Is Sectional Density a Practical Joke?

[Safarigent]

I cam across this write up on the net and it has left me confused!

http://www.gsgroup.co.za/articlesd.html


Sectional density is a number that describes the relationship of the weight of an object to any one of its sides. When applied to a bullet, it is generally used to apply a number to the relationship of the weight of the bullet to the diameter, as observed from the front or rear of the bullet.

The question then arises: Of what use is this information? Does it have any value and can it be used to describe a function that is of importance, value or interest to the mind that enquires? Let us embark on a search for the value of Sectional Density as applied to the world of ballistics.



Starting with a box of 180gr .30 calibre bullets, we observe that the sectional density of the sealed box sitting on the loading bench can be calculated from the point of view of the side that is in contact with the loading bench. If, however, the box falls off the loading bench and falls on its side, the sectional density value changes from the point of view of the floor. At this basic level then, it must be accepted that sectional density can vary, depending on your point of view. One need not use a box of bullets to draw this conclusion. The same would apply to a single bullet standing on its base on the bench. If it falls off the bench and rolls to the furthest corner of the workshop, the bench and the floor will argue deep into the night about which sectional density value is the valid one.

Sectional density values are usually quoted as indicative of the performance, or lack thereof, of a particular bullet. So we should move our investigation forward to beyond the stage where the bullets are loaded and ready to fire, as sectional density is not of interest in the actual reloading procedure. We must investigate where the value of sectional density is of importance, once we light up a primer behind a load and the bullet starts moving down the barrel.

We compare two bullets of identical sectional density but of different construction. Both are 180 gr .30 calibre bullets but one is a round nose, flat base, solid shank bullet that is virtually parallel sided. The other is a hollow point, spitser, boat tail, match bullet with a thin jacket and a bearing surface as short as is prudent. The barrel time and muzzle velocity of these two bullets will differ from each other. Should one attempt to load them to the same muzzle velocity, the powder charges and pressures will certainly vary. So with identical sectional density values, these two different types of bullet will perform in different ways down the bore of the rifle. Clearly, there is no usable connection between sectional density and anything else here.

Possibly sectional density values could be useful somewhere in the external ballistics picture. External ballistics consist of stuff like trajectory, wind drift values, time of flight, gyroscopic stability and retained speed. Trajectory is determined by the ballistic coefficient of the bullet and its speed. We observe that two bullets of identical sectional density fly over two very different trajectories, if their bc values and speeds differ. And of course two bullets of differing sectional density values fly over the same trajectory, if their bc values and speeds are the same. So sectional density has nothing to do with determining the trajectory of a bullet.

How about resistance to wind? Surely a bullet with high sectional density will be better in wind than one with a low sectional density? Using an external ballistics program, we find that changes in wind drift for a given bullet will only occur if the wind speed, bullet speed or bullet bc values are changed. Changing the weight of the bullet and thereby the sectional density, makes no difference to the wind drift values. While experimenting with the wind drift values in the ballistics program, we noticed that the time of flight and retained speed also remained unchanged, regardless of the weight of the bullet. Surely sectional density must be of use somewhere, so let’s take a close look at gyroscopic stability.

Gyroscopic stability is what makes a bullet fly in a stable manner. If the variety of conditions governing gyroscopic stability culminate in a gyroscopic stability value of less than one, the bullet is unstable and will fly funny. No amount of lecturing the offending bullet will make it straighten up and fly right. Something has to be changed to bring the gyroscopic stability value to more than one.

Gyroscopic stability is a rather complicated subject and one often hears of the Greenhill formula being used to calculate whether a bullet is stable or not. Using the Greenhill formula is better than nothing, like some makes of chronograph, but for more exact calculations and a true picture, one must turn to the work of one R.L.McCoy. Using the Greenhill formula results in an inconsistent effect on the gyroscopic stability of a bullet if sectional density is changed. The equation does not ask for the right information to accurately take into account varying material densities and forms.

Using McCoy’s method requires inputting the specific gravity of the bullet material as well as a number of form variations that will affect gyroscopic stability. Specific gravity denotes how dense a material is. If specific gravity changes, density changes. This must therefore lead to a change in sectional density! Eureka! A connection! Now we must investigate more thoroughly by making some comparisons to prove the connection.

