Complex ballistic formula?

[jbm]

Ahh YES.

You have decompiled them to look?

I actually have.

The tables are usually easy to find in a hex program listing.

The seven degree of freedom software (search on 'aeroballistics') is touchy stuff (I use it also).

It often takes days of tweaking to get it to come close to the tables, and they are measured truth.

Ahh NO. At least not my solutions. I don't have to "decompile" then to look. (Have you "decompiled" my solutions? If so, how did you get them?) I've been doing integrated solutions for more than 25 years. Yes, there are tables, but they are tabulated values for the drag functions. That is used to calculate values for the derivatives. You can find the equations here:

http://www.jbmballistics.com/ballistics/topics/cdkd.shtml

and the tabulated values for drag functions here:

http://www.jbmballistics.com/ballistics/downloads/downloads.shtml

I've also done integrated solutions on microcontrollers (PIC and FreeScale) with no problems. It takes less than 0.1 seconds to get an integrated solution to 1000 yards on a PIC16.

Computers and hardware have come a long way in the last 30 years...

Brad

 

[wharvey]

Eons ago (1980-ish) TAR published a ballistic program written in BASIC. Yes it used lookup tables and information from Hatchers notebook. I painfully typed it into my VIC-20 that had an ASR-33 teletype as a printer.
You could start a program listing, eat dinner, and it would still be printing after dessert. But it did work.

I remember that program. It was slow on an old XT but not too bad, nothing like your VIC20 experience. In fact it was quite fast after translating to C and running the compiled version.

As another poster said, the tables were for changing factors as velocity changed, not ballistic tables. There was one equation and about 6 coefficients that change. Near the speed of sound these changes happened every 10 fps.

 

[Zak Smith]

Excellent info, Brad.

 

[Clark]

JBM,
You made me think for a second.
It was awful.
I jumped away from computer and saved myself.

 

[Strykervet]

If you are really interested in this, you can get a decent book on basic physics, say good thick one that covers, in particular, mechanics 101 and 201. There are a lot of good ones on Amazon, and older editions are pretty cheap and fine for what you are doing (none of the physics has changed, they just juggle the problems and change those around so you have to buy a new book every couple of years --a greed scam, really).

Anyway, those books will have the trajectory equations in there that are easy to understand. It will have the energy equations, force equations, how they all relate, etc. The math you'll need to figure them out will most likely be present in the demonstrations in the book. If you took any calculus at all though, you should have no problems with these equations.

If you are interested enough, you can enroll in your local community college and study algebra, calculus, physics, etc., whatever you want, and get a transfer degree to a university. Just make sure to "upgrade" your GI Bill before you get out, because if you don't, you'll end up owing money every quarter. If you get injured, the VA will pay for it all. But make sure you use your college when you get out, I really had a blast! Great way to unwind after the army and get back into society, it really is.

Now if you want to add a lot of variables into the equation, you could end up with a differential equation that will take a lot more knowledge in mathematical kung fu and time with paper, pencil, and TI-200.

Still, being able to figure it out and knowing where it all comes from is enlightening. I majored in mathematical analysis and studied mechanics, my favorite area of physics. But when I go to the range, I have most of the basics of this in my head, I don't actually do any figuring, rather I just zero the rifle.

Usually what I'll do is look at the ballistics table for the round I'm using and go off that as a general idea. So I cheat. I also use a dope book to collect zero and range data when I shoot, so I'm constantly refining the zero for a particular weapon based on conditions. It would be impractical to do this mathematically.

 

[Strykervet]

Thanks all for posting. Yes, I would rather go to the range & zero, but my unit doesn't get range time. Yes, I'm in Iraq, and yes, it would be really nice to get range time, but no, it's not going to happen.

The zero range is relevant, as my adjustable sight cam is set for the 62 gn SS109 bullet out of the M4 carbine w/ the 14.5" bbl, based on a 300m zero. Yes, we shoot @ 25 yrd to approximate the 300m zero, but I'm trying to approximate the 300m zero w/ an admittedly inaccurate laser boresight. My eyes are not good enough to hold above or below @ even 25 m - I tried that - so I'm looking for an exact distance to place the rifle & check my sights. Given that the distance has to be calculated, it would be handy to have the formula IOT use it again someday. I take it there is no el neato formula available - it just has to be sussed out from ballistic calculators, which I have to learn how to use.

Farmers Fight!

backbencher

Thanks for your service. I appreciate it and I hope you and your unit are doing fine.

