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Why use "w" for mass? (Perhaps m would be better)
Why use "d" for diameter, then in the very next equation, use "d" for "average density"? (Perhaps use Greek rho or k for the density) Why bother to equate the term mass / area as equal to average density * length (Only correct for objects with constant cross section. For other shapes this relation is an approximation, not an equality.) —Preceding unsigned comment added by Matt in tx ( talk • contribs) 05:21, 6 February 2008 (UTC)
Maybe a list with common ammunition types / bullets would be not bad. -
Jack's Revenge 20:28, 23 July 2006 (UTC)
The part on the .270 Winchester sounds like an ad. Rather than talking about cartridges, individual bullets should be mentioned (caliber and weight) with a range of BCs available by the common manufacturers (Sierra, Speer, Hornady, Lapua, Berger, ...)
Like... Caliber / Weight / Common BC range 6.5mm / 130gr / 0.495-0.571 6.5mm / 140gr /......
Possibly more of an addition to a "list" page.
Or shrink it down to the 5 calibers with the highest BCs by common manufacturers and the 5 calibers with the lowest BCs by common manufacturers.
Would it make sense to add a section discussing rocket launches? Isn't the reason a rocket is shaped like a bullet because that optimizes the ballistic coefficient? Also, in both cases is there a tie-in with the center of gravity/center of propulsion concept that could be covered? Sdsds 18:56, 26 March 2007 (UTC)
This description of the general aerodynamic concept of the "Ballistic Coefficient" seems very strongly pointed toward the sub-genre of projectile ballistics. Suggest moving all the rifle+bullet stuff to another article (perhaps referenced as application examples) so the basic concept can be clearly seen, out of any clutter. With a good understanding of the basic concept, all the bullet observations should make sense. I'm not so sure you can easily go from a laundry list of interesting bullet trajectory observations to an understanding of the basic concept, however. Matt in tx ( talk) 05:43, 6 February 2008 (UTC)
Wouldn't a higher BC reduce heat during entry into earth's atmosphere? —Preceding unsigned comment added by 71.112.78.96 ( talk) 23:24, 31 March 2008 (UTC)
It would be nice to see some examples of how they are to be used. For instance, calculate the BC of a bullet or an airgun pellet. 87.59.100.37 ( talk) 12:37, 16 July 2008 (UTC)
The first section, BC as used in physics, is confusing. M is mass, but mass of what? Rho is density, but again it is unclear what is being described. I would expect M to refer to a projectile and rho to the fluid it moves through but I don't get that from the equations. RDXelectric ( talk) 09:23, 11 December 2016 (UTC)
Using lbs & in vs. m & kg changes things drastically. Also, the sectional density/i and M/A/Cd versions are not interchangable whatsoever. From what I can tell, the sectional density variant (with rectangular area instead of circular) is the one commonly used. There is no explanation for what 'i' is. It's not the coefficient of drag, and it's not the coefficient of drag*pi, so what is it? I'd edit this myself but the information isn't as easy to find as I'd like. I can't find it on the internet (yet). —Preceding unsigned comment added by 98.240.227.220 ( talk) 05:00, 17 September 2008 (UTC)
I am the person who reupdated the equations to what they are as you see them (12/07 i think to current). The "i" factor is 100% correct as is. It's a ratio of the bullets drag coefficient divided by the theoritical G1 bullet's drag coefficient. The sectional density/i is strickly for bullets only, while the M/(C*A) is for non bullets. i did put that in but it was taken out for whatever reason that person had for doing that. that should answer some of the miss understandings. i just cant believe that someone would take that "bullet only" out, trust me it would clear up a lot of thing if it was just there. the BC isn't a unitless quantity at all. it is normally expressed using imperial units. because of this, manufactures don't bother with showning the units. saying that the BC isn't a TRUE coefficient. now you can do it both ways in imperial and SI units. when i was doing my college paper on the subject, i used SI units to work with and when i got the final BC i converted it to imperial. i have the whole process of calculating a BC for a given round is from looking at the raw data to the final product which is the BC. when i have internet at my place i will again put the "bullet only" part and add the calculation part to it too. the SD/i part is very simple. the trick to the whole BC is figuring out how to calculate the drag coefficient. it takes some bit of calculus to do it. here is the key to doing it a = v(dv/dx). using the equation for drag force and dividing it by the mass will give you a good starting point. also the drag coefficient does change over the cource of