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10-03-2009, 06:26 PM
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This review was the September Contest Winner!
Prepared by:
Larry S. (aka sinclair from Conceal Carry Forum)
Introduction
I have made a decision to obtain a gun for self defense. I know several others who have done so and I have discussed this many times. I have also taken an excellent self-defense course and am familiar with basic gun safety. In fact, I am very familiar with firearms but like anyone else who is new to this topic, I am faced with a personal dilemma. Where do I begin and what do I need ? Everybody has an opinion but I do not want to make a selection by consensus. Before I start looking at what is available, I would like to know how the choices relate to each other and which choices might be right for me. I would also like that information to be as free from opinion and salesmanship as I can get. When I look at candidates, can the different calibers be related so I understand them better ? If I really like the large, ugly gun, will it take my hand off when I shoot it ? If I have an understanding of these things, then I believe I shall have no trouble finding one I like and want.
First, then, is how to relate the gun calibers to each other. The approach I finally decided upon is discussed in Appendix A. For those technically inclined, feel free to offer improvements upon it. While I believe this to be my own work and not a duplication of the efforts of someone else, I also believe it to be a good approximation and should give a genuine grasp of what is out there. In Appendix A, I discuss why I believe that most common calibers will fall in three distinct velocity ranges. For ease of presentation, I will show these in three graphs. Low Subsonic, High Subsonic, and Magnum performance. With that brief introduction, lets take a look using the IPSC (International Practical Shooting Confederation) modified method for calculating bullet momentum.
Caliber Comparison
First, the Low Subsonic category.
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CHART 1
As discussed in Appendix A, these calibers are grouped together because it is difficult to load them to High Subsonic levels without pushing safe pressure limits established by the Sporting Arms and Ammunition Manufacturer's Institute (SAAMI). The IPSC (International Practical Shooting Confederation) Power Factor was chosen as the best and most useful technique to display bullet momentum. All calibers shown are compared at MINIMUM SAFE LOAD starting levels.
Next, the High Subsonic calibers.
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CHART 2
For those more technically inclined, I believe by now you may have noticed something you would have a disagreement about, specifically, these power factors seem too low. If so, Appendix A is for you. For everyone else, I hope you can see that these charts are intended to help you scale the difference between calibers. Each chart is adding higher values to the IPSC Power Factor, which is itself a simple multiple of a bullet's momentum.
Now for the highest values yet.
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CHART 3
The above chart also represents the true magnum calibers. No matter how you load them, it is a stretch to get them subsonic. For the purists out there, the 32 H&R magnum is in the middle chart because that is where it calculates. The Appendix, remember ? One surprise I did not expect was the new (mid 90's) FN developed 5.7 x 28 FN, which has been appearing in the Five-seven pistol and others. It is a center-fire cartridge with ballistics equal to the rim-fire 22 WMR. I did not include the 7.62 Tokarev as a separate entry because it is identical to the 30 Mauser, and the dimensions are so close that those cartridges can be interchanged and fired in either caliber gun, with identical ballistics. Another ballistic twin, although they cannot and should not be interchanged in each gun caliber (the bullet diameters are too different), is the 9mm Makarov and the 380 Auto. The first chart does not show this because the 9mm Makarov is the only center-fire caliber I could not find “jacketed” bullet load data for, which is one of the criteria used for all the others. The best equivalent load data was for “lead” which creates a slight disadvantage in the computation for it. I believe the calculation should be the same as the 380 ACP but it is shown where the “lead” data places it.
I keep reminding myself to leave the technical in the Appendix and stay with the generic purpose here, which is to give a sense for how the properties of a bullet/caliber can be related to one another. What we have with the IPSC Power Factor serves more than one purpose. It represents a physical property of a bullet, a specific multiple of the bullet's momentum, in the same manner that an automobile has a momentum property when it is moving. With the different types and sizes of automobiles, one way to compare their momentum properties would be to get them moving at the same speed. With a bullet, it is a bit more involved but the details; yes, see the Appendix. It is in the appendix where the method for comparison is chosen to be the minimum safe loads for each caliber.
Another purpose for the IPSC Power Factor would be for that category of competitive shooting. Many who enjoy the sport of shooting either attend or become involved with the competitive aspects of the sport. IPSC is such a sport which can greatly enhance not only shooting skills, but self-defense skills as well. By measuring the relative momentum property by caliber, using the IPSC version, you already understand the basic technique for determining how your own self-defense gun can compare to the pistol categories used by IPSC.