Still using McCoy’s method, we find that two bullets, identical in form but made from different materials, have different gyroscopic stability values as well as different sectional density values. Changing the sectional density therefore changes the gyroscopic stability. The connection seems to stand. As expected, two identical bullets, made from the same material have identical gyroscopic stability and sectional density values. Not changing the sectional density, leads to no change in the gyroscopic stability and we have two out of two. Now we are cooking! Now we compare two bullets, made from the same material, with identical sectional density values but with different forms, one a semi-wadcutter and the other a spitser boat tail. Alas, they have very different gyroscopic stability values and disprove once again what seemed to be a possible use for sectional density. It is form, rate of twist, diameter and speed that are the big hitters when gyroscopic stability is calculated. As usual, sectional density just tagged along as a coincidental by product of the important stuff.

At this stage, someone will probably enquire indignantly whether the numbskull writing this realises that sectional density is only of importance when it comes to terminal ballistics. Sectional density is a measure of how well a bullet will smite the good, the bad and the ugly, they cry. There is an ideal sectional density and it is 0.3, they intone. So we must investigate, with a modicum of seriousness, this bullet with a sectional density of 0.3.



To compare a variety of bullets with a sectional density of 0.3, we shoot a hypothetical animal, which is self healing, in the same spot, several times. The distance is 50 paces and we aim for the shoulders in order to break it down so that it cannot come and stomp on us when it gets tired of being shot at with a sectional density of 0.3. It should also be tied down to ensure consistency of shot placement.

First we use a jacketed hollow point match bullet at 3000 fps. When it strikes, it turns to dust and the sectional density becomes nil. The animal also does not fall down. It seems there is a link: Zero sectional density equals animal not falling down. For the second shot we use the same bullet but slow it down some. This time the animal falls down and the recovered bullet weighs half of what it started at. It has also expanded to almost double calibre. The sectional density is difficult to calculate because of the deformed shape and we thumb suck it at about 0.12. Encouraged by the much better result, we still use the same type of bullet and slow it down some more. In fact we slow it down to 100 fps at impact. To deal with the trajectory of this shot we have to fit a new scope with a taller elevation turret. At the shot, the animal would have run away if we did not have it tied down. Upon examination we find the undeformed bullet stuck in the hide on the near side. It has retained all its weight and thus all its sectional density of 0.3. The fact that the animal has not fallen down is a problem. How is it possible that a sectional density of nil and a sectional density of 0.3 can have the same not falling down result? Clearly this type of bullet cannot be made to conform to the theory of a sectional density of 0.3, so another type must be tried.



These three bullets have the same weight but wildly differing sd values. Although all three once had the same sd, the more they deformed, the better they worked and the worse the sd became.

At the other end of the spectrum is the indestructible monometallic solid. We find one with a sectional density of 0.3 and shoot. The animal falls down. The bullet cannot be recovered and a careful search for fragments and a lack of same, supports the position that, this time, a sectional density of 0.3 resulted in success. Using the same monometallic solid, we speed it up and slow it down and, as long as it has enough speed to penetrate deep enough to reach a vital organ, the animal falls down. This is great as it seems that this sectional density of 0.3 works well, providing the shape and construction of the bullet can be relied on to stay more or less in one largish piece. One anomaly occurs with the solids with a sectional density of 0.3. Firing it at 100 fps produces the same not falling down result as with the match bullet that prompted us to try the solids as well. A nagging thought creeps in at this point. Is it possible that speed and bullet construction and post impact shape could be the important factors that determine fall down? We must experiment further!

Unfortunately we have run out of solids with a sectional density of 0.3 and all we can find is a box of solids with a sectional density of 0.25. Curiosity gets the better of us and we load them up and shoot. They seem to work as well as the sectional density of 0.3, providing we keep hitting the vital organs. Confused by this anomalous result, we load up partition style bullets, bonded core solids, monometallic hollow points and some others, all with a sectional density of 0.3. Some fail and some work. Some retain all their weight and some very little. The starting sectional density of 0.3 varies, after impact, from zero to 0.3 with no apparent connection to animals falling down. However, some patterns do emerge that support a number of theories that hold water.

