The Other Number

[roy reali]

We look at many numbers when reloading. Grains of powder, bullet weight, and ballistic coefficient, etc. One number that doesn't seem to get as much attention is sectional density. Is it important or not?

I looked at three bullets of one hundred grains each in three different calibers. The SD for 6mm's is .242, the SD for 25 caliber is .215, and the .270's SD is .186. If the three bullets hit the same animal at the same velocity and are made exactly the same, does it mean that the .243 will out penetrate the other two? Or would the larger diameter bullets do better because of their size?

In other words, should a bullets SD be a consideration in picking the right projectile?

 

[Brian Pfleuger]

In theory, that's probably true.

A larger frontal area of a bullet with equal mass means that it will slow down quicker after impact. More mass is required to achieve the same penetration. It's sort of like "inertia per square inch".

In reality, I doubt it's anywhere near that clean and simple.

It's also related to the bullets aerodynamics, for basically the same reason. A bullet with a larger frontal area needs more mass (inertia) to avoid losing speed to air resistance. For that reason, I do think it's considered as a factor by long distance target shooters, though probably often times not directly.

Sectional density is also sometimes considered as a factor, for the penetration properties that you describe, by people who are shooting big, gnarly animals that tend to eat or kill you if you don't get it right the first time.

 

[zippy13]

The sectional density (SD) of a bullet is simply the bullet's mass divided by its cross-sectional area. So, all bullets of the same caliber and same mass will have the same SD. Given several bullets with the same mass and different calibers, the smaller caliber will have the highest SD.

Sectional density gives us an indication of how well an object will penetrate air, and other objects, with respect to its mass. It's one of the reasons our ancestors developed spears and arrows that were slender instead of fat. They were maximizing SD.

Obviously, there are many factors that determine a bullet's penetration, and SD is just one of them. We're all aware of how penetration is changed based on the bullet's configuration/construction. A soft point may be the same shape, and SD, as a fully jacketed bullet, but the penetration will differ greatly because of different deformation/fragmentation characteristics. Who hasn't seen photos/videos of bullet performance in ballistic jelly?

Assuming all of the other factors governing penetration remain constant, the bullet with the higher SD will have greater penetration. So, if you are selecting a load for a given weight bullet, with the same characteristics, the smaller caliber will give greater penetration. When selecting bullets of the same caliber, the heavier bullet will have a greater SD and have greater penetration assuming all other factors are equal. I think most reloaders know this from common sense, they don't need sectional density nembers.

In reality, the other factors governing bullet penetration don't remain the same. If you decide to go for a heavier bullet, then your velocity will probably decrease. If you change caliber, then the jacket thickness to core ratio is going to change.

Back to Roy's original question, "should a bullet's SD be a consideration in picking the right projectile?" IMHO, don't concern yourself about the actual SD numbers. More important is your common sense about caliber, weight, velocity and the other factors about a bullet's configuration/construction that should be considered when selecting for penetration. If it was a simple process to select the "right" bullet, do you think there would be such a variety of them available?

One of the huge benefits of reloading is the ability to tailor your ammo's performance to your anticipated shooting environment. We've come a long way from days of telling the sutler,"Gimme some forty-five seventies," but, we still have numbers to deal with. Don't get carried away by the ones of little consequence.

 

[Hog Buster]

I agree with Pizza Dude, in theory the 243 will penetrate farther, all things being equal, which in fact rarely happen.

You ask if larger bullets would be better, that depends on what you’re hunting. A high sectional density infers better accuracy, but when bullet hits beast things change. While penetration is paramount in some game rapid expansion is more desirable in others. Sectional density in these cases may be much different because of bullet design.

While sectional density plays a role in bullet performance it’s not a limiting factor when choosing a hunting bullet design. Like everything else in life, it’s just part of a compromise.

 

[Jim Watson]

When I was new in the game, sectional density was an important factor.
Nearly all rifle bullets - except them newfangled and expensive Noslers - were of simple cup and core construction and needed sectional density to penetrate well. High SD also meant a lower velocity which kept the simple bullets from breaking up on impact.

Now we have all manner of controlled expansion bullets that give a nice mushroom without fragmentation or overexpansion limiting penetration. So you can load a lighter/lower SD bullet to high velocity for flat trajectory and still expect it will do a number on the critter.

