Bullet Impact Angle Question

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  • Last Post 27 August 2021
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Bryan Austin posted this 15 August 2021

Fellas,

 

Here is a question for all of you long distance shooters out there.

Where can I find a formula to figure out bullet impact angle at a particular range?

I have the bullet trajectory but can't wrap my brain around trying to figure out the impact angle at the target.


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45 2.1 posted this 15 August 2021

Fellas,

 

Where can I find a formula to figure out bullet impact angle at a particular range?

I have the bullet trajectory but can't wrap my brain around trying to figure out the impact angle at the target.

Well, it's either college level math and geometry or a Civil Engineer with access to Auto-Cad. You have listed one of the necessary things, but have not listed the other three.

 

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JimmyDee posted this 16 August 2021

"In a vacuum," as they say, where the bullet's flight would be parabolic, it's the tangent to a parabola at impact.

(To be clear: I'm not talking about the projectile axis relative to the trajectory.  Your holes look to be circular; I don't think you're asking about over-stabilization or keyholes, right?)

Since we're talking rifles under 300 yards and not artillery at 10 miles, let's ignore the "not a parabola" bit.

Relative to muzzle height, what are your downrange POI distances and heights for a single POA?  All I got from your video is 17" down at 100 yards and 28-3/4" down at 265 yards -- and I'm guessing that the muzzle and POA are about the same height, right?

Computing the parabola requires three points.  The elevations of three groups (25, 50, 100 yards, for example) fired from a rest with the barrel horizontal is a good starting point.  POI will always be higher than zeroed POA when the barrel is tilted either up or down; that's a different calculation.

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Bryan Austin posted this 16 August 2021

(To be clear: I'm not talking about the projectile axis relative to the trajectory.  Your holes look to be circular; I don't think you're asking about over-stabilization or keyholes, right?)

Since we're talking rifles under 300 yards and not artillery at 10 miles, let's ignore the "not a parabola" bit.

Relative to muzzle height, what are your downrange POI distances and heights for a single POA?  All I got from your video is 17" down at 100 yards and 28-3/4" down at 265 yards -- and I'm guessing that the muzzle and POA are about the same height, right?

Computing the parabola requires three points.  The elevations of three groups (25, 50, 100 yards, for example) fired from a rest with the barrel horizontal is a good starting point.  POI will always be higher than zeroed POA when the barrel is tilted either up or down; that's a different calculation.

Yes sir, bullet is stable. I was planning on setting up two targets, one behind the other a few feet and just figure it out that way.

Thanks for taking the time to try and help.

Muzzle height should be typical benchrest height. I can get detail measurements later but I'd say about 42 inches from the ground.

Downrange POA (for right now) is 265 yards.  The scope is zero at 200 yards. The 265 yard POA is 28 3/4 Higher than the bullseye or bullet impact area. However, the target is about 50 FEET LOWER lower (down hill) than the muzzle.

 

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Bryan Austin posted this 16 August 2021

The barrel is pointing at the 200 yard target in this photo, the 265 is just to the left. You can see the decline in elevation to the targets.

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beltfed posted this 16 August 2021

FWIW, 

The quick an easy is to , as you mention, place two targets/cardboard about 6 feet apart at the range chosen, 

carefully using spirit levels, etc you can measure the drop in the 6 feet and determine the angle of the bullet travel

at the target.  Othewise, Enjoy the mathmatical challenge of figuring that Modified parabolic trajectory.

Dan Theodore had done this "six feet apart" empirical measurement at 1000yds to determine what was the safety situation for Black Powder Cartridge rifles

at that distance as the bullets came over the pits.  The angle was something like 6 degrees. Not "like a mortar round" as 

some people had envisioned.  Also note the the BPCR bullets rise something like 46 feet in their trajectory over the thousand yards 

beltfed/arnie

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Bryan Austin posted this 16 August 2021

The angle was something like 6 degrees. Not "like a mortar round" as 

some people had envisioned. 

beltfed/arnie

I was guessing less than ten degrees from what I have seen. 

My brain hurts

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JimmyDee posted this 17 August 2021

Hmm... I thought you were wanting something that would work at any range.  If you're just wondering about one or two distances the "two targets, six feet apart" sounds like what you're after.  My bad.

