Horizontal dispersion due to muzzle velocity variations

Yesterday Say Uncle posted Ballistic Accuracy Classification. It looks good and thankfully they included a spreadsheet for doing all the calculations.

I commented that one thing that wasn’t mentioned, but it’s really just nitpicking on this observation:

There are two atmospheric effects that can finally create excess variance in one axis: Variable wind will increase horizontal variance.

This is true but it doesn’t tell the entire story. Variable muzzle velocity will also increase horizontal variance.

Ben then asked:

…the influence of velocity variance on horizontal dispersion… How far are these long ranges? Are the influences big enough to be measured or do they end up in the noise?

I didn’t have any numbers readily available off the top of my head so I ran the simulations with Modern Ballistics.

The simulations are with a 168 grain Match King bullet with a mean muzzle velocity of 2500 fps, sea level, 59F, a wind speed of 10 MPH coming from the left, with a perfect hold for the constant wind, and 1000 shots. The drift due to wind alone is 25.7” at 500 yards and 131.4” at 1000 yards.

The first two images show the horizontal and vertical dispersion with a muzzle velocity standard deviation of 20 fps at 500 and 1000 yards. For scale, the dimensions of the yellow target areas are 3” x 11” and 10” x 56” and the .30 caliber bullet holes are to scale as well.


This is with a standard deviation of 30 fps at 500 and 1000 yards with targets of 5” x 15” and 15” x 90”.


The takeaways are:

  • Velocity variations contribute to horizontal as well as vertical dispersion of your shots.
  • The horizontal dispersion at 1000 yards is about three times that at 500 yards.
  • The muzzle velocity contribution is something on the order of 5% to 15% of the contribution of the wind by itself. This is not just noise, but it’s not exactly major either.
  • Modern Ballistics is your friend.

Update: In the comments Monte points out I should have chosen a more realistic example. A 168 grain SMK with a MV of 2500 at 1000 yards is not good for much other than hitting the dirt in the area of the target.

Here is the same simulation with a 190 grain SMK with a MV of 3050 (approximately what I get with BlackHills Match ammo in my .300 Win Mag).

With a standard deviation of 20 fps the 500 yard target is 1.5” x 6” and the 1000 yard target is 8” x 45”.


With a standard deviation of 30 fps the 500 yard target is 2” x 8” and the 1000 yard target is 8” x 45”.


I don’t think this appreciably changes my conclusions.

Also of importance is there is a better way to do this. Just look at the numbers for the wind drift for different muzzle velocities. I don’t have the time to do that right now, but for future reference you can easily get nice numbers instead of just eyeballing a simulation.

When does recoil start?

Cool posting on “when does recoil start?”

When Does the Pistol Slide Start to Move?

It has some pretty good gif/animation and explanations.

Short version: once the bullet starts moving, Newton’s laws kick in. I think one of the most fascinating part of the animations is the smoke spurts; the 1911 has some at the breech, too, but they all have smoke exiting the barrel before the bullet. Cool stuff.

4000 meter rifle shot

While this is not particularly practical it may be that research into how to make such shots have application in extending the range in more ordinary situations:

They started at 100 m to establish zero

Then to 1000 m to confirm zero. Then to 3000 m. They ran into problems with ranging binoculars (Steiner & Vextronix) “stalling out.”

Consistent muzzle velocity is key. Their loads were within a small range, but a 1 m/sec change in muzzle velocity causes an 80 cm vertical shift in impact point — meaning 1 fps change alters that impact point almost 10″ in the same direction. So you see that firing at 4000 meters is really at the ragged edge of what’s possible with field-employable sniper-type equipment, in 2016. At 4000 m

Third, or possibly, fourth, shot was heard to connect by a forward observer.

Also, dropping a projectile in on a group of bad guys from such distances may cause them to slow or stop their current activities and attempt to deal with the perceived threat with low cost and little risk to the shooter. Sometimes slowing down enemy activities or distracting them, even by a small amount, can result in significant changes in outcomes.

Via email from kb.

A modest stopping power study

An Alternate look at Handgun Stopping Power.

Some things surprising, some things not so much. Shot placement counts for a lot. Some people give up when you start shooting at them. Sometimes it takes more than a single round to stop an attack. There is not nearly as much variation in overall effectiveness by cartridge as I’d expect when you get head/torso hits and don’t pause to admire your handiwork but just shoot until the threat stops.

