Talk:External ballistics

Magnus Effect

Perhaps I'm misunderstanding but reading the section on the Magnus Effect, I can't tell what the difference is between this and the gyroscopic preservation of angular momentum. Is the Magnus effect a more specific name for this, used in balistics? or is there a difference which I didn't spot? 81.97.166.238 (talk) 23:06, 30 October 2011 (UTC)

Small arms focus

This page is focused on small-arms ballistics. Great, but some of it applies to artillery and some of it doesn't and there's no indication which. The entry also needs to be split up into sections. I wish I knew enough ballistics to do this. --Andrew 02:12, Apr 17, 2004 (UTC)

As I originally wrote it, I focused on small arms ballistics because that's what I have experience with, and what most individuals would be dealing with. Artillery is pretty much a military only subject. The big difference between small arms and artillery ballistics has to do with the ranges involved; small arms generally aren't used at ranges of over 1000 yards, whereas artillery can be used at ranges of 20+ miles. In the cases of extreme range (possible for artillery because of the tremendous increase in BC due to the scale) elements like using a BC defined as a function of velocity rather than an average BC for all velocities really comes into play. Since artillery ballistics seems to be a superset of small arms ballistics, and of less general interest, perhaps the best organization would be to cover small arms ballistics then cover artillery ballistics in a separate section? --scot, 27 April 2004

That makes sense to me. I wasn't particularly looking at the military applications (I sort of think of all guns as military, which really isn't true; not even all guns for killing people are military) so much as the stuff that's relevant for mass drivers. Which won't really be helped by the artillery stuff. I just noticed this seemed oddly incomplete. --Andrew 18:04, Apr 27, 2004 (UTC)

I am quite skeptical about this explanation: "Since the target is co-rotating with the Earth, it is in fact a moving target, so in order to hit it the gun must aim slightly ahead of the target, the gun must be aimed to a point where the bullet and the target will arrive simultaneously." This explanation makes it sound like a shooter in a moving reference frame needs to anticipate the motion of a target in the same reference frame. I suspect that the author wanted to talk about the Coriolis effect here, which causes deflections in a rotating reference frame. -- Blaise Gassend, 25 July 2006

Bullets fired straight up

Any material on that? Believe it or not, we lawyers sometimes have to deal with a client charged with having fired a bullet straight up into the sky -- no one knows where it came down -- and this has been deemed a "violent act." Does a bullet, having been shot straight up, generate enough force to injure someone when it comes down?

Thank you.

April R. Goode Assistant Federal Defender April_Goode@fd.org

That depends on just how "up" it is fired. There are cases where guns fired up at moderate angles, maybe 30 degrees, have killed people, but that is because there is still a significant degree of forward velocity retained when the bullet impacts. Check out the information on the Sandy Hook tests, linked in the .45-70 article. That involves very heavy bullets at very long ranges, over 3000 yards. Those rifle bullets were hitting with the force of a heavy handgun bullet, and would certainly kill.

Now straight up is a completely different issue. In this case, the limiting factor is the terminal velocity of the bullet. This varies considerably based on the size and weight of the bullet, and is related to the sectional density. This is calculated by the bullet mass divided by the surface area (bullets tend to fall sideways, which exposes far more surface area in rifle bullets, moderately more in handguns). Smallbore firearms are not going to land with lethal force, and rifles, which tend to fire lighter bullets, will produce less severe wounds than handguns. There have been numerous studies on bullets fired into the air and their potential for wounding; I think the US military did one, maybe Hatcher. There was also a Mythbusters episode where they did testing using ballistic gelatin and an airgun firing the bullets at measured terminal velocity, and also did test with bullets fired straight up at full power and landing in packed dirt where penetration could be measured. scot 21:48, 6 September 2006 (UTC)

Uhh laws of physics. If it is shot straight up, the bullet will come back down at the same speed as it left the barrel of the gun, so yes it is quite lethal when it comes back down. Inforazer 17:16, 11 September 2006 (UTC)

And what planet do you live on? Here on Earth, the atmosphere limits the terminal velocity of small arms bullets to a few hundred feet per second. Go look in your physics book again, and look for the phrases "Ignoring friction..." and "Ignoring air resistance..." that preceed many of the excercises. If you still don't believe me, check out the experimental work done by Julian Hatcher and the Mythbusters (episode 50), both of whom have looked into this. scot 18:52, 11 September 2006 (UTC)

