Calculating Your Predicted Rollover Angle

[Rhino35]

Marveltone,

Thanks for clarifying the measuring point.

They make my brain hurt too.

The point of posting was that these tractors, with static tip over angles of over 40 degrees, are more stable than I thought. I had thought they might go over at about 30 degrees. Just interesting - and the other point was that the spacers made a difference. Not as much as I thought, but they make a difference.

Rhino

 

[Rhino35]

RickB,

I don't think it can be stressed enough that the things you mentioned will increase the likelihood of a rollover.

Rhino

 

[DarkBlack]

Rhino, "A" for effort, but I think you and your physics major friend missed a major parameter. I posted on this subject over a year ago.

"The front axle assembly is normally mounted to the frame by a free moving pivot point. Any widening aided tip protection from, say, rolling from running crosswise on a slope, will have zero to little added benefit from widening the front wheels. That would be the case until you hit the pivot limit of the front axle, but if you lifted the machine to that point, you will probably be rolling over anyways. "

You and your friend missed this huge game changer. You/he treated the tractor calculations as a rectangle shape. What your really have is a triangle, up to tip over angles of the front axle's pivot's limit. When you physically hit that rotary stop limit and it changes to a rectangle, the momentum alone throws your pre-calculations out the window. Also, with the loader ahead of this free pivot, calculating this mass becomes much more complicated.
Sorry for the bad news. I hope this explains why you had such incredibly steep slope angle predictions.

 

[Rhino35]

DarkBlack,

Thanks for the A for effort *grin*.

I remember reading your post - I read all I could find of this subject. I was thinking about getting front spacers and found your post interesting. I didn't get front spacers primarily for warranty reasons. But I don't think you're quite correct that they wouldn't help, or that we're dealing with essentially a triangle. My tractor's front tires were almost as wide in wheelbase as the rear before I put on the spacers. Do you know the angle at which the front axle would reach the stops and begin acting more like a fixed axle? I don't, but I would guess about 15-20 degrees? Let's try and picture this...

I imagine jacking up the tractor with the jack near the rear tire. As it goes up one rear tire goes up in the air, but the same side front tire, because of the pivot, stays on the ground. It would start coming up a little as we keep jacking, but mostly it pivots as the jack angle goes up. Instead of like the rear tire where that tire's contact point is increasingly towards the outside side wall, the front tire on the downhill side stays in solid contact with the floor. Somewhere in that jacking process the front axle pivot hits the stop. Now the uphill front tire comes up just like the back tire and the downhill side front tire begins to rest more and more on the outside edge. Just like the rear tire benefits from a wider track, after the pivot point is reached on the front axle, a wider front track would aid stability. Right? Or am I missing something?

Best,

Rhino

 

[CalG]

Rhino, "A" for effort, but I think you and your physics major friend missed a major parameter. I posted on this subject over a year ago.

"The front axle assembly is normally mounted to the frame by a free moving pivot point. Any widening aided tip protection from, say, rolling from running crosswise on a slope, will have zero to little added benefit from widening the front wheels. That would be the case until you hit the pivot limit of the front axle, but if you lifted the machine to that point, you will probably be rolling over anyways. "

You and your friend missed this huge game changer. You/he treated the tractor calculations as a rectangle shape. What your really have is a triangle, up to tip over angles of the front axle's pivot's limit. When you physically hit that rotary stop limit and it changes to a rectangle, the momentum alone throws your pre-calculations out the window. Also, with the loader ahead of this free pivot, calculating this mass becomes much more complicated.
Sorry for the bad news. I hope this explains why you had such incredibly steep slope angle predictions.

DarkBlack,

You are promoting a popular misconception.

It is not until the uphill rear wheel leaves contact with the ground that a pivoting front axle is required to move about it's pivot. Regardless of the degree of tilt. After that, the inside wheel is permitted to lift the full angular displacement provided for by the axle pivot before any resistance to further tipping will be obtained from the front wheels. I'm quite confident, that on a steep incline, that resistance will come much after a roll over is assured. On flat ground, using only cornering forces (roll) things will be much different.

