00 buckshot ballistics and death (LONG)

[Henry E. Schaffer]

A posting said two men were hit by 00 buckshot at a measured
distance of 155 yards. On man was hit in the throat and killed, the other
was hit in the leg and injured. (Each man was presumably hit by a single
pellet.) The question was whether this was reasonable? How hard would 00
buck hit at that distance? (There is a common perception that the danger
zone of a shotgun is considerably shorter than 155 yards. On the other
hand, there is a "legend" that a pellet of 00 buck is as dangerous as a
round from a .30-'06.) This seemed to be a simple question in ballistics
to answer, but it took me more time to investigate than I had thought it
would. My investigation might be of interest, and so here are the details
(lots of them :-).

This type of ballistics problem might seem to be routine, but the
common references deal much more with rifle and handgun bullets, and don't
say much in detail about shotguns, especially not beyond 40 yds. One
should be able to figure out this problem with knowledge of the Ballistic
Coefficient (I'll call this BC although in the literature it usually is
called C), the muzzle velocity, and the pellet weight. So the start is to
collect this information.

#From the NRA Firearms Fact Book 3rd Ed. p.192 (referred to as NRAFB -
a very useful little book)

00 Buck 53.8 gr. dia 0.33" 9 pellets in 12 ga.

distance muzzle 10 yds 20 yds 30 yds 40 yds
velocity fps 1325 1225 1138 1061 995
energy/pellet ftlbs 210 179 155 134 118

The 2 3/4" Magnum load is given as 12 pellets starting at 1290 fps and at
40 yards being 974.

This is a good start, but not everything we would like. Also I
wanted to verify the figures given here.

The 1989 Gun Digest has a table covering Winchester-Western, Remington-
Peters and Federal shotshell loads, but the entries are broad categories. For
a 4 dram equivalent 12 ga. 2 3/4" Hunting and Target group of buckshot a
nominal velocity range of 1075 to 1290 is given. For 3 3/4 dram eq. the
range given is 1250 to 1325. For a 3" Magnum buckshot the range is 1210 to
1225. The Lyman Shotshell Handbook 3rd ed. gives a lot more detail, and it
can be seen that the velocity varies greatly depending especially on the
weight of the shot. E.g., for a 3" Magnum load of 1 3/8 oz in a Federal
Plastic Hunting Case the velocity varies from 1290 to 1460, but for a 1 5/8
oz load the variation is from 1125 to 1310. For its tables of "Factory
Velocities" it gives 1325 fps for a 9 pellet 2 3/4" shell, 1290 fps for
a 12 pellet 2 3/4" shell and 1215 fps for a 15 pellet 3" shell.

The weight of a pellet is often given with some dispute as to the exact
value. Several references agree that 00 buck is 0.33" in diameter, although
the NRAFB gives this diameter also as .34". The Lyman Shotshell Handbook
3rd ed. has a Buckshot Size Table (p. 291) which says that 00 buck is .33"
dia. and that there are 115 pellets to the lb. --> 60.9 gr. and then says
that this is "based on soft, chilled shot. High antimony and/or plated shot is
lighter. Actual count will vary depending upon brand and lot." This is the
heaviest value I've found given for a pellet of 00 buck. The
Winchester shotshell reference card says that there are 130 pellets to the
lb --> 53.8 gr. I calculate that a pure lead (687 lbs/cu.ft.) ball with
a .33" dia. has a weight of 52.4 gr. The Lyman Handbook table discussed below
gives the weight of a .319 lead ball as 49 gr., which scales to 54.25 gr. as
the appropriate value for a .33 ball. The printout that Norm sent me (shown
below) gives the weight as 48.0 gr. The total range of weights (48 - 60.9)
is rather wide, but it indicates that the 53.8 gr. weight is a reasonable
value to use. Another pellet size I've found listed is in a table of
American Standard Shot in vol. 2 of Small Arms Design and Ballistics by
T. Whelen, 1946. It gives 00 buckshot as an "Eastern Size" which is .34"
and has 122 in a pound --> 57.4 gr. It could be that the "real" diameter
is between .330" and .340". Since weight varies with the cube of the
diameter, the increase in weight of .340" over .330" is over 9%.