"And what planet do you live on?" Leave comments like that out of a discussion please, it incites flames. A bullet is designed to be fairly aerodynamic, so air resistence is minimal, as a result it is still lethal when it comes back down. There have been incidents where people shot bullets straight up, and they came back down, and penetrated through the human skull. Take a look at this link, http://www.cnn.com/2003/US/South/11/24/klan.initiation.ap/index.html Inforazer 15:23, 26 September 2006 (UTC)

OK, sorry about that--however, if you're going to invoke the laws of physics, invoke 'em all, because leaving out air resistance in this case causes order of magnitude errors. According to Julian Hatcher's experiments, the terminal velocity of a .30 caliber rifle bullet, falling base down (as you would expect from being fired straight up) is about 300 feet per second. This is less than the velocity of the typical BB gun, and while the mass is greater, it's still unlikely to cause a lethal wound. The news article was seriously lacking in solid data; I suspect that, since he was tied to a tree, that he was hit by a richochet from a tree branch rather than a falling bullet. First, let's look at the energy. Assume a 115 grain 9mm at 300 fps; that will generate just 23 ft. lbs. of energy, far less than the 80 ft. lbs. of a standard velocity .22 Long Rifle. Next, consider the odds involved. According to my external ballistics program, a bullet with a ballistic coefficient of .13 fired straight up at 1150 fps (pretty typical 9mm load) is going to reach a height of 3500 feet in a time of 12.7 seconds before it starts to fall. If the barrel is off vertical by as much as 1 degree, it's going to be horizontally displaced by over 60 feet. Add to that the effects of wind on the bullet's travel (it's going to be much slower coming down) and you've got about 30 seconds to drift in the wind. scot 16:56, 26 September 2006 (UTC)

I've done a bit more digging for data and fiddling with my external ballistics code, and I've come up with a simulation that I think covers things. First, here's my assumptions, for a 9x19mm loaded with a 115 grain bullet:

Speer part 4618, .357 148gr hollow based wadcutter, BC 0.05, SD 0.165

Speer part 3996, 9mm 115gr total metal jacket round nose, BC 0.177 SD 0.13

Accurate powder load data, 115gr FMJ, max load of #7, 1196 fps

The 115 grain bullet is to get the ballistic coefficient when the bullet is travelling upwards, the wadcutter is to give me a ballistic coefficient for a flat nosed bullet. Since the wadcutter is heavier, giving it a higher sectional density, we multiply the 0.05 BC by 0.13 / 0.165, which gives us an estimated BC for the TMJ bullet falling backwards of about .04.

The simulation starts with the bullet moving upwards from a distance of 8 feet, with a velocity of 1196 fps, and a BC of 0.177. When the bullet reaches the peak, the BC is changed to 0.04 to represent its base-first fall. Note that this simulation does NOT account for atmospheric temperature or pressure changes as altitude changes, so in reality the bullet would travel a bit higher than the simulation states, do to the reduced drag. The simulation stops when the height drops to below zero. The code is based on a very precise 4 point curve fit to the ballistics charts in a Speer reloading manual, which are in turn based on the G1 drag model.

Here's the program output:

• Time 0.0, height 8.00, velocity 1196.00
• Time 1.0, height 952.32, velocity 748.80
• Time 2.0, height 1598.30, velocity 564.50
• Time 3.0, height 2106.33, velocity 459.10
• Time 4.0, height 2526.87, velocity 385.59
• Time 5.0, height 2882.88, velocity 328.44
• Time 6.0, height 3186.88, velocity 280.78
• Time 7.0, height 3446.40, velocity 239.04
• Time 8.0, height 3666.22, velocity 201.11
• Time 9.0, height 3849.45, velocity 165.67
• Time 10.0, height 3998.09, velocity 131.83
• Time 11.0, height 4113.43, velocity 98.96
• Time 12.0, height 4196.20, velocity 66.63
• Time 13.0, height 4246.78, velocity 34.56
• Time 14.0, height 4265.33, velocity 2.55
  • Peak height 4265.43, time 14.0796
• Time 15.0, height 4251.89, velocity -29.44
• Time 16.0, height 4206.54, velocity -61.18
• Time 17.0, height 4129.82, velocity -92.03
• Time 18.0, height 4023.11, velocity -120.99
• Time 19.0, height 3888.83, velocity -147.00
• Time 20.0, height 3730.38, velocity -169.21
• Time 21.0, height 3551.82, velocity -187.22
• Time 22.0, height 3357.31, velocity -201.16
• Time 23.0, height 3150.70, velocity -211.52
• Time 24.0, height 2935.23, velocity -219.00
• Time 25.0, height 2713.45, velocity -224.25
• Time 26.0, height 2487.26, velocity -227.89
• Time 27.0, height 2258.05, velocity -230.37
• Time 28.0, height 2026.79, velocity -232.05
• Time 29.0, height 1794.13, velocity -233.19
• Time 30.0, height 1560.54, velocity -233.94
• Time 31.0, height 1326.32, velocity -234.45
• Time 32.0, height 1091.69, velocity -234.79
• Time 33.0, height 856.78, velocity -235.02
• Time 34.0, height 621.68, velocity -235.17
• Time 35.0, height 386.46, velocity -235.27
• Time 36.0, height 151.16, velocity -235.33
  • Impact at time 36.6422, velocity -235.37

