Short-Range MOA

[j_bliss99]

Before I ask this, you must all know that I am a freshman in high school and I am completely new to MOA. I need it for a physics project. Now that you know this, I'll ask the question.
What are the steps for measuring MOA? I've looked all over and have not found a clear way to measure it. And to add to the challenge, I'll be using a pistol from anywhere between 10-25 ft. away from the target. And if you know that MOA isn't the best way for what I'm doing, could you recommend another way to measure accuracy? Thanks

[gothcopter]

National Shooting Sports Foundation has a nice page with a simplified explanation of MOA. Really, MOA is just another way of saying "one sixtieth of a degree".

http://www.nssf.org/video/facts/MOA.cfm

Be advised that their formulae for computing MOA are a simplification, so some computational error will be introduced. For example, the correct formula for computing number of inches (y) per MOA at 4 yards would be

tan(1/60) = y/(4*36) --> y=0.0419 in

whereas the NSSF formula (which is the same formula most shooters use) would yield

4/100 = y --> y=0.04

If you haven't had trigonometry yet, you're probably best off sticking with the NSSF formula.

[allaroundhunter]

There probably is a better method than worrying about MOA, but first we have to know what exactly it is that you are trying to measure.

[j_bliss99]

If you want to know what my project is to help you get a better understanding of what I'm trying to measure, I am trying to see if the mass of a bullet affects the accuracy. So I am trying to measure the accuracy of a group of bullets

[Dave P]

As they said, MOA is just one way to measure an angle. Just call it degrees, if you want.

Can you measure the angle (hypotenuse to adjacent side) of a 3-4-5 triangle with your compass?

Same idea with MOA.

[allaroundhunter]

Originally Posted by j_bliss99

If you want to know what my project is to help you get a better understanding of what I'm trying to measure, I am trying to see if the mass of a bullet affects the accuracy. So I am trying to measure the accuracy of a group of bullets

Well, MOA or any other system of measurement will work well. However, seeing as I highly doubt your judges will understand what an MOA is or you being able to completely explain it in the time you're given I wouldn't use it.

To test what you want, then you will probably want to test at 10, 25, and 50 yards. As opposed to a couple of feet. You won't see much difference at all at that distance. You will also want to be shooting 3 or more pistols probably (same caliber, same batches of ammo)

Also, how do you plan on testing the shooting?

[j_bliss99]

I'm not sure I understand on what you mean by "testing the shooting." Would it be better to measure from the two farthest holes and just compare the number of inches for the groups? I will be making my own bullets for this, and I don't know if I can get my hands on any pistols other than the .38 Special snub-nosed my grandfather owns. I do have a contact in the police station, and he said he could take me to their range and help and stuff. They'd probably let me use a .22 or something like that. I don't know if it would just be easier to pick a different hypothesis.. this is all so confusing for a 14 year old

[allaroundhunter]

Well, every gun shoots the same ammo a little differently. So to actually test whether one weight of ammo shoots better than another it would be a more accurate (no pun intended) test if you have multiple firearms testing the same ammo.

And I meant will you be shooting the guns off a rest, or will you have a rest to lock them in to so that you take shooter error out of the equation?

[James K]

Also note that MOA is an angle, not a distance or linear measurement. The fact that one MOA comes close to 1" at 100 yards is convenient, but pure coincidence.

Your subject line is a bit of a misnomer. There is no such thing as a short or long range MOA. An angle is an angle, whether the lines forming it extend an inch, a foot, or a million miles.

Jim

[Brian Pfleuger]

No need to measure MOA, just measure in inches. A group size is measured as the farthest distance between the outer edges of the two farthest apart two holes, minus one bullet diameter.

For example, if you fire 5 shots with your .38spl and 3 of them are touching in the center while 1 is a an inch low and left and another an inch high and right, your group size would be 2 inches minus 0.357, or 1.643 inches.

