Calculating Your Predicted Rollover Angle

[DarkBlack]

DarkBlack,

You are promoting a popular misconception.

It is not until the uphill rear wheel leaves contact with the ground that a pivoting front axle is required to move about it's pivot. Regardless of the degree of tilt. After that, the inside wheel is permitted to lift the full angular displacement provided for by the axle pivot before any resistance to further tipping will be obtained from the front wheels. I'm quite confident, that on a steep incline, that resistance will come much after a roll over is assured. On flat ground, using only cornering forces (roll) things will be much different.

It is true what you say that calculations taking into account momentum and inertia are more than complicated, but if I have read the OP correctly, this rough order of magnitude calculation is based on static conditions. Fair warning was included in the text regarding the many uncontrolled variables.

A triangle or a rectangle matters not one bit on the roll over angle based on the original assumptions.

And that is why tricycle steering gear is not more prone to tipping than a "conventional" front axle. (Assuming simple conditions)

Loaders screw up the CoG determination to no end! But a load on the back only shifts the fore and aft CoG closer to the wide rear tires. The calculation point.

Simplified, If the lateral CoG is allowed to move outside of the support plane, over it goes!

ps, I have done no work to confime the correctness of the maths, just going by the text description.

cheers

The facts I wrote are neither popular, nor are they misconceptions.

CG means nothing in calculations without factoring your roll axis, which roughly connects your front/rear roll centers. His calculation assumes the rear roll center to be a couple inches in on the rear tire ( close enough) since it's a ridged rear axle, but he didn't figure out the front roll center. His math assumed the front RC to be the same as the rear and IT IS NOT. The front roll center is at the axle pivot point. So draw a line from that point down and back to the bottom of the rear tire, and there is your roll axis- triangle shaped and rising to the front as I said before.

Still having a hard time with the tech, here's a couple of easy examples:

1) Stand a ball point pen on end on your table( table is front axle). It has a centered CG, and a pivot point in the middle like a tractor front axle. Is it stable?

2) Replace your fixed rear tractor axle with a free floating pivot axle like the front. Why did it just flop over on you?
As it flops over, is the CG moving toward the lower side wheels?

3) lift up on a side of your tractor and measure the force it took to lift the rear wheel off the ground. Now block your front axle solid with the frame, and repeat test, lifting front and rear wheels off the ground. Same? Different force?

Let me know what you figure out

 

[SPYDERLK]

Hello All,

Here is the bottom line...the sideways rollover angle for my Kioti DK40 Hydro FWD, with FEL positioned with an empty bucket parallel to the ground, and Tartar 6 bush hog - and in all likelihood most similarly equipped stock utility class tractors - is above 40 degrees.
Rhino

How have you accounted for the longitudinal position of the CG? Due the front center pivot the tractor gets more tippy the more the CG is moved forward -- a real issue with a FEL. Your calculations would be realistic only if the longitudinal CG is at the rear axle.
larry

 

[Rhino35]

The facts I wrote are neither popular, nor are they misconceptions.

CG means nothing in calculations without factoring your roll axis, which roughly connects your front/rear roll centers. His calculation assumes the rear roll center to be a couple inches in on the rear tire ( close enough) since it's a ridged rear axle, but he didn't figure out the front roll center. His math assumed the front RC to be the same as the rear and IT IS NOT. The front roll center is at the axle pivot point. So draw a line from that point down and back to the bottom of the rear tire, and there is your roll axis- triangle shaped and rising to the front as I said before.

Still having a hard time with the tech, here's a couple of easy examples:

1) Stand a ball point pen on end on your table( table is front axle). It has a centered CG, and a pivot point in the middle like a tractor front axle. Is it stable?

2) Replace your fixed rear tractor axle with a free floating pivot axle like the front. Why did it just flop over on you?
As it flops over, is the CG moving toward the lower side wheels?

3) lift up on a side of your tractor and measure the force it took to lift the rear wheel off the ground. Now block your front axle solid with the frame, and repeat test, lifting front and rear wheels off the ground. Same? Different force?

Let me know what you figure out

Hi DarkBlack (and other interested posters),

I think I am grasping the concept of a roll axis connecting the front and rear CG's. For purposes of discussion, let's imagine that if the front wheels are as wide as the rear, which they almost are stock, and the weight of the tractor and implements (FEL, bush hog) result in a CG that is equidistant between the front and rear axle and the same height above the ground. So this is a balanced CG.

In this balanced CG distribution, wouldn't my earlier post about the front axle hitting the stops be accurate? The static roll angle, even if the front axle pivots, would be about the same as my calculations? I say this because the pivot angle of about 20 degrees is less than the static roll over angle which I think we could at least agree is over 30 degrees. When it hits the stops the front axle behaves like the rear axle. Once those stops are hit we should be able to forget about there ever being a pivoting front axle. If we can agree on this, then we should be able to envision the effect of a lower or higher front axle CG. That imaginary "roll axis" line connecting the two CG's will go up or down, depending as you point out with the position of the FEL and the FEL load.

