Talk:Ballistic coefficient

Equation oddities

Why use "w" for mass? (Perhaps m would be better)

The truth be known: "w" is the the correct notation. Weight is not the same as mass. Mass is the amount of matter within an object. Weight is a measurement of gravitational pull on said object. Here on earth it is 9.80665 m/s^2 (32.174049 m/s^2). When speaking of the sectional density or density of a projectile the correct term within the equations of sectional density or pounds per square inch (pressure), is the measurement of weight not mass. However, engineers and scientist, as a matter of "connivance", just use "mass". Greg Glover (talk) 16:48, 14 August 2014 (UTC)

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)

The "d" found in the sectional density equation as d^2 is not "diameter". "d" is the correct notation for distance. d is equal to: SI in meters; Metric in centimeters and Imperial units in inches. The meaning of cross section is a measurement across the width of the body. It just so happens that the diameter of a bullet is also the cross section. Sectional density is not equal to pressure. Pressure is an measurement of area. Sectional density is an absolute value (loosely, as stated above, an equality). Greg Glover (talk) 17:01, 14 August 2014 (UTC)

Maybe a list with common ammunition types / bullets would be not bad. - Jack's Revenge 20:28, 23 July 2006 (UTC)

Winchester Advertisement?

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.

Launch vehicles

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)

The main reason a lot of launch vehicles are tall and narrow is for transportation reasons. If they made the vehicle wider then they wouldn't be able to deliver it from the factory to the launch site. Other than that, aerolosses during ascent are inversely proportional to ballistic coefficient, which in turn is essentially proportional to vehicle length. For a dense-fuelled vehicle about 20m long there are roughly 300 m/s losses. For liquid hydrogen stages, the vehicles need to be proportionately longer, because the density of the vehicle is lower.WolfKeeper 19:45, 26 March 2007 (UTC)

Entire thrust of the article too pointed toward projectile ballistics?

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)

I concur. It reads like a physics article hijacked by gun nuts. Bomazi (talk) 03:39, 16 October 2012 (UTC)

Heat during reentry

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)

Nah. It takes longer to slow down.- (User) WolfKeeper (Talk) 01:12, 1 April 2008 (UTC)

The formulas are good but we need to know how to use them

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)

Need some elaboration on units

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)

The observation that imperial and metric units changes things drastically is right. To avoid very large or small numbers metric units can be easily manipulated by using larger or smaller decimal subunits. In that regard metric units are very handy. In small arms related topics I have never encoutered BC (the SD could be presented in metric units) being expressed in metric units. BC is normally presented to its reader as a dimensionless quantity. The form factor "i" is like the drag coefficient a dimensionless quantity. At http://www.eskimo.com/~jbm/topics/secdens.html you can read something about the units commonly used and see BC is presented as a dimensionless quantity. Maybe it is better to remove the units section in the articles introduction and point out imperial units are normally ussed in samll arms related contexts for expressing the SD. Now the article communicates to its reader: dimension X = (dimension X / dimensionless quantity).--Francis Flinch (talk) 07:15, 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)

FYI Ballistics isn't just the study of bullets, and Ballistic coefficient doesn't just apply to bullets either. Missiles and spacecraft are usually described as also having ballistic coefficients, but the theory behind it is also useful for describing cars, aircraft etc. etc.- (User) Wolfkeeper (Talk) 00:40, 6 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)

Form Factor and G1 C_d Value

BACKGROUND: At this time, the wikiarticle has the following for Ballistic Coefficient (bold font used for emphasis):

$BC={\frac {M}{C_{d}\times A}}={\frac {\rho \times l}{C_{d}}}$

…

• A = cross-sectional area
• C_d = drag coefficient

…

$BC={\frac {SD}{i}}={\frac {M}{i\times d^{2}}}$

• i = form factor, i = drag coefficient of the bullet/drag coefficient of G1 model bullet (G1 drag coefficient = 0.5190793992194678)

This is an absolutely incorrect statement. Being very specific to smallarms projectiles within the study of ballistics as it pertains to the ballistic coefficient of a smallarms projectile, containing the specific statement call Sectional Density $i=C_{d}$ or Coefficient of drag within the Standard Models (G1, G2, G5, etc...). $i$ is also referred to as the form factor. Form factor, again specific to smallarms ballistics is: $i={\frac {C_{d}}{C_{p}}}$ and should not be conflated with other applications within ballistics.