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Bryan Austin posted this 17 August 2021

Hmm... I thought you were wanting something that would work at any range.  If you're just wondering about one or two distances the "two targets, six feet apart" sounds like what you're after.  My bad.

Oh no, I am looking for a mathematical formula that will work at all ranges. Doesn't mean I will know how to use it, just hoping I can learn. So far I see nothing.


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45 2.1 posted this 17 August 2021

Oh no, I am looking for a mathematical formula that will work at all ranges. Doesn't mean I will know how to use it, just hoping I can learn. So far I see nothing.

And you won't see anything BECAUSE you're not taking the major variables into account. College level math and understanding what is happening with the setup you use is the key. Inclination and declination of the line of sight has a lot to do with it. Usually people here say "this isn't rocket science".... well, it is here..... beginning rocket science, but it still is.



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Bryan Austin posted this 17 August 2021

Oh no, I am looking for a mathematical formula that will work at all ranges. Doesn't mean I will know how to use it, just hoping I can learn. So far I see nothing.

And you won't see anything BECAUSE you're not taking the major variables into account. College level math and understanding what is happening with the setup you use is the key. Inclination and declination of the line of sight has a lot to do with it. Usually people here say "this isn't rocket science".... well, it is here..... beginning rocket science, but it still is.


So basically no one here can give me an example?

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45 2.1 posted this 17 August 2021

Variables influencing angle of impact:

Rifle setup, height of sights above center line of bore.

Sight in distance and accuracy of load.

Muzzle velocity and ballistic coefficient or complete trajectory of load

Angle of inclination or declination of line of sight or elevation of muzzle and point of impact

 

With military tracking radar, your answer is a data line, but someone with Auto-Cad could plot the trajectory line properly as it is in reality, construct a normal line at the point of impact then construct a perpendicular and query what it's angle is thereby giving you your answer.  All this varies with angle of line of sight in the world.

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Bryan Austin posted this 17 August 2021

Variables influencing angle of impact:

Rifle setup, height of sights above center line of bore.

Sight in distance and accuracy of load.

Muzzle velocity and ballistic coefficient or complete trajectory of load

Angle of inclination or declination of line of sight or elevation of muzzle and point of impact

With military tracking radar, your answer is a data line, but someone with Auto-Cad could plot the trajectory line properly as it is in reality, construct a normal line at the point of impact then construct a perpendicular and query what it's angle is thereby giving you your answer.  All this varies with angle of line of sight in the world.

 

This is mind blowing stuff. Evry time I think I find something, it is just a formula to find a formula to find another formula...lol

Bullet is fired from a muzzle 45 inches above the surface.

Bullet is traveling at 1,478fps.

Bullet decelerates to 951fps impact velocity at 265 yards Bullet weight is 215 grains

Bullet impacts a vertical target 24" above the ground

Elevation difference from point of origin to impact is -58 feet, from 1,241 feet at the muzzle to 1,185 feet at impact, plus the 2 foot gain in elevation at impact on the target.

Muzzle angle is unknown, line of sight is level from the muzzle to 200 yards, plus 28 3/4" at 265 yards

Bullet trajectory's are approx. and can be corrected later...I think. I do not have exact data with me.

muzzle to 25 yards = +5 inches

muzzle to 50 yards = +8 inches

muzzle to 100 yards = +14.5 inches

muzzle to 125 yards = -- inches

muzzle to 150 yards = +10.5 inches

muzzle to 175 yards = -- inches

muzzle to 200 yards = + 0.5 inches

muzzle to 225 yards = -13 inches

muzzle to 250 yards = -- inches

muzzle to 265 yards = -28 3/4 inches I am hoping the angle at impact is less than 10 degrees. My plan is to set up two targets, one 6 feet behind the other and simply measure the different elevation of the impact holes of each target. I'd like to know the scientific method ;-) Still searching...

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45 2.1 posted this 17 August 2021

I'll be gone or very busy for the next three days, but will plot this out in the real world and see what happens.....You have given enough information to work it out. Stay tuned.

