Posted by llamas on March 12, 1998 at 07:06:11:
Regarding wide vs narrow front tractors.
There's two sets of forces at play - static and dynamic.
The statics is easy. If a vertical line through the cneter of gravity falls outside the polygonal plane defined by the tire contact points, the tractor's going over.
The dynamics is harder. If the roll couple imparted on the center of gravity by a combination of angular velocity is enough, in a given situation of grade, to move the vertical line through the center of gravity outside the polygon ... blah, blah, blah ... the tractor's going over.
What does this mean for stability and WF vs NF?
For greatest resistance to rollover due to static forces, the cneter of gravity should be as close to the centroid of the polygon as possible, and as low (near to the ground) as possible. Thecloser the CG is to the polygon, the greater the angle of tip required to move the vertical line outside it.
For greatest resistance to rollover due to dynamic forces, the roll axis of the machine should be as high as possible above the polygon. And the CG should be as close to the roll axis as possible.
Now, to practicalities. A wide-front has a large polygon, and generally speaking, if standing still, it can be tipped further in any axis before line through the CG moves outside the polygon. If one wheel is unsupported, eg falls into a hole, this reduces the effective polygon and/or produces an effectively much greater tip angle.
A narror front has a smaller polygon. If standing still, it will take less angle of tip in some directions to move the vertical line through the CG outside the polygon. This may be made worse if the CG is further forward. Once again, if one wheel drops into a hole, the polygon is the same but the angle of tip is effectively increased.
Dynamically, on flat ground, the wide front has a roll axis defined by the tire contacts - it can't roll about the axle pivot, the rear tires won't allow it. The roll axis is a more-or-less constant distance from the CG, which does not vary with steering or angular velocity. The roll couple required to tip it over due to angular velocity will always be roughly constant.
Dynamically, on flat ground, the narrow front has a roll axis which approaches the center of the tractor at thr front. Unless the CG is at or behind the rear wheels, the distance between CG and roll axis is always less than for a wide-front, so the roll couple required to turn it over will always be less for the same height of CG above ground.
In practice, this means:
If two tractors of the same weight, same height of CG above ground, same relative position of CG front-to-back, same rear-wheel track width, it will take a greater angle of tip and a greater roll couple to turn the wide-front over in any case.
The higher the CG above the ground, the easier it is to tip both, but it is even easier to tip the narrow front in some axes. As the CG moves forward from the rear axle, the narrow front will tip more easily than the comparable wide-front. The steeper the downhill grade, the more easily the narrow front will tip compared to the comparable wide-front, and it gets worse very quickly if travelling downhill any other way than straight down the grade.
It is the combination of forces that leads to trouble. A narrow-front can be gotten closer to trouble in some situations, where a bone-headed move, like a sudden change of speed or direction, will add enough roll couple to turn it over where the comparable wide-front could have stayed upright. But that's not to say that the wide-front would not tip with just a little more bone-headedness. Because of the variable width of the contact polygon, the narrow-front is much more sensitive to the direction of the grade and whether it's going up or down, and to the effective position of CG front to back. A wide-front is more tolerant of these variations, because the contact polygon is more or less constant.
They'll all tip if you push them far enough. On balance (no pun intended) a wide front has a larger enevleope of tolerance for tipping than a narrow front.
llater,
llamas