1. Animals fall down reliably if a vital organ is destroyed, regardless of sectional density of the bullet.

2. Animals fall down reliably if the bullet retains enough weight and has enough speed to penetrate to a vital organ regardless of sectional density. This is interesting, weight and speed are the factors that determine momentum and energy values.

3. The sectional density value seems to be of no importance at all, providing it did not disappear completely.

4. The post impact sectional density of a bullet is almost always less than the starting sectional density.

This leaves only one question unanswered. Who first came up with the theory of sectional density? Was it some ballistician with a macabre sense of humour? Did he put forward this theory as a joke and it got out of control? Sectional density seems to be the ballistic equivalent of an internet chain letter. No matter how illogical or outdated or disproved it is, it keeps on popping up. Almost like the concept of hydrostatic shock, but that is another story.

To your success,

Gerard Schultz


Now i used to think great SD meant greater penetration, like on the 7x57, 6.5x54, .318 WR calibres amongst others which have great penetration with their heavy for calibre high SD bullets.
This article has left me scratching my head.
:/

[xl_target]

Here is an excerpt from a Chuck Hawks article on SD:

Sectional density (SD) is the numerical result of a calculation that compares a bullet's weight to its diameter. To calculate a bullet's sectional density divide the bullet's weight (in pounds) by its diameter (in inches), squared. The higher the SD number the better the SD and the heavier a bullet is in proportion to its diameter. SD stays the same for all bullets of the same weight in the same caliber; shape does not affect SD.

SD is important because it has a significant effect on penetration. Other things being equal (like impact velocity, bullet design and material, etc.) the higher the SD number, the better the bullet's penetration. In other words, a skinny bullet of a given weight tends to penetrate better than a fat bullet of the same weight, because it concentrates the same force on a smaller area of the target.

http://www.chuckhawks.com/sd.htm
They key phrase is "Other things being equal (like impact velocity, bullet design and material, etc.)"

If you look at what the author that you quoted said:

At the other end of the spectrum is the indestructible monometallic solid. We find one with a sectional density of 0.3 and shoot. The animal falls down. The bullet cannot be recovered and a careful search for fragments and a lack of same, supports the position that, this time, a sectional density of 0.3 resulted in success. Using the same monometallic solid, we speed it up and slow it down and, as long as it has enough speed to penetrate deep enough to reach a vital organ, the animal falls down. This is great as it seems that this sectional density of 0.3 works well, providing the shape and construction of the bullet can be relied on to stay more or less in one largish piece. One anomaly occurs with the solids with a sectional density of 0.3. Firing it at 100 fps produces the same not falling down result as with the match bullet that prompted us to try the solids as well. A nagging thought creeps in at this point. Is it possible that speed and bullet construction and post impact shape could be the important factors that determine fall down?

we load up partition style bullets, bonded core solids, monometallic hollow points and some others, all with a sectional density of 0.3.

... all other things are not equal.

Read the Chuck Hawks article and see if it makes sense and also remember that there are very few absolutes in life.

[brihacharan]

Thanks xl_target for your response - looks like both of us were on to 'chuckhawks' and you beat me on the draw
However I take the liberty to add a bit of further elucidation on the subject...

Sectional Density for Beginners
By Bob Beers (Ref: http://www.chuckhawks.com/sd_beginners.htm)

Bullets have several quantifiable characteristics. One of the most important is Sectional Density (SD). It took me a long time to finally grasp its true significance, but once I did, much of my confusion about bullets just disappeared.
Sectional density, according to the SPEER RELOADING MANUAL No. 13, is defined as:
"A bullet's weight in pounds divided by the square of its diameter in inches" - Note that SD is independent of a bullet's shape. ALL BULLETS OF THE SAME CALIBER AND WEIGHT WILL HAVE THE SAME SD, REGARDLESS OF THEIR SHAPE OR COMPOSITION.

