Drag functions and drop charts
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Since nobody bothered to answer you, I will take a shot.
G1 is not sexy, but most bullets are listed this way and it makes your calculations look good /ubbthreads/images/graemlins/smile.gif
Sierra found that they do work well and while not perfect, for the average person this is probably the preferred model.
edge.
G1 is not sexy, but most bullets are listed this way and it makes your calculations look good /ubbthreads/images/graemlins/smile.gif
Sierra found that they do work well and while not perfect, for the average person this is probably the preferred model.
edge.
Mysticplayer
Well-Known Member
- Joined
- Jul 27, 2001
- Messages
- 1,459
The Drag or G function describes the type of bullet you use. I tried to find the definitions but my link no longer works. Flat base, Boat tail, Secant ogive, VLD are just a few of the broad categories that bullets fall into.
Each one is represented by a G function.
The BC is simply a number which illustrates the value for that G function. Can only be used to compare relative drag between bullets of the same G family.
Example a G5 bullet with 0.700BC will have less drag then a G5 bullet with a 0.500BC.
Without knowing what G function was used to generate the BC, it really is meaningless.
That is why some bullets fly substantially flatter despite having the same BC. The two bullets differ in G function which really defines how that bullet decelerates in flight.
Example a G1 bullet with a BC of 0.500 will not fly anywhere as flat as a G7 bullet with the same BC of 0.500.
The link will bring you to a site which has a ton of info on ballistics. Also, let's you generate drop charts and play with your data.
Unfortunately, there are no rules throughout the bullet industry to standardise the BC values. Some inflate their printed values to make their bullets look good. Others under estimate because the bullet follows a better drag function.
Some like Sierra give their BC's through shooting the bullets. Others just use the number that squirts out from a bullet form program.
Most BTHP match bullets follow a G5 function. Some poly tipped BT match bullets and VLD bullets follow the G7 drag function.
Also, bullets can change their relative G function and BC depending on the distortion incurred while travelling down the bore or at the velocities launched.
Confusing...You bet.
What I do is use a ballistics program to generate a drop chart. Use whatever printed data is given. This will get me close. I then make up a 'true' drop chart based on real world shooting on several days.
Jerry
http://www.eskimo.com/~jbm/calculations/calculations.html
Each one is represented by a G function.
The BC is simply a number which illustrates the value for that G function. Can only be used to compare relative drag between bullets of the same G family.
Example a G5 bullet with 0.700BC will have less drag then a G5 bullet with a 0.500BC.
Without knowing what G function was used to generate the BC, it really is meaningless.
That is why some bullets fly substantially flatter despite having the same BC. The two bullets differ in G function which really defines how that bullet decelerates in flight.
Example a G1 bullet with a BC of 0.500 will not fly anywhere as flat as a G7 bullet with the same BC of 0.500.
The link will bring you to a site which has a ton of info on ballistics. Also, let's you generate drop charts and play with your data.
Unfortunately, there are no rules throughout the bullet industry to standardise the BC values. Some inflate their printed values to make their bullets look good. Others under estimate because the bullet follows a better drag function.
Some like Sierra give their BC's through shooting the bullets. Others just use the number that squirts out from a bullet form program.
Most BTHP match bullets follow a G5 function. Some poly tipped BT match bullets and VLD bullets follow the G7 drag function.
Also, bullets can change their relative G function and BC depending on the distortion incurred while travelling down the bore or at the velocities launched.
Confusing...You bet.
What I do is use a ballistics program to generate a drop chart. Use whatever printed data is given. This will get me close. I then make up a 'true' drop chart based on real world shooting on several days.
Jerry
http://www.eskimo.com/~jbm/calculations/calculations.html
With all due respect, G1 was found to be the most consistent function with almost every standard bullet from flat base to Boat Tail. That is why Sierra adopted G1 for their bullets.
Clearly nothing beats shooting bullets from your rifle and in your conditions, but IMO, G1 is what almost every bullet manufacturer uses and unless you have independent data I say stick with G1.
edge.
Clearly nothing beats shooting bullets from your rifle and in your conditions, but IMO, G1 is what almost every bullet manufacturer uses and unless you have independent data I say stick with G1.
edge.
