Center of Gravity Calculations and static tipping angles. Am I doing this right?

[SPYDERLK]

LD1. In your tips are you lifting both the front and back? If the axles do not tip equally it is a different situation.
larry

 

[tcartwri]

I think if you draw a line through the crankshaft to the PTO you will have your answer. Same general rule of thumb applies to automobiles.

 

[LD1]

LD1. In your tips are you lifting both the front and back? If the axles do not tip equally it is a different situation.
larry

Not sure what you are asking?

Only tipping or lifting I did was to raise the rear axle 12" high and weigh the additional weight shifted to the front axle. So not sure what you are asking. Looking forward to more of your input.

I think if you draw a line through the crankshaft to the PTO you will have your answer. Same general rule of thumb applies to automobiles.

Have my answer to what?

 

[MossRoad]

Your center of gravity is higher with the brush hog on because the brush hog is not on the ground. It is suspended from the tractor at a point higher than the "normal" center of gravity as measured when the brush hog is off. Make sense?

 

[SPYDERLK]

LD1. In your tips are you lifting both the front and back? If the axles do not tip equally it is a different situation.
larry

Not sure what you are asking?

Only tipping or lifting I did was to raise the rear axle 12" high and weigh the additional weight shifted to the front axle. So not sure what you are asking. Looking forward to more of your input

Oh. I think thats a problem. Look at what actually happens on a sidehill. The whole tractor leans as if its a rigid 4 wheeler up until the rear lifts. While its leaning that vector from the front pivot stays vertical, pointing nearer and nearer to the downslope tire. Ill bet accounting for that weight transfer to the downside front will give answers that come closer to what you thot you should be getting.
larry

 

[LD1]

Your center of gravity is higher with the brush hog on because the brush hog is not on the ground. It is suspended from the tractor at a point higher than the "normal" center of gravity as measured when the brush hog is off. Make sense?

Possibly. I would have though with it kept low, it would lower the CoG, regardless of where it is suspended from. The FEL is suspended at a point higher than the CoG of the tractor, yet with it low to the ground, ot lowered it. And the higher the FEL is elevated, the higher the CoG

 

[LD1]

Not really a conclusive test, but I did some scale testing today with some model tractors.

Using a triple beam scale and dial calipers for pretty darn accurate measurements.

One of the tractors I tested was "square" so to speak in that the track width and wheel base were the same just like my kubota. 6.220"

Did the test the same as full scale, weighed each axle, raised the rear a good bit and measured the weight transfered to the front, plugged in the numbers and gave me a 3.05" CoG. Which by scale is higher than my tractor. This model is all plastic wheels and "drivetrain" so to speak and the hood is die cast. So It makes sense the CoG is shifted up and forward more.

So, using the same method of figuring max tip angle, I get 24 degrees.

So I place it on a flat board and attach my angle gauge. It held fast at 25+ degrees. Actually took 32+ to start to slide. And ~34 ish to actually tip.

So...I think this has to do with what mike said in post #9 about the front pivot being elevated. So I re-figured the numbers assuming the "stability triangle" is elevated at the front. At the CoG location of 3.5" forward of the rear axle, and the front pivot 2" high, puts the triangle 1.125" off the ground at the CoG.

So re-figuring that, I come up with 34 degree tipping angle.:thumbsup:

Not really any point to my experiments here, just having some fun with numbers while being bored:laughing: But I really do think it would take quite a bit to upset one of these tractors in a static situation. I know when I was mowing some 20-22 degree slopes, it seemed like alot. But stepping aways back from the tractor and holding the angle finder at 22 degrees and sighting it over the tractor, 22 degrees really dont look like much slope at all

I guess our sense of angles get all out of whack when you are actually on the slope.

 

[CalG]

Not really a conclusive test, but I did some scale testing today with some model tractors.

Using a triple beam scale and dial calipers for pretty darn accurate measurements.

