The REALLY, real- real BC

AlwaysLastPlace said:

Are you aware of any way to get Strelok anymore?

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Through the Samsung Galaxy app store.

Or installing it from an .apk file (➔ PM).

Matthias

This is interesting. I have figured out how to take raw shot data from LabRadar and all of the downrange velocity data and clean it up. (If you have a LR, it uses very simple math to give you downrange velocity. The radar data past 50y gets a bit choppy and their math increase the effect of that error).

So with smoothed and sensible downrange velocity data I’m looking forward to comparing it high quality ballistic models. Maybe, for once, the ballistic model, the LabRadar data, and actual holdovers will agree!

dgeesaman said:

This is interesting. I have figured out how to take raw shot data from LabRadar and all of the downrange velocity data and clean it up. (If you have a LR, it uses very simple math to give you downrange velocity. The radar data past 50y gets a bit choppy and their math increase the effect of that error).

So with smoothed and sensible downrange velocity data I’m looking forward to comparing it high quality ballistic models. Maybe, for once, the ballistic model, the LabRadar data, and actual holdovers will agree!

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Be careful how you smooth the data. The answer you get will often be distorted by the smoothing method used, to the extent that any drag curves you get can be completely the wrong shape. The only reason I know this is because I had to spend years analysing thousands of radar tracks and, at first, sometimes getting the wrong answers, not really what you want when you are producing fire control data. Many were obviously wrong, some demanding new laws of aerodynamics to explain them if they were correct (I even had one which required accelerating bullets).

The best method I found in the end was to take the unsmoothed data, carry out the analysis, and then smooth the final results. At the furthest ranges, you will probably end up having to do it by eye, as it gets more than the smoothing routines can deal with.

AlwaysLastPlace said:

Is it just me or is jsb being too conservative? I don't have 30 + inches of drop at a 100 yards. But if I use the .03 whatever number JSB says that is what shows up on the calc. Oh wait maybe I should just use their number and change only the drag law (a term I just learned) to back into what drag law they used? That could keep me busy for a while! I'm not really looking for the answer just a direction to head in learning that seems not to be a waste of time. Which is totally subjective.

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You might be mixing up POI with drop. At 100yds, 30inches of drop is about right for a subsonic pellet with a 0.03 BC.

Once sighted in at say 25 or 30yds, you have already set a significant amount of drop compensation. So you’ll only need another 12moa (approximately) of additional correction. That 12moa is not your total drop.

You probably have a time of flight of around 0.4 seconds. 30” is about how far something falls in that brief period of time.

Scotchmo said:

You might be mixing up POI with drop. At 100yds, 30inches of drop is about right for a subsonic pellet with a 0.03 BC.

Once sighted in at say 25 or 30yds, you have already set a significant amount of drop compensation. So you’ll only need another 12moa (approximately) of additional correction. That 12moa is not your total drop.

You probably have a time of flight of around 0.4 seconds. 30” is about how far something falls in that brief period of time.

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Gravity, makes our projectiles and balls droop given enough time.


-Matt

Multiple-BC use is very valid over long distance shooting, it's not an opinion, rather fact, no drag model I know of perfects this, however most ranges airguns are used, its negligible, but as people push further and further, Mutli-BC should not be left in the dust or forgotten.


Also worth noting, behind the scenes for ballistic / trajectory programs calculate an adjusted bc which takes into account your environmental conditions such as altitude and temperature, but they do not calculate new bc's for drops in velocity during the time of flight, which is up to the user to input with multiple bc's. It's why some manufacturers (not pellet) will list multiple bc's for different speeds, so you can use these in your calculations.

So, often times, if your having to fudge your bc, its more often than not your environmental factors are not inputted correctly (possibly due to deviance from where the manufacturer tested their listed bc), or your shooting at a very different speed than the manufacturer did for their testing. Once you determine your bc, a good ballistic program shouldn't need any more changes to that based on where you zero, provided they compensate for the enviromental changes and you input them correctly.

-Matt

Stubbers said:

Multiple-BC use is very valid over long distance shooting, it's not an opinion, rather fact, no drag model I know of perfects this, however most ranges airguns are used, its negligible, but as people push further and further, Mutli-BC should not be left in the dust or forgotten.