Free Recoil Comparison
Before selecting something from these charts, there is another consideration to look at. This one will be fun. How do the gun calibers relate to recoil, and which ones might not be fun to shoot ? To answer that, another bit of data is very important. How much does the gun weigh ? With a knowledge of the gun caliber (bullet momentum), and how much the empty gun weighs (including empty magazine weight for automatics), the “free recoil” of the gun can be calculated. Is this useful ? Another analogy applies to this one. Suppose the outside temperature shows as 68 degrees F. We can all agree that the temperature reading is correct, but some of us will feel comfortable outside while others will feel cool and need a jacket. Likewise for “free recoil”. It is different from “felt recoil” which tends to be every bit as subjective as how we “feel” temperature. Relating these things is what Appendix B is all about. For those less technically inclined, lets just take a look at the recoil relationships.
Free Recoil is the Translational Kinetic Energy imparted to the gun as a result of the powder charge in the bullet case expending it's chemical energy. Everything that goes out the barrel has a momentum property that, when totaled, must equal the momentum of the gun. (Newton's Third Law of Motion anyone ?) By computing safe load bullet momentum to derive our first charts, the only thing we need add is the momentum of the powder exhaust gas since the charge weight for each safe load is also known.
The charge gas drives the bullet out the barrel, and also exits. We can assume all of it exits for calculation purposes even though a small amount of residue remains. The charge momentum is thus the charge weight (even though it becomes a gas) times the charge velocity. For the purpose of these calculations we shall use single base nitrocellulose at a powder charge velocity of 1585 meters per second (5200 feet per second). With the total momentum of all forward moving items calculated, we have the rear-ward momentum of the gun. If we know the mass of the gun, we can use the classical relationship between momentum and kinetic energy to compute the kinetic energy imparted to the gun. By selecting a weight range for the gun, we can develop data for every caliber and gun weight we choose. This is a summary of Appendix B. From this data we can show several things. The gun weights chosen were 4 ounces to 40 ounces as representative of the majority of concealed carry gun options. Now, looking at our three categories of calibers, we can compare Free Recoil in the following three charts.
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CHART 4
Try as I might, the 9mm Makarov remains hidden between the 38 special and 44 Russian. Plus the graph rotations dislocate the caliber label alignment down and away from the associated color. The 9mm Makarov curve is virtually identical to the 380 ACP curve, which is fully visible. Since these are plotted with increasing bullet diameter, moving it is not an option as it actually is bigger than the 38 special.
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CHART 5
Again, the caliber labels are slightly dislocated down from their proper position on the associated color. This now appears to be an import problem from the spread sheet to this document. The 32 H & R magnum is almost hidden between the 30 Mauser and the 9mm Luger. This reflects the real-world problem with the lack-luster performance of the 32 H&R Mag. It is not a magnum by most definitions.
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CHART 6
There are now three charts that plot the free recoil of most all self defense guns to show the recoil value versus gun weight. Guns that do not exist yet can be compared by the weight they will have. The only problem is how to relate free recoil to what we experience when we shoot the thing. As mentioned when this section began, felt recoil is not unlike felt temperature. These charts represent the thermometer that measures the temperature. While we can disagree about whether 68 degrees F. feels cold or not, we are unlikely to disagree when the temperature is below the freezing point.
For the charts, it is time to examine the extreme conditions. In Chart 4, the least recoil value for any caliber is the 22 short. And the highest value for that caliber occurs at the minimum gun weight of 4 ounces. There is a gun in that caliber with that weight; the NAA 22 short revolver. It has a recoil energy of 2.7 Joules. If a 40 ounce gun were available in that caliber, the recoil energy drops to 0.27 Joules. This is close to a logarithmic relationship. I.E., Ten times the weight gives about one tenth the energy and visa versa. While this sounds like a bad thing (it is) in the 22 short it just is not a problem. That's because 2.7 Joules is a mouse fart compared to what some of the other calibers are doing. The main item to take note of is to compare the 22 short curve to the rest. At four ounces, the curve is just beginning to ramp up, where as most of the others look like a “ski jump”.
The other extreme is in Chart 6, the last curve and caliber being the 454 Casull. Yes, there is a real self defense revolver in that caliber and it weighs just a tad over 40 ounces. It is the Ruger Alaskan in 454 Casull, based upon a Super Redhawk frame with the barrel cut back to 3 inches. Most reviews I have seen indicate that this gun is painful for repetitive shooting. (Wears blisters in the web of the strong hand after one cylinder full) This curve is the calibration point. At 40 ounces, the recoil energy is 52 Joules. Let's call that our freezing point on the thermometer where everyone can agree it is cold or that the recoil is painful. Also notice where that occurs on the slope of the“ski jump”. Adjacent to the 454 Casull is the 44 magnum. 40 ounces is right for some of the 44 mag snubbies available, and that recoil energy is 32 Joules. Most reviews I have seen call the 44 mag snubbies to be “heavy” recoil.
