Looking for the math

[Savage Shooter]

I think you missed Ballistic coefficient and also the direction you are shooting relative to the earths rotation (to determine the Coriolis effect).

[IceAxe]

In reference to your question on powder burn rate and its effect, I think they are talking about temperature sensitivity. Higher temperatures can drive up the burn rate thus effecting pressure and resultant velocity. If known this factor can be used against a known baseline velocity to determine the delta for present conditions.

[JASmith]

Any suggestions for a starting point?
...

LRRPF52 is right about the complexity of the math when one works from first principles.

BUT, you can do a heck of a lot with minor extensions to the skill set you needed to get them 'thar paper patches out to 500 yards.

BTW Tell us what you did to gain confidence with them! A Grendelier or two might have an interest in black powder even the stuff will play hob with gas ports...

[SG4247]

Might check Bryan Litz web site here:

http://appliedballisticsllc.com

He has written software and books on the subject matter.

Sharp guy, and can do all of the math by hand. He is currently working at Berger bullets as chief of ballistics research.

[LRRPF52]

Wasn't trying to do anything new. Just wanting to know what equations the ballistic calculators are using and why each variable is asked for. Just trying to understand what each piece of information does.
And scripting one myself is simply because doing helps understanding.

Also understand that the different ballistics calculators use different math. A lesser program will show the same wind drift left and right at 1000yds, whereas the more advanced programs will have spin drift computed.

Bryan Litz's program is one of the best on the market, complete with his BC analyses for the bullets in the memory of the system.

One of the more overlooked programs with dead-on accuracy is Lapua's Quick Target Unlimited, which uses actual Doppler radar data for the Scenars, not theoretical drag models. Accuracy for trajectory prediction is 3cm at 1300m IIRC.

[Mecharius]

I think you missed Ballistic coefficient and also the direction you are shooting relative to the earths rotation (to determine the Coriolis effect).

As far as BC goes, I'm shocked I missed that. Thank you for pointing that out.

[LR1955]

Wasn't sure how else to put this...

While I wait for payday to order the next part of my Grendel build I have been trying to further educate myself on the more interesting side of long range target shooting. A handful of Google searches has shown me several good online and app based calculators. But very little information on what goes on underneath the GUI.

So far, what I have gathered is that I should know:
Optic height, as measure from center of bore to center of optic
Projectile weight
Muzzle velocity
Bullet trajectory
Barometric pressure
Temperature
Elevation
Elevation difference between target and muzzle
Humidity
Wind speed
Wind direction
Powder burn rate
Barrel length
Rifling twist rate
Number of rifling grooves
Wind direction

Am I missing something?

So, my question is, how do I use this information, if I want to hand jam it?

I have the rifleman's rule. But beyond that I'm at a loss. Either I am not searching the proper terms to find it, maybe I have accidentally skipped over where the information is stored, or the entire internet is conspiring against my love of math.
First two seem more likely.

I was hoping to do this without spending money on a book at this point. All my spending money is going into rifle parts and reloading supplies at this point. Once I have it built I may collect a shooting library. But for the now I am trying for the free education.

I understand how the majority of this information will affect performance. A few things I am iffy on:

Would powder burn rate be a direct affect on muzzle velocity, and thus not be needed as additional information?

I understand twist rate, but how does number of grooves affect point of impact calculations? I saw more than a few calculators ask for this information. Usually followed up with groove depth(if known) or something like that.

Wouldn't elevation difference be covered by rifleman's rule, or am I missing something?


I realize I am repeating some things which have most certainly been previously covered in this subforum, so I apologize for that.

Here is how you use this information to get a ballistic solution (elevation for a distance). Providing of course this is what you are after. Not really sure after I read your listing.

Ballistic Coefficient (G-7 if possible).

Muzzle Velocity.

Bullet Weight.

Altitude if you are above about 3000 feet.

Sight height above center of bore.

Plug into a simple ballistics calculator and you should come up with solutions that are quite good to the subsonic range of the load.

However, a few things you forgot that must be quantified in order to understand hit probabilities.

1. Mean radius of the ammunition so you can extrapolate Mean Radius at a distance.

2. Hit and Kill zones of target.

3. Probability that the shooter is able to hold well enough, estimate wind well enough, and pull trigger well enough for his shot to maximize the probability of hit / kill of his ammunition against a specific target at a specific range given specific environmental conditions. For this you will have to deal mostly with physical and psychological stress on the shooter.

Most of your variables, if they have significance, pale when considering the capability of a shooter to make a shot.

LR55

[JASmith]

Many of us who have done work on writing, coding, and debugging analogous math models understand how awesome the effort needed to create these apps is and we truly appreciate the magic they create.

Most of the trajectory calculators one can get are adaptations of the look up tables around since Ingalls did his work about a century ago. Adjustments to the ballistics coefficient to get very accurate results, coupled with the computer, make accurate and precise trajectory predictions possible without tons of work with nomograms, slide rules, and adding machines.

People working out artillery solutions knew about the Coriolis effect since at least the start of World War I when long range artillery shooting was routinely done. The Russians probably worked out the math in the last half of the 19th century.

If you are truly serious about writing your own code and integrating your own equations of motion, you can try a query to Ammoguide.com. Their ballistic calculator does indeed integrate the equations of motion and uses proper drag coefficients back converted from the BC to obtain the force on the projectile. The TANSTAAFL principle, however, is alive and well with this tool. It it takes a lot of compute cycles to numerically integrate the equations, so it uses your computer to integrate them.