If the boresight works and you have the book, you can get a decent better-than-nothing zero using the boresight and a dark room with the 25m target at 25m. You'll need to sercure the rifle real well so it doesn't move at all though. I've done this and had varying results, usually they would group off to one side or another several inches from POA. The boresight is really just to get you on paper before you go zero at the 25m range.

It isn't for the PEQ or PAQ lasers either, although I know the army likes to think they are --those are supposed to be zeroed at 300m using steel targets and tracers if need be. But that is why soldiers think they don't work, that they are junk. They are a true line of sight and if done right, they are super accurate from the hip with NODs at night.

There is an infintely better way to zero that rifle, but we can't go into it here, the army doesn't provide the training, and you probably can't get the KD ranges you'd need.

Unless you can get that thing down to a range to get a good zero, you are kind of screwed. But I bet if you go to the ranges and ask around, find a cool unit, someone will let you zero on their range. Hopefully, God knows you need a good zero right about now. Good luck!

 

[backbencher]

So...

I think what I'm looking for here is the angle of the bore relative to the sights. The sights are dead level, pointing out to a spot 300m distant (328 yds). They are, on a M4 flattop, until I get a better #, 2.6" above center of bore. We have a calculated trajectory, courtesy of Applied Ballistics' Point Mass Ballistics Solver 2.0, down to the hundredth of the inch, based on the G7 BC & a MV of 2900 fps. So for that trajectory, what should the angle of the barrel to the ground be, b/c that will determine the distance to boresight the rifle. Anyone's ballistic calculators figure that one?

Farmers Fight!

backbencher

 

[Zak Smith]

The distance where the trajectory intersects the sight line the first time is the first zero. You get this from the ballistic calculator.

The angle between sight line and the bore (ie same as angle between ground and bore) is used internally by all of them. Off the top of my head I don't know if any of them print it out. I can determine it using my program, but it's not useful for anything.

 

[wombat13]

Backbencher, thank you for your service. I believe it is theoretically possible to do what you want to do, but it may not work very practically. Let me rephrase what you want to do and please tell me if I am correct.

If one holds the rifle so that the sight line is perfectly level, the bore line is slightly inclined. This slight incline is what gives the bullet an upward trajectory. The trajectory of your ammo should be such that a 25m zero is the same as a 300m zero. The bullet crosses the line of sight twice at 25m and at 300m.

At the instant that the bullet exits the barrel it is traveling exactly along the bore axis (in theory; this ignores any effect of barrel vibration). Gravity immediately begins pulling the bullet down causing it to deviate from the line of the bore axis.

Therefore, if we know how much lower the bullet would be than the bore axis at 25m we should be able to use a bore sighter to sight in.

As an example, I have developed a spreadsheet that calculates the trajectory for the hunting loads that I use. If I zero my rifle (sight height 1.5") at 100 yards with the 180 gr Federal Fusion .300 win mag load, the required angle between the bore axis and the sight line is 0.0558 degrees. Using that angle, I find that the bullet will cross the sight line twice; first crossing will be at 71 yards and the second at 100 yards. In other words, the bullet will have risen 1.5" above the muzzle at 71 yards. The line of the bore axis will be above 1.5" at 71 yards.

What I need to calculate is the distance at which the bore axis would be 1.5" above the muzzle. I can calculate this distance using the tangent of the angle. If I divide 1.5" by tangent (0.0558) I get 42.8 yards. So, if I zero my rifle using a bore sighter at 42.8 yards my bullet should be zeroed at both 71 yards and 100 yards.

So here is what I would need to know to do the same calculations for you:

1. Sight height on your M4
2. Velocity data for your ammo out of an M4 at several distances, e.g., muzzle, 25m, 50m, 100m, 200m (this is how I calculate the time of flight of the bullet for with out using the BC of the bullet).

This data will allow me to calculate the angle between the bore axis and the sight line for a 25 m zero in your rifle/ammo combo in my Excel spreadsheet. It is then simple trigonometry to figure out the distance you need to use the bore sighter.

Please note: I did all of this as a mental exercise for my rifles because I enjoy physics and building mathematical models in Excel. These calculations are interesting, but they are not good enough for the men at the sharp end of the spear. You and your brothers-in-arms really need time at the range. If the velocity of your ammo/rifle combination differs from the published data these calculations will be inaccurate. Vibration in the barrel could induce error as well. There are probably many other sources of error.