H/T to Paul K.

Polymer tipped bullets

I have often wondered about the polymer tipped bullets from various manufactures. I have read of people seeing wisps of lead on paper targets that apparently came from lead tipped bullets that melted in flight. If the heat at the tip of a bullet can melt lead then the type of plastic used for bullet tips needs some serious consideration. But, I figured the bullet manufacturers knew a lot more about this than I did and had it all under control.

It turns out this was not the case:

the Hornady engineers observed a convex hump form when charting the new bullet’s drag. The hump was relatively small and usually occurred within the first 100 to 200 yards of flight, and following the hump the drag curve returned to its expected concave climb and drop. The irregularity may have been small and short-lived, but the shift from concave to convex, and back again, seen on the Cd vs. Mach Number graphs could only have one explanation: The bullet itself was changing shape in flight.

It did not take long for the Hornady team to realize it was not the whole bullet changing shape, only the non-metal component—the polymer tip.

The solution, of course, was to find a new polymer:

New polymers were tried and tested, and one was found that met the company’s criteria. With the new material, the Heat Shield Tip was born. Molded as precisely and consistently as previous polymer tips, the Heat Shield Tip boasts glass transition and melting points hundreds of degrees greater than the previous generation’s—475° F and more than 700° F, respectively.

This resulted in higher ballistic coefficients (BCs) which translates into less windage and drop.

My favorite bullet for .30 caliber long range shooting has been the Berger 210 grain VLD bullet. It has a G1 BC of .621. The Hornady 30 Cal .308 208 gr ELD™ Match bullet has a BC of 0.670. From 700 yards away with a .300 Win Mag with Boomershoot conditions this increases the velocity by 60 fps and decreases the drop by 2.6 inches. This isn’t enough of a difference to throw away my existing bullets but I think this is what I’m probably going to replace them with.

Powder puff load report

As I reported last week I was trying to make some very light loads in .40 S&W for new shooters. I made up 200 rounds with the 180 grain Rainier FP over 3.9 grains of Bullseye with an OAL of 1.131”. On Christmas day, while at Brother Doug’s place I shot some over the chronograph. This load yielded a mean velocity of 825 fps (standard deviation of 9.6 fps) for a Power Factor of 148.5. The expected result was 800 fps for a PF of 144. Not too far off from the actual. I would have preferred it be on the low side instead of the high side but still, not bad.

My typical handloads run about 940 fps for a PF of 169 or so. 180 grain factory loads run about 1000 to 1025 fps for PFs of 180 to 185. Hence these new loads are have about 80% of the momentum of a factory load and a little under 90% that of my usual handloads. This is better but I would like to do better still.

While in Idaho this weekend I bought a pound of Clays from Alan B. I loaded up 100 rounds of the 180 grain Rainier FP over 3.0 grains of Clays. I ran them over the chronograph today. Remember that the reloading manual said to expect:

180 grain bullet over 3.0 grains Hodgdon Clays => 727 fps with 131 PF

The result was 728.11 fps (standard deviation of 8.8 fps) for a PF of 131.06. Wow! That was freaky close compared to the expected result.

That gives me a load with about 78% of the momentum of my typical handloads and a little over 70% that of a factory load. And get this, it’s right at the same momentum as a typical 147 grain 9mm round but with a muzzle velocity that is about 100 fps less. That is even less velocity than a typical 230 grain .45 ACP. With such a low muzzle velocity it is much more of a push than a “snap” on the recoil. It’s a very comfortable load to shoot.

Thank you Mike B. and Alan B. for the Clays powder. That made a big difference.

I was thinking ahead to how to make a self-defense load with similar recoil properties and found that Speer makes a bullet they call Gold Dot Short Barrel for good self-defense characteristics with lower velocities. This sounds like just the ticket for Cherie. We have another range trip planned for the end of next month to do some more training and test out the new loads.

Powder puff

I decided I should make some low power loads in .40 S&W for new shooters that are recoil sensitive. “Powder puff” loads. After exploring lots of options I came up with these as the best possibilities. From Hodgdon:

135 grain bullet over 4.0 grains Hodgdon Clays => 940 fps with 127 PF
180 grain bullet over 3.0 grains Hodgdon Clays => 727 fps with 131 PF

Typical factor loads are in the 180 to 190 PF range. So this should be about 70% of the recoil of factory loads.

