ARROW LETHALITY
Part V:
Predicting Arrow Penetration on Real Animals
A
First Test of the Tissue Penetration Index (TPI)
BY
Dr. Ed Ashby
Is there a way to predict,
not infallibly, but with a high degree of reliability, the ability of a
particular bow/arrow/broadhead combination to penetrate real animal tissue
(hide, meat, fat, connective tissue, etc., and bone) under real hunting
conditions? The answer to this question
becomes of particular importance when truly "big" game is hunted with
the bow and arrow.
Being able to predict such
performance would also be of help in determining what combinations will assure
"adequate performance" on "normal" size animals when the
shot placement is less than ideal.
Exceptional arrow penetration then becomes necessary to achieve a quick,
clean, killing shot. Such information
would also be of more than passing interest to game department officials and
law makers when considering the "humanity" of bowhunting and for
developing realistic bowhunting regulations.
I have been seeking an
answer to this one question of "arrow and broadhead effectiveness"
for years. I would like to tell you
that I have found the "ultimate" answer but, alas, I'm not even sure
that there is an "ultimate" answer.
There is little question that the most important factors determining
broadhead "lethality" are shot placement, broadhead sharpness and
adequate penetration. Regardless of
one's skill, shot placement can never be guaranteed. Animal reflexes are simply faster than the very fastest of
arrows, and occasionally (?) most bowhunters "muff" even an easy
shot.
Sharpness is easy enough
to achieve, with a little effort, but, all else being equal, adequate (surplus)
penetration is the factor that can often render a marginal or poor hit quickly
effective. As the size of the animal
being hunted increases, the importance of adequate penetration is
magnified. This being the case, how do
we go about assuring that the equipment we use will deliver the amount of
penetration needed when hunting truly large animals or "when everything
goes wrong"?
There are some factors
which decidedly affect the potential for adequate penetration, and these
factors can be collated into an series of equations which appear to
offer a reasonable predictor of penetration when comparing one arrow/broadhead
combination to another.
Following the research on
broadhead performance, conducted under the auspices of the Natal Parks Board in
South Africa in 1984 and 1985, which I was fortunate to participate in, I
became almost consumed by a desire to understand, as fully as possible, the
factors which affect broadhead and arrow performance on real animal tissue. It is obvious that a number of factors are
at play in determining the penetration capability of an arrow/broadhead
combination on real tissue.
Using the data from that
original study, the largest ever conducted on real animals, I have struggled to
analyze it from all possible view points.
From that information, and data collected since then, I have gradually
formulated a theory. This theory is
based on the detailed examination of the wound channel of several hundred shots
on real game animals, not on the testing of a few arrows on substances as
"real" as styrofoam, ethafoam, cardboard, wood, ballistic gel,
de-boned beef sides, etc.
Some have used such test
on artificial medium to try and advance a particular concept as the
"ultimate answer" to predicting penetration. I will, however, continue to treat my
concept, which I have named the "Tissue Penetration Index", or
"TPI", as a theory, not the final answer to end all. Much field research, and possibly some lab
studies, remain to be done at this point.
I do, however, feel that use of the TPI comes a great deal closer to
correlating with actual measured performance on real animals than any other
"yard stick" I know of.
The purpose of this
article is to distribute the results of my work to date on the TPI, and the
results of the first field test of the TPI, so that others may examine it and,
hopefully, refine it through further analysis of real shots on real
animals. Such research is vital for the
sport.
Each year an increasing
number of bowhunters are going afield after the larger species of game. Without a thorough understanding of what is
required to achieve sufficient penetration, on large, difficult to penetrate,
and potentially dangerous animals, there will be a great deal of needless
wounding of game. This will surely
result in a "bad publicity rap" for bowhunting. Several such cases have already occurred
here in Africa. Should it continue,
this may result in unreasonable restrictions on bowhunting, or total bans on
bowhunting in some areas.
Even on slightly built
animals, understanding how to optimize arrow performance will result in an
increase in arrow lethality. This
"extra performance margin" becomes particularly important when Mr.
Murphy throws his "law" into motion against us, and the arrow does
not hit where we intended, ie: s--t happens, folks!
The TPI, is an attempt to
analyze the principle factors affecting arrow penetration, in terms of the laws
of physics, by use of mathematical formulas.
