Looking for the math

[Mecharius]

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.

[Mecharius]

So, everything. I think I asked for everything

[Mecharius]

I feel I should add, my long range target shooting experience at this point has been up to 500~ yards with a 540 grain 45 cal paper patch bullet. So the majority of this is all new to me. If I make mistakes or ask something which seems apparent or simple, you have my apology in advance.

[LRRPF52]

You will need to be adept at partial differential equations and highly advanced calculus to even begin to scratch just a few of those variables, one of the biggest ones not listed being gravity, although you would run it as a constant(even though it isn't).

You have to develop equations for each variable, then make those equations work together to provide a final solution for a specific space-time set of environmental conditions.

Just modeling the gyroscopic spin equations could be enough material to write a Doctoral thesis.

My dad sat down one day and calculated the orbital trajectory of the moon after his wireless keyboard "quit working". He's a physicist and researcher/aerospace engineer type who spent a career working on advanced programs for the DOD. He was a rocket telemetry data technician at the USAF Flight Test Center when I was born, conducting rocket motor plume signature analysis for space-based observation systems.

Anyway, after about a day, he calculated the orbital trajectory of the moon, and determined it to be some speed that was similar to the .270 Winchester. I checked the keyboard and saw that he had put the batteries in backwards...

Moral of the story is, you would need to devote a substantial part of your life to passionately studying and working with high math to begin to even have a rudimentary ballistics solution with just a few variables.

[Mecharius]

Any suggestions for a starting point?

Prior to joining the Army I worked as a machinist and spent four years of my life as an mech engineering major in a tech college. Although my math skills have faded, and some of this is new compared to my previous area of study I do have a good foundation for the understanding of some of the information required. At least I think that I do, anyway.

Once I start back at school in January, now having made to switch back to being a civilian (a daywalker, if you will, accounting for my reserve obligation) this would be an apt bridge between my hobbies and formal education. I do have to recover from four years lost (not lost, more like spent pursuing the idea of a greater good), but I still do have at least the basis of a head start.

[Mecharius]

Your dad definitely sounds like a scientist instead of an engineer.

Scientist finds alien computer: we have much to learn from this, and much to fear
Engineer finds alien computer: hey look! I got it to run Doom 3

[LRRPF52]

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.

[Mecharius]

I didn't mean on the fly.
I suppose I should have been a little more clear in my original post about that. I want to be able to do as much of it by hand as is possible so that I have a better understanding of what is happening when I put the information into the ballistic calculator. And maybe script my own calculator in python.

[Mecharius]

The cookie cutter approach of put the info in, get the results out, although practical, isn't any fun

[LRRPF52]

Keep us updated on how the modeling for each variable goes.

Maybe you could develop a new math using geometry instead of text numbers that makes it cave man proof.

[Mecharius]

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.

[cory]

What LRRPF52 said in his first post! I've done a little digging on this and it really is that complicated. I suspect that the calculators that are out there use real world data to add correction factors to the immense amount of math that goes into this. You have to remember that we're dealing with tolerances in the 0.001" range when working with numbers in the 100s of yards.

You can take a look at the following link. I've been meaning to download it and play with it, but I'm to swamped right now.
http://www.bfxyz.nl/

[Mecharius]

What LRRPF52 said in his first post! I've done a little digging on this and it really is that complicated. I suspect that the calculators that are out there use real world data to add correction factors to the immense amount of math that goes into this. You have to remember that we're dealing with tolerances in the 0.001" range when working with numbers in the 100s of yards.

You can take a look at the following link. I've been meaning to download it and play with it, but I'm to swamped right now.
http://www.bfxyz.nl/

Thank you for the link. Did a quick dig through some of the website, seems like it will help me.

[KentuckyBuddha]

LRRPF52's post was precisely what I was thinking too. His anectode was better but it made me think of the idea of using reletivistic equations when Newtonian will suffice...which I have had a...cough...cough...friend I knew do many times.


I love the math too...in this case...there is an app for that and it is best to just let it go if you can in any way stop yourself. But, I understand if you can't. I mean my FRIEND would understand if you can't. LOOOL

[Mecharius]

I will be using the App for when I actually need it. This, this is more for fun and increasing my own understanding.

[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.