Just how much influence does a bullet's shape have in supersonic flight? Obviously, the magnitude of drag has a lot to do with bullet shape, but what about the drag profile? Can the G1 ballistic coefficient be used to accurately predict the trajectory of a bullet in supersonic flight when that bullet looks like the G7 standard projectile?

Now that Berger Bullets is publishing both the G1 and G7 ballistic coefficients for their VLD bullets, it makes it easy to do some comparisons. Beger's #24530 has a diameter of 0.243 inches and a weight of 115 grains with a published G7 BC of 0.279 and a G1 BC of 0.545. That gives it a sectional density of 0.27822 lb/in� for a G7 form factor of 0.9972 and a G1 form factor of 0.5105. A form factor of 1.0 is the exact match for the referenced standard projectile, so Beger's #24530 is nearly a perfect form factor match to the G7 standard projectile and a poor match for the G1 standard projectile, and thus, any difference in drag profile would show up with this bullet.

Given a 3,500 f/s MV and using the equal time of flight to 1500 yards conversion of the G7 BC produces a G1 BC of 0.559, which is about 2.6 percent higher than the published G1 BC. You can see in the Drop values below that the G1 BC of 0.559 is a better match than the published G1 BC of 0.545 over the 1500 yard range. No doubt Beger is attempting to match their bullet's characteristics into the subsonic range, something I have the luxury of ignoring as I don't intend to go below Mach 1.2 for long range shooting.

  Rng Yards --> 100  300   500   700    900    1100    1300   1500
  G1 BC 0.545: -1.5 -14.4 -43.6 -93.7 -171.0 -284.0 -445.2 -671.2
  G7 BC 0.279: -1.5 -14.3 -43.0 -91.9 -167.0 -276.4 -431.5 -649.4
  G1 BC 0.559: -1.5 -14.4 -43.4 -92.9 -169.0 -279.8 -436.6 -655.2
Drop values are from JBM website using 0 altitude, 78% humidity, 29.92 in Hg corrected, 59 F, 0 sight height, all boxes at bottom unchecked.

The difference in drop between the G7 BC 0.279 and the G1 BC 0.559 at 1500 yards is 5.8 inches (0.4 MOA) and equivalent to a change in shot to shot muzzle velocity of just 14 f/s.

I've looked at a number of examples and the difference between G1 and G7 trajectory calculations is minimal to ranges where velocity gets down to around Mach 1.2. The difference between G1 and G7 shows up in the transonic velocity range, which it seems few long range shooters use. Apart from magnitude, apparently the drag characteristics of supersonic flight are insensitive to bullet shape. Thus, you can't look at the shape of a bullet and tell which standard projectile it best matches in supersonic flight as it doesn't seem to matter much what the shape is. Maybe that explains why the industry seems reluctant to follow Beger in publishing both the G7 and the G1 ballistic coefficients.

Credit for the conversion to different drag functions using equal time of flight to some distance belongs to Ken Oehler who sometimes visits the "Ask The Gunwriters" forum. He described the technique in a July, 2007 Shooting Times article. Ken's conclusion is that bullet manufactures should measure ballistic coefficients over long ranges similar to what the bullet is intended for. Seems like that would give us BCs that better match the intended purpose of all long range bullets.

Let me preface my post with this statement; I am not an aerodynamicist, nor do I play one on TV.

I will disagree with your assessment to a certain degree by simply pointing out that at supersonic velocity, the bow wave is formed from the meplat of the bullet back. If any part of the bullet ogive or full diameter is actually outside the bow wave, the drag on the bullet goes up significantly. So a VLD shame or a conventional shape that does not put any part of the bullet outside the bow wave should work equaly well, in my very humble estimation.

The base of the bullet is of critical import here and that is exactly why boat tail bullets have such a positive effect on long range bullets. I have come to appreciate bullets with a long boat tail with a boat tail angle that does not exceed something like 8.5 degrees. I tend to believe a clean end to a boat tail is the way to go, just as more recent airliners have a flat screwdriver appearance nowadays as opposed to the point of yesteryear; I figure there is a reason for that.

Certainly you're correct with regard to the magnitude of drag, but the example I gave shows the drag profile of Beger's #24530, which is an almost perfect form factor match for G7, can be accurately predicted using a G1 BC, and thus, the G1 standard bullet at velocities above Mach 1.2. The magnitude of the drag is taken into account by the BC value.

If long range shooters intended to shoot at ranges where their bullet velocity drops into the transonic range, then the G7 BC is a better match. Having asked how shooters determine a load's maximum range in another topic, it seems most shooters like to stay above Mach 1.2. In that case the G7 BC is no better a predictor of trajectory than an equivalent G1 BC as the drop numbers show.

Back when standard bullets were first being introduced around 1875 muzzle velocities were half what they are today, so much of the useful range was in the transonic and subsonic velocity range where the bullet's shape not only determines the magnitude of drag, but the drag profile as well. With modern rifles where the useful range is at supersonic velocities, the drag profile, and thus, the standard bullet an actual bullet is referenced to is nearly irrelevant. Ken Oehler's 2007 Shooting Times article demonstrated this using the G1, G5 and G7 ballistic coefficients.

Understood, and yes, my goal is to have my bullets above Mach 1.2 at the target for the reasons that I explained in the other thread. However even in the supersonic flight regime, the BC value for the bullet changes and you can see that at the Sierra website. I think the G7 value is more a deterministic and simpler value to use for all (supersonic) velocities and I have calculated the G7 BC for the long range bullets I use following the rather intense formula in Bryan's book and that's what I use for my trajectory charts at the JBM site, of which I have been a long time user.

You're right that Sierra publishes different G1 BC values for velocities above Mach 1.2, but what Sierra and others are doing is matching the change in velocity rather than the trajectory. So here's the question, do you really care what the velocity of your bullet is to within a few percent as it strikes the target or do you care about hitting the target? If hitting the target is the goal then bullet manufactures are chasing the wrong metric.

For example, just look at the drop numbers in the opening post of this thread and notice how far off the drop for Berger's published G1 BC is at 1500 yards relative to the G7 BC and as compared to the equal TOF G1 BC. The published G1 BC is off by 21.8 inches as compared to 5.8 inches for the equal TOF G1 BC. If you were only going to publish the G1 BC, as is the case with most manufactures, which value best matches the bullet for the way it's intended to be used? If you agree it's the equal TOF G1 BC, then Ken Oehler's conclusion is correct as to how BCs should be measured.

In my example I have assumed the published G7 BC perfectly matches the actual bullet, but if Berger's published G1 BC is off by 2.6 percent from a trajectory standpoint, then their G7 BC could also be off from a trajectory standpoint. I've read Bryan's book and understand the method he uses to come up with his BC values. As with others, he's trying to match change in velocity due to drag to that of a standard projectile. He does that for four velocity ranges and then takes the simple average as the final BC number. His method produces repeatable numbers, but he and others confuse repeatability with accuracy. Ken Oehler's suggested method is to measure initial velocity and then the bullet's time of flight over 1000 or more yards for long range bullets. This allows nature itself to perfectly average the bullet's characteristics for all velocities in between. The resulting BC best matches the trajectory of an actual bullet to a given standard bullet, and thus allows for the most accurate trajectory calculations under other altitude, wind and atmospheric conditions.

Ken Oehler's method is hard for the industry to adopt because, outside the military, I don't know of too many facilities that allow 1,000 plus yard testing under controlled conditions (indoors). You can do long range testing outside as Bryan has, but then wonder later what direction the wind was coming from as Bryan did in his book (1st edition, page 119).

I speculate that a G1 BC produced by Ken Oehler's method would more accurately match the trajectory of Beger's #24530 then their published G7 BC over the velocity range most long range shooters use. If so, then I expect a G7 BC produced by Ken Oehler's method would be better still. Of course, shooters won't get better numbers if they think the current methods of producing them are the best. I applaud Beger for publishing G7 BCs, but feel there's still room for improvement.

I think you mean "above" and not "about" in the first sentence; that changes the tenor of your post quite a bit, at least the first part.

My impression is that you are arguing for a better method of predicting the trajectory of a bullet, using a G1, G7 or modified G1 BC value. Arguing computer predictions is a rather sterile enveavor, because the real world is chaotic and doesn't care about your computer programs; something the climate alarmists are finding out to no small detriment.

Yes, you can predict the elevation pretty well, but there are undetected conditions that will be more than happy to upset your Apple or PC cart. Computer predictions will only give you a general impression on how to hold to account for the wind and other conditions that you can detect and measure. Miss one of them and it's GIGO time.

You might want to go view my 1000 yard match report from yesterday in the competition forum and then come back and tell me the computer could have predicted all that.

The only thing that is true is that when you launch a bullet, you allow Nature to do with it what it damn well pleases.

So speculate away, but Nature has the final word.

Yes, shooting is as much about skill and even art as it is about knowledge and science. Just a bit of wind is all it takes to blow a shot, literally. However, regardless of how you view computer predictions they are the reason for having ballistic coefficients, and particularly for Berger making the case for G7 ballistic coefficients. Anyone accepting the arguments for G7 might also be interested in knowing about an alternative technique for calculating ballistic coefficients that emphasizes trajectory over rate of drag deceleration. Of course, that assumes hitting the target is the goal.

You seem to be saying there's no point in bringing attention to that alternative technique "because the real world is chaotic and doesn't care about your computer programs", yet you admit to using the G7 BC in calculating trajectory charts at the JBM site. I understand what appears as a contradiction to some as being two sides of the same coin. On one side is the reality of shooting in the field and the other side is the planning and preparing we all do. This topic deals with the planning and preparing side of the long range shooter coin.

Exactly. But perfection is the enemy of good enough.

I find that using the G7 in my computer models is "good enough" for my purposes. I also think looking for "more better" methods of prediction is not something I would bother with, because as long as there is a human in the equation and that the universe is chaotic, it won't get better. Perhaps when maximum entropy is reached the models will work prefectly every time. Until then, I'll just try to read conditions better.

BTW, I do not denigrate computers after all it's been my career for 36 years now. But I also know their prediction capabilities in a chaotic world, which is why I laugh at climate alarmists.

Given your experience with computers you understand their limitations as well as their utility. Like you, I dismiss climate alarmist's use of computer models on the grounds that they can't model something they don't understand (don't get me started).

However, I hope I have made you aware of an alternative technique for calculating ballistic coefficients that more accurately predicts bullet trajectory in the supersonic velocity range. Likely it won't be adopted by any bullet manufacture due to the facilities needed to perform long range testing under controlled conditions. In that sense you're right, it's purely an academic exercise.

BCs can be a touchy subject. I will pass on saying anytihing about BCs other than no matter what form factor you choose to use there is a real need to actually shoot the rifle at any ranges that you anticipate taking a shot at an animal, especially if you are anticipating real long range shots. High velocity can mask BC errors especially with G1 BCs. I do not put a lot of faith in either form factor.

The science of ballistics is well researched and mature given its centuries long importance to the defense of every nation. It was for trajectory calculations that computers were first invented.

That said, I expect that pretty much everyone agrees with you about actually testing a new gun, scope or load before using it for hunting; it's just common sense. However, it's impractical to test every load under the wide range of conditions commonly experienced in the field, or to evaluate new loads, bullets, and calibers at the shooting range to find those that best fit a particularly need. That's where ballistics software comes into play.

I use the JBM site when posting numbers because it's free and everyone who's on the internet has access to it, and thus, they can go check my numbers for themselves. For my own exploration of the subject I use installed apps because they are faster, don't rely on a clunky webpage interface, present data in many different ways, include tools not offered on-line, and allow me to simultaneously compare multiple independent shooting scenarios.

I don't buy a gun or come up with a load and then wonder what it's good for. I start with what I need from a gun or load and use ballistic apps to find the best caliber, load and bullet for a given job. Buy, build or load the particulars and then go shoot to fine tune it. I expect lots of other shooters do likewise.

I don't see that a discussion on BC can be a touchy subject; it is what it is and there is nothing subjective about it. Yes, people can get lost in the minutia of the subject, and that can make for fun discussions but it's not like discussing the merits or lack thereof of the .270 Winchester or a discussion on barrel break-in or cleaning methods.

All bullets slow down in atmoshpere and gravity pulls them down to earth. BC is just a measure of how fast that's going to happen and what it does to the trajectory of the bullet and this happens to all bullets. As the OP says, ballistics is well-known and has been around a long time.

To my mind, bullet manufacturers advertise the G1 BC value because it's a higher number than the G7. Sierra is to be commended for taking the time and making the effort to educate the consumer about how the G1 BC values change depending on velocity. Berger is to be commended for publishing G1 and G7 BC values, thus furthering the education and presenting us with more complete data. Hornady should be chastised for publishing inflated G1 BC values for their bullets. Bring out the wet noodles.

Just like the OP explained, I also used JBM to narrow down my bullet and required MV for my game, and I used the come up values to get on paper at the various yard lines and I refined from there. This method saved a lot of components and barrel life, in other words: money.

I remember seeing Ken Oehler's article, but didn't grasp the significance of what he discovered until I read this thread. A friend and mentor of mine had an Oehler Model 43 and he took me along a few times when developing loads. The 43 is one magic box measuring many things including ballistic coefficient for each shot. This was about 15 years ago and you could select G1 or G7 as well as other drag functions when measuring BC.

