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.