Where as: $C_{p}$ is the actual drag of the test projectile (bullet) and $C_{d}$ drag coefficient of the Standard Model projectile. Again the drag coefficient of a Standard Model projectile is equal to, $1$ and only a reference to a specific shape that has specifically defined measurements in absolute values.

The original word usage for $C$ is Coefficient. Since there are many types of "coefficients" in physics a subscript "d" is used to stand in as the word "drag"; hence the notation, $C_{d}$. The word usage of "Drag coeficiant" as a term is used as a connivance and interchangeable with "Coefficient of Drag". Greg Glover (talk) 18:35, 14 August 2014 (UTC) Edited 2605:E000:7FC0:4B:1:A762:64C7:13B4 (talk) 20:20, 15 August 2014 (UTC)

• M = Mass of object, lb or kg

$m$ is the correct notation for mass. Greg Glover (talk) 18:43, 14 August 2014 (UTC)

• d = diameter of the object, in or m

$d$ is equal to distance, in inches or meters. It just so happens that the cross section and diameter of a smallarms projectile is the exactly same measurement. Greg Glover (talk) 18:43, 14 August 2014 (UTC)

ANALYSIS: Using subscript c for circular cross sections (e.g., bullets), A_c=πd²/4 & BC_c=M/(C_d • πd²/4)=(M/d²)/(πC_d/4)=SD/(πC_d/4).

Since the last term has the same form as the given equation for bullets, BC=SD/i, then:

$i_{c}={\frac {\pi C_{d}}{4}}={\frac {C_{d}}{1.27323954}}$

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)".

DISCUSSION

• [placeholder for first User's discussion point]

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)

$BC={\frac {M}{C_{d}\times A}}={\frac {\rho \times l}{C_{d}}}$ this does NOT equal this $BC={\frac {SD}{i}}={\frac {M}{i\times d^{2}}}$

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)>

Conflation of facts: the above BC is correct for other projectiles such as actual projectiles: bombs, artillery shells, aircraft cannons, test projectiles and actual smallarms projectiles. It it incorrect for the any Standard Model. The conflation is most notably A = cross sectional area. When in fact the BC for G1 or any other Standard Model is based in the simple cross section of d². Cross section is a measurement of width across a body. Aera is not used in the BC computation. Sectional density may look like pressure but in fact it is not. Sectional density is a an absolute value not a measurement. Also the equation conflates $\rho$ (materials density) with the Standard Model of $S_{d}={\frac {m}{d^{2}}}$. Any Standard Model is an absolute value devoid of materials density as it is not know what materials may or may not be used. Hence you have a standard which is an unprejudiced reference.

i = 1 in the G1 ballistics coefficient; not 0.5190793992194678. The .5191 is likely the form factor (i) for a 6 ogive, boat tail, spire point, cup and core, bullet. Generally said bullet has a form factor of .52 as predicated by G2.

I think the above analysis violates the "original works" policy of Wiki. I'll give this a week to stand without discussion then I'm pulling the information as misleading. I will correct the formula within the sub section Bullet Performance. I'll also reference said formula. Greg Glover (talk) 22:59, 13 August 2014 (UTC)

If someone wants to add back the deleted formula then reference it as it should be. A formula for an actual projectile. Greg Glover (talk) 16:09, 14 August 2014 (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)

G1 more formulas

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) / Log_e(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

Instead of 8000 use 7315 (with the ranges measured in metres). Be aware though that the above expression is based o the constant Cd model (Cd = 0.205 approx.) and is not particularly/acceptably accurate for any known practical application.GPConway (talk) 12:31, 12 January 2015 (UTC)

MadTankMan (talk) 02:51, 19 November 2009 (UTC) —Preceding unsigned comment added by MadTankMan (talk • contribs) 02:34, 19 November 2009 (UTC)