I remember one test where the measured BCs for 10 shots were all within half a percent of each other, but much higher than expected. Turned out we entered the wrong distance to the target. I bring this up because your statement that "...he and others confuse repeatability with accuracy" rings true in my own experience. I image you've learned that lesson from your own experience.

Not everyone uses the same algorithms for exterior ballistic calculations. Obviously, some are better than others. When I first started shooting long range competition, I played with the available software (no internet then). As long as the published BCs were solid, I had more faith in Art Pejsa's software than anything else I tried (Sierra et al). I could plug in Pejsa's numbers with the 140 Amax and 140 Berger's I shot and hit the sighter gong on the first shot. The others were always different. Even today, you can compare some of the various programs and get different values at the longer ranges. It is always best to see how each bullet corresponds to the predicted values. Once you do this, you can have faith in the program and can usually make first-shot hits at long range as long as you know how to read wind.

Just to be clear the Model 43 didn't use exterior ballistic calculations to come up with downrange numbers, it measured the downrange numbers using sky screens and an acoustic target. We only needed to enter the distances and conditions into the program running on a laptop which was connected to the 43. Fire a shot and the measurements were displayed in a second or two including where the bullet went through the target even though there's nothing there but air.

Being the algorithms are not visible in most exterior ballistics software the only things I can judge a program by are the results. For trajectory I find that nearly all programs now produce nearly the same numbers out to well past 1000 yards and are within a small percentage for velocity at that range.

You plugged Art Pejsa's software, so I guess it's safe to offer my favorite. What sets one program apart from another is the interface, outputs, tools and features. In that regard my favorite program is the one Ken Oehler sells on his site, which is called Ballistic Explorer.

Those familiar with Ballistic Explorer know how MacLorry got the equal TOF numbers he posted. The same tool can take several of the BC values Sierra publishes for their bullets and convert them into a single G1 BC or even a single G7 BC. I've been playing with that for the last hour to see how such a conversion works down into the subsonic range. No conclusion yet, but it's interesting to be able to do such tests when they can be done easily.

It seems most long range shooters missed the significance of Ken's article. Simply stated, one drag function is as good as another for predicting trajectory at supersonic velocities. A lot has been made of using G7 in the last few years, but unless you intend to shoot to ranges where your bullet goes subsonic, the numbers in the original post show it's not significantly better at predicting trajectory then G1.



Confusing repeatability with accuracy is an easy mistake to make particularly for shooters for whom repeatability seems almost synonymous with accuracy. As you discovered, however, an incorrect measurement or assumption can produce highly repeatable numbers that are grossly inaccurate. That's one reason scientific papers are peer reviewed before they are published. Even then, the results are sometimes garbage.

Simply stated, that is not a true statement. Not even close. Do you have a link to Ken�s article? I really hope he didn�t say that. I think it�s more likely you have read that into something he did say. OK, from the beginning�..

You are misunderstanding the significance of the form factor. It is simply a value, not a description of how �good a match� a particular bullet is to a particular drag curve. A bullet that is a good match to the G7 curve simply means its G7 form factor does not change significantly over a wide range of velocities. The actual value could be 1.3 or even 1.5 but as long as it stays exactly the same from the muzzle to subsonic would mean it�s a perfect match for the curve. Conversely, a bullet that is a poor match, with a form factor that changes significantly over those velocities, may in fact have a form factor of exactly 1.0 at some particular velocity or it may average that over a range of velocities�and yet it is still a poor match. Though in this case, that bullet is a pretty decent match--because it�s FF changes less than 1% over the range of velocity (per Bryan�s measurements), not because it happens to be close to 1.0.

What makes you think this is insignificant? That�s two clicks! Unless you�re aiming at something big, it�s very likely a complete miss. Hitting something at 1500 yds is hard enough, why would you purposely put the center of your theoretical perfect group all the way onto the edge of the target by using less accurate data?

Even at the closer ranges your data above begins to diverge by several inches at ranges many here shoot all the time. This will be noticed.

This is certainly where some of this is coming from. Of course you could just as easily say, �Since I won�t be shooting the bullets as far as they�ll go accurately I can get away with using less accurate data.� I don�t understand why you�d argue we should as well, much less that bullet companies should aspire to only provide data that�s �good enough� to Mach 1.2 when many of their customers use them below that by the thousands. You could also say you never shoot beyond 200 yds so bullet companies really don�t need to provide BC�s at all.

Seriously though, while the errors are not as great above that, they are there. If you have more accurate data, why not use it? Why say bullet companies should be less accurate?

Secondly, especially when talking about LR hunting rifles, 1000 yds isn�t anywhere close to far enough to be around 1.2 for many bullets and rifles. A 1000 yd TOF measurement wouldn�t tell you much. All the interesting stuff happens much after that with the big guns. If you think the logistics of doing this at 1000 are hard, try 2000 yds. Good luck with that.

That�s an awfully presumptuous accusation. Do you have any data which shows data he said is accurate to be inaccurate�from which you may surmise he doesn�t know what the word means? If so, let�s have it. While you�re certainly correct most shooters don�t know or don�t care about the difference (�sub-MOA accuracy� instead of precision), I can assure you Bryan is not most shooters.

What makes you think the two are not directly related? You�re obviously not talking about some obscure theoretical case in which a bullet flies in a particular way which allows it to generate its own lift. For the context of this discussion, if you know one metric you know the other. The better you know it, the better you know both.

Bullet shapes that decelerate at different rates drop at different rates�with respect to yardage, not time obviously. If you fudge the numbers so they match up at one particular long range, you will be off in the mid ranges. Then if you change anything, such as MV or the atmosphere, you aren�t even matched up at the same long range you were the first time.

While one measurement over a long range is certainly better than one measurement over a short range, it is not as good�much less �more accurate��than multiple measurements over the entire range. Less data never makes you smarter.

The holy grail of accuracy�a Doppler radar, gives you the exact drag profile of the bullet yard to yard but that�s just not doable for even many bullet makers, much less users. Short of that about the best we have are measurements such as Bryan�s, which can be many times better than a single measurement as they can actually tell you about the drag curve of the bullet�not just give you some single average value.

Using your proposed method, a bullet with a �good G7 shape� will have vastly different average G1 BC�s if measured from the muzzle to subsonic when launched at 3500 fps than when launched at 2000 fps. Are you also proposing manufacturers should give average G1 BC�s for each muzzle velocity?

Measuring such a bullet as you propose at one velocity would give horribly inaccurate results for somebody using it at the other velocity. You make no distinction. But if the bullet was one Bryan had measured, a guy has all he needs to get very good results at either velocity. Or if a Sierra, the velocity ranges listed with the BC�s would do the same. You seem to be wanting to fix something that isn�t broken (at least with those two companies)--or even break something that's been fixed.

Doing what you suggest would be a giant step backward. Now for some companies that provide no data or uselessly inaccurate data it would be a step forward, but you were specifically saying it would be better than the way Berger advertises or Bryan measures in his book. That�s just not the case.

JonA � MacLorry did cite Ken's article (July, 2007 Shooting Times) in the original post, and like I said, I read Ken's article. No link is needed just because you don't agree. In that article Ken demonstrated with numbers basically the same thing MacLorry demonstrated with numbers. You can go check those numbers yourself like I did.

To me, the theme of this thread is that we spend too much time hyperventilating over stuff like G7 that it turns out makes little difference at ranges where making a shot is more skill than luck.

My statement is true and the numbers prove it within the stated limits of supersonic velocities. Right now the Shooting Times website is being revamped and they are not offering their back issues on-line, but you can go to a good library and look up Ken Oehler's July, 2007 Shooting Times article yourself.



As for the use of form factor, I used it to select the candidate bullet. I wanted one that closely matched G7 of those bullets that Berger publishes G7 BC values for, and as you found out yourself, it's a good match. If the G7 trajectory for that bullet can be closely matched using a G1 BC, then it replicates what Ken did in his article with a G1, G5, and a G7 BC.

What Ken didn't have in 2007 was a bullet for which a manufacture published the G7 BC and which was shown to be nearly an exact form factor match to G7. I tested Ken's conclusions using such a bullet and found that his conclusions were still valid and did so using the JBM site so that anyone reading my post could check the numbers.

Maybe Bryan read Ken's article or maybe he noticed the same thing himself, which is that while the magnitude of drag depends a great deal on bullet shape at supersonic velocities, the profile (curve of the drag coefficient line on a graph) doesn't change significantly due to bullet shape at supersonic velocities. That's why Brian says "From about 2000 fps and faster, the drag curve of the typical long range bullet and the G1 standard do not change very much." in his book Applied Ballistics For Long Range Shooting (1st edition page 18).



All standard bullets have a form factor of 1.0, and thus, an actual bullet with a form factor of 1.0 is an exact match. More specifically, form factor is the actual bullet's drag coefficient divided by the standard bullet's drag coefficient at a given velocity. Simple math proves that a value of 1.0 represents a perfect match to a given standard bullet at a given velocity.

BC is an actual bullet's sectional density divided by its form factor. Whatever average form factor was used for Beger's #24530 can be calculated by dividing its sectional density by its BC. Thus, for #24530 the G7 form factor is 0.9972. A value so close to 1.0 is a strong predictor of how well #24530 matches the G7 form factor at all velocities. Knowing this, I didn't need access to the source data used to calculate #24530's G7 BC.



You may not think a difference of 5.8 inches is insignificant at 1500 yards, but as I pointed out, it represents a change in MV of just 14 f/s. Yes, it's nearly two scope clicks, but unlike bullets, optics are not subject to the same degree of cumulative errors over range, and thus, the change in MV is a better way to equate such an error. In practical terms, the consistency of a load's MV establishes what is or is not a significant error at a given range. By 1,500 yards 5.8 inches becomes insignificant.



Once again, these "several inches" are insignificant compared to those caused by normal random changes in MV.



I'm basing Mach 1.2 on what others in this forum stated in my topic "Determining a load's maximum range". The consensus is that shooters are well aware of the inaccuracies induced at transonic velocities and consider a load's maximum range to be where its velocity drops below Mach 1.2, with some wanting to say above Mach 1.6.



Like I stated, assuming the G7 BC trajectory is correct Beger's published G1 BC is less accurate than the one I calculated using Ken's technique. That suggests their technique for calculating BCs is not as accurate as Ken's technique, and thus, even their G7 value could be off. This assumes we care about predicting the trajectory of #24530 over the velocity range shooters will actually use this bullet for.



The same applies to the techniques manufactures now use. Sierra has a 300 meter underground range, which I think is the longest in the industry. As soon as you go outdoors you can't control the conditions nor can you even know them without an expensive instrumented range. As I said, this is likely why no manufacture is doing this, and while impractical, there's value in raising awareness of a potentially better approach to calculating BCs.



Of course they are related, but the numbers I posted show that you can't take the simple average of several BC values for a number of velocity ranges and combine them the way nature does to come up with the true BC. The flaw is in the math being used. Ken's technique lets nature combine the numbers perfectly over a large velocity range. Nature's averaging results in a TOF. Use the velocity and the TOF over a long range and you'll get a BC value that better matches the bullet's trajectory for the velocity range the bullet is intended to be used for. I posted example numbers and you can go to the JBM site and try them yourself for different MVs and ranges, I did. Ken's technique holds up well for any velocity #24530 was intended for. Same for every VLD bullet I tried.



The problem is the same as for measure BC over long range; once you go outside you can't control or even measure all the conditions that effect bullet flight. For example, Doppler radar can't see wind in clear air, so you can only measure bullet velocity relative to the radar antenna and only along a straight line from the bullet to the antenna. Being a bullet's trajectory is parabolic, the error of the measured velocity increases over range and can't account for the effects of wind at any range past the muzzle or where it's being measured independently.

What you end up with from Doppler testing is velocity vs. time data. If you use the velocity zone drag averaging technique to calculate BC you'll introduce the same error we see in current published data.

Lost River used Doppler data to calculate their BC values and Lapua went one step beyond by reportedly incorporating the Doppler data into their ballistics calculator program rather than dummying it down into a single BC value. Curious about that, I ran their downrange velocity numbers and used them to calculated BC values that I then used to predict downrange velocity numbers using JBM. The difference in the downrange results between Doppler based numbers and BC based numbers were insignificant. Go try it yourself.



Of course, and that's why it only works for supersonic velocities. You know, the velocities anyone using a VLD bullet would care about.



Not true for supersonic velocities from muzzle to the target, which is the distinction I made, it produces better trajectory predictions than current published BCs.



But the equal TOF BC gives better results over the velocity range such VLD bullets are intended for, and that's the point.



Have you tired comparing Sierra's multiple BC results with a measured G7 BC and then compared it to a properly calculated equal TOF BC? If not then you have no bases for your claim. If you have, post your numbers. I would like to see just how close Sierra is getting to matching a G7 trajectory with their technique.



I'm just raising awareness to the limitations in the current system. Some find that annoying, but that's how progress is made.



I demonstrated with actual numbers that the G1 equal TOF BC better matches the trajectory than Berger's published G1 BC relative to the G7 BC for a bullet that's a near perfect G7 form factor match over the velocity range that bullet will be used for. In doing so I've demonstrated a limitation in technique Berger and others are using assuming that hitting the target is the goal of publishing BCs. Anyone can check the numbers for themselves so it's not just my opinion.