its flight. so if you have 0-500 yards distance and the velocity of the bullet is taken at every 100 yards, you will end up with 5 different drag coefficients. just take the average of the 5 and that will be drag coefficient you will use in final BC calculation. my personal opinion though is that they need to change the name to something else when dealing with bullets. the SD/i formula is used because of historic background, while the M/(C*A) is the real deal and should carry the name of BC. however the M/(C*A) formula will not work for bullet because the bullet BC isn't a true BC in the physics definition. you want to calculate the BC of a rocket or a car use the M/(C*A). you want to do the bullet BC use the SD/i formula. i will change it back to Bullet only as soon as possible and have the calculations that i used for my physics presentation, and i guess because its important too i will put in the history of it as well (trust me it will clearify a lot). —Preceding unsigned comment added by 207.243.101.5 ( talk) 23:04, 5 November 2008 (UTC)
like i said yesterday (i am the guy that wrote whats above Wolfkeeper) i needed to get all this into a word document. i have done it but i did some equations using the equation editor in microsoft word but i don't know how to put them into this wiki. —Preceding unsigned comment added by Gulielmi2002 ( talk • contribs) 21:35, 6 November 2008 (UTC)
BACKGROUND: At this time, the wikiarticle has the following for Ballistic Coefficient (bold font used for emphasis):
…
…
ANALYSIS: Using subscript c for circular cross sections (e.g., bullets), Ac=πd2/4 & BCc=M/(Cd • πd2/4)=(M/d2)/(πCd/4)=SD/(πCd/4).
Since the last term has the same form as the given equation for bullets, BC=SD/i, then:
CONCLUSION: The denominator of the last term does not equal the wikiarticle's given value for the "drag coefficient of G1 model bullet (G1 drag coefficient = 0.5190793992194678)".
although a fine piece of math work, the work is invalid because it uses both the ballistic coefficient equation for bullets only and the phyics term ballistic coefficient as if they are one and the same and equal. i can't stress this enough that the BC used for rockets and aerodynamics of cars, planes and what not isn't the same thing as the BC for a bullet. you can look up the definition of what a G1 bullet is: a bullet with a diameter of 1 in with a mass of 7000 grains (1 lbs). you can do a bit of searching on the internet to find two velocities over a 100 yards distance by cross referancing G1 bullet physics. after same basics calculus you will have this equation to put those two velocities into: the drag coefficient of a G1 bullet = (-2*Mass*ln(final velocity/initial velocity))/(air density*distance traveled*cross sectional area). here is the link to that website: http://pittsburghlive.com/x/leadertimes/s_513904.html. here is the velocities from that website in a quote: "To measure BC you must know both how fast your bullet is going and how fast the bullet is losing velocity. Suppose that your bullet starts at 2,500 fps and loses 312 fps in 100 yards. The standard bullet loses only 84 fps starting at the same velocity under the same atmospheric conditions. The BC of your bullet is approximately 84/312 or 0.269." lets put that in the equations that I gave earlier: C=(-2*0.45359237 kg*ln(2500 fps/2416 fph))/(1.292 kg/m^3 * 91.44 m * 5.067e-4 m^2) and you get 0.5190793992194678. you see very simple. 100 yards=91.44 m; 1 lbs = 0.45359237 kg. and because you are taking a natural log of the velocity ratio you can ignor the velocities not being in SI units. oh and the magical equation i am using was got from integrating dx=(-2*M)/(p*v*C*A)*dv. this equation was taking from the definition of drag force. keep in mind that a=v(dv/dx) and there you have it. i am the one that originally posted the value however long ago it was. —Preceding unsigned comment added by Gulielmi2002 ( talk • contribs) 22:52, 21 July 2009 (UTC)
I am not trying to get on this guy's case because I know that it's a common mistake. Infact when I first was trying to figure this out, I did the exact same thing as he did. I will edit the main page so that this mistake won't happen in the future by others. —Preceding unsigned comment added by Gulielmi2002 ( talk • contribs) 17:25, 22 July 2009 (UTC)>
