# Please help me calculate ballistic coefficient using down range velocities from Shot Marker

#### 65WSM

##### Well-Known Member
Shot marker gives us the velocity of bullets at the target. Using Lab radar at the muzzle or Magnetospeed, you have two velocities to calculate the Ballistic Coefficient. Please direct me to an appropriate formula? I shoot at 540 yards, the back of the range, so there is the potential for some precision. Thanks.

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#### Trnelson

##### Well-Known Member
The easiest method would be to input your initial velocity in a ballistic solver and manipulate the given BC until the output velocity at the target range. Once this matches closely to what the shot marker is reporting you are going to be well on the way. Of course you will want to verify the actual observed drop at other ranges to further validate.

#### 338 dude

##### Well-Known Member
Shot marker gives us the velocity of bullets at the target. Using Lab radar at the muzzle or Magnetospeed, you have two velocities to calculate the Ballistic Coefficient. Please direct me to an appropriate formula? I shoot at 540 yards, the back of the range, so there is the potential for some precision. Thanks.
What bullet are you shooting I can help you by looking it up in Bryan Litz’s book

#### sable tireur

##### Well-Known Member
Ballistic Coefficient calculation

Commonly used nowadays is the ballistic coefficient (BC or G) according to Karpov (i.e. Dr. Boris Karpov, US Army Research Laboratory, 1944), which represents not only the characteristics of the shape and the weight of the bullet, but also takes into account the actual air resistance at a specific velocity.

To calculate the ballistic coefficient requires two velocities. The initial velocity (V0​), and then, at a certain point on the trajectory at the distance x from the muzzle, the Vx​ velocity. To measure V0​ directly is difficult; therefore V5​ and V100​ were measured, from which V0​ was subsequently extrapolated. The ballistic coefficient for one hundred metres is calculated using the following formula, in which x = 100 m. Similarly this is also applicable, of course, to other distances.
The ballistic coefficient was not adjusted in accordance with the altitude and should be considered as being universal, since Sellier & Bellot's ballistic testing laboratory is 400 m asl., which corresponds to the average altitude of the Czech Republic. A distance of one hundred metres was chosen because, at this distance, S&B also checks the accuracy of the ammunition and because this distance has long been considered as being a "hunting" distance. The actual tests were carried out in such a manner that, using the same series of ammunition, first V5​ and subsequently V100​ were shot from the same barrel. Since the shooting was not performed simultaneously, firing was repeated with other series and the uniformity of the results was monitored. The ammunition was always tempered to +21 ºC.
BCs are calculated to three decimal places, which is in practice is completely satisfactory. Even after correcting for the atmospheric conditions and the altitude, the weight tolerance of the bullet and its initial velocity (V0​) still come into play, and of course so does the length and the wear of the specific barrel.
The entire issue is actually much broader, because, for example, on the Internet it is possible to find articles that describe differences of up to 25% from the values reported by the manufacturer and discovered in the case of overshoot.
The values specified by S&B correspond very well with reality, because the velocity at a distance of 100 metres was measured and also because it is not a result that is based on a single firing. Also the documentation provided by the Sierra Company can be accepted as being reliable. The results, however, for the reasons described in the preceding paragraph, cannot be taken as dogma.

https://www.sellier-bellot.cz/en/products/ballistic-coefficient-calculation/

________________________________________________________________________________________________________________________________________________________

Differing mathematical models and bullet ballistic coefficients

G1 shape standard projectile. All measurements in calibers/diameters.

G7 shape standard projectile. All measurements in calibers/diameters.

Wind drift calculations for rifle bullets of differing G1 BCs fired with a muzzle velocity of 2,950 ft/s (900 m/s) in a 10 mph (4.5 m/s; 16 km/h) crosswind.[58]

Energy calculations for 9.1 grams (140 gr) rifle bullets of differing G1 BCs fired with a muzzle velocity of 2,950 feet per second (900 m/s).[59]

Most ballistic mathematical models and hence tables or software take for granted that one specific drag function correctly describes the drag and hence the flight characteristics of a bullet related to its ballistic coefficient. Those models do not differentiate between wadcutter, flat-based, spitzer, boat-tail, very-low-drag, etc. bullet types or shapes. They assume one invariable drag function as indicated by the published BC. Several different drag curve models optimized for several standard projectile shapes are available, however.