Note that due to the higher ballistic coefficient used in this run (0.177 vs. 0.13) the bullet travels significantly higher. The 9mm bullet shows a significantly lower terminal velocity than Hatcher's tests, which is exactly what I'd expect; the flat based 9mm bullet is lower in sectional density and less aerodynamic when falling than the boattail .30 caliber bullets that Hatcher tested with. scot 18:32, 26 September 2006 (UTC)

Merge

Agree The Bullet drop information is properly part of this subject and is mostly if not fully already covered here. Arthurrh 18:25, 19 October 2007 (UTC)

Agree I have no problem with such a merge by the proposer. Francis Flinch 12:03, 20 October 2007 (UTC)

Agree So, who's going to do the work? --'''I am Asamuel''' (talk) 22:05, 2 April 2008 (UTC)

Agree But a further comment It's two years on from the comments on handguns, and those comments still add up. The article is very technical, but doesn't answer basic questions like "how quickly does a projectile slow down" or even "what is the typical path of a projectile". You can't see the wood for the trees. Adding bullet drop will help, but really this does need a fuller non-technical introduction. I don't have the knowledge to add it - but I do know that this article doesn't tell me what I wanted to know. The Yowser (talk) 14:15, 13 June 2008 (UTC)

Does the magnitude Coriolis drift depend on the azimuth?

The magnitude of the drift depends on the location, azimuth, and time of flight.

The formula for the Coriolis acceleration in the Coriolis effect page doesnt show the direction of fire to affect the magnitude, as both north and easterly components of velocity affect the coriolis acceleration equally. I dont think that the azimuth/direction of fire affects the drift. Diablod666 18:37, 22 February 2009 (UTC)

Body lift can cause a bullet to rise

A friend (research physicist, former Army sniper and now competive shooter) says that some bullets actually do rise even if the bore is level, contradicting what is stated in the article. He writes (CG means center-of-gravity):

"The bulk of the "apparent" lift is due to the different height of the sights (most pronounced with a scope raised at ~ 1.5" above the bore) that once sighted in at 25 yds, it will hit point of aim at around 220 yds again. So this is "apparent" lift. However, for a long range match bullet with the CG not in the geometrical center front-to-back and high ballistic coefficient, there's a small angle of attack once the bullet escapes the bore that provides a small amount of lift. For the vast majority of rifles bullets used in hunting, the CG is not behind the geometrical center and there's no perceptible rise. Hunting bullets are mostly made with exposed lead tips for expansion in flesh, while most match bullets have a hollow cavity in the nose (BTHP) precisely in order to shift the CG toward the base of the bullet. How noticeable the body lift of a match bullet at something like 3000 fps is, is argued back and forth but the fact that heavier match bullets tend to exhibit better accuracy (in minutes of angle) at say 300 yds compared to 100 yds, is an indication of some body lift and delayed stabilization."

