For the sake of simplicity I provided a brief example
using Force=massxvelocity and added gunpowder grains divided by 1000 to give a relative metric of a rounds powers similar to IPSC knockdown factor, Optimal Game Weight, or Taylor Knockout Factor.
PPV the 22 magnum is surprisingly powerful.
Wrote my own program for free use here are some formulas I had collected.
III.d. Optimal Game Weight (OGW) Formula
The OGW formula was published in the April 1992 issue of GUNS magazine.
It is purportedly the result of careful examination of the various contributions
of "kinetic energy, momentum, bullet sectional density, bullet diameter,
bullet nose configuration, impact velocity and a number of other criteria" (pg. 62)
to terminal effect. The author, without elaborating on his methodology,
settled on the following formula:
OGW (lbs) = Velocity (fps) 3 x Bullet Weight (grs.) 2 x 1.5 x 10-12
This is, of course, nothing more than kinetic energy multiplied by momentum, then multiplied
by some constant to arrive at the desired weight range. There is absolutely nothing magical
about the game weights derived by this calculation; they are entirely the result of a
subjective selection of the constant, although the choice of this constant may be based
upon sage judgement, drawing on years of field experience. The basic premise of the formula
is worthy of closer examination. The OGW formula attempts to combine in one measure the
separate contributions of kinetic energy and momentum, the two schools of thought:
fast and disruptive versus slow and deep. This is well intentioned; however, simply
multiplying the two values is an unacceptable method of deriving a composite effect.
For instance, a certain load may have a very high velocity and therefore a high kinetic energy,
yet have a very light bullet weight and a correspondingly low momentum. How will it perform?
The most useful description of its performance would be found by separating its component
functions, cavitation and penetration, and analyzing these in relation to the game in question.
From experience, we know that very lightweight, small-bore ultra-velocity loads are poor
performers against large game. Yet an 85 gr., .243 cal light game bullet traveling at 3500 fps
would have an OGW rating of 389 lbs at the muzzle! Compare this to a 575 gr. ball traveling
at 850 fps with an OGW rating of 305 lbs. The former load is appropriate only for coyotes,
jackrabbits and extremely light framed deer. The latter load is for a 16 bore howdah pistol
intended to stop charging tigers!
Important caveats are in order. The author included an exhaustive list of cartridges and loads,
but the distinctions are only applicable between bullet weights and velocities.
The model itself makes no consideration whatsoever of the effect of sectional density,
bullet diameter or nose configuration, although these were "considered" in its development.
Most glaringly, bullet construction is neglected. A 150 gr. bullet moving at 2800 fps is
identical in this analysis, no matter whether it be a .264 caliber RWS H-Mantel or
.358 caliber Remington Core-Lokt. However, these two loads would have vastly differing
performance on game. The model assumes you have selected a reasonable bullet weight and
construction for the application in mind (in fairness to the author, Matunas makes
this point clear, but it does beg the question of just what this model does tell you
if you must already know the answer before you begin).
What the OGW Table really amounts to is an estimate of the maximum "walloping" potential
for all-aspect body hits against game using modern high-powered cartridges
(not 19th century big-bore blackpowder weapons or even early 20th century weapons)
using appropriate bullets. It attempts to describe the approximate weight of animal that
could be reliably killed from any angle (again, assuming the bullet selected was reasonable).
Unfortunately, by making velocity a third order term it wildly exaggerates the effect of this
component in terminal behavior, which (as will be shown) has surprisingly little meaningful
effect for deforming bullets. Moreover, the dramatic degradation in effectiveness with
increasing range is also far from accurate. A typical high velocity bullet is shown to
lose half its effectiveness between the muzzle and 250 yards; in practice nothing is lost
and indeed some performance gain may be observed with many bullets of conventional construction!
Worse, it suggests that if one uses light for caliber bullets, then the most effective employment
of these projectiles is at close range and very high velocity - in direct opposition to all
conventional wisdom! Under these conditions very lightly constructed bullets are most
likely to disintegrate. The occasional spectacular kill does not outweigh the unreliability
that will be seen. Comparisons between different calibers and bullet weights in this analysis,
as suggested by the author, are an absurdity for reasons outlined previously.
They are simply not valid.
III.e. Taylor Knockout (TKO) Formula
I almost hate to comment on this one because it happens to be a favorite of one of
my favorite gun writers, a man of outstanding skill and a reputable hunter whose guidance in
such matters should not be taken lightly (and I don't refer to Taylor!).
Taylor himself was also a man of unimpeachable experience and his views on rifles and calibers,
especially for dangerous game, is taken as gospel on the subject.
However, this formula has got to go.
I'm sympathetic to the motivations which brought about its creation.
The "smallbore cranks" were a cult phenomenon at the time, preaching vehemently about
high velocity and kinetic energy. A number of this following ventured to Africa,
and like their predecessors in the heyday of blackpowder "express" cartridges,
experienced miserable failures in the field, sometimes with fatal consequences to the
shooter or guides. Taylor was attempting to counter this "scientific" kind of argument
with a kind of scientific methodology. Applying his many years of experience to the
problem (and it must be confessed, his biases as well), he developed a formula which
favored the kind of bullets and cartridges he knew to work reliably:
TKO = Bullet Weight (lbs) x Impact Velocity (fps) x Bullet Diameter (in)
Regrettably, this formula is as misleading as any kinetic energy figures or OGW
or any other I've seen. For example, Taylor himself acknowledged that there wasn't
any appreciable difference in the killing performance of the various
.400s, .416s, .450s, .465s, .470s, .475s, and .500s on dangerous game when loaded
with reliable bullets of sound construction.
But his TKO formula (as often interpreted) exaggerates any difference that might exist
because it makes the bore diameter equally as important as the velocity;
thus a .488 caliber .475 Jeffery No. 2 is seen to be 7% more potent than
a .458 caliber .450 NE even though they both have the same ballistics.
The comparison becomes even more exaggerated between a .450/.400 NE and a .500 NE
in which the larger bore is calculated to be 55 % more potent, even though Taylor regards
them as being very similar in performance. In fairness to the author, the TKO value is generally
misinterpreted. Taylor himself said of it:
"I do not pretend that they [TKOs] represent "killing power"; but they do give an excellent basis
from which any two rifles may be compared from the point of view of the actual knock-down blow,
or punch, inflicted by the bullet on massive, heavy-boned animals such as elephant, rhino and
buffalo". (African Rifles and Cartridges, pg. xii)
"There seems to be a lot of misunderstanding about this word "shock"; men seem to be under the
impression that it implies killing power. But that is erroneous." (African Rifles and Cartridges,
pg. 58)
Elaborating, the author indicates that this stunning effect truly applies for the most part to near misses of the brain on elephant, enabling a more leisurely dispatch with a follow-up shot (possibly of lesser caliber) or, especially, permitting the shooting of other nearby elephants, while the first is down. Such tactics are no longer permissible and were never ethical in my view (Taylor was a self-acknowledged poacher). But the point here is that Taylor never offered this formula as an indicator of killing or even "shocking" performance for body hits.
"Both barrels from a .600 in the belly will have little more apparent effect on [an elephant] than a single shot from a .275 in the same place." (African Rifles and Cartridges, pg. 59)
Your new rifle might make a great short/mid range light varmint shooter?