G1 & G7 Tables?

[gnochi]

Hi,

I've spent some time googling and haven't had much luck - could someone please point me to the Cd-vs-Mach tables for G1 and G7? As many points as I can get would be ideal.

Specifically, I'm pulling together a MATLAB script (possibly a phone app, tbd) for taking actual drop data and back-calculating BC and MV.

Thanks!

Gnochi

 

[6.5SH]

JBM - Downloads

www.jbmballistics.com

 

[gnochi]

JBM - Downloads

www.jbmballistics.com

Not sure how I missed that... thank you so much!

 

[6.5SH]

You're welcome, good luck on your project.

 

[bulletbluesky]

JBM - Downloads

www.jbmballistics.com

I'm wondering what were the actual projectile sizes in experiments with standard projectile shapes to determine drag curves vs Mach numbers (for G1,G2,...G8 models)? And what kind of experiments (wind tunnels, actual firings etc)?

 

[DeathBeforeDismount]

4 years later.......

 

[bulletbluesky]

4 years later.......

100 years later!
In 1924. US Army published* systematized table of the Gavre resistance function for projectile type I (today known as G1 standard projectile shape). Gavre Commision of France worked with artillery shells at the dawn of 19th century. I'd like to know if, how, and to what extent of a precision follow up tests were conducted to confirm, not just projectile shape G1 but for the others too.

* Ref: Exterior Ballistic Tables Based on Numerical Integration; Ordnance Department, U.S. Army, 1924.

 

[DocUSMCRetired]

I'm wondering what were the actual projectile sizes in experiments with standard projectile shapes to determine drag curves vs Mach numbers (for G1,G2,...G8 models)? And what kind of experiments (wind tunnels, actual firings etc)?

The G1 Standard Projectile is 1 Caliber and 1 lb. Here is the math.

Section Density = weight / caliber^2.
Form Factor for the Standard is 1.0.
BC = Sectional Density / Form Factor.

So to get all 1's across the board you have.

1/1^2 = 1 SD
Form Factor = 1
1/1 = 1.0 or the Standard.

 

[bulletbluesky]

The G1 Standard Projectile is 1 Caliber and 1 lb. Here is the math.

Section Density = weight / caliber^2.
Form Factor for the Standard is 1.0.
BC = Sectional Density / Form Factor.

So to get all 1's across the board you have.

1/1^2 = 1 SD
Form Factor = 1
1/1 = 1.0 or the Standard.

Isn't SD per definition SD = mass/cross-section area?
So when we speak about axisymmetric projectile with circular cross section with diameter (caliber) d it should be:
SD = (4/π)*mass/d^2.
But I'm not here for simple math hair splitting.

I'm asking about projectile calibers used in experiments for establishing Air drag coefficient vs Mach number curves we use today for G1,G2,...,G8 drag models.
Physically, it's not necessarily true the drag coefficient of a projectile will remain the same if the projectile is scalled up/down in size.
The constancy assumption holds good in supersonic region in most of practical cases (AFAIK experimentally checked for some shapes over 0.1...10 caliber span). In subsonic, and deep subsonic region, where influence of Reynolds number might be important, I'm skeptical.
For smooth spheres the effect of size is dramatic:
https://www.arc.id.au/CannonballDrag.html

 

[DeathBeforeDismount]

If only there were a series of books that explained all of this in detail and is applicable to Long range shooting.............

https://thescienceofaccuracy.com/product-category/books-media/

 

[DocUSMCRetired]

Isn't SD per definition SD = mass/cross-section area?
So when we speak about axisymmetric projectile with circular cross section with diameter (caliber) d it should be:
SD = (4/π)*mass/d^2.
But I'm not here for simple math hair splitting.

I'm asking about projectile calibers used in experiments for establishing Air drag coefficient vs Mach number curves we use today for G1,G2,...,G8 drag models.
Physically, it's not necessarily true the drag coefficient of a projectile will remain the same if the projectile is scalled up/down in size.
The constancy assumption holds good in supersonic region in most of practical cases (AFAIK experimentally checked for some shapes over 0.1...10 caliber span). In subsonic, and deep subsonic region, where influence of Reynolds number might be important, I'm skeptical.
For smooth spheres the effect of size is dramatic:
https://www.arc.id.au/CannonballDrag.html

The formula for Sectional Density is Weight(in grains)/7000/Caliber Squared. I took some liberties here and simplified the formula. We convert from grains to pounds (7000 grains per pound) normally, but in this case it isn't necessary.

