The
Essential Ed Lowry on Shotgun Performance
Edward
David Lowry's long, successful career with WinchesterWestern and his
own further explorations of shotgun performance established Mr. Lowry
as one of the most prolific shotgun ballisticians of modern times. Mr.
Lowry's work was wellreasoned and superbly welltested in the lab and
in the field. Mr. Lowry released three major public items. They include
two books and his groundbreaking “Shotshell Ballistics for Windows.”
Though all are now out of print and otherwise unavailable, both his Windows
program and his book Interior Ballistics: How a Gun Converts Chemical
Energy Into Projectile Motion have long been two of my most valued
and most referred to works. For educational purposes only, here are a
few brief topics covered by Ed Lowry in various sources. Certainly while
not of interest to everyone, it is part of requisite shotgun basics. Ed
Lowry's concise description of the Gaussian Distribution of pattern is
the basis for much of the current shotshell pattern comparisons and predictions,
even though its roots, as noted by Ed Lowry, are from 1902 by Félix
Albert Journée.
ATMOSPHERIC
EFFECT on BALLISTIC PERFORMANCE
For
ballistic purposes of reference, "Standard Atmospheric Conditions"
are: a temperature of 59 degrees F (15 degrees C); a barometric pressure
of 29.54 " (75 cm) mercury, at sealevel; an absence of wind ; and
a relative humidity of 50%. Deviations from these reference conditions
will have the following effects on ballistic performance.
1.
Temperature A rise in temperature causes a drop in air density and, thereby,
a drop in the drag forces that decelerate a moving pellet and that induce
its dispersive (i.e. patterning) behavior.
2.
Barometric Pressure A rise in barometric pressure causes a rise in air
density, and thus an increase in the aerodynamic drag force. At near sealevel
(1000 foot altitude or less) conditions, which characterize the overwhelming
amount of populated land in the U.S., the normal changes in barometric
pressure cause such a small change in air density that the ballistic effects
are negligible. However, the effect of altitude on the average barometric
pressure can be considerable.
3.
Wind Head and tail winds (i.e. those moving toward or away from the shooter)
have a small effect on downrange velocities and an almost negligible effect
on patterning. A cross wind has essentially no effect on effect on velocity
or dispersion. However, a cross wind can cause sensible lateral movement
of the shot cloud.
4.
Humidity Humidity, even rain, has a negligible effect on downrange ballistic
performance and is therefore not considered.
CONVERSION
OF 3FT COIL MEASUREMENT TO MUZZLE VELOCITY
It
has been the industry practice to give the initial velocity of a shotshell
load as its velocity at three feet from the muzzle, as measured with a
coil disjunctor. This situation is further complicated by the fact that
the physical configuration of the shot column at three feet causes the
coil disjuntor to produce a somewhat misleading measurement.
For example, when a moving shot column passes through a full choke constriction,
the column strings out to several times its original inbore length. The
front pellets quickly separate and are immediately in free flight. Moreover,
at three feet from the muzzle, these front pellets are the only ones in
free flight since the remaining pellets in the column, although no longer
in contiguous contact, have not yet begun to disperse and are still traveling
in the turbulent wakes of others. The coil disjuncter actually produces
the average velocity of the entire shot column. But it is the velocity
of the forward pellets that determines the average downrange performance
of the whole shot charge.
Hence,
in order to ascertain the actual velocity at the muzzle, two corrections
to the three foot measurement must be made. The first one increases the
threefoot value by an amount that depends on pellet type and pellet size
and by the amount of choke constriction.* The second correction then simply
produces the muzzle velocity necessary to give the (corrected) resulting
threefoot velocity.
*
The basis for this was established in an extensive experimental program
by the Winchester Research Department in 1969.
LAGTIME;
LAGDISTANCE
An
example can demonstrate the meaning of lag time. Suppose that a projectile,
aimed at a target 40 yards downrange, leaves a gun muzzle at a velocity
of 1,200 feet per second. If there were no air resistance the projectile
would travel the 120 foot distance in one tenth of a second.
But, there is air resistance in our atmosphere. Suppose also, for our
example, that the projectile is a #2 steel shotshell pellet and the atmosphere
is at standard conditions (59 degrees F and 29.54" barometric pressure).
In this case the pellet would require .1457 instead of .1000 seconds to
travel the120 feet. Thus air resistance slows the pellet and causes it
to arrive .0457 seconds late. The .0457 second delay is the "lag
time".
The meaning of lag distance is definable in a similar manner. If there
were no air resistance during the .1457 second travel time it takes the
#2 steel pellet to travel the 120 feet, then it would travel at 1200 ft/sec
for .1457 seconds. In such a case the pellet would travel a total distance
of (1,200) times (.1457) = 174.84 feet.
The
extra distance, 174.84  120 = 54.84 feet (call it 55), is the extra distance
that did not get traveled because of the rearward push of air resistance.
This 55 foot distance is the "lag distance".
