Technical Discussion of BC and Bullet Design
The Ultra Low Drag (ULD) bullet represents the maximum theoretically possible ballistic coefficient for a given caliber and weight. Ballistic coefficient is simply a comparison of how quickly a bullet is slowed down by air resistance compared to a standard bullet fired at the same velocity over the same distance. It is NOT the same thing as accuracy, and in fact, if taken to extremes will destroy accuracy. BC is not a precise, one-number measure of performance, but more of an average over the range of velocities at a given air temperature and density as compared to some agreed standard bullet's performance in the same conditions. It has become a popular if misunderstood way to "judge" the potential drop and wind resistance for a bullet, but has some rather severe limitations as a figure of merit.
Accuracy may be used as a term that includes the shooter's ability to determine range and hold-over amount, and the bullet's ability to maintain a closer track to the point of aim in changing wind conditions. These two factors affect the accuracy, but it could be argued that they are not, technically, a part of the inherent accuracy of the bullet design itself. Rather, they are secondary effects of having a quicker flight to target at the same starting velocity (that is, less loss of velocity due to less drag effect).
In other words, under windless conditions at a known range, a very low BC bullet may be quite accurate even including the human-adjustment issues of accuracy. Eliminating the human factor and using a mechanical rest and firing device in a tunnel, the low BC bullet could even be more accurate than the high BC bullet simply because the shorter, larger projetile may require less spin to be stable over the flight path, and have less inherent spin related wobble from slight unavoidable imbalances in the materials or construction.
Regardless, the formula for BC is simply the weight of the bullet (in pounds) divided by the square of diameter (essentially, an inverse relation to the cross sectional area), times a correction factor that takes into account the shape of the bullet and its ability to overcome air resistance, or the inverse of the amount of velocity loss caused by passing through the air.
BC = i * (w/d^2)
There is no magic about it but there are many complicating factors involved in the term "i", which stands for the "Ingall's Coefficient". The value is affected by how pointed the bullet is, how much surface drag is created by the length of the shank, how the base shape affects the drag at the base (or, in other terms, how much turbulence is left in the bullet's wake to siphon off energy in its creation), how dense the air is at the time of firing and over the flight path, and how fast the bullet is fired (at Mach 1, the speed of sound for the density of air at the time of firing, a radical shift in the value of "i" takes place because of the creation of shock waves).
With a given caliber of bullet, you can do nothing about the diameter. It is fixed for that caliber. If all other factors were the same, making the diameter smaller would increase the BC quite a bit (since this is an inverse squared function for the BC). An identical shape and weight of 7mm bullet can't help but have a higher BC than the same weight and shape of .308 caliber bullet, for instance. No magic trick will change that.
In the same caliber, a heavier bullet of the same shape will always have a higher BC than a lighter bullet. That, too, is just basic physics and not subject to change by marketing hype or other forms of voodoo. A great many schemes have been brought forward by armchair engineers over the years, supposedly circumventing the physics. You can remove the center so air flows through the bullet and all you do is make the bullet lighter, and add a second surface to drag against the air stream. How this could possibly increase the BC as has been claimed in some rather non-scientific literature is a bit of a mystery. Some shooters have expressed the belief that using a different material, such as plastic on the one extreme or tungsten on the other, will make the BC higher. The material makes no difference if the bullet is the same shape and weight, except for one thing: length. If you make the core material more dense, such as using a metal heavier than lead (tungsten, gold, uranium, osmium, iridium...) then for the same weight you will have a shorter bullet. In one small way it has an effect on BC, and that would be skin drag effect. Less skin means less resistance, but this is a very tiny effect compared to the base drag (at subsonic velocities) or the nose and angle of shock wave generated (at supersonic velocities). It is not, in other words, really worth the cost (benefit/cost ratio is too low to be a practical technique).
There is a range of weights beyond which the bullet is not practical to fire in a typical hand-held firearm. There are other limits placed by the strength of the firearm action, its design, and of course the relation of weight to length and length to twist rate. As a bullet is made heavier and heavier without making the core material more dense, it becomes longer. Longer bullets require higher spin rate to maintain a nose-forward flight attitude. Higher spin rate amplifies any eccentricities or imbalances in the bullet. All bullets have some amount of eccentric or off-center weight distribution. There is no way to tell every molecule in the metal which makes up the bullet to distribute themselves in perfectly even fashion. We live with less than perfect bullets because it is a fact of nature. But if we don't spin them too fast, they will all land close enough to the same hole in the target so it doesn't really matter if they are less than perfect. Spin them faster, and they tend to drift off or even come apart at some rotational speed.