New to this thread and don't mean to hi-jack, but could someone please explain what a G1 is, and what a G7 is, and what the designation means? Thanks!

My agreement has nothing to do with it. Facts don�t care who agrees with them. When an incorrect statement is attributed to somebody it�s always a good idea to go back to the original source and verify. It�s possible much was lost in the translation.

Your statement is true, but you want to limit �supersonic velocities� to mean something other than �supersonic velocities?� That would be a different statement.

OK, even staying well within your Mach 1.2 limit (since you have the luxury of not worrying about where it really gets hard) your own data still shows error of 5.1� with one method and zero with the other at only 1300 yds. How exactly does five inches of error become �just as good as� zero inches of error? What does �just as good� mean to you, exactly?

Tell that to the target you just missed. Have you ever actually tried to shoot something at 1500 yds and hit it with your first shot? If you ever do, you may realize that you need an additional six inches of error on top of all the other potential errors inherent in making such a shot like you need a hole in the head. Especially when simply using more accurate data to which you have access can eliminate it. 5.1� at 1300 may even be worse as a percentage of �how far you miss with the first shot.�

A given velocity is only a single point on a curve. It tells you nothing about how good a match the bullet is for the rest of the curve.

Wrong. It�s a value. Not a predictor of other values. A curve is many values of one variable plotted against another, a single value is only a single point on the curve. Even an average tells you nothing beyond the average value�a vertical line and a horizontal line can have the same average value.

Without even getting out of the 6mm�s, Bryan�s data shows the Nosler 95 Partition, which has an average G7 I of 1.303 is actually a better match to the G7 curve than the bullet you chose, having only � the variation in form factor over the measured velocity range. And the Sierra 107 Matchking has an average I7 of 0.993�should be a �perfect match,� eh? Wrong. It has over seven times the variation the Nosler has. It�s actually a much better fit to the G1 curve than it is the G7 curve (even though its G1 I of 0.508 is quite a ways off from the �perfect� 1.0).

Again, this relies upon your definition of �significant.� If the targets you shoot at 1300 yds are so large that 5� is not significant, you might learn more by shooting at smaller targets.

Well OK then. You have a couple responses to one thread on this board. Obviously a new law of exterior ballistics has been created!

While some bullets don�t do so well below that and keeping above it means you never have to worry about it, it�s far from some all encompassing limit which means a ballistics method that ignores everything beyond it should be adopted as the industry standard. Many of us go below that all the time. My 6.5 Grendel would be pretty much worthless beyond 700 or 800 yds with typical loads if that was the limit. I have way too many sub-MOA groups at 1000 and even 1100 yds to know the right bullets can be fairly accurate well below that velocity.

Wrong. With a 300 yd range you can measure the drag of the bullet at different velocities by launching it at different velocities. With multiple data points, you can draw a curve. While far from ideal, you can get a boatload more information than a single TOF measurement from it.

Wow, I�ll bet nobody using that thing had ever thought of any of this before! I�ll bet they had no idea what a waste of money it was�. Seriously, I think you�re insulting the intelligence of the people.

The last time I checked, 2000 fps was supersonic. Another new rule?

Another 5� off is �better� than �right on� sort of way?

Again, the only data you have provided shows worse, not �better� results.

OK, let�s try to explain this again:


It�s really very simple. While Sierra doesn�t make as many VLD-shaped bullets as Berger, one I�ve used a lot is the 30 cal 210 SMK with listed G1 BC�s of: .645 @ 1800 fps and above, .630 between 1600 and 1800 fps, .600 between 1400 and 1600 fps, .530 @ 1400 fps and below.

In my above comparison, if you shoot this bullet from a big magnum at 3500 fps, for a large portion of the flight from muzzle to subsonic the bullet will have a G1 BC of .645+ (actually higher if you look at Bryan's data). This will increase its average G1 BC from the muzzle to subsonic.

If you shoot it from a smaller round with a MV of 2000 fps, it will spend very little time at .645 (actually it'll stay lower according to Bryan's data) and thus will have a much lower average G1 BC for the entire flight from muzzle to subsonic.

Two markedly different G1 BC values. Which would you print on the box? Which would you declare as "accurate?"

When you look into the numbers you�ll see this is exactly what is happening with the bullet you chose for the comparison (using Bryan�s G1/velocity data in place of Sierra�s). See below:


It suggests that to you because you don�t understand what is going on. There is no relationship from which you can form this conclusion.

Assigning a single G1 BC to a bullet which does not follow the G1 curve well is an inherently inaccurate exercise. Your discovery of this is no discovery at all and is not evidence of similar inaccuracies in the G7 values because the bullets follow the G7 curves much more closely, which makes that a fundamentally different problem.

A single G1 value for such a bullet will only be correct for a single set of conditions. If you change those conditions it�s likely the value will be wrong. Berger is damned if they do, damned if they don�t. It�s a lost cause�which is why they�ve switched to G7 for their bullets.

Case in point: You came up with a �more accurate� G1 value for that bullet�.under specific conditions you chose. Under different conditions, such as a lower muzzle velocity, the G1 value Berger advertises will be more accurate than the G1 number you came up with. Re-run and post the numbers you did in the very first post except change the muzzle velocity to 2500 fps. Which value is the �most accurate� now? As you can see, trying to put a single G1 BC on that bullet is inaccurate the way Berger does it, and the way you did it.

Hopefully that exercise will make you understand the folly of trying to use a single G1 value for a bullet that follows the G7 curve. When you look at the data, it�s obvious how that inherent inaccuracy of doing so in no way reflects upon the accuracy of using a single G7 value which will give accurate results for both velocities for a bullet which follows the G7 curve.

As you can see above, it may be annoying to study those numbers until you understand them, but after you do you will see no progress is made with your method at all. The real progress is made by using drag models which match the bullets� actual drag curves very closely. When that is done, a single BC can be pretty accurate for a bullet under any set of conditions. When the bullet�s actual drag curve is very different from a standard drag curve, any single BC of that drag curve will be a poor description of that bullet for all conditions no matter how you come up with it.

Naturally, there are some bullets that don't follow either curve very well. With multiple measurements such as are presented in Bryan's book, it is easy to identify such bullets so that you may come up with specific strategies to deal with them. With a single TOF measurement only, you'd never know.

Go look at Bryan's book and check his data points and you see that he only tests bullets from Mach 1.2 to about Mach 2.7. That's the same velocity range I'm using. Obviously, he understands how such bullets will be used. Are you willing to concede there's a practical velocity range or do you just what to argue for the sake of arguing?



The part you're missing is neither one can be exact because of random variations such as MV. Most rifles a person can carry on a hunt produce groups of at least 0.5 MOA which is 6.8 inches at 1300 yards. From an engineering standpoint any signal that's below the level of noise is insignificant as it can't be reliably measured. If you want to brag about how incredibly accurate your rig is and that you can reliable shoot less than 0.5 MOA groups at 1300 yards go ahead and make that claim. Most of us know better.



You need to brush up on your math. I gave you this equation yesterday. Form factor is the actual bullet's drag coefficient divided by the standard bullet's drag coefficient at a given velocity.

Now substitute the standard bullet's drag coefficient in the numerator for the actual bullet's drag coefficient. Now you have the drag of the standard bullet divided by the drag of the standard bullet and any number divided by itself is 1. Thus, all standard bullets have a form factor of 1.0 at all velocities. An actual bullet that perfectly matches a standard bullet also has a form factor of 1.0 at all velocities. An actual bullet that has an average form factor of 0.9972 is going to be a close match to the standard bullet over the velocity range the actual bullet was tested at. This is just the cold hard facts of math.



In general that's true, but we're talking about two specific curves here and perhaps I know something you don't. Below is a chart showing the G1 and G7 drag profiles where G1 has a BC of 1.000 and G7 has a BC of 0.500. In the center is a velocity zone between Mach 1.7 and 2.6 (1900 to 2900 fps) where the two drag functions coincide in a nearly exact relationship of 2 to 1 and then diverge above and below that velocity range.



What this means is no bullet of any shape or construction can exhibit a change in G1 BC within this velocity range without also changing by the same percentage relative to the G7 BC. In this important velocity range G1 BCs are as good a predictor as G7 BCs.

I don't expect you to take my word for it so you can test this for yourself on the JBM site by picking any G7 BC and doubling it to get an equivalent G1 BC for this velocity range. For example, using a G7 BC of 0.279 at 2900 fps MV the velocity at 650 yards is 1901.5 fps. For a G1 BC of 0.558 at 2900 fps MV the velocity at 650 yards is 1905.1 fps. Compare drop and you'll find that it remains within 2 inches out to 1100 yards even though the velocity has dropped to about Mach 1.2 at that range.

Looking at the chart you'll see that on the left in the low velocity zone the G1 line is below the G7 line, but on the right in the high velocity zone the G1 line is above the G7 line. This means we can extend the velocity range in which the G1 closely matches the G7. For example, on the JBM site I increased the MV to 3200 fps using the G1 and G7 BC values from before. At 800 yards the G1 BC has a velocity of 1929.6 fps and the G7 BC has a velocity of 1931.0 fps. Furthermore, drop remains within 2.2 inches out to 1400 yards.

In theory G7 BCs are a better predictor for VLD bullets in the transonic velocity zone, but that's only important for the long range shooters who believe they can maintain accuracy at such ranges. From the "Determining a Load�s Maximum Range" topic, that seems to be very few shooters. I say in theory because checking Bryan's book (1st edition) I don't see any data points below about Mach 1.2 and for most bullets, the lowest data points are around Mach 1.5, so he doesn't have any real data for VLD bullets going subsonic, at least not in the 1st edition. I don't consider that an oversight, only that being a long range shooter himself, Bryan realizes that long range shooters stay above about Mach 1.2.



If you take the G1 BC of 0.645 in the 1800 fps range and divide it by 2 for a G7 BC of 0.323 and plug them into JBM with a MV of 3500 f/s you'll find that the drop is within 2.7 inches out to 1000 yards even though the MV is outside the G1 � G7 drag convergence velocity zone. Bryan publishes a G7 BC of 0.316 for this bullet and plugging that number into JBM the drop is within 0.8 inches at 1000 yards and down to 0.3 inches at 1300 yards. If I reduce the MV to 3000 fps then the G7 BC of 0.323 is within 0.1 inches at 1000 yards and at 1.2 inches at 1300 yards.

A simple dividing of the G1 BC by 2 results in a G7 BC that gives trajectory predictions that are well within the normal group size of any hunting rifle out to 1300 yards for loads with muzzle velocities of from 3500 to 2800 fps using this bullet.

I expect Bryan's G7 number is more accurate outside the MV and range envelope I defined, but I didn't have to measure anything to get results that are practically the same for most long range shooting.

As for loading this SMK bullet to a MV of 2000 fps, its pure hypothetical. I don't know of any long range shooter in their right mind who would waste their time on such a load

The reason G1 has been so successful is not because it produces higher values, as some suggest, but because it's almost as accurate as G7 for VLD bullets in the velocity range where such bullets are used and it's more accurate than G7 for non-VLD bullets. G1 is the best all around standard and this allows shooters to compare bullet ballistics between all types of bullets from most manufactures.

The equal TOF technique I've been explaining takes advantage of G1's nearly exact 2 to 1 match with G7 over much of the usable small arms velocity range and its better match to non-VDL bullets.

Think about the chart I posted and what else it means. It has implications beyond what I've reveled so far, but at this point I don't think anyone but ballisticians care.

G1 and G7 refer to standard projectiles used in ballistics research. If you use any exterior ballistics calculator or program, the Ballistic Coefficient numbers you enter are assumed to be G1 unless labeled as something else. Berger bullets publishes both G1 and G7 BC numbers that you don't want to swap when working with an exterior ballistics calculator. The argument going on is about how best to measure BC values and which gives better results. In practice, it makes no difference to most people.

As I said, the source was cited. If you wanted to check you had all the information you needed to do so. You come across as one of those guys who wants links for the sake of links.



This is where you lost a lot of credibility, its 6th grade math that all standard bullets have a form factor of 1. A bullet that matches a standard bullet also has a form factor of 1. Your example Nosler bullets form factor values are further off 1.0 than 0.993. Don't tell me you think a form factor value over 1 means the bullet is a better match to the standard than something with a value of 1. That would be too funny.



Remember you're not the only one reading posts. Some of us want such detailed background info when a person then goes on to make a conclusion. It's what the better professors did in my college years. No one should take that as an insult let alone someone who forgot 6th grade math.

That's an eye opening graph you posted. I don't remember seeing anything like it before where the G1 and G7 are scaled. That explains lots including why the simple trick of just halving the G1 to come up with the G7 works so well.

I do agree with JonA in the sense of not wanting to abandon or down-play what Bryan is doing. He's done all shooters a great service in writing his book without which there would be little real data to compare and ponder. He also knows a lot about long range shooting few can match.

I'm not a ballistician, but I do want to learn more about the subject, so keep it coming.

I hope I�m not coming across as trying to down play what Bryan has done. If so, that's not my intent. Nonetheless, in order to discuss the merits of G7 there's no other source of widely available data to cite.

As it appears you�ve turned off all your �comprehension� and �learning� brain cells and poured caffeine on the �defense mechanism� ones, I�ll try and make this short and sweet so you can focus. I still think I can break through to you. Just concentrate on the facts presented.