The suggested calibration in the two above paragraphs gives a thermometer that looks like this: Recoil EnergySubjective "Feel" 3 JoulesLight Felt recoil 32 JoulesHeavy Felt recoil 52 JoulesPainful
To use the charts, pick the caliber you like from the first three, then obtain the gun weight and read the approximate recoil from that caliber at that gun weight. Look at the above thermometer and see where it reads. If you desire light recoil, then the closer you get to 3 Joules and the further away from 32 Joules, the better you will be. (Also avoid the high part of the “ski slope”, where recoil is shooting the moon.)
Caution: These charts are based upon minimum safe loads. Full power loads and +P loads will increase recoil energy significantly. Warning: Any +P+ loads are likely to double the recoil energy as well as cause potential damage and/or excess wear to the gun.
Selection Process
The best way to test any guide is to try to use it. A selection from each caliber category should do the trick. Selecting from the low supersonic category seems the best place to pick from the center. No particular reason except that I am aware that the lowest entry, the 22 short, is the oldest caliber still in production. It began as a self defense derringer cartridge but rapidly fell out of favor for that use. My inclination is to up the power factor a bit from there. The highest power factors on Chart 1 are around 160. The half way point is a power factor of 80. I see the 380 ACP is right on the money. Next, from Chart 4, I see that the 380, even at the lightest weight tops out at 15 Joules, half way between Light and Heavy felt recoil. I think that 4 ounces would be a small gun with a real snap to it so I would want the gun weight to go up a bit from 4 ounces. I would prefer a real joy to shoot and not be bothered by recoil on my first self defense gun. I see that at a weight of 20 ounces, the 380 ACP recoil energy is 3 Joules. Great, made to order. In real life, and very recently, I went through the true experience of looking at available 380 “Auto's” as they are called and found the closest in the shop to my target weight. I purchased the Bersa Thunder 380 which is 23 ounces, dripping wet, with empty magazine. I have not fired the weapon yet, but I am confident that I know exactly what to expect.
Next stop is Chart 2. Here is where I should have picked from the center. One caliber is centered numerically and almost by power factor, too. I am pleased so far with the 380 choice so maybe I can get lucky again. Thus I will pick the 9mm Luger. From Chart 5, and actually reading from the data tables in Appendix B, the 9mm Luger looks to be a caliber with a wide range of weights for low recoil, but it will most likely exceed the recoil of my choice from the first group. It also appears that around 10 to 12 ounces would be the point that recoil begins to be a worry. Thus my choice for a 9mm that I like will be at least 15 ounces or more. Nothing less. Since I do not purchase a gun very often, it is on my list for purchase with lots of time to find something that feels good in the hand and appeals to the eye. I will not look at anything that weighs less than 15 ounces.
On to Chart 3. If I ever wanted a small derringer style revolver, something like the NAA (North American Arms) Black Widow in 22 Magnum, and at 6 ounces looks pretty good. After putting these charts together, it seems to me that a center-fire derringer in 5.7 x 28 FN is going to show up sooner or later. If so, that caliber is capable of firing heavier weight bullets that the 22 Magnum, and might be a very interesting palm sized weapon. What really catches my attention is the 327 Magnum. The power factor compared to the 357 Magnum is good, and the comparative recoil from Chart 6 is even better. From the data in Appendix B, I see that the 357 Magnum looks like a heavy hand-hammer at 15 Ounces and 32 Joules, while the 327 at that gun weight is still at 18 Joules, about half the 357 recoil. Most of the magnum calibers are best applied in revolvers, which would likely range in the 30 ounce area. Both of my first two selections have been automatic pistols, so a good revolver will be a pleasant change. There are not many around in this new caliber, which was a joint effort by Federal and Ruger. Research indicates this caliber was designed specifically for the Ruger SP 101. It is a good firearm with reliable history, weighs in at 28 ounces (3 inch barrel), which gives 9 and a half Joules of free recoil. Looks to be a pleasant shooter for a magnum caliber, and though it is not the equal of the 357, it does come close. Put it on my list of three choices using the criteria in this guide.
Closing Comments
Preparing this document was a fun and learning experience. I was motivated to do something like this for a long time because age and a broken wrist (strong hand) has resulted in a reduced tolerance for recoil in many of the firearms I have enjoyed. The first to go was a NAA 454 Casull. I suspect it would have gone anyway as I never enjoyed shooting it. Still, the hand cannon is an experience to be remembered.
