Advanced Marksmanship Ballistics formula

[Twenitoo]

Hello,

I have been searching the internet for around 3 hours everyday for the last week to try and find out the bullet drop formula.

I've had lots of people say to use a calculator or find a table or check the manufacturers website, however i already have a decent ballistics calc., and my range charts.

If go hunting with say a .308 with a range card with my MOA/Mil adjustments for every 100 yards out to 600 yards and I have a target at say 466yards, I want to be able to figure out the exact drop for that range.

Yes i could make up a range card for every 20 yards but that would be fuckin huge, not very practical and a bastard to read.

Obviously, if people make ballistics software, then they must have the formula and that all im after.

Just something that says (bear in mind i havnt a clue what it is) i duno,

range(yds) x velocity x BC
__________________________ = drop in inches
gravity

I have seen a couple of formulas around however none of them put in a key i.e. M = muzzle velocity
H = horizontal range
Alpha = no. of times arse wiped in the morning

and without a key the formul is fcuking useless.

anyway, if anybody has spoke to the magic man in the sky and has located this elusive piece of jibberish, please let me know either its location or even better yet, just post it.

Thank you in advance.

 

[TackDriver13]

Re: Ballistics formula

I agree with dfoosking.

If you already have a ballistics calculator why not use the info it gives you and just make some sort of data card like most people? Ive seen guys put them on the inside of the flip up scope cap or tape them to the rifle stock...

I just use my pda with ballistic software in the field. I also have a simple card printed up with 25yrd increments out to 1500yrd on the off chance that my pda fails due to breakage or dead batteries.

Hope this helps... if not, I hope you find an answer that does!

 

[Sterling Shooter]

Re: Ballistics formula

First, I've never needed to know as much about trajectory as the OP perceives he needs to know. One thing for sure, even when we think we have enough information to get the job done, that is not always enough. Until there are laser guns, things will continue to perplex us all. What I do is take the ballistic chart and apply it. I record the divergence and use numbers for an x ring hit as a starting point.

 

[Twenitoo]

Re: Ballistics formula

Thank you for your input, however let me rephrase this slightly...

I do NOT want nor need a ballistics table , range card or holdover chart.

I DO, however, want the projectile drop formula for my own reasons.

If anybody has this, it would be much appreciated if you could post it here.

@ DFOOSKING 50 Yard increments will not suffice as in-between these increments there can be around a 10" drop at some ranges and that wont cut it for me. i need to be able to calculate the drop at the EXACT range and having even 25 Yard increments out to 600+ meters on a card wont work. It will be far to big to store and read. This is not just for the range but for the field aswell.

Thank you.

 

[AMOK!]

Re: Ballistics formula

What you seek is the 'raw' muti-variable equation, with dependent an independent relationships, for bullet drop. Check? You want to "see" an advanced d = d(not) + v(not)*t + 0.5*a*t^2 formula with inputs (variables) for BC, MV, T/P, drag, etc. Check?

Well, you won't find a universal equation for plug n play inputs. You know that's what the JBM Ballistics code/engine does. Aggregates all the indepent/dependent variables vis a vi differential equations and iterative calculations. Key word: iterative. And, you've seen the 'Downloads' links of C and BASIC code at JBM site?

Understand that you want to "see" such an equation, but unless you want to solve differential/integral calculus you will not be able to determine your bullet drop. Understand? IF you desire to solve the diff ballistic equations, you would be smart to use software (e.g. MATLAB, Mathmatica, Maple, etc).

A display of the mathematical prowess to achieve this feat: www.theblaze.com/stories/german-teen-solves-mathematical-riddle-first-proposed-by-sir-isaac-newton/

 

[Rob01]

Re: Ballistics formula

I put my data on a card about the size of a 3x5 card with data every 10 yards from 10-1000 yards for elevation, wind and movers for matches and it's not overly large or hard to carry.

You are trying to do something that isn't worth doing and going to be a waste of time and effort. Make a good card and fold it if needed and carry with your gear.

 

[kraigWY]

Re: Ballistics formula

The back of Hatcher's Notebook gives fomulas to determine bullet drop. I played with them a couple times, let me tell you, if you play with the fomulas you can get pretty accurate.

BUT, since you mentioned hunting, by the time you figure out the drop using these fomula's, what ever you're hunting will die of old age.

Yeah you can spend the time and effort and build a table to cover any range you want, and if you're careful you MIGHT come close to what you'd get using any of the free ballistic programs out there, you know, the ones that take a few seconds to spit out the information you're looking for.

I will add, that if you hunt at a distance that the angle of fall of a projectal gives you too much error between X25 and X50, bet you're gonna have more problems with the wind.

In hunting I do it the old fashion way. I find the vital size of what ever critter I'm hunting, and choose a rifle/bullet combination that keeps its trijectory inside that area, Some people call that Max Point Blank Range or the area where the bullet is never too high or too low to keep it in that area, and limit my hunting to that range.

