The Firing Line Forums Need some help with calculating bullet arc trajectories
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 June 16, 2018, 08:35 AM #1 Road_Clam Senior Member   Join Date: November 21, 2013 Location: New Hampshire Posts: 1,040 Need some help with calculating bullet arc trajectories Hey guys, I am trying to correctly calculate the bullet trajectory flight path of 2 different calibers at 600 yds ,( 308 and 45-70 ) . I'm trying to calculate the maximum arc of the two bullets. So in theory if I enter all the ballistics and set my zero at 600 yds then read the maximum vertical inches at 300 yds that should be my maximum arc ? I'm comparing 308 using 168 gr match bullet @ 2600 fps and a 540 Creedmoore gr cast bullet @ 1250 fps in 45-70 . According to my Strelok app the maximum vertical arc of the 308 is about 35" , and the max arc of the 45-70 is about 143" ? I just want to make sure i'm using correct math methods. I'm ultimately trying to calculate exactly where the 45-70 shots will be impacting our sand berm vs a standard 308 round. __________________ "To be old an wise you must have been young and stupid"
 June 16, 2018, 08:40 AM #2 TXAZ Senior Member   Join Date: September 5, 2010 Location: Cyber-Somewhere... Posts: 3,152 Do you have a smartphone? If so use “Shooter” for “pretty close”, or spend the \$30 for Applied Ballistics app if you want dead on. __________________ !أنا لست إرهابياً
 June 16, 2018, 11:10 AM #3 Don Fischer Senior Member   Join Date: March 2, 2017 Posts: 1,110 Why in the world would you want to do that? Why not just find out what a zero is you can hit a target you want to hit then find the difference between it and 600yds and re-set the scope?
 June 16, 2018, 12:02 PM #4 T. O'Heir Senior Member   Join Date: February 13, 2002 Location: Canada Posts: 9,804 Comparing 308 and a cast .45-70 is an apples and oranges comparison. As long as all the bullet hit the berm, you're good. Where they hit makes no difference to anything. I can't find any ballistics charts for a 540 grain .45-70. There are some charts with a 1330 FPS MV, jacketed, 405 at 500 yards. With a 100 yard zero, it drops 301.3 inches. That's a bit over 100 YARDS drop at 500. Kind of suspect you should forget a .45-70 at those distances. __________________ Spelling and grammar count!
 June 16, 2018, 05:01 PM #5 Brian Pfleuger Moderator Emeritus   Join Date: June 25, 2008 Location: Austin, CO Posts: 19,216 Maximum height of the projectile is not exactly 1/2 way to the target. One of the easier ways to get this info is JBM Ballistics. Set your target and wind speeds to 0, set your maximum range and zero range to 600, set your increments to something like 10 yards (or 1 if you want to be exact) and look down the "drop" list for the highest number. __________________ Nobody plans to screw up their lives... they just don't plan not to. -Andy Stanley
 June 16, 2018, 06:17 PM #6 Road_Clam Senior Member   Join Date: November 21, 2013 Location: New Hampshire Posts: 1,040 Guys, RELAX on the "why you doin' this" type replies. I do NOT care about comparing calibers, I care about comparing where both caliber trajectories will impact our 600 yd berm. The reason is that at the base of the berm has concrete blocks. Our pits are manned for scoring shots. These concrete blocks could create a ricochet safety concern if a bullet strikes the berm too low. I want to ensure the 45-70 trajectory does not have the potential to strike a concrete block. I already know where 308 caliber shots impact the berm, now I want to compare the 45-70 for some accurate data. I am ultimately wanting to bring BPCR shooting to our 600 yd range. We don't know for sure if our berm design can safely handle the large arc trajectory of the slow and heavy 45-70 calibers. __________________ "To be old an wise you must have been young and stupid" Last edited by Road_Clam; June 17, 2018 at 07:16 AM.
 June 16, 2018, 07:17 PM #7 Don Fischer Senior Member   Join Date: March 2, 2017 Posts: 1,110 I have a program in my chronograph that will give me the trajectory in MPBR. With my rifles I can figure it out at 300yds or what ever and the computer in the chronograph will read me out a trajectory, no sweat. Ya need the bullet muzzle velocity and BC of the bullet. I suspect there's plenty of programs around that will figure it for you at any range you want. I shoot 180gr cast out of a 308 and the mold maker, Lee, assigned the bullet a BC. My chronograph gives me the velocity. After you get the figure's, shoot the different ranges to verify how accurate they are. My 6.5x06 comes out right on the money!
June 16, 2018, 08:12 PM   #8
Scorch
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Quote:
 With a 100 yard zero, it drops 301.3 inches. That's a bit over 100 YARDS drop at 500.
You need to do your math again. That is just over 25 feet. But, hey! 25 feet, 300 yards, who's counting?
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 June 17, 2018, 05:19 AM #9 Mobuck Senior Member   Join Date: February 2, 2010 Posts: 5,961 "it drops 301.3 inches. That's a bit over 100 YARDS drop at 500." "You need to do your math again" What he said Many sources have bullet drop charts available. I often use the ones in the reloading manuals to "get close" based on BC and velocity
 June 17, 2018, 07:20 AM #10 Road_Clam Senior Member   Join Date: November 21, 2013 Location: New Hampshire Posts: 1,040 I'm actually using AutoCad Inventor to replicate our 600 yd range and the pit layout. I also plotted the bullet trajectory arcs. __________________ "To be old an wise you must have been young and stupid"
June 18, 2018, 08:39 AM   #11
kraigwy
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[quote]Why in the world would you want to do that?[/img]
Quote:
 Comparing 308 and a cast .45-70 is an apples and oranges comparison.
Good questions, and I suppose they should be addressed.

