solving for velocity and BC with balistic calcs

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taliv

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For years, I've been wanting a very accurate ballistic calc and really haven't been happy with any of the ones I've used. Shooter, on my iphone has been pretty close for me. always within .2 mil but that's often not good enough when you're shooting sub MOA targets. I also have KAC's BulletFlight and use JBM and several others, which all seem to be in the same boat. Usually, I think the problem is GIGO, but it's just always bothered me that the math should be closer, given the accuracy of the inputs.

So this Spring, I picked up a copy of Field Firing Solutions Delta V in the snipershide group buy from Ashbury which bundled the software with a vectronix PLRF10C. Over the summer, I bought a used Nomad (pic from FFS website) to run it on and I played with it a bit but was extremely disappointed that i couldn't get good data out of it.
Nomad%20Grn%20DIV.png Using the exact same inputs I use on another calc, I would get answers that were several tenths off. Frustrated by the time consuming suggestions to resolve the problem, I put it away for a few months. But this week, I decided to spend the time to really try it, and so I called the guy who wrote the software for some technical support and he was extremely gracious and spent a great deal of time correcting a lot of my misconceptions; about different drag functions used by different calculators, G1 vs G7, and especially the need to calibrate everything with real data. He patiently repeated the suggestions from his instruction videos: that I spend the time to calibrate both the muzzle velocity and the BC.

This post is about my experience with that process, which was a lot more effort than I wanted to go through, but was ultimately pretty successful.

To summarize, the challenge is there are 2 unknowns in the equation: muzzle velocity and ballistic coefficient. We have a chronograph to measure one, but it is likely not calibrated properly and thus not really trustworthy. We have published BCs for the other which are often pretty sketchy but even the good ones don't account for variations in bullet lot.

So how do you solve the problem? Blane's solution is based on the fact that at shorter distances, environmentals and BC don't make much difference, so you should shoot at something around 400 yards away and measure your drop and calculate your muzzle velocity based on this. Then, shoot at something at the farthest possible distance before your bullet gets into the transonic range. Using your recently calculated MV, you can now calculate the drop due to drag on the bullet. Once both are known, your calculator should be spot on within a velocity range.


SO... I start the process with one shot on a 5/8" dot to confirm zero, then I move back to 354 yards and shoot 3 rounds on paper. It was pretty stormy with winds gusting pretty bad and I couldn't see my impacts on paper, so I just guessed at my wind. The two shots on the left were a favor right and the other was a right edge hold.

Anyway, the zero looks good enough (not going to quibble over 1/4" low) and I'm going to say the average of the other 3 are about 1" low.
The velocities as measured by the magnetospeed are in the first column in the spreadsheet at the bottom of this post. They average 2941 fps, though when I use the FFS to calculate my mv based on drop, it tells me 2922 fps.
(note: if you're wondering where the 5th shot went, in the middle of my string, i decided to put round number 4 on the ipsc target head. no idea why. I just did. it's the one in the center.)
calib354y0.jpg

I went ahead and finished the process by shooting at distance (see other hit on the ipsc head link above from 1008y), but the numbers didn't work out. I get a BC of .6614 which works at some distances but not at others. So, the next day, I call back am advised that 350 is a little short and i should to try do 450 yards. (I secretly suspect it was the 10-20mph winds and not the distance that put me off, so...) I go out again today with light variable winds to shoot a more optimal distance. Unfortunately, being an idiot, I left my paper target at home and had to set up today on a 436 yard steel plate. Holding in the center of a 10" plate is kind of a guessing game, but I shoot 3 rounds on this target, with a bad trigger pull on the 3rd shot, so I ignore that from the group. (and then 2 at this 4" circle for no good reason).

Pretty sloppy shooting on the big plate and I am holding my thumb over 1/2" or so of the tape measure, but ignoring the shot i pulled, I figure I need to come up .5 inches. Using the FFS MV calculator, I get 2956 fps. Not too far off of what the magnetospeed says, but quite a ways away from the 2922 previously calculated. (an interesting side note: if i kept the 3rd shot and my group averaged POI=POA, I would still make a mv adjustment based on zero impact shift, because.... the calculator says my solution is 1.831 mils so the fact that my bullet says 1.800 means i'm off 0.031 mils. I know, I know. In that event, FFS computes my MV at 2936. Granted, all of this is based on pretty small sample size.)
calib436y18.jpg