 

[Unclenick]

Roy,

To address your second question first, yes, among same-shape, same construction bullets, impacting at the same velocity, the higher SD penetrates more, provided expansion is proportional to diameter and similar in shape. In other words, for a given nose diameter and velocity, more SD means you will have more momentum per square inch of frontal area. If the decelerating force at any given velocity is proportional to that frontal area, as it is in a homogeneous medium like ballistic gelatin, then that force will have to be applied over a greater distance to deplete the higher momentum of the higher SD bullet.

There are some on-line photos I've run into (can't recall where offhand) comparing 9mm and .45ACP penetration in ballistic gelatin that show exactly the above. Their relative penetration in a given design is about proportional to their momentum. Typically about 20-30% deeper for the .45. The impact velocity difference didn't seem to matter as much.

Another major SD factor is not in terminal ballistics but in exterior ballistics. Ballistic coefficients are a drag coefficient multiplier that adjusts the drag coefficient of a bullet to that of a standard projectile for trajectory comparison. The standard projectile, by convention, is 1 inch in diameter and weighs one pound. When you put those two numbers through the sectional density calculation, you get a sectional density of 1. That is, 1 lbm/in² (where lbm is a pound-mass (not force, as in psi) or almost 1/32 slug). The standard projectile is also assigned a ballistic coefficient of 1 to normalize others to it (that's how it serves as its shape's drag standard).

Any bullet with exactly the same shape as the standard projectile will have a drag curve proportional in shape to of the standard projectile's curve, but will go through the whole curve over a different distance, dependent on how different its sectional density is. Thus, a same-shape bullet with a sectional density of 0.5 instead of 1.0, like the standard, will slow down from a given velocity twice as fast. It's velocity curve will look the same as the standard projectile's, but compressed over half the distance. Since the distance is half the ballistic coefficient, by definition, is also half. In other words, among projectiles the same shape as the standard projectile, the ballistic coefficient and the sectional density are equal. BC=SD. Very simple.

The trouble starts when you shoot a different shape projectile. If the shape is more aerodynamic than the standard projectile's shape, then the projectile's BC will be higher than that of a same-SD projectile the same shape as the standard projectile. This is because its shape lets it coast further as it loses velocity, so the drag curve stretches over a wider distance with it, so its BC is higher. To compensate, a form factor is used. Simply put, the form factor is a drag multiplier that is divided into the SD to result in a corrected BC that gives the right velocity loss distances for the different shape.

Where i is the form factor:

BC=SD/i

To summarize, if the projectile shape is the same as the standard projectile, the form factor is i=1 and the BC still equals the SD. If the shape has less drag than the standard shape, the form factor is smaller than 1, and when it is divided into the SD it results in the BC being bigger. If the shape has more drag than the standard shape, the form factor is greater than one and reduces the BC when divided into the SD.

The only fly in this ointment is that different projectile shapes than the standard don't actually have the same drag curve shape. That is why there are often multiple BC's given with a bullet to reflect those curve differences at different velocities. It is also why there is more than one standard projectile shape. SAAMI standardized on the oldest, the G1 standard projectile, but Bryan Litz, among others, has shown the later G7 standard shape drag curve better matches pointed boattail shapes and lets the BC and SD be closer to equal again, and eliminates any practical need for the BC to change with velocity. You do need a ballistics program that works with G7 BC's, however. The one you can use free at Berger's site does this. So do the free online JBM calculators.

All that's left is interior ballistics. Here the increase in SD for a given diameter means more mass to accelerate, so it requires more pressure to accelerate as quickly as a lower SD bullet will. That greater resistance to acceleration may be thought of as an increase in degree of confinement. It raises pressure for any given powder charge, and since guns have pressure limits, that limits velocity. So, you settle for the higher SD bullets going slower than the lower SD bullets. That lower velocity is better retained in flight because of the higher BC.

So, how much velocity you think you need has to be decided when choosing the bullet as well as what range it will be expected to travel to the target. For any two bullets the same shape as one another (without regard to the standard projectile's shape), you will find the lower SD bullet has lower BC, but can be driven to a higher muzzle velocity in a particular gun. But, owing to its the lower BC, that fast lower SD bullet will lose velocity faster than the higher SD bullet launched at a lower velocity. So, at some point down range the velocities will be equal. Before that point, the lower SD bullet will shoot flatter. Beyond that point, the higher SD bullet, owing to its higher BC, will be the faster of the two and will shoot flatter.

 

[GeauxTide]

Thank God for Unclenick. Roy, you ask great questions that make my head hurt. I admit that the SD number that is more relevant, to me, is Standard Deviation. A low SD will generally mean a low Extreme Spread resulting in a smaller group.