Determining The Effective Killing Range of Rifle Cartridges
By Gary Zinn
Recently, I got interested in exploring the implications and possible applications of the G&S Online Rifle Cartridge Killing Power Formula. I summarized the results of this effort in the companion article, The G&S Online Rifle Cartridge Killing Power Formula: Implications and Applications.
I believe that one of the most important applications of the killing power formula is to use it to help define what I have dubbed the "Effective Killing Range" (EKR) of rifle cartridges. I will explain my concept of an EKR and how the killing power formula can be used to help define it in this article.
The G&S Online Rifle Cartridge Killing Power Formula was developed by Chuck Hawks, Owner/Managing Editor of Guns and Shooting Online. The formula calculates index values of the killing power of hunting loads, using downrange bullet energy, along with bullet sectional density and cross-sectional (frontal) area, as the input variables. Calling the output variable (rounded off to one decimal place) of the formula KPS (Killing Power Score), for a given load the formula is:
KPS at y yards = (Energy at y yards) x (Sectional Density x cross-sectional Area)
I will use a traditional .30-30 Winchester hunting load (Hornady brand) to demonstrate how the KPS formula works.
.30-30 Win., Hornady 150 gr. Interlock RN bullet; MV 2350 f.p.s.:
Thus the KPS of this load, calculated at 100 yards, is 20.7 This is merely an example, for a KPS can be calculated for any range. This capability is important in ways that I will demonstrate.
The KPS formula makes a lot of sense to me. My understanding of bullet terminal performance is that impact energy, sectional density and cross-sectional area are all quite important to terminal performance. The KPS formula combines these variables in a direct, easy to calculate way.
If anyone wonders about bullet weight, that is implicit in the KPS formula, because Bullet Weight in grains = SD x Diameter squared x 7000 (7000 is the number of grains in a pound). Bullet velocity is also not neglected, because the energy generated by a given bullet at any particular range is partly a product of its velocity squared. Thus, energy serves as a proxy for velocity in the formula and energy at the point of impact is more relevant to determining the killing effectiveness of a hunting bullet than is velocity, as such.
Whenever any of these variables change, the KPS number changes proportionally. For instance, between 100 and 175 yards, the energy of the 150 grain .30-30 load above decreases by 27.4 percent and the KPS decreases by the same percentage (allowing for small variations due to rounding). Thus, KPS numbers generated from different data inputs (energy, SD, or FA) are directly comparable. This comparability can be applied to different loads for a particular cartridge and comparisons of different cartridges.
An important implication of the killing power formula is:
The larger diameter and/or heavier the bullet, the less downrange energy it needs to achieve a given KPS value.
Understanding this implication quickly led me to conclude that I could use it to quantitatively compare the downrange performance of different sizes and weights of bullets, driven at different velocities. The key to such comparisons is specifying a KPS value of interest.
Suppose I wish to determine the energy level at which three different sizes and weights of hunting bullets would have a KPS value of 15. I start by mathematically rearranging (simple algebra) the KPS formula to read:
E = KPS / (SD x A)
Dividing the KPS value, 15, by the (SD x A) product of each of the three bullets specified below tells me the energy level at which each one would generate KPS = 15.
.243 dia., 100 gr. (SD .242, A .0464) - Energy for KPS of 15 = 1337 ft. lbs.
Things get interesting if a particular KPS value has a unique significance. Suppose I determine that 15 (or any other number) is the minimum KPS value that a bullet must have to be dependably effective in killing a particular size/type of game animal. I could then use this "baseline" KPS value to calculate the "Effective Killing Range" (EKR) of any cartridge/load combination that might be used when hunting the game in question. This is a powerful capability.
Simply put, the Effective Killing Range of a given cartridge/load is the distance at which the bullet has enough killing power (i.e., an adequate KPS value) to dependably dispatch a particular size/type of game animal (assuming a proper vital area hit).
Some popular cartridges, such as the .270 Winchester and .308 Winchester, are so powerful that there is no question they will dependably fell Class 2 game (e.g., deer, pronghorn, black bear, etc.) out to their +/- 3" MPBR distance, or beyond. All cartridges/loads do, of course, ultimately have range limits beyond which their killing power on a given class of game animal becomes questionable. However, when these are beyond the distance at which the hunter is willing to shoot (the +/- 3" MPBR in our case) they can be ignored.
However, what about milder or woods cartridges with a shorter MPBRs, such as the .30-30 Winchester? At what distance does the effectiveness of vital area hits become questionable? How can I define the EKR for a load? Can I apply what I learn to other loads?
In my youth, I hunted whitetail deer with .30-30s for some ten years, taking several deer during that period. I and others who used .30-30s normally zeroed our open sighted rifles at 100 paces (about 100 yards) and it was a rule of thumb among hunters that the .30-30 was most effective at ranges of 150 yards or shorter. This was with the 150 grain Flat Point factory ammo that almost everyone used at the time.
Analyzing the situation in hindsight, the 150 yard effective range rule I learned makes good sense. First, it is hard to obtain a precise aiming point with open sights at longer ranges. Using a 100 yard zero meant that bullet drop became significant beyond about 150 yards. (Zeroed at 100 yards, the traditional .30-30 load outlined above would hit about three inches low at 150 yards and almost nine inches low at 200 yards.) Thus, the 150 yard effective range guideline was both realistic and practical.
