BALLISTIC COEFFICIENTS/Twist Rates

Topshot

Well-Known Member
Kevin,
Always interests me how B.C.'s are derived.
When you did the testing. How was the B.C. calculated? Time of flight with multiple chronographs?
Need good equipment with such a short T.O.F. hey.

Any advice on the best method for a mug shooter could work out his own B.C. results.
I have been looking at a couple of projectiles that have a listed B.C. far lower than they should just looking at the bullet and would like to run a few tests on them.

Kevin Thomas

Well-Known Member
Topshot,

In a nutshell, it's nothing more than firing the bullet in question over a measured distance and determining the drag deceleration over that span. The rate at which the bullet sheds (or retains) its velocity is compared against a standard bullet for whichever drag model you're using. In most cases in the industry, this will be the well known G1 model. Thanks to Bryan's efforts, and the support thrown to his ideas by Berger, we're now seeing the G7 model (far better suited to many of today's very streamlined boattail bullets) used on a regular basis. Using a better suited model to derive a BC results in notably more accurate long range predictions in computer programs and the like. As I said, that's the Reader's Digest version. There's a range of considerations that goes into this process, including the distance over which the measurments are taken, velocity ranges the bullets are fired, and as we've mentioned, sometimes twist rates involved. We would normally shoot 50-60 rounds at various velocites, going from extremely high velocity, to loads that were on the verge of going transonic within the span we were measuring. You see some interesting results. And, just like velocity, BCs will show Highs, Lows, Extreme Spreads and Standard Deviations within such testing. The BCs that are eventually published by the maker are roughly the average of this testing.

The other way of doing this is the method that Lapua now uses; Doppler radar tracking of bullets. This results in absolute "true" data, and allows the ballistician to see what the bullet is doing throughout its flight, not just a snapshot of it as it passes the two known reference points (skyscreens) in the straight TOF method. While the data is far better, as you can imagine, the equipment isn't available to the average reloader. The units themselves cost several million dollars and an extensive support team to operate. I've been priviliged to shoot data this way at Yuma Proving Grounds, but outside of military facilities, there's not many private concerns that could ever fund this sort of thing.

An abbreviated version here, but I hope it helps!

Kevin Thomas
Lapua USA

Topshot

Well-Known Member
Thanks Kevin,
Good explanation. Not much hope then of the average mug shooter doing his own tests and coming up with any useful results?

If you just wanted to compare two different bullets of the same weight out of the same rifle. How would you do it?

J E Custom

Well-Known Member
Topshot,

In a nutshell, it's nothing more than firing the bullet in question over a measured distance and determining the drag deceleration over that span. The rate at which the bullet sheds (or retains) its velocity is compared against a standard bullet for whichever drag model you're using. In most cases in the industry, this will be the well known G1 model. Thanks to Bryan's efforts, and the support thrown to his ideas by Berger, we're now seeing the G7 model (far better suited to many of today's very streamlined boattail bullets) used on a regular basis. Using a better suited model to derive a BC results in notably more accurate long range predictions in computer programs and the like. As I said, that's the Reader's Digest version. There's a range of considerations that goes into this process, including the distance over which the measurments are taken, velocity ranges the bullets are fired, and as we've mentioned, sometimes twist rates involved. We would normally shoot 50-60 rounds at various velocites, going from extremely high velocity, to loads that were on the verge of going transonic within the span we were measuring. You see some interesting results. And, just like velocity, BCs will show Highs, Lows, Extreme Spreads and Standard Deviations within such testing. The BCs that are eventually published by the maker are roughly the average of this testing.

The other way of doing this is the method that Lapua now uses; Doppler radar tracking of bullets. This results in absolute "true" data, and allows the ballistician to see what the bullet is doing throughout its flight, not just a snapshot of it as it passes the two known reference points (skyscreens) in the straight TOF method. While the data is far better, as you can imagine, the equipment isn't available to the average reloader. The units themselves cost several million dollars and an extensive support team to operate. I've been priviliged to shoot data this way at Yuma Proving Grounds, but outside of military facilities, there's not many private concerns that could ever fund this sort of thing.

An abbreviated version here, but I hope it helps!

Kevin Thomas
Lapua USA

Thanks Kevin !!!!

Has there been any attempt to change the standard model from G1 to G7 in the bullet industry ?

I realize that the numbers of the G1 BC look better but they are not accurate enough for the
long range shooter and in order to have a accurate drop table and BC we have to shoot
over the course that we intend to hunt to be accurate.

Also is there a more accurate model or should the models be Bullet type specific (Spitzer flat
base, Boat tail match, VLD and so forth). After all there are not that many different styles of
bullets an accuracy of numbers is what we need.