This is how you find the drag coefficient of any object including the G1 model. It's fairly straight forward and comes directly from a free body diagram for an object traveling in the x-axis. (Bullets only) After you find the drag coefficients for both bullet and G1 model, you compare the bullet's drag coefficient to the G1 model's to get the form factor i in the equation in the above section

F_d=Force of drag (N)
M=mass (kg)
a_x=acceleration in the x-axis $(m/s^{2})$
$\rho$=density of air $(kg/m^{3})$
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 $(m^{2})$

$\sum F_{x}=Ma_{x}$
$-F_{d}=Ma_{x};F_{d}=.5\rho \ v^{2}CA$
$-.5\rho \ v^{2}CA=Ma_{x}$
${\frac {-.5\rho \ v^{2}CA}{M}}=a_{x};a_{x}=v{\frac {dv}{dx}}$
${\frac {-.5\rho \ v^{2}CA}{M}}=v{\frac {dv}{dx}}$
$dx={\frac {-2M}{\rho \ vCA}}dv$
$\textstyle \int \limits _{x_{1}}^{x_{2}}\,dx={\frac {-2M}{\rho \ CA}}\textstyle \int \limits _{v_{1}}^{v_{2}}{\frac {1}{v}}\,dv$
$\Delta x={\frac {-2Mln({\frac {v_{2}}{v_{1}}})}{\rho \ CA}}$
$C={\frac {-2Mln({\frac {v_{2}}{v_{1}}})}{\rho \ \Delta xA}}$

Gulielmi2002 (talk) 21:36, 23 November 2009 (UTC)

The above equations are for the application of actual projectiles. G1 or for that matter any Standard Model has a BC of 1. The original one inch, one pound, lead projectile was a reference on a piece of paper. It never really existed. As a matter of fact the original "one pounder" was not one pound. It was a metric measurement in centimeters and grams. The conversion was made by LtCol. James Monroe Ingalls. Greg Glover (talk) 16:22, 14 August 2014 (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)

Can we please use units when giving actual examples?

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)

lb/in² added to text.--Francis Flinch (talk) 11:06, 16 October 2012 (UTC)

Does anyone know what the form factor(i) for the G7 model is?

It doesn't matter. i (Coefficient of form) is always 1.00 for any "G" Model reference; that includes G7. All G7 exterior ballistics are computed using integrated number model that includes the mach number. It is a different computation than the original G1 retardation model. However any "G" Model i can be converted to be used in any type of trajectory model computation for exterior ballistic computations. $BC$ and the type of mathematical analysis used to compute the resulting exterior ballistic are really two different animals. Edited Greg Glover (talk) 03:11, 23 August 2014 (UTC)

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?

Form Factor = your bullet's drag / drag of a standard bullet (say the G7 standard bullet) — Preceding unsigned comment added by 72.188.56.99 (talk) 17:36, 23 March 2014 (UTC)

I'm gonna clean this misconception up by giving an expanded explanation of the "G" Models.Greg Glover (talk) 18:32, 24 August 2014 (UTC)

• For greater clarity, most if not all modern, commercially manufactured bullets are based on i = (2 ÷ n) * the Square Root of ((4 * n - 1) ÷ n) to compute the coefficient of form (i) found most prominently in Edgar Bugless and Wallace H. Coxe, series of ballistic charts called "A Short Cut to Ballistics" published by the DuPont Co. However Sierra Bullet Co. and Berger Bullets use the Sky Screen methodology. Edited Greg Glover (talk) 03:32, 23 August 2014 (UTC)

The "One Pounder" is Factitious

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)

Ballistic Coefficient: Physics and Ballistics

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)

No, drag coefficient and ballistic coefficient are related, but are not the same thing, so need not be in the same article. Nevertheless you could cover them in one article, since they're related, but the article would be too big, as they are right now, they're good sizes.GliderMaven (talk) 22:48, 15 August 2014 (UTC)