Today, many hunters would probably scoff at the 150 yard rule that I learned long ago and most would likely suggest that a .30-30 has an EKR of at least 200 yards. However, the "modern" hunter using a .30-30 rifle probably has a variable power scope mounted on it and also may be using the latest enhanced performance ammunition.
Musing about then versus now led me to reexamine the question of what is a reasonable EKR for the 150 grain .30-30 load. First, I looked at 205 yard data for the load. At that range, I observed that the energy of a 150 grain bullet is 785 ft. lbs. For comparison, the remaining energy at 150 yards is 996 ft. lbs.
I felt that the 205 yard energy was marginal, but that the 150 yard energy level was more than adequate for a .30 caliber, 150 grain bullet. I noticed that the energy at 175 yards was 894 ft. lbs., which almost exactly split the energy difference between the two ranges. I am comfortable with the idea that about 900 ft. lbs. of energy in a 150 grain .30 caliber bullet makes for adequate killing force on deer and other Class 2 animals.
I calculated that the KPS of the load at 175 yards was 15.0, a neat, easy to remember number. As a bonus, the far zero of the load is very close to 175 yards and I am a believer in using far zero (based on a +/- 3" MPBR) as a practical shooting range limit.
Putting all of this together, I called a KPS of 15.0 the baseline killing power value for hunting deer and similar game with a traditional 150 grain .30-30 load. I realize this is a judgment call, but I am comfortable with it. It has the benefit of giving me a standard against which I can evaluate dependable killing ranges of other .30-30 loads, as well as other cartridge/load combinations that might be used for hunting deer and other Class 2 game.
The procedure for determining the EKR of other cartridges and loads is fairly simple. It is most easily explained by way of an example. I will use the .243 Winchester cartridge to demonstrate the method and usefulness of comparisons of KPS and EKR across cartridges.
My example load is a Federal Premium .243 Win. load, with 100 grain JSP bullet. This is a standard 100 grain .243 Winchester factory load, with a 2960 f.p.s. MV from a 24" barrel. (I adjusted this to 2920 fps for a typical 22" barrel.)
.243 Win: Federal 100 gr. JSP, MV 2920 f.p.s., BC = .355
I started with the baseline KPS for the .30-30 Winchester, reasoning that a KPS that is adequate for one deer cartridge/load works for a different cartridge/load combination. Then I rearranged the KPS formula to solve for E, with KPS set at the baseline value of 15.0.
For the 100 grain .243 bullet, (SD x A) = (.242 x .0464) = .0112
This result means that the KPS of the load in question will be equal to 15.0 at the range where the energy of the bullet falls to 1339 ft. lbs. To find this range, I generated a trajectory table for the load, using five yard range increments. I read down the energy column of the table until I came to the closest energy value to 1339 ft. lbs. This was 1346 ft. lbs. at a range of 180 yards. Therefore, 180 yards is the EKR of this load.
It is notable that the EKR of this load falls well short of both its +/- 3" MPBR (280 yards) and far zero (240 yards). Some may find this result startling, but I have long been skeptical of the .243 bullet as a long range deer getter. The EKR analysis confirms my suspicions.
Most popular high intensity cartridges and loads have more than enough power to be effective on deer and other Class 2 game at extended ranges. For instance, the Remington Core-Lokt .308 Winchester load, with 150 grain PSP bullet, is my go-to factory load for deer hunting. Fired at an estimated 2820 f.p.s. from my rifle with a 20 inch barrel, this load gets a KPS of 15 at 435 yards.
The calculated EKR of this load, 435 yards, is a ridiculously long shot at a deer and I do not condone taking such a shot. For the .308 Winchester and other powerful, flat trajectory cartridges, a +/- 3" MPBR range is the absolute distance limit I would endorse (and that only under the most favorable conditions for setting up and executing the shot). Incidentally, the MPBR for this .308 Win. load is 260 yards and the KPS is 23.3 at that range.
Anyone who disagrees with the baseline KPS I established and used here may change the analysis to use any cartridge, load and ballistic parameters that they feel accurately reflect effective killing power and range, for deer or other game. The point is that KPS and EKR can be very useful tools for shooters who want to evaluate the killing performance of different cartridges and loads.
I am using the baseline KPS and EKR concepts developed here to work up detailed analyses of the .30-30, .243 Winchester, and .257 Roberts cartridges, focusing on their capabilities for hunting deer. I should have these articles ready to publish on Guns and Shooting Online in the near future.
Postscript: An appeal to elk hunters for information
I would love to establish a baseline KPS and do an EKR analysis of cartridges and loads suitable for hunting elk. However, I have no elk hunting experience, so I do not have a starting point for doing this. I would appreciate getting relevant information from experienced elk hunters. Please share with me your insights on effective elk cartridges. Essential information would include the cartridge and load (bullet weight and type), plus what you are confident is the effective killing range of the load in question on mature elk bulls. E-mail me at email@example.com.
Copyright 2017 by Gary Zinn and/or chuckhawks.com. All rights reserved.