Also worth noting, behind the scenes for ballistic / trajectory programs calculate an adjusted bc which takes into account your environmental conditions such as altitude and temperature, but they do not calculate new bc's for drops in velocity during the time of flight, which is up to the user to input with multiple bc's. It's why some manufacturers (not pellet) will list multiple bc's for different speeds, so you can use these in your calculations.

So, often times, if your having to fudge your bc, its more often than not your environmental factors are not inputted correctly (possibly due to deviance from where the manufacturer tested their listed bc), or your shooting at a very different speed than the manufacturer did for their testing. Once you determine your bc, a good ballistic program shouldn't need any more changes to that based on where you zero, provided they compensate for the enviromental changes and you input them correctly.

-Matt

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When I was using G1 for my .257 slugs, I used the Strelok multi-bc function and it worked well. Later, I switched to RA4 in Strelok and a single BC value worked close enough so I did not even bother with multi-bc.

If your drag model is a poor match for your projectile, multi-bc is a workable bandaid. If you use multi-bc, the drag model does not have to match well at all. So use whichever drag model you want. But you will usually have to get the BC values yourself for multiple velocities, and that’s more work.

Scotchmo said:

When I was using G1 for my .257 slugs, I used the Strelok multi-bc function and it worked well. Later, I switched to RA4 in Strelok and a single BC value worked close enough so I did not even bother with multi-bc.

If your drag model is a poor match for your projectile, multi-bc is a workable bandaid. If you use multi-bc, the drag model does not have to match well at all. So use whichever drag model you want. But you will usually have to get the BC values yourself for multiple velocities, and that’s more work.

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Multi-BC are objectively useful based on subjective experience, but there is no ballistic coefficient model that completely rules out the need entirely for everyone, objectively, however a good ballistic model could try to do it for you.

Add to that, the lower the bc of a particular projectile, the more it would benefit from multi-bc inputs in your ballistic program, due to the increase in velocity change between muzzle and target.

I think often times, people adjust their bc to get real world acceptable dopes at longer ranges, basically averaging what would be the use of 2 bc's, ie: .045 + .047 = .046, and then calling it good, without knowing, which then throws off their close range inputs. This is the band-aid you speak of. YMMV.

-Matt

The use of multi BC values was the reason purpose drag laws were introduced for fire control systems 60 years ago, because so many BC values were needed that it became pointless. Now the small arms industry has decided that it is the latest innovation, with bullet makers producing purpose drag laws. It is only a matter of time before they become the newest thing for airguns as well, particularly for slugs at long ranges. Currently though, there are no purpose drag laws for pellets available to the public, and you would have to doubt the ability of many of the manufacturers to produce them. Shooters can produce them themselves if they have the equipment and the data needed, but it is not easy.

It is up to the user to decide if a single BC, multiple BC's or purpose drag laws are needed for the accuracy they want. I personally use purpose drag laws for my work, mainly because that is what I was using at work and the software I have does not use BC.

Ballisticboy said:

The use of multi BC values was the reason purpose drag laws were introduced for fire control systems 60 years ago, because so many BC values were needed that it became pointless. Now the small arms industry has decided that it is the latest innovation, with bullet makers producing purpose drag laws. It is only a matter of time before they become the newest thing for airguns as well, particularly for slugs at long ranges. Currently though, there are no purpose drag laws for pellets available to the public, and you would have to doubt the ability of many of the manufacturers to produce them. Shooters can produce them themselves if they have the equipment and the data needed, but it is not easy.

It is up to the user to decide if a single BC, multiple BC's or purpose drag laws are needed for the accuracy they want. I personally use purpose drag laws for my work, mainly because that is what I was using at work and the software I have does not use BC.

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I'd love to see your newer formulas / models publicized, but until they are, I cannot integrate them into my software, and they aren't available with Sterlok.


Co-efficient definition:

In Physics: a number that is constant for a given substance, body, or process under certain specified conditions, serving as a measure of one of its properties

Therefore its just semantically illogical to state BC is supposed to be a constant, without adding 'under specified conditions', no co-efficient is constant under all conditions.