I shot a lot of both, 308 and cast 45-70 bullets. The 308 is relatively simple. There is tons of data on it as far as shooting close range and getting infor for distance. Heck in basice we shot 25 meter targets to get zeros for 300 and beyond.

The 45-70 is a bit different. Not so much data out there. Well there is but you need the old army manuals to find it.

Why cant we do it like the 308? Because they are apples and oranges, but like apples and oranges we like to have both.

I'll give an example. In my back yard I have a large ridge about 200 yards from my shooting bench.

I was planning to shoot a Creedmoor BPCR Match (800,900 and 1000 yards) with a Fun Mile Match following. These matches had to be shot with BP and I intended to use my 45-70.

So I did the math to determine where I had to hit at 25 yards to get a 1 mile zero. It would have to be 515 inches per hundred yards (if I remember right). That would have been 82.5 feet above my 200 yard target. Any errors could put my round over the hill into South Dakota.

Not something I wanted to do.

Someone mentioned the Shooter Program for the I phone. I did the math, played with the shooter program and when I got to the Match, it only took few practice rounds to get dialed in.

There are other ways to do it more accuratly, but it require a bit more math. Just like Artillary guys zeroing their cannons at distance when they dont have access to a range. MATH.
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 June 18, 2018, 04:08 PM #12 std7mag Senior Member   Join Date: June 23, 2013 Location: Central Pennsyltucky... Posts: 1,586 I use Strelok on my phone. They have a free version that should get you pretty close to what you need. The pay version ( \$6 if i remember right) has all kinds of useful inputs. Aka bullet database, velocity, wind speed and direction, elevation, temp. __________________ I am in earnest- I will not equivocate- I will not excuse- I will not retreat a single inch- AND I WILL BE HEARD! William Lloyd Garrison - The Liberator 1831
June 18, 2018, 05:19 PM   #13
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Quote:
 Originally Posted by std7mag I use Strelok on my phone. They have a free version that should get you pretty close to what you need. The pay version ( \$6 if i remember right) has all kinds of useful inputs. Aka bullet database, velocity, wind speed and direction, elevation, temp.
I use the Strelok app as well, pretty dam close dopes from my experiences. I did use both Strelok and Gundata.org's ballistics to compare the trajectories and they were almost identical so my trajectory plotting points must be good.
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 June 18, 2018, 11:24 PM #14 raimius Senior Member   Join Date: January 27, 2008 Posts: 1,832 If you are trying to find actual trajectories in relation to the ground, most free ballistics apps won't do that. They calculate in relation to the line of the "zero." A physics app that does kinematics (not the high school simplified without air friction) would probably work better.
 June 19, 2018, 08:24 AM #15 Road_Clam Senior Member   Join Date: November 21, 2013 Location: New Hampshire Posts: 1,040 Raimus, I plotted 3 lines, the first line is basically a straight line starting from the barrel then passing through our MR targets X ring and into the berm. I then plotted both 308 and 45-70 arcs also striking the x ring. I'm going to see if I can post a screenshot of my pit layout in AutoCad for you guys to see. __________________ "To be old an wise you must have been young and stupid"
June 19, 2018, 10:24 AM   #16
emcon5
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Quote:
 Guys, RELAX on the "why you doin' this" type replies. I do NOT care about comparing calibers, I care about comparing where both caliber trajectories will impact our 600 yd berm.
You mean you expect people to actually answer the question you asked, rather than the question they think you asked? That is crazy talk.....

I would do what Brian Pfleuger said. Don't assume that the apogee is at half range, look at the numbers and make sure.