The long range shooter is all about accuracy in every aspect and have forced bullet makers to
improve there bullets so why not improve the system for comparing them and predicting there
performance more accuratly.

J E CUSTOM

BryanLitz

Has there been any attempt to change the standard model from G1 to G7 in the bullet industry ?

I've written each of the major bullet companies, asking them to consider changing the standard reference to G7 BC's. So far no takers. I can see their point that it would cause confusion with the 90% of shooters who barely know what BC is to begin with. It all that confusion worth it to satisfy the top 10% of technical shooters who understand? I think the paradigm has to change and the confusion is a growing pain, but I also understand why their reluctant. There's also the marketing aspect of surrendering a higher (looking) BC for a lower one.

It used to be hard to find a ballistics program that could use G7 BC's. However all the new programs coming out have G7. I consider that a good sign that we're moving in the right direction but it's going to take time.

It would be possible to have a different standard reference projectile for all bullet types (G1, G2, G5, G7, G8, etc) all have their place, but some of them are quite similar to each other. The difference between G7 and G5 is very difficult to resolve. I chose G7 as a standard because it fit long range bullets best overall, and long range bullets (long ogives and boat tails) are the types of bullets we care most about having accurate numbers for.

I was turned down when I suggested to the other companies that we should move to a different standard. Maybe over time, if their contacted by enough customers with the same request, it just might happen.

Good shooting,
-Bryan

PS. I should add that there are several small bullet companies (other than Berger) who are adopting the G7 standard including:
http://www.bibullets.com/new-products/
and
http://precisionballisticsllc.com/default.aspx

LouBoyd

Well-Known Member
Thanks Kevin !!!!

Has there been any attempt to change the standard model from G1 to G7 in the bullet industry ?
(sni)
The long range shooter is all about accuracy in every aspect and have forced bullet makers to
improve there bullets so why not improve the system for comparing them and predicting there
performance more accuratly.

J E CUSTOM

As soon as you apply any "G coefficient" to a bullet reducing the information about the bullet to a single number (or even a few numbers) you have thrown away whatever useful information has been gathered about a specific bullet though testing. It's sort of like fitting clothing with the S M L XL XXL
designations but ignoring the variations of individual body parts.

G7 numbers are not inherently better than G1 numbers. They simply are a better but still limited model for slender boatail bullets typically used for long range shooting. G1 coefficients may be better for the bullets used in 100 yard benchrest and for small game hunting. Most 22LR bullets fit the G1 profile pretty well as do most bullets used for black powder rifles.

G1 and G7 coefficients are a handy way to compare bullets, and they are a useful marketing tool, but both are a detriment to precise ballistic calculations. What's is needed for precise ballistic calculations is to throw out all ballistic bullet models and simply measure (or calculate if there is sufficiently capable software developed) the actual drag curves for a standard atmosphere for each model of bullet made by each manufacturer in each caliber. All of that information would not fit in a practical size book, but it would probably fit on a single DVD ROM, or at least one from each manufacturer. The data would need to include a wide velocity range. It also needs to include stability information and the rate of spin decay vs velocity. There is presently no reliable method of calculating downrange bullet stability for a given bullet and atmosphere and determining it from shooting tests is very difficult. Existing published ballistic data is unreliable at transonic and subsonic velocities for any manufacturer that I'm aware of. Ballistic programs give answers you can't have any faith in it even when multiple BCs are given. Typical multi-BC data gives the lowest velocity BC number as covering "under 1800 fps" or similar.

What should a shooter do if they want an accurate drop chart for long range shooting with todays available data? The only answer I'm aware is not to rely on published BCs other than as a starting point. The only method is to use your own shooting tests instead. If you measure drop and lateral drift vs distance for several distinces over the range you shoot using your rifles and your loads along with measurements of the air density you can generate pseudo BCs which will give fairly accurate prediction of bullet drop and spin deflection. The existing ballistics programs are reasonably good for interpolation between the measured points and for adjusting for different air density. It's a lot of work and it will still have errors. Most ballistic programs have no model for handling bullet yaw, precession, and dampening so those errors will remain (and be more apparent) as air density changes from the conditions which existed when the shooting tests were made. The ballistic software simply has no code to account for those effects. Some software does exist (six degree of freedom models), but its usually impractical to obtain precise enough data in the input conditions to make the calculations more useful than the commonly used "McCoy" model.