The math was simply to show you how it works. The projectile standards are 1lb and 1.0 calibers. They are scaled up and down from there to different calibers. I was simply answering the question of "what were the actual projectile sizes in experiments with standard projectile shapes". The answer is 1lb projectiles at 1.0 calibers.

The current G7 model most companies use is the G7 Rev II from around 1956 ish off the top of my head.

We did an update years ago to the data, by making perfect models of the G7 Bullets in different calibers. I can't really share much more of that data, or go into depth. But that updated information is what is in our engine and the military applications we provide which is now 95%+ what most major military and governments now run. Most other civilian applications are still on the G7 Rev II from 75 years ago. That information is not what is used for CDMs or PDMs because they don't use a BC at all.

I can share this but the official detailed data we hold proprietary. This is the data currently standardized in most modern fire control units.

 

[bulletbluesky]

The formula for Sectional Density is Weight(in grains)/7000/Caliber Squared. I took some liberties here and simplified the formula. We convert from grains to pounds (7000 grains per pound) normally, but in this case it isn't necessary.

The math was simply to show you how it works. The projectile standards are 1lb and 1.0 calibers. They are scaled up and down from there to different calibers. I was simply answering the question of "what were the actual projectile sizes in experiments with standard projectile shapes". The answer is 1lb projectiles at 1.0 calibers.

The current G7 model most companies use is the G7 Rev II from around 1956 ish off the top of my head.

We did an update years ago to the data, by making perfect models of the G7 Bullets in different calibers. I can't really share much more of that data, or go into depth. But that updated information is what is in our engine and the military applications we provide which is now 95%+ what most major military and governments now run. Most other civilian applications are still on the G7 Rev II from 75 years ago. That information is not what is used for CDMs or PDMs because they don't use a BC at all.

I can share this but the official detailed data we hold proprietary. This is the data currently standardized in most modern fire control units.

View attachment 8400025

Definition of sectional density just as SD=mass/caliber^2 actually makes sense because of the use of "per unit system". For the standard projectile it can be defined as "SD= 1mass unit/1caliber^2 unit=1" and other projectiles just compared to it. In this way any other numerical constants in physical description after comparative division get canceled out .

But I did't know that experiments with 1 lbs, 1.0 caliber projectiles were extensively conducted to confirm-correct G1 data from early days!
Have you got reference for that (I was unable to find it)?
Same question for G7 model introduced in 1952.

 

[LastShot300]

The formula for Sectional Density is Weight(in grains)/7000/Caliber Squared. I took some liberties here and simplified the formula. We convert from grains to pounds (7000 grains per pound) normally, but in this case it isn't necessary.

The math was simply to show you how it works. The projectile standards are 1lb and 1.0 calibers. They are scaled up and down from there to different calibers. I was simply answering the question of "what were the actual projectile sizes in experiments with standard projectile shapes". The answer is 1lb projectiles at 1.0 calibers.

The current G7 model most companies use is the G7 Rev II from around 1956 ish off the top of my head.

We did an update years ago to the data, by making perfect models of the G7 Bullets in different calibers. I can't really share much more of that data, or go into depth. But that updated information is what is in our engine and the military applications we provide which is now 95%+ what most major military and governments now run. Most other civilian applications are still on the G7 Rev II from 75 years ago. That information is not what is used for CDMs or PDMs because they don't use a BC at all.

I can share this but the official detailed data we hold proprietary. This is the data currently standardized in most modern fire control units.

View attachment 8400025

That's a cubic polynomial...not a cubic function. Not the same thing though. In summary, a cubic polynomial is a function represented by an expression, while a cubic equation is a statement that sets the polynomial equal to zero and asks for the values of x that satisfy the equation.

On the other hand the statement below doesn't make any sense at all...because there is a defined G7 standard projo and that's it. If you came up with a differente profile, fine, just call it AB profile...not an "enhanced G7" profile.

We did an update years ago to the data, by making perfect models of the G7 Bullets in different calibers

 

[bulletbluesky]

On the other hand the statement below doesn't make any sense at all...because there is a defined G7 standard projo and that's it. If you came up with a differente profile, fine, just call it AB profile...not an "enhanced G7" profile.