The TPI couples the arrow momentum with the calculated mechanical
advantage of the broadhead (M.A.) and a
"drag factor" based on shaft diameters less than, equal to, or
greater than the broadhead ferrule diameter.
By definition from
physics, momentum, and not kinetic energy, is the correct formula to measure
the directional (in this case, forward) "impulse" of a body in
motion. It is the force exerted over a
period of time in one specific direction, ie: a unidirectional force
vector.
Kinetic energy (K.E.) is
scalar, or nondirectional,in nature, and includes all the types of energy of a
body in motion. K.E. has no direct
bearing on penetration. A tuning fork,
once struck, has high kinetic energy (it can shatter a crystal wine glass), but
has almost no momentum. It would makes
a darn poor penetrator of tissue!
For those with a
scientific bend, the formula for momentum of an arrow is: arrow weight in
pounds times arrow speed in feet per second divided by the acceleration of
gravity. In equation form, it would be
represented as:
Momentum = (arrow
weight on grains/7000) X arrow speed in fps
32 feet per second per second
The second factor in the
TPI is the mechanical advantage (M.A.) of the broadhead. A single blade broadhead, with a straight
taper, can be viewed, in terms of physics, as a "simple
machine". It is a series of
inclined planes. How the ferrule tapers
into the blade is a factor, but can be ignored in comparing one broadhead to
another if the two ferrules are relatively the same degree of taper. It is important that the broadhead be of
quality construction. If any portion of
a head bends of breaks on impact with any tissues (including bone), it negates
any methodology of predicting penetration, and almost assures poor performance.
For a simple broadhead
design, the approximate M.A. may be calculated by dividing the length of the
cutting blade (from tip to widest point of the edge) by one half the cutting
width of the broadhead (distance from the center line of the ferrule to the
widest point on the cutting edge) and multiplying by the number of cutting
blades. In equation form this would be
represented as:
M. A. = Length of cutting blade to
widest point
1/2 width of blade cut X number of cutting blades
The M.A. of single blade
heads, and some multi-blade heads, is easy to calculate. Broadheads of complex construction, with
blades of various plane angles, "bone breaker" tips, etc. are
difficult to calculate. Perhaps actual
penetration test in a uniform medium, such as ballistic gel, using a projectile
of uniform mass and impact velocity, would yield a "relative resistance
factor". This "relative
factor" could be used in place of the calculated M.A. to ascertain the
TPI. Testing of this degree is
certainly beyond my financial means.
However, I feel this concept is plausible, and warrants investigation.
The third factor used to
arrive at the TPI is a "shaft drag factor". This factor was derived from the data accumulated during the
Natal broadhead tests. It was determined
by comparing the average penetration depth when arrows of equal momentum, all
using the same broadhead, were shot on shafts with diameters smaller than
the broadhead ferrule diameter, equal to the ferrule diameter and greater than
the ferrule diameter. The
"multiplication factors" thus arrived at are 1.0, .9, and .6
respectively. Obviously "shaft
drag" is a major factor in penetration, equally as important as arrow
momentum and quality and M.A. of the broadhead.
The TPI is merely a
relative numerical value arrived at by multiplying the momentum of the arrow by
the M.A. of the broadhead and multiplying the product by the "shaft drag
factor". The TPI formula appears
to work as a predictor of penetration on real tissue, however much testing
remains to be done to establish the level of TPI needed for various species of
animals. Initial tests indicate that
the TPI does accurately predict the penetration capability (in real tissue) of
various arrow/broadhead combinations relative to each other.
I recently returned from
Mozambique, where I was able to test some arrows on fresh (immediately after
the kill) cape buffalo carcass. All
testing was done with the 190 grain Grizzly broadhead (which I believe is the
very best "Big Game" broadhead available, based on the Natal study)
and a modified version of the Grizzly with a narrower cut radius (giving a
higher mechanical advantage). This
eliminated differing broadhead quality and structure as a variable.
Working with arrows of
differing mass, velocity, and shaft diameters, I calculated the K.E., momentum,
momentum times the M.A., and the TPI for each combination prior
to testing the penetration. A heavy,
thin, shaft (900 grains) and broadhead of high M.A. was able to penetrate the
ribs and plunge through the opposite (off side) ribs of the buffalo
carcass. This combination had the
highest "scores" in all categories; K.E., M.A., and TPI.