[Jim Watson]

I am trying to see if the mass of a bullet affects the accuracy.

Unfortunately, there are many variables that affect accuracy. Mass is only one, and probably not a major one.

[parttime]

Accuracy and precision have different variables.
In order to measure the precision of a firearm/cartridge combination you first have to eliminate the inaccuracy of the shooter.
You can do this by holding and firing the firearm in a bench vise of some sort while using a selected group of cartridges.

Firing X number of cartridges at various distances at seperate targets, measuring their point of impact as discribed in an earlier post then switching to a different set of cartridges and repeating.

[g.willikers]

Wouldn't it be easier to show what you intend without complicating things.
Just use the one gun and measure in easy to explain inches or millimeters.
Using multiple guns introduces more variables.
And measuring in MOA requires more explanation - and glazed over eyeballs from your audience.

[44 AMP]

Welcome to TFL!

Let me help you with a couple of things, which may lead to you adjusting the parameters of your experiment.

First, MOA (minute of angle) is two things. It is a mathematic term, as others have described, and it is a slang term in the shooting sports.

When used as a descriptor of accuracy in shooting (in casual conversation) we drop the numbers after the decimal point, rounding it off to whole numbers (inches). 1 MOA is 1 inch at 100 yards. 1 MOA is 2 inches at 200 yards (group size), 10 inches at 1,000 yards, etc.

Second, Bullet Mass does affect accuracy (group size), in two different ways, both of which can be very subtle.

Increases in bullet mass increase the length of the bullet. Since the outside diameter of the bullet is fixed (bore size) as bullets get heavier, they must get longer.

There is a point where the twist rate of the rifling will not stabilize longer heavier bullets. This is most easily seen in rifles, only rarely being able to be recognized in typical handguns and their ranges.

Each barrel's rifling twist rate will stabilize a range of bullet weights (lengths of bullet). Bullets outside that range will be less accurate, being either under or over spun to fly "true".

The other effect of mass on accuracy is that bullets, being basically cylinders with pointed ends, longer (heavier) bullets, properly spun (rifling twist) are less affected by wind. More mass means a given amount of wind does not push the bullet as far off target.

Again, something most easily shown in rifles, and at rifle distances.

Your question is a good one, your experiment shows a sound reasoning basis.

BUT, with a handgun, at short range, I think you would find that the effect mass on accuracy will be so small as to be hidden within your margin of error. It is quite possible that, to someone outside the firearms field of interest, lack of clear significant results might be considered a failure to prove your theory.

Let me suggest a different experiment, but one that also involves the relationship between bullet mass and performance. And one that is easily shown and tested with a typical handgun...

Did you know that with handguns, lighter bullets will generally strike the target lower than heavier ones, with the same point of aim?

This would seem to be the opposite of what one expects to happen, but I assure you it is true. Heavier bullets move slower than lighter ones, so they ought to hit lower, but that is not the observed result. Why?

A lot of experienced pistol shooters know the answer, but your physics teacher may not. I'm not going to tell you the answer (not yet, anyway) but it does involve the mass of the bullet, along with other factors. It is an application of physics, and ought to satisfy your school project requirements about that.

And it is something with a clearly visible difference, that a non-shooter can see, and possibly understand. And it can be shown with the resources (handgun) that you have available.

Just a thought for you to consider.

Welcome to TFL! The folks here have, collectively, literally thousands of years experience covering virtually all aspects of shooting, and we really like helping out folks who are just beginning to learn about firearms and all their different aspects.

Come back and ask questions, whenever you have one.

[allaroundhunter]

Originally Posted by g.willikers

Wouldn't it be easier to show what you intend without complicating things.
Just use the one gun and measure in easy to explain inches or millimeters.
Using multiple guns introduces more variables.
And measuring in MOA requires more explanation - and glazed over eyeballs from your audience.

