"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.

 

[oosik]

My FEL Owners Manual has load lift charts. No formulas on how the charts were developed.

Basically - I can lift 3850 pounds in tight on the grapple and 6" off the ground.

This drops to around 1650 pounds at full height. If you have the nerve and are on VERY solid ground.

 

[LD1]

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.

I assume you were talking about the 3PH in this scenerio. Close but not quite accurate.

IF you had wanted to calculate the tension force on the toplink (for sizing a hydraulic TL)....then your math would be correct. Because measuring a given distance behind the pins.....is assuming the pins is the fulcrum.

In terms of "effectiveness" for ballast.....you have to use the center of the rear axle as your pivot. The OP will have to measure......but lets say the 3PH pins are exactly 4' behind the center line of the rear axle. And lets say his cutter's center of gravity is another 4' behind the pins. You have a total of 700# hanging 8' behind the rear axle. 700 x 8 = 5600lb/ft

So if you want something EQUAL to that but a more compact 1' behind the pins......that would still be a total of 5' behind the axle. 5600/5 = you would need ~1120 pounds to equal the same "ballast effect" as the 700# mower.

Similar math can be had for the FEL to get a "ballpark" number. But loaders are a WHOLE lot more complex. Since they lift in an arc....you have your MOST lifting force/capacity close to the ground. The higher you raise....the geometry of the cylinder to its pivots changes....and capacity is reduced. But for ballparking the loader lift with the lift cylinders.....measure from the rear pivot of the loader frame out to the bucket pin. Say its 8' and you have 2300# capacity to the pin. that would be 18400ft lbs. If you want a ballpark of what it will lift at 12'....18400/12 = 1533lbs. (That would be at the edge of your bucket )or close) that has a 4' bottom.

Curl is even trickier....because it has the 4-bat linkage. Full dump and full curl are actually the weakest two positions. And right in the middle is the strongest. But same ballpark method can apply. Look at the existing spec for rollback (curl) force....thats figured with OEM bucket so measure its distance in front of pin. Same math.....figure out how many ft-lbs. Lets say you have 4000# rollback force and standard bucket is 20". Thats 6667lb ft.Now you want a 4' bucket. 6667/4 = 1666lbs roll back force.

Again....this is all complicated.....and this is just ballpark stuff. As you can see....curl force diminishes ALOT faster than loader force. Think about that. Adding 2' to an 8' lever is not a huge change. Adding 2' to a 20" lever is a HUGE change.

 

[LS Tractor Owner]

My brain hurts now.....

 

[LD1]

Im gonna try and simplify my previous post, because I have a MX5100.....which is same tractor as the OP....and I did some measuring.

First.....lets attack the 3ph and ballast situation.

From the rear axle....(which is your pivot point for ballast effectiveness)....to the ball-ends is 32" or 2.67'

So take the weight of the cutter and multiply by the distance behind the rear axle the center of that weight is (usually the gearbox on a cutter)....and you will arrive at a lb/ft number.

IF the OP has a 6' cutter the gearbox is usually ~3' behind the pins. And if said cutter weighs 700#......700 x (3' + 2.67') = 3969 lb-ft. That is the effectiveness of the cutter as a ballast.

Most ballast boxes are only 1' behind the pins at the center of their mass. So 3.67' behind the rear axle.

3969/3.67 = 1081 lbs is what you would need to be the same effectiveness as the bushhog.

If you had a 1000 lb heavy 6' rotary cutter......thats 5667lb-ft. Which would require a (5667/3.67) = 1544lb ballast box 1' behind the pins to be equal in effectiveness.

Note: this is ONLY for ballast effectiveness. These calculations cannot be used for 3ph lift capacity due to the parallelogram linkage style that a 3PH uses. Hope that makes the ballast calculations clear.

 

[LD1]

Now lets talk about the loader. Mine is a LA844 loader.....but I believe the specs are the same (or very close)

At the pin....Kubota rates them to lift:
4180lbs at ground level
3030lbs to a height of 59"
2445lbs to full height

(notice the higher you lift the less the capacity). This is not for safety. Its due to geometry. They actually lose power the higher you go due to the angle of the lift cylinder changing.

The "pin" they refer to is the pin that the heal of the bucket pivots around. A useless number IMO because nobody lifts anything from the "pin". But this pin is exactly 7' away from the rear pin that the whole loader arms rotate around. So we can work with that.

So at the pin:
7' x 4180 = 29260lb-ft at ground level
7' x 3030 =21210lb-ft at 59"
7' x 2445 = 17115 lb ft at full height

So if you want to know a given point forward of that pin.....add that to the 7' and divide it by your lb-ft number.

Kubota kindly gives specs at 19.7" (500mm) forward of said pin. So lets see how we compare.
7' + 19.7" = 8.64'
29260/8.64=3386 at ground level
21210/8.64=2455 at 59"
17115/8.64=1980 at full height.

How do those numbers compare.....well kubota's published specs are 3260 / 2450 / 1840 Which are pretty darn close considering tape measure measuring and rounding.

