Talk:Sectional density

Sectional density

- a dilemma to be addressed

To help overcome the apparent dilemma as to the use of a cross sectional area A = π(d/2)^2 or A = d^2, where “d” is the diameter or calibre of the projectile or bullet; in the sectional density calculation of a projectile; the author offers the following comments...

In practice, the sectional density of a bullet is often compared with its ability to effectively kill certain sizes of animals. When used in this manner, it does not matter if the comparator uses A = π(d/2)^2 or A = d^2 in the denominator; as long as either option is consistently used in the comparison process. In this case the coefficient to d^2 is a redundant dimension.

However in the author’s opinion, when the sectional density of a bullet is used in the basic comparative manner described above, it is used incorrectly; as there are many things to consider in the terminal ballistic behaviour of the projectile. However given that each bullet has the same terminal ballistic properties, the assessor needs to consider the ability of the projectile to initially punch a hole through bunkers, body armour or bone…, and its ability to create a lethal bullet cavity within the target animal. The basic physics of the recommended alternative approaches are described below:

The Momentum Sectional Density

– the ability to punch a hole comparison

The terminal energy of the bullet

= F x D (F = force, D = penetration distance)

= M x a x D (M = mass, a = deacceleration)

= M x ∆V/t x D (∆V = terminal velocity V, t = time)

= MV x D/t (MV = momentum)

Ignoring the D/t component of the energy equation, the “momentum sectional density” of the bullet is equal to MV/A, where area A = π(d/2)^2 or A = d^2 for convenience of calculation. Note that d = the diameter or calibre of the bullet.

Lethality

– the ability to create a lethal bullet hole comparison

The terminal energy of the bullet

= F x D (F = force, D = penetration distance)

= M x a x D (M = mass, a = deacceleration)

= M x ∆V/t x D (∆V = terminal velocity V, t = time)

= MV x D/t (MV = momentum)

Ignoring the D/t component of the energy equation, it is assumed that the lethality of the bullet is proportional to momentum of the bullet, times the circumferential length of the bullet hole “C”, e.g., here it is assumed that a larger bullet will generate a larger tissue destroying shock wave, and a larger area for the animal to bleed out through. The “lethality” of the bullet in this case is equal to MVC, where C = πd or C = d for convenience of calculation.

Combined performance comparison

Considering the above discussion, choosing a calibre bullet that has good penetrating power and good lethality can be a daunting task. Hence one possible way to achieve the combine benefits of both considerations is to multiply the basic momentum coefficients together to obtain a combined performance comparison equation:

= d x (MV)^2 / d^2

= [(MV)^2]/d (M= mass, V= velocity, d = calibre)

How to use these comparisons

It is worth mentioning here that if a small calibre bullet has a poor lethality rating, its’ lethality rating my be improved by shooting the animal more than once, as this will improve the chance of hitting vital organs, and by increasing the lethal bullet hole cavity area e.g. it is not uncommon for small calibre military rifles to have a 2-3 round automatic burst feature for these reasons.

It is recommended that the comparator uses the above recommended formulas in conjunction with the ballistic chart characteristics of the gun and cartridge in question, and the recommended limiting penetration or lethality characteristics of the intended target. For example, it is often quoted from experience that a bullet must have a minimum energy of 1,000 ft.lbs (1,356 joules) to be able to effectively kill a deer, or 1,500 ft.lbs (2,034 joules) to kill an elk or moose, etc. However, it should be noted that a small calibre bullet with a high velocity can have the same momentum sectional density score as that of a recognised cartridge for hunting a large animal like a deer, however at the same time not have the required lethality score. The question that remains unanswered is... is this an adequate bullet for ethically hunting a large animal like a deer? One possible way to help overcome this dilemma is to use the combined comparison formula of [(MV)^2]/d, when comparing the performance of one bullet with another, and set this as the minimum standard for bullet lethality selection.

However there are always exceptions to the Combined Performance Comparator factor to be considered. For example, if the bullet is designed to pierce body armour and then some; then the Momentum Sectional Density factor is more relevant. In wartime, the opportunity time to perform a lethal shot is often limited, hence the Lethality factor is more important, i.e. every shot counts. However if the intended animal target stays still enough for a lethal shot to the brain to be undertaken, within the accurate rage of the firearm, then the Momentum Sectional Density factor is more important. If the shooter is considered to be an untrained marksman, then it is recommended that the Combined Performance factor [(MV)^2]/d be used.