Except only 1 gun is not a large enough sample size to draw a reasonable accurate conclusion. Especially since guns shoot ammo differently. If you want to prove that one is inherently more accurate than another then it needs to do so in more than one firearm.

[DaleA]

Unfortunately, there are many variables that affect accuracy. Mass is only one, and probably not a major one.

Jim Watson’s remark above is correct BUT you want to do this so let’s see how it COULD be done and you can throw the above statement in as a disclaimer at the end of your write up of the experiment.

(This is just a summary of what Brian Pfleuger, g. willikers and others have mentioned.

1. Use just the one gun. Using one gun is a good thing. Multiple guns would mean testing each one with the different bullets at the different ranges. Too much work. One gun is better.

2. You said you are making your own bullets. This is good too. You can make them up and explain how you made them. I’m assuming you are making them up in different weights and you want to see if the heavier bullets are more accurate than the lighter bullets.

3. Shoot the bullets at the targets at different ranges. You said 10 to 25 feet. This is fine. Use some kind of rest for the gun and do all the shooting yourself (heck, this is why you want to do this in the first place, so you can do some shooting yourself) and do it the same way each time. Do it this way and report the results. This is a scientific experiment. Doesn’t really matter WHAT the results are just show how you got them and what they are.

4. Use a ruler to measure the groups. Measure them from edge to edge. Just that. Be your own scientist, measure all the groups yourself and measure them all the same way and you will have consistent data for your experiment. Then write up the results.

Bells and Whistles. (Only if you want to do it.)

If you have a geometry (I don't think you need trigonometry) fan amongst the judges you might explain that shooters like to use ‘minute of angle’ measurements and then explain what that is. I don't think you need trigonometry for this but you might want to explain the ‘trigger-nometry’ that you used during your shooting!

For sure you want to explain other factors that might affect accuracy and which might even nullify, override or invalidate the results you found. This is honest. If you want a list of other factors that affect accuracy the group here would be happy to provide them. But look at each one and see if it is or is not a factor in your experiment. That is, someone might say some guns are more accurate than other guns. But since you used the same gun in all your shooting this is not a factor. Someone might say that the model of the gun you used is known to be so inaccurate and inconsistent that it completely overrides the bullet weight differences. This would be a valid point if true but if you get some consistent groups with the same bullets you can say 'Well the gun I used IS consistent, so there. (But leave out the 'so there' comment.)

Good luck.

[Lt. Skrumpledonk Ret]

There are too many variables on why this bullet impacted here and that bullet impacted there. Many of us spend so much money on marginalizing those variables only to realize we will never eliminate half of them. We're talkin lunar-gravitational-pull-coefficient-zenith-drag-cosine-MOA-type-stuff

[Buzzcook]

Just like to note that accuracy and precision are not the same thing in science.

An experiment can have results that are accurate or precise or both or neither.

For example when we shoot at a target we aim at the bullseye, or some other point of aim (POA).
We can have have a very small group of hits close together but not close to the POA. We could have a group which is relatively close to the point of aim but not grouped close together. There could be a group that is both close to the POA and close to each other. Finally the bullet holes could be spread all over the target, which is the way I shoot.

It might get you extra points if you make the distinction when you measure you targets.

When you have your report typed up, please post it here. I can say without reservation that we are all interested in your results.

[FlyFish]

I've spent my career in environmental research, which necessarily involves experimental design and statistical analysis. I just wrote a few paragraphs on both of those things that would have been well over the head of the average grad student, let alone a high school freshman, and would have also made me sound like a pompous ass, which I try not to be. So, I've erased all of that and will offer a few more appropriate (I hope) recommendations.

First, don't worry about your original question - you can measure your variable of interest in MOA or, more easily, simple linear dispersion on the target in inches, millimeters, or whatever. A basic rule of science is that results are independent of the units of measurement.