It has been years since I have last been on this particular page. The errors that were taken out of the page have some of them back due to edits based on misconceptions. I originally corrected this page because it has a lot of confusion on it; particularly in regards to physics/mechanical definition of BC vs. Commercial BC and how they relate. the drag coefficient of 0.5190793992194678 was based on actual test data that could be found on the net by a college physic department which now difficult to find. the drag coefficient of a G1 is not 1; its small arm BC (not to be confused with the actual physics BC) is 1. I don't know how it came to be written as i as it is a reference BC. removal of some information is in error or in poor choice. came back to this page looking for the information because I do not exactly have my notes on this topic on hand used as a presentation for a department, and was forced to route around in program made specifically to deal with this. some of the equations were not referenced because they are the result of Calculus computations that are difficult to do in Wiki. unfortunately they were correct so I fail to see the misleading aspect of them or violation of original works as it is on the same level as stating 2*(4+4)=16; that being said if you have a clear understanding of the math involve you could easily see getting from point A to C through point B. Gulielmi2002 ( talk) 22:14, 1 December 2015 (UTC)
This discussion is as confusing as the article. The BC of the standard bullet is 1 by definition. It is not meant to be the same BC as physics uses, it was specifically to study and approximate projectile trajectories. There is no single coefficient of drag but rather a table of values referenced by velocity in Mach number. There is a website by Kevin Boone that explains all this in detail, including the table and some Java code. — Preceding unsigned comment added by RDXelectric ( talk • contribs) 09:44, 11 December 2016 (UTC)
The following formula in addition to other highly useful is offerd at http://www.docstoc.com/docs/3424351/A-Very-Simple-Guide-To-the-Ballistic-Coefficient-with-particular
Allowing bc to be used similar to the formulas here except accounting for air resistance http://en.wikipedia.org/wiki/Trajectory_of_a_projectile
BC = (R1 - R0) / Loge(V0 / V1)*8000)
where:
BC = Ballistic coefficient
R0 = Near range (yards)
R1 = Far range (yards)
V0 = velocity at R0(Ft/s2)
V1 = velocity at R1(Ft/s2)
Is this correct and does anyone have a SI version with meters rather then yards
MadTankMan ( talk) 02:51, 19 November 2009 (UTC) —Preceding unsigned comment added by MadTankMan ( talk • contribs) 02:34, 19 November 2009 (UTC)
Fd=Force of drag (N)
M=mass (kg)
ax=acceleration in the x-axis
=density of air
v=velocity (units aren't important because you will be making a ratio of final vs initial velocities)
C=coefficient of drag (unitless)
A=cross sectional area
Gulielmi2002 ( talk) 21:36, 23 November 2009 (UTC)
the BC of G1 is 1 only when talking about small arm BC and not Physics are related BC (true BC). the 0.5190793992194678 is the drag coefficient. you are confused and have made this page convoluted and confusing. if I do this I = C/Creferance =0.5190793992194678/0.5190793992194678 = 1 which should not be shocking. it would be much clearer if you would say small arms BC of G1 is 1 vs. BC of G1 is 1 as this is incorrect and misleading. Gulielmi2002 ( talk) 23:04, 1 December 2015 (UTC)
Example:
"Sporting bullets, with a calibre d ranging from 0.172 to 0.50 inches (4.50 to 12.7 mm), have BC’s in the range 0.12 to slightly over 1.00"
Ok, stop right there. A BC of 1.0? You know, the very intro of this article notes that BCs may be given in different units. The references I can check for these are all dead too. This is... particularly egregious. - Theanphibian ( talk • contribs) 20:57, 5 June 2011 (UTC)
Does anyone know what the form factor(i) for the G7 model is?
Also the diameter and weight are only given for the G1 model and none of the others. Don't w need those numbers as well?
I added the paragraph from the Reference Notes for Use in the Course in Gunnery and Ammunition, Coast Artillery School, pg12 to stop the implication that the G1 Standard Model shape and/or Friedrich Krupp AG used/was an actual; 1 inch, 1 pound projectile with either 1 1/2 or 2 caliber tangent ogive.
If indeed someone thinks that there was such a "test" projectile used by Friedrich Krupp AG between between 1865 to 1930. Please post your reference for review before deleting my reference that it was a "factitious" model not an actual projectile. Thank you, Greg Glover ( talk) 18:00, 13 August 2014 (UTC)
I'd like to start a conversation as to were this Article is going. I remember back sometime ago. This article was very clean if not to specific. But I do remember when there was a difference between Ballistic Coefficient equations and denoted as such with the subscript physics and ballistics. I see the subscript for physics still exists.
I understand why article is devoted to smallarm projectiles. Ballistic coefficient is a sub set of Physics known as "drag"; specifically Drag Coefficient. The Article does not seem to explain this. As pointed out above, but conflated, drag affects; bullets, rockets, missiles, cars, aircraft, etcetera. However a ballistic coefficient in its purest form is specific to projectiles not under power. Those projectiles or presented surfaces, under power are then referred to as just having a "drag coefficient". Hence this article is really a stub of Drag Coefficient.
What say you?