When used in conjunction with the above formulae, this lethality information now informs the shooter the effective range limit of their cartridge and gun combination on the intended target. It should be further noted that these methods are approximate estimates only, as the terminal ballistic characteristics of bullets in animals can vary widely. However, a good hunter should also know the accurate range limitation of their gun and ammunition, the environmental limitations under which the shot is undertaken, including opportunity time, and know where to shoot an animal to obtain an immediate lethal outcome.

Scott McFarlane

— Preceding unsigned comment added by 119.17.142.23 (talk) 06:52, 25 June 2023 (UTC)

Formulas give different results

These two formulas are not the same and do not produce the same result. Example

.308 diameter bullet 150 grain weight

using Diam Squared .308 squared = .094864 using area of .308 = .074506

150 grains converted to lbs = .021429 lbs

.021429/.09486 = .225906

.021429/ .074506 = .287614

This should speak for itself. So I looked up the sectional density of a .308 150 grain bullet and it is listed as .226 I found the sectional densities of common bullets on the website below.

http://www.chuckhawks.com/sd.htm

— Preceding unsigned comment added by Rickster58 (talk • contribs) 13:32, 17 February 2009 (UTC)

Moving or deleting penetration factor concept section

At A Study of Sectional Density experiments regarding projectile penetration are described. Though the penetration factor model yields easily established numerical results using only the projectile energy and sectional density as input parameters, the study shows the obtained numerical results do not predict nor describe the complex process of projectile/target media interaction correctly. Since it is a terminal ballistics concept it should be moved to the terminal ballistics article.--Francis Flinch (talk) 09:12, 25 July 2009 (UTC)

Moved from article:

The Concept of Penetration Factor Penetration factor is a concept of the ability a given bullet in flight upon impacting can penetrate a consistant matter. The equation for the Penetration Factor is as follows; Energy in Ft lbs X Sectional Density= Penetration Factor (PF). Example:

.277 caliber 150 grain TBT with sectional density of .279

Range in yards_________Muzzle____100____200____300

Ft lbs(energy__________2,667_____2,313__1,997__1,716

Penetration Factor_____744_______645____557____478

.284 caliber 160 grain TBT with sectional density of .283

Range in yards_________Muzzle_____100____200____300

Ft lbs_________________2,785______2,448__2,143__1,870

PF____________________788_______692____606____529

If bullet construction remains the same between two cartridges, range of the target remains the same and the target is of consistant matter, the catridge with the greater PF will penetrate deeper. Sectional Density alone cannot determine Penetration, nor can energy alone. The energy(ft lbs)is needed to propel the Bullet, while the sectional density determines the efficiency of the bullets ability to penetrate the matter. These two factors work together to create the Penetration Factor. This measure of PF was originated by Dustin Slats.

--Francis Flinch (talk) 07:24, 28 July 2009 (UTC)

Who is Dustin Slats? I 've been use Tke x Sd for over 30 years. I thought I was the only one arguing sound scientific principals. I feel better that I'm not alone.

Greg Glover (talk) 20:55, 4 October 2012 (UTC)

Top half of article removed

As there is no definition (Websters and Oxford) or historical foot notes as to the use of sectional density outside ballistics. The conflation of the needle and penny to sectional density and area to diameter squared was removed.

Also there was the conflation of mass and Force

• (F = ma) = (w = mg)
• (F = ma) ≠ (F = m)

Greg Glover (talk) 00:19, 4 October 2012 (UTC)

Dictionaries are sadly not very good engineering libraries. All sorts of moving objects have sectional densities that matter. Think of spacecraft, cars or aeroplanes that generally have other (non-round) cross sections than bullets. Sectional density plays its part in ballistic coefficients and the coefficient of drag of such moving objects. You are right the references only deal with ballistics and mass is not the best way to express things.--Francis Flinch (talk) 07:45, 4 October 2012 (UTC)

Hi Francis Flinch,

I don't dispute that any matter has a sectional density; cars, plans and trains. What I do dispute, less the proper foot note, is that sectional density as a mathematical application is used outside of ballistics.

Specifically, the use of sectional density when employed in the G1 drag model. The G1 and G2 drag models are based on a projectiles shape and not a mathematical formula. The G1drag model (ca 1880) is a short cut to the more rigorous computed drag models going back to about the year1740. The famous Ingalls' tables where based on such computations used for artillery batteries all over the world. The Ingalls' tables are a battle field short cut to shell trajectory.

