My interest in starting this thread is to understand the physics and applied theory of MPBR. I came across the idea of MPBR years ago. I thought it seemed straightforward enough. But in starting to put it in practice, I discovered there are a couple of moving parts and I'm interested in people's views.

I got me a LabRadar chronograph. Shot 10 rounds per gun - ammo combination to get an average, minimum, and high values for initial velocity. I used an online MPBR website ( ShootersCalculation.com ) to calculate the Near Zero Yardage. I used a 6" target pipe for the MBPR as a proxy for an effective target zone. The calculations came up with a near zero yardage of 7 yards, far zero of 95 yards, and a Max PBR of 113 yards. I understand that for a range of 113 yards, the bullet is going to be plus or minus 3 inches to the vertical assuming the gun is perfectly shot from rest.

Here is where I realized the moving parts come in coming from my exposure to six-sigma manufacturing: For all practicality, I won't be aiming out to 113 yards. Plus, if I held the gun with a perfectly minimal wobble of 3 MOA which is the size of the red dot, that's an additional 1.5 inch at 50 yards. So I checked what happens with target sizes of 4, 3, 2, and 1. Please assume I have the Ballistic Coefficient and sight heights correct; they're not relative to the topic of interest which is the effect of target size and the applied theory of MPBR combined with the natural wobble of a hand-held gun. I'm only considering gravity's effect on the bullet and ignoring any wind effects. I guess to put it in context, it's a 9MM bullet coming out of 4.4" barrel.

My thought is, given the last paragraph: setting a target size of 3 or 4 inches considering a wobble of 3 MOA will keep the shot within the original six inches and the MPBR yardage is not drastically shortened. Or for nice round numbers, just zero at 10 yards which is with a target size of 2.5 inches. I guess for those inclined to ponder such things, I'm interested in your thoughts about my findings.

Seems like you're talking about handgun ballistics using those ranges and shooting unsupported. Why bother with MPBR?

quote:

Originally posted by apprentice:
Seems like you're talking about handgun ballistics using those ranges and shooting unsupported. Why bother with MPBR?

I use it for my MPX.

I got acquainted with the concept in Basic Training in the Army and have used the method for my ARs for years.

I don't use it for precision rifles for obvious reasons.

quote:

Originally posted by apprentice:
Seems like you're talking about handgun ballistics using those ranges and shooting unsupported. Why bother with MPBR?

Because I started with my carry handguns and plan to move to my long guns.

I'm bothering with it because, as I said in my first sentence, I'm interested in understanding the physics and applied theory of MPBR. It may be that ultimately one should not bother with MPBR for handguns given the data of Near Zeros, Far Zeros, and Max PBR yardages - it looks like zeroing at 7, 8, 9, or 10 yards are all in the ball park of each other. But I would not have the data on which to base it on if I had not explored the topic and compared the numbers.

I learned a long time ago that of all the ways people learn 1) doing it themselves aka trial and error, 2) someone showing it to them, 3) being given examples, 4) being shown the theory, and 5) some combination of the four, I learn best by theory.

I didn’t examine and analyze everything you wrote, but the PBR calculators I’ve seen assume that the bullet’s trajectory will be perfect with no dispersion due to the wobble you mention or the inherent imprecision of the gun and ammunition. In my calculations I haven’t tried to incorporate shooter instability, but I do factor in the size of the group from a stable rest. I.e., if it’s a 1 MOA gun and ammunition, then at 200 yards, for example, the point of impact could be as much as 1 inch from the point of aim. That in effect reduces the size of the acceptable target. I believe that’s equivalent to what you’re doing with the wobble size.

quote:

Originally posted by Rey HRH:
Because I started with my carry handguns and plan to move to my long guns.

MPBR works better with rifles than handguns. Think of a .308 or .270 hunting rifle, with an old 2x7 scope, capped turrets, no convenient way to adjust elevation, and simple duplex reticle. The hunter wants to know what distance ranges he can hold the crosshairs on center of vital zone and still hit somewhere in the vital zone.

A practical way to do this with a 9mm pistol is using a larger target -- maybe a paper or painted steel IPSC. Confirm your zero distance, then extend the target distance in 5 or 10 yard increments. Use the same POA, and determine the POI for the various distances.

quote:

Originally posted by sigfreund:
I didn’t examine and analyze everything you wrote, but the PBR calculators I’ve seen assume that the bullet’s trajectory will be perfect with no dispersion due to the wobble you mention or the inherent imprecision of the gun and ammunition. In my calculations I haven’t tried to incorporate shooter instability, but I do factor in the size of the group from a stable rest. I.e., if it’s a 1 MOA gun and ammunition, then at 200 yards, for example, the point of impact could be as much as 1 inch from the point of aim. That in effect reduces the size of the acceptable target. I believe that’s equivalent to what you’re doing with the wobble size.

