"Distance from pin" math

[Bullwinkle123]

When using pallet forks or other attachments where one end of the attachment is far from the other, what are the equations to calculate effective load? (Whether it's loader or 3ph)

For example, the rear of my rotary cutter is 8-9 feet from the 3PH, and the front edge of my new bucket is over 4 feet from the loader pin. Is there equation I can use (with simplifying generalizations where possible) to calculate how much load I can manage?

I have two primary cases where I'd like to know:

1) When using my pallet forks and/or new (very deep) bucket. Taking the simple case of a pallet, how many pounds can my LA1065 loader (~2300 lbs at pin) lift with a load uniformly distributed across the pallet?
2) I'd like to make a rear ballast that has at least the same ballast value as my 700 lb but very long rotary cutter but in a much more compact form so I can maneuver. Actually, I'd like to add quite a bit more ballast value than my rear attachments provide, which is why I'd make one - but for starters understanding some simplified math with the rotary-cutter-ballast-replacement scenarios is probably informative.

 

[sea2summit]

So this is very complicated math if you're looking for "uniformly distributed" loads. Most of the easier math would involve a point load, which you'd just assume the center of gravity for your load and use that point. It would still not be easy math.

To start with we need to know the weight of your tractor, the weight on the front wheels, the weight on the rear wheels, the distance from the front axle to the pins on the loader and to the pins on the 3PT (for this we'd assume the fulcrum is the front wheel for easier math). Then we need to understand the weight distribution of your rotary cutter to do the math on how much force it's applying. Then more maths, then we could make an educated estimate at exactly how much you'd have to place at the pins for equivalent forces.

It's a lot easier to just put a ballast box on and load it up with approximately "a lot" of weight More weight is generally better when it comes to the tractor and stability, especially with loader work.

ETA also the pins will be closer to the front axle if the FEL is all the way down and extend slightly forward as you lift so I guess there would be two measurements you need to provide based on where you want the equivalent force of the rotary cutter applied.

 

[bdog]

The math to calculate it exactly is rather complex but for quick and dirty calculations think of it as a linear relationship. 200 lbs one foot past the pins is equivalent to 100lbs two feet past the pins or 50lbs four feet past the pins.

Simplifying your cutter is 700lbs and 8 feet long so you assume a 700lb point load 4 feet back. If you wanted equivalent ballast that was 2 feet back you would need 1400 lbs.

The loader capacity on the forks is a bit more tricky as the pins are really just an arbitrary location with relation to the moving parts.

 

[Bullwinkle123]

It's a lot easier to just put a ballast box on and load it up with approximately "a lot" of weight More weight is generally better when it comes to the tractor and stability, especially with loader work.

Yes, but my concern is this. Say I wanted to provide ballast equivalent to my 700lb rotary cutter. If I just put 700lbs of steel and concrete into a 2' deep by 3' wide by N' high box on the 3PH, how much ballast have I lost compared to using my same weight rotary cutter? I'm thinking the difference could be substantial because of the difference in leverage. So I was hoping there was some equation I could apply so I know what I'm building before I build it

 

[bdog]

I looked up your loader and it says 2,275 lbs at the pin and 1,691 lbs 500 mm forward (~20”).

2275-1691 = 584 pounds

divide this by 20 and you lose 29.2 pounds of lift capacity every inch past the pins.

If your bucket lip is four feet out then you could do 48 X 29.2 and you would lose 1,400 lbs at the lip which would leave you with a capacity of 875lbs at the lip.

 

[Bullwinkle123]

The math to calculate it exactly is rather complex but for quick and dirty calculations think of it as a linear relationship. 200 lbs one foot past the pins is equivalent to 100lbs two feet past the pins or 50lbs four feet past the pins.

Simplifying your cutter is 700lbs and 8 feet long so you assume a 700lb point load 4 feet back. If you wanted equivalent ballast that was 2 feet back you would need 1400 lbs.

The loader capacity on the forks is a bit more tricky as the pins are really just an arbitrary location with relation to the moving parts.