That way I don't need a calculator, computer, Ipad or slide rule. I just make sure the critter is in range, and shoot for hair as oppose to air.

But what do I know.

 

[Greg Langelius *]

Re: Ballistics formula

We've all been where you are; wanting to understand the 'why' and 'how', besides the 'is' and 'should be'. While your reasons are very likely valid, mostly, you are probably just reinventing your own personal version the wheel.

Nothing wrong with that, and some folks find their understanding better that way.

But speaking from a long way further down that same road, I'll tell you plainly, it's routed across ground which has been picked bare. Shortcuts exist, and are truly the better way to get where you're going.

So please; listen to what these folks are saying. They are actually right.

Greg

 

[harbinger]

Re: Ballistics formula

If you have good dopes in hundred yard incriments you can use a basic math formula to find a pretty accurate correction for any yardage in between.

For example using the correction for my 308 in the Shooter App (which has been very accurate for me).

600 yards U17.8 MOA
500 yards U12.9 MOA

= a difference of 4.9 minutes of adjustment

since they are 100 yards apart, use whatever yardage in between as a percent. 545 yards = 45% of the difference (4.9)added to the 500 yard dope. 4.9x.45 = 2.205

2.205 + 12.9 = or U15.105. The ballistic app says 545 yard correction is U15.0. Not enough difference to even dial in unless you had tiny adjustment in your turret.

for what it is worth

 

[jbailey]

Re: Ballistics formula

The answers to your questions and more are found in McCoy's Modern External Ballistics. Fair warning however: the math is intense and his writing style is challenging. Amazing text book however.

Here it is on Amazon.com:
http://www.amazon.com/Modern-Exterior-Ballistics-Robert-McCoy/dp/0764338250/ref=pd_sim_b_2

 

[K2Ballistics]

Re: Ballistics formula

Don't get me wrong, James....Bob McCoy left us with a work of art before he passed, but unless the OP has some sort of math/computational background and can write a numerical solver for coupled, non-linear, differential equations, I'm not sure Bob's book is going to get him where he wants to be....which seems to be a simple, correct back-of-the-envelope equation for bullet drop.

If it actually exists, I love to know about it myself.

 

[Garvey]

Re: Ballistics formula

These men are telling you the way to get what you need the right way. And 600 isn't that far within the capabilities of these shooters and myself.

No different from anything else that is difficult to achieve. Want to make a 100 yard shot easy? Practice at 200. Want to make a 400 yard shot easy? Practice at 700. Most of us take the advice and use the methods of those that came before us. The method is to use a calculator, go to the field with the data and use the data. Record the results, good or bad, and learn from them. When good data is plugged into the calculator, good data will come out of the calculator. Some times no correction from calculated elevation compensation to field compensation is needed, they are that good.

Set up paper or steel at various ranges or only one target and move away from the target in increments.I keep a 25 yard card with the rifles and a 100 yard card in the scope cap. If I need to reference the card in the scope cap but need a 25 yard increment I just quickly split the difference in my head.

500 yard is 2.4 Mil, 600 yard is 3.2. I need to make a 560 yard shot, the difference from 2.4 to 3.2 is .8 Mil. half of .8 is .4 elevation for the shot is 2.8 Yes that would be for a 550 yard shot to be specific, but the 10 yard difference is so minimul that it need not be a factor. Plus a Mil scope won't adjust to a fine enough increment anyway.

 

[Killer Spade 13]

Re: Ballistics formula

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Garvey</div><div class="ubbcode-body">These men are telling you the way to get what you need the right way. And 600 isn't that far within the capabilities of these shooters and myself.

No different from anything else that is difficult to achieve. Want to make a 100 yard shot easy? Practice at 200. Want to make a 400 yard shot easy? Practice at 700. Most of us take the advice and use the methods of those that came before us. The method is to use a calculator, go to the field with the data and use the data. Record the results, good or bad, and learn from them. When good data is plugged into the calculator, good data will come out of the calculator. Some times no correction from calculated elevation compensation to field compensation is needed, they are that good.

Set up paper or steel at various ranges or only one target and move away from the target in increments.I keep a 25 yard card with the rifles and a 100 yard card in the scope cap. If I need to reference the card in the scope cap but need a 25 yard increment I just quickly split the difference in my head.

500 yard is 2.4 Mil, 600 yard is 3.2. I need to make a 560 yard shot, the difference from 2.4 to 3.2 is .8 Mil. half of .8 is .4 elevation for the shot is 2.8 Yes that would be for a 550 yard shot to be specific, but the 10 yard difference is so minimul that it need not be a factor. <span style="color: #FF0000">Plus a Mil scope won't adjust to a fine enough increment anyway.</span> </div></div>

THE answer . . .