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Bryan Austin posted this 17 August 2021

I'll be gone or very busy for the next three days, but will plot this out in the real world and see what happens.....You have given enough information to work it out. Stay tuned.

Awesome!

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Ken Campbell Iowa posted this 17 August 2021

while my mind is boggling from the above discussions, it is interesting ( or not ) that since the bullet at 140,000 rpm is gyroscopically stabilized with respect to the universe ...

if you shot it fast enough to put it into low earth orbit ...

at 1/4 around the earth it would appear to an observer there to be traveling with point straight up ...

halfway around the earth the bullet would zing by an observer's ear going base first ... 

*************

and now for some useful information ... somewhere on the internet you can download for free Dr. Mann's book on his experiments .. been a few years, but i think Bullet's Flight is the link.

i have read his book 6 times ... it still wears me out about half way through ...  heh ...

ken

 

 

 

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Bryan Austin posted this 17 August 2021

while my mind is boggling from the above discussions, it is interesting ( or not ) that since the bullet at 140,000 rpm is gyroscopically stabilized with respect to the universe ...

if you shot it fast enough to put it into low earth orbit ...

at 1/4 around the earth it would appear to an observer there to be traveling with point straight up ...

halfway around the earth the bullet would zing by an observer's ear going base first ... 

*************

and now for some useful information ... somewhere on the internet you can download for free Dr. Mann's book on his experiments .. been a few years, but i think Bullet's Flight is the link.

i have read his book 6 times ... it still wears me out about half way through ...  heh ...

ken

 

If I don't stop reading it, my brain is going to explode!! I don't think much of his information is really useful....I just like reading about the "things" they use to do back in the day.

I found a 1947 publication for $15....couldn't pass it up.

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RicinYakima posted this 18 August 2021

Mann's work is the bases for all 20th century work on cast bullets. Without that background, you are reinventing the wheel. If it takes ten times to understand it, you had better do it. Or else Mattern, Sharpe and Pope will mean nothing. 

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Bryan Austin posted this 18 August 2021

Mann's work is the bases for all 20th century work on cast bullets. Without that background, you are reinventing the wheel. If it takes ten times to understand it, you had better do it. Or else Mattern, Sharpe and Pope will mean nothing. 

I figured that would get someone's attention!!!!!!

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Bryan Austin posted this 18 August 2021

44-40 215gr bullet impact angle example at 265 yards. 951fps.

Angle don't look too bad huh? Any error in the chronograph angle would just increase the velocity.

 

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RicinYakima posted this 18 August 2021

Best I can tell from my research from two days, a gyroscopically stable bullet will be perpendicular to the the center of mass of the earth after it reaches to apex of launch flight. FWIW

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JimmyDee posted this 18 August 2021

Oh no, I am looking for a mathematical formula that will work at all ranges. Doesn't mean I will know how to use it, just hoping I can learn. So far I see nothing.


So basically no one here can give me an example?

I spent a little time trying to pull an example together while ignoring real-world factors like air, barrel at other than horizontal, etc.  I (1) used Hornady's ballistic calculator for a 215gr bullet with .15 BC at 1,300 fps using the G1 drag model to get some down-range points, (2) fed three of those into an on-line parabola calculator, then tried to (3) plot the resulting quadratic function using Google's plotter.

[ Google's  plotter is pretty sweet.  If you don't know what I'm referring to, go to google.com and type ' plot -x^2 + x + 1 ' in the search bar, hit enter or return or whatever, then drag the dot along the curve. ]

Step 1 was simple enough.  The down-range velocities were a bit lower than what you reported at 265 yards but the trajectory seemed to be appropriately rainbow-like.

Step 2 wasn't too bad but the coefficients looked like they came from Mars: lot's of zeroes.

So far, so good -- but the work products thus far aren't very useful.  The ideal would be to get Google's plot feature to generate an interactive graphic on which you could simply drag a dot across the horizontal axis (range) and it would compute the corresponding  function value (elevation).

Step 3 is where the wheels fell off: the coefficients seem to be beyond what Google's plotter can handle.  I tried to express them a couple different ways but haven't come up with anything useful yet.

I'll putz with it a bit more.

