Pondering the center of gravity (CG) of my tractor

[ctgoldwing]

Thank you all for your thoughtful responses. This has turned into a mini obsession for me now
The address some comments by previous posters. . . Yes when I got on the tractor the 1st time I said it felt better but that just might be a mind thing
I do not have loaded tires but have looked into beet juice and windshield washer solution (330lbs per tire vs 255lbs). You raise a really good question - how much would that lower the CG and therefore increase the tip angle???
Based on some comments here I reran my calcs using 25.5" and 31" as the CG. Again the advantage in the 3" spacers is small (2.3deg if the CG is 25.5", 2.7deg if the CG is 31")

I understand the 'real word' tip angle is a fairly complex issue. I am just looking for a static solution. When I'm perpendicular to the fall line on almost any grade I really creep along. At my age I want to keep whatever parts are still working. .

RSR nice analysis. I just don't see me jacking the tractor up on its side You are right though, you will know the static angle exactly

I think my next step will be to see how much ballast lowers the CG. Again I will have to assume how high it is to start but for this exercise I think it will give me a real world approximation. Ballast may in fact be the best bet to increase that tip angle.

Thanks again

 

[JethroB]

I suggest at our next annual TBN Tractorama gathering we perform the tipping test on a couple of tractors in the name of science. Volunteers are needed to provide come-a-longs, lawn chairs, hot wings, and a few kegs of beer. Oh yeah, and the tractors.

 

[Henro]

Here is what I would do.

I would measure the width of the tractor rear wheels. Then pick a reasonable height above ground when I thought the CG might be. No need to be exact.

Then I would calculate the angle where my assumed CG was directly above the outside of the rear tire at the ground contact point. This is the danger point where if the CG moves slightly more, the tractor will fall on its side. I would then calculate the horizontal distance the CG moved to get to that point directly above the outside of the tire.

I would repeat using the width addition that my spacer added. And again record the horizontal distance the CG moved to get to the tipping point. This will be larger than without the wheel spacer.

Finally I would divide the second number by the first, and see the percentage increase. This would not be exact, but would be representative of how much the spacers actually helped stability.

Adding ballast to the tires, or otherwise, would lower the real CG, and result in a greater increase in the percentage benefit.

I think a couple relatively simple calculations like I mention would be enough to satisfy my intellectual curiosity, and not be too painful to do.

 

[RSR]

Here is what I would do.

I would measure the width of the tractor rear wheels. Then pick a reasonable height above ground when I thought the CG might be. No need to be exact.

Then I would calculate the angle where my assumed CG was directly above the outside of the rear tire at the ground contact point. This is the danger point where if the CG moves slightly more, the tractor will fall on its side. I would then calculate the horizontal distance the CG moved to get to that point directly above the outside of the tire.

I would repeat using the width addition that my spacer added. And again record the horizontal distance the CG moved to get to the tipping point. This will be larger than without the wheel spacer.

Finally I would divide the second number by the first, and see the percentage increase. This would not be exact, but would be representative of how much the spacers actually helped stability.

Adding ballast to the tires, or otherwise, would lower the real CG, and result in a greater increase in the percentage benefit.

I think a couple relatively simple calculations like I mention would be enough to satisfy my intellectual curiosity, and not be too painful to do.

This is the exact example I worked through in my first post above, using the specifications of the tractor given in the linked article.

I repeated this for various "estimates" of height of center of gravity, and wheel width.

I then repeated my calculations multiple times because I was dumbfounded by the results.

Increasing your tire width by roughly 10% for just about any reasonable range of tire width and center of gravity only gets you about an extra 3 degrees before reaching the tip over point.

I would have guessed it was MUCH more.

 

[RSR]

I think my next step will be to see how much ballast lowers the CG. Again I will have to assume how high it is to start but for this exercise I think it will give me a real world approximation. Ballast may in fact be the best bet to increase that tip angle.

This should be pretty easy to do. A fair assumption is the center of mass of filled tires or wheel weights will be the axle height. Based on your guesstimate of the tractor center of mass, and the known tractor mass, you can use the second equation posted above and find the new center of mass really quickly.

Then, plus that into your existing trig equation (same as my first equation) and you've got it.

Another thing to think about is additional 3 point ballast can be a good thing. A well-designed ballast box with a very low center of mass (even below the axle centerline) can do as much or more for lowering the center of mass than filled tires.

Same thing goes for carrying loads in the bucket. Low carry height (below the axle height) = good. High (above the axle height) = bad. Just be careful bucket loads don't shift while moving.

 

[RSR]

I suggest at our next annual TBN Tractorama gathering we perform the tipping test on a couple of tractors in the name of science. Volunteers are needed to provide come-a-longs, lawn chairs, hot wings, and a few kegs of beer. Oh yeah, and the tractors.

Yes!!!

I'm a college professor and am continually looking for new research ideas. It's well outside my usual field of study, but I've always wondered if an agency like OSHA would fund a scientific study to investigate tractor tip over angles. As I linked to an earlier article, there is a little bit of scientific work done on this, but not much.

I think it would be great to have a large database of tractor data that includes measures of center of mass, and moments of inertia, similar to the Nebraska University testing center for tractor power outputs (Test Reports | Tractor Test Lab | Nebraska).

Really, it would be nice if manufactures just reported what the center of mass of their tractor's is. CAD packages are sophisticated enough you could get a quite accurate measurement without having to do any physical testing, but based solely off of the design files.

 

[EarPlug]

Yes!!!

I'm a college professor and am continually looking for new research ideas. It's well outside my usual field of study, but I've always wondered if an agency like OSHA would fund a scientific study to investigate tractor tip over angles. As I linked to an earlier article, there is a little bit of scientific work done on this, but not much.

Another research organization that might be interested would be NIOSH - National Institute for Occupational & Health.
CDC - The National Institute for Occupational Safety and Health (NIOSH)

Search Results | CDC "tractor"

 

[bcp]

Long ago I read an article that said the center of gravity was almost always within a few inches of the operator's resting foot position.

Modern tractors may be different.

Bruce

 

[RSR]

Another research organization that might be interested would be NIOSH - National Institute for Occupational & Health.
CDC - The National Institute for Occupational Safety and Health (NIOSH)

Search Results | CDC "tractor"

They have some programs too that I've looked into.

 

[oosik]

Just remember - all these exotic calculations will go down the drain when on a side slope and one wheel falls into a hole. I'm not brave or foolish enough to try with my tractor. However - I've "side sloped" with my ATV. The ATV will handle side slopes far beyond my level of comfort. I've never had to "side-slope" with my tractor and God willing, I never will.