Spyderlk,

Your question about longitudinal position of the CG may be related to the point DarkBlack is trying to make, but I didn't attempt to calculate the forward or aft rollover (the tractor going over backwards) because I don't think the longitudinal CG in the configuration I have while bush hogging (FEL arms parallel, empty bucket two feet off the ground, bush hog and loaded rear tires) has strayed too far from about the middle of the tractor.

Best,

Rhino

 

[CalG]

The facts I wrote are neither popular, nor are they misconceptions.

CG means nothing in calculations without factoring your roll axis, which roughly connects your front/rear roll centers. His calculation assumes the rear roll center to be a couple inches in on the rear tire ( close enough) since it's a ridged rear axle, but he didn't figure out the front roll center. His math assumed the front RC to be the same as the rear and IT IS NOT. The front roll center is at the axle pivot point. So draw a line from that point down and back to the bottom of the rear tire, and there is your roll axis- triangle shaped and rising to the front as I said before.

Still having a hard time with the tech, here's a couple of easy examples:

1) Stand a ball point pen on end on your table( table is front axle). It has a centered CG, and a pivot point in the middle like a tractor front axle. Is it stable?

2) Replace your fixed rear tractor axle with a free floating pivot axle like the front. Why did it just flop over on you?
As it flops over, is the CG moving toward the lower side wheels?

3) lift up on a side of your tractor and measure the force it took to lift the rear wheel off the ground. Now block your front axle solid with the frame, and repeat test, lifting front and rear wheels off the ground. Same? Different force?

Let me know what you figure out

I have no trouble with roll centers, having had several cars on the track.

An axle with zero roll stiffness is just that. Zero.


The solid rear axle is also just that, it's roll center is at the axle. and the CoG is supported by the wheels. Done

The CoG goes over the plane of support, and the system over turns.

If you are having a hard time with the tech, here is an easy example

Take the front axle off, balance the rig with rear counter weights

Let me know what you figure out!

cheers

 

[CalG]

OK

My apology. I need not be so antagonistic. Ego is a difficult companion.

Let me give some example of the logic envolved in determination of roll over angle with consideration of a center pivot solid front axle.

Firstly, is it obvious that the front axle pivot will not be asked to do anything until one rear wheel has left the ground plane? (this is the same as rolling into a depression or a rise in terrain, but since the tractor is not moving, rolling into a bump is not considered.) The ground plane of the tractor is determined by the line drawn between the two contact patches of the rear tires. And the front axle will not deflect until something upsets the rear axle from that plane. We are not considering fore and aft tip overs IIRC.

OK with that, please visualize this example.

Place the tractor in a sturdy box and secure it solidly by straps over, around, and through the rear wheel rims that positively locate the rear tire contact patches. Place a support block under the box a point midway between the front tire contact patches.

Now, Manipulate the box in such a way as to lift one side to achieve the attitude that might be experienced on sloping ground. How much will you need to tip the box before it overturns?

If the rear end is fastened securely to the box, does it matter if the front axle is free to pivot?

Does the tractor within the box start to tip over before the box does? (Now that is an interesting consideration) Note : in this theoretical visualization, the box size is the same as the outer most dimension of the two rear tires and the mid point between the front tires, no larger.

Without knowing the content of the box, what determinations could be made that will help in understanding the roll over angle of the box? Will CoG be useful?

Will Roll center of the contents be useful?

Take this to some extreme.

What if

The front axle were pivoted at the same height as the rear tire contact patch? (front axle removed for shipping and the pivot fitting pinned to a shipping block'=_)

The front axle were the same track width as the rear and wedged ridged? (requred condition when blocking the tractor to be split)

Both front and rear wheel sets were removed and the tractor was flat on the deck?

Stand the box on end and repeat the tilting experiment.


Now In juxtaposition, release the rear wheel tie downs, but constrain the tractor from sliding within the box. Counter balance all down loading of the rear wheels., but do not raise the CoG.
The entire tractor is free to tip about the front axle pivot. What happens at the first tipping of the box? Do both rear wheels stay unloaded?

Recall, this is a static condition, not dynamic.

At what angle must the box be tipped in order to overturn?


CoG is very important in tip over calculations, and a loader can sure mess with things. rear weight is your friend

Dynamic situations are more complex than static situations.

with that, Three point determine a plane ;-)



Cheers

 

[SPYDERLK]

Spyderlk,

Your question about longitudinal position of the CG may be related to the point DarkBlack is trying to make, but I didn't attempt to calculate the forward or aft rollover (the tractor going over backwards) because I don't think the longitudinal CG in the configuration I have while bush hogging (FEL arms parallel, empty bucket two feet off the ground, bush hog and loaded rear tires) has strayed too far from about the middle of the tractor.

Best,

Rhino

Im talking side roll. Due the center pivot, the front offers no resistance to roll until the last minute. That resistance comes into play only when the tractor is leaning ~10° more than the slope causing the roll. A CG forward of the rear axle causes the roll to start sooner, but the extra weight to the front may allow the front to arrest the roll. Very scary Id say.
larry

 

[CalG]

Rhino, "A" for effort, but I think you and your physics major friend missed a major parameter. I posted on this subject over a year ago.

