Question about Ballistic Scaling

[mechengr]

I'll start off by apologizing for being so wordy, but I'm hoping there's somebody with more technical knowledge here that can help satisfy my curiosity.

I've been reading Bryan Litz's Applied Ballistics for Long-Range Shooting. I got to the chapter about scaling the ballistic coefficient, so for fun I figured I would try the exercise with one of the bullets I shoot. I currently reload for a 25-06 using the 90gr Sierra BlitzKing which is not included in the appendix of tested bullets. These have a fairly significant boat tail compared to other similar weight offerings in .257 cal and so I'm intrigued about their ballistic potential for varmint hunting and plinking.

For the comparison, I referenced the appendix of ballistic data and selected bullets from a number of other calibers that seemed to have similar shape and dimensions to the 90gr BlitzKing:

• .243 Hornady 75gr VMAX
• .264 Hornady 95gr VMAX
• .277 Hornady 110gr VMAX
• .284 Nosler 120gr Ballstic Tip
• .308 Hornady 155gr AMAX

I first checked the scale of proportions of the selected bullets compared to the Blitz. I created a plot similar to the one in the Applied Ballistics book in Figure 12.2 to compare the scaled weight curve (scaled FROM the 90gr Blitz TO the corresponding calibers) with the actual listed weights of each bullet. Turns out that they actually match pretty well to the curve. The percent differences between scaled and actual weights ranged from 0.05% difference to 2.6% difference. Since the scaled weights are based on the assumption of identical i7 form factor, this tells me that I had selected bullets that were at least in the ballpark of the actual i7 for the 90 gr Blitz.

The equation the Mr. Litz presents for scaling BC by caliber ratio is derived from the ballistic coefficient equation and is also based on the assumption that the two bullets have identical i7 form factors. BC2 = (C2/C1)∗BC1

My question is in regards to the best way to select which bullet from that list is the ideal choice for calculating a scaled G7 BC for the 90gr Blitz. I used the measured G7 BCs from the appendix to predict the Blitz's scaled BC from each of the bullets on the list. Depending on which bullet is chosen, these predictions give BCs that differed by .0095.

Granted, at first glance this does not seem like a lot. Using a ballistics calculator to compare the highest predicted BC to the lowest predicted BC gives differences in fire solution of only 0.2 MOA (i.e. about one click on most scopes) at 500 yds. However, by 700 yds, this difference grows to over 0.5 MOA. Statistically speaking, that's not very beneficial to target hit percentage when a half MOA comes just from uncertainty in the BC value.

Now I know that this specific bullet is not going to be a 700yd+ long range king. I'm aware of Litz's section on the advantages of heavy for caliber bullets at extended ranges and there are definitely better cartridges/bullets/etc out there. I'm also aware that all this could be sorted out in verifying the BC by going to the range. I know there's functional ways around this question, but my reason for starting this thread is that I'm more interested in understanding the concepts in general.

To get to the heart of it: In general, is the best option to choose the bullet that most closely matches the scaled weight, i.e. has the most nearly identical i7 form factor? In the book, his example scales only between the 6.5mm and 7mm SMKs. Is there some disadvantage in scaling across large ranges of caliber? My intuition says NO since BC and i7 are both dimensionless terms.

Thank you, if you took the time to read all that garbage. I look forward to hearing from some of the gurus here, I've learned so much since joining this forum but I definitely still have a long ways to go!

 

[ShtrRdy]

I've been intrigued about using this approach but I've never tried it. It sounds like you have used the suggestions properly, from what I remember reading.

The best way to find out if this conversion worked is to shoot it at distance and see if the predicted drops match when using the predicted BC

 

[Mikecr]

The equation the Mr. Litz presents for scaling BC by caliber ratio is derived from the ballistic coefficient equation and is also based on the assumption that the two bullets have identical i7 form factors. BC2 = (C2/C1)∗BC1

Use of the formula seems out of whatever context it was in.

If you already know the form factors(derived from individual drag components combined & compared to G7 standard per mach#), you already know the BCs (simple sectional density divided by the known form factor).
The problem you end up with here is figuring out or testing to determine form factor. In no way could this be assumed, as it's weak enough in prediction.
If Bryan hadn't done it for you -then you would have to do it yourself (good luck with that).

In other words, forget rules of thumb for BC.

 

[mechengr]

I don't believe this formula is out of context since it is straight out of the Applied Ballistics book, used in the context of scaling bullets of similar shape (i.e. form factor). Like I mentioned, it's derived from the BC equation under the assumption of equal form factor. He doesn't explicitly derive it in the book, step-by-step, but that's where his scaling equation comes from.

I agree, if I already knew the form factor (as from Bryan's testing provided in the appendix) then this whole exercise would be unnecessary. My reason for doing this is because I do not already know an accurate form factor of this new bullet and thought I would try Bryan's scaling technique to predict a (hopefully) accurate G7 BC. Sierra's literature only lists G1 BC for this bullet.

 

[Mikecr]

I wish I had more time to lock into full sync with your question.
Having G1 BC at a velocity and atmosphere (like Std.Metro), puts G7 BC is within reach.
Sierra lists the 90Blitz BC @ .388 @ 3100 fps, they're usually at Std.Metro atmosphere.

I put together a spreadsheet that does what you're after, I just don't have time at the moment to step through it.

 

[mechengr]

Thanks for sticking with me on this one.

I've used these BC conversion tools before, like what's found on the JBM website. The only drawback I see is that even though this says "G7", it's still based on the largely velocity-dependent G1 standard. And as mentioned in Chapter 2 of Applied Ballistics, Sierra does provide segmented G1 BCs which are more accurate when used in conjunction with each other, but I don't have a ballistics calculator capable of utilizing those segmented G1 BCs.

Again, I'm not so concerned with the outcomes of this exact bullet, but more so the larger concepts in general.

As an aside question, does anyone use Sierra's ballistics software? I just looked it up on their website and it looks like they have set it up to use their segmented BCs (not surprisingly!). Is it any better/worse than other programs? Does the fact that it's tailored for these Sierra bullets make the program worth it?

 

[Mikecr]

BC is entirely dependent on velocity, as drag is.
I like Bryan's method of normalizing BC with a mean velocity, to provide a better BC in field use. Switching to G7 reduces disparities from predicted to real world even more, as the G7 drag curve more closely matches today's bullets.
I have no doubt Sierra's numbers are accurate, but IMO less useful.

 

[mechengr]

BC is entirely dependent on velocity, as drag is.

If I understand it correctly, I would argue that a properly chosen drag function applied to a bullet with a best-case scenario of form factor i=1.00 should yield a BC that will be completely independent of velocity. That's the appeal of using the G7 BCs with today's highly efficient bullets. I believe you are correct though in that drag is ALWAYS a function of velocity.

Switching to G7 reduces disparities from predicted to real world even more, as the G7 drag curve more closely matches today's bullets.

You've hit the nail on the head here, exactly why I'm trying to derive the G7 BC of this bullet. And more so, I hope to be able to confidently apply this technique to future new bullets I may come across that have not yet been tested by Bryan