Algebreic formula for ballistic charts?

[SA Friday]

Ok, so I'm sitting on the crapper this morning thinking deep thoughts and started thinking about algebraic formulas to determine a ballistic table. It can't be overly difficult, you know like requiring a super computer or something alongs that line. It should be reasonably done on paper.

The variables would be the bullet's mass, the ballistic coefficient of the bullet, the muzzle velocity, and your scope's zero. Essentially the bullet produces a very flat parabala (with the scope's zero being an x-axis intersect or possibly two), and is predictable as long as the variables don't change. The arc of the parabala would also be effected by gravity, but that is a constant effect so once factored into the equasion, is constant for every ballistic chart.

What I can't figure out is how to factor in the decelleration of the bullet based on the BC. I have no idea how to do that. I'm pretty sure every bullet will vary due to their profiles and differing friction levels with the air. Also, is the decelleration compounding or constant?

Anyone have insights into this? Ultimately, if you had the equasions, you could plug in any of the variables and determine your ballistic charts without having to lug around a laptop and purchasing software. I think you could even program it into a TI-83 or 84 or PDA and do the math very easy every time.

[BuffCyclist]

Checked out this page on Wikipedia:

http://en.wikipedia.org/wiki/Trajectory_of_a_projectile

I just read halfway down, there are a few derivations for the trajectory of a projectile with air resistance. However, having it be an algebraic equation and not involving calculus, might be a whole different story. Unless of course you are fine with calculus in which case hope that helps!

And it seems as though the "force of air resistance is proportional to the square of the particle's velocity". That might be where you're having problems.

I don't see why you wouldn't be able to program it all into a graphing calculator as a program, though the main issue that I would see is having to set up the firearm and get the exact orientation and angles.

edit: That math isn't all that hard, so if you need help understanding any of it let me know.

[MarkCO]

Yeah, I do these calcs occasionally.

If you have a college Physics book, look up 2-D projectile motion. You will end up with 4 equations (horizontal and verticle velocity and horizontal and verticle position. To use these, you need to know original angle and velocity. But these assume no air drag.

So, break out the Fluids book and get into computational Fluid Dynamics. The BC impacts the acceleration rate (which in the case of a bullet will be a negative number) in a given fluid (air). These are generally based on STP (Standard Temperature and presure, or 59F and sea level) but do not account for grains of water/pound of air, so really, they are useless. So you are now adding to the Physics 2-D equations.

So now we break out the Thermo book. Using Pv=nRT, we can assume a system around the bullet (1 cubic foot is sufficient), and calculate the pressure and temperature modeling the bullet as a piston. Then we get to derive an approximate shape factor for the range of velocities during the time of flight. If we use 100 fps intervals, that makes it a lot easier. In the back of the Thermo books are a bunch of charts, you will need 3 of these as well.

So now...oh forget it. Just go look it up...

This site: http://www.jbmballistics.com/calcula...ulations.shtml

Has the only calculations that I have been able to verify by both shooting and calculations. Make yourself some range cards and stop thinking while dumping. You never know what might come out, or maybe you do.

[rhineoshott]

Also, I would be curious as to an equasion to find muzzle velocity based on barrel length for diferent cartridges.

[MarkCO]

Checked out this page on Wikipedia:

http://en.wikipedia.org/wiki/Trajectory_of_a_projectile

edit: That math isn't all that hard, so if you need help understanding any of it let me know.

Which frankly is all accurate, but totally unrealistic and therefore worthless. Those are the equations you get from a physics book but they do not account for the shock wave, the compression of the fluid, and all the other necessary variables. Those equations will give you only "academic" values which can not be replicated in the actual exterior ballistics.

I had a 35 year veteran Police CSI forensic specialist babbling incoherently after proving to him that everything he had testified to in court for the past 20 years was totally inaccurate. Kind of sad really.

[BuffCyclist]

Which frankly is all accurate, but totally unrealistic and therefore worthless. Those are the equations you get from a physics book but they do not account for the shock wave, the compression of the fluid, and all the other necessary variables. Those equations will give you only "academic" values which can not be replicated in the actual exterior ballistics.

I had a 35 year veteran Police CSI forensic specialist babbling incoherently after proving to him that everything he had testified to in court for the past 20 years was totally inaccurate. Kind of sad really.

But it's a starting point for him. I rarely found the physics equations on wikipedia to ever be correct 100%. In order for the OP to get this programmed into a calculator (or on a piece of paper) he'd need a good starting point and background of the subject. I didn't really think about the fluid dynamics of it, but LOTS of equations go into play when shooting small objects, really fast at a small target. This is why it takes real skill to be a remarkable sniper, and it requires a deep understanding of physics and high-velocity objects.

[SA Friday]

No, I get it. I knew it would lead off into physics, but I never thought of some of what Mark was talking about. Hydro and thermo dynamics were not in my thought process at all.

OK, I'm going to wait till I'm done with my physics class to tackle this one.

I'm finding some of this stuff just totally cool, and considering I'm working for a degree in Criminalistics, I will eventually need to rully understand this info. I would just as soon not have Mark make me look like a retard on the stand.

[MarkCO]

True, but the point is, the exact accuracy in the calcs is NOT going to occur in field conditions.

Go look at the wiki part of the link on air resistance and see how far off the pure physics approximation really is. When you add in the variables of environmental temperature, humidity and pressure, you get another significant change, but less than air density. Now add in the Fluids and Thermodynamics variables and it is another, albeit less significant change. The actual variation based on a properly sighted in rifle shooting ammo with a velocity SD of 5 fps or less is smaller than the change based on the calcs.

I derived my own set of formulas in grad school for 5000 and 9000 feet for a .30-06 with a Berger VLD at 2700 fps and interpolated between them for elevations between those. It took 3 months. My POI and POA based on my math at 5000 feet with a measured PTH as compared to 9000 feet with a measured PTH was 1.3" at 500 yards (no wind). No correction resulted in a difference of 9". It was wearisome, but, I learned some tricks I otherwise would never have discovered, or even thought of, had I not been trying to replicate conditions. Like air duster up to bore to bring down barrel temperatures, and a microtorch to bring them up. Shooting over range with precision is not easy. Understanding the contribution of variables is not easy either.

I also found that almost every rifle is really capable of 1-2 MOA if you eliminate or properly account for all variables. Unfortunately, can't be done repeatedly. Once you fire one round, the conditions in your rifle and the path of the bullet have changed and will not reliably return for several seconds along the flight path and many minutes at the rifle. This is also why I beleive in the heat sinks on high fire rate rifles and how I proved to myself that fluting is not really benefiicial to pure accuracy.

[MarkCO]

I would just as soon not have Mark make me look like a retard on the stand.

For the record, I have never made anyone look like a retard, I just focus the lens so others can see it better.

[SA Friday]

So now...oh forget it. Just go look it up...

This site: http://www.jbmballistics.com/calcula...ulations.shtml

Has the only calculations that I have been able to verify by both shooting and calculations. Make yourself some range cards and stop thinking while dumping. You never know what might come out, or maybe you do.

wow, this thread was worth it for just this site.