Understanding G1 and G7 Ballistic Coefficients

[Jack Master]

The Mathematical Approach
Understanding G1 Vs G7 comes down to fluid dynamics and values used in the equations to define the resistance of flow. Has anyone else recognized the G1 is about 2x G7? Its a mathematical equation (minus Byan Litz' stuff, he actually tests the BCs).
This is a short image of how the BC is derived from a bullet's physical Geometry.

Note the G1 uses the Drag Coefficient of .5 and the G7 used the Stream line Body of almost 0. Once these values are place into the BC equation G1 is 2x G7.

Actual Testing and Truing
Bryan Litz's books push us to use the Measured (not calculated) G7, rather than G1, because the G7 Drag Coefficient better matches the actual bullets we are shooting for long range applications. He also wants shooters to understand the BC of a bullet is changing while in flight. The BC Changes with velocity and where we measure the actual BC of the bullet in it's flight is critical to use in Ballistic Programs. G1 is typically measured at the muzzle or in the first 300 yards of flight where the Velocity is very high. The G7 is typically measured at a further distance, like 600 to 800 yards where the velocity is slowing down. Measuring the BC at a further range for bullets that we are shooting further will give us a better representation of the actual BC average through the long flight of the bullet.

Here are the bullet flights paths that could happen using a bad BC.
G1 BC on very long bullet flight of a G7 shape bullet.

Notice the predicted path goes above the actual trajectory and then losses velocity and ends below the actual trajectory. This can make truing our ballistic programs very difficult and pain staking or not possible.

G7 BC on Very Long Bullet Flight of a G7 shape Bullet

Notice the Predicted Trajectory is much more in tune with the actual Bullet flight. This makes truing our programs mush easier.
Note - If you use a bad G7 BC, you could still get the predicted trajectory of the G1 shown above.

A choice to make
In the end each shooter has to make a choice. G1 or G7. If you are using G1 and getting good results and can true your programs, GREAT! Keep doing that! But, if your program is not giving your good results and its a Bit@h to get it to true up properly switch to the G7 and see if it helps. The HMFIC of this site likes to use G1 rather than G7 because it works for him. Results are what define success. Choose what works for you.

I hope this helps. Happy trails.

 

[Lowlight]

It's a very good topic and one that needs to be explored.

Going back into history, understand these tables are based on artillery from the 1800s and even then, with groups conducting the same experiments at the same time, they did not agree. We have a lot more models if you look at the writings from the time.

Today most programs use McCoy, I have issues with McCoy because of the way his information was compiled and used today. Others disagree with McCoy. So we get introduced to the other names like Pejsa. Today we have Litz, Ruiz, Boatright to play with the data. As things progress, our understandings change. This is what you find even back then with Ingalls, Siacci, Mayveski, etc. They recognized data changes and theories become obsolete.

It's not hard to find disagreement on how to manage this information. We can look at the Curvature of the Earth being discussed back in the 1800s that everyone points too. Today I say we exaggerate the number, back then it was clear, they didn't. One Ingalls table starts at 11,000 and shows 80 yards of variation. That is tiny of the range. So consider that with my advocacy for Left Hand Gain Twist barrels, if you have 1.25% of elevation for SD and about .72% for CE and then you mathematically add them vs mechanically oppose them, where we would get a much smaller number that can be ignored. This is where the 2% comes in, but it's wrong because CE is much smaller, and SD changes with conditions.

During Ingalls time they were already moving to longer nosed projectiles so the blunt nose examples were as noted obsolete, hence the use of Ingalls vs the originally described blunt nose projectile. In a few short years, they moved away from the idea of original model coefficients.

McCoy which most software today uses is 3DOF and yet we have MPM or 4DOF was written in 1966, which models close to Hornady.

Reading these texts, the one from James Ingalls and the Army 4DOF, you can see these debates, and how they looked at the data previously presented. McCoy is missing data, he had many holes in his work. So then you go to other sources for information. Like Pejsa which wrote his information in the 80s.

Pejsa published his work in 1986, you can find a host of ballistic publics around each war too. The white papers are online.

There are volumes and volumes on the subject and understand not everyone agrees with the conclusions and those conclusion change all the time. Even today, how they write the programs and who's models are included matters. Software with Pejsa DNA are not G dependent, meaning the which G Value you use does not matter. He recognized using a BC and apply a G value was a bad way of doing business because we don't shoot rifles like we do artillery, Yet we use Artillery models for most other software because it's super close to right and really easy to translate.