The real "test"
of the TPI came when evaluating the other combinations. There, some of the combinations with lower
K.E.'s and momentum consistently "out penetrated" those with higher
K.E.'s and momentum levels by a substantial margin. This performance was accurately predicted by the TPI. On even the massive Cape Buffalo, some of
these combinations will give reliable penetration, through the ribs and deep
into the thorax, and would be lethal on a perfect broadside chest shot.
Enclosed are graphs
comparing the K.E., Momentum, Momentum times M.A., and the TPI to the actual
measured penetration on the buffalo with seven arrow mass/velocity/M.A./drag
factor combinations. Examination of
these reveals a poor correlation for both K.E. and momentum as a predictor of
penetration. There is some improvement
when the broadhead's M.A. is incorporated with the momentum (ie: the TPI
without the shaft drag factor). The TPI
offers a very high correlation as a predictor of tissue penetration.
The cape buffalo is nearly
the perfect test animal for developing this performance data. The Cape Buffalo has ribs which overlap each
other, and all broadside shots (as all these shots were) must penetrate
a rib on entrance. The following table
gives the K.E., momentum, and TPI for each of the combinations used in the
testing.
COMBINATION NUMBER K. E.(FT.-LBS.) MOMENTUM (LB.-SEC.) TPI
1
54.84 .66 2.59
2 53.40 .61 1.77
3
53.40 .61 1.77
4
53.13 .60 1.75
5
52.33 .57 1.63
6
50.79 .55 2.13
7
50.48 .54 1.41
Combinations number 2 and
3 are identical and serve as a control.
Combinations number 6 and 7 are lighter arrows (654 and 650 grains) at
the same velocity (187 fps), with modified Grizzly broadheads of the same (very
high) M.A., but with number 6 having a shaft of diameter equal to the ferrule
and number 7 with a diameter larger than the ferrule diameter.
This concept is rather
complex, and a great deal of work needs to be done to develop information on
the TPI needed to assure adequate penetration on various species of game,
particularly on adverse angle hits (which can and do happen).
Using the TPI formula, a
60 pound longbow firing a 788 grain compressed cedar arrow, with a 190 grain
Grizzly broadhead, at 148 fps has only 38.34 ft. lbs of K.E., .52 lb.-sec. of
momentum, but has a TPI of 1.50.
That combination was used to repeatedly shoot through the scapula of a
large zebra stallion and through the thorax to the off side, often breaking
off-side ribs (never failing to penetrate the scapula and completely through
the thorax). This was compared to a
compound firing a 555 grain aluminum shafted Black Diamond at 229+ fps. This combination gives 65.21 ft. lbs. of
K.E., a momentum of .57 lb.-sec., but a TPI of only 1.27. That compound was, at best, able to
penetrate only 5 to 8 inched beyond the scapula, and occasionally failed to
penetrate the scapula at all on that same zebra carcass.
The 60# longbow/788 grain
arrow/Grizzly broadhead was also compared to a high energy compound firing a
450 grain carbon arrow tipped with a three blade head, with cut width of 1
1/8" and a cutting blade length of 2", at a velocity of 259+
fps. This combination yields 76.56 ft.
lbs. of K.E., .52 lb.-sec. of momentum, but a TPI of only 0.62. It was unable to penetrate the zebra
scapula.
Penetration of this
combination (compound, light weight carbon shaft and 3 blade head) on all the larger
antelope species is marginal at best.
This bears out the reduced penetration capability of this set-up
compared to the lower velocity longbow with its heavy arrow and single blade
broadhead of high mechanical advantage.
This even though the momentum of both combinations is identical (.52
lb.-sec.), and the compound has 76% more kinetic energy (67.56 ft. lbs. vs
38.34 ft. lbs.).
What we do know
from the broadhead research in Natal is that multiblade heads are a poor
choice for use on larger animals, even in the antelope class (because of
the poor M.A.). We know that the quality
and the design (mechanical advantage) of the broadhead is an
important factor. We know that arrow
mass is more important than arrow velocity (because arrow velocity is
rapidly lost down range, but arrow mass remains constant through the arrow's
flight - helping to maintain the arrow's momentum). We also know that bow draw weight DOES NOT translate directly
to arrow velocity, penetration capability, or killing capacity of the
arrow/broadhead combination. Some
bows are simply more efficient than others.
