Engineers in here? Need help w/ ballistics formula

[BigChongus 765]

Any mechies/physicists/ballistics-gurus feel like hooking another mechie up? Here's the deal...

 

http://www.ar15.com/media/viewFile.html?i=32939

 

I'm making a MATLAB program to run the above formulas, and so far it's dandy except I have no idea what R₁ (range other than that which the rifle is zeroed at), and it's required to find the final trajectory. Anyone have any idea what that is and how to calculate it? As far as I can tell it's a variable whereas R₀ is a constant, Making EL₀ constant for all ranges while EL₁ changes. I've tried every possible derivation possible for a relation between R and R₀ to obtainR_1, but it seems completely random. Here's my code if anyone feels like screwing around with it. In this case it's a .22LR Remington Golden Bullet:

 

 

c1 = 0.1384; % ballistic coefficient of bullet

mv = 1255; % velocity at muzzle

hs = 1.5; % sight line of bore axis in inches

r = input('Enter range from target--> ') % range actually fired from

r0 = 50; % range at which rifle is zeroed

r1 = ?????

RV = (sqrt(mv) - ((0.00863*r)/(c1)))^2; % remaining velocity

K = (2.878)/(c1*sqrt(mv)); % simplifying variable

TF = (3*r)/(mv*(1 - 0.003*r*k)); % time of flight

F = 193*(1 - ((0.37)*(mv - rv))/(mv)); % simplifying variable

DR = F*(TF^2); % bullet drop

MH = (48.6*TF) - (0.4*HS); % heigh of trajectory over sight line

EL0 = (100*(DR + HS))/(r0); % required elevation for r0 (MOA)

EL1 = (100*(DR + HS))/(r1); % required elevation for r1 (MOA)

BP = ((EL0 - EL1)*r1) / 100 % calculated trajectory

At 10-100yds in increments of 10 yards when zeroed at 50yds, BP should be the following:

-0.7in -0.14in 0.18in 0.23in 0.00in -0.49in -1.24in -2.34in -3.8in -5.5in

I realize that this is a pain in the neck, so thanks in advance for any help.

[Big John! 2,062]

2

[DLT 1,646]

Dude, I haven't worked vectors in over 25 years. But since the boy is entering high school this year, I guess I better brush up. Of course, you got a hell of a lot more variables going than just your standard distance, velocity, weight, gravity, windage....

[storm6490 2,768]

ArfCOM? matthew 7:6!

[magsite20 1,664]

I just use this one:

 

http://www.hornady.com/ballistics-resource/ballistics-calculator

 

being able to do the math is great but ease of use is cool.

[BigChongus 765]

I'm doing this for a lab project for an engineering statistics class at my college, so I need to show how I obtained everything

 

Good news is, I found a better formula that makes EL₀ and EL₁ obsolete, so for those interested:

 

Bullet path = (DR - hs) + (r/r0)*(hs + yz), where all variables are the same as before and yz is the drop at the range zeroed (which in my case is -3.1094). Positive values are above the line of sight and negatives are below.

Edited May 6, 2013 by W8lifter

[XD45 7,124]

Sorry, I was in tanks. We just point and shoot. Ask the arty guys...

[Juggernaut 11,054]

I'll ask my son, He's smart!

[thebuns1 4,323]

Ive always used this for the 5.45.

http://www.ada.ru/Guns/ballistic/545x39/index.htm

[Big John! 2,062]

So 2 was the wrong answer?

[BigChongus 765]

So 2 was the wrong answer?

 

Just off by a little bit. Gave a 100in drop at 100yds lol

[Trespasser 7]

I don't think you will find your answer as R1 is supposed to be an input. What I don't understand is the difference between R and R1. They both appear to be used as a distance variable.

 

Also, there must be some approximation going on. The only equation which R1 shows up is in the bullet path. It takes a elevation in minutes of angle times a distance in yards and divides by 100 for a distance in inches? At first I thought R1 might equal R, but in different units.

[Voltia 375]

Oh my God. That makes my head hurt. Holy unnecessary magic coefficients and variables, Batman.

 

See, this is the problem with throwing magic formulas out there, and not TEACHING. I've got some engineering

degrees, I've even taught ballistics, and that shit is crazy. It takes me 30 seconds to even figure out what they

are trying to say.

 

I'll work on this more a little later on, but, to answer the original question, that last equation is this:

 

BP= ((EL0-EL1)R1)/100

 

What that IS, in English, is the amount of drop is equal to the MOA difference, times the range at which you are shooting,

divided by 100. The 100 is there to simply drop your yardage down to a multiple.

 

This means that, at 200 yards, if you need 4 more MOA, your drop is 8 inches more. It's a retardedly overcomplicated way of doing it.

Ideally, you'd have separate equations, and end up with Drop = DeltaMOA*YardageMultiplier, where you'd define the deltaMOA

and the yardagemult, eslewhere.

[RED333 1,025]

WAY OVER MY HEAD, I just shoot and sight in as needed.

[Big John! 2,062]

[jerry52 893]

I think it is a variable in the formula to plot the drop on a graph, R1 is a value that is compared to (R or range zero)

[Conscript 99]

[Voltia 375]

I think it is a variable in the formula to plot the drop on a graph, R1 is a value that is compared to (R or range zero)

 

 

That makes sense. This would plot an exponential curve of the drop over range.

[Big John! 2,062]

I think it is a variable in the formula to plot the drop on a graph, R1 is a value that is compared to (R or range zero)

 

 

That makes sense. This would plot an exponential curve of the drop over range.

Duh... I posted a pic of the exponential curves for the dumbasses on the forum.

[breid1970 327]

Made my brain hurt.

[Voltia 375]

I think it is a variable in the formula to plot the drop on a graph, R1 is a value that is compared to (R or range zero)

 

 

That makes sense. This would plot an exponential curve of the drop over range.

Duh... I posted a pic of the exponential curves for the dumbasses on the forum.

 

Yes you did, Professor.