I use G1 becaues it's easy, it's been used by the military since the beginning. Remember they modeled G7 in 1940, they had similar bullets to today in the springfield and Garand, yet it wasn't until the mid 2000s did they switch. G1 has a wind value, and it's readily available. So I use it as I know where the numbers will be for most projectiles via memory.

Understanding all sides is important. But remember, this stuff is dynamic just like BC of a bullet.

 

[_Windrider_]

The Mathematical Approach
Understanding G1 Vs G7 comes down to fluid dynamics and values used in the equations to define the resistance of flow. Has anyone else recognized the G1 is about 2x G7? Its a mathematical equation (minus Byan Litz' stuff, he actually tests the BCs).
This is a short image of how the BC is derived from a bullet's physical Geometry.

View attachment 7238083
Note the G1 uses the Drag Coefficient of .5 and the G7 used the Stream line Body of almost 0. Once these values are place into the BC equation G1 is 2x G7.

Actual Testing and Truing
Bryan Litz's books push us to use the Measured (not calculated) G7, rather than G1, because the G7 Drag Coefficient better matches the actual bullets we are shooting for long range applications. He also wants shooters to understand the BC of a bullet is changing while in flight. The BC Changes with velocity and where we measure the actual BC of the bullet in it's flight is critical to use in Ballistic Programs. G1 is typically measured at the muzzle or in the first 300 yards of flight where the Velocity is very high. The G7 is typically measured at a further distance, like 600 to 800 yards where the velocity is slowing down. Measuring the BC at a further range for bullets that we are shooting further will give us a better representation of the actual BC average through the long flight of the bullet.

Here are the bullet flights paths that could happen using a bad BC.
G1 BC on very long bullet flight.
View attachment 7238061
Notice the predicted path goes above the actual trajectory and then losses velocity and ends below the actual trajectory. This can make truing our ballistic programs very difficult and pain staking or not possible.

G7 BC on Very Long Bullet Flight
View attachment 7238062
Notice the Predicted Trajectory is much more in tune with the actual Bullet flight. This makes truing our programs mush easier.
Note - If you use a bad G7 BC, you could still get the predicted trajectory of the G1 shown above.

A choice to make
In the end each shooter has to make a choice. G1 or G7. If you are using G1 and getting good results and can true your programs, GREAT! Keep doing that! But, if your program is not giving your good results and its a Bit@h to get it to true up properly switch to the G7 and see if it helps. The HMFIC of this site likes to use G1 rather than G7 because it works for him. Results are what define success. Choose what works for you.

I hope this helps. Happy trails.

Correct me if I'm wrong, but Litz only shoots at about 300 yards for his data. He lowers the powder loads to simulate distance. Only recently has he acquired his radar capabilities.

 

[Jack Master]

Correct me if I'm wrong, but Litz only shoots at about 300 yards for his data. He lowers the powder loads to simulate distance. Only recently has he acquired his radar capabilities.

Yes, 300 ...or 600. I cant remember if his microphones are 100 or 200 yards apart, but there are 3 of them. With that system he would change the muzzle velocity to simulate longer range, slower bullets.

 

[ShtrRdy]

Modern ballistics programs use numerical integration to calculate a trajectory. Today we don't have to rely on simplifications to come up with an estimate. If you look at Bryan Litz's books he shows us how well the G7 drag curve matches the modern long range bullet drag curve. Since they match so well you can use the BC at muzzle velocity or at down range velocity because they will be very close to each other.

 

[Lowlight]

it doesn't

Modern ballistics programs use numerical integration to calculate a trajectory. Today we don't have to rely on simplifications to come up with an estimate. If you look at Bryan Litz's books he shows us how well the G7 drag curve matches the modern long range bullet drag curve. Since they match so well you can use the BC at muzzle velocity or at down range velocity because they will be very close to each other.

Unfortunately, it's theoretical and his software purposely adds weight to G7 if you use his program, G7 can be a better answer but this is not the science part, because not everyone gets the same results.

If you read his books, he repeats McCoy, not much else. McCoy is flawed by everyone's observations and his calculations are 3DOF which is the weakest of options out there, to be honest. He takes the "good enough" approach to much of it in practice.

Bryan has done a ton for the community, but he is not the only word on the subject and much of it is repackaged McCoy.

 

[ShtrRdy]

it doesn't

Unfortunately, it's theoretical and his software purposely adds weight to G7 if you use his program, G7 can be a better answer but this is not the science part, because not everyone gets the same results.

If you read his books, he repeats McCoy, not much else. McCoy is flawed by everyone's observations and his calculations are 3DOF which is the weakest of options out there, to be honest. He takes the "good enough" approach to much of it in practice.