A rule of thumb like this would suffice, given sufficiently high confidence level in the rule I'm sure I don't know so I'm asking.

 

[bdog]

Without knowing the exact center of mass of your cutter it is about as good as you can do. It is probably fairly accurate. The gearbox and blades are heavy and in the middle. The body of the cutter is pretty uniform. The wheels off the back add weight but then so does the hitch. For what you are wanting to do I would just take the total weight of the cutter and assume it to be a point load at however far back your gearbox is.

For purposes of ballast the distance that really matters is the distance from the center of the rear wheel. Measure the distance from the center of the rear wheel to your cutter gear box and assume a 700lb load at that distance. You can then linearly calculate what equivalent load you need at any other distance from the center of the rear wheel.

 

[Bullwinkle123]

I looked up your loader and it says 2,275 lbs at the pin and 1,691 lbs 500 mm forward (~20”).

2275-1691 = 584 pounds

divide this by 20 and you lose 29.2 pounds of lift capacity every inch past the pins.

If your bucket lip is four feet out then you could do 48 X 29.2 and you would lose 1,400 lbs at the lip which would leave you with a capacity of 875lbs at the lip.

And of course the reality is much more complex because the load isn't uniform, or at the tip.

I spent the Saturday (between the rains) using my new 750 lb 49" deep 35 cu ft light materials bucket. It's definitely going to be useful and it was on Saturday, but the dynamics are severely different than the standard bucket on my loader, and there was definitely a sense that it was trying to make my loaded rear tires dance if I was too abrupt with some of my loader activity (even with my 695 lb rear blade hanging off the back). I was expecting this, more or less, now I need to make plans to deal with it.

However even taking the bucket + packaging off the delivery truck using my pallet forks shows that I would do well to get a clue about some kind of "how much can I carry" when using the deep attachments (like pallet forks). If unloading the bucket from the delivery truck is pushing it, I don't want to order something else that's 100 lbs heaver and I can't get off the truck. (Whether unloading the bucket was pushing my limit I don't know, I went very slowly and there were no issues, but it felt like a strain on the system).

 

[sea2summit]

Yes, but my concern is this. Say I wanted to provide ballast equivalent to my 700lb rotary cutter. If I just put 700lbs of steel and concrete into a 2' deep by 3' wide by N' high box on the 3PH, how much ballast have I lost compared to using my same weight rotary cutter? I'm thinking the difference could be substantial because of the difference in leverage. So I was hoping there was some equation I could apply so I know what I'm building before I build it

Yeah, how far behind the front axle is the center of gravity on the cutter. Then how far behind the front axle will the ballast box be.
example:
F1(force at pin)=at 7' infront of axle, with 700lb at 15' behind the axle=700lb (15'/7')= 1,500 (more math would give us newtons of force but I don't care right now)

Now F1=1,500=at 7' infront of axle with some weight, 12' behind the axle=1,500/(12'/7')=~874 so you'd need about 874#

But that's all assumptions/guesses.

 

[ericm979]

The math to calculate it exactly is rather complex but for quick and dirty calculations think of it as a linear relationship. 200 lbs one foot past the pins is equivalent to 100lbs two feet past the pins or 50lbs four feet past the pins.

I think that's not right for loader lift capacity but it's closer to right for curl. And the curl may be more limiting than lift. It is on my loader.

What you really need is to measure the distance from the load to the pivot. I.e. lets say that it's 8' from the pins to the loader pivot and the loader's rated for 1000 lbs at the pins. If the load is 2' out from the pins that's 10' from the pivot. 10' is 25% more than 8' so the capacity is reduced by 25%, or 750 lbs. Measuring the curl capacity would work the same only from the bucket pivot. Of course to be more accurate you also need to account for the attachment (bucket, forks) that is picking up the load, and it's position relative to the pivot does not change.

For a non point load you can use the load's CG as the lift point for the above calculation. If it's evenly distributed (i.e. firewood in an IBC tote) the CG is easy ti estimate as it's the middle of the tote.