The fulcrum is the front axle and does not move. All calculations are based on the center of mass of the weights involved and their respective distances from the center line of the front axle and are expressed in foot-pounds, as in the torque of a lever acting on a fulcrum.
Thank you for correcting my wording error. My brain tends to "autocorrect" when I proof and I'll read past my errors. Also, here on MTF, if I spend too long composing a message, I'm gathering my login will time out and then I can't post the message. The forum software also doesn't appear to perform an "autosave" that I can recover once that happens, so once my login times out and I attempt to post the message it is gone and I have to start over again. Very frustrating. Interruptions while creating a post are regular and, at times, lengthy. So often I'm hurrying to submit the post, so I can address the interruption, and then I'll come back later, if I remember, and edit the post to make corrections. It is why many of my posts are edited after the initial submission.
Such was the case with my wording incorrectly claiming the fulcrum point moving. What I meant to say is, "Ballast should be used to shift the payload weight rearward of the fulcrum point, transferring a portion to the rear wheels."
The point I thought I was emphasizing and I believe Kennyd did, as well, was the huge impact loader payload places upon the front axle, front tires, wheel bearings, the axle pivot point, and the steering linkage. Again, liquid filled rear tires do absolutely nothing to reduce loader payload impact on these components.
The 'Seat of the Pants" engineering measurements Diesel Powered made in the link you referenced very clearly establishes that ballast aft of the rear axle has a substantial impact on front axle load. Specifically, his measurements indicate that 6 suitcase weights (6 x 42 pounds = 252 pounds) hung on a rear weight transferred between 100 to 430 pounds from the front axle, depending on loader height.
Diesel Powered rear ballast weights were hung on a weight bracket. Hanging the same weights on a 3-point hitch drawbar would move the ballast aft several more inches and have a significantly more substantial impact reducing the amount of loader payload placed upon the front axle and the impact to it and related components.
KennyD did not miscalculate the ballast, as the emphasis of his post was the impact of loader payload to the front axle components, front tires, and steering components. As loaded rear tires do nothing to reduce or minimize the impact to these components, he appropriately did not include them.
While we all seek to minimize our costs, often folks jump at the low price remedy without factoring in all the issues. To that end, liquid filling the rear tires is a very low cost method of creating ballast and tends to be what is implemented for that reason. Absolutely, it is ballast and will play into to providing the counter weight to keep the rear tires planted on the ground, assist traction and braking. However, often the impact to the front axle, front tires, and steering components is over looked. Not to mention GT front tires have much less surface area to spread the load over and working in loose soil, which is frequently the case when performing loader work, increase the stress to these same components considerably. Further, loaded rear tires do nothing to lessen the impact to steering maneuverability and traction issues when the tires sink in and the loose materials acts like wheel chocks around the front tires. Shifting loader payload weight from the front axle to rear, with ballast aft of the rear axle, will lessen that impact.