If you use forks or a bucket with a LONG bottom......lets say from fork tips or bucket edge to pin is 4'.....just add the 4 to the 7.
29260/11=2660 lb capacity at ground level
21210/11=1928 lbs at 59"
17115/11=1555 lbs at full height.

use the same method for roll back force. I cannot find my manual and cannot quickly find a published spec. But whatever the bucket rollback force is.....thats with a standard bucket. Measure the distance from the bucket edge to the pin (same pin that the heal of the bucket rotates about). Take the force times that distance to get your lb-ft number. And then divide that by whatever you new bucket measures.

My standard bucket is 29" from pin to cutting edge. If you have a new bucket that is 48"....you are gonna have ~60% of whatever the published capacity is. If the new bucket edge is 58" forward of the pin....you will only have half the published capacity.

Does that clear things up?

 

[PILOON]

The formula is simple to most aviation types as we need to calculate center of gravity for safe loading an AC. (AC have known safe C of G ranges)
It all starts with a known datum point. (most AC use the firewall).
A simple example would be 100 lbs at 10 inches =1000.(inch pounds)
(moment is wt x dist)
So if 100 at 10=1000 then 10 lbs at 100 ins meets moment.

On a tractor they give U the bucket capacity so U can go from there once U determine a pivot point which I'd assume is the front axle as that is where the load would rotate from.
Assuming a bucket is 24 inches ahead of the axle then a 1000 lb bucket at 24 ins would have a moment of 24000.
So if a fork load is 36 ins ahead of the bucket you then have the new moment at 60.
Take moment of 24000 divided by 36= 666.666 lbs.
That would be your safe capacity limit using forks.

(Often seen on crates is a triangle mark to indicate the C of G of that crate as the contents might not be actually centered, that for safe fork lift operation)

LOL, all clear as mud?
I, moons ago, sold fork lifts and was also a pilot as well as a licensed aircraft mechanic.

On the practical side your 'pucker meter' (AKA, your butt) would soon advise U if that fork load was out of G of G range!

 

[nikerret]

Thank God others have provided good math. Not that I could do it, but I might have been inclined to try.

One thing I dont think has been brought up:

Don‘t forget to deduct the bucket or fork assembly from the pin capacity. It’s not as simple as deducting the weight, due to how far it is forward of the jobs also coming into play.

 

[Captain Dirty]

To rephrase an old adage: One experiment is worth 1000 expert opinions. Water weighs 8.33 lbs/gal; a 55-gallon drum filled with water would weigh 458 lbs. plus the tare weight of the drum, which, at 40-80# could be determined on a bathroom scale before filling. You could also calibrate rocks, concrete blocks, etc. that you may have lying about. Put the drums (and other stuff) on a pallet and see how the FEL behaves.

 

[LD1]

The formula is simple to most aviation types as we need to calculate center of gravity for safe loading an AC. (AC have known safe C of G ranges)
It all starts with a known datum point. (most AC use the firewall).
A simple example would be 100 lbs at 10 inches =1000.(inch pounds)
(moment is wt x dist)
So if 100 at 10=1000 then 10 lbs at 100 ins meets moment.

On a tractor they give U the bucket capacity so U can go from there once U determine a pivot point which I'd assume is the front axle as that is where the load would rotate from.
Assuming a bucket is 24 inches ahead of the axle then a 1000 lb bucket at 24 ins would have a moment of 24000.
So if a fork load is 36 ins ahead of the bucket you then have the new moment at 60.
Take moment of 24000 divided by 36= 666.666 lbs.
That would be your safe capacity limit using forks.

(Often seen on crates is a triangle mark to indicate the C of G of that crate as the contents might not be actually centered, that for safe fork lift operation)

LOL, all clear as mud?
I, moons ago, sold fork lifts and was also a pilot as well as a licensed aircraft mechanic.

On the practical side your 'pucker meter' (AKA, your butt) would soon advise U if that fork load was out of G of G range!

That front loader example is indeed valid.....if the goal is/was to calculate front loader capacity in regards to tipping the machine.

Actually I have no idea what the OP is after. SO I assumed trying to figure the front loader capacity as actually hydraulic capacity. Which can only be achieved with sufficient ballast to make the front axle NOT a pivot point

 

[Bullwinkle123]

That front loader example is indeed valid.....if the goal is/was to calculate front loader capacity in regards to tipping the machine.

Actually I have no idea what the OP is after. SO I assumed trying to figure the front loader capacity as actually hydraulic capacity. Which can only be achieved with sufficient ballast to make the front axle NOT a pivot point

Lots of good information, all helpful. I'm just trying to understand what I can safely do with my pallet forks and bucket, and also how to make my only-marginally-safe oversized bucket work better with what I have, which seems like it will require more ballast than my rear blade supplies. Combine that with my desire for a more compact rear ballast and we have the discussions here. Thanks much folks. I've absorbed some, other bits I will be rereading when I design the ballast. Hopefully the topic will be of use to future people as well.