I'm sorry, apparently I was not clear. but you did understand my greater point. Yes, "drag coefficient and ballistic coefficient are related". My point was that drag is the greater discussion as covered by drag coefficient within physics. And is covered well in that article. But here on Ballistic coefficient the article seems to pull in concepts of drag and plan presentation to drag. As well as mixing Standard Model drag reference with actual bullet drag calculations. I'm thinking maybe the top part needs to be cleaned up and straightened out. But excellent point GliderMaven Greg Glover (talk) 18:28, 16 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 $BC$ 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)

Clean up of Ballistic Coefficient Article

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 $BC$, 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)

I never got back to the Central Library. I drop the need for an explanation of trajectory under 16 degrees. My references from the late 1800's by the actual engineer should suffice. I think that would be self explanatory to those that understand ballistics as it pertains generally to small arms projectiles and not just any trajectory or projectile.Greg Glover (talk) 16:37, 20 September 2014 (UTC)

First Revision

Things Done

• The equation for $BC$ moved up to Formula. Section Formula renamed to Formulae. More formulas and solid references added. 21 AUG 14 Greg Glover (talk) 16:04, 23 August 2014 (UTC)
• Pulled the disclaimer for bullet BC as it was superfluous.22 AUG 14Greg Glover (talk) 16:04, 23 August 2014 (UTC)
• Pulled the disclaimer for bullet BC again as it was superfluous and had no reference.23 AUG 14Greg Glover (talk) 16:04, 23 August 2014 (UTC)
• Added back BC equals sectional density divided by coefficient of form as new formula for better clarification to the large population of firearms enthusiasts. Which was originally (before 21 AUG 14) an equality attached to BC equals mass divided by distance squared times coefficient of form. 23 AUG 14 Greg Glover (talk) 16:04, 23 August 2014 (UTC)
• Added reference to the small arms jargon for the word usage of "form factor". Form factor has several meanings within Physics. Traditionally within physics i is called Coefficient of form. 23 AUG 14 Greg Glover (talk) 16:04, 23 August 2014 (UTC)
• Added equations to find n when unknown. Again for more clarity on formula.23 AUG 14Greg Glover (talk) 16:43, 23 August 2014 (UTC)

Second Revision

Things done

• Bullet performance section reformatted. No changes to text. 24 AUG 14 Greg Glover (talk) 19:06, 24 August 2014 (UTC)Greg Glover (talk) 18:00, 20 September 2014 (UTC)
• Rough draft of new section. 02 SEP 14 Greg Glover (talk) 22:36, 2 September 2014 (UTC)
• Second draft being cleaned up, Referance Links checked and Wiki Links being made in Greg Glover, Sand Box. Greg Glover (talk) 03:03, 3 September 2014 (UTC)
• Continuing work on Second draft. It shouls be ready to post on or just after 20 SEP 14. Greg Glover (talk) 16:27, 20 September 2014 (UTC)
• Differing mathematical models and bullet ballistic coefficients made it's own section and The transient nature of bullet ballistic coefficients along with General trends sub sections within.Greg Glover (talk) 18:00, 20 September 2014 (UTC)
• Added new section of rewritten "Bullet performance".Greg Glover (talk) 18:00, 20 September 2014 (UTC)

Third Revision

Things proposed to be done

• Expand the introduction paragraph to the article and add more references. Greg Glover (talk) 16:12, 23 August 2014 (UTC)
• Remove Satellites and reentry vehicles section. I know someone put time and energy into that part of the article but there are no citations and the drag of space vehicles is more appropriate to the Drag coefficient article. Greg Glover (talk) 17:00, 21 September 2014 (UTC)

Hi.

Formulae -> Ballistics

higher form-factor means higher drag. so it must be i = cp / cg

You may be correct for a specific mathematical model. The generally accepted definition is i = 1.00/1.20 equaling 0.83. Where as i is the coefficient of form of 1.00, the standard G model drag and 1.20 would be that of an actual test projectile drag equaling a coefficient of form, 0.83; $i={\tfrac {C_{G}}{C_{p}}}$. The ratio is non-dimensional.