In any case, the laws of physics do not prohibit a bullet from rising relative to the bore direction, as aerodynamic forces can cause lift due to a positive angle-of-attack, as my friend notes. I believe the article is in error on this point. — Preceding unsigned comment added by Ewolin (talk • contribs) 18:25, 3 April 2012 (UTC)

The article mentions some subtle affects that effect trajectories in the vertical plane. Are your ideas pointing to the Magnus or Poisson effect, etc. and can they be referenced? The phenomenon of smaller angular groups at longer ranges also termed bullets "going to sleep" is a phenomenon with multiple explanations (aerodynamic jump near the muzzle, epicyclic swerve, drift, stability changes). Here is an interesting text/video regarding epicyclic motion of a bullet http://www.appliedballisticsllc.com/epswerve.html. The article contains text plus a reference regarding research into guided projectiles where this phenomenon is mentioned as observed by researchers for an experimental fin (no spin) stabilized projectile. I think the article can contain debatable, not elaborately studied or not well understood information as long as readers can easily see that.--Francis Flinch (talk) 12:10, 4 April 2012 (UTC)

Predictions of several drag resistance modelling and measuring methods

States that a 300 grain bullet was used. Should it not state caliber also? Msjayhawk (talk) 14:29, 21 November 2013 (UTC)

error 404 - snipers hide

http://www.snipersparadise.com/ballistics/bulletbasics.htm is currently an Error 404 203.129.45.210 (talk) 00:37, 31 August 2014 (UTC)

Compliment from a reader

From an email received via OTRS this morning:

I have viewed hundreds of pages over the years and contributed on one page so I can tell you nothing I have seen comes close to rivaling the technical information on the “external ballistics” page. Now that is a concise treatise of immense proportions with no wandering junk. Wow, simply excellent and I imagine was majority written by one author. Congratulations.

Well done to all involved with the content of this page; you're clearly doing something right! Yunshui ^雲_水

"unpowered projectiles"?

Doesn't external ballistics apply to powered projectiles such as rockets as well? It's the lack of lift that is important. Aiming an unguided rocket is identical to aiming a bullet, only the equation for how much it will slow in flight is different, since the rocket is accelerating during part of its flight. But you still have to account for "drop" and "windage", etc. What about base-bleed artillery shells?.45Colt 07:51, 8 September 2015 (UTC)

exterior ballistics ( according to Merriam-Webster dictionary)
noun plural but usually singular in construction
Definition of EXTERIOR BALLISTICS

a science that deals with the factors affecting the behavior of a projectile after the projectile leaves the muzzle of the firing weapon (such as the initial velocity of the projectile, the force of gravity, and atmospheric conditions)

Base bleed shells inject gas in the low pressure area behind a shell in flight to increase the pressure behind the shell to reduce drag.--Francis Flinch (talk) 17:35, 8 September 2015 (UTC)

Okay....but it doesn't say UNPOWERED projectiles, does it? In any case, a rocket behaves exactly like a bullet, except that it has thrust being provided to it. If that's not "external ballistics", then what is it called? Plain "ballistics"? A rocket motor only burns for a very short time; afterwards, its just an unpowered projectile. Think of the burn phase as an extra-long gun barrel (that also allows some bullet drop even during acceleration). As far as artillery shells, I was thinking of Rocket-assisted projectiles, which people seem to commonly call "base-bleed", even though they are different. In any case, I'm pretty sure "external ballistics" does NOT only apply to bullets from a firearm. Google "unguided rocket external ballistics". I see quite a number of references to unguided rocket external ballistics, and from some pretty professional looking sources. This one is a paper from the USAF "Foreign Technology Division, entitled" External Ballistics" (translated from Russian, apparently). Note that more than half of the topics in the index section are about rockets, the rest artillery. The introduction begins:

  "In this book are set forth the theoretical bases of external rocket ballistics and artillery shells". 
  "Are proposed the methods of investigations of trajectories...and the optimum solutions to external ballistics. It is estimated the effect of different perturbation factors on the stability of flight, scattering of trajectories and error after firing."

http://www.dtic.mil/dtic/tr/fulltext/u2/a067144.pdf

And then there is this, "Ballistic Design of Solid Propellant Rocket Motors", from the University of Defense in Brno, top of the second page:

  "One of the existing possibilities of the estimation improvement  can  be  the  determination  of  the  maximum  rocket  range  by  solving  the main task of external ballistics for the given rocket."
  "The main task of external ballistics is solved by numerical integration of the set of equations, describing the rocket trajectory in either Cartesian or polar co-ordinate system"

http://www.zmne.hu/aarms/docs/Volume3/Issue4/pdf/01kone.pdf

And how about a real book, "The Flight Of Uncontrolled Rockets", by F.R. Gantmakher:

  "The principle problem in the external ballistics of unguided rockets is concerned with the motion of the rocket as a rigid body..."

