This is a somewhat long and arduous question, (and is likely to help me in particular far more than it will help anyone else, since it's quite specific to my own project) but I hope you'll bear with me. I'm in the middle of writing a hard-scifi novel, and within it are massive events and battles which I intend to reflect true physics in every respect (at least relative to certain invented in-universe values). I understand many of the physical principles I need to account for and calculate, but I simply lack the math skills to calculate some of them properly.
I have a few directly interrelated problems. 1) is calculating the precise sizes and masses of various objects based on the Square Cube Law---in this case, railgun projectiles. In my novel there are 25 grades of a particular kind of railgun, each grade with its corresponding projectile:
1 | 2 | 3| 4 | 5 (1m/1.0 tons) | 6 | 7 | 8 | 9 | 10 (2m/8.0 tons) | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 (4m/64.0 tons) | 21 | 22 | 23 | 24 | 25 |  (8m/512 tons)
The materials, shape, and relative dimensions are identical from grade to grade. I already know that Grade-5 is 1m in diameter, with a mass of 1 ton (I simply invented that value, and used it to extrapolate the following values), Grade-10 is 2m/8tons, and Grade-20 is 4m/64tons. There is technically no Grade-40 in my novel, but as shown above, it would hypothetically be 8m/512tons. My largest grade, Gade-25, is 5m, but I haven't been able to figure out its exact tonnage. I'm sure the math is simple, but I'm ignorant of precisely what that math is, and how to accurately calculate the relative size differences of the odd in-between sizes that are not exactly double or half the size of another known value---which then leaves me unable to apply correctly modified Square-Cube values to them for tonnage.
2) Which itself is the second part of the problem. Since the in between values are not exactly double or half of the known values, I also don't know how to calculate modified Square-Cube values to multiply/divide with for those sizes (can't multiply/divide by 8 for those). It was easy for me to calculate the known values---I simply gave Grade-5 the value of 1.0 tons, and since Grade-10 is twice that size, I multiplied by 8 to get 8.0 tons, then by 8 again to get 64.0 tons for Grade-20.
3) With that being accomplished, the third related part of the problem is then calculating their kinetic energy (double the mass, kinetic energy is doubled---double the velocity, kinetic energy is quadrupled). Having now precisely calculated each projectile's mass, and assuming the same velocity for each, I need to apply the correct relative values---which I am currently unable to do for the same reasons as the above problems. To extrapolate the numbers for kinetic energy, I'll give Grade-25 a value of 1000.0 for kinetic energy, and all other grades will be proportionately less than that. Perhaps the same numbers that went into calculating the square-cube for each Grade will be used to calculate kinetic energy values for the same Grades?
Again, I know this is a long and arduous question, but if anyone could help me find the correct values for each Grade for both tonnage and kinetic energy, and show me the appropriate formulae for both (but also explain them so that a relative layperson like me can understand them, and perhaps then even be able to apply them to different situations), it would truly be most appreciated. Thanks in advance!