# Bullet drop formula?



## Frisco (Mar 31, 2011)

I've been searching for like an hour online and I can't find a formula to calculate bullet drop.

I don't need tables, I'm doing it for an assignment for my trig class so I have to do the math myself.
Any ideas?  I think I've calculated all the actual data I need, I just don't know exactly how to put it together..    Thanks.


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## Diamondback 2/2 (Mar 31, 2011)

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html


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## Marauder06 (Mar 31, 2011)

Isn't there an iPod app for that?


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## x SF med (Mar 31, 2011)

It's a slope formula with the added distractors of velocity, gravity, time - it could be even more complicated with spin and wind over distance.   It's a 4 dimensional slope equation.   Remember before there is drop there is rise  (ballistic jump)  so you have a parabolic/ballistic slope.


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## Marauder06 (Mar 31, 2011)

x SF med said:


> It's a slope formula with the added distractors of velocity, gravity, time - it could be even more complicated with spin and wind over distance.   It's a 4 dimensional slope equation.   Remember before there is drop there is rise  (ballistic jump)  so you have a parabolic/ballistic slope.



:eek:


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## Frisco (Mar 31, 2011)

I figured out the drop with a perfectly flat trajectory, the ballistic jump is where I'm having trouble I don't know how to factor it in.  I've got the effects of wind, spin drift, and the coriolis effect calculated, so I will factor those in once I find the drop...


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## SgtUSMC8541 (Mar 31, 2011)




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## Frisco (Mar 31, 2011)

If you calculated it for a prefectly flat trajectory out of the muzzle it would work if your barrell was exactly level with your scope.. IE your reticle is perfectly parallel to your barrell to begin with.. The parabolic slope only comes into effect if your already sighted in at a given distance.. right?


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## x SF med (Mar 31, 2011)

You need to calculate the 'vacuum parabola' from muzzle to the crossing point of the 'flat trajectory' if you figure poa/poi is essentilly flat at 100m, you can interpolate the rise by using 150m drop as being the height of rise at 50m (high point for ease of calculation (friction/velocity change/spin change/gravity actually pull the high point back toward the muzzle - but using center of flat is close enough) . This changes slightly with barrel angle for drop at greater ranges. Remember as the projectile loses energy/velocity/spin, the effect of gravity increases.

Think a long tailed student's  t distribution or a long tailed z distribution as the basic shape, the steep slope of the curve being the terminal side of the ballistic projection.


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## Mac_NZ (Mar 31, 2011)

x SF med said:


> You need to calculate the 'vacuum parabola' from muzzle to the crossing point of the 'flat trajectory' if you figure poa/poi is essentilly flat at 100m, you can interpolate the rise by using 150m drop as being the height of rise at 50m (high point for ease of calculation (friction/velocity change/spin change/gravity actually pull the high point back toward the muzzle - but using center of flat is close enough) . This changes slightly with barrel angle for drop at greater ranges. Remember as the projectile loses energy/velocity/spin, the effect of gravity increases.
> 
> Think a long tailed student's  t distribution or a long tailed z distribution as the basic shape, the steep slope of the curve being the terminal side of the ballistic projection.



Who are you and what have you done with the Troll?


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## Diamondback 2/2 (Mar 31, 2011)

Damn old man, where in the hell did all that come from? I would hate to read your data book…. lol:eek:


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## x SF med (Mar 31, 2011)

sometimes you actually have to do the math because you don't have the charts or a fancy computer.

I didn't get into charge versus projectile weight calculations and how that changes the actual initial parabola from muzzle, did I?    You guys always forget I was an 11B/18B before I got better and became a medic.  I still like making boomsticks do their magic.


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## Crusader74 (Mar 31, 2011)

x SF med said:


> You need to calculate the 'vacuum parabola' from muzzle to the crossing point of the 'flat trajectory' if you figure poa/poi is essentilly flat at 100m, you can interpolate the rise by using 150m drop as being the height of rise at 50m (high point for ease of calculation (friction/velocity change/spin change/gravity actually pull the high point back toward the muzzle - but using center of flat is close enough) . This changes slightly with barrel angle for drop at greater ranges. Remember as the projectile loses energy/velocity/spin, the effect of gravity increases.
> 
> Think a long tailed student's  t distribution or a long tailed z distribution as the basic shape, the steep slope of the curve being the terminal side of the ballistic projection.




Does that change during extreme weather?  Ie Rain or Hot Weather?  I remember a rd rises in rain and drops in hot weather..