 

[wombat13]

So...

I think what I'm looking for here is the angle of the bore relative to the sights. The sights are dead level, pointing out to a spot 300m distant (328 yds). They are, on a M4 flattop, until I get a better #, 2.6" above center of bore. We have a calculated trajectory, courtesy of Applied Ballistics' Point Mass Ballistics Solver 2.0, down to the hundredth of the inch, based on the G7 BC & a MV of 2900 fps. So for that trajectory, what should the angle of the barrel to the ground be, b/c that will determine the distance to boresight the rifle. Anyone's ballistic calculators figure that one?

Farmers Fight!

backbencher

I wrote my previous post before reading your post quoted here. If your sight height is 2.6", then I need the ballistic trajectory info you have. Give me all of the data you have calculated from the ballistics software. In particular, I need the velocity and bullet rise at the muzzle, 25m, 50m, 75m, etc. (or the muzzle and whatever distances you have calculated).

 

[Zak Smith]

There is no need for anything other than what the ballistics calculator outputs directly.

Simply pick the distance you want the bullet to be from the line of aim at the "boresight distance" and pick the range from the printout where that's true. That's the distance to boresight the rifle.

 

[backbencher]

Wombat, you're tracking. Zak, et al, here is the problem. Whatever distance we want to zero the rifle at, the bullet travels a curved path to get there. Our line of sight is straight; our boresight, either through the barrel, or via a laser, is straight. Ergo, whether we want to zero the rifle at 300 yards, or 100m, or 50 arshins, the line of sight and the boresight will intersect at a point above the trajectory of the bullet at that distance. As many ballistic programs will output in yards, I think what I'll do is take the rise in the 1st yard, & calculate the angle from that.

Yes, yes, we all need time @ the range, but btwn the budget, my night shift, & packing to leave Iraq, it won't happen. Rest assured it does happen for those whose business is outside of the wire. For those of us who don't, this might be a handy formula.

Wombat, if you rerun your trajectory @ 1 yard intervals, & take the drop from the 1st yard, now what is your angle & your boresight distance?

FF!

backbencher

 

[Zak Smith]

Zak, et al, here is the problem. Whatever distance we want to zero the rifle at, the bullet travels a curved path to get there. Our line of sight is straight; our boresight, either through the barrel, or via a laser, is straigh

Doesn't work.

Proof: changing muzzle device will usually change zero (point of impact at zero distance) a noticeable amount. A bore sight has no concept of the muzzle device. QED.

Also, a bore laser typically has too much slop to be very precise.

At close range (25-50 yards), there is little deviation from a straight line so you can bore sight at 25 or 50 and be reasonably close.

 

[wombat13]

Wombat, you're tracking. Zak, et al, here is the problem. Whatever distance we want to zero the rifle at, the bullet travels a curved path to get there. Our line of sight is straight; our boresight, either through the barrel, or via a laser, is straight. Ergo, whether we want to zero the rifle at 300 yards, or 100m, or 50 arshins, the line of sight and the boresight will intersect at a point above the trajectory of the bullet at that distance. As many ballistic programs will output in yards, I think what I'll do is take the rise in the 1st yard, & calculate the angle from that.

Yes, yes, we all need time @ the range, but btwn the budget, my night shift, & packing to leave Iraq, it won't happen. Rest assured it does happen for those whose business is outside of the wire. For those of us who don't, this might be a handy formula.

Wombat, if you rerun your trajectory @ 1 yard intervals, & take the drop from the 1st yard, now what is your angle & your boresight distance?

FF!

backbencher

Here are the parameters that affect the bore sight distance:

1. Sight height - The higher the sight height, the greater the upward angle of the bore.
2. Zero range - The closer your first zero distance the greater the upward angle of the bore.
3. Muzzle velocity - Faster muzzle velocity means less drop at any given distance and a lesser upward angle of the bore is required.
4. Bullet BC - Higher BC means the bullet will maintain velocity better which means less drop at any given distance and a lesser upward angle of the bore is required.

The spreadsheet I developed does not use bullet BC. Instead it uses published distance/velocity tables for a given bullet/load. This works quite well for factory ammo that has published data. It should also work if you have velocity/trajectory data from a ballistics program.