Greg Glover ( talk) 17:25, 14 August 2014 (UTC) Edited Greg Glover ( talk) 16:16, 15 August 2014 (UTC)
Maybe all that needs to be done is pull up the Standard Model ("G1") information into subsection Formula (adding references of course). Pull the misleading .519... from the near correct equation in Bullet performance and call it a day? Greg Glover ( talk) 19:02, 16 August 2014 (UTC)
I am reading this and can see there is a clear confusion going on between BC in physics and a BC in terms of small arms. the 0.5190793992194678 is a physics based Drag Coefficent and not i or a small arm BC. again with all the edits post 2009 have done nothing but make matters worse. don't have the time nor the unrusty memory to go through this article to correct the misconcepts and errors. Gulielmi2002 ( talk) 22:26, 1 December 2015 (UTC)
Okay I stared cleaning up the top half of the Article with real and verifiable References. The bottom part of Formulae without the reference will get cleaned up and references added. Or it may be pulled and put below. Pulled
I'm gonna attack Bullet Performance over the weekend. The top part above subsection General trends will get a new name subsection. Maybe "G" Model History. But something has to give. That section is all fuglied up. I'm gonna take one subsection at a time. Again I'll reference as much as possible with real references, but I'm not gonna plagiarize. Greg Glover ( talk) 23:03, 21 August 2014 (UTC)
For the equation of , I am going to add one more reference from Mc Graw & Hill's Encyclopedia of Science and Technology. I just need to get back to the Central Library. It also has a more specific definition for trajectory under 16 degrees. Which is correct for all small arms and many large arms. But this equation can be found in scores of books. I think the definition of trajectory under 16 degrees is very important. I'll also reference the other types of trajectory within these types of projectiles for the broader discussion of Ballistic Coefficient. I wouldn't want anyone to think I was just a "gun nut" ;) Greg Glover ( talk) 23:26, 21 August 2014 (UTC)
Hi.
Formulae -> Ballistics
higher form-factor means higher drag. so it must be i = cp / cg
also, drag coefficient of 1.000? absolutely not, that would be equal to a brick!
Re: "higher form-factor means higher drag. so it must be i = Cp / Cg"
I've always used i = Cp/Cg too - as per the reference to the Brian Liz/Berger Bullets article to which you refer. The references to the Form Factor in "Differing mathematical models and bullet ballistic coefficients" section would be incorrect too.
To be clear: Cd is generally used as a reference to a Drag Coefficient - the interpretation of such as has been used in Cd v. Velocity tables (G1, G2, G5, G6, G7, G8, GL … etc.) for the past 30 years or more.
The Form Factor (i) is usually written as i = Cd.proj / Cd.ref
where Cd.proj = the Drag Coefficient of the projectile at a particular velocity (usually derived from a flow-bench, chronograph testing or via Doppler retardation measurements) and Cd.ref = the reference Drag Coefficient at the same velocity (derived from the appropriate Cd v. Velocity reference table).
See
http://www.jbmballistics.com/ballistics/topics/secdens.shtml
In practical terms the BC value also depends on the ambient air density compared to that of the reference conditions so the BC expression should be written as :
BC = SD * Q / FF
where:
BC = Ballistic Coefficient,
SD = Sectional Density,
FF = Form Factor and
Q = Reference Air Density / Ambient Air Density
GPConway (
talk) 16:40, 13 January 2015 (UTC)
GPConway (
talk) 18:19, 11 January 2015 (UTC)
plus: can you please write somewhere in this article, that the drag-coefficient depends ALWAYS on the velocity (well, it's the reynolds-no to be 100% correct...)?
thx — Preceding unsigned comment added by 77.176.68.250 ( talk) 16:27, 18 September 2014 (UTC)
This sentence ...
"Circa 1665, Sir Isaac Newton derived the law of air resistance and stated it was inversely proportional to the air resistance."
is techno-babble. It is unclear what it should say.
Perhaps somebody (preferably with access to the cited references) can figure out what it is supposed to be saying and correct it.
87.115.82.105 (
talk) 16:28, 26 October 2014 (UTC)
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"G7 (long 7.5° boat-tail, 10 calibers tangent ogive, preferred by some manufacturers for very-low-drag bullets)"
Try to make a 10 * caliber radius tangent with the dimensions provided, it won't work. A secant could do it though. 2600:1700:8830:8DF0:D1A1:40AD:68C8:C482 ( talk) 06:12, 13 August 2018 (UTC)
2600:1700:8830:8DF0:942E:50F1:92B5:DB20 ( talk) 08:11, 14 August 2018 (UTC)