Unfortunately the match was rained out today so I've got some time on my hands back in the hotel today.
Mac,
From the figure in your last post, I think I'm beginning to understand what you're saying. You plotted 'retardation' vs Mach number. given the shape of the retardation curve that you've drawn, you're clearly talking about the force of drag (in newtons or pounds) that the bullet experiences as is flies, not the drag coefficient of the bullet. I think your straight line on that plot labeled 'zone average' is the key to this misunderstanding.
There cannot be a straight line on that plot. It's not possible from averaging anything. The reason is because the drag (retardation) is proportional to V^2, so the line will always be a curve. That curve is described by the equation:
drag (retardation) = 1/2*p*V^2*S*Cd
where:
p (rho) is the air density
V is the bullet velocity
S is the cross sectional area of the bullet
Cd is the Mach defendant drag curve.
I think what you�re saying is that my method of averaging results in a straight line on the retardation plot. It does not because even if Cd were constant (which is not so in my method), the curve would still be quadratic with V.
�My� method, which is actually a very standard method for defining ballistic coefficients simply averages the form factors over the flight of the bullet and applies that form factor to the standard projectiles drag curve. Note the drag curve is still a curve, just scaled by the average form factor.
My experimental procedure is to measure TOF in multiple intervals. The reason is so that several data points can be plotted, and form factors averaged. This way you don�t only get an average form factor and BC for the flight, but since there are multiple data points you can see how the curve is shaped and how much it matches or mis-matches any standard curve. If you only measured TOF over one distance, you wouldn�t know which curve that projectile followed best, or how much mismatch there was for any curve at any speed.
If your concern is that 'my method' assumes the bullet flies in each velocity zone for the same amount of time (which would be bad), it doesn't. When you measure Cd and average form factors the way I do (from raw TOF data), it properly accounts for (ie, assigns the proper weight for) the amount of time the bullet spends in each zone.
I decided to show and average data points for 1500, 2000, 2500 and 3000 fps because these roughly cover most of the velocity range that�s interesting to most shooters. Someone else might have chosen a different window and/or number of points; it is a subjective decision and certainly has an effect on the resulting averages.
However any selection of velocity windows is equally arbitrary and arguable. I feel that my method of averaging for the supersonic range of projectile flight is reasonable, accurate, useful and better than any previously existing data. If you want to shoot into the trans/subsonic zones, my supersonic averaged BC�s would be less than ideal. However, the averaged G7 BC would be much better than the G1 BC because that curve will more accurately extrapolate the trans/subsonic drag of modern long range bullets.
I did not establish my current methods of deriving BC�s from raw test data using a magic 8-ball. The method that I use was taught in Penn State�s college of aerospace engineering and applied for 6 years in the US Air Force by modeling the flight dynamics of air-to-air missiles. It�s actually rather standard and mature science. Sure there were some judgment calls to make about the best way to present the data. For example, I considered only offering G1 BC�s that were simply more accurate due to being carefully measured in a standard way and averaged over long range. I rejected that approach because of the errors resulting from the extreme mismatch between the G1 standard and most long range bullets. I also considered comparing the raw data to the entire list of standard projectiles (G1, G2, G5, G7, G8, etc�) and providing a BC referenced to whatever standard it best matched. This idea was rejected for two reasons: 1) it�s just more cumbersome and difficult to manage for shooters, and 2) because it prevents one from making fair comparisons between bullets based on BC. I also considered the possibility of providing complete custom drag curves for each bullet. This is technically the method with the greatest potential for minimizing error from a modeling point of view, however, it�s difficult to get (measure) data points at trans and subsonic speeds with acoustic equipment. There are other downsides to this method like #2 from above, as well as the fact that no commercial ballistics programs would be able to make use of the tables (except QuickTarget, but even then it would take a very savvy user).
In the end, I chose to represent the performance of modern long range bullets by referencing BC�s to the G7 standard. This approach seemed the most �do-able� from all angles, while sacrificing the least amount of accuracy.