Anyways, now that I have good guess at my actual muzzle velocity, it's time to see what the bullet thinks its BC is for the FFS drag function. So I back up to my 1008 yard target and take a couple pokes at the head on this full size ipsc. (first round fired on the body just to make sure my wind call was good, then rounds 2 and 3 at the head.) If I figure the center of the group is at the 2" mark, and the POA was at the 5.5" mark, that's 3.5" low.
(so again, being an idiot, I actually got the 7.3 mil solution from my iphone instead of FFS, and when I got home I realized FFS needs me to measure the difference between POA and POI using it's 7.1 mil solution, which was based on a bogus BC i'd calculated previously using bad velocity. If I'd held that, I would have been .2 lower. so quickly, at 1008y, the .2 mil difference is 7.26", plus my 3.5" low figure, gives me a net of 10.56" low.)

So, I input the data into FFS and it gives me a warning that my velocity at that distance is 1673 fps, above the optimum range of 1250-1500 fps, and suggests I shoot at a longer distance, but asks if I want to continue. well of course I do... so it thinks for a moment and outputs the answer: .6178 (Litz wrote .618 on the box the Bergers come in, but what does he know, right? :) )

So I select "use BC in firing solution" and it updates it to 7.39 mils up, which looks perfect to me.
calib1008y73.jpg

But I go ahead and put my last 2 rounds of the 5 rounds on my 12" plate at 1087 yards. My Iphone tells me 8.3 mils. With a right favor, I BARELY catch the edge of the target with the first round, so I hold right edge on the second and center it up a bit. Looks like about an inch of vertical, centered on 1.75" mark. With POA at 6", that is 4.25" low.
Now, with my good BC, FFS tells me the solution is 8.43 and to dial 8.4 on the turret. At that distance, the .1 mil is worth 3.9" up, so I'm going to subtract that from the 4.25" low and say my shots were .34" low. Going into the BC calculator tool, I again get a warning that my 1504 fps MV is out of the 1250-1500 fps optimum range. Undaunted, I press on. FFS doesn't mention anything about how silly trying to correct 1/3" is at almost 1100 yards. It gives me a .6172 answer. I think I'll stick with .618.
calib1087y83.jpg

Below are the magnetospeed readings for the 3 groups shot on 2 different days at 3 different temperatures. I used my previously calculated FPS/*F factor to adjust the 64* and 62* down to 60* numbers and averaged them all together. Not my best ES for sure, but not completely embarrassing.
calibchrono.png

If accurate, the average would mean my magnetospeed is about 14 fps slow, which is half a percent (0.47%) off. Not bad.

What is somewhat frustrating and remains a mystery is that I started in almost the same place I ended, using Litz' .618 bc and a 2950ish velocity as my inputs but now my data matches where previously I was getting numbers about .3 mils off.

In any event, i appreciate the education and learned a lot from the experience. I think the process works, and should work regardless of which calculator you use, although FFS certainly makes the math easier with a built in tool to correct your MV and BC based on measuring your impacts.

I'm looking forward to trying this with a larger sample size when the weather improves, but I don't expect the answer to change.

FFS also includes tools to correct for small deviations in your scope turrets, but fortunately I haven't needed to do that.

The targets above were shot with a slow practice load in 260AI (the rifle in the back) and with the magnetospeed bayonet attached (obviously).
vorticesharsh1.jpg
 
Lord Taliv--looks like you have a pretty good grip on the variables now--be nice to see a writeup on this stuff in Varmint Hunter mag.

I've been using Gerald Perry's Exbal for a number of years but the technology had advanced since 10 years ago or so. How would you rate Shooter if you're only going to 600-700ish?
 
Very informative, thanks Taliv. I've finally located a range in my area that allows for shots past a couple hundred yards, so will be looking to apply much of your shared expertise as I explore the world of long range shooting.
 
Thank you for the very informative post. I rarely shoot past 300 yards because it's just not my thing, but I found your post interesting.

Is the BC still valid for calculating wind drift with the newer copper bullets, which are longer for their weight? A 165 grain copper bullet is longer than a 165 lead bullet correct, so it should have a higher BC (assuming similar shapes)? Sort of like how a 30" wide 18 foot canoe is a lot easier to paddle than a 30" wide 12 foot canoe -- the rate at which you have to distort the fluid is lower so it moves through the fluid easier. But, the longer canoe is more succeptible to cross winds because there is more exposed surface area. Is the wind drift and Magnus effect more pronounced for the long non-lead bullets than the BC would suggest?

