SpudFiles

Let's say we take the function 1/X^2 (like the model for gravity) and try to model it using a polynomial.

No, you can't say "X^-2", because that's not a polynomial.
So you have to attempt to model it in a beastly way using stacked terms of the Nth order... getting closer and closer to it, but never acctualy modling it correctly.

Does this mean that your absolutely perfect dataset is wrong?

No, of course not. It means that you are using the wrong model... you should be modeling it as the function "1/X^2" instead. (which, I remind you, isn't a polynomial.)

(and, yes, I know that there are curve fitting approaches that use a weighted sum of squares... I used one!)

Wait a gosh darn flippen second. I just noticed something. Is X in your equation the Barrel:chamber ratio or the chamber:barrel ratio? In your explanation it says B:C ratio but the test data says C:B ratio.

I'm using B:C ratio. Means that barrel length is directly porportional to X.
No requirement that you do it that way, but I expect that it makes the math simpler. (I havn't checked)

B:C = 1/(C:B)

okay, so I'm probably flooding you with stupid questions but your equation doesn't take the mass and resistance of the projectile into account. Given that, what kind of projectile was this based on so that I can keep my estimates accurate.

"doesn't account for mass and friction"
Eh, that's where you are wrong.

For starters, it's simply a curve fit which happens to have an explanation for the most powerful terms... it may not have an individual term for everything, but I grantee you that it does model the combined effects of everything that happens during the launch cycle. (simply because it does)

Secondly, it accounts for mass (but not variable mass) with the square-root portion and the constants of the section inside it... if the mass was different, the constants would be different.

Thirdly, it does account for friction... it is part of the -X term inside the square root. (again, not it's own separate term, but it is there)

Anyway...
The projectile was a gasket slug which I estimate weighed <strike>removed</strike> grams. (I analyzed the picture of it that latke provided)

...I'm withholding the information because, if you had any clue how EVBEC works, you would've just looked in the code and found the relevent information.
...and you want to know how EVBEC works, because it'll help you with the rest of your project.
...contact me for an old version of EVBEC. (the new versions have all sorts of confusing numbers in their calculations, which you probably don't want to deal with.)