Jerry
There is nothing wrong with my numbers. As with any data set, there are a variety of ways we could choose to analyze the data. In this case I chose the simplest, which is (maximum velocity – minimum velocity) / (maximum length – minimum length). This gives us a good ballpark average of the effect of barrel length on velocity.
There are of course, other ways to approach the problem. The “best” would be to use nonlinear regression, which would give us a polynomial equation of the general form y = m(exp) + bx + c. I chose not to do this for two reasons: 1) most of the folks here would not understand how to use the equation, and 2) it would lead you to exactly the same conclusion that the simplest analysis does.
That conclusion is of course, for barrel lengths between 28 and 42 inches, barrel length has no meaningful impact on velocity. For hunting purposes, I could shoot deer with a 28” barrel or a 42” barrel, and I could kill deer all day long with either gun. If I happened to hit an inch or so higher or lower than I intended, the deer would be just as dead. If you want to shoot targets with Dan on the high plains desert where wind drift is a major factor, get bigger balls.
There is one really important feature of these data sets that you should notice. As Dan pointed out, there are a number of important variables that were not controlled. These include powder type (even to batch level), ball size, patch thickness, temperature, humidity and lube. Yet in spite of lack of control of these variables, all three tests show about the same effect. That is, for each inch in barrel length, the average change in velocity is on the order of 8 – 10 fps per inch. Or, roughly speaking, going from 28” to 42” will give you a velocity gain on the order of 100-150 feet per second.
We could of course, repeat this test with rigorous control of all the variables. This wouldn’t help much because it is a forgone conclusion that you gun is going to be different than the test gun.