From the Sierra website.
http://www.exteriorballistics.com/ebexplained/4th/44.cfm
2) G 1 is the Most Appropriate Drag Function Choice for Sierra's Bullets
The tests conducted in 1971 also compared four standard drag functions to determine which of these models was best for Sierra's boat tail bullets. The four drag functions were published by Winchester-Western:
G 1 - for all bullets except those in the categories below
G 5 - for low base drag bullets (i.e., boat tail bullets)
G 6 - for flat base, sharp pointed, full patch bullets
G L - for hollow point, lead nose bullets
Theory says that if the drag model matches the true bullet drag, the ballistic coefficient will be constant at all velocities. If the drag model does not match the true drag, then we will find different values of ballistic coefficient in measurements at different muzzle velocities.
Several bullets were used in the tests, both flat base and boat tail types. For each bullet type, several test rounds (typically 5 to 10) were fired at each of two muzzle velocities (typically 3000 and 2500 fps). For each test round four ballistic coefficients were determined ( C 1 , C 5 , C 6 , and C L ). This procedure gave two sets of four ballistic coefficient values for each bullet type, one set for the higher muzzle velocity and one for the lower. By comparing the values in the two sets, it was easy to see which of the four C's changed significantly (outside the measurement error band) and which did not. From theory we expected that the best drag model ( G 1 , G 5 , G 6 , or G L ) for each bullet type to be the one for which the corresponding ballistic coefficient ( C 1 , C 5 , C 6 , or C L ) changed the least amount between the two muzzle velocity levels.
Although we expected G 5 to be best for the boat tail bullets, the tests showed that G 1 was better. This was a surprise. The second surprise was that, while G 1 was best for flat base bullets, C 1 was not constant; it varied significantly with muzzle velocity.
With these observations, G 1 was adopted as the standard drag model for all Sierra bullets. Values of ballistic coefficients in all Sierra Manuals are referenced to the G 1 drag function.
Finding that G 1 was best for boat tail bullets was fortunate, because G 1 has been and continues to be used by all commercial manufacturers of bullets. Consequently, ballistic comparison can be made between bullets made by different manufacturers, as well as between bullets made by a single manufacturer. If different drag models were necessary for different bullets or different bullet styles, comparisons based on ballistic coefficients would not be possible. Another advantage of G 1 is that it is the drag function for the Ingalls Tables, so that ballistic trajectories can be calculated using those tables.
http://www.exteriorballistics.com/ebexplained/4th/44.cfm
2) G 1 is the Most Appropriate Drag Function Choice for Sierra's Bullets
The tests conducted in 1971 also compared four standard drag functions to determine which of these models was best for Sierra's boat tail bullets. The four drag functions were published by Winchester-Western:
G 1 - for all bullets except those in the categories below
G 5 - for low base drag bullets (i.e., boat tail bullets)
G 6 - for flat base, sharp pointed, full patch bullets
G L - for hollow point, lead nose bullets
Theory says that if the drag model matches the true bullet drag, the ballistic coefficient will be constant at all velocities. If the drag model does not match the true drag, then we will find different values of ballistic coefficient in measurements at different muzzle velocities.
Several bullets were used in the tests, both flat base and boat tail types. For each bullet type, several test rounds (typically 5 to 10) were fired at each of two muzzle velocities (typically 3000 and 2500 fps). For each test round four ballistic coefficients were determined ( C 1 , C 5 , C 6 , and C L ). This procedure gave two sets of four ballistic coefficient values for each bullet type, one set for the higher muzzle velocity and one for the lower. By comparing the values in the two sets, it was easy to see which of the four C's changed significantly (outside the measurement error band) and which did not. From theory we expected that the best drag model ( G 1 , G 5 , G 6 , or G L ) for each bullet type to be the one for which the corresponding ballistic coefficient ( C 1 , C 5 , C 6 , or C L ) changed the least amount between the two muzzle velocity levels.
Although we expected G 5 to be best for the boat tail bullets, the tests showed that G 1 was better. This was a surprise. The second surprise was that, while G 1 was best for flat base bullets, C 1 was not constant; it varied significantly with muzzle velocity.
With these observations, G 1 was adopted as the standard drag model for all Sierra bullets. Values of ballistic coefficients in all Sierra Manuals are referenced to the G 1 drag function.