How exactly do you believe he measures a bullets BC AT Mach 1.2? How would you measure the BC of a bullet AT Mach 1.2? Shoot it at that velocity over an �instant BC generator?� Or measure the velocity drop or TOF a ways above and below so you get an average at that velocity?

Your scientific method is flawed. That other variables may not remain constant does not excuse the inaccuracy of another. It�s not just a copout of your ballistics argument, it�s not a scientifically valid one. Have you heard of a thing called a �scatter plot?� Real Engineers use them all the time. So do shooters�they just call them �groups.�

Which part of �a� velocity do you not understand? You are talking about a CURVE in which the X-Axis is VELOCITY. To populate that curve you either need an equation that defines drag as a function of velocity�which you don�t have�or you need to measure the value (drag) at different velocities. Bryan did the later. You are doing neither. You are �assuming� data which does not exist to draw your curve. Your curve is an imaginary one.

Again, you are describing a curve for which you have no data. You are using imaginary data to populate the curve. Try using actual measured data for the 107 SMK as suggested. The numbers are right in front of you in black and white. Actual measurements. You can only burry your head in the sand so long.

First, note how widely divergent they are at the 3500 fps muzzle velocity you began the thread with (and remember what happens at the muzzle affects the entire rest of the flight).

Secondly, you need to acknowledge that real life bullets may not follow either curve, so that chart means nothing with respect to the above. In fact, virtually all bullets will diverge from one of the curves at least a little bit. It would be a rare bullet indeed that followed one of the curves exactly . This is why actual values must be measured. Bryan isn�t doing all those measurements just for his health.

I wish you would have spent that effort on the real comparison I suggested, or re-doing your �real, accurate� numbers from the beginning of the thread as I suggested. Let�s do one, it�ll be undeniable.

Wrong, as you would have seen had you done the example. But just to make you happy, we�ll do it staying above Mach 1.2 to eliminate that from your quiver of excuses.

Have you ever heard of the 6.5 Grendel? 6mmAR? BR? SPC? Etc? While not the first choice for hunting, where you actually need to kill something, a bullet doesn�t need to be going fast to punch a hole in a piece of paper. Dave T was using the 240 SMK out of a .308 for a while�.

What rounds to you believe people are using to shoot the 115 Berger at 3500 fps? I guarantee you it�s a pretty small percentage that get launched that fast.

But to eliminate that excuse from your quiver as well, we�ll do the below example at 2500 fps instead of 2000. I�m really stacking the deck in your favor here, if your conclusions were accurate.

So you fudged the numbers to reduce the error to �insignificant� levels by your standards�. You keep claiming something is �more accurate� but then keep defending its increased error as �insignificant.� If it was more accurate you wouldn�t have to keep doing that.

I don�t know if you were being lazy or if you somehow knew if you had run the numbers as suggested you would have been proved wrong so you avoided it. Either way, I�ll do it for you. Please, follow along.

--------------------------------------------------------------------------------------------------------------------------------------

Let�s pretend that bullet follows the G7 curve exactly. It has an average form factor of 1.0000 so it must, right? It actually doesn�t but you may still be wrestling with that so let�s just pretend that it does.

At standard conditions, launched at 3500 fps its TOF is 2.205 s to 1600 yds (stays above Mach 1.2). This equates to an average G1 BC of .637. That is the exact measurement method you advocate in the beginning of the thread.

At standard conditions, launched at 2500 fps its TOF is 1.550 s to 950 yds (stays above Mach 1.2). This equates to an average G1 BC of .621.

So, which do you print on the box? According to your first post, you would print .637 and believe it is �more accurate� than the G7 BC Berger prints somehow and you believe that is what Berger should do. It would be pretty accurate for a 30-378 with a 30� barrel.

But some poor schmuck out there is going to load it in his .308 and use your .637 G1 BC value because that�s what is printed on the box. What happens? He misses, that�s what.

Your .637 �accurate� G1 BC value says he�ll have 338.5� of drop from a 100 yd zero when launched at 2500. If you had used the .621 value which will be much more accurate for a 2500 fps muzzle velocity, the predicted drop would have been 343.2�. That�s nearly 5� of error at only 950 yds. That�s using the exact method you outlined as being �more accurate� at two reasonable velocities for different rifles. That�s staying above Mach 1.2 where you say there will be no significant difference�go below that and it gets worse. Do the comparison at 2000 fps like I originally said and it�s worse.

Of course I shouldn�t have to remind you that for a bullet that follows the G7 curve, a single G7 BC printed on the box will give accurate results for both rifles, at both velocities.

Do the exact same comparison for the bullet you posted in the beginning of this thread and you�ll see the exact same thing. Don�t come back with some meaningless argument about how hunting rifles have such crappy accuracy we�ll never notice the difference, therefore your less accurate method is actually more accurate�.

Run the numbers! Tell us what your �more accurate� average G1 BC for the 115 Berger from a gun that shoots it at 2500 fps. Then try and explain why it�s something different than .559 but we should still agree .559 is the most accurate!

Since you can see the numbers plain as day, can you now give me one single reason why �the industry� should try and put a single G1 BC on bullets that more closely match the G7 curve?

You began this thread with the assumption that the difference in G1 BC�s was due to poor methodology by Berger/Bryan. By now, the lightbulb should be going on for you. You should realize the difference was cause by the inherent problem of describing a G7 Bullet with a G1 value�it will never be correct for all the rifles that will use it. And since the error clearly is not caused by methodology, your assertion that it brought the accuracy of their G7 published values into question was without cause.

Cited? Quoted? Mis-Quoted? Paraphrased? If somebody goes around saying 2+2=5 and lists me as the source, I would hope people would come to me and verify before making assumptions.

Maybe lost credibility with a 6th grader who doesn�t know what a coefficient is or what it is for. A coefficient simply scales a curve up or down. Hopefully my explanation above covered this for you. A FF of 1.0 at a certain velocity simply means the bullet�s actual curve crosses the theoretical G7 curve at that single point. It means nothing about how close the curves are over the rest of the graph. The rest of the curve could be wildly different.

The shape of the curve is what matters. This is what is programmed into your ballistics program. How far away from the X-Axis the curve is (a form factor of 1.0 vs. 1.3) has no influence on the accuracy of your results. This is why you input the ballistic coefficient into your program, so it can scale the curve up or down and give you the proper results. If the bullet�s actual curve is much different from the theoretical drag curve, you will get inaccurate results even if the bullet�s average form factor is 1.00000000.

That�s simplified, but hopefully it works for you.

You know; I have been told that Jeff and I can really get into nano-nit picking. I now know that impression is totally wrong. My good friend Jeff and I are pikers compared to you hosers. Talk about killing electrons for no good reason.

Says the guy who always gets spotter shots to discover both windage and elevation before he pulls the trigger for real. If the idea of a first round hit is lost on you, that's fine. I won't call you a hoser for it.

Hmmmmmm

Boy, was I wrong or what?

Go look at Bryan's drag coefficient charts where he calculates BC. They all show his data points. Please read the chapter where Bryan explains how to read his data.



Every shot is subject to random variations in MV and barrel movement and these variations produce "groups" as you acknowledged even when shooting indoors using a machine rest. When a manufacture brags about how accurate their rifles are they say they are Sub-MOA, meaning they produce "groups" of less than 1 MOA. Check out the Weatherby site if you don't believe me. You can argue that variations less than 0.5 moa are significant all day long, but most shooters and manufactures know better.



Anyone can take a single sentence out of contest and argue against it. I did say "at a given velocity" in that sentence and then went on to expand the definition for velocity ranges in the following sentences. How did you miss them?



I picked the 115 Berger because Bryan has 18 data points for it as compared to only 6 data points for the 107 SMK. The more data the more accurate the form factor and variation data is going to be. Had Bryan tripled his testing of the 107 SMK the results would likely have been different. Furthermore, Burge publishes the G7 BC for their bullets and Sierra doesn't. For a valid and fair comparison I wanted to use a manufacture's own published values. Nevertheless, I'll used another bullet you picked in another test below.



Of course, what happens outside the convergence velocity zone affects the rest of the flight, but it can be calculated and for those of us who understand significance, useful conclusions can be made.



Of course actual bullets seldom follow either curve, but you are missing the point. In the convergence velocity zone there is only one curve. If a bullet doesn't follow it then it's not following either the G1 or G7 drag function. The topic is about how the G1 compares to the G7, and in the convergence velocity zone, they have the same curve.



Yes, but none of them can use this .308 cal. bullet, and about the heaviest bullet anyone makes that could be stuffed into 6.8mm Rem SPC is the 150 grain SGK.



I said I don't know of any long range shooter in their right mind who would waste their time on such a load. If Dave T was using the 240 SMK in a 30-378 Weatherby he might get it up to 2600 fps or so. Maybe you could use that for long range hunting, but that's different than launching a VLD type bullet at 2000 fps.



Thing is, you could lower the MV to 3200 or even 3000 and my example still works out better for the equal TOF BC.



Using the 0.308 210 gr SMK bullet you picked I ran the numbers to see how well Bryan's G7 BC of 0.316 matches Sierra's multiple G1 BC values. I also tested the equal TOF G7 BC to see how well it matches Sierra's multiple G1 BC values as compared to Bryan's G7 BC value.

I wanted to use the JBM site for this comparison, but it doesn't support multiple BC values. They have a Drag Function Array Conversion tool, but that's not the same thing. I used a program that does support multiple BC values in the way Sierra specifies to get both the drop and velocity values. Just so there's no question about accuracy, I also ran the G7 BC values on JBM and have included those in the graphic below.

I picked 3200 fps for the MV as that's about as fast as any standard caliber, such as the 30-378 Weatherby Mag, is going to push this 210 grain bullet. I took the calculations out to 2000 yards to get numbers well into Sierra's lower velocity range as that seems to be where you think there's a problem. I outputted the numbers to Excel to make it easier to compare both drop and velocity. The equal TOF G7 BC was calculated relative to Sierra's multiple G1 BC values from a MV of 3200 fps out to 1500 yards.

The drop values are in columns A through D and the velocity values are in columns F through I. The ballistics program's values are in rows 3 through 11 and the JBM values are in rows 16 through 24. The Sierra multiple BC value columns C and H have a yellow back ground. Bryan's G7 0.316 BC values are in the column just to the left of the Sierra column and the equal TOF G7 BC values are in the column just to the right of the Sierra column. The green background shows which values are closest to the Sierra values at the same range.



You can see how close the JBM values come to the ballistics program values, which gives confidence that the values for Sierra's multiple G1 BC are also accurate.

If we assume Sierra's multiple G1 BC values best matches their own bullet's drag characteristics, then it's clear that the equal TOF G7 BC value better matches that bullet then does the Bryan's G7 BC value for both drop and velocity for most ranges.

Below the drop and velocity values you'll see the results from the JBM Drag Function Array Conversion tool. Note that the tool uses the velocity zone conversion technique and comes up with the same value Bryan did by taking the simple average of the zone values. It's the same technique Bryan uses for evaluating his data, but the down range values show that the equal TOF conversion technique produces a BC that better matches Sierra's values. This is more evidence that measuring velocity and then TOF over long range produces more accurate values when measure BC, which was Ken's conclusion.



Of course JBM doesn't support Sierra's multiple BC values, so your TOF, and thus, your BC is off. The correct TOF is 2.186 at 1600 yards for an equal TOF G1 BC of 0.644.



The correct TOF is 1.532 at 950 yards for a G1 BC of 0.641. You got to use the right tool, and when dealing with Sierra's multiple BC values JBM is not it.

Being this 0.308 210 grain bullet will likely be launched at no more than 3000 fps I would use that for the MV and calculate the equal TOF BC to 1350 yards where velocity is near Mach 1.2. That value is a G1 BC of 0.641. Calculating from 2500 fps out to 950 yards I still get 0.641. That's the best single G1 BC for how this bullet will be used by most shooters.

As for G7, well I've already shown above that the equal TOF G7 value is more accurate then Bryan's value. Of course, I realize the differences are insignificant, but the question is, do you?

Long odds that something you wrote would be published in Shooting Times or some other publication, but if it were no one needs to check with you first to talk about what you wrote as long as they properly cite the source. That was done for Ken�s article. If you don�t think what MacLorry is saying is right then find a copy of Ken�s article and make a specific point. It�s not anyone else�s obligation to provide it for you.



From the dictionary: coefficient is a numerical constant that is a measure of a property of a substance. 6th grade math shows that a bullet with the same form factor as a standard has a value of 1. If it�s a perfect match it has a value for 1 at all velocities. Pick any velocities you want and plot them to get your curve. You can make the strawman argument that even the Y-axis intercepts the standard bullet�s curve if that makes you feel smart, but the context is VLD bullets. You only need look at the bullet drawings in Bryan�s book to see that every one with an i7 form factor close to 1 has a shape similar to the G7 standard bullet on the cover. What�s obvious seems to escape you in your attempt to disagree at all costs.

It�s pretty obvious your real goal is to disagree regardless of how dumb or out of contest your arguments are. I�ve ran all MacLorry�s numbers and more and what he�s saying is correct. My contention is that it doesn�t make much difference in the real world. Still, I�m going to buy Bryan�s second edition book because I think having an independent verification of other manufacturer�s BCs is important to long range shooting. I hope you can at least agree with that.