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The transient nature of bullet ballistic coefficients​

Variations in BC claims for exactly the same projectiles can be explained by differences in the ambient air density used to compute specific values or differing range-speed measurements on which the stated G1 BC averages are based. Also, the BC changes during a projectile's flight, and stated BCs are always averages for particular range-speed regimes. Further explanation about the variable nature of a projectile's G1 BC during flight can be found at the external ballistics article. The external ballistics article implies that knowing how a BC was determined is almost as important as knowing the stated BC value itself.

For the precise establishment of BCs (or perhaps the scientifically better expressed drag coefficients), Doppler radar-measurements are required. The normal shooting or aerodynamics enthusiast, however, has no access to such expensive professional measurement devices. Weibel 1000e or Infinition BR-1001 Doppler radars are used by governments, professional ballisticians, defense forces, and a few ammunition manufacturers to obtain exact real-world data on the flight behavior of projectiles of interest.

-Matt

Wikipedia is not the best reference for anything to do with external ballistics, in fact a lot of it is complete rubbish. For instance, the first sentence in your quote from Wiki, BC, if derived properly, does not vary with air density as it should be calculated at standard atmospheric conditions which of course do not vary. Any calculations using the BC should include atmospheric conditions. It is all standard ballistic calculation methodology, which the Wikipedia author obviously does not know. It is because of things like the Wiki articles and a lot of what you read in magazines and on internet forums that there is so much basic misunderstanding of aeroballistics.

Ballisticboy said:

Wikipedia is not the best reference for anything to do with external ballistics, in fact a lot of it is complete rubbish. For instance, the first sentence in your quote from Wiki, BC, if derived properly, does not vary with air density as it should be calculated at standard atmospheric conditions which of course do not vary. Any calculations using the BC should include atmospheric conditions. It is all standard ballistic calculation methodology, which the Wikipedia author obviously does not know. It is because of things like the Wiki articles and a lot of what you read in magazines and on internet forums that there is so much basic misunderstanding of aeroballistics.

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I'd love the internet forums and wikipedia to be absolved of any inaccuracies, perhaps you should re-write the Wikipedia definition of Ballistic Coefficient? This is an honest statement, not an attempt to troll, I'd love for it to all be corrected. You seem to be the right guy to do it, anyone can edit the article. It would be awesome if you would publish your new GA2 formulations and models here, for transparency and for the good of anyone interested in learning.

Aside from that..most external ballistic models will take into account the change of the conditions (air density and velocity), thus adjusting the bc within the model to represent the real world data being presented, such as the Pesja model, which uses a retardation co-efficient for any given slope constant factor if velocity data points are known.

The Doppler radar measurements disagree for a constant BC below...



"The initial rise in the BC value is attributed to a projectile's always present yaw and precession out of the bore. The test results were obtained from many shots not just a single shot. The bullet was assigned 1.062 for its BC number by the bullet's manufacturer Lost River Ballistic Technologies."

Does the BC change if I shoot a projectile at 150 fps versus 500 fps, 900 or 1500 fps, or 2500 fps? At Sea level, or in 30,000 ft? If so, its not constant.

-Matt

Is Hornady wrong too?


"As Hornady moves the industry to drag coefficient based trajectory calculations for these types of projectiles, the Ballistic Coefficient is becoming somewhat irrelevant. Exceptions are for those still using BC based trajectory calculators or when using BC as rating criteria for bullet performance.

The Science Behind It​

Ballistic Coefficient (BC) values can, and usually do change in value with changes in velocity. Most bullets exhibit a lowering BC as velocity slows. The extent of how much a BC will change depends on each unique bullet shape. When comparing BCs of different bullets, it is important to use an apples-to-apples approach.


To do this, bullets should be compared at a given Mach number (e.g. Mach 1 = 1116.48 fps @ ICAO Standard Atmosphere). Mach number is the velocity of the bullet divided by the speed of sound. If a Mach number is unavailable, velocity can be used if the BCs are corrected to Standard Atmosphere which is fairly typical practice within the industry."

-Matt

G1 gives us something to use for comparison, even if it’s not a good match to every projectile we want to compare. Slug specific drag models won’t work for comparisons.

To calculate a BC, we need environmental conditions (mostly barometric pressure), V1, V2, and distance between them. In general changes to environmental conditions don’t affect the BC as long as the current conditions are applied. Environmental conditions affect drag.