Bryan has done a ton for the community, but he is not the only word on the subject and much of it is repackaged McCoy.

Oh, man, I'm bummed. I thought what I was learning from Bryan Litz's books was the truth.

 

[Lowlight]

You are learning, you’re learning ballistic history from the 50’s 60’s etc

it’s not new, search google there are older books for free

 

[Dthomas3523]

This is why I am not a hard and fast “my chrono said my velocity is this, so it’s a known and I should stick with it at all costs” type.

While yes, it is pretty much a known, much of what we currently use in software either isn’t a known or is still very old information. Current formulas get us very close, but still need tweaking.

We haven’t scratched the surface yet on what we will likely have in the future for ballistic simulations.

As Frank pointed out, the proof is in different software coming up with slightly different answers despite the inputs being the same. If we had this stuff figured out properly, most would be doing it all the same.

 

[Deleted member 10043]

I have a couple of Pejsa's books. You're going to need a spreadsheet to translate those formulas into something you're familiar with to get the picture. And read the text several times to put the variables together.

 

[Deleted member 113831]

I wonder how many calculators simply recalculate the G1 into a G7 before doing the computation.

 

[THEIS]

I wonder how many calculators simply recalculate the G1 into a G7 before doing the computation.

Hi,

Combine that with the reality that very very few projectiles in use today truly fall into the G1 OR G7 profile used to right the respective G1, G7 formulas.

Projectile that has anything but a 7.5 deg BT and 10 caliber tangent ogive....well, where do they fall into?

Sincerely,
Theis

 

[Jack Master]

I wonder how many calculators simply recalculate the G1 into a G7 before doing the computation.

I was wondering the same thing, but as old as the trajectory formulas and technology is (1960's), I though they might turn the G7 into a G1 and run the same old calculations/algorithms.

I would like to know if the ballistic calculators actually use a different process (calculations) for a G1 vs G7. Or do they always use a G1 and turn G7 values into a G1 (or vise-versa) and use the same program? If you were an programmer or developer it sure would make sense from a time standpoint.
What programs are based on a G1 and what programs are based on G7? This could help with getting started in the right direction and make truing easier.

 

[Dthomas3523]

Lol. And I got flamed last year by guys who “shot the finale” when I mentioned we don’t know what’s actually under the hood in calculators, so we should be tweaking the numbers we have access to.

MV, BC, sight height. We can’t go under the hood, so manipulate those numbers to match your dope and roll on.

 

[_Windrider_]

So essentially every ballistic computer is just spitting out “try dope” regardless of the scrutiny of data one could obsess over. There is no equation that could account for all the variables in firing a shot (Shooter, equipment, environment, etc.) This only leaves true data on previous engagement. Shooting in all variables and recording your own data. Your very own, personalized solution.

This is why we always say you true the calculator to the rifle, not the other way around. Nothing beats a data book.

 

[Lowlight]

You can download the free Excel data, I think even in Bryan's books he provides the original PM Information

Here is the Arthur Pejsa spreadsheet that was calculated 20 years ago

This stuff works in Excel, so you should be able to see what it is doing under the hood

 

[FN-Whitney]

Taking a different look at BC's last year I purchased a Kestrel with Hornady 4DOF and after in putting accurate data and using the 4DOF form factor instead of the BC it is amazingly accurate, not perfect but much closer than using either G1 or G7.

 

[DocUSMCRetired]

Correct me if I'm wrong, but Litz only shoots at about 300 yards for his data. He lowers the powder loads to simulate distance. Only recently has he acquired his radar capabilities.

This is incorrect.

 

[DocUSMCRetired]

Yes, 300 ...or 600. I cant remember if his microphones are 100 or 200 yards apart, but there are 3 of them. With that system he would change the muzzle velocity to simulate longer range, slower bullets.

We have multiple facilities, and multiple RADAR systems. Some of which are more than 2000 yards, it just depends on the bullet and data needs.

 

[DocUSMCRetired]

it doesn't



Unfortunately, it's theoretical and his software purposely adds weight to G7 if you use his program, G7 can be a better answer but this is not the science part, because not everyone gets the same results.

If you read his books, he repeats McCoy, not much else. McCoy is flawed by everyone's observations and his calculations are 3DOF which is the weakest of options out there, to be honest. He takes the "good enough" approach to much of it in practice.

Bryan has done a ton for the community, but he is not the only word on the subject and much of it is repackaged McCoy.

This has incorrect information.

