Worthless tip over calculations...are interesting!

[Anonymous Poster]

Hi,

I got curious about where my tractor might tip over as expressed in degrees of slope. Naturally, trying to calculate this is impossible if the tractor is moving, at least if one is limited by the head I happen to have resting on my shoulders /w3tcompact/icons/smile.gif.

BUT...STILL... it seems like a static calculation could be of some usefulness...even if the amount of usefulness it might have is debatable.

It seemed to me that the tractor center of gravity could be conservatively placed between the top of the rear tires and the top of the wheel rims. My rear tires are filled with WW fluid to the top of the rims, and the front tires are foam filled. Actually the center of gravity might be below the tops of the rear wheels. If so, that would add to the stability of the tractor.

I made some measurements on my Kubota B2910, which has R4 tires. They came out as follows:

Tire height to top of tread: 37 inches
Height to top of rear rims: 26 inches
Width of tire to outside of tread contact patch: 52 inches
Width of tire tread to inside of contact patch: 29.5 inches

Since the tractor is for practical purpose symmetrical, the center of gravity should, for practical purposes, be centered between the rear tires. So the variables of most importance, is the vertical position of the center of gravity, and the place on the surface of the tire contact patch that is effectively supporting the tractor. Both of these are really variables and unknown to me. But I can guess the limits of possibilities.

The limits are the outside and inside edges of the tire contact patches, and the maximum and minimum range of likely heights of the center of gravity.

Using these limits it should be possible to calculate the best and worse case static tip over angles.

Again, let me emphasize STATIC, as once the tractor starts moving other factors come into play that can reduce the static angles considerably.

The worst case is having the center of gravity at the tops of the tires and the point at which the tractor is supported at the inside edges of the tires. For my tractor, IF this were the case [I am sure it is not] the calculated angle at which the tractor would tip over would be a slope of 21 degrees!

The other extreme would be the lowest center of gravity position and the widest support point at the outer edges of the tire contact points. This calculates out to a slope angle of 45 degrees!

The midpoint between the two extremes calculates out to be a slope of 33 degrees where the tractor would roll over.

Again, this would be without any movement. A rock or hole that a front wheel hits would lower these numbers considerably!

Here�fs a summary:

(Degrees)
Height <font color=blue> 1/2 Width</font color=blue> Tip Angle

37 inches <font color=blue> 14.34 inches</font color=blue> 21 Degrees
31.5 inches <font color=blue> 20.5 inches</font color=blue> 33 degrees
26 Inches <font color=blue> 26 inches </font color=blue> 45 degrees

1/2 the tread width is used for the calculation, because the point of tipping occurs when the center of gravity to beyond the point directly above the tire's point of contact.

Like I said, these numbers are interesting, but worthless, because of the other variables that come into play when we are using our tractors. Like the weight of the operator and how the operator himself changes the center of gravity of the tractor/operator combination. Or what's hanging on the back. Or, the height of the loader and what's inside it. Or..or...or...

Or the dynamic effects of the tractor moving and hitting a bump/hole.

Still, this exercise in futility has given me something, as I may be on a slope and be maneuvering at about a speed of 1 foot per minute, and feeling pretty unsure of myself.

I think I may feel a little more comfortable in an almost stopped situation now...

Prior to this, I was puckering at probably 15 degrees when stopped. Just had no feel for anything at all. Now I will pucker at 15 degrees and enjoy it!

I now at least have a little gut feeling about what the maximum limits MIGHT be...

This means something to me, as I can�ft bring myself to go out and traverse increasingly steep slopes until the tractor rolls over for educational purposes!

In another thread where I posted some pictures of slopes that were mowed that looked crazy to me, some others felt that they were doable mowing without too much concern.

My simple calculations support their observations.

A 20 degree cross slope still seems quite steep to me though. That is about the maximum on my property and I have not been across one yet.

For what it�fs worth...this exercise was of some interest to me!

<font color=red>Don't forget, these numbers mean nothing in the real world!</font color=red>

Any comments?

Bill in Pgh, PA

 

[bgott]

"Any comments?"