https://books.google.com/books?id=Pc2jBQAAQBAJ&pg=PA290&lpg=PA290&dq=unguided+rocket+external+ballistics&source=bl&ots=wXi4j1cRuG&sig=tB5YJTtoAxSwvTJ83xtyjpU6fN0&hl=en&sa=X&ved=0CCcQ6AEwAmoVChMIrdXTiue1yAIVJ_5yCh2bPAWp#v=onepage&q=unguided%20rocket%20external%20ballistics&f=false

This mentions rocket "exterior ballistics" as a keyword: https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/AD436405.xhtml And the Free Dictionary says (for what it's worth):

  " Exterior ballistics is concerned with the motion of a projectile while in flight and includes the study not only of the flight path of bullets but also of bombs, rockets, and missiles."

To me "external" ballistics means "the behavior of a powered or unpowered, non-lifting projectile after leaving its initial support", be that a gun barrel, a rocket rail, a bow, or a catapult sling..45Colt 17:26, 9 October 2015 (UTC)

No, the definition of exterior ballistics includes, traditionally, only unpowered rocket flight. If it's powered; if the rocket is thrusting, it's part of interior ballistics.

That's how it's normally defined.GliderMaven (talk) 01:34, 10 October 2015 (UTC)

External links modified

Hello fellow Wikipedians,

I have just added archive links to one external link on External ballistics. Please take a moment to review my edit. If necessary, add {{cbignore}} after the link to keep me from modifying it. Alternatively, you can add {{nobots|deny=InternetArchiveBot}} to keep me off the page altogether. I made the following changes:

• Added archive https://web.archive.org/20071107104656/http://www.snipersparadise.com/ballistics/bulletbasics.htm to http://www.snipersparadise.com/ballistics/bulletbasics.htm

When you have finished reviewing my changes, please set the checked parameter below to true to let others know.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—^{cyberbot II}_{Talk to my owner:Online} 04:08, 7 January 2016 (UTC)

Coriolis

I just reinstated some changes I made yesterday. Here is the link to the diff: [1]

I think the new version is much clearer and less garbled, but more importantly, it removes several erroneous statements. For example, the old text confuses the centrifugal force with the Eötvös effect, which is actually the vertical component of the Coriolis force, and erroneously claims that it is automatically compensated when line-of-sight is the reference.Rracecarr (talk) 16:28, 12 January 2017 (UTC)

I readded some information + links without the claim that Eötvös is automatically compensated when line-of-sight is the reference. I think we have to make clear that Eötvös influences gravity as further described in the eqiuvalence article.--Francis Flinch (talk) 20:36, 12 January 2017 (UTC)

Thanks for the reply. I think the section is currently in a pretty decent state. However, I am dubious of the claim that the equivalence principle is relevant--is there any source for this? I also don't think the Eötvös effect reference ([2]) is very good: it is hosted at an extertal website, but is obviously a direct copy from the internal Eötvös effect page. Rracecarr (talk) 00:09, 13 January 2017 (UTC)

The Loránd Eötvös and Eötvös experiment articles contain some more information. I will remove the connection with the weak equivalence principle to avoid overly complex concepts. The (vertical) effect of moving trough the gravity field of our planet is counterintuitive enough for the general reader in its simplest form. When using the Paris Gun during World War 1 the Germans had to factor in Coriolis.--Francis Flinch (talk) 09:30, 13 January 2017 (UTC)

The article states "The deflection is to the right of the trajectory in the northern hemisphere, to the left in the southern hemisphere" and "The direction of this horizontal curvature is to the right in the northern hemisphere and to the left in the southern hemisphere". Surely this is not dependent on the hemisphere, but on the direction? Wouldn't a northward shot on the southern hemisphere have a deflection in the same direction as a northward shot in the northern hemisphere? And since left and right are dependent on the orientation of the observer, wouldn't it be better to use east or west? As a last aside: the link to reference 63 is dead. 217.103.1.27 (talk) 12:28, 14 June 2017 (UTC)

