Bryan,

Thanks for the detailed response. I appreciate the time it takes to put that much detail into a post. The chart I posted in my 6/22/11 comment shows retardation or deceleration of the standard G7 projectile due to drag forces. The units would be feet per second^2. The straight line is not really a plot, but a representation of the effect of averaging 4 numbers of equal weight, when in fact, the declaration is a curve. It might not have been the best way to illustrate what I'm trying to get at, but taking the unweighted average of BC values in the 4 zones can't account for the non-leaner, non-symmetrical nature of retardation in each zone.

Another way to get a view into the weighting error is to compare your published G1 and G7 values for the Berger 0.243" dia. 115 grain bullet over the Mach 2.68 to 1.34 (3000 to 1500 fps) velocity range you use in your analyses. Launching at 3000 fps and using the published G7 BC of 0.279 the velocity drops to 1500 fps at about 1030 yards. Finding the G1 BC that gives the same TOF to 1030 yards I get 0.557 (equal TOF G1 BC) as compared to your published G1 BC of 0.545, which is a 2.2 percent difference.

The following chart shows the deceleration of the published G7 BC of 0.279 relative to the G7 standard as the green line with the published G1 BC of 0.545 and equal TOF G1 BC of 0.557 relative to the G1 standard as the blue and red lines, respectively. Whatever the actual bullet's true retardation, these lines are the retardation curves assigned to that bullet by the various BC values.

[Linked Image]

If we assume the green line of the G7 BC best represents the true retardation of the actual bullet, then which of the other two lines best matches the green line?

I'm not suggesting you change your G1 BC. What I'm pointing out is that even though you calculate the G7 and G1 BC values using the same data and the same method, there's a different G1 BC value that better matches the G7 value over the velocity range most shooters are going to use this bullet for. The cause of that discrepancy is the result of using velocity zone BC averaging with equal weighting where the actual retardation from velocity zone to velocity zone is neither linear nor symmetrical. You can see how the blue and red lines are offset due to this effect. Most likely the G7 line is offset from the true retardation of the actual bullet due to the same effect.

To demonstrate what's being represented in the above chart with actual numbers just plug the published G7 BC, published G1 BC, and equal TOF G1 BC values into any accurate ballistics program and you get results similar to the following.

The difference in drop at 1030 yards relative to the G7 BC of 0.279 is 0.3 inches for the equal TOF G1 BC and 4.5 inches for the published G1 BC. The equal TOF G1 BC matches the drop of the G7 BC to within 0.71 inches out to 1200 yards where velocity drops under Mach 1.2. The drop for the published G1 BC is off by 7.12 inches at 1200 yards. Beyond 1400 yards the published G1 BC more closely matches the published G7 BC, but velocity is below Mach 1 by that point.

Regardless of the pedigree of the method you're using, it's relatively easy to calculate a G1 BC that better matches the trajectory of the published G7 BC than the published G1 BC does. I believe that's only possible because of an error that's induced by the method you're using, and because you're using the same method for the G7 BC, I expect the same error is induced relative to the true retardation of the actual bullet.

The magnitude of that error seems to be about 2 percent which would be hard to rule out on the basis of testing done outdoors where wind is a factor. You even talk about an 8 MPH wind that might have been off by 10 degrees from being a direct tail wind on page 119 of your first edition. Maybe I misunderstood what you were saying, but I took it to mean that such a shift might have occurred without being detected during the testing. If so, then maybe there could have also been a 2 MPH shift in wind speed down range that went undetected. The photo of the set up doesn't inspire confidence given the wind break near the shooting position, a hill some distance down range to the right and who knows what beyond the 187 yard target.

It seems you're making an appeal to authority for the accuracy of your methods, being you learned them at Penn State's college of aerospace engineering and have 6 years experience using them in work for the Air Force. No anonymous poster can counter such an argument. My case rests only on what I have been able to demonstrate using equal TOF BC values that better fit the published G7 BC values than the published G1 BC values do. You may disagree with why that's the case or even if it's a better fit, but that leaves the door open for someone to provide G7 BC values that better fit the trajectory of actual bullets over their most usable velocity range.

Regarding paradigm shifting, you make a good point that long range shooters are the people who care about accurate BC values. Even so, Sierra never made any headway with their multiple BC values method even though it may be even more accurate than G7 if you accept what Sierra says bullets experience in the transonic velocity range. Then again, the multiple BC values method is ungainly to the point that only 2 or 3 ballistic programs properly implement the scheme.

I agree with your statement that "Unfortunately tone often gets lost with the written word." I greatly respect the work you have done for all long range shooters and appreciate the professional demeanor you demonstrate in your comments. I can only hope I come across half as well.