, load shift, etc. All of these things lead to a sudden change in the stability of the tractor. Rolling because you just flat out exceeded the tilt limitations without turning, hitting a low spot or high spot is pretty rare, IMHO.

Think about your statement...
Now, you have an axle that pivots a few degees (I'm not talking about steering) perpendicular to the longitudinal axis of the tractor. What is the weight of the tractor going to do as you start across the slope? The solid rear axle is going to resist any twisting movement, but there is some (enough to cause the front axle to pivot to it's limits (stops) if the slope is steep enough).
Unless you hit the abrupt change in the ground as you enter the slope, the axle is already at it's limits...any effect (the weight shift described in my previous post) has already occurred.

Now, how much slope would it take to overcome the resistance to twist provided by the rear axle? That's going to depend on the design and materials of the tractor and the degree of slope.
That would be a very interesting calculation, but I doubt any one here has the parameters required to calculate it...even in a static setting (tilt table, for example). That math might be in that ANSI spec the tractor manufacturers test to, but the materials, design etc. would be variables the manufacturer would have to provide.

 

[SPYDERLK]

Yeah Roy. .. But once youre on a steep enuf slope that will cause a well weighted uphill rear to lift it will continue. The front pivot will offer no resistance until you hit the stops. It would take a very wide front stance to stall the tip in such an instance. Very likely the tractor would roll.
larry

 

[RoyJackson]

Yeah Roy. .. But once youre on a steep enuf slope that will cause a well weighted uphill rear to lift it will continue. The front pivot will offer no resistance until you hit the stops. It would take a very wide front stance to stall the tip in such an instance. Very likely the tractor would roll.
larry

Yep, if it's steep enough...and once that rear tire bounces or lifts...well, just hope the ROPS and seatbelt work as designed!
But I'm assuming most of us wouldn't attempt crossing a slope like that. I know I wouldn't...

 

[TripleR]

Out of curiosity, do all the tractors have pretty much the same degree of movement before contacting the stop, any difference in 2WD or 4WD?

I don't intend on testing these theories, but just curious.

My son mows on slopes I won't get near and he has never lifted a wheel that I know, so appearances can be deceiving.

 

[RoyJackson]

Out of curiosity, do all the tractors have pretty much the same degree of movement before contacting the stop, any difference in 2WD or 4WD?

I don't intend on testing these theories, but just curious.

My son mows on slopes I won't get near and he has never lifted a wheel that I know, so appearances can be deceiving.

I always thought 2WD tractor axles don't pivot like the 4WD ones do... And, there's so many different tractors...just focusing on CUT 4WDs, I'd guess most front axles pivot (remember, we're not discussing the pivoting as they steer). All the Deere CUTs I've seen do...

Like you wrote, your son can handle more slope then you can...I can handle more of a slope in one direction then the other (inner ear problem on one side). And, I'd guess most tractors can handle more of a slope then most operators.

BTW, TripleR: antidisestablishmentarianism
How's that some a lot of syllables???

 

[North Country]

Think about your statement...
Now, you have an axle that pivots a few degees (I'm not talking about steering) perpendicular to the longitudinal axis of the tractor. What is the weight of the tractor going to do as you start across the slope? The solid rear axle is going to resist any twisting movement, but there is some (enough to cause the front axle to pivot to it's limits (stops) if the slope is steep enough).
Unless you hit the abrupt change in the ground as you enter the slope, the axle is already at it's limits...any effect (the weight shift described in my previous post) has already occurred.

I've thought about it, and I keep coming to the same conclusion.

Take a tractor - put it on top of a big hardcover book. Start opening the book. (That's us, driving across a slope that's getting steeper and steeper.)

I say that no matter how much you open the book, as long as both rear tires are on the ground, there's no movement at the front pivot point. Not until the upper rear tire lifts does the tractor start to twist about the front pivot, and by the time you hit the stop - too late! You already have enough angular momentum to roll right over.

From what I understand of what you're saying, you are saying that as you open the book, the tractor twists about the front pivot and at some point - well before rollover - it hits the stop. Did I get it right?

Now I've left frame twist out of the simplified example above. I believe it to be negligible for what we're talking about. I'll also say that if a tractor frame twists enough to hit the front stops on a smooth but steep slope, I don't want to be on that tractor.

 

[RoyJackson]

Now I've left frame twist out of the simplified example above. I believe it to be negligible for what we're talking about. I'll also say that if a tractor frame twists enough to hit the front stops on a smooth but steep slope, I don't want to be on that tractor.

Tell you what...I've got to mow on Sunday (08 May) if it dries out enough. It needs mowing but too wet today. I have a pretty decent slope I mow across (8-10 degrees or so, measured quite a while back by a tiltmeter).
I know the slope is safe from mowing it the last 10 years. I'll get off my tractor and look at the front axle. I don't normally carry a camera, but I will get a pic if possible.

 

[North Country]

Sounds like a great idea. I'll do the same here tomorrow (trying to keep the tractor off the grass for one more day - it's like walking on a sponge here.)

If you've got a particular slope you want, I'm sure I can find it somewhere around here. The steepest I drive on regularly is 22 degrees - straight up & down only. I'm chicken. I do have some 25+ degree slopes with trees on them and I'm not sure how I'm going to get the lumber this spring - I may just use my favorite 1/2 hp tractor.

 

[TripleR]

I always thought 2WD tractor axles don't pivot like the 4WD ones do... And, there's so many different tractors...just focusing on CUT 4WDs, I'd guess most front axles pivot (remember, we're not discussing the pivoting as they steer). All the Deere CUTs I've seen do...

Like you wrote, your son can handle more slope then you can...I can handle more of a slope in one direction then the other (inner ear problem on one side). And, I'd guess most tractors can handle more of a slope then most operators.

BTW, TripleR: antidisestablishmentarianism
How's that some a lot of syllables???

Maybe we are related, I am much more comfortable mowing with my right side up hill. I have recently had to park my Harley, but rode motorcycles on the street and dirt for many, many years and was never as comfortable turning left as turning right and I don't have inner ear problems, though the jury is out on the rest of the contents of my cranium.:laughing:

I grew up farming in the flat lands, but we have owned property in the hills since 1986 and you would think I would be comfortable working on slopes, but I am still always a little uneasy on anything very steep even those I have mowed for years.

You win with antidisestablishmentarianism.:laughing::laughing:

 

[RoyJackson]

Sounds like a great idea. I'll do the same here tomorrow (trying to keep the tractor off the grass for one more day - it's like walking on a sponge here.)

Only get on there if it's safe to do so...I wrote that slope I'll do the test on is safe...but that's when it's dry.
I'll walk mine first and feel the bottom of those blades of grass and the ground. My 4400 is considerably heavier then your 2305 and will rut if the ground is wet or soft.

...but I am still always a little uneasy on anything very steep even those I have mowed for years.

Same here, and that's a good way to be...