Finding that G 1 was best for boat tail bullets was fortunate, because G 1 has been and continues to be used by all commercial manufacturers of bullets. Consequently, ballistic comparison can be made between bullets made by different manufacturers, as well as between bullets made by a single manufacturer. If different drag models were necessary for different bullets or different bullet styles, comparisons based on ballistic coefficients would not be possible. Another advantage of G 1 is that it is the drag function for the Ingalls Tables, so that ballistic trajectories can be calculated using those tables.
Mysticplayer
Well-Known Member
- Joined
- Jul 27, 2001
- Messages
- 1,459
I have little doubt that Sierra uses the G1 function in their BC calcs and that the tests done back then was a fair representation of the bullets manf at that time.
However, times have changed and so have bullet profiles.
We now have bullets of same weight with a huge variety of shapes and lengths. We now have both secant and tangent ogives. Bullets made with a variety of shapes usually lumped as VLD bullets.
We have poly tips, grooved bullets, small HP, wide HP, trimmed HP and on it goes.
So G1 does not represent all bullets manf today. All one needs to do is shoot conventional HP bullets like Sierra Matchking next to HP like the Lapua Scenar or poly tips like the Amax, SST, interbond, ballistic tip/accubond.
Although the BC suggests their ballistics to be similar, drop at distance indicates otherwise.
When I did my own tests a few years ago, I compared Nosler J4 (identical to Sierra MK), Nosler BT and Hornady Amax of equal weight. All launched at the same velocity as it was measured during firing. All had basically the same 100yd zero.
At 700yds, the HP bullets dropped consistently more then the poly tipped bullets. Impact groups/accuracy was similar between bullets. The drop extended as distance increased to 2 to 3MOA more scope elevation needed for the HP bullets at 900yds.
Recent tests with SST and Interbonds show that these can fly even flatter. Bullet lengths have increased for the given weight. This indicates an increase in streamlined shape. However, printed BC is pretty close to the same.
While playing with Amax in a few rifles at distances out to 940yds, the drop charts used would not agree with real world impacts. The real world drops were substantially less.
By playing with the program, nothing worked. Wasn't until I started plugging in different G functions that things started to agree.
So, G1 may work for some bullets very well, they don't work for all bullets today. By the way, the amax was a 162gr 7mm and the data agreed with my shooting when I used a G7 drag function with the printed BC of 0.625.
Now compare that to the G1 value....
Jerry
However, times have changed and so have bullet profiles.
We now have bullets of same weight with a huge variety of shapes and lengths. We now have both secant and tangent ogives. Bullets made with a variety of shapes usually lumped as VLD bullets.
We have poly tips, grooved bullets, small HP, wide HP, trimmed HP and on it goes.
So G1 does not represent all bullets manf today. All one needs to do is shoot conventional HP bullets like Sierra Matchking next to HP like the Lapua Scenar or poly tips like the Amax, SST, interbond, ballistic tip/accubond.
Although the BC suggests their ballistics to be similar, drop at distance indicates otherwise.
When I did my own tests a few years ago, I compared Nosler J4 (identical to Sierra MK), Nosler BT and Hornady Amax of equal weight. All launched at the same velocity as it was measured during firing. All had basically the same 100yd zero.
At 700yds, the HP bullets dropped consistently more then the poly tipped bullets. Impact groups/accuracy was similar between bullets. The drop extended as distance increased to 2 to 3MOA more scope elevation needed for the HP bullets at 900yds.
Recent tests with SST and Interbonds show that these can fly even flatter. Bullet lengths have increased for the given weight. This indicates an increase in streamlined shape. However, printed BC is pretty close to the same.
While playing with Amax in a few rifles at distances out to 940yds, the drop charts used would not agree with real world impacts. The real world drops were substantially less.
By playing with the program, nothing worked. Wasn't until I started plugging in different G functions that things started to agree.
So, G1 may work for some bullets very well, they don't work for all bullets today. By the way, the amax was a 162gr 7mm and the data agreed with my shooting when I used a G7 drag function with the printed BC of 0.625.
Now compare that to the G1 value....
Jerry
I agree to disagree /ubbthreads/images/graemlins/smile.gif
IMO, and according to what I have read, the B.C. changes as velocity decays so to assume that a single B.C. works from the muzzle to 1k is wrong.