MacLorry - you sound like one of my old college professors - dry to the bone but with info that knocks the socks off. Looking at your G1 and G7 Drag Profile graph it came to me that two of Bryan�s velocity zones are completely within the Mach 1.7 to 2.6 range and a third velocity zone is about half in. All the data in the world within the Mach 1.7 to 2.6 range can�t tell you if a particular bullet better matches G1 or G7.

For some bullets like the DRT .308 200 grain all of Bryan�s data points are within that single line zone. You can guess from the shape of that bullet it will best match G7, but it�s a guess. Paging through I found the Sierra .338 250gr, Lapua .224 69gr, Hornady .243 100 gr, Hornady .243 105gr and Berger .243 108gr are some others with all their data in the Mach 1.7 to 2.6 range. Ouch!

You did say the graph had other implications � that�s an understatement.

Thanks, I think



Maybe I shouldn't have posted it, but you and JonA are the only ones paying any attention, so I don't think it will get any attention.

Whatever you intended to mean by that, I hate to burst your bubble but technical expertise means very little in getting something published in a gun magazine. Guys like Ken and Bryan are the exception, not the rule.

Now that you�ve added the second sentence, you have a correct statement. Congratulations. Unfortunately it does not apply to the bullet you said it did. The bullet I gave as an example has an i7 of .913 at 1500 fps and 1.051 at 3000 fps. You claimed it was a perfect match because at one particular velocity it has an i7 of close to 1.

Do you stand by your original statement? Would you expect a ballistics calculator using the G7 curve to give more accurate predictions with this bullet or a bullet with an i7 of exactly 1.30 over its entire velocity range? Is the lightbulb on yet? Did you happen to notice in Bryan�s plots that compare the data to the curves they are �scaled by the bullet�s form factor?� What do you think that means?


My goal is to teach correct information. What�s obvious is you have picked a side with your emotions. That�s unfortunate. Hopefully you�ll be able to see the data above through the red mist well enough to realize I gave correct information the first time and your emotional tirade was unwarranted.

His contention was the method outlined in his first post (not Sierra�s method to which he has now switched) gave a single G1 BC that was more accurate that what Berger gave for a bullet following the G7 curve. If you have really run all his numbers, as well as running them again at a different velocity as I suggested, you know that to be a false assertion.

It pains me to see the extent to which you�re �dug in,� now doing anything and everything in an attempt to win an argument. You�re jumping through hoops like a circus animal trying to sweep your errors under the rug, just so you can avoid being seen as �being wrong.�

It happens. It�s OK. It�s how we learn. No need to feel shame.

I�ll skip right to the important stuff, so only the truly interested need read the details.

You began this thread saying the G1 BC of .545 Berger provided for their 115 VLD was not accurate. You showed another method and came up with a G1 BC of .559. You accused them of using poor methodology to cause the error and due to that suspected their G7 BC�s may also be inaccurate.

Since I believe you�d rather recite the entire text of War and Peace than do any of the simple calculations which I told you to do and which prove you wrong, I have done the important one for you. Using the bullet you chose, using the exact same assumptions you used, using the exact same methodology you used, when launched at 2500 fps that bullet has an average G1 BC of .548 from the muzzle to Mach 1.2.

It is very clear to anybody who can read, that you were wrong. The large difference was caused not by Berger�s methodology, but by your choice of a very high muzzle velocity and the fundamental fact that one G1 number will only be correct at one velocity for this bullet. By now, this should be painfully obvious to everybody and I suspect, had you understood it in the first place, you never would have started this thread.

The number Berger uses is actually very close to this value. This value is the one that will be closer for the vast majority of users for that bullet. For the few shooting 378�s necked down to 6mm, your value will be closer.

That no single G1 value works for all applications with this bullet is most obviously not a fault of Berger�s methodology. It�s due to the fact the bullet follows a different curve.

That is all. Case closed. You started the thread for nothing. You were wrong. I know that is painful to admit (maybe try and prove yourself right using the Pejsa method now?) but it would be for the best.

For more details:


Yeah sure, by all means, just keep changing the inputs and methods until you get the answers you want. That�s how real science is done, right?

What in the hell are you doing using multiple BC values? Your first post, the reason you started this thread, was not to declare how accurate Sierra�s stepped BC method was. Quite the contrary. It may help confuse the issue so you can sweep the important stuff under the rug, but the rug can be lifted.

The only reason I used a Sierra bullet is because you asked for one as an example. Forget it and go back to the 115 Berger (or any other closely following the G7 curve) that you chose and the methodology you were advocating in the beginning of the thread.

You didn�t start this thread to prove using multiple G1 BC�s could give you accurate results. It is quite revealing that your final number-crunching comparison to prove you are correct did not contain the methodology you started the thread advocating as the best. That�s a concession without saying it outloud.

Again, more gibberish to cover up ballistics errors. You claimed a more accurate ballistics method. I have demonstrated it is less accurate.

What kind of shooters do you hang out with? Have you ever actually shot something at long range? I doubt there�s a single person who tries for first round hits at 1000 or beyond who will agree with you.

If I missed them, would I have highlighted them? You said them, you just failed to apply them. That�s why I highlighted them for you.

Isn�t it nice how things work out so well when you can simply make up data? From what basis do you �guess� the above? Again, your first claim word for word:

I gave you an example to illustrate your misunderstanding, a bullet with a i7 of near 1 and an i1 of near 0.5 that happens to follow the G1 curve better than the G7. And your response is if Bryan had kept shooting longer he would have gotten the opposite results? Very weak.

Your initial belief also suggests any bullet with an i7 closer to 1.0 than its i1 will follow the G7 curve better. This is untrue for a multitude of bullets. Bryan�s book is filled with examples.

It sure can. Most easily and accurately by using the drag curve that matches the bullet or using stepped G1 BC�s as Sierra does�neither of which did you advocate in your first post. Your first post allowed that divergence to give you a final G1 BC that will actually be less accurate than the one provided by Berger for most users. You claimed it would be more accurate than Berger�s number. You were wrong. Proven by your own methods.

Purposely missing the point.

Then you must not know many. You see, long range shooters like to shoot. A giant magnum that burns the barrel in less than 1000 rounds is great for taking some of the guesswork out of a single shot when hunting and provides a sure kill, but it�s a poor choice if you want to shoot thousands of rounds a year�or even a month as some here do. For that, most of us have other rifles that burn a lot less powder. With that comes much lower working velocity ranges.

Uhm, he was using it in the .308 Winchester at a much slower velocity than that. I believe he won a national trophy out to 1000 yds with it. Maybe you wouldn�t consider him a �real long range shooter� though.

So you think most users are using, what, 240 WBY�s instead of 6mm-378�s? Just how popular do you think rounds like that are compared with 243�s, 6mm Rem�s, etc?



I really do hope you can keep from bursting a vein and use this as a learning experience. You began a thread based upon a faulty premise. You were proved wrong. It�s OK, really. It happens.

In the end, you should now know why Berger�s G1 BC�s won�t necessarily match what you come up with if you chose a wildly different muzzle velocity. You should also understand the reason for the difference and how that has no bearing on the accuracy of the G7 numbers for bullets which follow the G7 curve relatively well. I hope you can put that to good use. Maybe try going out and actually shooting every now and then.

You�re busting a gut trying so hard to ignore the obvious and now you�re confusing BC with form factor. Back to basics for someone who thinks they�re teaching on this topic. Form factor is an indicator of how well a bullet�s shape matches the standard bullet�s shape; form as in shape. Take the time and look at the drawings in Bryan�s book and you�ll see that every one with a form factor close to 1 looks a lot like the G7 standard on the cover. Bryan makes the point about the G1 standard not being as close in SHAPE to modern VLD bullets as the G7 and that�s why the G7 is a better standard; are you saying he's wrong?



Wow, such an ego for a guy who has had his ass handed to him in nearly every post. You picked a Sierra bullet and listed out it�s BC/Vel values and then when MacLorry uses it with real numbers to prove you wrong you crap your pants and retreat back the original bullet. The only thing you�re teaching is how to dodge a lost point.



I read his original post again and it�s not his contention at all. His contention is that his method produced more accurate results for the G1 BC using the G7 as the reference. He infers from that FACT that his method (actually Ken Oehler�s method) would produce an even better G7 BC if applied when that bullet was tested. Nothing you�ve posted counters that argument because you were too engrossed on arguing that 5.8 inches is a big deal. With your head in the sand you didn�t realize you were not even arguing about the right thing � now that�s funny

It's no secret that if you pick a different MV the equal TOF BC may come out different. The real question is, is my original G1 BC a better value for this bullet than Berger's published G1 BC over a wide range of MV? If so, then my point about there being a better technique for calculating BCs is correct. Here are the numbers.



As you can see for a MV of 3000 fps the equal TOF G1 BC is more accurate as compared to the G7 BC than Berger's published G1 BC is out to 1300 yards even though velocity drops to 1.2 Mach at 1150 yards. For a MV of 2500 fps the TOF G1 BC is more accurate out to 700 yards and actually to 850 yards where the velocity drops to Mach 1.2. This is more evidence that the equal TOF technique is better for calculating BC values in the velocity range these VLD bullets will be used by most long range shooters.

That said, I made reference in my original post that Berger's number showed they were concerned with predicting their bullet's performance in the subsonic range. The numbers above demonstrate that as well.



For all your blustering you've only shown that my original post is correct even when extended down to a MV of 2500 fps.



I picked it because you offered the SMK as a counter example even taking the time to list out the multiple BC values. Using the bullet you picked I again demonstrated that the equal TOF value produces a more accurate G7 BC value than the one Bryan and JBM calculate using their velocity zone averaging technique.

Now you want to go back to the 115 Berger, which I did above and once again demonstrated that my original G1 BC is better even at the 2500 f/s MV.



No, but you offered up the SMK as a counter example. Neither of us has the original firing data for that bullet, so the only valid comparison for my G7 BC and the one Bryan and JBM calculate is Sierra's own BC values. What were you thinking would be the reference when you listed the multiple BC values?



You've said that a difference of 5.8 inches at 1500 yards is a significant error, but I'm not advocating using the equal TOF G1 BC in place of the Berger's G7 BC. The point is that the equal TOF G1 BC more accurately matches the G7 BC than Berger's published G1 BC. If you want to claim 5.8 inches is significant then the 21.8 inches from Bergers G1 BC is 3.7 times bigger difference. You call that less accurate?



Go look at Bryan's data points for the two bullets. You'll see the 115 Berger has a much wider velocity spread and more data points. The "guess" as you call it is based on understanding variability and confidence levels.



Just so there's no question later as to which bullet you now offer up, here's what you wrote before �the Sierra 107 Matchking has an average I7 of 0.993�should be a �perfect match,� eh? Wrong. It has over seven times the variation the Nosler has. It's actually a much better fit to the G1 curve than it is the G7 curve (even though its G1 I of 0.508 is quite a ways off from the �perfect� 1.0).� The Nosler you were referring is the Nosler 95 Partition.

We can use Sierra's multiple BC values to see if their .243 107 grain Matchking better follows the G7 or, as you claim, the G1 curve. No need to use JBM as it doesn't support multiple BC values and my prior post shows the program I'm using gets nearly the same values as JBM does.

The G1 BC values are 0.527 down to 2500 fps, 0.522 down to 1800 fps, 0.509 down to 1600 fps, and 0.495 below 1600 fps. Obviously, Sierra doesn't think their bullet matches G1 well or they wouldn't need to publish four BC values for it, but let's continue and see what the data says.

I'm going to use 3500 fps and take the data out far enough to get into the subsonic range to see which of Bryan's BC values best matches Sierra's own multiple BC. That way we get into velocities were there's a difference between G1 an G7 outside the profile convergence velocity zone. Bryan give this bullet a G7 BC of 0.262 and a G1 BC of 0.510. Here's the data out to 2000 yards.



Your contention that this bullet better match G1 than G7 is wrong. If you look at Bryan's data for this bullet you'll see that he has only 6 data points. Remember what I was saying about getting a different result with more data points, well this is a classic example. Also, most of Bryan's data is within the drag profile convergence velocity range where the G1 and G7 are indistinguishable. There's also a flaw in the way Bryan calculates Variation.

Like Bryan said, this bullet shouldn't mach the G1 standard better than the G7 standard, and it doesn't. The Form Factor theory is proven correct. If you weren't so busy trying to teach maybe you could learn something.

If you have any other bullets you want to offer as counter examples please do the work of posting the actual downrange numbers. It will save me time debunking your contentions.

Clearly wasting my time, so I'll be short:

Turn to page 288. "The solid black and gray lines are the G1 and G7 standard drag curves scaled by the bullet's form factor."

Can you understand what that statement means? I'm confusing BC where? Look at all the graphs--note how the data points for bullets, even those with form factors far from one, such as the 1.3 bullet I mentioned, are ploted right on the line.

Because that's what matters.

You mean he changed to the Sierra method after realizing his original method would give very poor results. Why would you expect me to argue the against Sierra method when I've said many times it's a decent way to do things?


Fixed that for you. More data below. Please actually read it this time.

Apparently it was a secret to you when you started this thread. That's what lead you to proclaim your BC of .559 what �more accurate� without a specific velocity qualification or ranges (as Sierra gives). Game, set, match.