Has anyone ever experimented with super-long for weight bullets? Like a 165 grain aluminum bullet that's 4-5x as long as the lead equivalent? At some point it would be difficilt to spin stabilize, and there would be a lot of force required to push it down the barrel, but it would be a fun experiment (I'm sure someone somewhere has had to try something like this at one point or another).
 
corn, i have to admit i have no experience paddling canoes and never thought about them aerodynamically. but generally, the ballistic coefficient is just a reference number. it kind of takes into account the shape of the bullet, but in practice, it seems the drag functions used in the calculators accommodate different shapes.


Jim, you still use a BC, but the point is at short distances, the BC is less important. As you know most centerfire rifles have a pretty similar trajectory for the first 300-400 yards, whether they're 223 or 308 or 338, and variances in that trajectory are primarily due to differences in velocity, not BC. So if your BC is off quite a bit, you're still able to get a relatively close muzzle velocity calculation. Then you calc you BC, then my intent is to go back and recalc MV based on the new BC calc. I'm curious to find out what happens if you keep iterating on this process.
 
How do you back calculate muzzle velocity from drop on target without a BC?
Just a guess; but if you know the drop you know the time of flight. Even though you don't know the BC, you know that the rate of velocity loss is proportional to the velocity squared, so if you have two points you should be able to fit a curve of velocity vs distance and calculate the velocity when the distance equals zero (i.e. at the muzzle).
 
How do you back calculate muzzle velocity from drop on target without a BC?

At shorter ranges (< 500 yards or so), drop is weakly dependent on BC, so only a rough estimate of BC is needed to determine muzzle velocity from drop, especially if the air density is known, the height of the scope from the bore is accurately determined, the wind is minimal, and the drop can be accurately determined by firing small groups, as demonstrated here.
 
taliv said:
I'm curious to find out what happens if you keep iterating on this process.

When you consider that BC is a function of the drag coefficient which is a function of velocity and fluid density which is a function of temperature, you might have a lot of iterating to do. Great post by the way. I'll be shooting at steel at 1,250 yards to 1,500 yards with a .338 LM soon so I really enjoy your informative posts. Few are willing to share the knowledge when it comes to long range precision shooting so it's definitely appreciated.

Some bullet and ammunition manufactures are using Doppler to back out BC values with great accuracy but Doppler is still beyond the budgets of many of those companies, let alone the rest of us.
 
When I was looking for BC's for rimfire bullets to input into some calculators I often saw the companies give slightly different values for supersonic, transonic and sub sonic. Yet we only see single values given for most center fire bullets.

Mind you this likely reflects the fact that most center fire rifle bullets will stay supersonic out to most of the usual hunting distances. But depending on the bullet and when shooting to more than 1000 yards I see from the Hornady online ballistics calculator that most rounds drop to transonic and subsonic at 800 to 1100 yards. So would this not become an issue for really long shots?

Another issue I wonder about is air density changes with height above the ground. I know that on dead still mornings the ground moisture generates a layer of moist air. This shows up often enough as a ground fog that extends up to 30 to 100 feet depending on conditions. Yet a lot of situations involving really long distance shooting have shooters on one the ground and targets sitting up on a hillside. So in addition to a height change I'm thinking that a truly good calculator would gain something by separate temperature and density readings for the shooter's and target's locations?

Of course this is getting highly OCD. But then isn't that what really long range shooting is about? :D

It's all fascinating stuff. And when it all comes together and a shooter can put that first cold bore shot right on the target at 1500 yards it must be a wondrous feeling.
 
Then you calc you BC, then my intent is to go back and recalc MV based on the new BC calc. I'm curious to find out what happens if you keep iterating on this process.

Yes, it will be interesting to see how many times you can go around the daisy chain of iterations until the BC and MV converge on the "right" values.

Many years ago, Gun Digest had an article "The Trajectory Chronograph" with a pre-PC version of the process.
 
taliv,

I seem to remember some software or ballistic units that have a verification feature...

For example, using modeled dope, you shoot various distances. Plug in the correct dope and the unit would then adjust the velocity/BC for the rest of the dope table (filling in the blanks)?

It seems like that is nearly what you did...
 
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That's what Exbal does, and it's close but not perfect--but I think his older software (the one I have) just used G1 drag coefficients.
 
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