Bryan,
You'll find I don't do 'drive by'.
Glad to hear that. My comment was based on your post count of 17, now 18, since 04/21/09. It seemed unusual that you commented at all, and after two days, I expected you weren't going to return and the topic was done.
If you have methods/techniques that you have found work better for testing large numbers of bullets for BC I would be interested in hearing your results.
It depends on your budget. I've had the pleasure of seeing some really well equipped testing ranges and the data they produce. Take a look at the published multiple BC values for Sierra's HPBT MK #1570. Above 2500 fps they assign a G1 BC value of 0.527 and below 2500 down to 1800 fps they assign a value of 0.522. That's less than a 1 percent change in BC value. I know you understand the quality and volume of data needed to establish with a high degree of confidence that such a small change is real.
An experiment was conducted as follows: chronograph at the muzzle, and a tof sensor at 1000 yards in addition to a special chronograph at 1000 yards. For each shot I derived a G1 and a G7 BC from both the tof and the velocity decay data. �
I look forward to seeing the details, but the results don't surprise me.
when a bullet is shaped similar to the standard projectile for which you're referencing it's BC to, the BC you derive will be less sensitive to the method used to determine it.
For an actual bullet that exactly matches the drag profile of a standard bullet you can calculate the BC at any velocity and it will be correct for any other velocity. That was the driving force behind The Reverend Bashforth's invention of standard projectiles. In the real world and with the precision of modern instruments it's become obvious that few bullets actually match any standard projectile perfectly.
The drag characteristics of supersonic flight are most definitely sensitive to bullet shape! You point out that for a specific velocity range the curves are similar in shape, but they diverge at faster and slower speeds for the different (G1 vs G7) shapes. Most of our LR bullets, even those without secant ogives, are much better matches to the G7 standard than G1. In light of this fact, I find it hard to accept your above quote, as well as the claim that you're not advocating G1 as a reasonable standard for modern long range bullets.
For the velocity range of Mach 2.6 to 1.7 (2900 to 1900 fps) the G1 and G7 drag profiles are nearly identical when scaled at a 2 to 1 ratio for G1 to G7, respectively. You can see this 2 to 1 ratio holds true to within less than 1 percent in the experimental drag and BC data of your book in the Mach 1.79 and Mach 2.23 zones. Even within the Mach 2.68 zone the 2 to 1 ratio holds true to within 2.5 percent. Factor in measurement errors and the 2 to 1 ratio between G1 and G7 from Mach 2.68 to 1.79 holds amazingly well. The Mach 1.34 zone is where G1 and G7 diverge, but as stated in the link to Wikipedia, the transonic range starts at Mach 1.2. It's in this context that my following statement must be read.
Apart from magnitude, apparently the drag characteristics of supersonic flight are insensitive to bullet shape. Thus, you can't look at the shape of a bullet and tell which standard projectile it best matches in supersonic flight as it doesn't seem to matter much what the shape is.
Hopefully you won't argue the term "insensitive" is more exact than what your own data demonstrates, or that the term "supersonic" means any speed from Mach 1 to the speed of light. I assume you picked the four velocity zones for your experimental drag and BC data based on the velocity ranges that concern long range shooters. I did likewise.
You said that you aren't contesting that G7 BC's are better for LR bullets than G1's, but you disagreed with my assessment that the paradigm toward G7 BC's will continue. This is confusing.
Perhaps you see it differently, but long range shooting is a small part of the sum of all shooting sports. Major manufacturer's offer bullets for all these segments such that only 23% of Hornady bullets could be described as long range. For Remington it's just 16% and 18% for Nosler. While 43% of Sierra bullets could be described as LR, they have their own method of using multiple G1 values. If Sierra splits velocity zones with less than a 1% change in BC, they might find that multiple G7 values were needed for their LR bullets, but that multiple G1 values would better fit their other bullets as even Berger list N/A for the G7 BC for many of their bullets.
How then should a Major manufacturer label their bullets that doesn't cause confusion for the majority of their customers? It's in that context that I wrote the following:
Perhaps Large bullet manufactures don't want to confuse customers with notations like G7 that apply only to a minority of bullets, and Sierra handles the problem by publishing multiple G1 BC values. Maybe I'm wrong, but I don't expect the paradigm shift Bryan talks about will happen anytime soon outside the long range shooting niche.
Hopefully, you can now accept my statement that I'm not promoting G1 over G7.
What I really want to discuss I stated in my first post to you, which is as follows:
What's really being compared are the methods for calculating BC from raw shooting data. That is, what's the accuracy of average BC values for several velocity ranges (velocity zone BC averaging) as compared to allowing nature to average BC values over an infinite number of velocity ranges by using TOF. If BC values represented a linear rate of change in retardation from velocity zone to velocity zone, then the velocity zone BC averaging method would produce the same results as using the TOF.
However, the rate of change in retardation is not linear with respect to BC across different velocity zones. For the G7 standard bullet with a BC of 1.000, and relative to Mach 2.23 the retardation is 1.414 times less at Mach 1.79 and 1.326 times more at Mach 2.68. Thus, averaging the BC values in these ranges doesn't accurately represent the true retardation from Mach 2.68 to 1.79 as each zone is being given equal weight. Rather than using complex methods to correct for non-linear retardation, simply using TOF over a long range allows nature to perfectly average the BC values.
While I accept the claim that your testing produces values repeatable to within plus or minus 1 percent, I question the accuracy of the resulting BC values because of the velocity zone BC averaging method you are using in your book. The following diagram illustrates the error of giving equal weight to zone values when in fact the change in retardation rate is non-linear and non-symmetrical from zone to zone.
![[Linked Image]](http://farm3.static.flickr.com/2693/5858731651_dbc0d8203b.jpg)
A quick and crude analysis suggests an error of up to 4.8 percent is being introduced by averaging the form factor or BC values in the four zones using equal weight for each zone. Yes, Robert McCoy and others did the same thing, likely because such a small error in BC is unimportant outside long range shooting. To claim accurate BC values to within plus or minus 1 percent you may want to do some more research into how to properly weight each zone.
With your velocity zones from Mach 2.68 to 1.34 you've selected a velocity range over which to average BC values. If you use TOF over that same velocity range you'll get the same BC values minus the weighting error. If the actual bullet doesn't match G7 well through transonic and into subsonic velocities it doesn't matter which method you use as both will result in the same degree of error. All you can do is assume the actual bullet matches G7 well enough. In fact, you're already making that assumption given you have almost no data points at Mach 1.2 and below.
I believe that one of the reasons you picked the method documented in your book is to document which standard projectile a given bullet best matches. You can still do such analyses and also calculate the TOF BC from the same raw data and see how close it compares. If you find the difference is consistently more than 1 percent you might consider modifying your methodology and go with the TOF value as the final published value. If there's little difference, then you can tell critics like me that you've used two methods to double check your BC numbers. If you really want to impress critics put your raw test data on the CD that comes with your book.
Sorry if I've ruffled any feathers. It's a courageous act to publish any technical book on the subject of exterior ballistics and show your methods and data points, but that's what's necessary if you want to change the paradigm.
