Understanding Long Range Bullets Part 1
There are two ways to go about projecting BC's for other calibers. In the first method, call it quick and easy, we assume perfect scaling. In this case, the increase in caliber translates to a scale factor, just like when we scaled the mass in the last section. We'll scale up to 7mm again for BC. The scale factor was 1.077. Since mass is proportional to the cube of the scale factor, and area is proportional to the diameter squared (in the denominator of the BC equation), we can 'scale' the BC from the 6.5mm benchmark (.565) 2 to the 7mm like this:
And so in the end, you're simply multiplying the original BC by the linear scale factor to get the BC for the other caliber. It's just that easy, or is it?
As with all things, the quick easy method is also the least accurate. The average advertised BC of the 7mm bullet is 0.596 for the speed range of interest (2000 to 2850 fps). Our first method estimated 2.1% high. There's another way that's almost as easy, and a bit more accurate.
In the first method, we assume that the bullet scales perfectly from the benchmark, in which case it would weigh 177 grains. The real 7mm bullet weighs only 175 grains. So a more exact way to calculate BC is by calculating the form factor for the benchmark, and using it for the other bullet. According to the BC equation, and the advertised BC of the benchmark 142 gr bullet (0.565), we calculate a form factor of i = .515. Furthermore, we'll use the actual weight of the 7mm bullet (175 gr) in the BC equation to get a better estimate of the 7mm's BC:
Using method #2, we arrive at an estimate that's only 1.0% different than the advertised BC of the 175 gr 7mm bullet for the same speed range. Figure 2 shows the advertised and calculated BC for a range of calibers based on the principle of scaling (Method 2). These calculated values are compared to advertised BC's for the same bullets. You can see there are two BC's for each caliber. The top one is for high velocity, and the bottom one is low velocity. You can see that the advertised BC's generally fall within the predicted corridor. There are a few things I'd like to point out about Figure 2. First, you might wonder why the 6mm data point is so high. Well, I can think of two reasons why the 6mm might be an outlier.
Both items 1 and 2 above would act to elevate the reported BC. Item 1 is an apparent increase. I'm sure that at lower velocities, like around 2000 fps, the BC of the 6mm bullet is less than .585, probably averaging about .570 between 2000 and 2850 fps.
Item 2, however, is a real reason for the 6mm bullet to have a higher BC. The benefit of the (VLD) secant nose is an advantage at all speeds. In this way, the 115 grain 6mm bullet is an outlier compared to the other bullets in our lineup.
Another thing you may note is that the BC of the .308 bullet averages at the low end of the band. If you remember when we scaled up the 30 caliber bullet, we found that its weight should be 229 grains. The real bullet is 9 grains lighter than if it were perfectly scaled. If the .30 cal bullet weighed 229 grains, the BC would be .653. That's right smack in the middle of the predicted band. The .244 caliber and 7mm bullets match the BC trend well.
In this way, you are able to use knowledge about trends in scaling to spot when something is out of place, for better or worse. There are names for things that don't follow trends. They're called outliers. Understanding outliers empowers you to choose equipment that has a better than average chance to win. Without an understanding of the fundamental governing trends, you can't spot outliers. You're at the mercy of commercials, old wives tales, and soothsayers.
Take the VLD for example. The 11 caliber secant ogive used on the 6mm bullet is a relatively mild secant ogive, yet the reduction in drag is real, and significant. Consider the 7mm Berger 180 grain VLD with an advertised BC of .682, which is completely off the chart in Figure 2! Even though this is a calculated BC (not a 'fired' BC like Sierra uses), and even though the BC is probably for a higher speed than our average, we can still say the following things about the Berger.
For these reasons we can identify the Berger as a legitimate outlier even if we didn't know what the reported BC was. We would at least know it's worth a look; the US F-Class team is on to it. The VLD design, characterized by the more aggressive secant ogives, has its own BC trend line that's parallel to the one in Figure 2, but higher. The secant ogive, in general, can reduce the form factor by up to 12%, which increases BC by the same amount.
