A quick word on BC

Discussion in 'Rifles, Bullets, Barrels & Ballistics' started by Michael Eichele, Feb 3, 2010.

  1. Michael Eichele

    Michael Eichele Well-Known Member

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    Technically, BC = (drag deceleration of the standard bullet) / (drag deceleration of the actual bullet). The reference of the standard bullet used is 1.000.

    The below statements are not all there is to BCs. rather, the info below is BC in its most simple state used for comparison purposes to show the relation between sectional density and BC.

    BC is (for the most part) a simple function of Sectional Density and Form Factor.

    SD = Bullet weight (in pounds) / bullet diameter^2

    BC = SD / FF

    Change the SD and not the FF and you change the BC plain and simple.

    Two bullets of identical demensions where one is made of aluminum (specific gravity of 2.69) and the other is tungsten (specific gravity of 19.62) the tungsten will have a MUCH higher BC. If you have a jacketed lead bullet and an all copper bullet of identical demensions, again the jacketed lead bullet has a higher BC. You could have an aluminum bullet twice as long as a tungsten bullet utilizing the same form and the tungstun bullet will still win. It would take an aluminum bullet 7.3 times longer than a tungsten bullet to surpass the BC of the tungsten bullet. So if a bullet made of tungsten was 1" long, it would take an aluminum bullet of 7.3" to surpass the BC of the 1" tungsten bullet.

    A current example is the 180 ACCUBOND and the 180 E-tip. One is longer than the other. They both have the same SD yet not the same specifec gravity. The Accubond has a specifec gravity of around 10.5 and the E-tip around 8.89. This meens that in order to get the E-tip up to the same weight of the Accubond, it has to be made longer. The nose and boattail appear to be the same. Note that the published BC data shows the E-tip to be higher than the Accubond. In the real world, this is not the case. Mathematically and physically, they will be extremely close to eachother. The AB is published at .507 where as the last time I double chronied them they were .523-.524 which is where Nosler publishes the E-tip. I have not chronied the E-tip and cannot vouch for it but would bet nearly anything that they are neck and neck.

    Regardless of how long the bullet is, bullet length in and of its self does not equate to a higher BC.

    Bullet length with a specific form factor made of a material that has a given specific gravity will make up it's weight. Make it longer and the BC goes up due to the added weight and subsequent SD. In the case of the E-tip versus the Accubond, they maintaind the same static form factor (ie: nose profile, boattail etc...) lengthened the bullet, changed the material (specific gravity) but the SD and subsequent BC remain the same. This is where we find that when we take two different bullets of equal weight and equal form yet one is a smaller caliber such as in the case of a 180 30 cal and a 180 284 cal the smaller caliber will always yeild a higher BC. This is because the weight to caliber ratio offers a much greater sectional density. Remember, increase the SD and the BC goes up all other components being equal.

    Granted there will be other factors at play where the BC is concerned such as bore quality, velocity, stability factor etc.........The above is geared towards the basic mathematical components where all other factors such as bore quality, velocity etc.... are equal. Also it should be noted that the above statements are based on the G1 drag model. It is somewhat difficult to compare ballistic properties of different bullets if the BCs are refering to different drag models. With all the computers in the world, as powerfull as they are and what knowledge of mathematics we have, there is no substitute for measuring BC accurately without firing tests. Be it doppler, TOF (by way of bullet activated relays), double chronies, or drop tests. We can predict them with a reasonable degree of accuracy. Accurate enough to get on a big peice of paper anyway to be fine tuned.

    So in short, in a sense, bullet length has alot to do with a bullet's BC but not in and of its self. Only how it relates to the overall bullet weight which in turn gives life to the SD.

    Clear as mud??

    M
     
    Last edited: Feb 3, 2010
  2. Kiwi Nate

    Kiwi Nate Well-Known Member

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    Very interesting.

    Next question. Why does a match bullet have the opposite form of an aeroplane wing, the wing functioning like a match bullet fired backwards? Which is more aerodynamic, the wing or the bullet?
     

  3. Fitch

    Fitch Well-Known Member

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    Excellent write up.

    The part of the BC equation that confounds me is form factor. Every time I go through that swinging door I end up back in the street.

    Is there a reference set, pictures, something one can use to estimate form factor? A page of shapes, rules of thumb, something? I read about folks estimating BC before doing testing, but they never seem to quite mention where they got the form factor they used.

