As an example, take the statement that pattern density is a function of temperature and altitude. This is a true statement but we can easily take it to the next step if we can relate it to a standard and hopefully end that discussion for all time. This standard was adopted at the beginning of the 20th Century. It has evolved over the years to what is referred to as the ISA or ICAO standard, called density altitude (DA), which takes into account the variables that make up air density. It is easy to compute, happens to be a series of linear equations, and can be used for a basis of comparison when looking at different pattern densities. It does not make any sense to me to try and separate air density into its components and draw any conclusions. If you are so inclined, you can calculate the effect of each individual component but what is the point. Density altitude is density altitude wherever it is calculated because it is a standard. Here is the background:

"The effects of altitude and atmospheric conditions on aerodynamic drag are very closely coupled and must be treated together. This was not understood very well by ballisticians until about the beginning of the 20th century. Many firing tests took place in Europe in the latter half of the 19th century, especially in England, Germany, France and Italy, in an effort to understand aerodynamic drag and develop theoretical models for drag. Ballisticians found it difficult to compare measured data when the firing tests were made at locations having different altitudes and different atmospheric conditions.

Ballisticians gradually came to realize that drag measurements made in different locations, or even at the same location under different atmospheric conditions, could not be compared unless the measurements were somehow referenced to a set of standard altitude and atmospheric conditions. This led to the adoption of a standard set of altitude and atmospheric conditions to which measurements could be referenced. At the same time, analytical methods were developed to convert data measured at nonstandard altitude and atmospheric conditions to their standard values. Data from different locations and/or different atmospheric conditions could then be compared.

In the United States, standard altitude and standard atmospheric conditions were adopted by the U.S. Army Ballistic Research Laboratory at the Aberdeen Proving Ground in Maryland at about the beginning of the 20th century. These conditions, called the Standard Metro conditions, are used for ballistics computation."

As I said the Standard Metro evolved to the ISA or ICAO standard and is used worldwide. There is an app for smart phones or you can use any of the on line calculators. So when you are do pattern testing, record the DA and you have a basis for comparison and eliminate one of the chance variables.

The interesting point from the history above is the reference to aerodynamic drag. I initially thought it may be relatively easy to calculate because Newton’s laws and the principals of flight are well understood. NASA has calculated lift and drag coefficients for everything under the sun. After 30 minutes, I realized it was deep dark hole.

I resorted to Google. Sure enough, the Army had been down the same path.

"In any estimate of the trajectories of shot fired from a shotgun, the drag of the system of pellets might be expected to vary with the degree of damage incurred by the pellets and with the Mach and Reynolds Numbers. Results of experiments are presented for representative shot fired from a riot gun for five loading conditions.

Pellet distributions, damage incidence, and aerodynamic retardations are determined from spark shadow graphic traces. Pellets with severe launch damage indicate higher drag than corresponding spheres launched individually. BRL 1967" (Believe it or not, they counted pellets)

So the hole got deeper, but there is a whole lot of research that has been done since 1967. The answer has to relate to the Ballistic Coefficient (BE) of a pellet. About 30 minutes later, it soon became apparent that the BE of a single pellet, let alone a whole mass of pellets, is constantly changing from the instant the cap is popped. We are now dealing with a dynamic event as opposed to a static event and probabilities

Is there a way to improve the aerodynamic characteristics of a pellet? The easiest way is to make it harder. Are there any other ways? None that I am aware of. So we are truly left with unpredictable flight of pellets, most likely arranged in a normal distribution “until they are not”?

Here is a discussion that may make a few relative points for some:

“Misconceptions about the nature and practice of science abound, and are sometimes even held by otherwise respectable practicing scientists themselves. Unfortunately, there are many other misconceptions about science. One of the most common misconceptions concerns the so-called “scientific proofs.” Contrary to popular belief, there is no such thing as a scientific proof.

Proofs exist only in mathematics and logic, not in science. Mathematics and logic are both closed, self-contained systems of propositions, whereas science is empirical and deals with nature as it exists. The primary criterion and standard of evaluation of scientific theory is evidence, not proof. All else equal (such as internal logical consistency and parsimony), scientists prefer theories for which there is more and better evidence to theories for which there is less and worse evidence. Proofs are not the currency of science.

Proofs have two features that do not exist in science: They are

*final*, and they are

*binary*. Once a theorem is proven, it will forever be true and there will be nothing in the future that will threaten its status as a proven theorem (unless a flaw is discovered in the proof). Apart from a discovery of an error, a proven theorem will forever and always be a proven theorem.

In contrast, all scientific knowledge is

*tentative*and

*provisional*, and nothing is final. There is no such thing as final proven knowledge in science. The currently accepted theory of a phenomenon is simply the best explanation for it

*among all available alternatives*. Its status as the accepted theory is contingent on what other theories are available and might suddenly change tomorrow if there appears a better theory or new evidence that might challenge the accepted theory. No knowledge or theory (which embodies scientific knowledge) is final.

Further proofs are binary; a mathematical proposition is either proven (in which case it becomes a theorem) or not (in which case it remains a conjecture until it is proven). There is nothing in between. A theorem cannot be kind of proven or almost proven. These are the same as unproven.

In contrast, there is no such binary evaluation of scientific theories. Scientific theories are neither absolutely false nor absolutely true. They are always somewhere in between. Some theories are better, more credible, and more accepted than others. There is always more, more credible, and better evidence for some theories than others. It is a matter of more or less, not either/or. For example, experimental evidence is better and more credible than correlational evidence, but even the former cannot prove a theory; it only provides very strong evidence for the theory and against its alternatives.”