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## x SF med (Mar 31, 2011)

any significant change in Barometric mmhg will effect the round/ballistics.  Rain - lower poressure, more friction and the possibility of minor deflections.  hot weather lower friction, higher pressure.

Most of that is internal calculus...  better known as Kentucky windage.


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## Chopstick (Mar 31, 2011)

XSF is really Stephen Hawking???:confused:


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## x SF med (Mar 31, 2011)

I have warned all of you not to be fooled by my Trollish figure...  there is more to me than meets the eye...  one of these days you will believe me.  Until then, beware.  I may surprise yet again.


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## Marauder06 (Mar 31, 2011)

SgtUSMC8541 said:


>



Math?  Math can be sexy(2nd from right)...


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## policemedic (Mar 31, 2011)

This thread just satisfied my daily learn-something-new requirement.  Times 12.


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## AWP (Mar 31, 2011)

This thread made my brain hurt.


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## SgtUSMC8541 (Mar 31, 2011)

Its shit like this that made us invent Nerds to make calculators. Oh, and BDC's.


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## Robbie2213 (May 17, 2011)

I'm right there with you xSF....is that sad or what?  Mathletes unite!


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## Polar Bear (May 17, 2011)

Marauder06 said:


> Math? Math can be sexy(2nd from right)...
> 
> View attachment 3889



Is You? I knew you where a chick


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## DA SWO (May 17, 2011)

Polar Bear said:


> Is You? I knew you where a chick


Bwahaha

I'd let all of the play with my slide rule.


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## Polar Bear (May 17, 2011)

Frisco said:


> I've been searching for like an hour online and I can't find a formula to calculate bullet drop.
> 
> I don't need tables, I'm doing it for an assignment for my trig class so I have to do the math myself.
> Any ideas? I think I've calculated all the actual data I need, I just don't know exactly how to put it together.. Thanks.



If you pull the trigger and see some dirt fly up in front of the target raise your front sight. Just saying


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## Etype (May 18, 2011)

x SF med said:


> It's a slope formula with the added distractors of velocity, gravity, time - it could be even more complicated with spin and wind over distance. It's a 4 dimensional slope equation. Remember before there is drop there is rise (ballistic jump) so you have a parabolic/ballistic slope.



But we do understand, the bullet doesn't actually travel 'up' during the rising branch, right? That's just because of the angle between the line of sight and and the bore. The bullet is being acted upon by atmospherics from the time it begins to move from the case, and is being acted upon by gravity from the time it leaves the barrel- so, it's dropping from the moments the tail passes the crown, it just has the illusion of a rise because POA/POI is not 0m.


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## x SF med (May 18, 2011)

Etype said:


> But we do understand, the bullet doesn't actually travel 'up' during the rising branch, right? That's just because of the angle between the line of sight and and the bore. The bullet is being acted upon by atmospherics from the time it begins to move from the case, and is being acted upon by gravity from the time it leaves the barrel- so, it's dropping from the moments the tail passes the crown, it just has the illusion of a rise because POA/POI is not 0m.


 
I was making it easy ... it's actually a straight decreasing parabolic function based on the angle of the barrel, speed, weight and twist of the bullet, with a few other added distractors/forces working on the projectile besides gravity...

What you are saying is true - a bullet fired from a perfectly level barrel is being acted upon by gravity in a perpendicular manner from the instant the projectile is clear of the sides of the barrel - but gravity is mitigated by velocity and spin, which are mitigated by atmospherics and friction....


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## AWP (May 18, 2011)

And so dies the "Bravo's couldn't pass the math portion of the Charlie course" myth.


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## RetPara (May 18, 2011)

Marauder06 said:


> Isn't there an iPod app for that?


Actually there is.  It's Ballistic v2.5.2   Works real nice.  It also has a range log  and distance calculator to work off the scope data.


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## Marauder06 (May 18, 2011)

RetPara said:


> Actually there is. It's Ballistic v2.5.2 Works real nice. It also has a range log and distance calculator to work off the scope data.