Before we move on to scaling effects on stability, I feel obligated to say a few words about the dependence of BC on velocity.
The commercial sporting arms industry has universally adopted the G1 drag standard for referencing form factors and ballistic coefficients. Remember the purpose of the form factor? It's to relate the drag of a particular bullet shape to the drag of a standard projectile. Well, there are several standard projectiles to choose from (G1, G5, G7, etc) which may fit certain projectiles better over a wide range of velocity. The G1 drag standard is a compromise for all bullets from .38 caliber pistol bullets up thru shotgun slugs, standard hunting bullets and long-range bullets. Since long range bullets are at the extreme edge of the spectrum in terms of low drag profiles, the G1 standard is actually a poor fit. The consequence of the poor match is that the form factor, and hence the BC is very dependent on projectile velocity3. Most of the 'smoke and mirrors' stigma associated with BC's comes from this velocity dependence. At this point, I could go into an entire discussion about Siacci's method, and how trajectories are computed, etc. I'll save that for another day.
One more thing to be careful about with BC is knowing how they're computed. Every company has their own way of figuring BC. Most calculate it, while Sierra actually test fires their bullets to determine BC. All of these methods have their pros and cons in terms of accuracy and cost. You should expect typically +-10% error between the BC's reported by different methods. A bullet company may be able to compare their own BC's to each other with great precision, but comparing the advertised BC's from one company to another is a different story. Again, methods to calculate BC's will be left for another day. For now, I hope you're confident enough in your ability to spot outliers, and to make your own comparisons between bullets based on what you know about the consequences of scale.
In part 2, I'll talk about how BC affects wind deflection, and some of the trade-offs involved in chasing the high BC's.
3 The form factor that relates your projectiles drag to the standard projectile drag is not constant. It's because the two shapes have different 'drag profiles'.
And so in the end, you're simply multiplying the original BC by the linear scale factor to get the BC for the other caliber. It's just that easy, or is it?
As with all things, the quick easy method is also the least accurate. The average advertised BC of the 7mm bullet is 0.596 for the speed range of interest (2000 to 2850 fps). Our first method estimated 2.1% high. There's another way that's almost as easy, and a bit more accurate.
In the first method, we assume that the bullet scales perfectly from the benchmark, in which case it would weigh 177 grains. The real 7mm bullet weighs only 175 grains. So a more exact way to calculate BC is by calculating the form factor for the benchmark, and using it for the other bullet. According to the BC equation, and the advertised BC of the benchmark 142 gr bullet (0.565), we calculate a form factor of i = .515. Furthermore, we'll use the actual weight of the 7mm bullet (175 gr) in the BC equation to get a better estimate of the 7mm's BC:
Using method #2, we arrive at an estimate that's only 1.0% different than the advertised BC of the 175 gr 7mm bullet for the same speed range. Figure 2 shows the advertised and calculated BC for a range of calibers based on the principle of scaling (Method 2). These calculated values are compared to advertised BC's for the same bullets. You can see there are two BC's for each caliber. The top one is for high velocity, and the bottom one is low velocity. You can see that the advertised BC's generally fall within the predicted corridor. There are a few things I'd like to point out about Figure 2. First, you might wonder why the 6mm data point is so high. Well, I can think of two reasons why the 6mm might be an outlier.
- I wasn't able to find a BC for this bullet on the Sierra website like I did the others. I got the one and only value of 0.585 from a different internet resource (Ref 5). The BC for this bullet was only reported for 2850 fps, while the other BC's are averages for velocities between 2000 fps and 2850 fps. So the comparison is not exactly fair.
- The 6mm bullet has an 11 caliber secant ogive, whereas I think all of the others have a 9 to 9.5 caliber tangent ogive. This means that the 6mm bullet has a different nose shape, like a VLD and has less drag. This would have the effect of lowering the form factor, and elevating the BC.