If you read the old books, none of the engineer used m as mass for weight. They always used w for weight. And if you read some of my references you will see they preferred to use ${\tfrac {d^{2}}{w}}$ for what we call Sectional density. So, for correct historical purposes, the ratio of i (coefficient of form, formally called coefficient of drag), is the standard projectile divided by actual projectile. Let me add the the ratio for a local acceleration of gravity. $g_{n}={\tfrac {g_{0}}{g}}$ Where $g_{n}$ is the local acceleration of gravity, $g_{0}$ actual site acceleration of gravity and $g$ is the acceleration of gravity. This is the inverse equations you may be more used to seeing. Greg Glover (talk) 03:46, 19 September 2014 (UTC)Greg Glover (talk) 15:54, 19 September 2014 (UTC)

also, drag coefficient of 1.000? absolutely not, that would be equal to a brick!

Absolutely yes! Remember this is for the "G Model" for small arms exterior ballistics at direct fire. That is why I'm rewriting that whole section.Greg Glover (talk) 03:46, 19 September 2014 (UTC)

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...)?

Not true. You are conflating the use of the standard model with one of several modern mathematical models. If you employ the old out dated Mayevski/Siacci Method or simple mathematical regression bases on one average BC you need not employ the Reynolds number, mach numbers or k factor. The single BC found for most all commercially produced bullets is general based on the Coxe/Beugless Model coinciding with $G_{1}$. Most of the exterior ballistics tables printed in older reloading manuals use the simple mathematical regression method. It is generally good to within a half Minuet of Angle to 457m (500yd). Most of today's computerized software programs use calculus within the mach number method. You are free to add the formula for calculating BC based on muzzle velocity and mach number as found at http://www.jbmballistics.com/cgi-bin/jbmgf-5.1.cgi.

Your comments, although well thought out pertain to the greater subject of Drag coefficient. This sub article is about Ballistic coefficient and most of it specific to small arms. I hope you read my rough draft (link for my sandbox posted above).Greg Glover (talk) 03:46, 19 September 2014 (UTC)

ADDED:

I understand this article looks like it has been taken over by the small arms community. I hope my newly post part of the article sheds some light on the reasons why. Wiki protocol demands neutrality. Not so much here on the talk page. So let me say what can't be written on the article page.

If you read in the newly added part of the article, under G Model, paragraph 7, the Physics and Engineering community abandoned BC for higher mathematical models of drag.

Unfortunately the Physics community has put a higher priority on drag (as is scientifically demanded) without communicating the history. Even though ballistic coefficient and drag coefficient are mathematical the exact same concept; resistance. Ballistics is specific to things that go up and come back down and drag is general to all things that encounter resistance of fluidity. But really for things like the SpaceX Dragon capsule or a Lamborghini Veneno the appropriate place of understanding, is the Drag coefficient article page.

For the reason given above, ballistic coefficient here has taken a back seat to bullets. Military ordnance and space vehicles are now address in terms of drag to their specific environmental condition. As it pertains to today’s views of drag, the main article is really Drag coefficient and the stub is really Ballistic coefficient. The discussion of bullets and small arms projectiles in a direct fire context really, be belongs here. Stuff that goes up and comes back down like the space shuttle needs to be discussed on the Drag coefficient page.

What I didn't address is the the mach number computations is really just a modern day update of the Mayevski/Siacci method using 25 restricted zones. See 2.5 Doppler radar-measurements for a graph of an actual .50 Cal LAPUA bullet. You will also see the the drag for the bullet between .4 (447ft/s) and 0 (0ft/s) Mach is .230. Therefore, velocity and a Reynolds number is not ALWAYS needed. But I did understand your point. Greg Glover (talk) 17:28, 21 September 2014 (UTC)

thx — Preceding unsigned comment added by 77.176.68.250 (talk) 16:27, 18 September 2014 (UTC)

Your welcome Greg Glover (talk) 04:58, 19 September 2014 (UTC)

Background - revision request

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 claims to be a tangent ogive when it is geometrically a secant ogive

 "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)

In my research, I found this source, confirming my assumption: SBT STANDARD PROJECTILE

2600:1700:8830:8DF0:942E:50F1:92B5:DB20 (talk) 08:11, 14 August 2018 (UTC)