In recent years, Michael Courtney has posted a number of papers on this and other forums which present modifications to the original Miller stability formula for things like plastic, aluminum, and open tip match bullets. These papers make some claims which are based on faulty reasoning and testing procedures. Unfortunately, the result of applying the Courtney's formulas can result in compromised ballistic performance at long range. Due to recent ongoing conversations on this forum and others, I was compelled to read the Courtney papers on stability, and what I found is definitely worth a discussion.
Bad research is published on the internet all the time and much of it is harmless. I’m compelled to address this subject because the conclusions of this work can make it harder for shooters to hit targets, and thats' something I'll take issue with.
Rather than present a line-by-line breakdown of the various Courtney stability papers, I’ll explain how the underlying key assumptions and methods are in error in a way that most shooters will understand.
We’ll start with the data. Courtney’s live fire experimental data is primarily based on shooting .22 caliber varmint bullets, usually over 50 yards thru two CED M2 chronographs. Stability is lowered for these varmint bullets by downloading them to transonic speeds and firing from standard twist barrels. Plots showing the reduction of G1 BC for lower velocity points are used to quantify the ‘increase in drag for lower stability conditions’. There are several problems with this approach. First, it’s common knowledge that a bullets G1 BC is lower at lower speed. The primary reason for this is due to the G1 drag model not being representative of typical bullets. Stability may have something to do with a drop in G1 BC, but with the known effect of drag curve mismatch, it’s impossible to say what’s due to stability, and what’s due to drag. Courtney attributes all of the decrease in G1 BC to stability, which is the first primary flaw in this method.
Furthermore, at low supersonic speeds, dynamic stability is a major issue as well. When Courtney’s test data indicates low stability, it’s fully described with a static (gyroscopic) stability formula with no accounting for the dynamic stability condition which is actually the driver of total stability at transonic speed, especially for varmint bullets.
The second flaw with this testing method is that a bullet fired at a reduced charge does not generate the same stability condition as a bullet fired at normal muzzle velocity and allowed to slow down to transonic speed over long range flight. On a real long range shot, the bullets spin rate is much greater than when you download it to transonic speed and fire it from a standard twist barrel. For this reason, the stability conditions of the test are very different from the actual stability conditions of a bullet on a long range trajectory. If you want to simulate long range stability conditions by downloading the MV, you have to use a faster twist barrel which more accurately replicates the bullets true stability condition at long range.
One additional flaw in the experimental data is the assessment of accuracy for the measurements. Courtney describes how the CED chronographs are ‘synched’ by shooting thru them in close tandem to determine any bias, then separating the chronographs by 50 yards to make the drag measurements. The flaw in this method is that measurements taken with chronongraphs using optical skyscreens are sensitive to the optical planes being parallel. Non-parallel skyscreens manifest as a different velocity being measured depending on where the bullet passes thru the screens. Furthermore, the frame of the CED chronograph is relatively flimsy, and a small breeze can bend and twist the assembly enough to result in inaccurate velocity measurements. When you’re only measuring BC over 50 yards, you need extremely accurate velocity measurements, which simply aren’t possible with the set up used by Courtney. The preceding analysis of chronographs isn’t theory, it’s based on my own extensive 'exploits' with the CED and many other chronographs, some of which are published in Modern Advancements in Long Range Shooting.
The above are only the most glaring points on which the experimental data is either flawed or overly confident. Courtney repeatedly claims 5% accuracy for his formula, although no higher fidelity ‘truth’ data is presented in which his method is shown to be within 5% of.
More concerning than the above problems with the data are the modifications which are being made to the original Miller formula based on this work. Unlike the Courtney modifications, the original Miller formula was developed using very high fidelity ‘truth’ data (from the ARL spark range) on a number of bullets including open tip match bullets, FMJ’s, plastic tips, and solids (PS article from 2009). The math of the original Miller formula does assume constant density, but the formula also accounts for the effects of lighter ‘front ends’ (basically assuming a different CP) which is why the original Miller formula compares so well with so many different bullets without any of the recent Courtney modifications. From the Miller paper of 2009 comparing his original formula with 12 bullets of various construction, some at various velocities, Miller noted that his formula was accurate to within 5.2% for 95% of the comparisons with the ‘truth’ data.
Thanks to Courtney, we now have numerous modifications to the Miller rule for plastic tipped bullets, aluminum tipped bullets and open tipped match bullets. However none of these modifications are justified with any real truth data beyond what was gathered with varmint bullets between two chronographs 50 yards apart. Nevertheless, the Courtney mods to the Miller formula have infected numerous software tools and are touted as being accurate within 5%.
The entire charade has been an exercise in taking something that was perfectly suitable and complicating it unnecessarily, and for no benefit. The only thing the Courtney papers on stability have accomplished is turning the attention towards themselves on the subject of stability, now that the true author of the original work has passed away.
Now we get to the really damaging part for shooters. By applying the Courtney corrections to the Miller formula, one is lead to accept slower twist rates for bullets than what would be suggested by the original Miller formula.
This should be a red flag for any long range shooter who’s observed the effects of shooting at extended range. It's a common observation that faster twist is better, where long range shooting is concerned, especially when the bullet slows near the speed of sound. My own recent work on this subject was comprised of 100’s of rounds fired at long range with bullet TOF measured thru transonic. According to this work (which is also published in Modern Advancements in Long Range Shooting) it’s clear that there are advantages to faster twist rates in terms of transonic drag, certainly faster twists than the Courtney modifications would suggest.
If Courtney’s circus of bad math, inaccurate data and unrepresentative test conditions would have resulted in a something that suggested faster twist rates, at least it wouldn’t be damaging.
