Which Published Berger BCs Are From Predictions Rather than Measurements?
- Thread starter Michael Courtney
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Michael Courtney
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This post makes some good points. The best Doppler radars used in balistics measure velocity with an accuracy of 0.03%, which can then determine velocity dependent drag curves to an accuracy of 0.3% or so. I'm not sure I'd put Doppler ahead of what is possible at the ARL spark range at Aberdeen Proving Ground.
Sierra claims to be using Doppler for some of their bullets. Here are some links for ballistic radar using Doppler:
exterior ballistics
Ballistic Explorer Help
Lapua Offers Radar-Tested Drag Data for Lapua Bullets « Daily Bulletin
Lapua Offers Free Advanced Ballistics Software « Daily Bulletin
QTU Lapua Edition - Lapua Ballistics - Customer Center - Lapua
http://www.konyvtar.zmne.hu/docs/Volume11/Issue2/pdf/01.pdf
LabRadar - My Personal Radar
I would caution that not all Doppler radar works the same. The best, most expensive radars track the velocity and position in three dimensions at very short time intervals. Other Doppler radar (like used in speed traps and to measure velocities of baseballs, etc.) is one dimensional and only determines the component of velocity along one line. There is a new product coming out purporting to bring radar to shooters, but it remains to be seen how it works or how accurate is will be.
I'm not sure I will accept "determined with Doppler radar" as a guarantee of BC accuracy for several reasons:
1) The projectiles or data could be cherry picked. If you test 20 lots of bullets and they have a range of BCs and you publish the highest one, you have not really given your customers an accurate expectation of what they can expect if your lot to lot variation is big. Some bullets can have 5-10% shot to shot variations, so a result of only measuring 1-2 bullets may not be representative of the real mean. Did you know that in some cases the Litz BCs are only based on 2 shots of a given bullet?
2) The inexpensive product may not be as accurate as the military radars.
3) At some level, the ability to determine drag coefficients depends on the ability to determine air density accurately, which comes down to accurate measurements of pressure, humidity, and temperature. 0.5% is not too hard. 0.3% is much harder. But this is a detail that the experimenters must pay careful attention to. Using altitude rather than accurate temperature, pressure, and humidity readings can introduce a 5% error.
4) Misreferencing ICAO and Standard Metro atmospheric standards add about 2% error. Would you believe that some techs at the bullet companies don't know the atmospheric standard for their bullets?
Michael Courtney
Silver Member
Many parties that express confidence in BCs published by one party over others fail to appreciate important subtleties in the way BCs are experimentally determined and the velocity ranges over which validity and accuracy are claimed. The attached figure is useful for discussion.
The red Xs in the figure are drag coefficient measurements taken from Bryan's book, "Applied Ballistics for Long Range Shooting." The blue squares are our original measurements over a much wider range of Mach numbers. Bryan's measurements represent 2-4 shots and a range from M2.25 to M2.52 or so. Our measurements represent 80 shots from M1.36 to M2.97. Each blue point is the mean of the Cds at a given Mach number, with 10-20 shots at each Mach number. In most cases, the error bars are less than 1% and covered by the data point itself.
No one should lose any sleep over the small vertical displacement between Bryan's data and ours given that the experiments were performed with different rifles, different twist rates, different boxes of bullets, different measurement systems under different atmospheric conditions. That the two data sets are so close is a testament to the care taken in both experiments.
The real issue is that Bryan claims in his book that his data over such a small range of Mach numbers is sufficient to accurately determine ballistic coefficients from 1500 fps (M1.34) to 3000 fps (M2.68). Since our original Cd data actually spans M1.36 to M2.97, we could easily compute G1 and G7 BCs over that range. At Mach numbers where the uncertainty in the Cd is 1%, the corresponding uncertainty in BC will also be 1%. Except for M2.05 (close to 2%), most of our uncertainties are close to 1%. However, it would be a significant mistake to extrapolate our data and claim to have determined similarly accurate Cds or BCs at Mach numbers below M1.36 or above M2.97. It is without doubt that our paper would not have passed peer review had we done this.