In science, one can lose credibility very quickly when caught pushing down on the scale with a finger. Credibility is hard to earn and easy to lose.

Since your modification of �supersonic flight� to mean �above Mach 1.2 wasn�t good enough, you conveniently omitted the most important data above Mach 1.2�data that did fit your narrow definition. Why did you do this?

Of course it�s obvious. It proves you wrong. At 850 yds, where the bullets are still above Mach 1.2, the drop values are the following:

G1 .545 309.1 -1.8
G1 .548 308.3 -1
G7 .279 307.3 0.0
G1 .559 305.3 +2.0

You can see, of all three G1�s, your original claimed �more accurate� BC is the least accurate.

I do agree with you in one area though�Berger knows many users are not going to adhere to your artificial Mach 1.2 limit. You came up with that, not them. So just for fun, at 1000 yds where the bullets are still easily supersonic:

G1 .545 468.5 -1.3
G1 .548 466.9 -0.3
G7 .279 467.2 0.0
G1 .559 461.4 +5.8

Your BC has over four times the error. It also shows the bullet traveling nearly 70 fps faster than it really will be which could cause somebody to think it�ll stay supersonic farther than it really will. Things like that are important to those of us who actually do this in the real world.

So again, can you give Berger one good reason they should print .559 on the box as you said they should in the first post?

And to the much bigger point how exactly does your bogus .559 G1 call into question the accuracy of Berger�s G7? Yes, they do print a G1 on the box for the masses, but to anybody interested in the most accuracy they say to use the G7 values.

So now that you understand the ballistics, what exactly was the point of your first post? How does your method give me more accurate information than using G7 BC�s for bullets that follow the G7 curve?

Only when you delete the most important data. Shame. Shame. Shame.

You asked me for numbers to show one can obtain more useful information from Sierra�s data than a single number. You asked for them, I posted them. Then you proved me correct by adopting Sierra�s method over your own. I said it would be more accurate and you apparently agreed.

You believed you had reason to question the accuracy of their G7 BCs. Your opinion was the industry should adopt the method that produced the .559 G1. I�m glad to see you have changed your mind.

Here we go again�. I�m glad you like Sierra�s method so well.

And Sierra has how many, exactly? Do you know? So, Bryan and Sierra�s data don�t agree. You use Sierra�s data to prove Sierra�s data is correct. I hope you didn�t pull a muscle running in a circle like that.

You have the book. There are a bunch of examples of bullets fitting the G1 curve better (all those where it is dark black and the G7 is grey) who have i7 form factors closer to 1 than their i1. Your original belief was this would not be possible for any bullet. That an i7 of 1 at any velocity (a single data point) was proof it would follow the G7 curve perfectly, even without knowing what its values are at other velocities. Now you�re trying to sweep it under the rug with circular arguments�one was enough before, now we don�t have enough with six.

I'll boil it all down to a very simple yes or no question:

Do you still believe Berger should print .559 on the box?

Yes, but you don't seem to understand what it means where the black and gray lines merge. So if you weren�t confusing BC with form factor, what was this statement all about? How far away from the X-Axis the curve is (a form factor of 1.0 vs. 1.3) has no influence on the accuracy of your results. This is why you input the ballistic coefficient into your program, so it can scale the curve up or down and give you the proper results.

Scaling of BC is done by sectional density not by form factor.

Don�t get me wrong, guys like you do serve a useful purpose. MacLorry includes a few gems in his responses that might not come to light otherwise. The best is his �G1 and G7 Drag Profile� graph. With that gem in mind and paging through Bryan�s bullet data I found his BCs matched well with the 2 to 1 ratio of G1 to G7 for the middle two velocity ranges. That verifies the accuracy of the graph and also shows why most of Bryan�s data can�t help in picking between G1 and G7. That job is left to the low velocity range; often having just 1 or 2 data points. Ever hear of insufficient data?

As I�ve said before, I�ve used the Oehler Model 43 on several occasions going back 15 some years. There�s your instant ballistic coefficient machine; one for every shot and in real time. You obviously think you know more than MacLorry, but do you really think you know more about measuring BC than Ken Oehler?

But hay, don�t worry about your reputation, change your Huggies and put your ass out there again and again, it�s good entertainment seeing you get it handed back to you

MacLorry,

Thank you for your analysis of the G1 vs G7 BC based trajectories. I have responses to several of your statements.

I agree that the method described by Ken Oehler (deriving a G1 BC over long range based on tof) is the best way to derive a G1 BC, if you have to use a G1 BC. It's also the best way to derive a G7 BC. Since most modern projectiles are shaped more like the G7 standard, the G7 BC is a better representation of the bullets Mach dependent drag characteristics than G1. In other words, there is a 'best practice' for using the poor G1 standard, but it's still a poor standard. Granted the error between G1 and G7 is small, but it's still error, so why would you choose to use it when the G7 BC is known?

Regarding predicted remaining velocity. You're correct that the G1 BC, if derived from tof data, will produce inaccurate estimates of remaining velocity. You argue that it's not important to you and that's fine. It is important to some who are using hunting bullets with known terminal velocity performance thresholds. So again, you're not arguing that G1 is better, just that this particular downside is not important to you.

I will point out that Berger is not the only major bullet company who's adopted the use of G7 BC's. Earlier this year, Lapua began offering G7 BC's for their bullets as well:
http://www.lapua.com/en/products/reloading
I'll remind you that Lapua has tested all their bullets under radar and has a very accurate picture of each bullet's supersonic drag characteristics and has decided to represent them with G7 BC's. In other words, don't just take my word for it.

Aside from predicting trajectories, don't forget about the smoke and mirrors games that are possible when advertising different G1 BC's. A company can advertise an inflated G1 BC for a bullet that's technically 'accurate', but only at high velocity and of no use for predicting long range trajectories. The adaptation of G7 BC's cuts down on these kinds of uncertainties that add up to missed targets.

I will acknowledge that for most bullets, in most of the supersonic range of flight, the G7 vs G1 based trajectories are very similar (assuming you've averaged the G1 BC for just the right velocity range). But I ask, why would you knowingly choose to incur a small amount of error with G1 BC's when G7 BC's will allow for predictions with less error?

I'll close by saying that since my book has been available which provides accurately measured G7 BC's, the general trend has been overwhelmingly positive. I see and get a lot of good feedback from shooters who are using G7 BC's to hit targets with far greater regularity at far greater ranges than ever before. The fact that you might be able to get close with a G1 BC is one of the reasons why the paradigm shift towards a better (more representative) standard will take time, but I believe that the merits of G7 BC's are strong enough that the paradigm will continue to shift.

Take care,
-Bryan

very entertaining discussion. obviously some very informed people here. but what does all this mean to average joe hunter who just wants to shoot a deer at long range?

about 40 years ago in my home state of pa. i had the following experience.
while driving along a dirt mountain road i encountered a small group of guys.
they had two vehicles and one had two bucks secured to a roof rack.
i was familiar with shooting deer at distance and prided myself in having done some of that.
or so i thought. i was about to be educated about shooting deer at distance.
they were shooting a wildcat 7x300 weatherby with a 30" heavy barrel. the scope was a 15x unertle ultra varmit.
bullets were 162 hornady bt match.
the system was simple. they found deer by scanning the sidehills with large tripod mounted binnoculars. they used a ww2 surplus rangefinder for getting the distance. they had a click chart taped to the rifle stock. elevation was added according to the distance.
the key to their success was the person following the shot thru the binnoculars. corrections were made in the event of a miss.
its possible brian litz wasent born yet at that time.
i now know for a fact one of those guys couldnt have even read that book.
most of the bullets discussed here didnt exist either.
information was gathered by what was called mountain side testing. that settled all the arguments.
that system is still being used in that region.
it will work equally well wherever similiar conditions exist.
certainly the plains of wyoming pose a different situation.
the necessity of a first round hit can vary depending on the animal. antelope for example wont hang around like deer do.
it is also more important for some individuals than it is for others.
to my mind there is no right or wrong way. its what were having for supper that counts.

Bryan,

Thanks for stepping in and helping resolve this issue. I'm sure you didn't have the time to read all my posts on this topic, which has lead you to the misconception that I'm promoting G1 over G7. I assure you that's not the case. I'll summarize my position.

If a manufacturer is going to publish a single BC value for a given bullet, be it G7 or G1, my understanding of Ken's contention from his July 2007 Shooting Times article is that the best method to calculate BC is to measure the velocity near the muzzle and then the TOF over a long distance.

To test that contention without having shareable raw data to work with, I assume that either Berger's published G7 BC or Sierra's multiple G1 BC values more closely match their bullet's real retardation than the published G1 BC. That assumption is based on the fact that the shape of these VLD bullets is more similar to the G7 standard projectile, or that multiple G1 BC values compensate for the shape of the G1 standard projectile.

If Ken's method results in a more accurate BC value than the method currently being used, then a calculated equal TOF G1 BC relative to the G7 BC (or multiple G1 BCs) should also be more accurate than the published G1 BC.

Before starting this topic I opened the "Determining a Load's Maximum Range" topic where the consensus was that a load's maximum range is where remaining velocity drops to Mach 1.2. The few claims of accurate shots into the sub-sonic velocity range often got the BS card played. I understand there are exceptions, as in anything, but manufacturers should publish BC values that best represent their bullets for how shooters will most often use them.

I've posted downrange data for several bullets showing the equal TOF G1 BC better matches the published G7 BC than the published G1 BC does. My conclusion from such comparisons is that Ken's method would result in a better G1 BC value as well as a better G7 BC value if applied to the raw shooting data. Better as in predicting trajectory more accurately for how most shooters will use a given bullet.

What's really being compared are the methods for calculating BC from raw shooting data. That is, what's the accuracy of average BC values for several velocity ranges (velocity zone BC averaging) as compared to allowing nature to average BC values over an infinite number of velocity ranges by using TOF. If BC values represented a linear rate of change in retardation from velocity zone to velocity zone, then the velocity zone BC averaging method would produce the same results as using the TOF.

However, the rate of change in retardation is not linear with respect to BC across different velocity zones. For the G7 standard bullet with a BC of 1.000, and relative to Mach 2.23 the retardation is 1.414 times less at Mach 1.79 and 1.326 times more at Mach 2.68. Thus, averaging the BC values in these ranges doesn't accurately represent the true retardation from Mach 2.68 to 1.79 as each zone is being given equal weight. Rather than using complex methods to correct for non-linear retardation, simply using TOF over a long range allows nature to perfectly average the BC values.

I'm aware of Lapua using Doppler radar and have already talked about some of the problems with that method on this topic if it's done outdoors. Assuming they collect perfect data for a given bullet, they still have to fit it to the G7 standard to calculate the G7 BC. If they use velocity zone BC averaging to make that fit they will introduce the same errors as before. If they use TOF over a long range, they'll get a better BC value, but in measuring TOF, Doppler radar is no more accurate than other far less expensive methods.

The Military uses Doppler radar, but they don't try to fit the data to a given standard projectile, the actual bullet is the standard. It seems Lapua did the same thing and incorporated their radar data into their ballistics program. Only then is Doppler radar data better than BC methods of calclating down range values. That is, as soon as you fit the radar data to a standard bullet by converting it to a single BC value you lose all the data that doesn�t fit the drag profile of the standard bullet.

I assume Lapua used radar data in their ballistics program as they weren't publishing BC values for some of the bullets listed in their exterior ballistics program. When I used the output of their ballistics program to calculate an equal TOF BC, there was little difference in downrange data between their program as compared to another program when using that equal TOF BC value, which was surprising. Either there's no real accuracy advantage or they were really converting the radar data to a single BC within their program in order to work with existing algorithms. I might cover that in a future topic.

As for your book, I find it very useful and as another member reminded me, it's about the only independent source of BC data covering several manufacturers. I know your second edition is out and I intend to order a copy as soon as next year's budget is approved.

Now that Bryan has joined the topic I hope to resolve several issues. His first post was based mostly on the misconception that I'm promoting G1 over G7, which I'm not. See my response to Bryan.

Hopefully Bryan will respond to my post to him and we'll see if we can get agreement on some key points. Until such time as Bryan responds, or it becomes clear he's not going to, there seems to be little point in continuing to argue with you about the same things.

It's just hyperventilating over BC that makes little diff for those shooting 500 yards or less, but the forum is Long Range Hunting, so dudes here want to play at shooting to 1000 or even 1500 yards and beyond. Like you, many did that before the they had computers.

Having a buddy watch bullet vapor trails and correcting hold works great if your target doesn�t run off. To increase the odds from nothing to something at hitting game on the first shot some shooters play on their computers finding the best bullets for their guns. Don�t get me wrong, you learn lots playing with ballistics programs, but using them for first shot hits at long range is a crap shoot. Just a bit more or less wind puts the bullet off target and few if any can read the wind accurately at a 1000 yards.

Seen on TV where a marine sniper was trying to duplicate a famous long shot, but conditions were different and they couldn�t even see where their shots were hitting the side of a mountain. No vapor trails that day in the desert. Future guns may be equipped with radar bullet trackers

all of the above just illuustrates the importance of using a spotter for long range hunting.
no doubt conditions can make it difficult to see vapor trails. wind can also cause that.
there comes a point when we should just walk away unless spot and stalk is an option.
as you pointed out reading wind is difficult at best. im personaly of the opinion there are no real experts on that.
thermals are yet another rarly mentioned wind problem. they are often encountered when shooting across wide deep valleys.
as for an animal walking or running off, again using a spotter is an advantage. sometimes poor hits are what caused that. a lone shooter might be hard pressed to determine if that happened. certainly all shots should be followed up. but lets be honest about human nature.

