How to Determine Maximum Ordinate without Ballistic App

[ShooterGavon]

Robert McCoys book is the book for ballistics, I will say its not for everyone very math heavy.I have recommended to a few people that could not get through it. I believe you can download it as a pdf and read it

Have you heard of (Ballistics: Theory and Design of Guns and Ammunition- Donald E. Carlucci) ? A fella just PM'd me about it. It seems like a university level textbook for students interested in Ballistics. It's about $140.00 lol.

There were also some books on Armament and Artillery that looked very interesting, I believe in Artillery they have to deal with a lot of the questions we Distance Precision Shooters do, as artillery shells go out up to and past a mile. Idon't know about the MO or if it comes in to play, I know Coriolis does.

Bryan Litz -Applied Ballistics was decent, but more for the laymans general inquiry.

 

[dcali]

Have you heard of (Ballistics: Theory and Design of Guns and Ammunition- Donald E. Carlucci) ? A fella just PM'd me about it. It seems like a university level textbook for students interested in Ballistics. It's about $140.00 lol.

There were also some books on Armament and Artillery that looked very interesting, I believe in Artillery they have to deal with a lot of the questions we Distance Precision Shooters do, as artillery shells go out up to and past a mile. Idon't know about the MO or if it comes in to play, I know Coriolis does.

Bryan Litz -Applied Ballistics was decent, but more for the laymans general inquiry.

I have the Carlucci book. It’s pretty good, and is a little easier to digest than McCoy, but it’s still a college level text. Mccoy’s is more thorough, but more dense. Carlucci has sections on internal and terminal ballistics as well - these are not covered by McCoy at all.

 

[JPeelen]

ShoooterGavon,
none of the books mentioned will help you finding the "app free" solution you are searching for.

Yes, there is a simple formula for roughly estimating(!) the maximum ordinate: 1.226 multiplied by (time of flight squared)
or in short: 1.226 * t^2
(result in meters; replace 1.226 by 4.022 to get the result in feet).
BUT it requires to know the time of flight and there is no "app free" solution to that.

By the way, in my view, the Carlucci book is not easier to understand than the McCoy book, because practically all small arms ballistics related material in Carlucci is cited from McCoy.

P.S. I grew up with slide rules and via TV saw Neil Armstrong live climbing down the ladder of the Lunar Module. To put the record straight: no slide rules involved. Command as well as Lunar Module had the same type of onboard computer with 4 kilobytes RAM, 72 kilobytes Read-only memory and a processor speed of 1 Megahertz. The printout of the software for controlling Apollo guidance was a stack of paper about 5 feet high. Main planning and preparatory work was of course done on IBM mainframes.

 

[hawkeyeshoooer]

Computing the Ordinates to Trajectory

Y=X/1000*(Ar-Ax)

Y = height of desired ordinate in yards
X = horizontl distance to desired ordinate
Ar= Angle of departure in mils for trijectory being computed
Ax = Anangle of departure in mils for the range of X

Example you want the 1000 yard ordinate of a 2000 yard drajectory

Ar = 44.5 mils
Ax = 11.1 mil

1000/1000 X (44.5 - 11.1) = 33.4 yards ( using Mil = 3.375 Minutes)

Another method/example: Determine the 800 yard ordinate of a 1200 yard trajectory

Ar for 1200 = 19.9 mil
Ax for 800 - 9.4 mils
Value of ordinate = 10.5 mils

800 X 10.5 /1000 = 8.4 yards.

 

[Ballisticboy]

Is that the 2nd edition? The first edition is riddled with errors. I haven't seen any in the 2nd, not that I've really looked carefully.

I believe it was the latest edition, bought only 2 or 3 years ago. It just happened to be one of the first equations I looked at but as I said I cannot for the life of me remember which it was. There used to be a website dedicated to correcting the errors but most of those were corrections to the gramma not the maths. It was not Bob's fault of course as he sadly died before the book was completed. I was priviledged to exchange work with him while he was still working.
I would never try to read his book from cover to cover, it is far too deep for that, It is good as a reference and aid to learning like the other books mentioned. The equations are usable if somewhat complex on occasions, all I would say is try to follow their derivation and understand what is being done as a check for the final equation.

As an aside, many years ago, when word processor packages were a new thing, I wrote a report which was particularly maths heavy with many complex equations involving variables of differing powers. We had trouble finding a printer which could print the report with all its equations but eventually found one which printed the first couple of test pages perfectly so we printed the entire report, had it published and distributed. It was some time later that I noticed that after page 10 all the variable powers in the equations had been changed to one less than they should be even though the file was correct when viewed on a screen. No one could ever explain how the printer and word processor managed to do it.

 

[mikecr]

for trijectory being computed

Which takes you right back to computing, and therefore being computed.
For every rule of thumb ever devised, truths are far separated.