For the lay person, SD can be considered to be a calculated value that represents how much mass of a given cross-sectional area is necessary to push a bullet through a given medium (such as a game animal).

It's calculated as follows:
Sectional Density = (bullet weight in grains) % 7000 x (bullet dia. in inches) x (bullet dia. in inches)
As the frontal area (think caliber) of a bullet increases, the weight behind it must increase accordingly to achieve the same penetration.
The value of Sectional Densities for various classes of animal seems to have been empirically derived by the family of hunters over many, many years. Their collective experiences indicate that these (or similar) values seem to work well. Given that a Sectional Density of .180 is good for small animals, .200-.230 is good for medium size animals, .270-.280 is good for large animals, and .300+ is good for larger and tougher animals. In other words, as the penetration resistance increases (the frontal area increases) the push behind it (weight) increases at the same rate, thus maintaining the expected depth of penetration for a given animal or class of animals.

Note that the sectional density remains constant for a given animal class and as the caliber increases the weight of the bullet must increase to push the larger frontal area of the bullet through the animal. The benefit of the larger calibers is that their bullets make larger holes (wound channels).

As the animals become larger, as we move from small to medium, medium to large, and large to thick-skinned, the bullets become progressively larger as well. From class to class, the sectional density of the bullet progressively increases, which increases the bullet weight, so that the bullet will penetrate deeper into larger animals and drop them for good.

It's been my personal experience & observation - when I had used 150gr / 180gr / 220gr in my 30.06 Winchester to take the following game when it was legal in India:
1. Deer
2. Wild Boar
3. Sambhar
Briha

[Grumpy]

I think Gerard Schultz has got a bee in his bonnet about sectional density and is not prepared to listen to rational argument. He either doesn`t understand the relevance of sectional density .... or doesn`t want to understand.
Don`t be confused, read and believe the Chuck Hawks article and ignore Mr Schultz.
As regards those calibres that exhibit high Sectional Densitiy it should be remembered that it is a bullet that is heavy for calibre that has a high SD. The 6.5x55 ( or 6.5x54 ) has a high SD with a 156-160 gr bullet. With 140 gr bullets the SD is nothing special.
The Woodleigh Bullets website is very for the detailed specifications it lists for the excellent bullets they manufacture. The website is : http://www.woodleighbullets.com.au/
Take note of the SD figures as you may be surprised in some instances ..... both as regards how high a particular SD might be or, in some instances, how low.

[TwoRivers]

If this is the Gerard Schultz I think he is, he is mainly writing for his fellow South Africans, who are firm believers in sectional density, a bullet long for diameter, for hunting. He makes an all copper, hence low sectional density bullet.

All other things equal, sectional density equals penetration, allowing the bullet to reach a vital organ even if you don't have a straight-on shot. In the days of simple lead-core jacketed bullets, that was an important consideration. While lighter bullets could be shot faster, with less recoil and flatter trajectory, they had a tendency to blow up and fail to penetrate on heavier game. Nowadays there are much better bullets, bullets that expand reliably, yet give deep, or adequate, penetration. So sectional density alone is no longer of such importance. Modern bullets are much less likely to blow up and not penetrate, and lighter bullets that give higher velocity and flatter trajectory with reliable deep penetration are common in "Premium" ammunition.

[Grumpy]

Oh, monolythic solids. Yes, that should have occurred to me. Oh well, at least someone is on the ball.
As regards SD he could, of course, compared one of his bullets with a lighter - and shorter - version which would have proved the point he was trying to dismiss...... Too obvious perhaps ?

[timmy]

Here is my opinion of the Gerard Schultz essay on sectional density:

First of all, what Two Rivers says here is true:

All other things equal, sectional density equals penetration, allowing the bullet to reach a vital organ even if you don't have a straight-on shot. In the days of simple lead-core jacketed bullets, that was an important consideration. While lighter bullets could be shot faster, with less recoil and flatter trajectory, they had a tendency to blow up and fail to penetrate on heavier game. Nowadays there are much better bullets, bullets that expand reliably, yet give deep, or adequate, penetration. So sectional density alone is no longer of such importance. Modern bullets are much less likely to blow up and not penetrate, and lighter bullets that give higher velocity and flatter trajectory with reliable deep penetration are common in "Premium" ammunition.