It is true what you say that calculations taking into account momentum and inertia are more than complicated, but if I have read the OP correctly, this rough order of magnitude calculation is based on static conditions. Fair warning was included in the text regarding the many uncontrolled variables.

A triangle or a rectangle matters not one bit on the roll over angle based on the original assumptions.

And that is why tricycle steering gear is not more prone to tipping than a "conventional" front axle. (Assuming simple conditions)

Loaders screw up the CoG determination to no end! But a load on the back only shifts the fore and aft CoG closer to the wide rear tires. The calculation point.

Simplified, If the lateral CoG is allowed to move outside of the support plane, over it goes!

ps, I have done no work to confime the correctness of the maths, just going by the text description.

cheers

 

[IslandTractor]

Hello All,

Here is the bottom line...the sideways rollover angle for my Kioti DK40 Hydro FWD, with FEL positioned with an empty bucket parallel to the ground, and Tartar 6 bush hog - and in all likelihood most similarly equipped stock utility class tractors - is above 40 degrees. Add 4 spacers on each rear wheel and you'll add, as expected, a measurable margin of safety to the rollover angle in either direction. In this post I'll show the math so you can play around with your tractor's dimensions. This was a real confidence-builder for me to see these predicted rollover angles. So if you want to have a full understanding, or join in a discussion, or check my math, please read on.

I recently bought my 4 inch rear wheel spacers from Motorsport-Tech in Reno, NV,, a sponsor of this forum, and I am extremely pleased. Lenny, the owner, was great to work with throughout - and very concerned I would be happy with my product. I have no doubt that if your spacers arrived and didn't fit, or were damaged, Motorsport-Tech would build ones that met your needs at their expense. I had them installed by my dealer two weeks ago during the 50 hour tractor service - they fit perfectly and came with quality hardware. Before and after photos below. I had them anodized black by Lenny for an additional $25 each to better keep the aircraft grade aluminum from corroding where bare aluminum might touch any bare dissimilar metal - bolts, nuts, washers, axle ends and rims. The anodizing, if not scratched, will prevent corrosion. I added another layer of protection by spray painting them with Kioti Charcoal Gray paint, which was an exact color match to the anodizing. Painting them only cost 15 bucks for the can of spray paint so why not? My anti-corrosion obsessed brain sleeps well knowing they should look new in 30 years when I'm 87 *grin*.

Driving the tractor with spacers felt entirely normal. I felt more comfortable seeing the wider rear wheelbase from the driver's seat. We all can take one look at a wider wheel base and imagine, all other things being equal, that it will take more jacking up of one side on level ground to tip it over. But I wanted to know - how much extra stability do 4 spacers buy us? 6 degrees? 10 degrees? What's your guess? Mine was 6-7 degrees, but that wasn't correct.

I consulted a physics major who knew how to do the math to figure out the roll angle at which a tractor will tip over. Warning! Disclaimer! Don't shoot me! I offer this exercise believing it is correct, but it is for informational purposes only. I bear no responsibility for any accidents anyone might have if they decide to drive on steeper side hills because of what this static, level ground, and admittedly incomplete formula predicts their rollover angle might be. It's incomplete because there are a lot of constantly changing rollover variables in any moving tractor. I'll list some here - and mention what we need to realize about how they might affect a rollover. The thread by Kentuckytractorboy and others have great comments, but I'll still recap here.

The incline of any side hill is what we're basically talking about - but the hillside's angular degree is rarely constant as we drive across it. Uneven terrain can quickly increase the effective hillside's angle. Tractor speed when a tire hits a bump or depression needs to be slow to avoid any catapulting effect that would temporarily increase effective hillside angle. Speed in a turn where centripetal force is exerted can significantly affect a rollover. Differential braking is dangerous at speed since it creates a turning moment. Centripetal force always increases the likelihood of a rollover opposite the direction of turn, however there is one situation where a turn might prevent a rollover. If you fear a side hill rollover is imminent, or beginning, a quick turn downslope and the resultant centripetal force you generate may offset gravity in time. A turn downslope will also effectively decrease the angle of the side hill relative to your tractor's horizontal CG. So slow is always good and fast is almost always bad. The equation doesn't consider all these dynamic factors. It doesn't consider any coefficient of friction for the surface being driven on either - it assumes the tractor tires will not slide sideways. A static computation should be accurate enough for us to make intelligent operating decisions as long as we think about these variables.

