#5354986  06/21/11 04:52 PM
Re: Bullet Shape and Supersonic Flight
[Re: MacLorry]

Campfire Ranger
Registered: 12/09/04
Posts: 1849
Loc: Everett, WA

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 And this is why I enjoy listening to fingernails on a chalkboard more than having a technical disagreement with a nontechnical 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. So if you weren’t confusing BC with form factor, what was this statement all about? 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. Scaling of BC is done by sectional density not by form factor. 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. Ever hear of insufficient data? 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. 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. 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. You obviously think you know more than MacLorry, but do you really think you know more about measuring BC than Ken Oehler? 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. 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. 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.

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#5354988  06/21/11 04:53 PM
Re: Bullet Shape and Supersonic Flight
[Re: MacLorry]

Member
Registered: 04/21/09
Posts: 25

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 weeklong 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 revisit the conversation. Sorry if I misunderstood 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: 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. 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 nonrepresentative (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

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#5355811  06/21/11 11:04 PM
Re: Bullet Shape and Supersonic Flight
[Re: BryanLitz]

Campfire Guide
Registered: 06/25/10
Posts: 3143
Loc: polar orbit

Bryan, You'll find I don't do 'drive by'. 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. 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. 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. 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. … I look forward to seeing the details, but the results don't surprise me. 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. 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. 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. 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. 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. 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. 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. 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: 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. 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: 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 nonlinear retardation, simply using TOF over a long range allows nature to perfectly average the BC values. 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 nonlinear and nonsymmetrical 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.

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#5359792  06/23/11 09:44 AM
Re: Bullet Shape and Supersonic Flight
[Re: MacLorry]

Member
Registered: 07/13/10
Posts: 218
Loc: east central fl. /n/c pa.

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.

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#5360075  06/23/11 11:24 AM
Re: Bullet Shape and Supersonic Flight
[Re: yobuck]

Member
Registered: 04/21/09
Posts: 25

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 mismatches 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 8ball. 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 airtoair 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 ‘doable’ from all angles, while sacrificing the least amount of accuracy. I wouldn’t be happy that my method was right until it had been verified by alternate testing methods. This verification was completed and documented in my book. The test involved shooting thru a chronograph, and a screen at 200 yards placed above the line of sight, while sighting on a 1000 yard target. Based on the muzzle velocity and placement of the shots above the line of sight at 200 yards, a standard ballistics program was used to estimate the fall of the shots at 1000 yards using my averaged G7 BC’s which were derived with my standard method. The experiment showed that the shots landed within +/ ONE INCH from where the program predicted them to fall. This test was conducted with two rifles and two bullets with the same result. For me, this test was the final verification that my method was producing BC’s that were accurate, meaning that they were useful for predicting trajectories at long range. Another account of my method being verified was the Phoenix test which is documented in the second edition and that I described in an earlier post. Even though a complete description of my methods, there origins, verification of their validity was published, I still knew they would be challenged. That’s OK, scientific conclusions have to be able to stand up to scrutiny. However in this case I don’t think that my actual methods were questioned. Rather, a misunderstanding about my method was challenged. I hope the explanation and clarification that I provided here has addressed your concerns (Mac), in particular your misunderstanding that my averaging method implies a retardation that is linear with velocity (or Mach). Such a method certainly would be wrong, but that’s not what I’m doing at all. On the other discussion regarding paradigm shifting; I agree that long range shooters are a vast minority in the wide world of shooting in general. However, long range shooters are the ones who care about, and need accurate BC’s most of all. That’s why I think the evolution to G7 referenced BC’s will take place; because those who really need and care about them recognize they’re merit. So what if 90% of other shooters don’t notice, they didn’t care about the original BC’s in the first place. But this is a speculative conversation with no clear right or wrong answer; time will tell. Lapua’s choice to adopt G7 BC’s is encouraging. Maybe Hornady, Sierra, Nosler, etc will never change from G1 BC’s. But if all the serious long range shooters are using the G7 BC’s I’ve provided and ignoring the advertised G1’s from the manufacturers, I’d say that counts as significant paradigm shifting. In other words, it’s not what the companies put out that matters, it’s what serious shooters use to hit targets that matters. computers aren’t savvy enough to know you left your ammo in the vehicle last night and it went down below zero. or your chart being established for 5000 ft. but were actualy 6000 right now i think. could those type things account for a first round miss in a hunting situation? Yobuck, You’re right about the fact that computers cannot do our thinking for us (thankfully). The computer program is there to give outputs based on inputs. If YOU know the effects of having your ammo frozen, you can enter the altered muzzle velocity into the program and the effect will be accounted for. Likewise, if you’re actually at 6000 feet DA and you tell the computer that, it will accurately account for that as well. The results of a computer prediction are only as accurate and complete as the inputs. You can’t expect the ballistics program to tell you what time the sun sets, the air pressure in your tires, the point of impact shift your woodstocked 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

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#5361663  06/23/11 10:09 PM
Re: Bullet Shape and Supersonic Flight
[Re: BryanLitz]

Campfire Guide
Registered: 06/25/10
Posts: 3143
Loc: polar orbit

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 nonleaner, nonsymmetrical 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.

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#5361878  06/24/11 04:22 AM
Re: Bullet Shape and Supersonic Flight
[Re: MacLorry]

Member
Registered: 04/21/09
Posts: 25

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.

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#5367368  06/26/11 07:37 AM
Re: Bullet Shape and Supersonic Flight
[Re: MacLorry]

Member
Registered: 04/21/09
Posts: 25

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

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#5368137  06/26/11 01:28 PM
Re: Bullet Shape and Supersonic Flight
[Re: BryanLitz]

Campfire Guide
Registered: 06/25/10
Posts: 3143
Loc: polar orbit

Bryan, 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. 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. 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. 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. Of the above 4 predictions, I consider the stepped G7 to be the most accurate representation of the bullets' true trajectory. 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. 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. . 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. 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. 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.

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