The choices made as an example above are easy to defend. The 380 auto is capable of shooting the same bullet weight and velocity as the old Colt 1851 Navy, the gun that made Colt's reputation and was winning the west long before the 45 Colt appeared on the scene. The 9mm Luger is as venerable and classic as the 45 Auto with an equal history. The 327 Magnum may fade as soon as it has appeared, but the gun it was designed for, particularly in a stainless version, would quickly become a collector, thus an easy trade-up in caliber.
Appendix A
A Heuristic Method to Compare Bullet Caliber
http://www.thefreedictionary.com/heuristic
"relating to a usually speculative formulation serving as a guide in the investigation or solution of a problem."
Momentum P = m * v (mass times velocity)
The goal is to make as unbiased, fair comparison of bullet calibers as possible, and base this as firmly on sound principles and reasoning as can be found. There are heuristic methods in abundance in the gun world. Most of them are used to compare the relative striking power of a bullet. Naturally, that opens a debate which can be quite heated. To minimize that debate, the selection of gun physics, and in particular, Conservation of Momentum, will allow for computing properties of the gun, and bullet in a more exact form. To avoid the most heated debates, a comparison of the momentum properties of a bullet will not be used to predict the effectiveness of that bullet on specific targets.
In the main text, a physical comparison between different makes of automobiles was suggested as an analogy. To get a good momentum comparison between the different cars, the easiest method is to have each car travel at the same speed. Obviously, the heaviest car will have the highest momentum, and there would be no need for obtaining momentum. Just weigh the cars and the heaviest is the one that will always have the most. That is not where the analogy breaks down. It perfectly illustrates the property of momentum. When objects have the same velocity, the heaviest mass will have the most P. Likewise, when objects have the same mass, the highest velocity object will have the most P. With bullets, the lighter bullets travel faster with the same charge and tends to break the weight dependency for momentum, and each caliber can be loaded with multiple weights which can break the velocity dependency. Our comparison problem is no longer trivial nor weight/velocity dependent, and really compounded when trying to get this diversity to comparable weights or velocities.
Therein lies the insight to begin a comparison. There is a growing popularity with subsonic loads for pistols. One reason would be for sound suppression. The less obvious but more important reason is because most pistol calibers can break the sonic barrier but not enough to maintain that velocity all the way to the target (say 25-50 yards). As they slow down, the sonic wave can catch up and disturb the bullet, seriously impacting accuracy. Subsonic loads are becoming more popular with competitive shooters for this reason. Many ammunition manufacturers are beginning to aim for this “subsonic” market. Around 1150 feet per second, depending on altitude and atmospheric factors, is the rough sonic barrier. To stay subsonic independent of the variable factors, the load target is usually between 1030 and 1050 feet per second. This reminds me of another insight. IPSC Shooting competitions determine the shooting class (Major or Minor for pistol) based upon a modification to the bullet momentum. That modification is very interesting for what this Appendix is about. In a way, IPSC rules almost set a speed limit for bullets in this sense: If you multiply bullet momentum (bullet mass in pounds time velocity in fps) by seven (7) you get the IPSC Power Factor (Yes, I know that is not how it is calculated by IPSC, but the math is there). Now remember our car analogy. If they travel at the same speed, just weigh the car ? If you can get your loads at 1000 feet per second, no need to calculate either momentum, or IPSC Power. The IPSC Power Factor = bullet weight (in grains) AT THAT SPEED. And the bullet momentum is equal to the IPSC Power Factor divided by seven. (except that IPSC rounds down on Power Factor, meaning that 124.999 does not equal 125. It stays 124)
I like that “magic” number (1000 fps). The problem now is how can it be used fairly with every caliber on the market ? The first problem is that some calibers cannot be safely loaded to even reach 1000 fps. The next problem is that all calibers that can reach that velocity are also capable of exceeding it. Finally, some calibers, even in mild loadings, will stay supersonic. This is where ammunition liability laws come to assist this effort. Standard factory loads, economy loads, or bulk ammunition is assembled considering the “worst” clunker-gun out there. The ammunition liability creates a need to market loads that will be safe in most anything. How this is done is hard to find and most likely proprietary information. There is another source. More ammunition is loaded in this country by “hobbyists” than is produced by the factories. The way the “hobbyists” do this is common knowledge, not proprietary. They work up loads for each individual gun to determine what loads are safe for that gun. The “rule of thumb” is to reduce the maximum powder charge by ten percent and gradually move up to the full charge that approximates the SAAMI caliber pressure standard. What better way to compare calibers ? Reduce all caliber loadings to the hobbyist's safe starting loads and measure them. Each and every load is then compared at starting pressure levels where all guns should safely work, and every measurement level for every caliber has the potential to be improved with full pressure loads, or even the so called +P and +P+ loads which need not be addressed at all.