IMO, a B.C. will get you "on the paper", but most likely you are better served by shooting the bullets over several ranges and making a drop chart. How stable the bullet is as it exits your rifle can have a dramatic effect on drop at long range. Bullet quality at long range may influence POI more than most other factors.
I enjoy the discussion.
edge.
IMO, and according to what I have read, the B.C. changes as velocity decays so to assume that a single B.C. works from the muzzle to 1k is wrong.
IMO, a B.C. will get you "on the paper", but most likely you are better served by shooting the bullets over several ranges and making a drop chart. How stable the bullet is as it exits your rifle can have a dramatic effect on drop at long range. Bullet quality at long range may influence POI more than most other factors.
I enjoy the discussion.
edge.
Mikecr
Well-Known Member
BC is dependent on drag. From the muzzle or any other point. It varies only because drag varies. The bullet's curve. BC could be used as a constant because of this, but it's used as a variable in software. Unless some other decay factor is used. From what I've seen, it's often used wrong(like using a G1 BC WITH a G7 drag curve, or claiming a ridiculous G1 BC from a bullet which is really following G7 curve at a G7 BC)
Adjustment of a bullet's drag curve to match in ballistic software would be great. Seems like someone was working on this with what they called a 'DK' adjustment(bain). It flattened the curve to match field observed drops at different distances.Not just 2 distances either. Far superior to BC adjustment, which can only actually be correct at 2 points. Sierra's BCs at different velocities offers potential for more, close points. A pretty poor bandaid, but what else could they do given that nearly all ballistic software available has set drag curves which do not match our bullets. The only control Sierra has over this market is in their BC numbers.
Adjustment of a bullet's drag curve to match in ballistic software would be great. Seems like someone was working on this with what they called a 'DK' adjustment(bain). It flattened the curve to match field observed drops at different distances.Not just 2 distances either. Far superior to BC adjustment, which can only actually be correct at 2 points. Sierra's BCs at different velocities offers potential for more, close points. A pretty poor bandaid, but what else could they do given that nearly all ballistic software available has set drag curves which do not match our bullets. The only control Sierra has over this market is in their BC numbers.
JBM
Well-Known Member
[ QUOTE ]
BC is dependent on drag. From the muzzle or any other point. It varies only because drag varies. The bullet's curve. BC could be used as a constant because of this, but it's used as a variable in software. Unless some other decay factor is used. From what I've seen, it's often used wrong(like using a G1 BC WITH a G7 drag curve, or claiming a ridiculous G1 BC from a bullet which is really following G7 curve at a G7 BC)
[/ QUOTE ]
Originally, the BC was used to relate a "standard" bullet's drag to that of the bullet in question. The idea was that if you had a good enough drag function, you could use one BC to represent a bullet of the same "type" (or drag curve shape).
I agree that it doesn't make sense to use a G1 BC with a G7 drag function. It's just plain wrong.
I think it's important to keep in mind what is really going on here. You are using two values to find the CD (drag coefficient) of the bullet as a function of mach number (not distance). The CD is proportional to G/BC (there is also a velocity term, density and some constants in there see my website for the formula -- it's at CD and KD). So if you have the right G function, and the right BC, or list of BCs you can get a good value for the CD as a function of mach number depending on how many BCs you want to use. If you use enough, you can use any drag function you want, of course the less the drag function "fits" the bullet, the more BCs you'll have to use.
This gets us to the point of using different drag functions. If you can find a drag function that fits a bullet well, you only have to use one drag function -- in other words, the CD is proportional to G.
As an example, look at a .223 caliber boattail:
1.000 0.268
1.100 0.295
1.200 0.317
1.300 0.335
1.400 0.349
1.500 0.360
1.600 0.367
1.700 0.372
1.800 0.377
2.000 0.383
2.200 0.390
2.500 0.404
3.000 0.439
3.500 0.488
4.000 0.541
4.500 0.595
The first column is the mach number and the second column is the BC (G1). This data is taken from my online Drag/Twist calculation.
For a G7 BC we have:
1.000 0.212
1.100 0.201
1.200 0.192
1.300 0.190
1.400 0.189
1.500 0.188
1.600 0.188
1.700 0.188
1.800 0.189
2.000 0.193
2.200 0.197
2.500 0.202
3.000 0.208
3.500 0.208
4.000 0.209
4.500 0.210
Note that there is much less variation using the G7 drag function. If I had to pick one BC, I'd use the G7 drag function and a BC of about 0.200 (I'm guessing by looking at the data, in practice, it would probably be a weighted average over the velocity range I was interested in, but it wouldn't make that much difference!).
