J J Mac wrote: J J Mac wrote:
Frank Lopez wrote:Again, I agree that the work is statistically invalid and that it is by Brezny, so it is somewhat questionable. However, I also believe that you are reading too much into thing to suggest that I'm basing things on a single article. Ballistics Coefficients are typically established computationally. That number is then revised after several test firings and observations to arrive at a reliable number. To my knowledge, ballistics programs use the same BC when dealing with shotgun pellets. This may be a big mistake. Lowry observed that things weren't happening exactly as predicted with steel shot, so he revised the tables basing his work on 7/8 inch steel balls (IIRC). Still, the data was based on single projectiles, not pellets flying in a swarm. That swarm and the way the pattern blooms may have some effect on the pressure wave in front of the shot swarm.
Are you saying that Ballistic Coefficients for bullets are used for shotshell pellets? Ballistic Coefficients have several different definitions. Please define the Ballistic Coefficient you are talking about in blue above
so we can discuss further. Here is a link that does a pretty good job of defining the different Ballistic Coefficients.http://www.exteriorballistics.com/ebexplained/5th/221.cfm
Here is a link that gives info on Ballistic Coefficients also. http://www.exteriorballistics.com/ebexplained/5th/221.cfm
Please define the Ballistic Coefficient you are talking about as described in the first article being as specific as possible.
Frank, where are you?
Sorry for your impatience. I've had some family business that has kept me away. Nevertheless, I'll see if I can address your concerns.
The Ballistic Coefficient of a projectile is a measure of how well that projectile is able to resist the opposing forces of aerodynamics and retain velocity. It is mathematically defined as the Sectional Density (Weight in pounds / Diameter squared in inches) divided by the Coefficient of Form. The Coefficient of Form, or Form Factor, is a number assigned to the projectile by comparing the projectile shape to the shape of a standard bullet. It is then revised by the data obtained form test firings of the projectile. This works well with uniform, symmetrical single projectiles that are stabilized around the axis of flight.
The problem with shotgun projectiles is that they are not so uniform, except in some very high quality loads, they are not stabilized around the axis of flight and are subject to tumbling similar to a knuckleball in baseball, and the pellets fly in a relatively close group.
If you cut open one of the heavier than lead tungsten based products, you'll find very irregular pellets. And while these irregularities can enhance the form factor (elongated or teardrop shapes), they are just as likely to hurt it (mushroom capped shapes). Then we have the latest craze of highly irregular shaped pellets like Blindside and Black Cloud. You might be able to assign a Coefficient of Form for the projectile as it travels in one aspect, but you'd have a completely different Coefficient of Form when it tumbled. Plus, as these pellets tumbled and presented different cross sections to the atmosphere, the sectional density would change.
Finally, and probably most important, is that shotgun pellets fly in a group. This group tends to share the burden of overcoming atmospheric pressure among the central portion of the pattern (a personal observation). There is a high speed video of a canister round from the 120mm smooth bore gun on an Abrams M1 tank. The pressure wave is very visible in the video. You will see that as the lead pellets are pried away from this central core, they tend to rapidly slow down. My take on this is that this is the point when the pellets are falling out of the influence of its companions and begin acting like single projectiles.
Finally, as I said earlier, it isn't just a single article. The F&S articles are interesting because the data is there even if the author is drawing some rather odd conclusions. (For the sake of clarity, the author wasn't looking at the difference between a ballistic program and an actual field result.)
So, when you stated
To my knowledge, ballistics programs use the same BC when dealing with shotgun pellets.
, I believe you are 100% correct. But, that is the problem. The BC doesn't really reflect what is actually happening down range.