Determining the BC can be done in several ways. One way is to use the
figures for velocity from the NRAFB, and then use the Ingalls' Ballistic
Tables in Hatcher's Notebook to solve for the BC. The muzzle velocity and
40 yd. velocity from the NRAFB yields a BC of .038, for the Magnum load it
is 0.37. While this looks low, it is clear that the BC < .09, because
this is the lowest BC in Mannes' Tables of Bullet Performance (1980, Wolfe
Publishing) which shows that a bullet with BC = .09 and muzzle velocity
1300 fps has a velocity of 1092 fps at 50 yds. Another comparison is that a
148 gr. HBWC .357 bullet has a BC of .047. Hatcher gives a formula to
determine the BC as the sectional density divided by a "form factor". He
gives three different form factors for three different muzzle velocity
ranges. Using these form factors, and calculating the BC's for .33"
balls of 50 and 53 gr. weight gives

50 gr. 53 gr.
under 1,000 fps .0328 .0348
1,000 - 1,300 fps .0386 .0409
over 1,300 fps .0469 .0497

The Ingalls' Tables, and the formulas are in the last chapter, XXIII, in
Hatcher's Notebook. It took me a while to figure out the vocabulary and
which formulas and examples to use, but then use was fairly simple.

I called Sierra Bullets and talked to one of their ballistics people.
The ballistician I talked to didn't have shotgun ballistics info and
referred me to the Lyman Reloading Handbook, 46th ed. In Table 2-3 of BCs
for Black Powder guns, it says that a .319" cal lead ball has a BC of .045 at
over 1300 fps, of .037 at 1000-1300 fps and .031 below 1000 fps. This agrees
quite well with the values derived above. (The Lyman table gives the weight
of this ball as 49 gr.) The Sierra ballistician said that time of flight
measurements are needed provide the needed values. (See the Exterior
Ballistics section of the Rifle book of the Sierra Reloading Manual for
more discussion. I have the 3rd ed.. The 4th ed is available and
probably has a similar treatment. It explains why time of flight is used in
estimating the BC. It also has a fairly thorough treatment of exterior
ballistics.) He also didn't think that the initial travel of a pellet as
part of a column of shot, instead of as a single ball, would seriously affect
the computations, since the shot would spread apart quite quickly. It is
clear that the BC is more complicated than just giving a constant value. The
NRAFB bases its exterior ballistics data on "Siacci tables for spheres by
Miller", and an additional complication is that the shot pellets may be
deformed during firing and so not perform ballistically as ideal spheres.

Norm Johnson sent me some information a computer program provided.
Some exerpts are:

#The program that I used has special built-in tables for round ball
#ballistics. The BC is calculated according to the alloy used. For a
#.33 cal pure lead ball it is .063; projectile weight is 48 grains.

#CARTRIDGE: 00 Buck STANDARD METRO
#BULLET WEIGHT (GRS): 48.0
#MUZZLE VELOCITY (FPS): 1210 BALLISTIC COEFF:.0629

#RANGE REM. REM.
#YARDS VELOC. ENERGY
# FPS FT-LBS
# 155 495 26

This is both a higher BC, and a lower 155 yard velocity than my
calculations give, which is a contradiction. A weight of 48 gr. of pure
lead implies a diameter of just about .32". So I'm wondering if Norm's
program really is giving info for a .319 rifle ball instead of a .33
pellet. Norm also has another program which estimates a BC of .06 for
this pellet. There is a disagreement between these high values and
everything else I've found. This made me want to seek another example
to see what was going on. In looking through vol. 2 of the Hornady
Handbook of Cartridge Reloading 4th ed, I found a bullet with a BC of .040
(pg 279, a 32 cal 90 gr. lead hollow base wadcutter.) The highest muzzle
velocity given was 1100 fps, and then the velocity at 150 yds was given
as 625 fps. This combination of a lower muzzle velocity (1100 vs 1210
and a higher terminal velocity 625 vs 495 - disregarding the difference
between 150 and 155 yards as being insignificant compared to this
difference in velocities) again argues that the .06+ BC value is not
appropriate. Hornady's given BC's are based on data from test firings
they made, and so their .040 value is actual rather than theoretical.
Since everything else is roughly consistent, I'll use the .03+ values
for now.

Taking the BC = .038, muzzle velocity of 1325, and using Ingalls' Table,
the 155 yds velocity is 633 fps with a resulting energy of 48 foot-lbs for a
53.8 gr. pellet. Taking lower values for everything, a BC of .035, a muzzle
velocity of 1275 and a 52 gr. pellet weight gives a 155 yd. velocity of 594
fps with a resulting energy of 41 foot-lbs.

