I'm wondering if there's any way to determine MPI of one load on a rifle zeroed on irons for another load, relative to the trajectory that the rifle is zeroed on.

The rifle is being zeroed on 7.62 NATO ball ammo at 200m with the sight at the 200m setting. I'd like to figure out where Federal GMM 168s will impact using the same point of aim used when shooting the former type of cartridge. Seems like there should be some way to figure this out mathematically, but Google searches are worthless to this end and I'm just not finding the info that I need. Or is this something I'll just have to shoot and find out that way? I'm heading out to go shoot in the morning.

Using a ballistics calculator I was able to find out the trajectory for each, but it is based on the idea that the rifle is zeroed for each cartridge. The trajectories don't look dramatically different if I were to zero for one and shoot it, and then zero for the other and shoot it, but I'm not sure what to do with the data that I have to see where I should be hitting with one cartridge with the rifle zeroed for the other.

Also, does anyone know the BCs for the British and Belgian NATO projectiles? I can only find the G7 BC for the American M80 projectile and have been using that, but the ammo I'm shooting right now uses the British projectile design. I doubt they are more than marginally different.

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At the very least, I think you need to shoot both rounds at the same distance and POA to see how the POIs compare at that distance.  Then, depending on what degree of precision you want/need, you can stick your data in a ballistic calculator and start putting things together...  I think you can assume that the bullets have similar BC for the sake of this exercise.  If you get real BC data later, you can substitute that where applicable for tables that are closer to reality.

M80 has a .200 G7 BC, which converts to about .398 for G1 BC. I suspect that the other NATO ball designs are very close. 168 gr. SMK G1 BC is .462.

I'm going to start off at 25m and go from there.

I would like to know if there's a way to do this mathematically since I have other rifle/ammo combos I'm wondering about with respect to similar circumstances, such as with my Mosin Nagant. The sights are calibrated for a 200 grain projectile and the light ball stuff is hitting so high that by 300m I'm almost entirely off paper with the rounds sailing over the target when I aim at the ground with the sights on the corresponding setting. If there was a way to compare trajectories given a zero for the former cartridge without wasting a bunch of ammo that'd be awesome.

If you zero the rifle with each type of ammo at the same (pick your favorite common distance - 100 yards?) and you have the information necessary to put into a ballistic calculator to generate a table (bullet info, MV, atmospherics, etc.) you should be able to generate ballistic tables for each type of ammo zeroed at the same distance so you can compare the tables and know where each ammo is in comparison to the others out of the same rifle...  that's the only mathy way I know how to do it.  There might be a calculator that can do what you want but I have never seen one...

Well, at 25m the 168 grain GMM ammo has a MPI a bit higher than the Malaysian ball given the same POA.  A comparison of the trajectories, which of course presume that the rifle is zeroed for the cartridge in question (as opposed to another), show the GMM hitting over 1/4" above POA at 25m, but I'm not sure how that corresponds to a zero on the ball ammo.

After I moved out to 100m (with plans to end the day at 300m), things got weird.  I got the rifle zeroed on the Malaysian ball ammo at 25m, which based on the tables should mean about the same POI relative to POA at 200m, which is what I want.  But when I went to 100m, with the target stapled near the bottom of the backer, aiming at the bottom of the black, I found no impacts.  Happened again.  I shot at a rock near the target stand and the round impacted the ground well in advance of the rock.  I decided to aim at the top of the white of the target (about 13" square) and the MPI ended up being at about the centre of the 6" black, maybe a bit below that (eyeballing it).  According to the ballistics tables, I should be hitting 2.7" (JBM) or 2.8" (Hornady) above the POA.  Instead I'm hitting several inches below POA.  I didn't bother going out further at that point, especially since it was getting close to sunset and I wanted to get out of the desert area I was at before dark.  I'll have to go out and shoot again.  I really need to find some milsurp ball ammo for comparison.

I don't necessarily need a calculator.  A mathematical formula would suffice, I think.

Try Hornady's 4DOF calculator: https://www.hornady.com/team-hornady/ballistic-calculators/#

Set up the ballistics for what you know your zero is.  Once you have that, then check the use zero angle box in the firearm section.  Your known information should get you your angle of departure.  Then using that same angle, you can change bullet and velocity and have a pretty good idea where it'll go.

Their projectile library doesn't have any of the NATO ball projectiles in it.  Doesn't look like I can use it for any projectiles not in their library.

