Sorry for the delayed and long response but here goes my last thoughts (?)
I've enjoyed the discussion and always open to change my when wrong and also to learn from other's opinion.
Of course, I absolutely agree that it’s more practical to first add width to the rear axle if at all possible. But the OP first asked if both front and rear tires needed to be in line with each other. He also simply asked for the pros and cons of spacers in both locations. Hence the disagreement over the blanket statement offered that adding spacers on the front pivoting axle had no affect on stability.
I think your interpretation of stability for you is much narrower that NHS’s, mine, and possibly others. I view stability as a variable that can range from completely stable (a tractor at rest on level ground), very stable (safe operating practices under the given conditions whether on level or inclined ground), to extremely unstable (unsafe operation that can easily lead to a rollover or accident, whether on level or inclined ground). It really wouldn’t have to end in a rollover to be considered unstable. (Which seems to be our main point of contention.) Example: Isn’t it considered unstable if the ride would become so bumpy that the operator loses control and strikes an object causing damage and injuries to the tractor, himself, and/or others? And the range from very stable to extremely unstable can be wide to very narrow depending on each tractor’s configuration, operating speed, skill of the operator, common sense, and more.
In a way, you even agree with us in some of your earlier statements. Think of it this way and using just a bare tractor as an example (no loader, no attachments):
A tractor with a very solid narrow front fixed axle hitting a small object under one front wheel will tilt the whole tractor to an extreme angle
if the speed was excessive enough where both wheels on that side would leave the ground before rocking back and forth between opposite tires front to back. There is momentum at play here because of the unsafe speed.
Now, the same tractor with a much wider front hits the same small object at speed but because the angle of tilt is much less (as in NHS’s drawing). Less tilt at the same speed equals greater stability and a less chance of rollover.
Now take the same tractor with a narrow pivoting front axle and hit that same small object and the tractor may hit the pivot stop (or not) but any tilt wouldn’t be quite as extreme as with the solid axle. Maybe not much less but still it would be less. (Geometry is the more technical math description for the reason). Now with a wide front pivoting axle chances are much greater that it would not hit the pivot stop at all, the rear wheel is still on the ground till it strikes the same smaller rock. Only one rear wheel off the ground now and less momentum built up that could lead to a roll over. Thus, more stability.
Another way to look at it: Think of the pivoting front axle as a kind of shock absorber. If front and back wheels are in line it might be only the back wheel striking the same small obstacle that will cause the tractor to tilt. If two equally small objects spaced in line at the exact wheelbase (front to rear) were struck at the same time then again, possibly only the rear tire would cause the tractor to tilt. If the wheels were not in line and only the front wheel hits the small object, then without the front axle hitting the pivot stop, the tractor wouldn’t tilt at all. The pivoting front axle therefore does improve stability and the wider the stance the better. Again, speed, momentum, safe operating under the conditions, etc. all contribute as much to the stability. And the pivoting front axle acting as a kind of a shock absorber can help to keep your tractor from tilting whether it hits the stop or not. Thus, it’s more stable. And consider small rocks on one side with a rut on the other. Double trouble for a fixed axle. Not so much for a pivoting axle depending on the sizes. But still......less.
You stated earlier above that with the pivoting axle hitting a smaller object you might not feel it at all unless the axle hits the stop. With a fixed axle you would. That goes along with what we are saying. Wider is better in all cases until practicality and those other costs dictate otherwise. But just as the range of stability can be very narrow, so can the range of practicality over the width of the front pivoting axle. But the blanket statement that adding to the width doesn’t matter on that axle is technically not correct in and of itself. IMHO, of course.
If a person were operating on only flat, level ground or on completely smooth inclined ground you may not agree. If you add rocks, bumps, pitted cow pasture, badger holes, hidden cut off stumps, or any unseen objects to that same terrain I think that person would agree that a wider front, pivoting axle smoothens the ride which helps to maintain control by adding to the stability. And if you’re cruising home in road gear at the end of the day on a smooth country road and didn’t notice that gopher mound or small rock……it would help convince you even more. Daylight between your pants and the tractor seat was fun when I was young and fearless. Now it can be quite scary. But less daylight between is certainly better, no matter how small the difference.
Just another thought: If a pivoting front axle doesn’t aid in stability until it reaches its stops: Then what is the function? Wouldn’t a tractor’s 3 basic goals be power, traction and stability? I’ll have to think more on that one.
If the responses had been something like, “For most practical reasons, it’s much better to add rear spacers first before considering the front spacers”, we likely wouldn’t have had this interesting discussion. But this has been a good, civil and fun discussion. Even just for safety’s sake, it will give people pause to consider all the reasons and what ifs. I’ve appreciated the discussion and respect everyone’s views. Thanks to all!