My spreadsheet does calculate all of the values in 1 yard increments, but my data would be useless for you because the parameter values for all of my rifles are different from yours. I could easily set the spreadsheet up in metric to answer your question, but I need the following data:

1. Sight height - you state is 2.6"
2. Velocity and at the muzzle and several other distances (e.g., 25m, 50m, 100m, 200m, 300m, etc.)
3. Bullet rise at all of the same distances (I use this to check that the spreadsheet is working properly).

I would be happy to set the spreadsheet up and will e-mail it to you when it is done if you can send me the necessary data.

 

[backbencher]

Zak,

Why be reasonably close when we can be exactly close? Ok, we can't compensate for the flash hider. Got it. Some of us are not satisfied w/ "aim @ this point 25m away & move your sight up 1/2" when it could be "adjust your sights to the dot @ 3.25X+32.7cm(sq rt mv)"

wombat,
I think we're on the same page now. I can figure my angle from the ballistic calculator based on the rise in the 1st yard. I have to confirm the sight height of the M4 BUIS set to 300m, & have to ping a few folks so I can pick a MV # bwtn 2900 & 2970 fps.

Farmers Fight!

backbencher

 

[Zak Smith]

You can't be exactly on based on theoretical math alone because of muzzle device, barrel/rifle vibration/harmonics, and crown.

There is exactly nothing wrong with setting a zero at a given distance and then making an adjustment (ie "aim @ this point 25m away & move your sight up 1/2") because that's precisely how we dial the long-range data on precision rifles.

 

[backbencher]

Zak,

Good, good. What is the adjustment @ 25m for M855 from an M4 carbine w/ the issue BUIS?

Farmers Fight!

backbencher

 

[Zak Smith]

M4/M855 @ 2907
Z 25m  2000'DA
RANGE  ELEV-  moa    mil     | WIND(10) moa   mil   RANGE
  25    0"    0.00  -0.0mil  |   0"   0.25   0.1mil   25
  50   -2"   -4.00  -1.2mil  |   0"   0.50   0.1mil   50
  75   -4"   -5.00  -1.4mil  |   1"   0.70   0.2mil   75
 100   -6"   -5.00  -1.5mil  |   1"   1.00   0.3mil  100
 125   -7"   -4.70  -1.4mil  |   2"   1.25   0.4mil  125
 150   -8"   -4.50  -1.3mil  |   3"   1.50   0.5mil  150
 175   -8"   -4.00  -1.2mil  |   4"   1.70   0.5mil  175
 200   -8"   -3.50  -1.0mil  |   5"   2.00   0.6mil  200
 225   -7"   -2.70  -0.8mil  |   6"   2.50   0.7mil  225
 250   -6"   -2.25  -0.6mil  |   8"   2.70   0.8mil  250
 275   -5"   -1.50  -0.4mil  |  10"   3.00   0.9mil  275
 300   -2"   -0.70  -0.2mil  |  12"   3.25   1.0mil  300
 325    1"    0.25   0.0mil  |  14"   3.70   1.1mil  325
 350    4"    1.00   0.3mil  |  16"   4.00   1.2mil  350
 375    8"    2.00   0.6mil  |  19"   4.50   1.3mil  375
 400   13"    3.00   0.8mil  |  22"   4.70   1.4mil  400

If you have a 25 meter zero with a M4 shooting 2900 fps at 2000' Density Altitude, then come up the number of MOA in column 3 to establish a zero at any other distance, e.g. to transform to a 175 yard zero add -4.0 MOA to your zero, IE, come down 4 minutes.

 

[backbencher]

I'm not tracking what you think the boresight should be @ 25m to match a 300m zero.

 

[backbencher]

The formula is B=(I*H)/R, where:

H is the height above center of bore of the center of the rear sight aperture
R is the rise of the bullet in the 1st increment of the calculated trajectory
I is the distance of the 1st increment of the trajectory from the muzzle
B is the distance where the boresight and the line of sight are coincident.

Using the following assumptions:

M4 BUIS sight height set to 300m - 2.6" (may change on receipt of further information)
A G7 BC of .154 from Applied Ballistics for Long-Range Shooting, by Bryan Litz
A bullet weight of 62 gn from the NATO specification
A MV of 2900 fps (may change on receipt of further information)
A 300m zero from Army doctrine
The ballistics calculator @ http://www.jbmballistics.com, using 1m increments.

We get a boresight range of 28.43389 yards, or 26m, given the above assumptions. It looks like JBM's calculator gives the bore angle as well, which would add to the accuracy of this calculation. An alternate calculation, then, would be B=H/TanA.

Farmers Fight!

backbencher