I've been using their regular calculator to get ballistics tables.

Something's not right with my trajectory, in any case.  It differs radically from what the calculators say it should be.

Trying to do it "mathematically" without comparing zero and POI from each round at 200 at best is going to give you a rough estimate.  You really need to see how each round actually performs through a given rifle/barrel.

What did was pick my gold standard round, in this case FGMM.  I zeroed it for 200 yds and recorded the data.  For any new rounds or loads I leave my scope or sights set for that standard and see where it goups at 200 relative to the standard.  I record that data, and make the relative adjustment for a given range.

For example, if a round grouped 1.25 moa high and .75 moa right compared to my standard at 200, and my chart or calculator says com up 6 moa elevation and right 1.5 moa for a given distance and a wind for the *current round*, I would adjust elevation up 4.75 moa and windage right .75 moa instead to account for the difference.

Edit: noticed my mistake and changed it  "standard round" to "*current round*".

Do you know the 100 yard poi or each load? Say the 168 is 2.375" high and 2" left.

If so a ballistic solver will tell you.

I have multiple loads for each of my precision rifles but use one mechanical zero on my scope, I never re-zero.

To answer your question, no, there is no way to(accurately) estimate poi at any given distance if you don't know a base line distance poi.

I have the tables. I can't recall what the GMM does out of my barrel length off of the top of my head (I'll check when I get home), but the Malaysian should be hitting about 2.8" above POA.

While shooting at 25m, the GMM MPI was higher than the Malaysian MPI after I got it zeroed to POA. I never got to try the GMM at 100m, as it was getting late and my Malaysian trajectory was far off from the tables. I only have 15 rounds of GMM left to spare, so I need to use it wisely.

At 25m, using the Malaysian ball ammo, MPI relative to POA should be virtually identical to MPI at 200m based on the tables. Zeroed at 25m, at 100m my MPI was 7" below POA when it should be 2.8" above POA. I have no idea why there is about a 10" discrepancy. Without knowing what exactly is going on, I don't think I can figure things out with respect to the GMM.

I'm going to try to get some Hirtenberger ball ammo and see how that compares (and see if I stop getting case separations; so far this Malaysian stuff seems like garbage).

Windage at 25m is about the same for both loads, though.

What is a "ballistic solver"?

Alright, so I measured the targets and looked at the tables.

At 25m, the Malaysian should be hitting less than 1/200" above POA. At 100m it should be hitting a bit over 2.8" above POA. This is for a 200m zero.

For a 200m zero with 168gr. GMM, MPI should be 0.16" above POA at 25m, and 3.15" above POA at 100m.

On paper, the average MPI for the Malaysian was 0.15" above POA at 25m once I got it dialed in, which is less than half a click in adjustment from zero. At 100m, MPI for a 15-round group (all groups shot at 25m were 5-rounders for both loads) was 9.8" below POA, which is 12.64" below where it should be at that range based on the ballistics table, maybe a bit lower, actually, since it's a tad above where it should be at 25m (12.8" perhaps?).

The average MPI at 25m for the GMM was 1.35" above POA, for an average difference of 1.2" over the MPI of the Malaysian ball at that range.

@bigstick61
Going by a chart is not going to cut it. There are far too many variables to use generic data.

Ballistic solver predicts drops at various distance from your known zero. It requires muzzle velocity, ballistic coefficient of the bullet, zero, sight height over bore and air temp at a minimum to get close.

Different but similar loads can have drastic poi differences at 100yds, I think maybe your 25m zero may be too close to show that so that could be why it seems so far off at greater distances.

But you really cannot go by published muzzle velocity data, it can be so far off that it would be useless for what you are doing. It(MV) needs to be measured for your rifle at the time and conditions in which you are shooting.

It's unlikely that I can get a chrono in time before my last opportunity to go shoot prior to Cola Warrior (I used factory figures adjusted for barrel length for GMM, and other people's chrono results, similarly adjusted, for the ball ammo). I'll just have to zero for GMM when I go shooting this week, as the trajectory at longer ranges seems to be quite off. Excluding flyers (I consistently get one low and to the left in my 5-shot groups), I'm hitting over a foot above POA and 3.3 inches to the right in terms of MPI at 200m with the sights zeroed for ball ammo. At 25m it was on average 1.8" high and 0.7" to the right relative to POA.