The difference between power factors of 127 and 131 with equal weight bullets is probably undetectable in your hands. But because the 127 PF load is with 135 grain bullets versus the 180 grain for the 131 PF you get a much different recoil impulse. The lighter bullet is going over 200 fps faster and that means the recoil impulse is much shorter and hence will feel sharper. So, the 180 grain load looks like the winner. That nice because I have lots of 180 grain bullets around.

But I don’t have any Hodgdon Clays powder. I started looking online. Nothing.

[Heavy sigh.]

So what other options do I have and do I have any powders that could come close to this? I have an older version of the Hornady Handbook of Cartridge Reloading and they list Bullseye powder for a mild load.

180 grain bullet over 3.9 grains Bullseye => 800 fps with 144 PF.

I have some Bullseye powder left over from my explosives experiments with it about 1996 or ‘97. This would be a good opportunity to get rid of it. This isn’t as good at the loads with Clays but it is still less than 80% of a factory load.

I loaded up 20 rounds Saturday and went to the range to see if it would cycle my gun and if it was accurate. I used some 180 grain Rainier truncated cone FP bullets I had won at a match this summer. I have had problems with the accuracy of Rainier HPs once I went beyond about 7 yards so I was a bit skeptical of these too.

The ammo cycled and fed well in two different guns. The accuracy wasn’t great at 7 yards but it was far better than new shooters can manage. And I don’t have them shoot beyond that distance anyway.

Today I loaded up 180 rounds using some nickel plated brass I had laying around. I used the nickel plated so I could easily keep track of it being “special”. I’ll load up the remaining 300 Rainier bullets in that configuration in the next couple of days.

It turns out the loaded ammo looks particularly pretty. Barb said it looks like Christmas:


I suppose it does. We have Powder Puff Christmas ammo.

IMR powder recall

IMR Powder, a subsidiary of Hodgdon Powder Company, announced a product recall and safety warning for its IMR 4007SSC rifle cartridge reloading powder. The company says certain batches of the powder are unstable and can spontaneously combust.

Yikes. Spontaneous combustion is a rather undesirable characteristic in a gun powder. I don’t remember seeing 4007 SSC in my manuals, and don’t have any. I use several other IMR and Hodgdon powders though. They’ve always worked well, and my family armory has yet to explode.

Firing 40 S&W in a 10 mm Glock

Over at The Truth About Guns.

Pretty interesting. I was confused for a bit though, until I realized that by “excessive headspace” the author really means “excessive case length” which would result in inadequate headspace. Using the shorter 40 S&W cartridge in a 10 mm barrel results in excessive headspace, so it’s a sort of Opposite Day article in that regard. It’s a well-written and interesting article otherwise.

The greater implication, at least for Glock shooters, is that you can go ahead and trim your brass at or below minimum spec and the gun will run just as well and possibly better. This would explain some of the commercial ammo I’ve seen, which has what appears to be a roll crimp rather than the prescribed taper crimp. That COULD result in a dangerous situation, as the crimp opens up across the chamber shoulder. So long as the case is short enough though, that the case mouth never touches the chamber shoulder, everything’s fine and dandy.

I’m one of those people who regularly checks finished rounds by plunking them down into the chamber (barrel removed from gun) to check for headspace. That’s a fine idea for several reasons, but this article puts all that into a rather different light when it comes to Glocks.

I have some 40 ammo lying around, though I don’t own any guns chambered for it, so now of course I’ll have to try it in my G20.

As an aside; I wish we could get past the little, political/legal/social dance we often perform when it comes to disclaimers. The author of that article asserts that using 40 in a 10 is actually safer than using 10 in a 10 or 40 in a 40, but still feels the need to dance the “Don’t try this at home, Kids” dance. I understand how this social twitch came about (I witnessed the whole thing) but really you can stop any time you like.

Words still mean things II

When writing a review on a firearm, some ammo, or an optical sight, etc., it is probably not a good idea to say that you had “zero issues” or “zero problems” or “zero failures” with it. I’m going to be left wondering exactly what these specific zero issues/problems/failures were, and why you’re not telling us more about them. If you had “no issues” then it would be best if you put it just like that. “Zero issues”, on the other hand, are a whole different subject, and they are potentially very frustrating.

(for those of you who aren’t part of the gun culture, your “zero” is that particular adjustment, or set of adjustments, of your sighting system that puts your bullet right on target at a specific distance when using a specific load [often under specific atmospheric conditions])

Must be at least six inches

Height over bore, that is.