 

[DocUSMCRetired]

1) The AB Engine is not BC dependent, we use the actual drag modeling which is produced in our laboratory at the heart of it. The G1 and G7 BCs are published for users who prefer them, and to give users the ability to compare bullet performance when they want to. But the engine itself at its heart uses the actual data from our lab.

2) You are close in your assumption, and while not always perfect and of course dependent on where the BC or how the BC you are using was produced the factor you are looking for is 0.512.

 

[Lowlight]

It's not incorrect it just disagrees with what you put out,

If we run BOTH numbers using say, Lapua G1 vs G7, it's barely a .1 off to the transonic zone.

Now the G1

I went to 1200 because it does jump a tiny bit, this prior to any truing of the software which is usually required.

If the models were so far apart as the information would have you believe we'd see a much bigger variation. But the fact is, on any given day, with any given system or shooter we can easily see one work more so than the other.

Now as far as changes moving forward, at the time prior to Doppler, the data provided was not being tested to 2000 yards, and it wasn't until recently it moved past 300. Sure stuff changes everyday, but those changes are mostly recent.

Now let's look at the numbers via the Lapua CD Data, which is doppler compared to Litz, because this totally proves my point you're being sold a false narrative on the differences

This is CD information

Here is Litz numbers

There a BIGGER deviation, CD vs G7 as opposed to G7 vs G1

So clearly G7 vs G1 is a wash when looking at the numbers we have to do the EXACT same amount of work, or we have the Doppler CD Data which is a 3rd data set which equally does not align

Like I said, Bryan, AB does great work fr the community, but the idea one is better than the other is completely false. The programs can easily make any of this data work as noted with the Coldbore data, that does not try to weigh one against the other.

Neither model is truly correct which is why it 's different from rifle system to rifle system, shooter to shooter.

 

[DocUSMCRetired]

**snip**

Except that this does not account for the fact that some bullets have very large variations from the G1 standard, and some do not. Here is the Doppler data from one of our tests. In this case, your example would not work. What you see in this data, is how much this bullet varies from the G1 drag model, and from the G7. A flat line would indicate very little variation and the use of a G1 to work out ok. Now in this example if you are staying super sonic the G7 drag model would work very well, but the use of a G1 would not as it almost never shows consistency in G1.

I have seen this data on hundreds of bullet models, and thousands upon thousands of bullets tested. This is where I am getting my data from, real world experience. Not really here to argue the case but to simply to share facts.

This graph indicates how much the bullets actual flight performance varied from the standard as tested beyond 2000 yards.

 

[Lowlight]

Real-world experience contradicts what you are saying

We don't see big real-world differences, as both can work equally well, if it was so black and white, we'd have a line in the air detailing it.

That chart is pretty meaningless in terms of data.

 

[DocUSMCRetired]

Real-world experience contradicts what you are saying

We don't see big real-world differences, as both can work equally well, if it was so black and white, we'd have a line in the air detailing it.

That chart is pretty meaningless in terms of data.

My experience is real world experience. We have hundreds of thousands of users, and I have worked with thousands upon thousands of users from all walks of life. We are implemented into dozens of systems, many more to come, and some systems users don't even realize run our engine.

This chart is very relevant, and matches up with my experience literally helping people and companies on a daily basis to include analyzing firing solution predictions vs real world results. I won't even touch on the massive number of people I have had the pleasure helping to train.

My experience is real world, and world wide. And our data is a big part of what makes a difference.

 

[Lowlight]

I think what you are trying to show is this

There are a bunch of ways to show a dopplar created real world model,

Variable effects can show up in any number of ways, powder, rifling, bullet, brakes, suppressed

The changes are dynamic in nature

Rifling Effects

Been through all the lessons on the subject, I get it doppler is a bit different, but we are doing the identical amount of work with G1 vs G7 the CD stuff is better, and your CDM via the mobile lab is awesome because it works with the shooter's equipment and it's not based on other systems data. This is more so why things are off, we test with one platform and execute with a different one.

 

[DocUSMCRetired]

I think what you are trying to show is this
***snip***

That is not at all what I was attempting to show. The graph I provided showed the variation from the G1 and G7 standard drag models that particular bullet showed over its flight path. Not a Mach vs CD table.

 

[_Windrider_]

That is not at all what I was attempting to show. The graph I provided showed the variation from the G1 and G7 standard drag models that particular bullet showed over its flight path. Not a Mach vs CD table.

If I could interject something that I believe would benefit all of us who use the AB ecosystem as well as AB.