Second, you're attempting to determine the spread (deviation) of groups of shots using different bullet weights while keeping all other variables constant, or at least assuming you can and therefore throwing any of that additional variability into your "error" term. What you're measuring is precision, not accuracy. Precision is a measure of repeatability, accuracy is a measure of comparability to a known correct value (in your case, the aiming point). If one bullet weight shoots smaller groups than another it's more precise, not more accurate. You improve accuracy by moving the sights. Yes, just about everyone uses the terms incorrectly. (Edited to Add: But not Buzzcook, who posted a good description of the difference while I was typing)

Third, don't use group spread as the measure of precision. It has a number of flaws, notably that it only uses "information" from two shots, is highly dependent on low probability events ("flyers"), varies with group size, and can never become smaller as additional shots are added to the group. The pros use average deviation (it has other names as well), which is the average distance that each shot in the group falls from the group center. When I test loads, I measure each impact as the x,y distance from the aiming point and then it's a simple matter to calculate the center (average x, average y) and then, using the Pythagorean Theorem, the distance of each shot from that center. You can quickly and easily set up a spreadsheet do the calculations.

Finally, you obviously will see a difference between bullet weights. The question, however, is whether that difference is real or whether it's simply due to chance. That's what statistics can tell you. Test your results using some simple statistics, like the t-test (if you only have two bullet weights involved) or the somewhat more complicated Analysis of Variance (for three or more), or their even simpler analogs, (for example) the Mann-Whitney or Kruskal-Wallis tests. You can find them in any introductory statistics book, or on-line, or perhaps your teacher can help you with them (hope so!).

Good luck - please come back and share your results with us.

[dayman]

Did you know that with handguns, lighter bullets will generally strike the target lower than heavier ones, with the same point of aim?

This would seem to be the opposite of what one expects to happen, but I assure you it is true. Heavier bullets move slower than lighter ones, so they ought to hit lower, but that is not the observed result. Why?

A lot of experienced pistol shooters know the answer, but your physics teacher may not. I'm not going to tell you the answer (not yet, anyway) but it does involve the mass of the bullet, along with other factors. It is an application of physics, and ought to satisfy your school project requirements about that.

As both a teacher, and as a firearms enthusiast, I like it.
Also, it will be much easier to cover effectively within the bounds of a high school physics project, which - based on your age - I'm assuming is descriptive physics rather than anything calculus based.
And as a bonus, if/when you do take calculus based physics, you could re-hash it, and actually come up with an equation for where a bullet of a given weight would wind up.

[James K]

Group size is conventionally measured from CENTER to CENTER of the farthest apart bullet holes. The reason is that measuring the distance from the outer edges would automatically increase the group size for larger calibers.

If it is not easy to measure center to center, measure edge to edge and subtract the caliber.

Jim

[j_bliss99]

Thanks for all the help and suggestions, guys! Unfortunately, I have already turned in my proposal it was accepted about 2 weeks ago. However, I believe I might know the answer to your question, 44 AMP, if it is as simple as I am thinking; is it because the greater amount of momentum in heavier bullets keeps them going in a straighter line? I have managed to tweak my project a bit to where I'm using a rifle and not having to make my own bullets, if that helps any. And I'll be sure to post the final results! Thanks again!

[j_bliss99]

Another quick question, any ideas on what rifle/caliber I should? Thanks again!

[Cowboy_mo]

Group size is conventionally measured from CENTER to CENTER of the farthest apart bullet holes. The reason is that measuring the distance from the outer edges would automatically increase the group size for larger calibers.

which is why most people subscribe to

No need to measure MOA, just measure in inches. A group size is measured as the farthest distance between the outer edges of the two farthest apart two holes, minus one bullet diameter.

However, there is an easier way to measure "center to center". Take your measurement from the outside of hole A to the inside of whole B and your measurement will actually be "center to center" without performing subtraction of 1 hole.

[Spats McGee]

Originally Posted by j_bliss99

Another quick question, any ideas on what rifle/caliber I should?

What are your options?