You foot note #1 is for ballistics and not for outside use. I will go to the library and look in the Mc Graw Hill Science and Technology encyclopedia for sectional density. If it does cite F /A , I’ll replace your #1 foot note with that. If not I'll post the words before and after where sectional density would be. I'll post the volume and page too. Then if you don't beat me to it by posting the correct foot note from a source within science and engineering, I'm pulling the top half of article.

I don't want any edit-waring. But we need to make sure we are properly documenting what we are talking about. Again I don't argue that you and I have a sectional density. We do and its called Body mass index not sectional density.

Sectional density is F /d². Well... That's what I know, but I'm always open to new applications.

Thanks for keeping the article mathematically correct. I've been working hard on just that let alone all the above.

Greg Glover (talk) 15:43, 4 October 2012 (UTC)

Thanks for your positive input. The Mc Graw Hill Science and Technology encyclopedia might contain more information regarding sectional density than a ballistics internet website. At http://www.accessscience.com/home.aspx I got 4 pages worth of "sectional density" hits that often do not point to ballistic article subjects. Beware encyclopedia's are still no match for a proper technical university library. I agree sectional density is generally only used in ballistics. I had a problem the article zooms in at (round) bullets. Non circular shapes like kinetic energy penetrators fired by tanks or some space craft sadly have more complex shapes. Ballistic models and calculations can and are also applied on such non circular shapes. As you wrote G models are no modern ballistic modeling method. I think however the drag curves of the various G models are still practical tools for obtaining useful predictions for normal hunting situations etc. Nowadays we can deduct from actual flight measurements that rifle bullets and artillery shells - assuming sufficient stability (static and dynamic) during flight - present more or less circular (varying) sectional shape(s) during their flight trough to a relatively thin fluid like air. The more or less part is generally subtle, but a main reason for making ballistic predictions and mathematic models and designing projectiles that are accurate enough to be useful when complications like long ranges and flight times are involved challenging.--Francis Flinch (talk) 08:40, 5 October 2012 (UTC)

Hi Francis Flinch,

I see you add some more information on the article page. Again this information that you footnoted is for “ballistics”. This is the crux of my argument. There in no credible information available to the general public that Sectional Density pertains to physics in general.

I did go to a couple of branch libraries here in Los Angeles but to no avail. I will try to get over to the main library downtown. All the Science and Technology Encyclopedias are there.

I also went to the link you provided. Thanks so much. Yes there are over 4 pages (100 per page ) of hits for the words, sectional density. However, there are 0 hits for the word, “sectional density”. I opened some of the links from the hit page and none of them seemed to have anything to do with sectional or density.

Also can you remove your footnote #2. I think that p, being represented as pressure and Wiki linked to the Pressure page is adequate.

Greg Glover (talk) 19:20, 22 October 2012 (UTC)

I feel linguistics are the main reason why I interpret things somewhat different. Since I think you are a native (US) English speaker, which I am not, and after reading some Poncelet (a French mathematician and engineer who contributed to basic projectile penetration theory during the Napoleon era) differential equations you must be right. Beware Poncelet does not use Normal force but Mass in his equations. That is logical, since his equations do not need to factor in gravitational field strength and will work on any planet. As I understand now "sectional density" will most probably be exclusively applied to straight traveling spin stabilized projectiles in US English. I found however this article in South African English Sectional Density - A Practical Joke? By Gerard Schultz by a bullet manufacturer that interprets things different. If you are open to such non-mainstream concepts depends on your personal curiosity and attitude.--Francis Flinch (talk) 18:07, 23 October 2012 (UTC)

Area of a circle

At least twice now, editors have raised (in various ways) a good point that the definition of area for a circle, such as the ballistic cross-section of a bullet, is πr², which is πd²/4 not πd² (that would be area of a square cross-section!). The formulas in our article, and the external refs tabulating SD values for various types of ammunition, seem to use the d² variant. Perhaps this omission of the "1/4" constant is a convention in the field of ammunition, or ballistics generally? Regardless, this basic physics and math contradiction needs to be fixed or explained. I've tagged he section accordingly. DMacks (talk) 12:20, 16 September 2022 (UTC)

Thanks for pointing it out. I have changed the formula. Given the units and the fact that projectiles generally have a circular cross section, it is obvious that the area of a circle should be used. Sauer202 (talk) 19:04, 27 February 2024 (UTC)