Does that mean that the G1 BC is wrong? If you used software that allowed any number of BCs as a function of mach number (or velocity at some conditions) and put in these 16 BC values for G1 and G7, you wouldn't see any difference. If you picked a single BC and ran it, you would.
So is it wrong to use multiple BCs? If you use a single drag function, then you pretty much have to use multiple BCs for some bullets.
[ QUOTE ]
Adjustment of a bullet's drag curve to match in ballistic software would be great. Seems like someone was working on
[/ QUOTE ]
You're better off using CD versus mach number and just ditching the whole BC idea (that's what my modified point mass program does). Of course there are market considerations that the bullet manufacturers have to deal with that I don't. Can you imagine trying to sell a bullet with a G7 BC of half the value of your competitors G1 BC and trying to explain to all your customers that it has less drag? No thanks.
[ QUOTE ]
this with what they called a 'DK' adjustment(bain). It flattened the curve to match field observed drops at different distances.Not just 2 distances either. Far superior to BC adjustment, which can only actually be correct at 2 points.
[/ QUOTE ]
I'm not sure why you say this. Why two points? I would think it's really only valid at one point. Manufacturers have chosen BC values over a range of velocities to give decent accuracy (I'm not sure how they define that though).
[ QUOTE ]
Sierra's BCs at different velocities offers potential for more, close points. A pretty poor bandaid, but what else could they do given that nearly all ballistic software available has set drag curves which do not match our bullets. The only control Sierra has over this market is in their BC numbers.
[/ QUOTE ]
Yep. I can tell you from personal experience that when you mention CD versus Mach number, the eyes roll back into people's heads and the lights turn out (not for everyone granted, but it's typical).
JBM
BC is dependent on drag. From the muzzle or any other point. It varies only because drag varies. The bullet's curve. BC could be used as a constant because of this, but it's used as a variable in software. Unless some other decay factor is used. From what I've seen, it's often used wrong(like using a G1 BC WITH a G7 drag curve, or claiming a ridiculous G1 BC from a bullet which is really following G7 curve at a G7 BC)
[/ QUOTE ]
Originally, the BC was used to relate a "standard" bullet's drag to that of the bullet in question. The idea was that if you had a good enough drag function, you could use one BC to represent a bullet of the same "type" (or drag curve shape).
I agree that it doesn't make sense to use a G1 BC with a G7 drag function. It's just plain wrong.
I think it's important to keep in mind what is really going on here. You are using two values to find the CD (drag coefficient) of the bullet as a function of mach number (not distance). The CD is proportional to G/BC (there is also a velocity term, density and some constants in there see my website for the formula -- it's at CD and KD). So if you have the right G function, and the right BC, or list of BCs you can get a good value for the CD as a function of mach number depending on how many BCs you want to use. If you use enough, you can use any drag function you want, of course the less the drag function "fits" the bullet, the more BCs you'll have to use.
This gets us to the point of using different drag functions. If you can find a drag function that fits a bullet well, you only have to use one drag function -- in other words, the CD is proportional to G.
As an example, look at a .223 caliber boattail:
1.000 0.268
1.100 0.295
1.200 0.317
1.300 0.335
1.400 0.349
1.500 0.360
1.600 0.367
1.700 0.372
1.800 0.377
2.000 0.383
2.200 0.390
2.500 0.404
3.000 0.439
3.500 0.488
4.000 0.541
4.500 0.595
The first column is the mach number and the second column is the BC (G1). This data is taken from my online Drag/Twist calculation.
For a G7 BC we have:
1.000 0.212
1.100 0.201
1.200 0.192
1.300 0.190
1.400 0.189
1.500 0.188
1.600 0.188
1.700 0.188
1.800 0.189
2.000 0.193
2.200 0.197
2.500 0.202
3.000 0.208
3.500 0.208
4.000 0.209
4.500 0.210
Note that there is much less variation using the G7 drag function. If I had to pick one BC, I'd use the G7 drag function and a BC of about 0.200 (I'm guessing by looking at the data, in practice, it would probably be a weighted average over the velocity range I was interested in, but it wouldn't make that much difference!).