I don't show the numbers because it didn't change the zero yardage but I also calculated the numbers for the lowest initial velocity and the highest initial velocity for each 10 shot sample. What changed slightly are the far zeros and the maximum point blank range yardage. So I think the MPBR calculation isn't too sensitive to ammo variations and, while I can understand a gun's accuracy can change over a number of shots, I think the change from one shot to the next would be imperceptible.

I think you may have given me a clue to increase my understanding: I know the target size should be directly related to the target's vital zone but I think target size is also related with the shooter's overall precision in terms of group size. Assuming all resulting MPBR yardages are within working distances, then I think the target size should be the vital zone reduced by the overall imprecision, assuming the impression is smaller than the target size.

quote:

Originally posted by fritz:

quote:

Originally posted by Rey HRH:
Because I started with my carry handguns and plan to move to my long guns.

MPBR works better with rifles than handguns. Think of a .308 or .270 hunting rifle, with an old 2x7 scope, capped turrets, no convenient way to adjust elevation, and simple duplex reticle. The hunter wants to know what distance ranges he can hold the crosshairs on center of vital zone and still hit somewhere in the vital zone.

A practical way to do this with a 9mm pistol is using a larger target -- maybe a paper or painted steel IPSC. Confirm your zero distance, then extend the target distance in 5 or 10 yard increments. Use the same POA, and determine the POI for the various distances.

I have yet to confirm whether the theoretical trajectories track with actual shots but, yes, I see that MPBR is optimal for long distances where you don't want to worry about holds. I think it applies also for handguns but more so for having an understanding of the bullet's trajectory.

I remember zeroing guns at 10 yards as an initial step and then moving to the 25 yard range where I thought I would just finesse the adjustments. MPBR explains to me why I was frustrated in that my POI and POA was drastically different at the 25 yard range after doing all the work of zeroing at the 10 yard range.

quote:

Originally posted by Rey HRH:
I remember zeroing guns at 10 yards as an initial step and then moving to the 25 yard range where I thought I would just finesse the adjustments. MPBR explains to me why I was frustrated in that my POI and POA was drastically different at the 25 yard range after doing all the work of zeroing at the 10 yard range.

I recommend your revisiting your results and your underlying assumptions.

JBM Ballistics
115 grain 9mm FMJ bullet from Hornady
1100 fps muzzle velocity
.6" sight over bore height -- My G17 measures around .55", my P226 measures around .65".
Air density altitude of 5,000'. Results change little if one goes down to 0' or up to 8,000'.
Zero at 10 yards.

At 20, 25, and 30 yards -- POI is .3" high
Zero again at 40 yards.
POI is .6" low at 50 yards.
1.6" low at 60 yards.
2.9" low at 70 yards.
4.6" low at 80 yards.
POI is 9.0" low at 100 yards.

I first shot full-sized IPSC steel out to 100 yards with a G17, G19, and 45ACP at a Rifles Only training course. The above numbers are reasonable. I've shot 9mm, .40 S&W, and .45ACP at my own range at IPSC targets, and the numbers hold for 8,000' Density Altitude.

quote:

I remember zeroing guns at 10 yards as an initial step and then moving to the 25 yard range where I thought I would just finesse the adjustments. MPBR explains to me why I was frustrated in that my POI and POA was drastically different at the 25 yard range after doing all the work of zeroing at the 10 yard range.

I didn't read your entire posts, but I can relate. My P229 was originally zeroed at 20 yards using aftermarket sights (Heinie). The ballistics changed when I had the barrel and slide ported.

As you might expect, holding the muzzle down lowers POI. It actually started dropping at only 15 yards (maybe even less). So I developed an alternate sight picture system which I use at any distances beyond about 10 yards. You can see by the chart below how this "holdover" system works.


P229R Sighting by kpkina, on Flickr

(It is interesting how the ballistics of the 9mm come into play even below 25 yards. There is significant drop even at those short ranges. Contrast that with something like .357 Magnum. Its velocity keeps it a flat-shooting round even out to 100 yards, no holdover needed.)

quote:

Originally posted by fritz:

quote:

Originally posted by Rey HRH:
I remember zeroing guns at 10 yards as an initial step and then moving to the 25 yard range where I thought I would just finesse the adjustments. MPBR explains to me why I was frustrated in that my POI and POA was drastically different at the 25 yard range after doing all the work of zeroing at the 10 yard range.

I recommend your revisiting your results and your underlying assumptions.

I'm not arguing especially since I'm just starting to explore this subject. But I entered my numbers to the ballistic trajectory chart and got the results below. The .9668" Sight Height is the middle of the RDS window to the bore centerline.

You can see zero at 10 yards and at 25 yards, it's 0.9 inch high. It seems to reach a peak at 40 yards and starts coming down so that at 50 yards, it's 1.09 inch high.

With your numbers, it seems you're saying the bullet flies straight flat and .3" high above the zero sight line through 20, 25, and 30 yards before going down to zero at 40 yards. At first, I thought the difference is in the sight heights that we use but, you know, the bullet can't travel straight flat at .3" above zero through 20, 25, and 30 yards. Do you have another explanation?