Yep. I think you're thinking way too much. /w3tcompact/icons/grin.gif

 

[Anonymous Poster]

Yep, read it too early this morning and thinking about it made my head hurt. I had to study the center of gravity concept/principle in the Coast Guard ( as relating to boats/ships) it made my head hurt then. And yes if movement is involved most bets are off. The various directional thrust factors of engine torque, wheels turning and dipping in holes, and even the fuel sloshing in the tank all will effect the center of gravity. Just get to know your tractor slowly and play it safe. Even if you don't get hurt it may wreck your toy

Ben in Ky

 

[Anonymous Poster]

Hey!

I can live with "get a life".../w3tcompact/icons/smile.gif

But... I must warn slowrev that I also am a Coast Guard vet /w3tcompact/icons/shocked.gif...watch out! After a few years this is what you may turn into!

Life is tough here at the moment. I had to watch my tractor leave on the dealer's truck this morning for a warrenty repair!

I tried playing with the loader after the tractor left, but it is heavier than it looks.../w3tcompact/icons/frown.gif

Life is good...but better when the both the wife and Kubota are home...and presently both are out of town!

Poor me....

Bill in Pgh, PA

 

[Anonymous Poster]

Hey Bill, Not picking on ya, This type of stuff always frustrated me because all you can do is get close when most of the variables are constantly changing. Sorry to hear about the illness in your family ( tractor ) and hope all is well soon. I wasn't a real Coastie just in the Auxiliary for several years. It was a lot of fun and work, however I was the youngest Aux person around at 48 Spent most of my time looking out for boaters doing stupid stuff, Teaching boating safety courses, and the rest of the time helping the older folks in my group. They are a great group of people and it was a sad day whenever we had to drop someone's crew qualifications because they were too old ( physically ) to handle the duties.

Coastie's have great respect from me.

Ben in KY

 

[Hermio]

The math for this is not difficult. The maximum static angle is equal to 90 degrees -arctan(2* cg/width), where cg is the height above ground of the center of gravity, and width is the distance between contact lines of the tires. For example, if the contact width is 72" and the cg is 48" high (fairly high for most tractors of such a width), the static tipover angle is 36.86 degrees. Trust me, I will never traverse a slope at such an angle! Of course, dynamic conditions are different. For example, if the tractor slides sideways on a slope and hits a rock, rut or tree stump, the inertia may cause a tipover at far less than the static angle. I do not feel comfortable beyond 20 degrees.

 

[KiotiKowboy]

Please test your calculations and let us know how it worked out

 

[Hermio]

Can't do the calculations without knowing the location of the center of gravity. And, as I mentioned, they are static calculations. Movement and acceleration drastically affect the results. As an example, you can rest a 1-lb hammer on your thumb without discomfort or injury. But swing it at, say, 20 mph at your thumb, and I think the results will be quite unpleasant.

 

[CalG]

On
most tractors without a front loader. The CoG is best estimated at the junction between engine and transmission (where a clutch would be if not Hydrostatic) and at crank shaft height.

A cab will raise the CoG a bit, but do the math on a 4000 # tractor and a #300 cab. Loaded tires may or may not change the CoG height. But will always "help" not hurt.

This topic has been discussed previously.

 

[Hermio]

Interestingly, that would put the CoG quite low in such a formula. It would make the tip angle around 45-55 degrees. The loader will not raise the CoG much, if at all, if it is kept low to the ground, especially if the bucket is full. The sub-frame of a loader weighs about as much as the lift arms, and the bucket can be pretty low. IMHO, no tractor tips due to being above the static tip-over angle, as it will slide sideways first. Instead, if it slides and hits something, over it goes. That is why I plan to limit my slope angle to 20 degrees. My Mahindra 5035 with FEL seems a bit taller than my old Ford 4110, so I am more concerned about this. I am thinking about getting an inclinometer to test the angles I encounter. I can move the tires out further (3.6" further apart, to be exact,) but this is not that great of a change; it only adds about 0.5 degrees to the static tipover angle. And it puts the valve stem on the inside, where it is harder to get to and more subject to damage.