Steps we can take to increase rollover angle under all operating conditions are to lower vertical CG and/or widen the wheelbase. If the tires are loaded with fluid the CG will be lowered. How heavy and how high the rear implement is carried (if installed) will affect vertical CG (and horizontal CG if weight is out to one side). How high the FEL is off the ground and its load is a very large variable. Positioned lower and carrying lighter loads is very important. The weight and height of the driver will have some effect since the driver sits above the normal vertical CG. Even if the fuel tank is full or empty will have a small effect - full raises the CG slightly.

Unfortunately I don't know my tractor's exact CG in terms of its vertical height off the ground - and as mentioned above it does dynamically vary when the rear implement and the FEL are in use. For purposes of showing how stable our tractors are stock, and the difference with spacers, we can explore a range of likely vertical CG's.

I do know my before spacer installation horizontal distance, with the widest stock placement of the tires in relation to the rim which the manual allows that I had the dealer perform at delivery, and I know the distance of that same tire configuration after rear wheel spacer installation. To determine your horizontal distance from an assumed middle of the tractor CG measure from about one inch outside your tractor's rear wheel tread midpoint on one side to the same one inch outside your tractor's other wheel midpoint and divide by two. I chose this measurement point instead of the outside edge of my rear tires because my Industrial tires are flat only in the middle couple of inches and they round down towards the outside of the tire. Our tires will also flex to some degree with thousands of pounds of force being increasingly exerted on the edge of the sidewalls as the side hill angle increases. In fact, if you have too underinflated tires the tires may "t麹uck under", or roll off the rim, and lose more pressure, all of which is a bad thing. Your wheelbase quickly shortens and your rollover angle correspondently decreases - over you may go. So my measurement point is a conservative, safer measurement point compared to the very outside of the tires and yields a slightly lower predicted rollover angle. Here are a number of static rollover angles based on a range of vertical height CG's.

Rhino's Kioti DK40 Rollover Angle Calculations

Vertical CG Horizontal CG Predicted Rollover Angle Diff. with 4" Spacers
25 inches 32 inches 52.00 degrees
25 inches 36 inches 57.20 degrees 5.20 degrees
31 inches 32 inches 45.90 degrees
31 inches 36 inches 49.25 degrees 3.35 degrees
33 inches 32 inches 44.15 degrees
33 inches 36 inches 47.50 degrees 3.35 degrees
36 inches 32 inches 41.65 degrees
36 inches 36 inches 45.00 degrees 3.35 degrees
40 inches 32 inches 38.70 degrees
40 inches 36 inches 41.98 degrees 3.28 degrees
46 inches 32 inches 34.83 degrees
46 inches 36 inches 38.00 degrees 3.18 degrees
55 inches 32 inches 30.19 degrees
55 inches 36 inches 33.20 degrees 3.01 degrees

and, lastly, a really high, heavy FEL load best vertical CG guess...

72 inches 32 inches 24.00 degrees
72 inches 36 inches 26.50 degrees 2.50 degrees

Here is how you calculate a static rollover angle. You'll need a calculator capable of performing "t麹an" functions. I'll do it for one of the above examples. Just plug in your own values.

Divide your estimated (or known if you know it) vertical CG height by the horizontal distance from the center of the tractor to about one inch outside your rear tractor tire's centerline. Measure from tire to tire and divide by 2 to get this horizontal distance. 33 vertical CG divided by 36 horizontal distance equals .9167. Write this number down.

Now you have to do some trial and error calculations to find a corresponding tangential angle. If the above number is less than 1 clear your calculator and pIck an angle less than 45, then hit "tan". A decimal will be shown. If it is greater than 1 pick an angle greater than 45 and you'll get 1 plus a decimal value. The goal is to close in on the same number as .9167 - in my example - or whatever you got as a value. A higher angular guess will yield a higher number. So 44 degrees and hitting t麹an yields .9657. I need a lower number so I'll try 43 = .9325 - still not there. 42 is .9004 - too low. 42.5 is .9163 - close enough!