To check on whether I'm using Ingalls' Table correctly, I worked an
example with a BC = .1, muzzle velocity = 1300 fps, range = 150 yards. This
predicts a velocity of 912 fps. The same data entered into Mannes' table
shows a velocity of 918 fps. I consider this excellent agreement. As
another check I used the Hornady Handbook data given above (muzzle
velocity = 1100, 150 yd velocity = 625) in the Ingall's Table to solve for
the BC, and got a value of .0417 vs. the .040 stated.

There is an additional complication possible. Should the solution
be done using one BC, or should it be done piece-wise, using the
different BC's for different velocity ranges? For ease of calculation,
I checked this with an example, starting with a velocity of 1,300 fps and
used an initial BC = .04, and below 1,000 fps a BC = .034. It takes 115.6'
for the pellet to slow from 1,300 to 1,000 fps, and then in the distance
remaining to 155 yds it slows to 602 fps. So the piece-wise solution
doesn't change the results very much.

All of these results show an energy slightly below that of the 50
yd. energy of the .25 ACP cartridge with factory specs for a 50 gr. bullet.
A table in Gun Digest (1989) (no mfr. shown) gives at the muzzle 760 fps,
64 foot-lbs - dropping to 707 fps, 56 foot-lbs at 50 yds. While the .25 ACP
is not highly rated for either stopping power or lethality, I think that
there is no question that it can wound/kill. Therefore I conclude that the
same is true of a single pellet of 00 buckshot at 155 yards.

The Sierra ballistician pointed me to the section "Disabling Energy" in
the NRAFB. According to this, the Army has determined that the energy to
produce a casualty is 58 foot-lbs, corresponding to the standard U.S. Army
shrapnel ball of .49" dia, 167 gr. hitting at 400 fps. He also discussed some
of Dr. Martin Fackler's comments on how little energy it takes to kill if a
vulnerable spot is hit. He agreed with my conclusion that a single 00 buck
pellet at 155 yards has injury/lethality potential.

There is a major difference between the "effective" range and the
"danger" range for a shotgun. The effective range depends on accuracy and
shot pattern as well as on the energy per pellet. No responsible hunter
would shoot at game at 155 yards with 00 buckshot. However, the danger
range doesn't require accuracy or a good pattern, because it refers to
possible harm from being hit, intentionally or not. Therefore if a single
pellet at 155 yards has wounding/lethality potential then the danger zone of
the shotgun extends past that distance.

After I had reached the conclusions discussed above, I came across a
section "Extreme Range of Shot" in the Shotgun Ballistics chapter of
Col. Townsend Whelen's vol. 2. The chapter is mostly about the "ordinary
small sized shot, No. 2 and smaller", how they pattern, velocities at
ranges to 40 yards, and descriptive material about shotshells, but then
near the end of the chapter is the following paragraph.

"Because of safety reasons the extreme range of a shotgun should be
known. The distance to which the pellets will range depends on the size,
that is the weight of the pellet, and on the angle of elevation of the gun.
As with the rifle, the extreme range occurs when the barrel is elevated at
an angle of about thirty degrees. At this angle large buckshot, round
balls, and rifled slugs, when fired at a muzzle velocity of 1300 f.s., which
is about the average, should be assumed to have a range of about 900 to
1,000 yards and to be more or less dangerous at these distances."

Note that 00 buck is the next to the largest buckshot size (with only
000 buck (.36" dia.) being larger. Therefore 00 buck is certainly
included in Col Whelen's admonition, although it is in the lightest part
of the group he is discussing. At the time he was writing "f.s." was a
common way of abbreviating "feet per second".

This was, for me, an interesting excursion into the field of ballistics.
I didn't really expect it to get so complicated or to take so much effort
to track it down. But once I got started it was hard to stop - and besides
it was a good excuse to work through Chapter 23 in Hatcher's Notebook.

Comments, suggestions, and even criticisms are welcomed.

--henry schaffer n c state univ

[joo...@yahoo.com]

This sounds reasonable. I have heard of stories of "less than lethal" riot
control rubber/plastic bullets killing people with as little as 33 ft lbs of
energy. In one particular indecent they were told to aim for the torso but
someone accidentally took a hit to the head. They stopped using that for riot
control.