Gun Math

[aprentic]

WARNING this gets a bit mathy.

I've got a Ruger K77/22-VBZ that I shoot at 25, 50 and 100 yards.
I'm trying to make a distance compensation chart for my scope.
I know I could just use trial and error but I'm a bit of a nerd so I'd like to take a more precise approach.

How do I figure out the velocity?
There are two parts to this question. What is the muzzle velocity? What is the deceleration?
I think if I can shoot at targets at 3 known ranges I should be able to figure out the bullet drop over each of the ranges and then back calculate both of these values (solve 3 equations for 2 unknowns). But how do I figure out the bullet drop? I don't have a tool to determine if the target is at the same height as the muzzle of the gun so I won't know if the gun is exactly level when I fire it. If I assume that the ground is level I can measure the height of the target and the height of the gun but will that be accurate enough?
Is there a well known method to do this that doesn't involve expensive equipment?

WARNING this part gets very mathy. (it probably won't make much sense unless you've taken statistics)
Also it seems to me that accuracy calculations are done incorrectly. Most people seem to consider grouping as a measure of accuracy by measuring the maximum distance between shots. However, from a statistical perspective this is a bad approach since it leaves out information from all of the other shots. It seems that a better method would be to map out the coordinates of each shot on the target. Then you could calculate mean (are you hitting the target on average), standard deviation (what is the spread of your shooting), skewness (do missed shots tend to miss more in one direction than in others) and kurtosis (is your miss rate driven by really wild shots). Aside from the difficulty of doing these calculations wouldn't this be a better measure of accuracy and provide better feedback to the shooter?
Is there some software out there that will let me scan in targets and do these calculations automatically?

 

[M1911]

Ballistics charts already exist and are very easy to find. http://www.federalpremium.com/products/details/rimfire.aspx?id=843

 

[whatluck]

I found this: Scientific Target Analysis Software

 

[dixidawg]

Don't recreate the wheel:

http://www.remington.com/pages/news-and-resources/ballistics.aspx

 

[aprentic]

I found this: Scientific Target Analysis Software

That's pretty cool but $125 is pretty steep. Do you know of any open source version? Also it would be nice if it could take scanned images an analyze them instead of having to input the data by hand.

 

[aprentic]

Pre existing balistics charts.

I've seen the pre existing balistics charts. The problem is that they assume a uniform (and often unspecified) barrel length.
The reason I mentioned the particular gun I have is that it has a slightly longer than average barrel (24" rather than 20"). This should give it a higher muzzle velocity but I don't know by how much.

 

[THUNDERCHIEF]

Also, wouldent temperature change the air density and therefore change deceleration?

IDK, just thinking out loud.

 

[aprentic]

Also, wouldent temperature change the air density and therefore change deceleration?

IDK, just thinking out loud.

I think it would. I know that pilots say that take offs and landings are easier in cold weather because of the increased air density.
So ideally I should do all the shots at the same temperature and record that temperature. If I did that on different temperatures I should be able to factor temperature in.

 

[SeanT]

No offense, but the trial and error approach you mention in the OP sounds a lot more fun than this.

 

[M1911]

I've seen the pre existing balistics charts. The problem is that they assume a uniform (and often unspecified) barrel length.
The reason I mentioned the particular gun I have is that it has a slightly longer than average barrel (24" rather than 20"). This should give it a higher muzzle velocity but I don't know by how much.

With .22lr, I strongly suspect that the difference will be unimportant compared to the other variables, and that you are way overthinking this.

 

[aprentic]

No offense, but the trial and error approach you mention in the OP sounds a lot more fun than this.

I can do both. I'll do the math and then check it with trial and error

 

[aprentic]

With .22lr, I strongly suspect that the difference will be unimportant compared to the other variables, and that you are way overthinking this.

It's all together possible that all of this isn't really necessary. It's just something I'd like to do.

 

[MisterHappy]

Shotguns are more my thing ( the fact that the target is moving gives one more ready-made excuses) but I'd say that there are far too many variables to attempt to comoensate for.

As for muzzle velocity, if you belong to a club, ask around and see if there is anyone with a chronograph that you can use. Then there'll be no need to "calculate" a muzzle velocity.
Also, you don't mention the type of ammo - a bullet that starts its trip at above the speed of sound, but slows to below it before encountering the target ( as a 22 lr will ) will become unstable as it transitions to subsonic. More variables!

As to temperature affecting density, that's definitely a factor with planes ( it's called "density altitude") and often needs to be factored in. Colder air is "thicker" ( and the speed of sound is, therefore, higher)

And, since 22 lr ammo is not generally made to the same specs asn meticulous handloads, with each case, bullet and powder charge measured and matched for optimum performance, I think that the variables inherent in the ammo itself will make all of your calculations moot.

I'd say, shoot more, and, if you want a definable metric for performance, bet money on it!

Good luck!

 

[Tim94gt]

You could buy a chronograph to measure muzzle velocity. Check here http://www.cheaperthandirt.com/ItemListing.aspx?catid=318

 

[KMM696]

JBM Ballistics is an excellent online ballistics calculator that can generate a drop chart for you, among other things.

I have a target analysis program at home called OnTarget Calculator - freeware one, requires a scanner or can work off of a target .jpg file. It doesn't get as in depth in statistical analysis as you sound like you're looking for, though.

 

[KBCraig]

The U.S. Army Field Artillery School has more than a century of math and theory at their disposal, which they use to develop wonderful charts. And then they proceed to test those charts against real-world conditions, and toss the theory in favor of empirical evidence. That's how they develop firing tables that take into account everything from range to weather to the rotation of the earth during flight of the projectile.

Yes, I was a redleg.

 

[bpm990d]

You are correct that a better method is to use mean radius. Just remember that precision & accuracy are two different things.

If you like the nerd stuff, you might be interested in a couple of articles by John Leslie. They are listed under statistics on the link. Using Quantitative Methods to Analyze Shooter Skill and Is "Group Size" the Best Measure of Accuracy.

You can measure velocity doing it the way you want, but you will run into a problem with launching the bullet so it is parallel with the ground. Gun sighting systems are not set up for that. You could probably use a laser bore sighter, or in a pinch take the bolt out and sight down the barrel. I would guess that it's probably not precise enough to get a good measurement. The same thing can be done for measuring the ballistic coefficient of a bullet, but you run into some of the same problems that leads to an imprecise measurement.

The best way to figure out sight settings for a particular range is to actually shoot it at that range and record the settings. It gets rid of all the potential problems associated with the assumptions we have about our equipment. For example, do the scope adjustments exactly measure 1/4 MOA...etc....etc....?

Beyond that, you really need a chronograph and a ballistic program to model the trajectory.

B

 

[aprentic]

Thanks for all the feedback. I'll let you know how it goes.