Had a round keyhole with one group at 200m. There were a few twigs from a bush in its path, but if that can cause that, then 1:12 must not stabilize the 168 grain GMM well.

I'd still like to know how to calculate trajectory for one load relative to the one a rifle is zeroed for, given appropriate inputs. I asked my brother the other day and he started talking about LaGrangian this, and Hamiltonian that.

@bigstick61

A 12 twist should be plenty for 168s.

You need to know both zeroes (poi at a distance).
Example
Sight height= .75"
Standard atmos conditions

Load A is zeroed at 100 yds
Load B is 12" high at 100 yds

Load A is 175smk .238G7 2550fps

Load B is 168smk .218G7 2600fps

Load A
25 yds 0.0"
100 yds 0.0"
200 yds -5.4"
300 yds -18.2"
400 yds -39.4"

Load B
25 yds +3.0"
100yds +12.0
200yds +18.7"
300yds +18.0"
400yds +9.3"

I know this is an old post, but I figured I'd chime in.  I am trying to do the same for 77gr and 62 gr 5.56.  This is what I came up with.  

What we really want to know is the angle of departure of the bullet in relation to the optic.  Without actually diving deep into the formulas, there is a crude way to do this.  

1) Use a ballistic calculator to find the rise of the bullet at a very close distance (when gravity hasn't yet worked its magic with any significance) I used 5 yards. At 5 yards (180 inches) my 77gr rises .39 inches according to the calculator.  
2) Put the new BC, grain weight, and velocty of the 62 grain bullet, and see what happens.  For me, the rise at 5 yards at the same zero distance was .34 inches.  Not what we want.  
3) Adjust the zero distance on that new load in small increments, until your rise at 5 yards is the same as the first load's (.39 inches in this example).  

Turns out for the loads I was looking at, my 200 yard 77gr zero is equivalent to a 235 yard zero with the 62gr load.  I have not checked IRL to verify the accuracy of this method, but it is theoretically sound, albeit not very precise.

Cheers!

Fire at zero distance. Measure offset. Say 2moa up, 2moa left.

Figure ballistics. -3moa at 300yds from zero. Ok, but you impact 2moa high. Your actual drop should be 1moa at 300yds. Say drop at 500yds is supposed to be 12moa. Then your actual impacts should be 10moa low.

In a rough, DIY field sense, this is as good as you're going to get. Just a simple offset. With a highpower rifle, I'd want to do this at 100yds for zero, to maximize the flat shooting.

What Fritz said..............  
You can't use any mathematical solutions until you see how differently the 2 cartridges shoot in your rifle.  
You have to shoot them first, there is no way around that.


Shoot the 2 cartridges out as far as you can.... ie 200yds.  
Then compare the different point of impacts..........
THEN use the charts to compare the two.  

ie I run a 200yd zero, so I shoot load "A" which is zero'd.  When I shoot load "B" it may be say 4" left and up from "A."
THEN use your theoretical charts to compare the trajectories.....  

But to honest, save yourself the headache.....  make note of the 2 zero's, tape them to the rifle.
Shoot "A", use "A" zero.  Shoot "B", use "B" zero.  
THEN run the charts for whatever further zero you don't have.                          

No, there isn’t.  

Many people seem to think that the difference in the points of impact between two different loads fired from a rifle with the same windage and elevation settings on the sights are due solely to the difference in the exterior ballistics (trajectory) of the two loads. This notion is false.  There isn’t a ballistic program on the planet that can predict these changes in the points of impact and trying to do so using the different muzzle velocities and different ballistic coefficients of the two different loads is a wild-goose chase.  

The difference in the points of impact between two different loads (with the same sight settings on the rifle) out to say 75-100 yards will be due in large part to matters of interior ballistics; barrel harmonics and recoil vectors for instance. These components may not be the same from rifle to rifle and are not predictable using ballistic software. The only way to know what the difference in the points of impact will be, is to shoot the different loads in your weapon.

To illustrate the above points with a specific example, the graph below shows that there is nearly no discernable difference in the trajectories of the Sierra 55 grain BlitzKing and the Hornady 70 grain GMX out to 100 yards.





Yet, when I actually fired the Hornady 70 grain GMX load from an AR-15 that had been zeroed for POA=POI at 100 yards with the 55 grain BlitzKings, the group of the 70 grain GMX impacted 2.9” LOW and 3.7” TO THE LEFT of the point of aim.





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