Any chronograph will prove that a properly set up compound bow will
generate higher momentum levels with any given arrow mass than a conventional
bow of equal draw weight.
I hope the reader will
find this data of interest and of some use.
As far as bowhunting legislation is concerned, I feel that placing
unreasonable bow weight requirements, or requiring use of specific arrow shaft
materials which must (because of their very nature) result in use of lighter
weight arrows would be detrimental to bowhunting.
These test are further
evidence that legislated requirements for a specific bow draw weight for
specific size animals is a total fallacy, nor is legislation of a specific
level of kinetic energy or arrow momentum the answer. They simply do not correlate with penetration in real tissue.
The TPI is still in a
fledgling state, and sufficient testing has not been conducted to even consider
its use as a "standard" of adequacy for the various animals, but it
can be used as a guideline in calculating what should work
reliably. At this stage, it would be
better to require reasonable bow weight (and we do have much historical data to
rely on here), arrows of significant mass, and restrict the broadheads used to
those of excellent quality and high mechanical advantage (on the larger
animals) as the "benchmark" for adequacy.
No one would argue that
light arrows and multiblade broadheads are not adequate on the smaller animals
- a great many are routinely taken with them.
(Although I personally feel that use of "excess penetration
capability" turns many a non-lethal hit into a very lethal hit, even when
hunting light game.) The real issue is
solely with the larger, heavier, and particularly the potentially dangerous
species of game.
I also have reservations
about the wide-spread requirement for minimum broadhead widths, particularly on
the larger animals. The wider the
broadhead, for a given length, the lower the M.A. of the head. With the larger animals, penetration is the
problem. What is needed is a long,
deep, wound channel rather than a wider, less deep, wound channel.
A blunt or round-nosed
"solid" (non-expanding) rifle bullet, even of small caliber, driven
at a moderate velocity, will kill the largest of animals when driven through
the chest cavity. Even elephants, as
Bell, Stiggand, Blunt and others proved.
(And, according to Peter Capstick, at least two elephants have been
killed with the lowly .22 Long Rifle cartridge on heart shots!). Remember also that even the .600 Nitro
Express' solid bullet is less than 3/4" in diameter. No one would question its ability to kill
any animal on a chest shot!
I have used, and seen
used, a large number of such bullets on animals, and have examined hundreds of
such wound channels. Tissue damage and
"tissue shock" are minimal from such a solid bullet's wound when
velocity is moderate. The animals so
hit (where no bone or nerve center is hit) die from blood loss and/or lung
collapse, just as with an arrow. Such a
wound produces a rate of blood loss much slower than with a broadhead of
similar width.
The American Indians
frequently made very tiny flint broadheads.
For many years, these were believed to be for use on small animals and,
indeed, were commonly called "bird heads". More recent archeological research has shown that these tiny
broadheads were really used to kill the American Bison! Bison are substantial animals, with bulls
often weighing in excess of 3000 pounds.
With the weak bows used by the "Plains Indians" (those tribes
co-habitating the great American prairie with the Bison), the only way to
achieve adequate penetration was to reduce the force needed to penetrate to a
minimum.
Just as the "Plains
Indians" discovered long ago, with a
broadhead tipped arrow,
penetration is the problem on the larger species. They found that a wide broadhead, cutting a wide path, was
useless, as it often failed to penetrate sufficiently to reach the vital
areas. A small broadhead, penetrating deep
into the thorax was sufficient to be quickly fatal.
A 3/4" wide broadhead
through the lungs will most assuredly kill more quickly than a similarly placed
"solid" rifle bullet at moderate velocity. In the 1960's, before their use was legislated out of existence
in the States, I used many very narrow broadheads, some as narrow as 1/2",
and have never once had one fail to kill any large animal hit. Perhaps this concept should also be
"re-visited" and some valid research performed. Smaller broadheads have received a lot of
"regulation" and "bad press" without any objective data to
back up those restrictions.
I have devoted a great
deal of time and effort into this research over the last twelve years, and feel
that I most likely have the largest amount of data on arrow and broadhead
performance on real animal tissue of anyone. It is my deepest hope that other independent, objective,
researchers will take some interest in this work and conduct their own testing
to expand the bowhunting community's understanding of just what it takes for a
hunting arrow to be effective under real field conditions. Truly, my feelings will not be hurt if the
results are different from my data. It
will all expand our knowledge of how to be better bowhunters.