As things are, applying the Courtney corrections to stability calculations can result in suppressed ballistic performance at extended range thru inadequate stability, and that’s what ultimately compelled me to take issue and write this post.
-Bryan
Bad research is published on the internet all the time and much of it is harmless. I’m compelled to address this subject because the conclusions of this work can make it harder for shooters to hit targets, and thats' something I'll take issue with.
Rather than present a line-by-line breakdown of the various Courtney stability papers, I’ll explain how the underlying key assumptions and methods are in error in a way that most shooters will understand.
We’ll start with the data. Courtney’s live fire experimental data is primarily based on shooting .22 caliber varmint bullets, usually over 50 yards thru two CED M2 chronographs. Stability is lowered for these varmint bullets by downloading them to transonic speeds and firing from standard twist barrels. Plots showing the reduction of G1 BC for lower velocity points are used to quantify the ‘increase in drag for lower stability conditions’. There are several problems with this approach. First, it’s common knowledge that a bullets G1 BC is lower at lower speed. The primary reason for this is due to the G1 drag model not being representative of typical bullets. Stability may have something to do with a drop in G1 BC, but with the known effect of drag curve mismatch, it’s impossible to say what’s due to stability, and what’s due to drag. Courtney attributes all of the decrease in G1 BC to stability, which is the first primary flaw in this method.
Furthermore, at low supersonic speeds, dynamic stability is a major issue as well. When Courtney’s test data indicates low stability, it’s fully described with a static (gyroscopic) stability formula with no accounting for the dynamic stability condition which is actually the driver of total stability at transonic speed, especially for varmint bullets.
The second flaw with this testing method is that a bullet fired at a reduced charge does not generate the same stability condition as a bullet fired at normal muzzle velocity and allowed to slow down to transonic speed over long range flight. On a real long range shot, the bullets spin rate is much greater than when you download it to transonic speed and fire it from a standard twist barrel. For this reason, the stability conditions of the test are very different from the actual stability conditions of a bullet on a long range trajectory. If you want to simulate long range stability conditions by downloading the MV, you have to use a faster twist barrel which more accurately replicates the bullets true stability condition at long range.
One additional flaw in the experimental data is the assessment of accuracy for the measurements. Courtney describes how the CED chronographs are ‘synched’ by shooting thru them in close tandem to determine any bias, then separating the chronographs by 50 yards to make the drag measurements. The flaw in this method is that measurements taken with chronongraphs using optical skyscreens are sensitive to the optical planes being parallel. Non-parallel skyscreens manifest as a different velocity being measured depending on where the bullet passes thru the screens. Furthermore, the frame of the CED chronograph is relatively flimsy, and a small breeze can bend and twist the assembly enough to result in inaccurate velocity measurements. When you’re only measuring BC over 50 yards, you need extremely accurate velocity measurements, which simply aren’t possible with the set up used by Courtney. The preceding analysis of chronographs isn’t theory, it’s based on my own extensive 'exploits' with the CED and many other chronographs, some of which are published in Modern Advancements in Long Range Shooting.
The above are only the most glaring points on which the experimental data is either flawed or overly confident. Courtney repeatedly claims 5% accuracy for his formula, although no higher fidelity ‘truth’ data is presented in which his method is shown to be within 5% of.
More concerning than the above problems with the data are the modifications which are being made to the original Miller formula based on this work. Unlike the Courtney modifications, the original Miller formula was developed using very high fidelity ‘truth’ data (from the ARL spark range) on a number of bullets including open tip match bullets, FMJ’s, plastic tips, and solids (PS article from 2009). The math of the original Miller formula does assume constant density, but the formula also accounts for the effects of lighter ‘front ends’ (basically assuming a different CP) which is why the original Miller formula compares so well with so many different bullets without any of the recent Courtney modifications. From the Miller paper of 2009 comparing his original formula with 12 bullets of various construction, some at various velocities, Miller noted that his formula was accurate to within 5.2% for 95% of the comparisons with the ‘truth’ data.
Thanks to Courtney, we now have numerous modifications to the Miller rule for plastic tipped bullets, aluminum tipped bullets and open tipped match bullets. However none of these modifications are justified with any real truth data beyond what was gathered with varmint bullets between two chronographs 50 yards apart. Nevertheless, the Courtney mods to the Miller formula have infected numerous software tools and are touted as being accurate within 5%.
The entire charade has been an exercise in taking something that was perfectly suitable and complicating it unnecessarily, and for no benefit. The only thing the Courtney papers on stability have accomplished is turning the attention towards themselves on the subject of stability, now that the true author of the original work has passed away.
Now we get to the really damaging part for shooters. By applying the Courtney corrections to the Miller formula, one is lead to accept slower twist rates for bullets than what would be suggested by the original Miller formula.
This should be a red flag for any long range shooter who’s observed the effects of shooting at extended range. It's a common observation that faster twist is better, where long range shooting is concerned, especially when the bullet slows near the speed of sound. My own recent work on this subject was comprised of 100’s of rounds fired at long range with bullet TOF measured thru transonic. According to this work (which is also published in Modern Advancements in Long Range Shooting) it’s clear that there are advantages to faster twist rates in terms of transonic drag, certainly faster twists than the Courtney modifications would suggest.
If Courtney’s circus of bad math, inaccurate data and unrepresentative test conditions would have resulted in a something that suggested faster twist rates, at least it wouldn’t be damaging.
As things are, applying the Courtney corrections to stability calculations can result in suppressed ballistic performance at extended range thru inadequate stability, and that’s what ultimately compelled me to take issue and write this post.
-Bryan