I consider the term BC to mean "Before Computers" more than "Ballistic Coefficients". They were useful in the first half of the 19th century when ballistic calculations were done by hand using books of log and trig tables. Error correction (in the math) was handled by having multiple people do the calculations and comparing the results. At that time using a few simple ballistic bullet models made a lot of sense. But mathematical computation is no longer a limitation. Complete ballistic modeling can be done using a \$300 PC from WalMart in less than a second. What's missing is the drag vs velocity measurements and stability data for each bullet from each manufacturer. Yes, that's a lot of data. Few manufacturers (any?) have it to publish.

A few manufacturers are giving G7 instead of G1 coefficients for bullets where the G7 is a better model in the velocity range most hunters and target shooters use. As long as people belive that "better" BCs are desirable bullet manufacturers will continue to publish them. Shooters seeking the highest accuracy are still free to ignore the published BCs.

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BryanLitz

Lou,

I understand the approach your advocating, but disagree that it's the right approach for modeling ballistic trajectories for 99.9% of shooters.

To start, the difference between a trajectory modeled with BC referenced to the closest standard, and a trajectory modeled with the bullets unique drag curve will be less than 1 click thru the bullets supersonic range (which is where most shooters, and especially hunters are concerned).

When the bullet slows into the transonic speed range, stability becomes questionable and the trajectory becomes unpredictable as you said. However custom drag curves for each bullet will not solve that problem. You have atmospherics affecting stability in a way that indirectly affects the drag (induced drag) of the bullet, as well as the effects of different rifling patterns (depth, smoothness, # of riflings, etc become important when dealing with transonic stability). In other words, transonic flight is determined by way more than drag. Heck, most bullets just tumble at this speed, making any efforts to predict their trajectories impossible and irrelevant.

Am I correct in understanding your suggested way of 'predicting' a trajectory is to shoot your rifle and write down the drop?!?! Talk about Before Computers! Of course it's a good idea to verify your predicted drop just to be sure the theory matches reality, but don't forego the step of predicting the trajectory in the first place, it's quite useful! Plus you can't shoot in every condition (elevation, slant angle, wind, etc) so at some point you have to rely on a predictive model.

Using a good ballistic solver with accurate input data (including an accurate G7 BC) will result in trajectory predictions that are accurate within 1 click thru the supersonic range of the bullets flight. Below supersonic speeds, I agree, all bets are off. However I also understand that to actually predict trajectories thru the transonic speeds for most bullets requires aerodynamic models that are not available (or would take years and \$100K's - doplar radar - to develop for each round) AND would only be relevant for a particular rifle barrel... All this to predict trajectories beyond what most have the accuracy to hit a vital zone anyway... I don't think that's a 'better' way.

Traditional BC's as we use them are very useful not just for comparing bullets to each other, but also for computing very accurate trajectories for the relevant flight envelope of the bullet.

-Bryan

J E Custom

Well-Known Member
Very good information Lou and Bryan !!!!!

I had not thought about using the flat base bullets in over 50 years because I have all ways
liked to shoot as far as my ability and equiptment would allow and the only choice back before
computers was the boat tailed bullets.

All of my trajectories tables/ drop charts had to be fired back then to recent times because
listed BC were calculated differently from one bullet maker to the next and could not be
trusted.

But now that we have the computer it would be nice not to have to re zero for changes in altitude,
temperature,humidity and so forth buy actually shooting a group under these
conditions and have to modify your drop charts across the range to be used.

What I see as the main benefit of good BCs for each bullet fired in a particular rifle is
the ability to calculate a solution that will allow a shooter to correct for all known conditions
and be able to predict bullet impact at any reasonable distance.

I am not very computer literate but I do know that the better information you put in the
better you get out of it. so that's why I would like accurate BCs not high numbers that don't
work in anything well.

What's the saying- Close only works with horse shoes and hand grenades.

Please keep the debate going for the less informed members Like me.

Thanks
J E CUSTOM

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LouBoyd

Well-Known Member
(snip)
Am I correct in understanding your suggested way of 'predicting' a trajectory is to shoot your rifle and write down the drop?!?! Talk about Before Computers! Of course it's a good idea to verify your predicted drop just to be sure the theory matches reality, but don't forego the step of predicting the trajectory in the first place, it's quite useful! Plus you can't shoot in every condition (elevation, slant angle, wind, etc) so at some point you have to rely on a predictive model.
(snip)
However I also understand that to actually predict trajectories thru the transonic speeds for most bullets requires aerodynamic models that are not available (or would take years and \$100K's - doplar radar - to develop for each round) AND would only be relevant for a particular rifle barrel... All this to predict trajectories beyond what most have the accuracy to hit a vital zone anyway... I don't think that's a 'better' way.
-Bryan