Does that mean that the G1 BC is wrong? If you used software that allowed any number of BCs as a function of mach number (or velocity at some conditions) and put in these 16 BC values for G1 and G7, you wouldn't see any difference. If you picked a single BC and ran it, you would.
So is it wrong to use multiple BCs? If you use a single drag function, then you pretty much have to use multiple BCs for some bullets.
[ QUOTE ]
Adjustment of a bullet's drag curve to match in ballistic software would be great. Seems like someone was working on
[/ QUOTE ]
You're better off using CD versus mach number and just ditching the whole BC idea (that's what my modified point mass program does). Of course there are market considerations that the bullet manufacturers have to deal with that I don't. Can you imagine trying to sell a bullet with a G7 BC of half the value of your competitors G1 BC and trying to explain to all your customers that it has less drag? No thanks.
[ QUOTE ]
this with what they called a 'DK' adjustment(bain). It flattened the curve to match field observed drops at different distances.Not just 2 distances either. Far superior to BC adjustment, which can only actually be correct at 2 points.
[/ QUOTE ]
I'm not sure why you say this. Why two points? I would think it's really only valid at one point. Manufacturers have chosen BC values over a range of velocities to give decent accuracy (I'm not sure how they define that though).
[ QUOTE ]
Sierra's BCs at different velocities offers potential for more, close points. A pretty poor bandaid, but what else could they do given that nearly all ballistic software available has set drag curves which do not match our bullets. The only control Sierra has over this market is in their BC numbers.
[/ QUOTE ]
Yep. I can tell you from personal experience that when you mention CD versus Mach number, the eyes roll back into people's heads and the lights turn out (not for everyone granted, but it's typical).
JBM
Mysticplayer
Well-Known Member
- Joined
- Jul 27, 2001
- Messages
- 1,459
JBM, thanks for the info. Been using your software for the last few years and am very happy with the results. Nice to see all the changes on your site. Now I can't find anything /ubbthreads/images/graemlins/grin.gif
I think you hit the nail on the head. BC has become the holy grail that is used/misused to sell product. It really is a meaningless number unless you take into account the assumptions that are made.
Precious few shooters actually know what the BC means in real terms.
I think that many bullet manf are understating their BC so that consumers will not go BS and slag the company.
What would happen if someone said BC 0.625 BUT a G7 curve? Run that through a G1 comparison as on your software and HOLY S...can't be true.
Conversely, there are some who use an 'elevated' BC number by using a more favorable drag curve function in their calculations.
No standards and too much smoke/mirrors.
Only way to know for sure is to launch them in your rifle, your scope and rangefinder. Then you create data that is precisely incorrect except for this one set of circumstances.
Ultimately, if it is reliable and repeatable, that is what matters to LR shooters/hunters. The actual numbers don't really matter.
But it makes for great conversations...
Jerry
PS the drop table I created for that 162gr Amax shooting 7RM agreed with my real world drops out to 940yds to the click. One BC number can work IF the drag curve/scope/rangefinder/shooter/etc. fit. Unfortunately, that is very rare.
I think you hit the nail on the head. BC has become the holy grail that is used/misused to sell product. It really is a meaningless number unless you take into account the assumptions that are made.
Precious few shooters actually know what the BC means in real terms.
I think that many bullet manf are understating their BC so that consumers will not go BS and slag the company.
What would happen if someone said BC 0.625 BUT a G7 curve? Run that through a G1 comparison as on your software and HOLY S...can't be true.
Conversely, there are some who use an 'elevated' BC number by using a more favorable drag curve function in their calculations.
No standards and too much smoke/mirrors.
Only way to know for sure is to launch them in your rifle, your scope and rangefinder. Then you create data that is precisely incorrect except for this one set of circumstances.
Ultimately, if it is reliable and repeatable, that is what matters to LR shooters/hunters. The actual numbers don't really matter.
But it makes for great conversations...
Jerry
PS the drop table I created for that 162gr Amax shooting 7RM agreed with my real world drops out to 940yds to the click. One BC number can work IF the drag curve/scope/rangefinder/shooter/etc. fit. Unfortunately, that is very rare.
