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.

 HorizontalDispersionVia20StdInMv500YardsHorizontalDispersionVia20StdInMv1000Yards

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

HorizontalDispersionVia30StdInMv500YardsHorizontalDispersionVia30StdInMv1000Yards

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”.

HorizontalDispersionVia20StdInMv500yardsHorizontalDispersionVia20StdInMv1000yards

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

HorizontalDispersionVia30StdInMv500yardsHorizontalDispersionVia30StdInMv1000yards

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.

6 thoughts on “Horizontal dispersion due to muzzle velocity variations

  1. the moral of the story?

    shoot at the big parts at long ranges. and, if you can, and still maintain your ability to sneak away in all the hubbub you will be causing, sneak closer.

    and, in spite of what you see in the movies and on t.v., the “sniper” doesn’t always hit his target at great range. the more candid long range shots will confirm this. it doesn’t take more than about a 15 to 20 feet error in range determination to turn a good “solution” into a miss at extended range, especially with the .308 winchester.

    truth.

    john jay

  2. p.s. if you hear shooting, and there is a slim chance that it might be you who is the target, go find a big rock and sit down behind it. on the “correct” side.

    figure out what the heck is going on.

  3. Is it because with the variable muzzle velocity the wind has more time to act on the bullet when slower? If you ran that with zero wind would you get any horizontal dispersion?

  4. Probably could have picked a more realistic example. I rather doubt you’d be hitting any thing @ 1000 yds with regularity (besides dirt) running a S168MK @ 2500 fps.

    Variable wind drift due to MV would be the least of your problems.

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