So, basically, if the BC is made too high, the bullet has to become too long, requiring too high a spin rate, and the accuracy goes down. This is not a switch, on or off. It is a curve. The attempt to get the BC higher and higher in the quest for a flatter flight path is a good one, but at some point the accuracy deteriorates enough so that the flatter path doesn't help as much as the damage done by a wider circle of dispersion at the target!
All of this having been said, there are ways to "tweak" the bullet design toward a higher BC without necessarily destroying the accuracy in the process. One of them is to make the nose as pointed as the particular firearm and load will feed and fire reliably, without at the same time making the bullet too long or taking too much weight away from the shank portion and pushing it all into the ogive portion. If the nose of the bullet is too heavy, the bullet becomes "over-stable" which is a way of saying that it acts like a shuttle-cock and wants to maintain the launch attitude all the way through the trajectory. A bullet that is too nose heavy will shoot OK for short ranges. But when the range includes any significant amount of curve or drop in the flight path (a significant trajectory curve), the bullet begins flying at more and more of an angle to the direction its nose is pointed. This of course will cause it to tumble and fly far from the point of aim when taken very far in the nose-heavy direction.
Pilots of aircraft learn in basic flight training that one must co-ordinate the rudder and the ailerons to make a turn. Otherwise, the aircraft will be flying with its nose pointed at some angle other than the direction of travel. This is a horizontal example of what happens to the bullet's vertical flight path if the spin rate is not able to allow the bullet to tip in the direction of travel and maintain an angle of flight with the nose leading.
Hollow base wadcutters and Foster-style shotgun slugs are good examples of nose-heavy bullets that tend to fly nose first even with a small or no spin velocity. But they are typically not launched at targets very far away. During their flight, the curve is moderate in their path to the target. So if the nose keeps pointed in the direction of the barrel at the moment it emerged, it will still be fairly close to following the flight path with the bullet tip. If you put a light material in the back of a bullet, and a heavy one up front, you can to some extent shift the center of gravity so that the bullet does not require as much spin to be stable. But at some point, the bullet will have so much shift in the CG that it will become like the hollow based wadcutter, or shotgun slug.
If fired at a target so far away that the bullet follows a large trajectory curve, requiring perhaps 20 degrees angle from a horizontal path to the target under normal circumstances, this nose-heavy bullet might keep flying with the nose pointed 20 degrees from horizontal all the way to the target if it were not for the sad fact that it would be presenting a rather non-concentric surface to the direction of travel as it approached the top of the trajectory curve. The air striking the side of the bullet tips it even more and makes it fly off in a direction best described as "somewhere else" besides the target. The BC of such a bullet would be completely different when it is flying at an angle to the direction of its normal trajectory: much, much lower. It may drop in a quite unexpected short range compared to the same caliber and weight of bullet, fired at the same velocity, but having the weight centered further from the nose.
The idea that a bullet can become too "stable" is sometimes hard to understand. A bullet needs to have a good rotational stability, and a good ability to follow a curved path, which is a balance between the gyroscopic effect of its spin and the tendancy of the bullet to flip over and present its heavier base forward. That tendancy to flip over is the instability which the spin corrects and utilizes, in order to make the bullet point in the direction of travel all through its curved flight. If the weight is too far back, the spin has to be too high. If the weight is too far forward, the spin is not able to make the bullet follow the path with its nose. As with nearly everything in life, there is a range of balance that can be used to suit our purposes without going too far either way.
Essentially, then, there are four ways to achieve a higher BC in a given caliber of bullet:
- Increase the weight.
- Reduce the drag factors.
- Use a less efficient standard bullet for comparision.
- Select an advantageous velocity for measurement.
The last two ways can be a bit of a marketing trick. Since most people don't really understand what BC means, they tend to use it as a sort of performance number, much in the way the processor chips compete on clock frequency. The fact that some chips might be designed to do more operations on a single clock cycle than others which do fewer at a higher clock rate is beyond realm of the 30 second commercial to convey. Having people float around in colorful suits to zippy music with the implication that they do this because they bought the computer with the faster chip is a more effective way to sell the chip and focus on clock speed as a marketing tool. "It's faster so it's better -- buy it today!" Never mind that the less market-oriented competitors actually do more work using parallel processes with slower clock speed.
In a similar way, it is far easier to "tweak" the standards and conditions a bit and generate a higher number for BC than a competitive product might be advertising, than it is to explain why the product is superior, and what exactly makes it so. So long as shooters are willing to take a number such as BC at "face value" and only comprehend a portion of its real value, one can hardly blame a marketing department for using this to good advantage.