GAUSSIAN
DISTRIBUTION OF PATTERN
After
the pellets in a shot charge clear the muzzle, and are in free flight,
each of their individual flight paths experiences a number of deflections
which vary randomly in both direction and magnitude. The deflections of
any one pellet, moreover, are unaffected by those of any so that the pellets
all move independently. Yet, collectively, their points of impact produce
a definable frequency distribution on the signature sheet.
The
dispersion of pellet holes on a signature sheet conforms to the socalled
"normal" or "Gaussian distribution", more familiarly
known as the "bell shaped curve". This was reported by Journee
in his 1902 "Tir de Fusils de Chasse", subsequently corroborated
with hundreds of patterns at the Western Cartridge Co. (now the Winchester
Division of Olin Corp.) in 1946 and also publicly reported by Oberfell
and Thompson in 1957. A further number of extensive experimental programs
at the Winchester research range established the effects of range, choke
constriction, shot size and atmospheric conditions on pattern values.
MEASUREMENT
OF PATTERN
A
shotshell pattern is a large signature sheet on which is recorded the
impact locations of pellets from a moving shot cloud. Its purpose is to
provide a measure of lateral pellet dispersion at some predetermined downrange
point. In current practice the standard measure of this dispersion is
the pattern percentage. To obtain its value, the user places the signature
sheet on a flat surface and then determines the largest number of pellet
holes that can be covered by a 30 circle. The pattern percentage is this
number, divided by the total number of pellets in the load, times 100.
The customary downrange location of a signature sheet is at 40 yards.
Hence when a gunammunition combination is said to give a certain pattern
percentage, it is generally understood (unless otherwise specified) that
the percentage number refers to its average value at 40 yards.
SHOTGUN
RECOIL SENSATION
Various
experiments have shown that the disagreeable "kick" sensation
experienced by the shooter correlates primarily with the kinetic energy
that has been imparted to his recoiling gun. The total sensation is probably
influenced by other factors that are difficult to measure, such as the
method of holding, the resulting noise, etc. But a gun's recoil energy
can be established from the known properties of the gun and of the ammunition.
Determination of a shotgun's recoil energy follows directly from the laws
of motion established by Isaac Newton. One direct consequence of these
laws is the principle of the conservation of momentum. It tell us that
if we let
W
be the gun's weight.
V be the gun's recoil velocity.
ws be the shot charge weight.
ww be the weight of the wad.
v be the muzzle velocity.
pw be the propellant weight.
pv be the average velocity (at the muzzle) of the propellant gases.
Then
[W times V] is equal to: [(ws + wv) times v] plus [pw times pv].
For a given gun and shotshell load, six of the above quantities are assumed
to be either measurable or known. The seventh, the gas velocity (actually
the velocity of sound in the propellant gases), is approximately 4,000
feet per second for shotshell propellants. Hence, if all quantities are
given in pounds or feet per second, then it follows from algebraic manipulation
and from the definition of kinetic energy that the gun' s recoil energy
is given as
[M
times V squared] divided by [2 times g], where
g is the gravitational constant and assumed as 32.16 ft/dec/sec.
SHOTSTRING
EFFECTS
As
a cloud of pellets flies toward a target its individual pellets disperse,
both laterally (patterning) and longitudinally.(shotstring). The way that
a shot cloud disperses laterally is covered by the "Shotshell Patterning"
and by the "Target Hits" sections of this Shotshell Ballistics
program. This lateral dispersion is further covered under "Miscellaneous
Topics". While pattern measurements are readily obtainable, as is
done with downrange signature sheets, the measurement of a shotstring
is not so easily managed. Methods for shotstring measurements are covered
in the three references listed below.
The pertinent property of a shotstring is its length. This is usually
specified (in the US) as the shortest length that includes 90% of the
load's pellets at 40 yards from the muzzle. The key question about a load's
shotstring centers on the relative effect of its length on the load's
lethal effectiveness this question breaks down into two parts: the effect
on pellet energy delivery and the effect on the total number of hits delivered
against the target.
The
effect of shotstring length on energy delivery is difficult to ascertain.
A long shotstring, which represents a large spread in pellet traveltimes,
suggests that the trailing pellets in the shot cloud are meaningfully
smaller and/or more distorted than the leading pellets. But the actual
degrees of pellet size variation and of pellet deformation are not easily
predictable. Moreover, since the actual value of the shotstring length
for any given shotshell load can only be roughly conjectured, a procedure
with poorly known input values is only marginally useful.
References:
1  Bob Brister  Shotgunning, The Art and The Science, (Chapter on The
Shot String Story) Winchester Press, 1976
2  Gerald Burrard  The Modern Shotgun, (Chapters V and VI) A.S. Barnes
and Co., Inc. New York, 1961
3  E.D. Lowry  The Effect of a Shotstring, The American Rifleman, November
1979
Copyright
2013 by Randy Wakeman. All Rights Reserved.