Then subtract 42.5 from 90 degrees. 90 - 42.5 equals 47.50. This is my predicted rollover angle for that vertical height CG and the horizontal distance with spacers. If you are like me you'll need to do these calculations a few times to feel you understand it. Try a few of my examples above and if you get the same predicted rollover angles you're on track. Then go measure your tractor's wheelbase and try some likely vertical CG's of your own.

Conclusions

The good news is that with the stock widest wheelbase tire/rim setup my Kioti predicts pretty high side hill stability at the most likely vertical CG's with which I would be bush hogging. My FEL arms are roughly parallel to the ground and the bottom of my empty bucket is raised one to two feet off the ground. My best guess is that in this bush hogging configuration, full fuel and my 215 pounds in the seat the vertical CG of my tractor is between 33 and 36 inches. Without the spacers the predicted rollover range would be between 41.65 and 44.15 degrees and with the spacers a predicted rollover angle of between 45 and 47.5 degrees.

Even knowing these values I know my comfort zone on side hills will never get above 25 degrees. But it's pretty comforting to know 25 degrees shouldn't ever roll me over - or even a momentary screw up where one side of the tractor comes up 10 degrees or the other goes down 10 degrees.

Hope this was useful. Safety first.

Rhino

That is interesting and useful. Two points: 1) My sphincter tone starts going up at about 12 degrees. At about 15 degrees I suddenly consider getting religious. And that is moving very slowly with my eyes peeled for bumps on the high side or dips on the low side. I would have gone through a weeks worth of underwear before getting past 25 degrees much less 40. 2) your calculations are presumably static tip points. We never use tractors in a manner where that is critical unless you are loading a pickup or something while on a slope. The real hazard is not the angle that you can read with an inclinometer as you drive along a slope but rather the instantaneous angle generated when the upside hits a bump or the low side dips into a rut or hole. Travel speed and terrain are therefore big independent variables that static calculations ignore.

That said, the spacers do obviously help. I worry a little about extra loads on the axle but the Kioti rear axle is so massive that it shouldn't matter. Did you put spacers on the front wheels too? That would concern me more as the loader is so strong that the forces on the front axle need to be considered. Also, having the wheels jut out another couple of inches on each side can interfere a little with raking or possibly mowing.

 

[Sysop]

Granddad had a 2wd tractor setup to run on side slopes. He had the downhill side front and rear tires extended out, had the front pivot wedged so it couldn't tip to the downhill side. I think he kept the topside tires loaded too, but I'm not positive. He ran sideways on hills the tractor couldn't climb up and down.

 

[Rustyiron]

All I know is when I get that cottony taste in my mouth, it's my underware, and time to level out things!:laughing:

 

[Xfaxman]

Pictures of a rollover. This machine has a solid front axle and a pivoting rear steering axle.

This happened 8-9-2006. Was using the forks to knock the dirt off of the root ball on a willow tree that the dozer dozed over. Backed up, but it didn't turn uphill, because the right front tire was almost flat (slow leak). The right front dropped into a hole, and the TORO went over, I fell off of the seat onto the side panel. The engine was still running, I had to raise up and reach under my butt to turn off the key. I was right at the edge of the water, the loader tower was in the water. I got my tractor, put a chain on the left loader arm and pulled it upright.

Looking south from the dam.


Bottom view.


Rear view.


Front view.


After I pulled it upright, you can see the chain on the tower.
This is the root ball I was knocking the dirt off of. Didn't seem like I was much of a slope.


Notice the counterweight. a 100 pound block of steel at the lower right, that fell off of the brushguard.

I left it chained to the tractor, got on, crossed my fingers, it started and I backed up the hill.
The loader wasn't up very high and the hole wasn't very deep, but it sure went over fast.

After this I reversed the wheels, to make it wider and added 75 pound wheel weights.

Wider tread and wheel weights, from July 2009, with the brush fork.


From last month, to show that it is still running!

 

[CalG]

Just examining the picture after "righting", it looks like you might have just driven out from under the CoG.

High chain and all. The slope didn't help, but from the photo, it does not appear to be sufficient to cause over turning.

Looks nasty too, you are fortunate not to have been mained or drownd!