Likewise, there is very little reason to assign validity to Bryan's published BCs that are well outside of the range of Mach numbers where the drag coefficients were actually measured. In this case, accuracy is ascribed to the published BCs from 1500 fps (M1.34) to 3000 fps (M2.68) in a case where measurements were made from M2.25 to M2.52. Careful review of the data on pp. 332-521 of Litz (2009) shows that in the majority of cases, the actual range of Cd measurements is much narrower than the M1.34 to M2.68 range for which BCs are presented that are purported to be accurate.
This is not to say that these measurements are without value, but rather that some have ascribed overly optimistic levels of accuracy and validity. A BC determined over a limited range of Mach numbers is still much more valuable than BCs determined by model predictions with no measurements at all.
The red Xs in the figure are drag coefficient measurements taken from Bryan's book, "Applied Ballistics for Long Range Shooting." The blue squares are our original measurements over a much wider range of Mach numbers. Bryan's measurements represent 2-4 shots and a range from M2.25 to M2.52 or so. Our measurements represent 80 shots from M1.36 to M2.97. Each blue point is the mean of the Cds at a given Mach number, with 10-20 shots at each Mach number. In most cases, the error bars are less than 1% and covered by the data point itself.
No one should lose any sleep over the small vertical displacement between Bryan's data and ours given that the experiments were performed with different rifles, different twist rates, different boxes of bullets, different measurement systems under different atmospheric conditions. That the two data sets are so close is a testament to the care taken in both experiments.
The real issue is that Bryan claims in his book that his data over such a small range of Mach numbers is sufficient to accurately determine ballistic coefficients from 1500 fps (M1.34) to 3000 fps (M2.68). Since our original Cd data actually spans M1.36 to M2.97, we could easily compute G1 and G7 BCs over that range. At Mach numbers where the uncertainty in the Cd is 1%, the corresponding uncertainty in BC will also be 1%. Except for M2.05 (close to 2%), most of our uncertainties are close to 1%. However, it would be a significant mistake to extrapolate our data and claim to have determined similarly accurate Cds or BCs at Mach numbers below M1.36 or above M2.97. It is without doubt that our paper would not have passed peer review had we done this.
Likewise, there is very little reason to assign validity to Bryan's published BCs that are well outside of the range of Mach numbers where the drag coefficients were actually measured. In this case, accuracy is ascribed to the published BCs from 1500 fps (M1.34) to 3000 fps (M2.68) in a case where measurements were made from M2.25 to M2.52. Careful review of the data on pp. 332-521 of Litz (2009) shows that in the majority of cases, the actual range of Cd measurements is much narrower than the M1.34 to M2.68 range for which BCs are presented that are purported to be accurate.
This is not to say that these measurements are without value, but rather that some have ascribed overly optimistic levels of accuracy and validity. A BC determined over a limited range of Mach numbers is still much more valuable than BCs determined by model predictions with no measurements at all.
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Well those two contributions resolve it all. Lotta value there.
I'm not trying to resolve anything. I'm reading to learn things I didn't know before. Not all of the information has immediate application to my specific hunting/shooting. Some does and I appreciate it. Can't you move on to another Thread, without further disruption to this one?
Who died and made you God?
Who died and made you God?
Likewise. Len can decide if his forum is "... the wrong forum to be discussing this issue ..."
In the interim, who made you so selfish that you won't allow other members to engage their interests without posting interference? Must you pursue the silencing and suppression of others you disagree with? By the way, you still recording bullet speeds with your stop watch? Click click...
Even Len (with my utmost respect) as the owner cannot resolve this issue. Which part of between Berger and the OP don't you understand?
Where did I suppressed, disagreed, or silenced anybody?
Michael Courtney
Silver Member
It appears as if Berger has abused the opportunity to publish information on this forum to propagate their misinformation. Len has graciously allowed Berger to publish their data sheet here including BCs.
http://www.longrangehunting.com/forums/f19/berger-bullets-tech-data-list-39871/
When a poster asked how Berger determined their BCs:
Bryan Litz replied:
It now seems clear that this was not exactly true. While 35 or 36 bullets in the Berger catalog had their BCs determined in the manner described, why was there no mention of the 30 or 31 bullets (as of the post in 2009) that had their BCs predicted with a theoretical model because they had not actually been measured?
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