It's understandable why you believe this topic is "just hyperventilating" and you're right, none of this makes much difference at ranges out to 500 yards. Difficult as it may be to make first shot hits on targets at long range, a number of people are interested in doing so and they want the most accurate data available for bullets they might use. That's why Bryan is measuring and publishing G7 ballistic coefficients for many brands of VLD bullets.

It would have been useful to discuss this more with Bryan, but it looks like his comment was just a drive-by that mostly missed the mark as a result of his misconception that I was promoting G1 over G7.

His post did serve a usefully purpose in helping resolve a key issue.



That's has been one of my major points from the beginning of this topic. The means I used to demonstrate the merits of Ken's method relied on using published BC values rather than raw shooting data. I believe the limitations of using such data lead to most of the disagreements. As Bryan confirmed, BC's produced by Ken's method would be more accurate particularly if used to produce G7 BC values for VLD bullets.

That was stated in my third post where I wrote the following:



I still feel there's room for improvement even if some manufactures are now using Doppler radar to calculate BC values. Regardless of the source of raw data, accuracy in calculating BCs comes down to the method that's used to process the raw shooting data. See the details in my response to Bryan.

In my first post I wrote the following:



This is confirmed by the following chart:



In the velocity range of Mach 2.6 to 1.7 (2900 to 1900 fps) there is no effective difference between G1 and G7.

Take any VLD or any other type of bullet's G1 BC and divide it by 2 to get the G7 BC. Plug the numbers into any accurate ballistics program and you'll find that for muzzle velocities up to 2900 fps and out to ranges where remaining velocity drops to 1900 fps there's no meaningful difference in predicted drop or velocity. For a G1 BC of 0. 502 and a G7 BC of 0.251 launched at 2900 fps JBM shows a drop difference of just 0.1 inch and a velocity difference of just 3.9 fps at 600 yards.

Beyond the velocity zone where G1 and G7 converge there's minimal difference between G1 and G7 from Mach 3 to Mach 1.2 (3350 to 1345) as can be seen in the following chart of larger scale (0 to Mach 4).



This chart helps explain why G1 has been used so successful for so long. For the vast majority of shooters it doesn't make any difference if they use G1 or G7 BC values even with VLD bullets. Load the Berger #24530 to 3000 fps and fire it out to 500 yards and the difference in predicted drop is less than 0.4 inches (0.08 MOA) between the published G1 and published G7 ballistic coefficients. At that range the difference in predicted velocity is just 18 fps, which is within the variability of premium ammunition.

Some argued that the Mach 1.2 low velocity limit was my own invention despite having arrived at that number by consensus in another topic. In reality, Mach 1.2 is well known as the high limit of the transonic velocity zone as can be seen in the following quote from Wikipedia External Ballistics.



Regardless of the reliability or accuracy of information on Wikipedia, the quote confirms Mach 1.2 was not something I contrived on my own to make the data support my argument. The reason most long range shooters stay above Mach 1.2 is also supported in another quote from Wikipedia.



The useful range of a load is determined by where the remaining velocity drops to Mach 1.2. Those who want to go further should use larger caliber bullets if the Lapua Doppler radar data is to be believed.

Only long range shooters need G7 BCs and only for VLD bullets as most other bullet types fit G1 as well or better than G7. If you look at the number of viewers there are for this forum as compared to other hunting forums you soon realize that long range shooting is a niche market. Even within this forum many seemed drawn to this topic more by the colorful put-downs than the content.

Perhaps Large bullet manufactures don't want to confuse customers with notations like G7 that apply only to a minority of bullets, and Sierra handles the problem by publishing multiple G1 BC values. Maybe I'm wrong, but I don't expect the paradigm shift Bryan talks about will happen anytime soon outside the long range shooting niche.

And this is why I enjoy listening to fingernails on a chalkboard more than having a technical disagreement with a non-technical person. When one lacks fundamental understanding of the subject material, he will also fail to recognize the errors in his own argument and truly have no clue whose �ass got handed� to whom.

It�s �about� the fact I understand how ballistics programs work you you clearly do not. A typical program does its calculations based upon a particular drag curve. If a bullet�s form factor for that drag curve changes with velocity the program will not give accurate predictions for that bullet. If a bullet�s form factor remains constant over the velocity range in question, whether it is 0.5, 1.5 or 1.0 matters not�the program will give accurate predictions for that bullet.

The fact a single BC number is entered in lieu of a separate SD and form factor is immaterial. The SD will remain constant throughout the flight and does not affect the drag curve of the bullet. If it matches or not is dependent upon the bullet�s form factor remaining constant throughout the flight. Not near 1.0. Constant. At whatever value.

Wrong. You can scale BC by sectional density but that has nothing to do with this discussion. This discussion is about fitting a drag curve. I�ve explained this to you several times now. Bryan�s book has hundreds of those charts in it to graphically represent my explanation�in those charts to determine which curve a bullet follows best, they are scaled to the form factor such that all data points for each bullet fall on/around each curve instead of all above or all below the curve for a bullet with a form factor different than 1. How they match the shape of the curve is what is important, not how far above or below they would be without scaling.

If you can�t understand that, I can be of no further help to you. You have been led to water. Drink.

First, no amount of data or lack thereof changes the fundamental concept outlined above. Second, you are not remotely qualified to determine the sufficiency of Bryan�s data.

If that is true, then you know it does not give you an instantaneous BC at a particular velocity and location. It needs to measure the bullet over a distance and give you an average for that distance. If you had actually ever set one up I think you�d remember that.

Ken has made no statement here for me to disagree with. MacLorry�s application of whatever the article actually said was full of errors and misunderstandings. That�s why I asked for a link to the article in the first place�the errors are likely entirely MacLorry�s doing through misapplication and/or reading things into it that weren�t specifically said by Ken.

It was MacLorry who concluded Bryan�s .545 BC for that bullet was �inaccurate.� Not Ken. In fact, I�m reasonably confident Ken would acknowledge that if that method is used at two radically different velocities for a bullet which is a poor fit to the G1 curve, two significantly different answers will result. It�s really quite simple.

Agreed. You made several mistakes but won�t admit it. Relentless pounding from me isn�t going to change that. I have more important things to do with my valuable time.

Hopefully when Bryan has more time he will read the entire thread and respond in detail.

Maybe he�ll even agree with you on the �key point� that he doesn�t know what the word accuracy means.

Or he�ll agree with you on the �key point� which caused you to start this entire thread in the first place�that the reason he came up with �wrong� BC for that bullet was that his methodology was flawed. Not that you looked at it over a different velocity range which will naturally give a different average G1 BC for such a bullet.

Maybe, but I doubt it.

Mac,

You'll find I don't do 'drive by'. My absence has been due to the fact that I responded to this thread just before leaving for a week-long shooting tournament; I got to the range late that night. The match was delayed yesterday due to rain so we had a late finish and I didn't check this thread. Today we finished on time so this evening is the first chance I've had to re-visit the conversation.

Sorry if I mis-understood your point in the first thread. I can see clearly now that you're not disagreeing that G7 referenced BC's are superior to G1 BC's for modern long range bullets. It seems your major concern is the method by which BC's are determined. We agree that the method that Ken describes is good, but possibly for different reasons.

I like the tof method because it's far more practical than measuring downrange velocity (chrono strikes are expensive, etc). Also, maximizing the range over which you measure tof is important for reducing experimental error. Both these reasons have to do with practicality. If you have methods/techniques that you have found work better for testing large numbers of bullets for BC I would be interested in hearing your results.

You indicated not having the second edition of my book yet. There's an addition to the BC chapter that is relevant to this discussion; here�s a summary. An experiment was conducted as follows: chronograph at the muzzle, and a tof sensor at 1000 yards in addition to a special chronograph at 1000 yards. For each shot I derived a G1 and a G7 BC from both the tof and the velocity decay data. Summary of results: the bullet that looked most like the G7 standard (Berger 155 VLD, Dyer 155 HBC) had derived G7 BC's there were nearly identical from the tof and velocity data. However, the G1 BC's were quite different for the tof vs velocity data. These �G7� bullets had drastically different G1 BC�s depending on if you derived them from tof or velocity. Bullets that were shaped a little different from the G7 standard (examples are tangent ogive bullets like the 155.5 FULLBORE and 155 SMK) had G7 BC�s that were similar, but not quite the same, and G1 BC�s that were still quite different. The conclusion from this data which I find interesting and relevant to this discussion is that: when a bullet is shaped similar to the standard projectile for which you�re referencing it�s BC to, the BC you derive will be less sensitive to the method used to determine it.
I think this addresses your statements about BC testing methods, and the places in which G1 and G7 BC�s are similar, but I�m not sure. To be honest, it�s been difficult for me to nail down what your position is exactly. You said that you aren�t contesting that G7 BC�s are better for LR bullets than G1�s, but you disagreed with my assessment that the paradigm toward G7 BC�s will continue. This is confusing.
I agree that the method Ken described for determining BC�s from raw data is a good method for both academic and practical reasons. But this does not support the statement from your original post that:
The drag characteristics of supersonic flight are most definitely sensitive to bullet shape! You point out that for a specific velocity range the curves are similar in shape, but they diverge at faster and slower speeds for the different (G1 vs G7) shapes. Most of our LR bullets, even those without secant ogives, are much better matches to the G7 standard than G1. In light of this fact, I find it hard to accept your above quote, as well as the claim that you�re not advocating G1 as a reasonable standard for modern long range bullets.

I think you give �the industry� too much credit when you imply that their reluctance to adopt the G7 standard has anything to do with scientific reasons, and more to do with marketing. Of course it�s possible for someone to advertise a G1 BC that was averaged for the exact velocity range that a shooter needed it for, and for a shooter to hit a target with that BC. However, I ask, what happens when the bullet doesn�t stay within that speed band? The prediction goes to crap, that�s what.

In closing, I�m not interested in arguing about the best way to manage the problems of a clearly non-representative (G1) standard. If you want to go on talking about the best way to use G1�s for long range bullets, and postulate that they might be effective it used properly (which the industry has clearly demonstrated that they won�t), then I won�t comment. I also hold to my belief that in time the paradigm will shift because using representative standards is less sensitive to the methods used to derive BC�s, and therefore more useful for doing predictive analysis.
One further comment to those who commented on the �shoot and spot� hunters. No doubt this is an effective method for getting on target at long range: make a somewhat educated guess; shoot; spot the miss, and adjust for the next shot. Provided the game animal doesn�t spook and prevent a follow up shot, this can work. However, this isn�t what this conversation is about. This conversation is about representing the trajectory of the bullet before it�s fired so that a first shot can be on target. Any idiot with a spotting scope can get a shooter on target. But it�s the science of ballistics and the shooters ability to apply it that will enable first round hits. This isn�t meant to be an insult to anyone, just a definition of the purpose of ballistics; which is to be predictive, not reactive.

-Bryan

Bryan,



Glad to hear that. My comment was based on your post count of 17, now 18, since 04/21/09. It seemed unusual that you commented at all, and after two days, I expected you weren't going to return and the topic was done.



It depends on your budget. I've had the pleasure of seeing some really well equipped testing ranges and the data they produce. Take a look at the published multiple BC values for Sierra's HPBT MK #1570. Above 2500 fps they assign a G1 BC value of 0.527 and below 2500 down to 1800 fps they assign a value of 0.522. That's less than a 1 percent change in BC value. I know you understand the quality and volume of data needed to establish with a high degree of confidence that such a small change is real.



I look forward to seeing the details, but the results don't surprise me.



For an actual bullet that exactly matches the drag profile of a standard bullet you can calculate the BC at any velocity and it will be correct for any other velocity. That was the driving force behind The Reverend Bashforth's invention of standard projectiles. In the real world and with the precision of modern instruments it's become obvious that few bullets actually match any standard projectile perfectly.



For the velocity range of Mach 2.6 to 1.7 (2900 to 1900 fps) the G1 and G7 drag profiles are nearly identical when scaled at a 2 to 1 ratio for G1 to G7, respectively. You can see this 2 to 1 ratio holds true to within less than 1 percent in the experimental drag and BC data of your book in the Mach 1.79 and Mach 2.23 zones. Even within the Mach 2.68 zone the 2 to 1 ratio holds true to within 2.5 percent. Factor in measurement errors and the 2 to 1 ratio between G1 and G7 from Mach 2.68 to 1.79 holds amazingly well. The Mach 1.34 zone is where G1 and G7 diverge, but as stated in the link to Wikipedia, the transonic range starts at Mach 1.2. It's in this context that my following statement must be read.



Hopefully you won't argue the term "insensitive" is more exact than what your own data demonstrates, or that the term "supersonic" means any speed from Mach 1 to the speed of light. I assume you picked the four velocity zones for your experimental drag and BC data based on the velocity ranges that concern long range shooters. I did likewise.