Both items 1 and 2 above would act to elevate the reported BC. Item 1 is an apparent increase. I'm sure that at lower velocities, like around 2000 fps, the BC of the 6mm bullet is less than .585, probably averaging about .570 between 2000 and 2850 fps.
Item 2, however, is a real reason for the 6mm bullet to have a higher BC. The benefit of the (VLD) secant nose is an advantage at all speeds. In this way, the 115 grain 6mm bullet is an outlier compared to the other bullets in our lineup.
Another thing you may note is that the BC of the .308 bullet averages at the low end of the band. If you remember when we scaled up the 30 caliber bullet, we found that its weight should be 229 grains. The real bullet is 9 grains lighter than if it were perfectly scaled. If the .30 cal bullet weighed 229 grains, the BC would be .653. That's right smack in the middle of the predicted band. The .244 caliber and 7mm bullets match the BC trend well.
In this way, you are able to use knowledge about trends in scaling to spot when something is out of place, for better or worse. There are names for things that don't follow trends. They're called outliers. Understanding outliers empowers you to choose equipment that has a better than average chance to win. Without an understanding of the fundamental governing trends, you can't spot outliers. You're at the mercy of commercials, old wives tales, and soothsayers.
Take the VLD for example. The 11 caliber secant ogive used on the 6mm bullet is a relatively mild secant ogive, yet the reduction in drag is real, and significant. Consider the 7mm Berger 180 grain VLD with an advertised BC of .682, which is completely off the chart in Figure 2! Even though this is a calculated BC (not a 'fired' BC like Sierra uses), and even though the BC is probably for a higher speed than our average, we can still say the following things about the Berger.
- At 180 grains, it's 'above the trend line' in terms of weight.
- With its aggressive, long radius secant ogive nose, you can bet the drag (form factor) reduction is even greater than for the 6mm.
For these reasons we can identify the Berger as a legitimate outlier even if we didn't know what the reported BC was. We would at least know it's worth a look; the US F-Class team is on to it. The VLD design, characterized by the more aggressive secant ogives, has its own BC trend line that's parallel to the one in Figure 2, but higher. The secant ogive, in general, can reduce the form factor by up to 12%, which increases BC by the same amount.
Before we move on to scaling effects on stability, I feel obligated to say a few words about the dependence of BC on velocity.
The commercial sporting arms industry has universally adopted the G1 drag standard for referencing form factors and ballistic coefficients. Remember the purpose of the form factor? It's to relate the drag of a particular bullet shape to the drag of a standard projectile. Well, there are several standard projectiles to choose from (G1, G5, G7, etc) which may fit certain projectiles better over a wide range of velocity. The G1 drag standard is a compromise for all bullets from .38 caliber pistol bullets up thru shotgun slugs, standard hunting bullets and long-range bullets. Since long range bullets are at the extreme edge of the spectrum in terms of low drag profiles, the G1 standard is actually a poor fit. The consequence of the poor match is that the form factor, and hence the BC is very dependent on projectile velocity3. Most of the 'smoke and mirrors' stigma associated with BC's comes from this velocity dependence. At this point, I could go into an entire discussion about Siacci's method, and how trajectories are computed, etc. I'll save that for another day.
One more thing to be careful about with BC is knowing how they're computed. Every company has their own way of figuring BC. Most calculate it, while Sierra actually test fires their bullets to determine BC. All of these methods have their pros and cons in terms of accuracy and cost. You should expect typically +-10% error between the BC's reported by different methods. A bullet company may be able to compare their own BC's to each other with great precision, but comparing the advertised BC's from one company to another is a different story. Again, methods to calculate BC's will be left for another day. For now, I hope you're confident enough in your ability to spot outliers, and to make your own comparisons between bullets based on what you know about the consequences of scale.
In part 2, I'll talk about how BC affects wind deflection, and some of the trade-offs involved in chasing the high BC's.
3 The form factor that relates your projectiles drag to the standard projectile drag is not constant. It's because the two shapes have different 'drag profiles'.
- Next page: Understanding Long Range Bullets Part 1:
- Previous page: Overview
