Home Forums Reloading Reloading Software Ken Howell Article

http://www.24hourcampfire.com/chronograph.html



Anybody understand why he is using 1/12? That is the only part I can't wrap my head around.

Makes the head hurt, doesn't it? My guess---and ONLY a guess---is that the fourth difference is derived from the third difference, and 3 x 4 = 12. If there had been one more shot added to the analysis, there would have been a fifth difference derived from the forth difference, and 5 x 4 = 20, so you would have divided by 20.

I am just GUESSING. I like math in general but statistics does make my head want to explode.

I think it may be a simple means to approximate the fourth root of 26 which is 2.25. The standard deviation is the square root of the sum of the positive differences. SQRT(549) = 23.4. There is obviously nothing wrong with his chronograph if his adjusted MV to simulate 5 shots through analytical statistics is going to be only +2.2 fps for the middle load. Keep in mind he is trying to keep it simple. Run the same thing through Excel's regression analysis tool and you get a standard error of 2.75. Close enough. I still don't understand the 1/12 part though.

It's one thing to apply a statistical method to data and another thing to know if that method produces useful results, which Ken seems to be saying he doesn't know. In general, 5 shots is too small of a sample to even determine average velocity accurately as Ken then demonstrates in the remainder of his article.

Wikipedia Least Squares

First and foremost, Mr. Howell did a great job with the article. He clearly states this is how it works but the guts are for mathematicians (that apparently also shoot). I use statistics in my job but the topic itself is broad and my practical use is narrow (statistical sampling). And as MacLorry suggests, one should read the entire article for it is not until the end he gets into average velocity overall.

But YAY! This is going to be TMI but I figured out the 1/12 part. Var(x)=(1/12)(b-a)^2. Also known as Uniform Distribution, which is a probability theory. I just needed to keep researching so I could get back to working again.

He is doing the (b-a) part in the chart, which is fine. If you do (b-a)=26 and follow his instructions you get 2.166667, which he is rounding to 2.2 fps. However if you do the (b-a)^2 instead you get 56.3333. 56.33333/2.166667=26. At 95% confidence level you will get about the same t-test = 17.6 fps using regression analysis. You don't need the tables anymore because we have smart calculators for that now.

So to sum up he is stating with 1 shot for 5 different but "uniform" loads one could expect with 95% confidence that the variance of his chronograph will only be a one sided 2.2 fps for the middle load. But one could expect as much as 17.6 fps to be normal variance for a whole string of shots (actual velocity). So long as the regression line and analysis (including the F-test is less than .05, which is the case) is not out of the ordinary the prediction is valid as far as statistical analysis goes. Also, can say with confidence that he has a very good chronograph .

I have used Mr. Howell's method and found that my chronograph is off within 1%, which corresponds with its advertised error rate, compared to my countless strings of shots I have recorded over time that comes to the same conclusion through trajectory validation in the field. Remember, Mr Howell is referencing Homer S. Poley who in certain circles is a legend in exterior ballistics. Mr. Powley's technical memorandums are hard to find.

Anyway, I appreciate the replies and this has been interesting.