 June 19, 2018, 01:25 PM #17 Don Fischer Senior Member   Join Date: March 2, 2017 Posts: 1,110 Something to remember about whatever data you use. Before you get crazy, go out with what you have and shoot the rifle at the same distance's and compare the actual rifle to the data you got.
 June 19, 2018, 07:57 PM #18 Road_Clam Senior Member   Join Date: November 21, 2013 Location: New Hampshire Posts: 1,040 Above is a cross section layout of our 600 yd pits. The 145" dimension represents a standard MR 600 yd target at full mast. The lines passing through the target are all intersecting at theoretical bullseye center. The 30 degree angle represents our sand berm. The arc near the center represents the typical "impact" bowl for standard rifle calibers. The straight top line represents rifle bore , the next lower arc represents a typical 308 caliber impact, the the bottom arc represents my predicted 45-70 impact. So by my numbers looks like my 45-70 bpcr trajectory will only impact about 9" lower than a typical 308 trajectory. This is a graph of the max trajectory arcs of both 308 (lower arc) and the 45-70 arc (top). Again the straight line represents bore axis. __________________ "To be old an wise you must have been young and stupid" Last edited by Road_Clam; June 20, 2018 at 04:13 PM.
 June 20, 2018, 10:18 AM #19 emcon5 Senior Member   Join Date: July 10, 1999 Location: High Desert NV Posts: 2,700 How far is it from the target to the berm? Using your 145" dimension as a scale, it looks to be around 10 yards. You can sanity check your numbers by putting that distance as your Range Increment in your ballistics program. with a 600 yard zero, compare the drop number at 610 yards to get the difference. Just for grins, I ran a 168 SMK @ 2600 through JBM and it says it will be ~3" low. Your 45-70 bullet isn't in JBM's database, so I used a Hornady 500gr @ 1250 FPS and it says it will be ~13" low at 610 yards, so according to JMB at least, the impact point will be about 10" low 10 yards beyond your target. Assuming the CM 540gr has a little higher BC than the Hornady 500gr, it would retain the velocity little better, and your numbers don't seem out of line.
June 20, 2018, 04:15 PM   #20
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Quote:
 Originally Posted by emcon5 How far is it from the target to the berm?
I updated the pit layout dwg and it's about 35' if measured by the bore line.
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 June 20, 2018, 07:30 PM #21 raimius Senior Member   Join Date: January 27, 2008 Posts: 1,832 Looking over your posts, I'm confused as to why you need the maximum height of the arc. As far as not hitting the blocks at the berm, I think a standard ballistics app with a zero at the Target and result at the berm is a correct method.
 June 21, 2018, 08:58 AM #22 emcon5 Senior Member   Join Date: July 10, 1999 Location: High Desert NV Posts: 2,700 The thing you want to look most closely at is where does a low shot go. Looks like you should be OK for a 10-ring shot, but you need to do the same plot starting at the top of the berm in front of the target pits. The shot in the black is not the problem, it is the one that barely clears the berm. Looking at your drawing, if the berm location is accurate, that would be roughly 4.5" lower than your normal impact area. If that is not the berm, and just the front concrete wall of the pits and the berm is on top of that, then you should find that height and add it to your plot. Eyeballing it, that still looks OK, but you should confirm, and also go have a look at that berm, and find the lowest point and use that in your calculations. Those never seem to be level in my experience, and rebuilding it if necessary if there is any excavation/erosion from low shots.
June 21, 2018, 04:46 PM   #23
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Quote:
 Originally Posted by raimius I'm confused as to why you need the maximum height of the arc.
To plot an arc you need 3 points on a curve. Vertical points from the barrel's straight line : Point #1 = gun barrel, Point #2 = X ring on target, point #3 = maximum vertical arc measurement taken at 300 yds.
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 June 21, 2018, 11:39 PM #24 raimius Senior Member   Join Date: January 27, 2008 Posts: 1,832 Ah, not necessarily. Due to air friction, the bullet slows during flight, while acceleration due to gravity is constant. The arc will be flatter near the muzzle, and more vertical at the end of flight. If you take a ballistic computer and start plugging in numbers every 25 yards, you'll notice the drops get larger and larger per increment as you get to long ranges.
June 22, 2018, 06:44 AM   #25
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Quote:
 Originally Posted by raimius Ah, not necessarily. Due to air friction, the bullet slows during flight, while acceleration due to gravity is constant. The arc will be flatter near the muzzle, and more vertical at the end of flight. If you take a ballistic computer and start plugging in numbers every 25 yards, you'll notice the drops get larger and larger per increment as you get to long ranges.
I'm not trying to send a rocket to Saturn. My arc plot points are close enough for my berm impact estimate data intent.
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