One of the tractors I tested was "square" so to speak in that the track width and wheel base were the same just like my kubota. 6.220"

Did the test the same as full scale, weighed each axle, raised the rear a good bit and measured the weight transfered to the front, plugged in the numbers and gave me a 3.05" CoG. Which by scale is higher than my tractor. This model is all plastic wheels and "drivetrain" so to speak and the hood is die cast. So It makes sense the CoG is shifted up and forward more.

So, using the same method of figuring max tip angle, I get 24 degrees.

So I place it on a flat board and attach my angle gauge. It held fast at 25+ degrees. Actually took 32+ to start to slide. And ~34 ish to actually tip.

So...I think this has to do with what mike said in post #9 about the front pivot being elevated. So I re-figured the numbers assuming the "stability triangle" is elevated at the front. At the CoG location of 3.5" forward of the rear axle, and the front pivot 2" high, puts the triangle 1.125" off the ground at the CoG.

So re-figuring that, I come up with 34 degree tipping angle.:thumbsup:

Not really any point to my experiments here, just having some fun with numbers while being bored:laughing: But I really do think it would take quite a bit to upset one of these tractors in a static situation. I know when I was mowing some 20-22 degree slopes, it seemed like alot. But stepping aways back from the tractor and holding the angle finder at 22 degrees and sighting it over the tractor, 22 degrees really dont look like much slope at all

I guess our sense of angles get all out of whack when you are actually on the slope.

I have yet to see the significance of for and aft weight shift on lateral tip over.
That is, Your "testing" indicates that you lift one rear wheel, and then measure the weight transfered to the off side FRONT wheel. This makes no sense!
The front pivot will see the weight transfer associated with lifting the rear end, be it one wheel or two. But that single pivot will also distribute the added weight to BOTH front wheels. And this has absolutely NOTHING to do with lateral weight transfer. (If the front axle were blocked solid, you might have something to calculate, but why?) Do the same evaluation with tricycle gear for comparison ;-)

For my money, lift one rear wheel, measure the new weight on the off side rear wheel, subtract the weight transfer to the front axle. Then run whatever calculations you please.

With that, If you put the CoM at the crank centerline left to right, and at the clutch plate front to back and Vert., you will have your CoM for all practical purposes. The need is to know a dynamic tipping point. and that is a tough one to get exact.

For the static case, when will the ground tilt uniformly below you as you sit motionless on your tractor?

 

[flusher]

Interesting discussion.

Question for the OP: is this CoG business of academic interest to you only? Or do you operate or plan to operate your tractor on slopes steep enough to exceed your pucker factor?

Since these calculations are probably only more or less crude estimates, in the interest of safety, it might be better to consider modifications to your tractor to increase it's inherent stability if you plan to work on slopes.

Perhaps rear dualies? Or converting your tractor to a low rider configuration like, for example, my 1964 MF135 diesel.



The normal 12.4/11-28 rear wheels have been replaced by 18.4-16A, lowering the tractor by 6 inches and increasing the track width to 84". The front spindles were shortened to keep the tractor level.

Just a couple of suggestions that come to mind.

Good luck and be careful out there.

 

[mikehaugen]

Interesting discussion.

Question for the OP: is this CoG business of academic interest to you only? Or do you operate or plan to operate your tractor on slopes steep enough to exceed your pucker factor?

Since these calculations are probably only more or less crude estimates, in the interest of safety, it might be better to consider modifications to your tractor to increase it's inherent stability if you plan to work on slopes.

Perhaps rear dualies? Or converting your tractor to a low rider configuration like, for example, my 1964 MF135 diesel.

<img src="http://www.tractorbynet.com/forums/attachment.php?attachmentid=390049"/><img src="http://www.tractorbynet.com/forums/attachment.php?attachmentid=390050"/>

The normal 12.4/11-28 rear wheels have been replaced by 18.4-16A, lowering the tractor by 6 inches and increasing the track width to 84". The front spindles were shortened to keep the tractor level.

Just a couple of suggestions that come to mind.

Good luck and be careful out there.

That is one bad*ss tractor, Flusher.