    I would think, given the power of finite element modeling, there would be a way to more accurately calculate BC, at least for supersonic flight, than seems to be the current state of the art, but so far I haven't found a reference to it, and it may not exist even in the dusty DOD archives. I think I need to get McCoy's book, wrestle with the errata, and go through it. Maybe if I understood more about how BC is used to model a trajectory it would clear things up for me.

    My curiosity is just that, curiosity. I've always had it, which is probably why I had such a good fun career in engineering. Litz's book combined with the QuickLoad, QuickTarget, QuickTarget Unlimited suite of SW, and the RSI SW, gives me all the tools I need for any practical purpose related to hunting and target shooting. It's just annoying to find what I've come to call the "fickle factor" in the denominator of the BC equation just sitting there, grinning at me, totally taking away the ability to trace trajectory to fundamental physical principles.

    Thanks
    Fitch
     
  4. Topshot

    Topshot Well-Known Member

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    Form Factor? Hmmmmmmmmmm

    The way I look at it two bullets of the same calibre, with the same shape pointy end and same shape boat tail will have about the same form factor.

    If they are slightly different weight then that doesn't matter so much as the bit in the middle (the shank) doesn't effect drag very much.

    Am I on the right track?
     
  5. britz

    britz Well-Known Member

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    they would have close to the same bc. But the added mass will help the bullet defeat the friction it encounters in the air. force = mass x acceleration.
     
  6. Topshot

    Topshot Well-Known Member

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    Britz, I was talking about form factor not B.C.

    If two bullets had the same form factor but one was heavier than the other then the heavier one should have a higher B.C.as it has a higher SD and momentum.
     
  7. eddybo

    eddybo Well-Known Member

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    I really have no business posting in this discussion as it is way over my head. I really do not care how the number is derived, what it represents, or any significance of BC other than this one thing........when I plug that sucker into a ballistics program, are my drops and windage corrections correct. Whether that number is correct or contrived, if it works to give me information that allows me to hit stuff at whatever range, then the BC is correct to me. I gave up a long time ago trying to wrap my little brain around the engineering aspects of long range shooting and external ballistics.

    But, I have some questions, something that came to mind recently during all of this debate on BC, is what happens to a bullet when fired? What dimensions of said bullet change? Doesn't a bullet obiturate (can't spell it or even know exactly what it means). What effect could this have on BC? Could this "swelling" of the bullet cause a change in BC? Couldn't this "swelling", since each barrel is different cause BC to vary from barrel to barrel?
     
  8. Topshot

    Topshot Well-Known Member

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    No, or not much anyway. These two "spent" bullets were found after my long range testing. They started at 2850 fps and 3100 fps.
    Not much change in shape here!
    [​IMG]
     
  9. eddybo

    eddybo Well-Known Member

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    Yea I have picked up my share of 168 SMKs that have bounced into the pits, but have never measured them against an unfired bullet. Was just wondering, not like it matters so long as those numbers give me correct calculations. Not really into how things work, so long as they work.
     
  10. MontanaRifleman

    MontanaRifleman Well-Known Member

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    Nate, actually a wing isn't the reverse shape of a bullet. Close, but not quite. The upper surface of a wing is curved to create more surface area vs the relatively flat bottom surface of the wing. The greater surface area of the top of the wing causes the air molecules to be stretched out in distance between each other as they pass over the surface of the wing which causes a lower pressure above the wing than below the wing which is where the wing gets its lift. Bullets dont generate lift because they have the same shape top and bottom which is necessary for spinning and stability.
     
  11. MontanaRifleman

    MontanaRifleman Well-Known Member

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    Michael, I agree overall and I'm not sure how much lengthing a bullet affects it's BC. As to the differences between the shapes of the E-Tips and The ABs, when I seat to the Lands with my 200 AB's and 180 E-Tips, I get different COALs which suggests different nose shapes. I'm not sure if that would hold up with the 189 E-Tips?

    Another interesting observation is what you found in your testing to be the BC of the 180 AB's vs Bryan's. When I run the Litz 180 AB in JBM and take the MV and 1000 yd velocity and plug them into the balastic calc, I get .486 for the AB. Now 1000 yds might be farther than you set your chrony's, but I think it just goes to show that all of us amatures can come with fairly significant differences when we're using our lower grade equipment and methods.

    Just something to think about.