Range Report Elevation Adjustment Formula Question

[bbpl]

Hey guys, i dont know if this is the right place to put this but her it is anyways. So ive been going crazy trying to find a formula in which i can figure out how to adjust my elevation when im shooting at a target, but cant seem to find anything. The only two variables that i have is the distance to the target "d" and the bullets speed and weight. Pretty much what i want to figure out is say i have a target at 500yds, and my ZERO is at 100, what is the formula to figure out how much will that bullet drop at that distance in order to know how much ill have to adjust my elevation by, and without taking any air resistance in too consideration. Im shooting a .308 150gr cartridge at 2820fps. So just the formula to figure out how much that bullet will drop at 500yds from my ZERO, or any distance, and the formula to figure out how many MOA's to adjust due to the drop.

thank you

and if there already is a topic on this, please direct me to it, i tried searching for it but couldnt find anything

 

[Topstrap]

Re: Elevation Adjustment Formula Question

There are a lot of variables that go into that equation, it's a whole lot easier to put all your info into this program and it'll tell you what you need to know. Good info in... good info out. I'd not be afraid to shoot a match just based on the information JBM gives me for any particular day and distances.

http://www.jbmballistics.com/cgi-bin/jbmtraj_simp-5.1.cgi

Topstrap

 

[mattj]

Re: Elevation Adjustment Formula Question

OP: If you're asking for actual shooting purposes, do what Topstrap said. The "no-friction projectile motion" problem is of no use for any real-world scenario.

If you're asking because you're trying to get us to do your high school physics homework problem for you, shame on you for checking out the blonde girl during instead of listening during class...

 

[bbpl]

Re: Elevation Adjustment Formula Question

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: mattj</div><div class="ubbcode-body">OP:
If you're asking because you're trying to get us to do your high school physics homework problem for you, shame on you for checking out the blonde girl during instead of listening during class...

</div></div>

Hahaha no, im already done with physics and ended the year with an A+ in the class so im good, but i did stare alot at this really hott chick, who was in fact blonde lol, but back to the subject, i was asking because i want to know the formula in order to do it myself, i already have an an app that tells me everything, bulletflight, its from the people of Knight's Armament, i just want to know the formulas that they use in order to figure all that out, i already have all the wind and temperature formula's and how to calculate elevation by seeing how low or how high im shooting over what im aiming for, but i want the formula to be able to find the range of the target and be able to calculate how much the bullet will drop, adjust to it, and then shoot, instead of having to shoot first, and then adjusting for it, catch my drift?

 

[wadebrown]

Re: Elevation Adjustment Formula Question

Get a copy of Robert McCoy's book and a few years of calculus through differential equations, then you will have the formulas that most of the ballistics solvers start from and the mathematical background to use them. Unfortunately, just having the starting equations without the math will probably just frustrate you.

Also google for the errata sheets for McCoys's book as there are a lot of typos and McCoy died before another edition could be done. A great book even with the typos.

I have written accurate ballistics solvers but use JBM and shooter on my Android because they have a bullet library and a better interface than mine.

wade

 

[bbpl]

Re: Elevation Adjustment Formula Question

Ima have too, but here's what i have pretty much come to understand and sorta put together. the variables affecting the bullet flight without taking wind into consideration are these, H-height of launched projectile initially (7in), S-speed of projectile (2820fps), g-force of gravity (32.2 f/s^2), and R-distance traveled by projectile. Now all these variables are what make the downward flight of the bullet (except R), and how far itll go before it hits the ground, And knowing the distance it takes before the bullet hits the ground, and how much it drops per certain amount of yds or meters (every 50 or 100)will make you determine the angle that you'd need to either raise or lower the bullets flight by and therefore with that angle, at whatever distance, you can figure out how high or low your bullet would hit if it were traveling without the effect of gravity with a simple trig equation -> Angle Side Angle or b^2= c^2+a^2-2(a*b)cos"beta". So all im trying to do is figure out how to put all these variables together, and in one simple equation, where all i have to do is plug in all the variables and bamm, i know how high or low itll hit, convert it into MOA's and then into MIL's, and done, i have my elevation adjustment

 

[wadebrown]

Re: Elevation Adjustment Formula Question

You are ignoring the effects of air resistance on the bullet and your estimates will not be very close to your actual elevations when you go out and shoot. In your physics class all of the work ignored air resistance and friction. not because they did not matter, it was because the math was too involved. You may have done some labs and your data matched up real well with the predicted results, and your predicted results did not take air resistance into account.