After I wrote the last paragraph above, I decided to input your muzzle velocity and sight height over my ballistic coefficient and atmosphere where we're in the same altitude. I then ran the calculation. I can confirm your numbers: 20 yards is .28", 25 yards is .30, 30 yards is .25" and 40 yards is -0.09. Far zero is at 38 yards. So, I think each of our numbers support what we are saying for our situation.

The story I related above about zeroing at 10 yards then thinking I could just finesse it at 25 yards was with a 1911 pistol with a mounted tube sight definitely higher than an inch above bore. So I'm thinking my experience could be driven by the sight height and the slower initial velocity of the 45 ACP. For the 9MM, I can only see the difference in sight height as being the driver for the differences between the vertical offset from zero between your relatively flat trajectory versus mine.

quote:

Originally posted by kkina:

So I developed an alternate sight picture system which I use at any distances beyond about 10 yards. You can see by the chart below how this "holdover" system works.

(It is interesting how the ballistics of the 9mm come into play even below 25 yards. There is significant drop even at those short ranges. Contrast that with something like .357 Magnum. Its velocity keeps it a flat-shooting round even out to 100 yards, no holdover needed.)

You went the other way from where my thinking is now with iron sights. I figure I'm doing well if I can keep the top of the front sight level with the top of the rear sight.

With what I'm learning about MPBR, I figure I can't make any adjustments to "sight-in" my iron sights to a particular distance. I remember the threads on "why is my Sig shooting low" and the "because Sig uses combat sighting method" justification. At this point, I think the best any one can do is for a given iron sight and ammo, 1) capture the initial velocity then 2) determine at what yardage it zeros. That gives you a picture of the trajectory.

The 100 fps difference between the FMJ and JHP ammo changes the POI. (I know that's like a no-brainer for some.) And, on the other hand, the difference would be moot with the least wobble from unsupported shooting but it's an "aha" moment for me.

quote:

Originally posted by Rey HRH:
With your numbers, it seems you're saying the bullet flies straight flat and .3" high above the zero sight line through 20, 25, and 30 yards before going down to zero at 40 yards. At first, I thought the difference is in the sight heights that we use but, you know, the bullet can't travel straight flat at .3" above zero through 20, 25, and 30 yards. Do you have another explanation?

Because JBM rounds trajectory to tenth's of an inch. Calculating trajectories to the hundredth of inch produces cute data that means nothing in the real world.

quote:

Originally posted by Rey HRH:
The story I related above about zeroing at 10 yards then thinking I could just finesse it at 25 yards was with a 1911 pistol with a mounted tube sight definitely higher than an inch above bore. So I'm thinking my experience could be driven by the sight height and the slower initial velocity of the 45 ACP.

JBM ballistics
230 grain .45 FMJ bullet from Hornady
900 fps MV
1.25" sight over bore height
Air Density altitude of 5,000'.
Zero at 10 yards

At 20 yards POI is .8" high
1.1" high at 25 yards
1.2" high at 30 and 35 yards
1.1" high at 40 yards
.6" high at 50 yards
.4" low at 60 yards
1.8" low at 70 yards
3.7" low at 80 yards
9.0" low at 100 yards

A 1" vertical POI difference with a handgun at 25 yards is insignificant for pretty much anything other than world-class competitive shooting.

quote:

Originally posted by fritz:

Because JBM rounds trajectory to tenth's of an inch. Calculating trajectories to the hundredth of inch produces cute data that means nothing in the real world.

I did say I confirmed your numbers, right? When you said I should revisit my results, I took that to mean you doubt the validity of my numbers. My ability to replicate your results with your numbers pretty closely validates the numbers I got using the same process.

quote:

A 1" vertical POI difference with a handgun at 25 yards is insignificant for pretty much anything other than world-class competitive shooting.

As I said, my interest is in understanding the physics and applied theory. Not fully understanding the ballistic trajectory was significant enough to surprise me a long time ago to discover that a perfectly zero'd gun at 10 yards would be off at 25 yards. I wrongly expected the shot dispersion at 25 yards to simply be a magnified pattern extending from the 10 yard point. I knew about gravity but I didn't think it would affect the bullet by an inch between 10 yards and 25 yards. Now I know.

As target distances increase, accuracy challenges increase. Can be issues of POI/POA, elevation, windage, consistency...

Sometimes the differences between intent and actual make sense and are readily explainable. Other times, not so much. After years of formal instruction, personal training, and competition I've learned that we shooters are almost always the weakest link in the accuracy chain. Well, excluding FMJ ammo and a few rifles known for lackluster accuracy.

A quality firearm with quality ammo and good sights produces accurate and repeatable results. But only if we shooters break shots and follow through without disturbing the sight picture.

With accurate data input, modern ballistics engines produce quite accurate POI predictions. As you extend your target distances and push beyond your comfort zones, concentrate on shooting fundamentals -- you'll find that actual results become increasing closer to predicted results.