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## RetPara (May 19, 2011)

Mara I don't think that is the app from my post.  That's "Bulletflight" from Knights.  It was pulled completely out of the Apple App Store in the last... year and a half?  Then in the App Store it was replaced by a more water down version.  You could also install it from Knights web site.  The software download has been pulled off that site also now.  Knight actually sells a "ballistic computer" now.
http://www.knightarmco.com/bulletflight/index.htm


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## Marauder06 (May 19, 2011)

RetPara said:


> Mara I don't think that is the app from my post. That's "Bulletflight" from Knights. It was pulled completely out of the Apple App Store in the last... year and a half? Then in the App Store it was replaced by a more water down version. You could also install it from Knights web site. The software download has been pulled off that site also now. Knight actually sells a "ballistic computer" now.
> http://www.knightarmco.com/bulletflight/index.htm


 
Not sure which one it is, it was the only one I had in the clipart vault ;)


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## Etype (May 19, 2011)

ATrag is the tits, it's a PDA ap.  It has more variables than some other programs and puts you DEAD on.  Like MOA accuracy to 1,000m.


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## Totentanz (May 25, 2011)

Anybody got a solid ballistics book/reference?  I understand the math well enough and I've been through 100-level mechanical physics, but I've never really had the fundamental mechanics driving internal/external ballistics torn apart in detail.


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## x SF med (May 25, 2011)

Totentanz said:


> Anybody got a solid ballistics book/reference? I understand the math well enough and I've been through 100-level mechanical physics, but I've never really had the fundamental mechanics driving internal/external ballistics torn apart in detail.


 
*Computational Ballistics III*


*Edited By: C.A. BREBBIA, Wessex Institute of Technology, UK and A.A. MOTTA, Brazilian Navy Research Institute, Brazil 
*

*Price: USD170.00 
*ISBN: 978-1-84564-077-4
eISBN: 9781845642815
Pages: 256
Book Series: WIT Transactions on Modelling and Simulation
Series Volume: 45
Published: 2007
Hardback

The study of computational ballistics is one of the most challenging scientific endeavours, not only because of the diversity of time and space scales involved in practically all problems, but due to its interdisciplinary character. Interest in ballistics has grown considerably recently as a result of the complexity of the political and military situation in many parts of the world.

The classical subdivision into internal, external and terminal ballistics now encompasses numerous applications on how to model and protect against accidental or man made explosions. Many other civilian applications of ballistics are also of growing importance as impact, crash and blast problems are a by-product of more sophisticated techniques involving dimensions and speeds impossible to achieve a few years ago.

This volume contains papers presented at the Third International Conference on Computational Ballistics . The volume covers the following topics: fluid flow aerodynamics, interior ballistics, terminal ballistics, experimental mechanics/ballistics and field testing, new developments in computational techniques, and systems and technology.

site:
*http://www.witpress.com/978-1-84564-077-4.html*

site link will get you to the contents and preface through another link.


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## Totentanz (May 26, 2011)

Troll,

I appreciate the link, but the material seems to be more at the postgrad/postdoc level.  I'm looking for something around the 200-300 level.  More like a mechanics text with a focus on ballistics, but without all the retarded "If we assume [frictionless surfaces, rods of infinite length, atmospheric conditions are negligible, etc]" statements and actually start discussing the meat of those assumptions.... if that makes sense.

Cool material being discussed there - stochastic modeling on a 60mm, data mining on mil systems, and counter-mortar ssytems are all cool, just not quite what I'm looking for.


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## x SF med (May 26, 2011)

Totentanz said:


> Troll,
> 
> I appreciate the link, but the material seems to be more at the postgrad/postdoc level. I'm looking for something around the 200-300 level. More like a mechanics text with a focus on ballistics, but without all the retarded "If we assume [frictionless surfaces, rods of infinite length, atmospheric conditions are negligible, etc]" statements and actually start discussing the meat of those assumptions.... if that makes sense.
> 
> Cool material being discussed there - stochastic modeling on a 60mm, data mining on mil systems, and counter-mortar ssytems are all cool, just not quite what I'm looking for.


 
Okay...  I give up...  I out geeked the math geek....  I am ruined and should go into hiding.:eek:


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## Marauder06 (May 26, 2011)

The Troll is officially too smart for Shadowspear, he should be banned.  Chop too.


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## x SF med (May 26, 2011)

Marauder06 said:


> The Troll is officially too smart for Shadowspear, he should be banned. Chop too.



So, if I prove I'm a dumbass and not a witch, I can stay and you'll ban Chop?
Proof of dumbassedness = exiting perfectly good aircraft in flight using CARP.
Proof I'm not a witch... Chop turned me into a newt, twice.

See ya later Chop... looks like you get an unplanned 1 week vacation from the site...