I wouldn�t be happy that my method was right until it had been verified by alternate testing methods. This verification was completed and documented in my book. The test involved shooting thru a chronograph, and a screen at 200 yards placed above the line of sight, while sighting on a 1000 yard target. Based on the muzzle velocity and placement of the shots above the line of sight at 200 yards, a standard ballistics program was used to estimate the fall of the shots at 1000 yards using my averaged G7 BC�s which were derived with my standard method.
The experiment showed that the shots landed within +/- ONE INCH from where the program predicted them to fall. This test was conducted with two rifles and two bullets with the same result. For me, this test was the final verification that my method was producing BC�s that were accurate, meaning that they were useful for predicting trajectories at long range.
Another account of my method being verified was the Phoenix test which is documented in the second edition and that I described in an earlier post.
Even though a complete description of my methods, there origins, verification of their validity was published, I still knew they would be challenged. That�s OK, scientific conclusions have to be able to stand up to scrutiny. However in this case I don�t think that my actual methods were questioned. Rather, a misunderstanding about my method was challenged. I hope the explanation and clarification that I provided here has addressed your concerns (Mac), in particular your misunderstanding that my averaging method implies a retardation that is linear with velocity (or Mach). Such a method certainly would be wrong, but that�s not what I�m doing at all.
On the other discussion regarding paradigm shifting; I agree that long range shooters are a vast minority in the wide world of shooting in general. However,
long range shooters are the ones who care about, and need accurate BC�s most of all. That�s why I think the evolution to G7 referenced BC�s will take place; because those who really need and care about them recognize they�re merit. So what if 90% of other shooters don�t notice, they didn�t care about the original BC�s in the first place. But this is a speculative conversation with no clear right or wrong answer; time will tell. Lapua�s choice to adopt G7 BC�s is encouraging. Maybe Hornady, Sierra, Nosler, etc will never change from G1 BC�s. But if all the serious long range shooters are using the G7 BC�s I�ve provided and ignoring the advertised G1�s from the manufacturers, I�d say that counts as significant paradigm shifting. In other words,
it�s not what the companies put out that matters, it�s what serious shooters use to hit targets that matters. computers aren�t savvy enough to know you left your ammo in the vehicle last night and it went down below zero.
or your chart being established for 5000 ft. but were actualy 6000 right now i think.
could those type things account for a first round miss in a hunting situation?
Yobuck,
You�re right about the fact that computers cannot do our thinking for us (thankfully). The computer program is there to give outputs based on inputs. If YOU know the effects of having your ammo frozen, you can enter the altered muzzle velocity into the program and the effect will be accounted for. Likewise, if you�re actually at 6000 feet DA and you tell the computer that, it will accurately account for that as well.
The results of a computer prediction are only as accurate and complete as the inputs. You can�t expect the ballistics program to tell you what time the sun sets, the air pressure in your tires, the point of impact shift your wood-stocked rifle will have when wet vs dry, if your scope parallax is properly adjusted, what the wind speed and direction is and when it will change. The program IS there to provide a very specific output based on specific inputs. If you�re able to manage the other challenges of shooting
and use the program effectively, you will be better able to hit long range targets on the first shot than if you don�t use the technology, or if you use the technology improperly.
The �shoot and spot� method (aka �sighter shots� in competition) allow us to not know about anything technical and still hit small targets at long range; eventually, and as long as they stay still. If this is your goal, and it doesn�t matter how many shots it takes to get centered, then the science of ballistics has little to offer you. There are many very successful benchrest and other competition shooters as well as long range hunters who know didly about ballistics, but do manage to center groups based on observing misses. When you become interested in putting the FIRST shots on target at long range is when ballistics has something to offer.
(Yo, Please don�t take any disrespect from my last two paragraphs. I read back over them and they read with a bit more �attitude� than I intended. Unfortunately tone often gets lost with the written word).
Hopefully this rain will clear up for the last day of the tournament tomorrow.
Take care,
-Bryan