They guy who wrote the code (tloc54) is very active on their forum and the guy whio implemented the calculator (ammoguide) in Java is the head honcho of the site. They might give you tips and hints on how to proceed. You might want to try running their calculator a few times to see how well the GUI work and to compare results with those of JBM and of Litz.

PS You will need at least an intuitive understanding of the factors LR1955 enumerates in his 3rd bullet if you are willing to take this from an academic discussion to practice and helping inform the rest of us:

...However, a few things you forgot that must be quantified in order to understand hit probabilities.

1. Mean radius of the ammunition so you can extrapolate Mean Radius at a distance.

2. Hit and Kill zones of target.

3. Probability that the shooter is able to hold well enough, estimate wind well enough, and pull trigger well enough for his shot to maximize the probability of hit / kill of his ammunition against a specific target at a specific range given specific environmental conditions. For this you will have to deal mostly with physical and psychological stress on the shooter.

Most of your variables, if they have significance, pale when considering the capability of a shooter to make a shot.

LR55

[Mecharius]

Might check Bryan Litz web site here:

http://appliedballisticsllc.com

He has written software and books on the subject matter.

Sharp guy, and can do all of the math by hand. He is currently working at Berger bullets as chief of ballistics research.

The website its self doesn't seem to provide too much direct information after a quick digging through. But I think k I may be able to gain something g from it when compared to other resources. So thank you for sharing

[Mecharius]

Also understand that the different ballistics calculators use different math. A lesser program will show the same wind drift left and right at 1000yds, whereas the more advanced programs will have spin drift computed.

Bryan Litz's program is one of the best on the market, complete with his BC analyses for the bullets in the memory of the system.

One of the more overlooked programs with dead-on accuracy is Lapua's Quick Target Unlimited, which uses actual Doppler radar data for the Scenars, not theoretical drag models. Accuracy for trajectory prediction is 3cm at 1300m IIRC.

Going to have to check out Lapua's program. Was unaware that they had one, though it's not surprising.

[Mecharius]

Here is how you use this information to get a ballistic solution (elevation for a distance). Providing of course this is what you are after. Not really sure after I read your listing.

Ballistic Coefficient (G-7 if possible).

Muzzle Velocity.

Bullet Weight.

Altitude if you are above about 3000 feet.

Sight height above center of bore.

Plug into a simple ballistics calculator and you should come up with solutions that are quite good to the subsonic range of the load.

However, a few things you forgot that must be quantified in order to understand hit probabilities.

1. Mean radius of the ammunition so you can extrapolate Mean Radius at a distance.

2. Hit and Kill zones of target.

3. Probability that the shooter is able to hold well enough, estimate wind well enough, and pull trigger well enough for his shot to maximize the probability of hit / kill of his ammunition against a specific target at a specific range given specific environmental conditions. For this you will have to deal mostly with physical and psychological stress on the shooter.

Most of your variables, if they have significance, pale when considering the capability of a shooter to make a shot.

LR55

The list was everything I had been asked for after sampling a few different ballistic calculators online and from the Google play store. I think there were a few things I left off.

As far as the abilities of the shooter go, that will come later. Starting with the ideal settings, then will slowly work in probability of user error.

[Mecharius]

Many of us who have done work on writing, coding, and debugging analogous math models understand how awesome the effort needed to create these apps is and we truly appreciate the magic they create.

Most of the trajectory calculators one can get are adaptations of the look up tables around since Ingalls did his work about a century ago. Adjustments to the ballistics coefficient to get very accurate results, coupled with the computer, make accurate and precise trajectory predictions possible without tons of work with nomograms, slide rules, and adding machines.

People working out artillery solutions knew about the Coriolis effect since at least the start of World War I when long range artillery shooting was routinely done. The Russians probably worked out the math in the last half of the 19th century.

If you are truly serious about writing your own code and integrating your own equations of motion, you can try a query to Ammoguide.com. Their ballistic calculator does indeed integrate the equations of motion and uses proper drag coefficients back converted from the BC to obtain the force on the projectile. The TANSTAAFL principle, however, is alive and well with this tool. It it takes a lot of compute cycles to numerically integrate the equations, so it uses your computer to integrate them.

They guy who wrote the code (tloc54) is very active on their forum and the guy whio implemented the calculator (ammoguide) in Java is the head honcho of the site. They might give you tips and hints on how to proceed. You might want to try running their calculator a few times to see how well the GUI work and to compare results with those of JBM and of Litz.

PS You will need at least an intuitive understanding of the factors LR1955 enumerates in his 3rd bullet if you are willing to take this from an academic discussion to practice and helping inform the rest of us:

Ammoguide appears to be a fantastic resource. Feel that I will be spending a good deal of time on their website.

I may not be an expert at it, but I do have a respectable amount of experience with python. Depending upon how far I go with this project, I think I may become intimately familiar with the language.

[Mecharius]

You all have given me a good bit of information to start with and several good resources to look over. I'm going to find through this my starting point, and post back up about it in a few days with my progress. I thank all of you.

[incognito]

If you can calculate partial differential equations with all those variables on the fly, DARPA will come snatch you up and you'll never be seen again.

Get a ballistics program, enter the variables, and go shoot would be my advice.

this

[Mecharius]

It's way too easy to burn through a couple hours a day on this, feeling like I've accomplished alot, without making any progress. I was hoping to be able to post something up to show the effort I've been putting into this, but all I've got is a handful of sheets of scrap paper covered in random notes. Maybe next week at some point I will have something worth showing.