frnkeore wrote: GP, no disrepect intended. I was just pointing out that Joe doesn't accept low amounts of data accept, when it suits his position. His state ment doesn't support what real world impacts do.

I've done a lot of chronographing and you can have low impacts with higher V and high impacts with lower V. There are a lot of variables in internal and external ballistics.

FrankFrank; A few posts back I interpolated some of gpidaho's data and got an estimate of the relationship between powder charge and velocity. This kind of calculation is commonly done, I think I remember that our Gary has a formula that he has recommended.

This kind of calculation is done because of the large sample sizes required to more precisely estimate velocity change per powder weight change.

The experiment would be simple, shoot a sample of shots charged with some weight of powder and record the velocities. Then shoot a sample of shots charged with a different weight of powder and record the velocities. Average each set of velocities and make a statement.

That's the easy part. The hard part is deciding how many shots are needed. When we measure a characteristic, like velocity with a chronograph, we are estimating the “true” value of the characteristic. For any number of shots chronographed we can say that: we are some percent like 95% sure that the “true” V is between some number like 1950 fps and another number like 2000 fps, for example. To increase that 95% or decrease the distance, from 1950 to 2000, for example, to 1960 to 1990, we have to increase the sample size.

The sample size required to estimate the velocity change due to a .3 change in powder charge, in the example cited several posts back, is large enough to be at least impractical and certainly unlikely.

We have to estimate two things for each string of shots, the average and the standard deviation. Fortunately we have the work done. It's in the book. 7.8 CHRONOGRAPHS AND STATISTICS HOW MANY SHOTS SHOULD WE CHRONOGRAPH?               Chronographs commonly calculate and report the average, x bar, and the standard deviation, s, of a set of shots.             The more shots we chronograph, the more accurate are our estimates.               Based on the information below, I believe that we should chronograph a minimum of 10 shots for the minimum acceptable accuracy of estimates. This is a matter of informed opinion, not scientific or mathematical analysis. Your opinion may differ after examining what follows.   MU             The x bar of a string of shots is an estimate of the population average, MU.             With x bar and s we can calculate the error, or how close x bar is to MU to any confidence level.             The table below shows that error with a 95% confidence level.             See the bold 10 for n = 5 and s = 8 fps. We are 95% sure that MU is within 10 fps of x bar. If x bar is, for example, 1450 fps, then we're 95% sure MU is between 1440 fps and 1460 fps.

            Note that as n increases the error decreases, as SD increases the error increases. See “CONFIDENCE INTERVAL ESTIMATOR OF MU” in the excel workbooks. SIGMA   The sample standard deviation, s, is an estimate of SIGMA, the population standard deviation. We can calculate, with s and n, how close SIGMA is to s, and how confident we are of that answer. Here we use a confidence level of 95%.  

This table shows how close s is to SIGMA as n varies. When n = 5, we are 95% confident that SIGMA is between 60% and 287% of s. If we chronograph 5 shots and get an s of 10 fps; then we are 95% sure that SIGMA is between 6 fps and 28.7 fps. If we chronograph 30 shots and get an s of 10 fps; then we are 95% sure that SIGMA is between 8 and 13.4 fps.    See “CONFIDENCE INTERVAL ESTIMATOR OF SIGMA SQUARED” in the excel workbooks.