I’ve only half jokingly mocked other “future weapon” designs in the past, saying that the trend is toward an ever more clownishly high sight axis. My educated guess is that this is in fact a psychological problem.

With the lower velocity of the grenade/shotgun, it would make actual sense to put it on the bottom, with the flatter trajectory rifle barrel closer to the sight axis.

The new terms like “Soldier integrated such and such” (which obviously turn ordinary warfare into something totally new and different) are also the result of psychological problems. Years ago, while reading one of the supposedly big cheese U.S. military publications, I found that such a thing as an “army” is, technically speaking, no more. No, ladies and gentlemen; we now have a “Soldier-Centric Force Structure” instead, don’t you know, which no doubt changes EVERYTHING.

The advantage you see is that people who have actual experience in stuff are no longer needed, and can therefore be safely and conveniently brushed aside. Who needs an Army General when you can have a shiny, new, Soldier-Centric Force Structure Command and Control Engineering Specialist? Hmm? Was General Patton a Soldier-Centric Force Structure Command and Control Engineering Specialist? I don’t think so. All he did was lead an Army to kill a bunch of folks and break things. Feh!

And who needs a stupid old rifle when you can have something that looks like it came out of a bad Sci-Fi movie written by an ignoramus, and having the ergonomics of a cinder block?

Is this better?

A few days ago I posted this image and asked “What does this look like?


I have updated the image to this:


In addition to tracing over the top of an image of an actual supersonic bullet in flight I simplified things some. I have a strong tendency to dive deep into details when it isn’t necessary and even when it is counter productive. This represents a lot of restraint on my part.

As some people guessed this was for an update for my ballistics program, Field Ballistics, for Windows Phone. There are some other changes as well. The most important of the changes:

  • Elevation measurements are expressible in mils as well as MOA
  • Native support in various resolutions for Windows Phone 8.0.
  • When the “Wide Tile” is pinned to the start page it show the current conditions, cartridge, and target selected.
  • All of Hornady’s match ammo has been added to the “Factory” cartridges.

If you have it installed on your Windows 8.x phone it may have already updated automatically. If not then go to this link to update.

What does this look like?


Ignore the red color. In use that part of the image could be green, blue, yellow, brown, pink, whatever. The white part is supposed to be an icon representing something.

The thing it is supposed to look like and what I suspect it looks like to many people is “below the fold”.

Continue reading

Online version of Field Ballistics

About a year and half ago I upgraded my Windows hosting service from ASP.NET 3.5 to 4.5. This broke http://field.modernballistics.com.

I checked log files and, as I suspected, almost no one was using it. So I didn’t bother to fix it. I was using a beta version of Field Ballistics (or maybe even released it) and it was so much better that I didn’t even use the web version myself.

Today someone at a manufacturer of airgun pellets sent me an email saying they really liked it (I think they were referring to that version, English isn’t their native language) and wanted to know how much it would cost to support them. I asked about what sort of support they needed and then poked around on my website some. It turns out it was trivial to get it working again. So… in case anyone is interested here is a mobile friendly web based exterior ballistics calculator intended for use in the field.

Shooting a rifle upside down

Ry pointed out this thread to me on ARFCOM. Probably many people will want to stop at the picture and move on after that but the more interesting part to me is solving the sighting problem.


Here is my thought process on the problem:

The drop is the same regardless of the gun orientation. Keep in mind that drop is independent of point of impact (POI) relative to point of aim (POA).

To solve this problem in general look up the drop for this range on the ballistics table for your ammo.

With the gun zeroed for this range the barrel is angled up such that it compensates for both the drop and the height of the sight (Sight Height or SH) above the bore.

Suppose the drop is 2 inches and the sight height is 1.5 inches. Hence the angle of the barrel is such that the bullet rises, relative to the muzzle, 3.5 inches between the muzzle and the target.

When you invert the gun you have the angle of the barrel giving 3.5 inches additional “drop” to the gravity induced drop for a total of 5.5 inches.

But you have the sight below the barrel which means you “get back” twice the sight height of the total. So the gun will be shooting -5.5 + (2 x 1.5) or 2.5” low.

Hence, the general solution for a gun zeroed at a given range when you turn it upside-down it will have a POI of:

POI = POA + SH – 2 x Drop

Or probably more useful is the POA relative to the POI:

POA = POI + (2 x Drop) – SH