.50 cal accuracy test

[thejere]

Thanks to cockerpunk for posting this thread.
My first conclusions:
.68 has better velocity consistency than .50cal, but not by much. If you combine all 66 shots the SD for .68 is 5.9fps with an average velocity of 291fps v SD for .50 of 7.0fps with an average velocity of 288fps
.50 cal had a tighter grouping at 50ft (low SD in x and y direction) but at 100ft and 125ft it is harder to tell. .50cal has all SD in the x-direction but higher SD in the y-direction.

This doesn't agree with TK's tech tips on accuracy/consistency which state a more consistent muzzle velocity will give a tighter shot grouping. So what's the deal?
We are missing the LINEAR distance each shot is from the center of the grouping, how far each shot deviates from the expected location.
If you calculate those values(see bottom of post for method):
SD from center
.68 .50
50ft 1.9 1.2
100ft 3.7 4.1
125ft 5.0 5.9

The .50cal is unquestionably tighter at 50ft but at 100ft and 125ft the .68cal is tighter.
I don't think this closes the door on the .50cal but it does detract from the claim that they are more accurate.

Calculating deviation from center:
Solve for the mean of the all x vaules (mx) and mean of all the y values (my)
solve for the deviation (dx) of each x value (x_n) from the mean of x (mx)
solve for the deviation (dy) of each y value (y_n) from the mean of y (my)
use Pythagorean theory to solve for total deviation (d)
d^2 = dx^2 + dy^2 = (x_n -mx)^2 + (y_n - my)^2
calculate Standard deviation of all deviation values, determine which cal had the tighter grouping.

[cockerpunk]

radial coordinates certainly are interesting, and when we first were deriving out "vector" system i considered them. there are a couple of reasons why we use the vector method which is in rectangular coordinates:

1. paintball guns dont really shoot circles. they almost always shoot ellipses of some type or another. the vector method takes into account this skew and punishes those setups that shoot them. the issue gets worse when you consider collecting a sample mean and SD compared to a true mean and SD.

2. it is computationally easier to stay in rectangular coordinates. not a huge deal.

now, im not saying that radial coordinates are no good, just that i personally feel that rectangular coordinates model the situation. feel free to do the analysis in radial coordinates if you'd like.

as to velocity consistency being directly related to accuracy, i have to disagree with TK's conclusion as well. we have shot easily a couple of hundred different setups and chronoed every single shot from them. we have seen that even consistency in the +/- 15 fps range still will shoot a pattern comparable to a +/-5 setup.

we believe this is a matter of initial conditions vs system characteristics. the gun provides the initial conditions (spin, velocity, and such) and then the system takes over the instant the ball leaves the barrel. so the assumption is that the closer the initial conditions, the more predictable the outcome of the system is.

however, that doesn't really stand up to the data we have collected. this is probably because of the random nature of vortex shedding that TK also worked on. and it turns out that beyond +/- 15 fps, the initial conditions are similar enough that the system of random vortexes is a MUCH larger factor.