Well Charlie, as nice as it is to have someone check my math, if you’re going to correct me “without doing the math, I would guess its' probably double that minimum (12% or more)”, perhaps you could state your assumptions and show the your calcs.
I think you understand the general nature of the concept, but perhaps a review of statics is in order. It isn’t the lever arm which cancels out in the math, it is the mass or weigh at the center of gravity. Draw a free body diagram like you would back in school, you’ll get it. And then if there’s an error in my math we’ll both be able to see it.
Thanks, this is a topic that many like to conjecture on, but few seem to follow the physics. Now in my calcs, as I stated, my estimate is based on a static situation. Once momentum is involved, well you probably just rolled a tractor. I’ll let the ME or physics guys detail that for us. Perhaps that’s you?
You sure are an angry little Elf Mr. Griz.... I'll state my assumptions and what I believe to be actuality. You can try to pick this apart if you want... What I will explain is static conditions.
First, never presume or assume... it gets you in trouble when trying to determine a real life condition. Why would you presume the center of mass is at the mid point of the tractor rear axle? Is it really? always? It's not, there are many things that determine the center of mass, it is not always at a mid point, it can be, but often is is not, or it can be changed. Changes in material density, distance from pivot point (yes.... that useless lever arm again) all potentially change the center of mass. By displacing the forces along the base (or axle) furthest from the tipping point, it will locate the center of mass in lateral axis further away from the midpoint of the axle. This can be calculated by the use of forces/moments and of course, that pesty little lever arm. Now... we just added weight (as to how it affects the overall moment) to the non pivot side of the tractor by separating that heavy weighted tire as it's own entity. Now, the center of mass just moved away from the tipping point.... now go back to your free body diagram... do your stick figures and notice how much more of an angle is now required to get the center of mass over the tipping point (which would be opposite/low side tire). When this tipping point is established, it has a zero lever arm 0x0=0, where all of the other forces against it, including the opposite tire at the extended 4", which calculates 70"x400lbs(?)... quite a force. See how that center of mass has moved? Therefore increasing the degree of slop required to reach the tipping point.
Let me ask you something.... when you look at your tractor from the side, where is the center of mass? Now, add the bucket and a scoop of gravel, did the center of mass change? (hint: it did) (the tractor is in a static position, just a different condition, just so we're on the same page). Now.... your a tractor guy and you don't like the calculations anymore of your presumed center of gravity vs. your now real life condition... it doesn't feel safe does it?.... what do you do?? holy smokes... we should add more weight to the opposite side of that pivot point (front tires) (the one you say doesn't matter).... maybe a ballast box, loaded tires, an implement? I don't know, maybe some farmer will figure out a way to offset that pivot point by adding a moment in the opposite direction of the loader?? That Damn Lever Arm agian! Bastard! Hum...interesting concept. it seems when considering tipping points in length direction of the tractor, with the addition of ballast we were able to adjust the moment by moving weight (counter weight) away from the pivot point .... frickn lever arm again, uff.... anyway, I'm sure you get the concept.
No... the free body diagram doesn't trump actual physics. That was the starter kit. I will give it to you.... without the consideration of reality, your math was correct. But, your math does not take into account the potential displacement of loads and their affect on the reactions they generate. These loads I say are displaced are still considered static. The more weight to the outside, the more stable the condition. If you were analyzing a solid brick.... I'd give you an A+
Ever wonder why the leaning tower of Pisa hasn't yet fallen over? it's because they continue adding weights, opposite the side it's leaning.... short lever arm ... dam it, again... so lots of weights. Anyway.... they continue to shift the center of mass by adding these weights. So, if and when they cannot counter balance the continued leaning the center of mass will drift past the pivot point.... this temporary fix won't last that much longer unfortunately.
We'll just agree to disagree on this one. you are right ... I needed to get my statistics "in order"... Have a Merry Christmas... honestly.