External links modified

Hello fellow Wikipedians,

I have just modified 4 external links on External ballistics. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Added archive https://web.archive.org/web/20080219154147/http://www.lima-wiederladetechnik.de/Englisch/LM-Class-Bullets.htm to http://www.lima-wiederladetechnik.de/Englisch/LM-Class-Bullets.htm
• Added archive https://web.archive.org/web/20090802154317/http://02b0516.netsolhost.com/blog1/?p=62 to http://02b0516.netsolhost.com/blog1/?p=62
• Added {{dead link}} tag to http://www.lapua.com/uploads/media/LapuaBulletsDragCoefficient.pdf
• Added {{dead link}} tag to http://www.lapua.com/uploads/media/LapuaBulletsCD-Data.zip
• Added archive https://web.archive.org/web/20071107104656/http://www.snipersparadise.com/ballistics/bulletbasics.htm to http://www.snipersparadise.com/ballistics/bulletbasics.htm
• Corrected formatting/usage for http://www.snipersparadise.com/ballistics/bulletbasics.htm

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 12:11, 26 September 2017 (UTC)

Relativistic Effects

Currently, the article states that:

 In super gun artillery cases, like the Paris gun, very subtle relativistic effects that are not covered in this article can further refine aiming solutions.

The muzzle velocity of the Paris gun is 1500 m/s and firing range is 100 km, and these numbers are far lower than the ones that usually come up in the presence of relativistic effects.

Is there any credible resource for this claim? — Preceding unsigned comment added by 134.3.205.210 (talk) 09:38, 4 October 2017 (UTC)

External links modified (January 2018)

Hello fellow Wikipedians,

I have just modified 13 external links on External ballistics. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Added archive https://web.archive.org/web/20080524043934/http://www.lima-wiederladetechnik.de/Weite-Schuesse/Weite-Schuesse-3.htm to http://www.lima-wiederladetechnik.de/Weite-Schuesse/Weite-Schuesse-3.htm
• Added {{dead link}} tag to http://www.lapua.com/uploads/media/338LapuaMagnum2009.pdf
• Added {{dead link}} tag to http://www.lapua.com/uploads/media/338LapuaMagnum300grScenar2009.pdf
• Added archive https://web.archive.org/web/20080829171747/http://home.sprintmail.com/~pejsa/aboutartpejsa.htm to http://home.sprintmail.com/~pejsa/aboutartpejsa.htm
• Added archive https://web.archive.org/web/20120701181622/http://www.lapua.com/en/customer-center/lapua-ballistics/download-lapua-edition.html to http://www.lapua.com/en/customer-center/lapua-ballistics/download-lapua-edition.html
• Added archive https://web.archive.org/web/20120701033430/http://www.lapua.com/en/customer-center/lapua-ballistics/lapua-ballistics-software.html to http://www.lapua.com/en/customer-center/lapua-ballistics/lapua-ballistics-software.html
• Added archive https://web.archive.org/web/20160107040743/http://www.appliedballisticsllc.com/spindrift.html to http://www.appliedballisticsllc.com/spindrift.html
• Added archive https://web.archive.org/web/20100503054138/http://www.jbmballistics.com/calculations/common/bclibrary.shtml to http://www.jbmballistics.com/calculations/common/bclibrary.shtml
• Added archive https://web.archive.org/web/20090310233917/http://www.remington.com/products/ammunition/ballistics/remington_shoot_ballistics_software.asp to http://www.remington.com/products/ammunition/ballistics/remington_shoot_ballistics_software.asp
• Added archive https://web.archive.org/web/20071206032204/http://www.bestpalmsoftware.com/mathematic/misc/pocketssf_sharpshooterfriend344.htm to http://www.bestpalmsoftware.com/mathematic/misc/pocketssf_sharpshooterfriend344.htm
• Added archive https://web.archive.org/web/20120701181622/http://www.lapua.com/en/customer-center/lapua-ballistics/download-lapua-edition.html to http://www.lapua.com/en/customer-center/lapua-ballistics/download-lapua-edition.html
• Added archive https://web.archive.org/web/20120701033430/http://www.lapua.com/en/customer-center/lapua-ballistics/lapua-ballistics-software.html to http://www.lapua.com/en/customer-center/lapua-ballistics/lapua-ballistics-software.html
• Added archive https://web.archive.org/web/20110202102802/http://chairgun.com/ to http://www.chairgun.com/
• Added archive https://web.archive.org/web/20110422180219/http://appliedballisticsllc.com/Articles.htm to http://www.appliedballisticsllc.com/Articles.htm
• Added archive https://web.archive.org/web/20111016210915/http://lutz-moeller-jagd.de/Schiessen/Weite-Schuesse/Weite-Schuesse-4.htm to http://lutz-moeller-jagd.de/Schiessen/Weite-Schuesse/Weite-Schuesse-4.htm

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 21:09, 22 January 2018 (UTC)