I'm not advocating trying to make a complete drop chart for each bullet/load/rifle. What I'm suggesting is that accuracy can be improved by doing shooting tests at the ranges you expect to shoot a particular rifle, then adjust the ballistics program to give a better match to real trajectories. It does help to have some instrumentation like a chronograph, a method of measuring air density, and to do the test in low/no wind conditions. The BC is a reasonable number to tweak to get the drop to match if you have good certainty of your velocity and air density, particularly since many programs already allow for multiple BC vs velocity inputs. For those programs which calculate spin drift the twist rate input to the program can be tweaked to match the shooting measurements of horizontal drift. Wind can certainly interfere with the tests, and can easily be larger effects than the errors that the shooting tests are attempting to correct. I use manufacturers BC's as a starting point and G7 values when they're available. I'm not trying to write a new ballistics program wich does not use BCs and there would be no available input data if I did. Should shooters attempt to do make these corrections? Only if they have the time and care to go to the effort.
At lest though they should make some shooting tests just to verify that their computations are close to reality. It's a little late after they shoot an elk in the leg and it hobbles off over a hill 800 yards away.

Shooting tests are a way to correct for situations such as the original poster was asking about, in that case why the spin rate appears to affect BCs. Few ballistics programs include the code to predict that effect, whatever the physical explanation may be. For most hunters getting hits close to the point of aim on first and subsequent shots are more of an objective than understanding the physics of how air affects bullets.

I agree that shooting though the transonic region is wrought with problems. Existing McCoy based ballistics programs and BCs are nearly useless for predicting transonic performance. The spin rate of the bullet as it goes transonic is rarely known at all and the programs like McGyro don't calculate the decay of the spin rate vs velocity or time. I am not recommending hunting or even target shooting beyond transonic range and velocities. It's interesting though that transonic shooting used to be common for the military. Many WW1 rifles had sights calibrated to 2000 yards or 2 km. They were used for volley fire on massed troops. It is possible to get pretty good accuracy shooting transonic. Few "long range" modern rifles however have spin rates or bullet designs which make it practical.

I'm in that 0.1% you mentiond who is interested in trying to understand the physics including shooting subsonic and shooting though the transonic range. I suppose this is the wrong forum to even bring it up. I do think though that every shooter who uses ballistics software should be aware that all programs are limited models and they need to understand what the limitations are. Used outside of those limits they can give very wrong answers. There are many small amplitude ballistic effects with few, if any, available programs even address. No, I don't expect BCs will go away for sports shooting. Both Sierra's multiple G1 BCs and Berger's publishing of G7 BCs are fairly successful methods for improving the predicted trajectories.

Bryan, I don't disagree with anything you said in your last post. You support Berger bullets and their objective is to sell bullets and make them useful to the shooting public. For that I think you and Berger are doing an excellent job. Even I don't think there would be a practical advantage in developing new ballistics programs and doing millimeter radar measurements to get drag functions for each projectile. It could only be cost effective if the equipment was used by many bullet manufacturers.

You've reminded me that the effort required and money spent would be better directed. Some of it no doubt toward developing a practical instrument to accurately measure the wind along a bullets trajectory. That would give a greater improvement in long range shooting accuracy than making new ballistics models possibly could even if they are perfect.

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BryanLitz

Lou,

We're on the same page for the most part. I only took issue with your treatment of BC's as a useful concept because you seemed to imply that BC's weren't 'good enough' for general use.

As far as 'tweaking' BC's to match observed trajectories, I have to raise a caution flag there as well.

There are many variables that can make it look like the BC is in error, when in fact it's something else. For example, a common one is scope reticle movement. If the program predicts 10 MOA of drop and you dial your scope 10 MOA and hit low, well, the BC must be off, right? The serious shooters here on LRH know better but many shooters are quick to question the BC because it's the most mysterious and (generally) the least understood variable. You can 'tweak' the BC to get it to make up for an out-of-calibration scope, but it won't really be right. You end up chasing your tail by defining multiple BC's to make up for the scope error, and in the mean time your predicted impact velocity, energy, wind drift, etc are all in error because you're feeding the program a false BC to force it to match the skewed drop values resulting from the out-of-calibration scope.

The out-of-calibration scope is just one example of a common error source but there are many others that tempt people to 'tweak' BC's to match their observed trajectories.

Even having said all that, I acknowledge that there are still some cases where a certain rifle with a certain barrel will fire a bullet in a way that slightly affects the effective BC that bullet flies with. Variations in BC tend to be small for accurate rifles. If too much yaw is induced, or too much surface scaring, etc, the rifle will probably not be accurate by our standards.