The resulting drag curve models for several standard projectile shapes or types are referred to as:

• G1 or Ingalls (flatbase with 2 caliber (blunt) nose ogive - by far the most popular)[60]
• G2 (Aberdeen J projectile)
• G5 (short 7.5° boat-tail, 6.19 calibers long tangent ogive)
• G6 (flatbase, 6 calibers long secant ogive)
• G7 (long 7.5° boat-tail, 10 calibers secant ogive, preferred by some manufacturers for very-low-drag bullets[61])
• G8 (flatbase, 10 calibers long secant ogive)
• GL (blunt lead nose)

Since these standard projectile shapes differ significantly the Gx BC will also differ significantly from the Gy BC for an identical bullet.[62] To illustrate this the bullet manufacturer Berger has published the G1 and G7 BCs for most of their target, tactical, varmint and hunting bullets.[63] Other bullet manufacturers like Lapua and Nosler also published the G1 and G7 BCs for most of their target bullets.[64][65] How much a projectile deviates from the applied reference projectile is mathematically expressed by the form factor (i). The applied reference projectile shape always has a form factor (i) of exactly 1. When a particular projectile has a sub 1 form factor (i) this indicates that the particular projectile exhibits lower drag than the applied reference projectile shape. A form factor (i) greater than 1 indicates the particular projectile exhibits more drag than the applied reference projectile shape.[66] In general the G1 model yields comparatively high BC values and is often used by the sporting ammunition industry.[65]

Courtesy of Wikipedia​

_________________________________________________________________________________________________________________________________________________________________________________________________________​

Ballistic Calculator:

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#### phorwath

##### Well-Known Member
I see nothing in the prior post that allows the input of the actual atmospheric conditions at the location you shoot and collect bullet velocity. Until the link to the JBM ballistics calculator.

If your station atmospheric condition data (Pressure, Temperature) is off just a little bit, you'll end up with error in your BC calculation. I changed temperature just 1 degree Fahrenheit yesterday when calculating BC values using LabRadar velocity data. Was surprised how much it affected the BC value calculated by my ballistics program.

To have any chance of calculating an accurate BC, you need to collect, and input, accurate atmospheric conditions into the ballistics program.

#### sable tireur

##### Well-Known Member
As you well know, there is always an introductory to these technical presentations. Too much information and math usually scares some folks away.

Yes, there is always more details to create the full set of calculations. Plus I wanted to offer a slight introduction to G1 and G7. Otherwise I would stuck writing a complete book on this subject and then being told I still left something out...

#### phorwath

##### Well-Known Member
Hey, at least the JBM link was included! I think the OP will now rely on it...

#### sable tireur

##### Well-Known Member
Maybe, maybe not. But who really cares. People that really want to figure something out will eventually find a way.

Have a great day!

#### Trnelson

##### Well-Known Member
Maybe, maybe not. But who really cares. People that really want to figure something out will eventually find a way.

Have a great day!

I to struggle with trying to settle on an appropriate level of detail as well when responding. I’ve arrived at the conclusion that most folks don’t care why or how, and further probably won’t understand those details, especially if it involves arithmetic. Normally anymore I just give the simplest solution I can think of with the least amount of effort or calculation. Though I personally enjoy geeking out over the equations.

#### nksmfamjp

##### Well-Known Member
Ballistic Coefficient calculation

Commonly used nowadays is the ballistic coefficient (BC or G) according to Karpov (i.e. Dr. Boris Karpov, US Army Research Laboratory, 1944), which represents not only the characteristics of the shape and the weight of the bullet, but also takes into account the actual air resistance at a specific velocity.

View attachment 379565

To calculate the ballistic coefficient requires two velocities. The initial velocity (V0​), and then, at a certain point on the trajectory at the distance x from the muzzle, the Vx​ velocity. To measure V0​ directly is difficult; therefore V5​ and V100​ were measured, from which V0​ was subsequently extrapolated. The ballistic coefficient for one hundred metres is calculated using the following formula, in which x = 100 m. Similarly this is also applicable, of course, to other distances.
The ballistic coefficient was not adjusted in accordance with the altitude and should be considered as being universal, since Sellier & Bellot's ballistic testing laboratory is 400 m asl., which corresponds to the average altitude of the Czech Republic. A distance of one hundred metres was chosen because, at this distance, S&B also checks the accuracy of the ammunition and because this distance has long been considered as being a "hunting" distance. The actual tests were carried out in such a manner that, using the same series of ammunition, first V5​ and subsequently V100​ were shot from the same barrel. Since the shooting was not performed simultaneously, firing was repeated with other series and the uniformity of the results was monitored. The ammunition was always tempered to +21 ºC.
BCs are calculated to three decimal places, which is in practice is completely satisfactory. Even after correcting for the atmospheric conditions and the altitude, the weight tolerance of the bullet and its initial velocity (V0​) still come into play, and of course so does the length and the wear of the specific barrel.
The entire issue is actually much broader, because, for example, on the Internet it is possible to find articles that describe differences of up to 25% from the values reported by the manufacturer and discovered in the case of overshoot.
The values specified by S&B correspond very well with reality, because the velocity at a distance of 100 metres was measured and also because it is not a result that is based on a single firing. Also the documentation provided by the Sierra Company can be accepted as being reliable. The results, however, for the reasons described in the preceding paragraph, cannot be taken as dogma.

https://www.sellier-bellot.cz/en/products/ballistic-coefficient-calculation/

________________________________________________________________________________________________________________________________________________________

Differing mathematical models and bullet ballistic coefficients

G1 shape standard projectile. All measurements in calibers/diameters.