 

[Katahdin]

Re: Ballistics formula

I understand you want something to take into the field with you that is in your head, that way you can stay on the scope and at the same time be efficient with a firing solution.

After studying my dope card for a long time I came up with this chart below. I'm running a 24" .308 MV 2621fps using 168 SMK FGMM.

Basically I memorize my dope per one hundred yards out to 600 yards. I can use the information below to make an accurate elevation adjustment for any range in between.

For example my elevation for 600 yards at 2000' DA is 15.5 MOA. Knowing this if a target presents itself at 660 yards I add 3MOA + 15.5 MOA = 18.5 MOA.

When compared to JBM 18.5 MOA is my 675 yard dope, it is pretty close. Again this is something I can keep in my head, obviously if the opportunity presents itself I will always use my data card, but if I need to make a field expedient call I can use this and be very close.

I should note your rifle is more than likely going to be a little different. Study your range card and I am sure you will come up with your own solution.


From
100 yds - 200 yds you will need approx 1 moa every 50 yards
200 yds - 300 yds you will need approx 1 moa every 40 yards
300 yds - 400 yds you will need approx 1 moa every 33 yards
400 yds - 600 yds you will need approx 1 moa every 25 yards
600 yds - 800 yds you will need approx 1 moa every 20 yards
800 yds - 1000yds you will need approx 1 moa every 15 yards

 

[hessian]

Re: Ballistics formula

You need to get a book. My keyboard does not have the symbols/keys to type partial differential equations.Pejsa's book has some math.

 

[damoncali]

As others stated, the "formula" is a system of differential equations with no analytical solution that I am aware of. You must use a ballistics calculator unless you're willing to accept errors of 10-15%. If you are (and I don't know why you'd be willing to do this, but since you asked), you can do this: Use a ballistics calculator for your load. Take the results and put them in a spreadsheet and plot them. Then add a polynomial trend line to the chart with an order of 2, and make sure you check the box that displays the formula for the trend line on the chart. That's your formula. It will be bad, but it's as good as you're going to get. You might get reasonable results out to about 500 yards - but only for that load and velocity.

You're better of with a table.

 

[gstaylorg]

I understand that you want the "equation"; I'm the same way. I also understand that you aren't digging the idea of a drop table. There is where I think you might want to reconsider. One thing you might try is to generate some drop tables using your ballistic calculator of choice, inputting increasingly small range increments out to some maximum distance, say in 10 yd increments from 100 yd down to ten yd. I think if you do this you will find that you reach a point pretty quickly where the change in drop is smaller than you could ever reasonably hold. That increment is likely to be in the range of ~25 yd or so. If the change in drop over that increment is less than the best that the shooter and weapon system could reasonably manage, then what is the purpose of generating drop data more accurate than the shooter/system? You won't be able to take advantage of it even if you have it. It's all about limiting (biggest) sources of error.

 

[[email protected]]

Before I got a G7 BR2 range finder, i used to use excel and print out a card for 25 increments to 700 yards. I knew i could shoot further, but without being able to calculate angle, pressure, and temp I just didn't feel comfortable shooting that far at an animal..i do know though

Its really not that hard to get out to 700 yards in 25 Y increments on a scope cap, if you have good eyes. I used a 5.5 font.

 

[LRRPF52]

The formula will change depending on one large variable: barometric pressure with a temp sensitivity factor. Modern hand-held ballistics apps have changed the practical effective range of riflemen who are able to exploit their Weapon-Optic-Mount-Ammunition-Accessory system.

I grew up with a physicist for a father, who was literally working at the Rocket lab on Edwards AFB when I was born. Physics is his lifelong passion, not just a skill set. There hasn't been a day gone by of my childhood where I didn't hear the term, Partial Differential Equation. That is what the OP is asking, and I can assure you, your data card on the stock with 20yd increments will be much smaller than the equation. You will also need some type of instrumentation to measure barometric pressure and temp, otherwise, 500yds is your cut-off for maximum ethical hunting with just a drop/drift chart, and that's for someone who has married the system, registered a shot beforehand, and has a great deal of experience reading and accurately calling the wind.

 

[Analytical Rifleist]

While interest in this thread may have waned in the months gone by, I would like to note there is a two equation formula for drop posted on my web site, Trajectory Parameters - The Analytical Rifleist. It relies on the velocity parameters describing the bullet trajectory which can be acquired several ways.

 

[p_pops]

[MENTION=93331]Analytical Rifleist[/MENTION] - Interest in the thread might have waned because people likely realized the OP was disingenuous with his post.

"I DO, however, want the projectile drop formula for my own reasons."

This sounds like someone who wants to build their own ballistics software but has no clue as to what it is they desire to attempt. There are dozens of books on the science of ballistics the OP could have checked out and read. In fact, the OP never posted again after AMOKI mentioned that you can download the source code for the JBM engine if one was so inclined. So, searching for 3 hours every day for a week (21 hours!!!!) and not running into the JBM site and the mountain of information regarding the required calculations....Well I call BS on the OP.