I like it when manufacturers give a G1 BC value, but if it is not a good match at all velocities, they should give the velocity range where that BC applies, and maybe even give G1 BCs at different velocities. If there is a good match drag model (RA4 or G7 for instance), they should give that BC as well.

G1 gives us a familiar value that we can compare.

Stubbers said:

I'd love the internet forums and wikipedia to be absolved of any inaccuracies, perhaps you should re-write the Wikipedia definition of Ballistic Coefficient? This is an honest statement, not an attempt to troll, I'd love for it to all be corrected. You seem to be the right guy to do it, anyone can edit the article. It would be awesome if you would publish your new GA2 formulations and models here, for transparency and for the good of anyone interested in learning.

Aside from that..most external ballistic models will take into account the change of the conditions (air density and velocity), thus adjusting the bc within the model to represent the real world data being presented, such as the Pesja model, which uses a retardation co-efficient for any given slope constant factor if velocity data points are known.

The Doppler radar measurements disagree for a constant BC below...

View attachment 498121

"The initial rise in the BC value is attributed to a projectile's always present yaw and precession out of the bore. The test results were obtained from many shots not just a single shot. The bullet was assigned 1.062 for its BC number by the bullet's manufacturer Lost River Ballistic Technologies."

Does the BC change if I shoot a projectile at 150 fps versus 500 fps, 900 or 1500 fps, or 2500 fps? At Sea level, or in 30,000 ft? If so, its not constant.

-Matt

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If you have the MERO ballistic app, you can find listings of all the drag laws so far developed for pellets and slugs.

No model should ever adjust the BC. The model should adjust the aerodynamic properties such as Mach number and air density to take account of the atmospheric conditions both at the time of analysis of velocity data, and when the calculated BC is being used for trajectories. In this way, the BC will not change for any muzzle velocity or altitude. The only time BC will change is if the projectile drag law changes, thus changing the form factor in the BC equation.

When using purpose drag laws for artillery, we did not change the drag laws depending on the gun elevation, despite the shell travelling to altitudes of up to 50000 ft during some trajectories. There is an argument that there should be small changes in Cd due to Reynolds number changes at high altitudes, however the changes are so small and the air density is so thin that the effects on the trajectory are negligible compared to all the other error sources. I don't think many shooters, even with the highest energy big bore air rifles, will be getting anywhere above 50000 ft.

As regards the radar results, I do not have access to the full report. However, I would want to know what radar they were using out to 2000m, where was the radar situated relative to the gun, what meteorological systems were being used, and what were the imposed wind limits, what reference drag law was used and what is the projectile shape, and if they have a radar sophisticated enough to track to 2km, why on earth are they using BC's at all??

The shape of the BC variability suggests to me, they were attempting to use a fixed head radar, which would mean that they are getting angular errors at the start and end of the trajectories. When I was tracking bullets from 4.6mm calibre up to 14.7mm we used a $2000000 Doppler tracking radar with a moving head, operated by a world-class radar tracking expert, definitely not me. The radar is not something many other places have access to. The other reason could be simply a poorly matched reference drag law.

Ballisticboy said:

If you have the MERO ballistic app, you can find listings of all the drag laws so far developed for pellets and slugs.

No model should ever adjust the BC. The model should adjust the aerodynamic properties such as Mach number and air density to take account of the atmospheric conditions both at the time of analysis of velocity data, and when the calculated BC is being used for trajectories. In this way, the BC will not change for any muzzle velocity or altitude. The only time BC will change is if the projectile drag law changes, thus changing the form factor in the BC equation.

When using purpose drag laws for artillery, we did not change the drag laws depending on the gun elevation, despite the shell travelling to altitudes of up to 50000 ft during some trajectories. There is an argument that there should be small changes in Cd due to Reynolds number changes at high altitudes, however the changes are so small and the air density is so thin that the effects on the trajectory are negligible compared to all the other error sources. I don't think many shooters, even with the highest energy big bore air rifles, will be getting anywhere above 50000 ft.