G7 shape standard projectile. All measurements in calibers/diameters.

Wind drift calculations for rifle bullets of differing G1 BCs fired with a muzzle velocity of 2,950 ft/s (900 m/s) in a 10 mph (4.5 m/s; 16 km/h) crosswind.[58]

Energy calculations for 9.1 grams (140 gr) rifle bullets of differing G1 BCs fired with a muzzle velocity of 2,950 feet per second (900 m/s).[59]

Most ballistic mathematical models and hence tables or software take for granted that one specific drag function correctly describes the drag and hence the flight characteristics of a bullet related to its ballistic coefficient. Those models do not differentiate between wadcutter, flat-based, spitzer, boat-tail, very-low-drag, etc. bullet types or shapes. They assume one invariable drag function as indicated by the published BC. Several different drag curve models optimized for several standard projectile shapes are available, however.

The resulting drag curve models for several standard projectile shapes or types are referred to as:

• G1 or Ingalls (flatbase with 2 caliber (blunt) nose ogive - by far the most popular)[60]
• G2 (Aberdeen J projectile)
• G5 (short 7.5° boat-tail, 6.19 calibers long tangent ogive)
• G6 (flatbase, 6 calibers long secant ogive)
• G7 (long 7.5° boat-tail, 10 calibers secant ogive, preferred by some manufacturers for very-low-drag bullets[61])
• G8 (flatbase, 10 calibers long secant ogive)
• GL (blunt lead nose)

Since these standard projectile shapes differ significantly the Gx BC will also differ significantly from the Gy BC for an identical bullet.[62] To illustrate this the bullet manufacturer Berger has published the G1 and G7 BCs for most of their target, tactical, varmint and hunting bullets.[63] Other bullet manufacturers like Lapua and Nosler also published the G1 and G7 BCs for most of their target bullets.[64][65] How much a projectile deviates from the applied reference projectile is mathematically expressed by the form factor (i). The applied reference projectile shape always has a form factor (i) of exactly 1. When a particular projectile has a sub 1 form factor (i) this indicates that the particular projectile exhibits lower drag than the applied reference projectile shape. A form factor (i) greater than 1 indicates the particular projectile exhibits more drag than the applied reference projectile shape.[66] In general the G1 model yields comparatively high BC values and is often used by the sporting ammunition industry.[65]

Courtesy of Wikipedia​

_________________________________________________________________________________________________________________________________________________________________________________________________________​

Ballistic Calculator:

While this is the correct way, I think @Trnelson ’s method would be more my speed!…..and, yes I’m an engineer.

#### waveslayer

##### Well-Known Member
Your BC will change with Velocity , so you can calculate it for super sonic, transonic,, and then subsonic... for 595 yards BC isn't a factor. Just use velocity.

Unless you're trying to take your load to distance then BC will play a factor. Anything below 600-800 yards BC really doesn't matter

#### phorwath

##### Well-Known Member
... for 595 yards BC isn't a factor. Just use velocity.

Unless you're trying to take your load to distance then BC will play a factor. Anything below 600-800 yards BC really doesn't matter

Just use velocity for what?

Not following your train of thought. Curious why you feel BC really doesn't matter out to 800 yards?

#### waveslayer

##### Well-Known Member
Just use velocity for what?

Not following your train of thought. Curious why you feel BC really doesn't matter out to 800 yards?
Velocity to tune or True your data. You can use a close proximity for BC.

BC plays the major role as you get farther out. . That's why when you true your calculators you only true velocity out to 600-800 yards. Past that you don't touch Velocity you true BC.

#### Mikecr

##### Well-Known Member
While this is the correct way, I think @Trnelson ’s method would be more my speed!…..and, yes I’m an engineer.
No it's not correct. BC = Sectional Density/Form Factor
Sellier & Bellot should have run this with any modern ballistic calculator to see that their posted G1 formula does not represent BC.
What it likely leads too is total drag, which is divided by a G1 drag coefficient at velocity -for G1 Form Factor.

And simply defining a result at 400m asl, at 100m, is not the same as prediction otherwise.

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