As to the test results from the original poster, I can't remember the details now, but when questioned, I seem to remember some missing information like some key atmospherics, or velocity measurement, or something that the measured BC's were based on. No disrespect to the tester, but truly accurate BC testing is HARD. Even if your test procedure is sound, you can easily have instrumentation error that you don't know about. Is your Kestrel calibrated? How do you know your chronograph is accurate? What about your laser rangefinder? When you test BC's, every single variable has to be known to a high degree of certainty or the error will compound on the final result.

I do think that unique drag functions are useful for those projectiles that remain comfortably stable thru transonic. If the bullet exhibits low pitch/yaw, then it's trajectory can be predicted quite well at all speeds, but most bullets fly unpredictably at transonic, making prediction a futile effort.

Thanks for the healthy exchange Lou. Always good to investigate and discuss alternate approaches.

Take care,
-Bryan

groper

Well-Known Member
Good info bryan, id have to agree 100% with your comments on "tweaking" the BC to match known drops.

My last scope tracking was unknowingly out by 5%. So instead of dialing 8mils i was actually dialing 8.4mils. I ended up chasing my tail for ages tweaking velocities and BC`s to match the trajectory i was getting, never getting it 100% correct until i finally found the problem. Same goes for the Zero, it has to be 100% spot on and remeber to rezero it if you tweak your load in any way or shoot in different weather conditions.

Bryan, i found your ballistic testing and measured/calculated G7 BCs be of greatest help in this regard also. Using your G7 BCs i tweak my velocities now to line up my trajectories with known drops at 1000yds and it gets me **** close, certainly less than 1 click at this distance which is certainly closer than using my chronographed velocities and tweaking the BC. Obviously my chrony isnt accurate enough. lightbulb

Topshot

Well-Known Member
Good info bryan, id have to agree 100% with your comments on "tweaking" the BC to match known drops.

My last scope tracking was unknowingly out by 5%. So instead of dialing 8mils i was actually dialing 8.4mils. I ended up chasing my tail for ages tweaking velocities and BC`s to match the trajectory i was getting, never getting it 100% correct until i finally found the problem. Same goes for the Zero, it has to be 100% spot on and remeber to rezero it if you tweak your load in any way or shoot in different weather conditions.

Bryan, i found your ballistic testing and measured/calculated G7 BCs be of greatest help in this regard also. Using your G7 BCs i tweak my velocities now to line up my trajectories with known drops at 1000yds and it gets me **** close, certainly less than 1 click at this distance which is certainly closer than using my chronographed velocities and tweaking the BC. Obviously my chrony isnt accurate enough. lightbulb
Good point Groper,
Lets talk "Tweaking"............
Say you have a scope that is out 5%. What's the best way to compensate for this error given that shooting under a hunting situation, the distance, pressure, temperature etc will always be different?

I have two scopes that have about 7% error in the elevation adjustment. What I do is measure the velocity, then calculate the real drop required at about the maximum range that I intend to hunt using the best available B.C. numbers that I can find including Bryan's G7.

I then shoot at that distance and measure the error on the target. I then adjust the dial cap to read the calculated dial up and then shoots at closer ranges. The closer you are to the target the less the error matters.

ie, Say I am out by 2 MOA at 800 yards. I move the turret 2 MOA and lock it in position.

I may then be 1 MOA out at 400 yards and 2 MOA out at 100 yards but that is better than being 2 MOA out at 800 yards. If you follow my drift.

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groper

Well-Known Member
Well luckily my ballistic calculation software allows me to input a "custom click value" so i simply get it to output the elevation in "0.105 milrad clicks" instead of "0.1 milrad clicks" like its supposed to be.

Failing that capability, i would simply adjust the total elevation required by 5% and round that number to the nearest click. In your case 7% adjustment.

So if your calc is telling you you need 35MOA for the shot and your scope is out 7% over for instance;

multiply 35MOAx1.07= 37.45MOA = rounded dial ON THE SCOPE 37.5MOA.

If its out by 7% under;
divide 35MOA/1.07 = 32.71MOA = rounded dial ON THE SCOPE 32.75MOA.

DO NOT tweak the G7 BCs that bryan has published, they are closer than 1% accurate, they do not need tweaking. Its the velocity and scope where the problems lie.
Reverse calculate the ACTUAL drops from the elevation you dialed on your scope taking into account 7% error.
TWEAK YOUR VELOCITY, to match the ACTUAL drops at as much distance as you can, No less than 800yds preferably but the more the better, 1000yds is ok.

IF you dont have a tested verified G7 BC from bryan, then things get a whole lot more difficult and the best way forward would be calculate your own BC from shooting thru 2 chronies as far apart as possible, 1 at the muzzle and 1 at 500yds would be ok.

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