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Rifles, Reloading, Optics, Equipment
Rifles, Bullets, Barrels & Ballistics
Let's argue about BC's
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<blockquote data-quote="Michael Courtney" data-source="post: 480102" data-attributes="member: 28191"><p>Magnitudes of BC Variations</p><p> </p><p>I appreciate all the contributions to an interesting discussion. "Significant difference" has two meanings as commonly used. In one sense it means large enough to reduce the probability of success. In this usage, the meaning is subjective to both the expected application and to the values of the shooter. A shooter who cares only about extra drop and not about added wind drift or reduced impact velocity probably cares less than a shooter who would like to be able to make a tough shot on a windier day or values the shorter tracking job that usually results from more reliable expansion due to higher impact velocity.</p><p> </p><p>In its other sense it means "statistically significant difference" which means that the uncertainty in two measured numbers is not larger than the difference between them (the error bars do not overlap). This is the more objective sense in which I most commonly use the word. </p><p> </p><p>How can we better quantify and understand variations in BCs between rifles, between bullets in the same box, and between different lots of bullets? In this post, let's concentrate on variations between bullets in the same box.</p><p> </p><p>A lot of valuable data has been published by Bryan Litz. For example, Bryan's careful measurements have shown that bullets from a box of Berger 155 VLDs with a narrower meplat diameter (0.066") have a BC 2% higher than bullets in the same box with a wider meplat (0.072") and that pointing the tip to 0.053" can increase the BC by about 4% above the nominal meplat. </p><p> </p><p>Even more interesting are the shot-to-shot drag variations in the multitude of graphs in Bryan's book (which everyone with an interest in long range shooting should own and read carefully). Bryan's book has a very informative graph of drag coefficient vs. Mach number for every bullet for which he reports BCs in the book. The ballistic coefficient of any bullet at a given velocity is inversely proportional to drag coefficient, so variations in the measurement of drag coefficient are roughly the same percentage variation in Bryan's measurement of ballistic coefficient. Of course, variations may well result from measurement errors rather than true BC variations, but since Bryan has estimated the accuracy and repeatability of his measurement system at 1%, and since some bullets do show drag coefficients clustered within 1% of each other for nearly the same velocity (Mach number), it is probably safe to suggest that drag coefficient variations more than 1% are most likely due to shot-to-shot variations in the bullets' BC and not to random measurement errors. Therefore, Bryan's graphs of drag coefficient are useful for estimating shot-to-shot variations in BC for bullets from the same box.</p><p> </p><p>One bullet with a lot of shot-to-shot variation is the Nosler .308 caliber 165 grain Partition (p. 488). The graph shows that near Mach 1.5, the drag coefficient varies from roughly 0.41 to 0.49, which is close to 16%. Near Mach 2.1, the variation is from near 0.35 to 0.42, also close to 16%. Of course, the standard deviation is smaller than the extreme spread, but harder to estimate from a graph. Match bullets tend to show smaller BC variations than lead tipped hunting bullets. For example, near Mach 1.75, the drag coefficient of the Berger .264 caliber 140 grain VLD (p. 402) varies from roughly 0.27 to 0.31 which is about 13%. (Of course, a better way to analyze these deviations is to compute the standard error from the best-fit drag model, because this incorporates the deviation from the best-fit drag model of every point in the data set. Another good approach would be to compute the standard deviation of BCs determined for each shot. However, these methods require access to the raw data in tabular rather than graphical form.) Of course, a lot of bullets show smaller BC variations than these, and I have not done sufficient analysis to determine whether these are typical shot-to-shot variations for most different bullets or whether these are two boxes of bullets demonstrating particularly large shot-to-shot variations. I have shown that some boxes of bullets show significant shot-to-shot variations in BC.</p><p> </p><p>Michael</p></blockquote><p></p>
[QUOTE="Michael Courtney, post: 480102, member: 28191"] Magnitudes of BC Variations I appreciate all the contributions to an interesting discussion. "Significant difference" has two meanings as commonly used. In one sense it means large enough to reduce the probability of success. In this usage, the meaning is subjective to both the expected application and to the values of the shooter. A shooter who cares only about extra drop and not about added wind drift or reduced impact velocity probably cares less than a shooter who would like to be able to make a tough shot on a windier day or values the shorter tracking job that usually results from more reliable expansion due to higher impact velocity. In its other sense it means "statistically significant difference" which means that the uncertainty in two measured numbers is not larger than the difference between them (the error bars do not overlap). This is the more objective sense in which I most commonly use the word. How can we better quantify and understand variations in BCs between rifles, between bullets in the same box, and between different lots of bullets? In this post, let's concentrate on variations between bullets in the same box. A lot of valuable data has been published by Bryan Litz. For example, Bryan's careful measurements have shown that bullets from a box of Berger 155 VLDs with a narrower meplat diameter (0.066") have a BC 2% higher than bullets in the same box with a wider meplat (0.072") and that pointing the tip to 0.053" can increase the BC by about 4% above the nominal meplat. Even more interesting are the shot-to-shot drag variations in the multitude of graphs in Bryan's book (which everyone with an interest in long range shooting should own and read carefully). Bryan's book has a very informative graph of drag coefficient vs. Mach number for every bullet for which he reports BCs in the book. The ballistic coefficient of any bullet at a given velocity is inversely proportional to drag coefficient, so variations in the measurement of drag coefficient are roughly the same percentage variation in Bryan's measurement of ballistic coefficient. Of course, variations may well result from measurement errors rather than true BC variations, but since Bryan has estimated the accuracy and repeatability of his measurement system at 1%, and since some bullets do show drag coefficients clustered within 1% of each other for nearly the same velocity (Mach number), it is probably safe to suggest that drag coefficient variations more than 1% are most likely due to shot-to-shot variations in the bullets' BC and not to random measurement errors. Therefore, Bryan's graphs of drag coefficient are useful for estimating shot-to-shot variations in BC for bullets from the same box. One bullet with a lot of shot-to-shot variation is the Nosler .308 caliber 165 grain Partition (p. 488). The graph shows that near Mach 1.5, the drag coefficient varies from roughly 0.41 to 0.49, which is close to 16%. Near Mach 2.1, the variation is from near 0.35 to 0.42, also close to 16%. Of course, the standard deviation is smaller than the extreme spread, but harder to estimate from a graph. Match bullets tend to show smaller BC variations than lead tipped hunting bullets. For example, near Mach 1.75, the drag coefficient of the Berger .264 caliber 140 grain VLD (p. 402) varies from roughly 0.27 to 0.31 which is about 13%. (Of course, a better way to analyze these deviations is to compute the standard error from the best-fit drag model, because this incorporates the deviation from the best-fit drag model of every point in the data set. Another good approach would be to compute the standard deviation of BCs determined for each shot. However, these methods require access to the raw data in tabular rather than graphical form.) Of course, a lot of bullets show smaller BC variations than these, and I have not done sufficient analysis to determine whether these are typical shot-to-shot variations for most different bullets or whether these are two boxes of bullets demonstrating particularly large shot-to-shot variations. I have shown that some boxes of bullets show significant shot-to-shot variations in BC. Michael [/QUOTE]
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