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## Marauder06 (May 26, 2011)

x SF med said:


> So, if I prove I'm a dumbass and not a witch, I can stay and you'll ban Chop?
> Proof of dumbassedness = exiting perfectly good aircraft in flight using CARP.
> Proof I'm not a witch... Chop turned me into a newt, twice.
> 
> See ya later Chop... looks like you get an unplanned 1 week vacation from the site...



OK, deal.  The Troll stays, Chop goes.


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## HOLLiS (May 26, 2011)

Easiest thing,  a ballistic calculator,  they got 'em for PC and smart phones.  No math involved, it does it all except inter bullet data and velocity.   Some even have a nice graph.

Troll, just out smarted Mara,,,,,,,,,,,,,  he is smart and why not.,   When a good looking guy is turned into a troll by a witch (Chops).  It makes all the much more neater for the witch when the victim remembers what they were like.    Another reason not to mess with the Witch.


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## x SF med (May 26, 2011)

HOLLiS said:


> ... When a good looking guy is turned into a troll by a witch (Chops). It makes all the much more neater for the witch when the victim remembers what they were like. Another reason not to mess with the Witch.



Nope, always been a Troll...  except for the two occasions when witchipoo turned me into a newt...  I'm taken aback at your insinuation that Trolls are of below average intelligence... your prejudice is showing and this is disturbing to me that I drink beer with such a bigot....   where's the friggin bottle opener and seared animal flesh?


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## Turtle (May 27, 2011)

Face it, Troll IS a ballistic computer


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## HOLLiS (May 27, 2011)

x SF med said:


> Nope, always been a Troll... except for the two occasions when witchipoo turned me into a newt... I'm taken aback at your insinuation that Trolls are of below average intelligence... your prejudice is showing and this is disturbing to me that I drink beer with such a bigot.... where's the friggin bottle opener and seared animal flesh?




This weekend,  seared flesh, beer and shooting these:


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## Totentanz (May 30, 2011)

x SF med said:


> Okay... I give up... I out geeked the math geek.... I am ruined and should go into hiding.:eek:



LOL, when it comes to ballistics and the surrounding physics... you got me there.

H: I trust ballistics calculators, but I'm not really interested in just computing dope. I want to actually understand why a bullet stabilizes with a certain velocity and twist, why it behaves the way it does when it goes subsonic, why one ogive is better than another, etc. Most rigorous collegiate-level physics texts (at least the ones I've come across, hence the question) don't want to address those questions in a real-world manner without their assumptions.... and I'm skeptical of most internet sources.

FWIW, I did find this page (http://www.jbmballistics.com/ballistics/topics/topics.shtml), which seems to be in the ballpark and grounded in reality.


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## Etype (May 31, 2011)

You seem to have researched this a bit, so if my redneck explanation is insulting, consider it intended for the other people.

A bullet will fly well in supersonic flight and in subsonic. Whitworth rifles, 40mm rounds, etc. are examples of pretty darn accurate subsonic rounds. It's the subsonic realm that destabilizes a bullet.

Two good terms to understand-
Transonic- when there is a variation of velocities around the bullet, some of the air is supersonic, some of it is subsonic. Think of the Supersonic 'wave' (that you see as trace) catching up to the bullet and flowing across it.

Wave Drag- Shock waves created by air moving at supersonic speed around or near a non-supersonic object.  (someone help me out if you have a better definition)
How does this effect a bullet? During transonic flight, air moves fastest around the largest part of the bullet (venturi effect, maybe?), however, it slows down to below the speed of sound before it reaches the rear. Since the whole bullet is not moving at the speed of sound, the supersonic shock wave effects the rear of the bullet and induces wobble/tumbling.

Nutshell non-scientific explanation-
The sonic boom that you hear from a supersonic bullet (or jet) is all the sound (or energy from the bullet pushing the air apart) compressed until all the sound waves are stacked on top of each other. Since the bullet is moving faster than the speed of sound, they stack up (really they are just sound waves that are very close together). That 'stack' of compressed air and sound has a lot of energy, anyone who's had supersonic rounds fired right over their head (think the pit at a sniper range) knows this from the sound- that little bullet makes a lot of noise.

During transonic flight, which I believe covers less than about 200m of flight, all of that energy sweeps back across the round from rear to front (think the cool videos of fighters breaking the sound barrier, except in reverse). This is what causes a supersonic bullet to wobble in transonic and early subsonic flight, and eventually tumble. Luckily, it happens somewhat predictably and we can obtain data on the range and on good systems like ATrag, however it's nowhere near as consistent as supersonic flight.


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