For instance, you can have any BC number you like for any bullet. Just compare it to, say, a beach ball, as your standard instead of a 1-inch boattail spitzer cannon projectile. Whatever is assigned the value of "1" becomes the standard. If your bullet exactly matches the same trajectory when fired at the same initial angle and velocity, it too has a BC of 1. If the trajectory is more curved and the bullet hits the ground closer to you, it will have a smaller number, such as 0.9 or 0.533 depending on how much more quickly your bullet slows down than that beach ball. Of course, with that example, any real bullet would have tremendous BC numbers, probably on the order of 200 or 500 at least. If your standard of comparison was changed to a golf ball, then the numbers would drop somewhat but still be quite impressive to people who didn't know what you were doing. Use a .308 180-grain 8-S ogive flat base bullet as the new standard and now your bullet may have a higher or a lower BC than 1.0 depending on how it tracks the same trajectory at the same velocity and launch attitude, in the same air density. Many popular bullets with BC numbers of 0.85 or 0.79 would suddenly become 1.5 or 1.2, to the delight of the marketing department initiating this "new standard" of performance!
Of course, before long other bullet marketing people would see what was happening, and change their BC standard bullet to match or be even slower and more drag producing. It might not be long before they actually did use a beach ball! But even the most math-adverse handloader would quickly realize something was wrong as the BC numbers kept shooting skyward on the same bullets. The old adage about the frog in the boiling pot would prove too true, once again: change things fast enough and they can't help but be noticed. (Imagine if instead of income tax withholding, every citizen had to come up with the full amount of income taxes in April each year! The "death by small cuts" would turn into a beheading, bringing home all too clearly how high the tax really is.)
All this is only by way of illustrating that BC is a comparison to some standard, a ratio of how one bullet is overcoming air resistance compared to the other one. It isn't a figure of overall merit, has little or nothing to do directly with accuracy, expansion, or anything else except the rate at which the bullet sheds velocity by comparison to another one. Because most bullet makers do use the same standard, the comparison at least has some relevance as a relative gauge with which to compare bullets. But because the same exact conditions are not necessarily maintained both for the standard and the tested bullet (such as the air density and other ambient factors), even using the same standard bullet doesn't guarantee two bullets assigned the same BC actually follow the same trajectory at the same initial launch speed and angle. They ought to be close, just probably not exactly the same.
Carrying the decimals out to five places is about as useful as it would be when applied to your car's odometer. It's doubtful you'd miss the off-ramp if the sign said 5 miles ahead and your odometer told you you'd gone 5.01526 miles. Plus or minus what? Is an odometer accurate to even a tenth of a mile? But like a $20 micrometer with readout to six decimal places, you can have as many numbers rolling off as you wish, disconnected from reality. The BC can be specified or calculated to many decimal places, as it is with Corbin software such as the DC-1001 BC Calculator.
This is useful for preliminary comparison purposes. When you are designing a bullet, it is useful to know that some change you made in the tip shape, meplat diameter, weight, or ratio of core to jacket, has made even a small positive or negative effect on the BC. It may not be useful in the field, but it is a great tool for helping refine your design. It can help you determine whether a change that would cost money is actually worth doing (such as buying a different shape of point forming die to go from 10-S ogive to 11-S ogive). If the BC goes up by 0.1 or so, this might be worth considering. If it only goes up by 0.01 or less, weigh the cost/benefit ratio rather carefully (using a scale that goes to at least 0.001 plus or minus?).
The key to understanding BC is to use it primarily as what it is intended to be, a comparison with another bullet fired under the same conditions. You can use sophistocated but easy to operate software such as the Corbin DC-1001 BC Calculator or the Corbin DC-TWIST spin rate calculator to best advantage if you use them primarily to compare two bullets, rather than to give isolated facts about one bullet. In other words, once you have determined what a certain bullet design is doing in general terms in the real world, you can run the numbers for this bullet, then change some factors such as shape or weight, tip size, etc., and calculate how these factors might change the BC or spin rate. You don't necessarily get a number that is "accurate" in the sense that it will always be true under all circumstances for that bullet. But you do get a number that is accurate when compared to another bullet in the same circumstances (velocity, air density). Under these conditions, the prime standard used to generate the Ingall's number is not important, because it is "nulled out" by being the same in the equations used for both of your comparative bullets. The figures may not tell you exactly where the bullets will land, but they will accurately tell you which of two bullets will fly farther and retain more energy, and by how much.