If I understood right, he only implies that they made accurate G7 projectiles bullet specimen shapes, calibers ballpark 0.223-0.408, in order to cross-check and update old data from G7 Rev II pub. They probably didn't made 1.00" caliber monolitic G7 projectile for resistance firings (that chunk of metal would weight around 5300 grains LoL)! The expected difference in range above 1.3 Mach would be very small/negligible anyway, and for practical use of rifle bullets the supersonic range is the most important. However, as stated before, I'm interested in effects of significant scale change in subsonic region becouse ballistic tables for all drag models are published down to 0.1 Mach

 

[LastShot300]

If I understood right, he only implies that they made accurate G7 projectiles bullet specimen shapes, calibers ballpark 0.223-0.408, in order to cross-check and update old data from G7 Rev II pub. They probably didn't made 1.00" caliber monolitic G7 projectile for resistance firings (that chunk of metal would weight around 5300 grains LoL)! The expected difference in range above 1.3 Mach would be very small/negligible anyway, and for practical use of rifle bullets the supersonic range is the most important. However, as stated before, I'm interested in effects of significant scale change in subsonic region becouse ballistic tables for all drag models are published down to 0.1 Mach

Hard to say, because the original G7 is an english design not sized like the G1. So, it'was not a 1.00" 1 pound sample. Subsonic is very interesint but usually very stable, I think most interesting is the transonic region. Makes sense?

 

[bulletbluesky]

Hard to say, because the original G7 is an english design not sized like the G1. So, it'was not a 1.00" 1 pound sample. Subsonic is very interesint but usually very stable, I think most interesting is the transonic region. Makes sense?

Well, for big projectiles, like artillery shells, transsonic region, as regards dynamic stability, is no problem (if that's what you're alluding to).These heavy mofos have a lot of inertia and rotating energy so they are not affected in the same way as a small arms projectiles. That's one more consequence of a scalling things up/down .
The following expository table is from "Modern Exterior Ballistics - The Launch and Flight dynamics of Symmetric Projectiles" by Robert L. McCoy:

Cdsp stands for 9/16" dia sphere. The textbook doesn't mention what about size for others? Probably based on 70 + years old data. Size matters more in subsonic. Well, it always does

 

[DocUSMCRetired]

If I understood right, he only implies that they made accurate G7 projectiles bullet specimen shapes, calibers ballpark 0.223-0.408, in order to cross-check and update old data from G7 Rev II pub. They probably didn't made 1.00" caliber monolitic G7 projectile for resistance firings (that chunk of metal would weight around 5300 grains LoL)! The expected difference in range above 1.3 Mach would be very small/negligible anyway, and for practical use of rifle bullets the supersonic range is the most important. However, as stated before, I'm interested in effects of significant scale change in subsonic region becouse ballistic tables for all drag models are published down to 0.1 Mach

This is sort of correct. It wasn't only to verify the current tables in use. But also to provide an update to when tables are used. Like when a user wants to use a G7 or G1 etc. Instead of using the old data sets from 75 years ago, it makes it possible to implement new data sets devised from new lab testing. If that makes sense. Essentially it created a G7 Rev III 2016. We have done this with others as well.

On the other hand the statement below doesn't make any sense at all...because there is a defined G7 standard projo and that's it. If you came up with a differente profile, fine, just call it AB profile...not an "enhanced G7" profile.

You don't understand the difference between a bullet profile and the data used in prediction modeling systems?

 

[DocUSMCRetired]

Have you got reference for that (I was unable to find it)?
Same question for G7 model introduced in 1952.

I did that research years and years ago when I needed to produce a historical portion for a bunch of training stuff. If I remember I can go back and find those references. Get the vacuum out and dust off some books etc lol.

 

[LastShot300]

You don't understand the difference between a bullet profile and the data used in prediction modeling systems?

I do and unless you can show some data backing your statemente, I stand correct. Call it AB profile and that would be fine. Renaming things in a funny way, only contributes to the general mystification of this matter. You said If that makes sense. Essentially it created a G7 Rev III 2016...well, it doesn't. And the reason is pretty obvious...it's not the same projo nor tested with the same specs (mass and form), etc. Make the data public and we would be able to assert your statements with utmost confidence in a peer review, which is the only way acceptable to true science.