But in saying this, there are other issues which may be discussed. For instance, back on the "old days," when fast moving light bullets tended to break up badly and get hunters in trouble, it was not a matter of ammunition makers not knowing how to make effective, fast moving bullets that would not break up. These things were known and effective bullets and designs did exist, but often times, sportsmen did not avail themselves of them. Whether this was due to people just not knowing about them, or the distribution channels not making these bullets available, or sportsmen simply not wanting to spend the extra money is another subject of discussion. I suspect all three issues were at play.

Brenneke TUG bullets have been available for decades, and are known to be effective. http://en.wikipedia.org/wiki/Brenneke

Nosler Partion bullets have been available for almost as long as the Brenneke TUG. http://en.wikipedia.org/wiki/Nosler

My pont hère being, that small caliber bullets that could be pushed at high speed and not break up upon hitting game have been available for a very long time.

But regarding Gerard Schultz, Two Rivers is putting the finger on what's going on with him with this statement:

If this is the Gerard Schultz I think he is, he is mainly writing for his fellow South Africans, who are firm believers in sectional density, a bullet long for diameter, for hunting. He makes an all copper, hence low sectional density bullet.

In other words, if I may paraphrase, Schultz disagrees with the South African view of high sectional density bullets being needed for certain game, so he is "shaping" or "tilting" his arguments to make a certain point.

Now this may be a fine technique for argumentative purposes, but when an argument leaves out facts, then it can hardly be considered instructional. At that point, how does one tell whether Schultz is conveying a fact, or whether he is twisting, omitting, misrepresenting, or is simply ignorant of what he's talking about?

As an example, Schultz says:

Possibly sectional density values could be useful somewhere in the external ballistics picture. External ballistics consist of stuff like trajectory, wind drift values, time of flight, gyroscopic stability and retained speed. Trajectory is determined by the ballistic coefficient of the bullet and its speed. We observe that two bullets of identical sectional density fly over two very different trajectories, if their bc values and speeds differ. And of course two bullets of differing sectional density values fly over the same trajectory, if their bc values and speeds are the same.

This part is all true, but when he says this, you know that he is "3 bags full," as our British friends would say:

So sectional density has nothing to do with determining the trajectory of a bullet.

This is simply either stupid or deliberately misleading. The formula for the ballistic coefficient is:

C=m ÷ i × d2, where:

C is the ballistic coefficient
m is mass (Not weight, as most people relate this. There is a difference!)
i is the form factor, and is = drag of the bullet in question ÷ drag of the model bullet
d2 is the diameter of the bullet squared.

Now, if you remember your algebra, you can state this to be C = Sectional Density ÷ I, because m ÷ d2 is the formula for sectional density.

So, Schultz is in great error, because Sectional Density is a key factor in determining the Ballistic Coefficient, which he admits does matter. His statement is as silly as saying, the speed at which you can drive a car around the racetrack is determined by how well it handles, but it doesn't matter whether you have new or bald tires on the car.

However, while he is correct in saying that bullets of the same Ballistic Coefficient will have the same performance and trajectory at the same speed, we should note here that the lighter bullet in this comparison is assumed by Schultz to be driven at the same speed as the heavier bullet, but in reality, a lighter bullet is generally driven at a higher velocity than a heavier one. This means greater energy in most cases, because, while mass of the bullet is a linear factor (double the mass, double the energy, quadruple the mass, quadruple the energy, etc.), velocity is squared and thus is a geometric factor. Higher velocity will buck the wind better, as well.

When I read something like what Schultz wrote, I am eager to learn, which requires him to know something I don't. If we both know it, I cannot learn, but only agree. But in this case, where he twists facts to support his claims and in the process, makes misleading statements and wrong conclusions, I generally disregard such writings as rubbish and move on.

Going back to Two River's points, I think that the requirement for caliber choice is determined by the sort of hunting to be done (e.g., dangerous vs. non-dangerous game, or thick-skinned vs. thin-skinned game) and what bullets are available and used.