Center of gravity??

[Paddy]

While posting on another area here on the topic of Roll overs, I was wanting to run more precise moment calculations.

So here is the question; Where is the CG on most tractors viewing from the rear?

I want to determine this location without attachments, loaded tires or FEL. my guess would be 65% of the tire height. Anybody have actual spec on this?

Patrick

 

[SkyPup]

There is more than just the CG involved.


http://www.cdc.gov/nasd/docs/d000701-d000800/d000746/d000746.html

 

[daTeacha]

That's a good read, but I kind of wonder how many posters will read through the whole thing.

To summarize, hitch low, at the drawbar when simply pulling something. DO NOT hitch to the top link for a simple pull. That point is for use in conjunction with the two lift arms only.

Tractors can overturn either on a left-right axis or a front-rear axis or some combination of the two. Keep all weight as low as possible at all times, and be especially careful -- avoid if possible -- traversing hills from side to side, where the relatively high longitudinal roll center could set you up for a nice view of the bottom of your tractor or worse.

When going uphill while pulling a load, be very careful lest the front end comes over. If the steering gets light, back off and put some weight out there. This one could find the tractor standing on it's head pretty quickly.

I've seen guys hitch to the front axle or weight rack with chains run under the tractor for uphill pulling of heavy loads, but I wouldn't want to try it. At least they didn't rotate the tractor around the rear axle.

 

[California]

</font><font color="blue" class="small">( I've seen guys hitch to the front axle or weight rack with chains run under the tractor for uphill pulling of heavy loads, but I wouldn't want to try it. At least they didn't rotate the tractor around the rear axle. )</font>

However it's still going to rotate around the point where the chain touches the bottom edge of the rear axle. I'm not sure this is an improvement compared to pulling from a drawbar that is lower than the axle.

 

[Paddy]

From a point of calculating moments (static), there is nothing more than knowing the mass(es) and there location. From a dynamic point of view, many factors do come forward.

A tractor's ability to stay up right....parked .....on a slope would scare the **** out of most folks.

The attached file stated 10" above the axel as the CG of most tractors. My tractor comes in at 4100lb but there are many here with light weights at 2000lb. So..about 10" won't do. That is why I was pushing a percentage of your wheel height.

I did note that the report also stated the CG was 24" in front of the axel.

Having fun here and hoping to make a simple calculator where you enter your tractor parameters.

Patrick

 

[daTeacha]

That link was based on older design tractors with the tranny and engine being the backbone of the machine, the hood, seat, fenders, etc. just sort of hung on that. The new compacts, when viewed from the side have practically no mass immediately in front of the seat. There is the mass of the engine assembly, some sort of frame structure thin enough in cross section to provide a flat floor, and the mass of the differential/rear axle, etc located under the seat. This arrangement will give a greater polar moment than a classic design like my B7100 or an 8N where a side view of the tractor shows considerable mass from the front to the back. Exactly what effect this has on the position of the center of mass I don't know, but it isn't likely that it's as shown in the link.

This line of thinking brings up a point about loading tires. There is a train of thought that says the rears should only be loaded up to halfway to keep the weight below the axle center line. An opposing point of view says to load them with the valve at the top and keep pumping fluid in until it's up to the valve. It seems for stability the former system is better, but if you want weight for traction, the latter is the way to go. There is some thought that the fluid can get to sloshing around in a half filled tire, but I personally don't think even my maximum road of 9 mph will cause a problem in that respect. -- Opinions??

 

[Paddy]

I was apart of that discussion, half full vs max, on the Yanmar site. Without completely rehashing it, the added mass at the extreems/wheels, creates a great moment. With the down hill tire as the pivot of roll, the entire axel acts as a lever. More weight, more power to prevent the roll. The height of the mass does not mater until very far in the roll. The diagram in the attachment shows it quite well. The the CG of the tractor is straight over the pivot and still the up hill tire is aiding to slow the roll.

I posted here to get a general idea as to the CG of a tractor. Once the CG is known, the calculation is quite easy...with a bit of trig. If I go with the 10" above axel center, I'm at 75% of wheel height.

Patrick

 

[N80]

I would also think that at 50% full there would be too much room for movement of water within the rim that could result in some unpredictable movements which could be disastrous when the tractor is already in a precarious position.

I'm physics impaired, but does the vertical center of gravity decrease as the rear wheel position is widened? At least the 'effective' center of gravity in regard to roll-over? In other words, even if the mathematical CG remains unchanged, the stability of the tractor is improved by widening its stance. Is there a better term than 'effective CG' to describe what I'm trying to say?

 

[RayH]

Actually if you widen the track of the tractor, the CG (mathematically and effectively) will move lower. Imagine if you grabbed the tractor by the ROPS and pulled it over on its side. There will be a point where the tractor is perfectly balanced on two wheels. Draw a vertical line straight from the point where the tires contacts ground. Where that line intersects the mid line of the tractor is your CG.

That being said, I think trying to find the CG of a particular tractor, with a particular operator, and a particular implement in a particular position, carrying a particular load with a particular amount of fuel and so forth is ridiculous. Youve also got a dynamic CG that constantly moves around the tractor as it accelerates and changes direction. Then, in relation to roll overs, you have the effects of the terrain, is it sloped, rocky, slick, soft, etc.
In short, its nice that these topics come up to put roll over safety in the forefront, but to actually sit down and mathematically figure out "when is my tractor going to roll" is impossible.

 

[BobReeves]

I don't believe widening the tires changes the actual CG. It gives the tractor a larger foot print changing the angle of the dangle required to tip it over side to side only.