The 20 or so detailed responses you all gave this bogus poster are why I love this site though. So many people are willing to help.

 

[Analytical Rifleist]

p_pops -- Thanks for the note. I suspect that for every one who is motivated enough to actually do a post, there are dozens who are interested, so nothing gets "wasted".

 

[p_pops]

[MENTION=93331]Analytical Rifleist[/MENTION] - So, I noticed this written on your website:
"Neither drag functions nor ballistic coefficients are used. Dispensing with drag functions is possible because of modern radar based velocity measurements. Velocities which required calculation in the past can be and are now being measured directly."

I guess I don't understand the comment. Why do radar based velocity measurements allow the dispensing of the drag functions? Surely from a design perspective it would be good to simulate your expected results and then verify them using actual measurement data. While the drag functions may have been used in the past to provide insight into what the actual limited data we were able to measure meant I would think those approximations could now be used on the front end of the process to help influence design.

 

[Pinecone]

Because with drag equations, you are estimating the velocity along the path. With radar, you are actually measuring it. You KNOW the change in velocity.

And drop is based on time. And velocity along the path, tells you how long it actually takes the bullet to get to the target. Or with radar, you can figure out the exact time of flight for a given range.

All the equations do is estimate that for you.

 

[Analytical Rifleist]

Pinecone: You have the basic idea. More accurately, drop is based on both time and drag; drop is less than1/2 GT^2 from the factor (V/Vz)^.3

 

[Analytical Rifleist]

p_pops: If you are designing bullets or guns, you definitely need drag functions. If you are shooting, most all the information you need is what is on the back of the box these days along with a way to find your muzzle V. I don't see a way around some sort of calculator, but it doesn't have to be be connected to anything or used any stored data.

 

[Analytical Rifleist]

I should add that what has changed over years is that bullets today are mostly all stable for much of their trajectory and at high speed have a simple V(S) profile so it is possible to do the trajectory "bookkeeping" in a way that was not possible in and around Mach 1.

 

[p_pops]

[MENTION=93331]Analytical Rifleist[/MENTION] - You've confirmed my thought. It's basically what I've seen in other industries. For example, we used to estimate heat dissipation over a circuit board and had fancy formulas. Then the data from the formulas started to get confirmed by more advanced measuring tools. Now modeling tools that implement the new improved formulas are used and can give you great simulations to show heat dissipation across the entire surface of the board. It's really had a radical impact on how we design boards.

It's an analytical maturity to the industry that's progressing. Data->Information->Knowledge

In each case I've seen this maturity occur in an industry the technology advances seen in the industry quicken. It's my layman's measuring stick to know we're likely to see a dramatic improvement in a potentially radical way to projectile construction and design.

 

[Analytical Rifleist]

p_pops:

"It's an analytical maturity to the industry that's progressing. Data->Information->Knowledge"


I think W. E. Deming called this "profound knowledge".


The next generation of devices is being constructed, and may already exist someplace. It will give both velocity and trajectory info non-destructively. This will give the amateur some serious data to think about.

http://www.coe.montana.edu/ee/rmaher/publications/maher_aac_0406.pdf


AR

 

[Strykervet]

I'm in a unique situation for this thread. I was an SDM instructor and afterwards I went to university for math. Father was mathematician and engineer too.

Shooters: use a computer.

Mathematicians: CAN write it out, BUT use a computer.

Wanna be a shooter or a mathematician? Either way you'll end up doing the same thing.

That's how it works in the real world. I can do it by hand, but I studied math at university for years. When I need to do this kind of shit, I use the computer. I compile what I learn from that and experience into a dope book so it become instinctual. I don't think about shit when I'm shooting, it's more of an art to me than a science because the science is too complicated for our weak brains in the time allowed.

I CAN setup a shot, one shot, take data, work with that and then calculate within error every permutation of that shot. But I've got better things to do like pulling pud.

I've never had time to calculate multi-var partial differential equations under stress (1 hour, 2 question analysis tests were hard enough in the math library with the clock ticking).

I'm a good shot, and I can work equations too. But there are some dumber than dogshit folks on this very site that I'm sure could shoot me under the table. That's how I know it's an art.

Good luck, the math and physics is enlightening and well worth learning, but not just to put lead on paper.

 

[Analytical Rifleist]

Don't get me wrong, James....Bob McCoy left us with a work of art before he passed, but unless the OP has some sort of math/computational background and can write a numerical solver for coupled, non-linear, -----

If it actually exists, I love to know about it myself.

K2 Are you still interested these many months later?
Velocity profiles decouple the equations.
AR
P.S. I agree with your comment about McCoy's book