Air resistance on an object moving through the air is highly dependent upon the velocity of the object and the faster the object is traveling the greater the air resistance. I would hazard a guess that your bullets will be traveling much faster than the objects you tested in labs.

 

[bbpl]

Re: Elevation Adjustment Formula Question

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: wwbrown</div><div class="ubbcode-body">You are ignoring the effects of air resistance on the bullet and your estimates will not be very close to your actual elevations when you go out and shoot. In your physics class all of the work ignored air resistance and friction. not because they did not matter, it was because the math was too involved. You may have done some labs and your data matched up real well with the predicted results, and your predicted results did not take air resistance into account.

Air resistance on an object moving through the air is highly dependent upon the velocity of the object and the faster the object is traveling the greater the air resistance. I would hazard a guess that your bullets will be traveling much faster than the objects you tested in labs. </div></div>

yes i know air resistance is a major factor, but what im asking for is the basic bullet drop formula. The parabolic equation of the bullet's path when gravity is the only force acting on it, i have all other wind, temp, elevation, and bc formulas, the only one im missing is the bullet drop. Bullet drop is the first formula that you have to solve for in order to know and predict how much that bullet will drop at whatever distance youre shooting at, and if you think about it, without knowing the bullet drop or "path", you cant factor any of the other variables cause there'd be no path to affect, and once you have that predicted then you can start adding all the windage, elevation, bc's, and temp formulas cause all those do is add too or take away from the bullet's drop, left or right movement, and how much farther or closer itll travel than what youre aiming at. But you have to have a starting point, or maybe better said a "control" point to start with before you take all other variable's or "independent" variables into account and start taking too and from t i wanthe "control" point --> the point where that bullet would drop or hit at whatever distance youre shooting at. and thats what

 

[CoryT]

Re: Elevation Adjustment Formula Question

f=g[1 - b (V-v/V)]

g = gravity at 32.17
b = .4 for velocities down to the first 2/3rds of muzzle velocity
V = muzzle velocity
v = velocity at range

Of course, since you don't have a drag function that will give you the velocity at the target range, you are pretty much out of luck. This is why there are ballistic tables for various drag functions. to get a meaningful answer for drop, you need to know the drag in the current conditions, so you can know the velocity decay.

Refer to 'Exterior Ballistics' by McShane, Kelly and Reno for copies of Ingall's tables and functions.

 

[Topstrap]

Re: Elevation Adjustment Formula Question

Now I know why I have that JBM printout with me, sure does save me from getting a BIG headache with all that number crunching. Quick glance at the printout comparing it with real data notes and there isn't a distance we can't be spot on.

If you enjoy the challenge, hope you find what you're looking for and can put it to good use.

Topstrap

 

[jbmillard]

Re: Elevation Adjustment Formula Question

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bbpl</div><div class="ubbcode-body">
yes i know air resistance is a major factor, but what im asking for is the basic bullet drop formula. The parabolic equation of the bullet's path when gravity is the only force acting on it, i have all other wind, temp, elevation, and bc formulas, the only one im missing is the bullet drop. Bullet drop is the first formula that you have to solve for in order to know and predict how much that bullet will drop at whatever distance youre shooting at, and if you think about it, without knowing the bullet drop or "path", you cant factor any of the other variables cause there'd be no path to affect, and once you have that predicted then you can start adding all the windage, elevation, bc's, and temp formulas cause all those do is add too or take away from the bullet's drop, left or right movement, and how much farther or closer itll travel than what youre aiming at. But you have to have a starting point, or maybe better said a "control" point to start with before you take all other variable's or "independent" variables into account and start taking too and from t i wanthe "control" point --> the point where that bullet would drop or hit at whatever distance youre shooting at. and thats what </div></div>

I've never seen a solution that started with a vacuum trajectory and applied corrections. All the ones I've seen start with the differential equations of motion and go from their (even Siacci does this).

As for the formula, you can find it here:

CD and KD

For a vacuum trajectory, just set the density to zero. Then of course, the equations of motion are just

a = g

where a and g are 3D vectors.

Brad