 

[Ballisticboy]

There were also some books on Armament and Artillery that looked very interesting, I believe in Artillery they have to deal with a lot of the questions we Distance Precision Shooters do, as artillery shells go out up to and past a mile. Idon't know about the MO or if it comes in to play, I know Coriolis does.

155mm artillery shells when fired out to about 25km max range reach a maximum height of around 10km. In high angle fire they reach around 14-15km if I remember rightly but that is not used very often as you cannot hit anything. The maximum height or the height at a certain range is important when firing over high ground at a target the other side. The artillery relies totally on computer simulations to tell them where to aim the gun or how to correct their aim in observed fire since they cannot normally see their target.
I would say Distance Precision Shooting is more akin to tank fire as you are both aiming at a small target which is in sight.

 

[dcali]

I believe it was the latest edition, bought only 2 or 3 years ago. It just happened to be one of the first equations I looked at but as I said I cannot for the life of me remember which it was. There used to be a website dedicated to correcting the errors but most of those were corrections to the gramma not the maths. It was not Bob's fault of course as he sadly died before the book was completed. I was priviledged to exchange work with him while he was still working.
I would never try to read his book from cover to cover, it is far too deep for that, It is good as a reference and aid to learning like the other books mentioned. The equations are usable if somewhat complex on occasions, all I would say is try to follow their derivation and understand what is being done as a check for the final equation.

As an aside, many years ago, when word processor packages were a new thing, I wrote a report which was particularly maths heavy with many complex equations involving variables of differing powers. We had trouble finding a printer which could print the report with all its equations but eventually found one which printed the first couple of test pages perfectly so we printed the entire report, had it published and distributed. It was some time later that I noticed that after page 10 all the variable powers in the equations had been changed to one less than they should be even though the file was correct when viewed on a screen. No one could ever explain how the printer and word processor managed to do it.

There was a document that contained errata for the 1st edition floating around for a while - it was reportedly created by "colleagues" of McCoy. It was over 10 pages if I recall correctly. That, as I understand, was used to create the 2nd Edition. Wouldn't surprise me if they missed a few. The ones I noticed myself in the 1st were pretty obvious.

 

[JPeelen]

The errata document for the first (1999) edition of McCoy's book (running to more than 20 pages) can still be downloaded from jbmballistics.com (bibliography section).
The second (2012) edition has been available online on archive.org since July 2017. The bound book can be easily recognized by a clearly visible "2" on the front of the book cover.

I am amused that one of the most outstanding U.S. books on small arms exterior ballistics ever, is dicussed on this forum as if it were some remote third world publication which nobody has ever seen.

 

[dcali]

The errata document for the first (1999) edition of McCoy's book (running to more than 20 pages) can still be downloaded from jbmballistics.com (bibliography section).
The second (2012) edition has been available online on archive.org since July 2017. The bound book can be easily recognized by a clearly visible "2" on the front of the book cover.

I am amused that one of the most outstanding U.S. books on small arms exterior ballistics ever, is dicussed on this forum as if it were some remote third world publication which nobody has ever seen.

I don't want to divert the discussion, but the copy on archive.org is almost certainly an unauthorized version. Given that this is *the book* (at least as far as easily obtainable books go), it's worth chipping in for the real deal. Off my soapbox now.

 

[dstoenner]

I have been wanting for a while to see what is presented on this topic so this afternoon I had some time so I opened it up and read the original posters question and then all of the responses. I think most have missed the mark.

My read of this OP was basically, "how can I in the field get an estimate of what my apogee f the shot is. Quickly and without a calculator"

I am going to assume one thing that the OP has at his disposal a list of distances and come ups. I am a MOA guy not a MIL guy but the math is still the same just some constants change. Armed with that simple come up table you can pretty well guess what your maximum height is with a few simple mental calculations. No it isn't exact but that is not the point. I think why he is asking this is that he wants to know will that 20 foot tree stand buffer the wind value or am I going above them so I need to factor in a different windage.

I have read and heard it said that the maximum height occurs about 60% to the target. I didn't want to take the for a fact so I used my ballistic program, Shooter, and set the zero distance as 1000 yards and then looked for the maximum drop. With a resolution of 50 yards it occurred at 650 yards. So we are good with that assumption. I will stick with 60% because it is a lot easier to mentally multiply a value by 6 rather than 6.5.

So if I am correct in my assumptions here goes.

1) we know the distance to the target in yards and the come up we need to dial in MOA.

2) What is really happening here is the the line of sight, looking through the scope sets the horizontal while the barrel is actually pointed to a point above the target by MOA * (distance to the target in yards/100). If there were no gravity that is the line the bullet would take (bore line). By about 60% to the target the bullet has pulled away from the bore line and started its downward part of the parabola.

3) we can quickly get the height of the point on the bore line by using similar triangles and solving for the distance from the line of sight to the bore line.