Perhaps you see it differently, but long range shooting is a small part of the sum of all shooting sports. Major manufacturer's offer bullets for all these segments such that only 23% of Hornady bullets could be described as long range. For Remington it's just 16% and 18% for Nosler. While 43% of Sierra bullets could be described as LR, they have their own method of using multiple G1 values. If Sierra splits velocity zones with less than a 1% change in BC, they might find that multiple G7 values were needed for their LR bullets, but that multiple G1 values would better fit their other bullets as even Berger list N/A for the G7 BC for many of their bullets.

How then should a Major manufacturer label their bullets that doesn't cause confusion for the majority of their customers? It's in that context that I wrote the following:



Hopefully, you can now accept my statement that I'm not promoting G1 over G7.

What I really want to discuss I stated in my first post to you, which is as follows:



While I accept the claim that your testing produces values repeatable to within plus or minus 1 percent, I question the accuracy of the resulting BC values because of the velocity zone BC averaging method you are using in your book. The following diagram illustrates the error of giving equal weight to zone values when in fact the change in retardation rate is non-linear and non-symmetrical from zone to zone.



A quick and crude analysis suggests an error of up to 4.8 percent is being introduced by averaging the form factor or BC values in the four zones using equal weight for each zone. Yes, Robert McCoy and others did the same thing, likely because such a small error in BC is unimportant outside long range shooting. To claim accurate BC values to within plus or minus 1 percent you may want to do some more research into how to properly weight each zone.

With your velocity zones from Mach 2.68 to 1.34 you've selected a velocity range over which to average BC values. If you use TOF over that same velocity range you'll get the same BC values minus the weighting error. If the actual bullet doesn't match G7 well through transonic and into subsonic velocities it doesn't matter which method you use as both will result in the same degree of error. All you can do is assume the actual bullet matches G7 well enough. In fact, you're already making that assumption given you have almost no data points at Mach 1.2 and below.

I believe that one of the reasons you picked the method documented in your book is to document which standard projectile a given bullet best matches. You can still do such analyses and also calculate the TOF BC from the same raw data and see how close it compares. If you find the difference is consistently more than 1 percent you might consider modifying your methodology and go with the TOF value as the final published value. If there's little difference, then you can tell critics like me that you've used two methods to double check your BC numbers. If you really want to impress critics put your raw test data on the CD that comes with your book.

Sorry if I've ruffled any feathers. It's a courageous act to publish any technical book on the subject of exterior ballistics and show your methods and data points, but that's what's necessary if you want to change the paradigm.

there is absolutly no doubt we are light years ahead of where we were 40 years ago. that thanks to minds like brians who have
created better bullets, powders, etc etc.
also for creating the information for applying these improvments.
some of us seem to crave more and more technichal information.
some of us want just enough to get the job done.
i happen to fall into the latter categorie.

id appriciate being alerted when somebody sets a new 1000 yd world record without having fired sighter shots. especially a record for high score.
im very much aware of the importance of first round hits in some types of events.
lets not forget much of the data discussed here is computer generated.
computers arent 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? ive named just two.
not to worry, the idiot, i mean the spotter can help you out on that.
now if we could just figure out what to do in the event he dosent stand still long enough for us to hit him.

hopefully techknowledgy will find a solution.

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.



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

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.



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.

Packing up the hotel now, preparing for the last day of the tournament then the long drive home so I won't be able to get back to this thread for a day or two, but I will comment.

Bryan,

Sorry to be such a pain in the ass. Some of us have too much time on our hands in the summer and end up imposing on others busy pursuing their careers. You could be correct that the discrepancy I'm seeing is the result of the TOF method optimizing the BC to match the trajectory, while your method better matches remaining velocity. Without a source of sharable high quality raw shooting data there's no way to pin this down further.

I have argued that optimizing for trajectory is better than optimizing for remaining velocity, but as you can see from many other comments in this thread, that's a subjective discussion that leads to colorful put-downs rather than a definitive resolution.

I have shown in an easily verifiable chart the uncanny 2 to 1 relationship of G1 to G7 from Mach 2.6 to 1.7. That chart gives insight into why G1 is as good a predictor of VLD bullet trajectories as it is, and also shows why testing must be done outside this velocity range to detect which drag function best matches an actual bullet.

I hope you don't feel this exchange has been a complete waste of your time, but likely it will become so without a source of raw shooting data we could both work from. I'll leave it at that.

Best wishes,

Mac,

I've spent quite a bit of time running numbers and thinking about your argument for equal tof G1 BC's. To sum up my conclusion in words, I can say the following;

The fact that an 'equal tof' G1 BC can match the G7 based trajectory more accurately than the published G1 BC is a case of two wrongs making a right.

The fundamental fact that the G1 standard drag curve is so different from the bullet in question means that when the raw data is reduced correctly, the resulting predictions should be inaccurate (first of two wrongs). Finding a way to make the G1 and G7 based trajectories match by 'tweaking' the G1 BC to match the G7 tof is the second wrong which is required to correct for the first one.

Furthermore, don't forget that the range (or lower velocity, or tof) at which you choose to identify the equal tof G1 BC is completely arbitrary (just like the windows I defined). You can come up with an equal tof G1 BC that is 'optimal' for a given window, but has more error than the published G1 BC at ranges outside that window.

To investigate the matter further, I ran the following comparisons. Using my published averaged and stepped BC's, the following trajectory metrics were produced:
*Berger 6mm 115 grain VLD, 3000 fps MV, standard sea level ICAO atmosphere, 1.5" sight height, 1000 yards.

G7 average (drop/tof)
275.5"/1.408s

Stepped G7 BC (drop/tof)
275.7"/1.410s

G1 average (drop/tof)
279.4"/1.418s

Stepped G1 BC (drop/tof)
277.8"/1.419s

Of the above 4 predictions, I consider the stepped G7 to be the most accurate representation of the bullets' true trajectory. Second most accurate would be the average G7 BC trajectory (only -0.2" error). Then the stepped G1 BC at +2.1" error. Finally, the average G1 BC is the least accurate at +3.3" error.

What strikes me about the above comparison is the inconsistent effect that tof has on drop. For example, the difference in tof between the stepped G7 and the average G7 is 0.002s, and the difference in drop is only 0.2". However, the difference between the stepped and averaged G1 is only 0.001s in tof, but the difference in drop is 1.6". In other words, the tof and drop aren't correlated as one might expect when you compare trajectories based on averaged vs stepped BC's.

The inconsistency above can be explained in the following way: Although the tof may be the same from point a to point b, it is possible for the drop to be different based on the shape of the drag curve. And this is the best way I can describe why the equal tof method you're advocating is not a better way to reference BC's to standard curves when the shape of the curve is known. That last part is an important distinction. If you don't have any information about the shape of the curve (as in the case when you only measure overall tof), then you only have one single tof, no knowledge regarding the shape of the curve, and all you can do is derive a BC based on the single tof. In that case, I agree with Ken, it's the best you can do. However, I specifically designed my test procedure to measure tof in several increments so that I would have information on the shape of the actual bullets drag curve. This allows for the comparison/averaging practice that you say produces less accurate (predictive) BC's. In fact, the BC's that are defined with knowledge of the drag curve are more accurate than BC's that are defined without knowledge of the drag curve.

Thinking back over this debate, it's very easy to understand why you would believe so strongly in equal tof BC's. The fact that they have less error when compared to more appropriately referenced (G7) BC's seems to be compelling evidence that it's a better way, and if the original G7 BC's were defined based on a single tof alone that they would also be improved. But for reasons I described above, it's a case of two wrongs making something closer to right, for a specific case. If all you care about is the result at a particular range, and you don't have a way to calculate G7 based trajectories, I can certainly understand why you might do it this way. However, I cannot butcher the ballistics in that way for several reasons.
One; I simply know it's not the right way (after all, I paid a lot for my college education! Why would I blatantly do something I know is wrong?)
Two; my results have to be able to stand up to scientific scrutiny by my peers. If I took the 'two wrongs make a right' path, my methods would be identified as such and my peers would be the ones explaining to me on some internet forum what's wrong with my methods.
There are other details which are variations on the above two major reasons why I cannot reduce the data as you're suggesting. Again, if you choose to do so, feel free. I understand your reasons and in certain circumstances the error would be negligible enough that it would hurt you too much.

-Bryan

Bryan,



The actual bullet has its own drag curve that matches neither G1 or G7 perfectly. However, unless the published G7 BC poorly represents the actual bullet's drag curve, then the G7 BC is a valid proxy for the raw shooting data for the purpose of analysis. To improve that relationship, the bullet I picked for my original post was a good match for G7.

If you are going to publish a G1 BC for the bullet's you test they should be as accurate as possible. However, what's meant by accurate is subjective being that different BC values better match remaining velocity or they better match trajectory over the most useful velocity range.

Without raw shooting data to work from I don't consider using the G7 BC to finding a G1 BC that more accurately matches the trajectory of the G7 BC to be �two wrongs� for the purpose of analysis.

I'm not suggesting the equal TOF G1 BC is a substitute for the published G7 BC. How could it be if the G7 BC was the source of the data used to calculate the equal TOF G1 BC? I believe your �two wrongs� comment is based on the false assumption that I'm promoting G1 over G7.



Were getting back into the subjective arguments. The velocity range is not completely arbitrary, in that it represents the most useful velocity range for most shooters. That is, a MV as high as a particular bullet is likely to be fired down to Mach 1.2, where Lapua Doppler radar data shows the accuracy of most bullets degrades. I linked to it some posts back.

In a prior post I used an equal TOF G1 BC calculated for 3500 fps and showed a comparison with the published G1 BC relative to the trajectory of the published G7 BC at 3000 fps and 2500 fps. In all cases the equal TOF G1 BC matched the drop of the G7 BC at more ranges than the published G1 BC down to Mach 1.2. Here's that data.



My conclusion from such comparisons was that there was a flaw in your method. I no longer think that's the case, but that no single BC value, G1 or G7, can best match an actual bullet's remaining velocity and also its trajectory. A BC value can be optimized to match remaining velocity or it can be optimized to match trajectory or it can be a compromise between the two. The difference between these two BC values is about 2 percent, which is beneath the notice of most.



I did use the published G7 data for the Berger 6mm 115 grain VLD and made each velocity ranges equal in size. The G7 BC steps are then 0.284 between 3250 and 2750 fps, 0.281 between 2750 and 2250, 0.275 between 2250 and 1750, and finally 0.275 between 1750 and 1250. The MV was 3250 and I ran the test out to 1385 yards where remaining velocity of the stepped BC is 1252 fps. The calculated equal TOF BC is 0.280 compared to the published BC of 0.279. Relative to the stepped BC, the equal TOF BC is slightly closer for drop all the way out to 1600 yards where velocity is subsonic.

I tried this same technique for several bullets and the more variation in BC from velocity zone to velocity zone the better the equal TOF G7 BC matches the stepped G7 BC as compared to the average G7 BC.

I made the same assumption about Sierra's stepped G1 BC values being the most accurate representation of their bullets' true trajectory and posted the following on 6/17/11.



Surprisingly, the equal TOF G7 BC better matched remaining velocity than the published G7 BC. The weakness in this comparison is that mostly likely two different lots of bullets were used and I know from personal experience that manufactures make subtle changes in their bullets and don't change the BC values.






Regardless of the shape of the drag curve, drop is always closely related to TOF. Apart from a slight aerodynamic lift, the bullet is accelerating away from the line of departure at a constant 32.174 ft/s^2 for a horizontal shot (standard gravity). TOF represents the average velocity of the bullet between two points and average velocity is the result of the initial velocity and the average retardation of the bullet. It's not possible for the drag curve to change without changing TOF, and thus, drop changing in proportion. An equal TOF BC will always optimally match the trajectory of an actual bullet to a given standard drag curve over the velocity range it's calculated for. If the velocity range is the likely maximum of a given bullet down to Mach 1.2, the equal TOF BC is optimized for the most useful velocity range of the bullet, and thus, for most users. Only when you consider ranges where the bullet goes trans and subsonic is your method more accurate, and I wrote in my original post that Berger was obviously concerned about the subsonic velocity range. We've come a long way around only to verify what I wrote in the opening post of this thread.

Of course, what the most useful velocity range is, is subjective. I can accept that it's not the best BC value to publish without knowing more about how a given bullet will be used. It might be better for loaded ammo where the MV is known.

*emphasis added

I think we understand each other's positions here for the most part. I think you would agree that the difference between our methods is very small (you've identified a ~2% difference). I also think we agree that no matter what method is used to define BC, if the shooter employs the bullet in a different velocity range than what the BC was assigned for (which will be the case more often than not) using either method, error will be incurred which results from the bullet flying in a different velocity band. At that point, the 2% difference between methods becomes less critical.

I'm currently working on developing a ballistics program for mobile devices (deployable on android, iPhone, iPad, iPod, Windows Mobile, and BlackBerry) which will have the option of using standard G1 or G7 referenced BC's, as well as the option to use the custom drag curve of a particular bullet. This capability will end all the discussion about the best way to define and use BC's because none of the methodology 'judgment calls' will apply. The curve will be a valid representation of the specific bullet's drag at all speeds, and no methods of averaging form factors or BC's will be necessary.

I won't have much more time to devote to this thread after this evening; it's back to work for me tomorrow. I hope my involvement has helped to explain why I do things the way I do.

Thank you for keeping the discussion civil.

-Bryan