TLDR: beginners who are trying to learn how to set component tolerances on their own, should visit the fundamentals of internal ballistics before they waste time and money on tests that are hopeless. Check the basic shop math on that parameter before you start planning your work so you have a chance to know if weighing or measuring is worth it compared to what you are buying.
When it is too complex for shop math use tools like GRT to understand the parameter and remember it is just one of many in the RSS of all the things that go into your target's error size. The fundamental math will only tell us the potential difference, it is going to take work to make that stand out on its own.
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We will talk bullet weight tolerance first because it doesn't require thermodynamics to explain the first principals. The thread will go too long to do the same for case wight or volume, but you will get the gist of this pre-planning concept. Let me use an oversimplification to demonstrate how weight change as an independent variable affects trajectory.
Let us say something like F=MA is fundamental. Now let me hypothetically freeze the F and keep the tolerance of it at a perfect zero.
Hypothetically the A will vary with the tolerance of the M.
If we set up that test in an imaginary perfect gun in a vacuum but with gravity, and with zero friction or losses, then the variation in the trajectory will map one to one with the variation in mass because we have no other losses and perfect force.
If the F were from a pressure pulse, we would just integrate the force over time and we would get our perfect F value. Let us call that the kinetic energy, or KE for now. We would use that concept to derive a muzzle velocity based on that hypothetical perfect force, and by now most folks are familiar with the concept that KE = (MxV^2)/2
We would see the exact relationship if we held the F perfect which is to say the KE was held perfect and find that the change in muzzle velocity just due to a change in mass is easy to understand. (2xKE/M)^0.5=V
We would be able to take two shots to demonstrate the relationship of the weight tolerance because F=MA is hypothetically perfect.
Suppose we are still paying attention.... if we set a goal for a muzzle velocity ES maximum of say 30 fps, and assume something in a medium caliber we can estimate the first-order-principals maximum allowable bullet weight change in this perfect world.
Let us pretend that is a 308 with a 175 SMK, so roughly 2650 fps. (Many would be doing back-flips if their average speed or their ES were held to 30 fps and as I say in class, I will let the students go figure out how much waterline change they see at 1000 yards with a 30 fps change.)
The KE would be 2729 ft*lbs, now keep that energy constant and see what happens if we play the game. At 2650fps -30fps = 2620 fps but with the same energy the bullet weight must now be 179 grains.
So, in this perfect hypothetical example.... an increase in the bullet mass to explain a 30 fps change is on the order of 4 grains.
Now, in the real world... the weight of a bullet ties back into other problems with making them, and it also has feedback on the pressure and friction. It really is complex, but the first order weight sort is based on the above homework before we get into PhD level relationships on how bullets are made and how they play with internal ballistics and barrels.
We don't get perfect forces. Our powders do not produce zero tolerance, nor do our primers. Our guns are subject to friction and thermodynamics, the barrel is fouling with the bullet jackets and propellent residues and the air between the muzzle and the target is not static. Add in the recoil and skills of the operator... just to name a few of the multiple real world parameters that all contribute to the system tolerance.
Those things that cause the explanation to get complex when friction and real world thermodynamics get involved, do not change the underlying fundamentals. They just make both the required tolerance difference and the testing shot count to find a change on the target go way up because any one parameter sits in a giant RSS (Root Sum Squared) that clouds the results.
Now we settle down and study how tolerances add up. Let us keep this at elementary level and say we would RSS the tolerances of all those things and the result of unsorted bullets and cases resulted in a P95 group size of 1 MOA at 1000 yards for an ordinary cartridge.
Now we sort the bullets and play with changes in bullet weight spreads like 0.5 grains.... I will save you the trouble and tell you you couldn't shoot enough shots to find that in the real world when you have to account for the RSS of all the other tolerances that are at play at the same time.
Those other parameters all have a spread that makes finding this one nearly impossible till you get into the weight change of at least a few grains, and even then it takes HM skill and a very tight rifle to show it.
By now I am again suggesting that folks like the OP should grab a copy of GRT or QL to make it easy on themselves and to avoid the lengthy explanation of how case weight/volume affect internal ballistics in the same way I have explained above. You can demonstrate the effect downrange based on case volume tolerance, but only if you have your homework done and you can shoot at Master or High Master levels.
Good brass is worth the trouble and unless they screw up and send you an escape (defect), you can play with the ballistic models to see how big that change has to be in order to have a chance of seeing it down range. YMMV
Merry Christmas and Happy New Year