"The front axle assembly is normally mounted to the frame by a free moving pivot point. Any widening aided tip protection from, say, rolling from running crosswise on a slope, will have zero to little added benefit from widening the front wheels. That would be the case until you hit the pivot limit of the front axle, but if you lifted the machine to that point, you will probably be rolling over anyways. "

You and your friend missed this huge game changer. You/he treated the tractor calculations as a rectangle shape. What your really have is a triangle, up to tip over angles of the front axle's pivot's limit. When you physically hit that rotary stop limit and it changes to a rectangle, the momentum alone throws your pre-calculations out the window. Also, with the loader ahead of this free pivot, calculating this mass becomes much more complicated.
Sorry for the bad news. I hope this explains why you had such incredibly steep slope angle predictions.

DarkBlack

Rereading your first post, I missed your point.

There is certainly a triangle that needs be considered . My responses (abrasive though they are) acknowledge your description.

I was thrown off when you moved to "the momentum alone" statement, having understood the OPs premises of static conditions with extensive explanation of same.

That "triangular calculation" in no way changes the significance of CoG and the roll over attitude for an axle with infinite roll stiffness.

 

[DarkBlack]

Hi DarkBlack (and other interested posters),

I think I am grasping the concept of a roll axis connecting the front and rear CG's. For purposes of discussion, let's imagine that if the front wheels are as wide as the rear, which they almost are stock, and the weight of the tractor and implements (FEL, bush hog) result in a CG that is equidistant between the front and rear axle and the same height above the ground. So this is a balanced CG.

In this balanced CG distribution, wouldn't my earlier post about the front axle hitting the stops be accurate? The static roll angle, even if the front axle pivots, would be about the same as my calculations? I say this because the pivot angle of about 20 degrees is less than the static roll over angle which I think we could at least agree is over 30 degrees. When it hits the stops the front axle behaves like the rear axle. Once those stops are hit we should be able to forget about there ever being a pivoting front axle. If we can agree on this, then we should be able to envision the effect of a lower or higher front axle CG. That imaginary "roll axis" line connecting the two CG's will go up or down, depending as you point out with the position of the FEL and the FEL load.


Best,

Rhino

Rhino, I'll tray to answer some of your questions:
The roll axis connects the front/rear roll centers-not the CG's. CG has nothing to do with them. Where the CG happens to be, has no effect on this example because the frame is not sprung like a car( ignoring tire deflection ). So on a tractor you have a simplified model because it is not sprung. So your rear roll center is the outer edge contact of the bottom tire and the ground, and your front RC is the center axle pivot center. These are the 2 points that the rolling motion will revolve around. Your CG could be anywhere, but you will still rotate around these 2 points. Draw a line to connect these. This is your roll axis.

In a tractor the rear roll center is way below the CG. The front roll center is close to the CG- ( that's another chapter ).
In any case, The tractor rolls on this axis, until it encounters the mechanical limits of the front axle limit stops. This causes the whole tractor to become ridged, which moves the front roll center to the bottom of the front lower outside tire.- which moves the roll axis to a straight line connecting them. This change of course instantly makes the front CG higher than the new roll axes.
Hopefully I've explained it clear enough that you can see this moving roll axis, and use it to tweak your calculations.:drink:

 

[CalG]

Rhino, I'll tray to answer some of your questions:
The roll axis connects the front/rear roll centers-not the CG's. CG has nothing to do with them. Where the CG happens to be, has no effect on this example because the frame is not sprung like a car( ignoring tire deflection ). So on a tractor you have a simplified model because it is not sprung. So your rear roll center is the outer edge contact of the bottom tire and the ground, and your front RC is the center axle pivot center. These are the 2 points that the rolling motion will revolve around. Your CG could be anywhere, but you will still rotate around these 2 points. Draw a line to connect these. This is your roll axis.

In a tractor the rear roll center is way below the CG. The front roll center is close to the CG- ( that's another chapter ).
In any case, The tractor rolls on this axis, until it encounters the mechanical limits of the front axle limit stops. This causes the whole tractor to become ridged, which moves the front roll center to the bottom of the front lower outside tire.- which moves the roll axis to a straight line connecting them. This change of course instantly makes the front CG higher than the new roll axes.
Hopefully I've explained it clear enough that you can see this moving roll axis, and use it to tweak your calculations.:drink:

This is just NOT the case.

DarkBlack, You are confused.

Consider the tractor of your description, "rolling about it's roll axis". As the front axle rolls and tilts, what happens to the rear?

NOTHING!

And if the rear can not roll, the front can not roll either! As you have pointed out, the tractor is not on springs!

Back to your "example", Remove the front axle and support the front of the tractor on a pencil tip. Now PUSH on the tractor sideways anywhere!, does the pencil topple and the tractor "tip over" , lifting the inner rear tire and toppling over the side due to the instability of the front end?

NO!

If the brakes are on, and the tractor can not swivel, NOTHING HAPPENS, until the side ways push is strong enough to lift the near side rear wheel high enough to send the CoG over the far side wheel contact point.


Think sensibly man!

 

[cartod]

I like buttered toast.