As regards the radar results, I do not have access to the full report. However, I would want to know what radar they were using out to 2000m, where was the radar situated relative to the gun, what meteorological systems were being used, and what were the imposed wind limits, what reference drag law was used and what is the projectile shape, and if they have a radar sophisticated enough to track to 2km, why on earth are they using BC's at all??

The shape of the BC variability suggests to me, they were attempting to use a fixed head radar, which would mean that they are getting angular errors at the start and end of the trajectories. When I was tracking bullets from 4.6mm calibre up to 14.7mm we used a $2000000 Doppler tracking radar with a moving head, operated by a world-class radar tracking expert, definitely not me. The radar is not something many other places have access to. The other reason could be simply a poorly matched reference drag law.

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I don't doubt your reasoning or logic entirely, however, current literature does. I find it hard to believe that every source I review on the subject matter is wrong.

"The Problem with Ballistic Coefficients of Bullets​

Bullet ballistic coefficient (BC) values actually varies with velocity Mach number, so a bullet’s claimed BC is only an approximation for one part of a bullet’s flight path, usually the fastest part, right out of the muzzle to about 300 yards. Modern ballistic solvers often use stepped BC to account for this variation, and there is a push towards Doppler radar to measure a bullet’s true drag performance throughout its trajectory. While most manufacturers provide an average BC for their bullets, a Cd vs. Mach curve for a bullet will give a much better representation throughout the flight path. This is obviously not needed for hunting or most gong shooting competition which take place inside of 400 yards, but for PRS and long range shooting, it exponentially increases the chances for hits over longer ranges in varying wind and atmospheric conditions."


I could give endless citations that disagree with the statement "BC should remain constant based on projectile SD and FF"...however, I am uncertain you can give countless citations that support your argument, other than your word. Until such citations and articles are published, we're dealing with a Schrödinger's box...and discussing the matter on an online forum is far less fruitful than either editing wiki pages, or publishing your own articles via places like researchgate...


Then you add in, the effects of high velocity drag or high density air that could, alter soft leaded projectiles shape even microscopically, thus, producing a different BC even by your logic (alteration of FF), even if its by a thousandths, simply due to the velocity. Add in unstable flight at particular speeds for particular projectiles, the BC is clearly not the same in unstable flight as it is stable, thus, does twist rate not change the projectiles ability to overcome air resistance, or effects its flight path to some degree? AFAIK MERO doesn't have a twist rate input, but twist rates definitely effect trajectory? What gives? I ask because, I do not know, so please don't take offense to that question. Also, I will assume it does not take into account spin drift? A tumbling projectile certainly cannot have the same BC as one that does not tumble, or enter angular precession. Likewise, a rifle with no twist rate will definitely not have the same POI as one with a 7" twist rate.

It is in my humble opinion, stating BC should be constant is a form of idealism that can only be achieved in a perfect world, which we do not live in. If boundaries can be pushed thus breaking a drag law, then, they should be accounted for, such as "BC *should* remain constant in ideal settings with ideal drag laws applied"...however this isn't the case, and unfortunately the perfect drag laws for every projectile do not currently exist, and aren't widely known or accessible.

I saw some conversation about radar technology being out of reach for civilians with ordinary budgets.

I've been playing with the Labradar data files. The first thing to note is that they provide a summary page for each string, and there are lines showing the velocity at the five downrange distances you chose (up to 100y). These velocities (dark blue) are quite rough. I spent a lot of time looking at them, averaging them, comparing shot-shot variances, which were significant.

Then I dug deeper into the tracking file for each shot. This gets more interesting because it records the measured distance at regular time intervals (500 distances/second) and also calculates the velocity for each distance. Those velocities are produced by some simple v = (d2-d1)/(t2-t1) kind of math. As the SNR drops with distance and errors in d2 and d1 become significant, these simple velocities start yo-yo'ing up and down and require better processing.

So I used the worlds greatest (ahem: most readily available) data processing tool and plotted distance vs. time, fitted a polynomial function to it, and took the derivative. Seems way better than the downrange velocities spit out by Labradar. (red plot)

Sample shot is a 22LR but I suspect air rifle data will be similar. So I guess the next step is to compare this to ballistics calculator data. Not sure what else to do beyond that because learning new math to derive custom ballistic models is probably beyond my current interest level. (When I need to know trajectory data I shoot it and plot the holdovers manually).