Doc, when you guys integrate the engine don’t let whomever only use parts of it. You tell them they use it all or nothing. The foretrex is limited, the kestrel is limited, even AB mobile is limited when compared to AB analytics. Without using and buying CDM’s, there has to be a more efficient way

 

[Lowlight]

As I have noted in the past,

We need to take real-world dope from people, list it out and then compare the predictions using both, I think people will see with the most popular calibers and bullets, not some one-off outlier, the data will be right down the middle, both working equally well.

Take your dope, scratch it out from 200 to 1000, 1200 is better, and then do a generic prediction using both G1 or G7 and it's going to be within a 10th or 2 of dead on. Do it for 6mm, pick two different bullets that are popular, 6.5, 308, and then do 338, the numbers will be so close it will be silly.

The common values should be, Atmospheric, use sea level, Sight Height, 2.5" is good, then match the muzzle velocities and let the programs do the rest. The variations will require the same amount of effort to make it line up with the real world.

Most people do live in the real world and see real-world data every day it's only those lost in the digital world who are surprised by real-world revelations. It's the same.

 

[THEIS]

Hi,

@DocUSMCRetired

What is the current status of this offer in regards to you saying that jacketed bullets have less BC variation than monolithic bullets???

Sincerely,
Theis

 

[ShtrRdy]

My experience is real world experience. We have hundreds of thousands of users, and I have worked with thousands upon thousands of users from all walks of life. We are implemented into dozens of systems, many more to come, and some systems users don't even realize run our engine.

This chart is very relevant, and matches up with my experience literally helping people and companies on a daily basis to include analyzing firing solution predictions vs real world results. I won't even touch on the massive number of people I have had the pleasure helping to train.

My experience is real world, and world wide. And our data is a big part of what makes a difference.

Doc, thanks for the example of how some bullets don't match very well when comparing G1 and G7, or more accurately, the drag curves.

Also, could you comment on the calculation of BC(G1) and BC(G7) in the first post? This doesn't agree with the explanation Bryan presented in the AB book(s).

 

[Lowlight]

What a kiss ass,

what did he prove exactly?

LOL, you guys are funny some times, cause nobody has "real-world experience".

maybe they can highlight the process they used for the Warner Tool bullets and why they were 12% off everyone else including Doppler, that might help, I was within 1% and calculated it via G1, vs the 12% difference they posted which ran counter to everyone else who tested them.

 

[seansmd]

The current AB G7 in the kestrel is 0.291 (the custom curve matches this) Hornady recommends 0.326 to 0.321 depending on velocity. AB seems to modify the G7 to match their custom curve at a different velocity. I need to run the numbers with the kestrel G1 I'm gonna guess their going to match AB and not what Hornady publishes.

 

[LastShot300]

Except that this does not account for the fact that some bullets have very large variations from the G1 standard, and some do not. Here is the Doppler data from one of our tests. In this case, your example would not work. What you see in this data, is how much this bullet varies from the G1 drag model, and from the G7. A flat line would indicate very little variation and the use of a G1 to work out ok. Now in this example if you are staying super sonic the G7 drag model would work very well, but the use of a G1 would not as it almost never shows consistency in G1.

I have seen this data on hundreds of bullet models, and thousands upon thousands of bullets tested. This is where I am getting my data from, real world experience. Not really here to argue the case but to simply to share facts.
This graph indicates how much the bullets actual flight performance varied from the standard as tested beyond 2000 yards.

The difference of a bullet's Cd from the G1 or G7 standards is completely irrelevant, so you are again back to a sales pitch void of any real content.

Lowlight put out the real proof of what it really matters...in case you missed the point and it it's called ballistics solutions and I or somebody else can prove for once and forever that given two really solid G1 and G7 for the same bullet the discrepancies are really minor

But AB knows better...marketing for sure. Not any real scientific debate here, just a sales flyer.

 

[TripleBull]

McCoy which most software today uses is 3DOF and yet we have MPM or 4DOF was written in 1966, which models close to Hornady.

View attachment 7238104

You're dusting off the cobwebs of my mind, Frank. Lieske and Reiter is a manageable study and not too long. You can download it here:

Equations of Motion for a Modified Point Mass Trajectory. | National Technical Reports Library - NTIS

Back in '71, I wrote a review of it for my high school physics class. The local public library apparently had a ballistician lurking in the stacks because they had this, Lieske & McCoy and other reports in a binder. It was mind blowing to me to think about then, and it still is today. We have mucho tools and knowledge at our disposal.

 

[pyrotechnic]

Doc, in your image you plotted the G1 and the G7 bc on the same graph.

So since the G1 bc is a larger number to begin with (roughly 2x the g7) the same percentage deviation is going to look like 2x as much as the g7 deviation on your graph.