4) In an example of my 260 Remington here goes. Shooting 140 Berger Hybrids at 1000 yards, I have a come up of 24.1. Using 1 inch per MOA (yes I know it is exactly 1.047 but I want this to be an easy to solve in your head solution) at 1000 yards the point we are aiming at is 24.1*(1000/100) or 241 inches.

5) We now know the main triangle with a base of 1000 yards and a height of 241 inches. The 60% triangle in the middle is 241/1000 = X/600. Solving for X we get an equation of

X=241*600/1000

or really 241 * 60% or 144.6 inches or 12 feet.

My Shooter solution told me that the real solution was 92 inches. But if my original interpretation of the OP's quest for an answer is correct then this would let you quickly evaluate the shooting path for what does and does not need to be accounted for.

HTH

David

 

[ShooterGavon]

I have been wanting for a while to see what is presented on this topic so this afternoon I had some time so I opened it up and read the original posters question and then all of the responses. I think most have missed the mark.

My read of this OP was basically, "how can I in the field get an estimate of what my apogee f the shot is. Quickly and without a calculator"

I am going to assume one thing that the OP has at his disposal a list of distances and come ups. I am a MOA guy not a MIL guy but the math is still the same just some constants change. Armed with that simple come up table you can pretty well guess what your maximum height is with a few simple mental calculations. No it isn't exact but that is not the point. I think why he is asking this is that he wants to know will that 20 foot tree stand buffer the wind value or am I going above them so I need to factor in a different windage.

I have read and heard it said that the maximum height occurs about 60% to the target. I didn't want to take the for a fact so I used my ballistic program, Shooter, and set the zero distance as 1000 yards and then looked for the maximum drop. With a resolution of 50 yards it occurred at 650 yards. So we are good with that assumption. I will stick with 60% because it is a lot easier to mentally multiply a value by 6 rather than 6.5.

So if I am correct in my assumptions here goes.

1) we know the distance to the target in yards and the come up we need to dial in MOA.

2) What is really happening here is the the line of sight, looking through the scope sets the horizontal while the barrel is actually pointed to a point above the target by MOA * (distance to the target in yards/100). If there were no gravity that is the line the bullet would take (bore line). By about 60% to the target the bullet has pulled away from the bore line and started its downward part of the parabola.

3) we can quickly get the height of the point on the bore line by using similar triangles and solving for the distance from the line of sight to the bore line.

4) In an example of my 260 Remington here goes. Shooting 140 Berger Hybrids at 1000 yards, I have a come up of 24.1. Using 1 inch per MOA (yes I know it is exactly 1.047 but I want this to be an easy to solve in your head solution) at 1000 yards the point we are aiming at is 24.1*(1000/100) or 241 inches.

5) We now know the main triangle with a base of 1000 yards and a height of 241 inches. The 60% triangle in the middle is 241/1000 = X/600. Solving for X we get an equation of

X=241*600/1000

or really 241 * 60% or 144.6 inches or 12 feet.

My Shooter solution told me that the real solution was 92 inches. But if my original interpretation of the OP's quest for an answer is correct then this would let you quickly evaluate the shooting path for what does and does not need to be accounted for.

HTH

David

You pretty much summed it up. I could very easily get the info from any number of free ballistics calculators online, however, I want to distance myself from as much tech as possible with regard to long distance precision shooting.

I want to go back to the basics. Re-teach myself how to engage targets at 800-1100yds using a pen and paper. If battaries or the electronic grid go, then so does my trimble, my kestrel, etc.

 

[Mozella]

....... snip..............
P.S. I grew up with slide rules and via TV saw Neil Armstrong live climbing down the ladder of the Lunar Module. To put the record straight: no slide rules involved. Command as well as Lunar Module had the same type of onboard computer with 4 kilobytes RAM, 72 kilobytes Read-only memory and a processor speed of 1 Megahertz. The printout of the software for controlling Apollo guidance was a stack of paper about 5 feet high. Main planning and preparatory work was of course done on IBM mainframes.

True, the moon missions were performed in the age of computers even though they weren't nearly fancy enough to control a modern smart phone. But it wasn't too many years prior to that when getting rockets into space involved manual number crunching. One of my calculus instructors was one of a HUGE team of mathematicians involved in the early space program. He was a number cruncher using lots of paper, pencils, and a slide rule to figure out things like how to shoot a guy into earth orbit and get him back down on a reasonably small spot on the earth. Or, how to shoot an atomic bomb into space and get it to come down to earth on top of some Russian guy's house.

When I was a kid, only classmates with rich fathers could afford a primitive hand-held electronic calculator. To avoid looking like a real dork, I used a circular slide rule which I could more easily hide from potential girlfriends than the typical 12 inch "slip stick".

 

[mensajd]

Why not use a laser rangefinder and ballistic app as a sanity check on your tech-free range determinations and calculated firing solutions? That way you can practice old school methods in the field and then have the ability to check your homework right away to see if you are getting better.