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45 2.1 posted this 19 August 2021

As drawn to actual specs as you've listed with a 58 foot drop from muzzle to point of impact. The bullet is a downward angle (declination) of 4 degrees 39 minutes (4.65 degrees) at impact. The center line of bore is a downward angle (declination) of 3 degrees 49 minutes (4.82 degrees) at the muzzle. Don't use this as an example of level shooting either.... note the slight increase of the impact angle versus the starting angle at the muzzle. 

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Bryan Austin posted this 19 August 2021

I also came up with these three screenshots. The first two shooting at 200 yards and the third at 265.

I think the tables are fairly level, but the sides could be offset. Also the items on the table like the wood, blanket and other items may not be perpendicular to the muzzle.

I will confirm angles next time I visit the range if it helps.

Position 1 - aiming at 200 yard target #1

 

 

Position 2 - aiming at 200 yard target #2

 

Position 3 - aiming at 265 yard target #1, decrease in muzzle angle

 

 

Aside from impact angle - I am thinking this angle (as far as "slope shooting" is concerned) should only be about a cosine of 98% making the POA as if the target is at 250 yards? So much to learn, so little time, so little brain!

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Fiddler posted this 19 August 2021

On a level range you could, using a ballistic calculator, determine drop at 240 yds. and 265 yds. Input a 265 yd. zero and take the elevation difference and divide by 900 (inches in 25 yds) that will give you the Tangent of the angle. Using your BC of .150 at 1300fps with a 265 yd zero, I come up with 0 degree 40 min. 16sec. That's not what I expected to see, seems rather shallow. Is my thinking at fault? Checked at 975 and1000yds. and came out with 8 deg. 2 min.

A bullets path when fired in an atmosphere is not a parabola so that would introduce some error.

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Bryan Austin posted this 19 August 2021

On a level range you could, using a ballistic calculator, determine drop at 240 yds. and 265 yds. Input a 265 yd. zero and take the elevation difference and divide by 900 (inches in 25 yds) that will give you the Tangent of the angle. Using your BC of .150 at 1300fps with a 265 yd zero, I come up with 0 degree 40 min. 16sec. That's not what I expected to see, seems rather shallow. Is my thinking at fault? Checked at 975 and1000yds. and came out with 8 deg. 2 min.

A bullets path when fired in an atmosphere is not a parabola so that would introduce some error.

I am still learning here so bear with me!



Preliminary test results

Chronographed Velocity


1,478fps @ muzzle
951fps @ 265 yards

Level 25 Yards - POA 5" Low, (+5" at 25 Yards)

Level 50 Yards - POA 8" Low, (+8" at 50 Yards)

Level 100 Yards (target 1) - POA 14.5" Low, (+14.5" at 100 Yards)
?? Decline100 Yards (target 2) - no data yet

58' Decline 265 Yards - POA 28 3/4" High, (-28 3/4" at 265 Yards) (possible slope .98% correction, POA may actually be 250 yards)

 

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Bryan Austin posted this 25 August 2021

Okay,

Below is a photo of what I did. I tried to replicate the targets at home as they were at the range. I had the two targets tied together with wood strips at the top, which can be seen in the photo.

The targets were "square" but the angle I was shooting was off. The targets are set to replicate as can be seen, one is off-set to replicate a "straight shot".

This does not replicate "groups" because I have different POA's due to the off-set nature of the two targets. Even so, vertical group is 11" which should not have changed, only windage....or something like that....

5 shots measured 12 degrees and 1 shot (#3) measured 11 degrees. Shot #3 as well as shot #1 hit the wood frame and may have deflected slightly.

Target 1 is positioned 42" in front of target 2

12 degree trajectory path at impact at 265 yards is not bad at all. I do have a video if anyone wants to see it.

Temp was about 75 but the humidity was horrid, at least 100% at 90am, sky clear...hazy

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Bryan Austin posted this 25 August 2021

If the impact angle is 12 degrees, how would the 58' slope decline effect angle of impact if it was level?

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Bryan Austin posted this 27 August 2021

I removed all content from Youtube. I moved most current videos over to Full30.com here: 

https://www.full30.com/channel/44-40-cartridges

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