Next, a selection method that favors no caliber but will provide all the data needed.
All calibers will use jacketed bullets, since lead bullets tend to move slower at the same weight/charge levels. All caliber data will use only recommended safe starting load levels from the same source. Two exceptions shall be allowed; rim-fire cartridges and the new 327 Federal Magnum.
The heaviest weight bullet in each caliber that can achieve the target velocity of 1000 fps with minimum load levels will be selected. All such calibers will be placed in the category of “High Subsonic”.
When there is no load for a given caliber that can reach the target velocity, the highest velocity available for any bullet in that caliber at minimum load levels shall be selected. All such calibers will be placed in the category of “Low Subsonic”, even if their full SAAMI pressure loadings can attain the target velocity.
The first three methods fail when encountering the true magnum calibers (other than the 32 H&R Magnum) since even minimum magnum load data is supersonic. This means that magnum calibers will be biased by our criteria. Thus they are separated and the criteria adjusted as follows: The heaviest weight bullet in each magnum caliber that can achieve a target velocity of 1500 fps at minimum load levels will be selected. This modified velocity recognizes the nature of a true magnum and selects a velocity that will still be supersonic at target ranges (25-50 yards), thus addressing the accuracy problem imposed by the subsonic criteria on all other calibers.
To apply this selection criteria using a single center-fire cartridge loading source, I have selected the Lyman Reloading Handbook, 49th edition, Published by Lyman Products Corporation. The 22 Rim-fire sources are discussed and cited below the tables since this selection criteria cannot apply to rim-fire.
The new 327 Federal Magnum load data is scarce and I will use the only source I have found for it.
Using this selection criteria on the sources gives the following results:
Low Subsonic Calibers Part 1
Cal.22 Short25 ACP32 ACP32 SWL380 ACP38 SW38 Spl Mass gr.2935608595150110 Charge4 gr1.2 gr2.7 gr2.5 gr2.4 gr2.8 gr4.1 gr Vel. fps653774968842861688875 P2.713.878.310.2211.6914.7413.75 IPSC PF182758718110396
Low Subsonic Calibers Part 2
Cal.9mm Mak44 Russian44 Special45 ACP45 GAP45 Colt Mass gr.95180180185185185 Charge3.2 gr4.9 gr7.3 gr7.4 gr6.3 gr10.8 gr Vel. fps672776823917923876 P9.1219.9521.1524.2424.3923.2 IPSC PF63140148169170162
The tables are almost self explanatory; the Capitol “P” is Momentum in Lb-Feet/Sec and the IPSC PF is the Power Factor from IPSC competition, in accordance with the current rules of the IPSC that can be downloaded from http://www.ipsc.org/pdf/RulesHandgun.pdf
The charge is the powder weight for the bullet mass and velocity combination taken from the primary source. Powder brand is not listed and not needed for computations.
To convert grains into pounds, divide by 7000 (grains/pound) for momentum calculation.
IPSC Power Factor is computed by multiplying bullet weight in grains times velocity, the total then divided by 1000.
The 22 calibers will be addressed after the tables are presented. The 9mm Makarov is a sample to show that the selection criteria has a problem when it cannot be adhered to. In particular, the primary source does not have metal jacketed loads, only lead for this caliber. I suspect this is due to the shortage of components for this caliber. If jacketed were available, this column would most likely be identical to the 380 ACP column because the velocity would be nearly the same as well as identical bullet weights. The next table will also be in two parts.
High Subsonic Calibers Part 1
Cal.22 LR30 Luger30 Mauser32 HR Mag9mm Luger38 Super357 Sig Mass gr.40939371125147147 Charge5 gr4.5 gr6 gr4.5 gr7 gr8.3 gr6.2 gr Vel. fps1000100010421000100010471030 P5.7113.2913.8410.1417.8621.9921.63 IPSC PF40939671125153151
The 22 calibers will be addressed after the tables are presented. Note that according to the selection criteria the 32 H&R Magnum is magnum in name only. It does not meet magnum performance selection criteria.
Whenever a listed velocity is very close to 1000 fps, that is the listed table velocity provided the actual velocity does not significantly change the momentum. When it does the actual velocity is used, as for example the 1030 fps of the 357 Sig.
High Subsonic Calibers Part 2
Cal.40 S&W10mm Auto Mass gr.155200 Charge7.2 gr6.3 gr Vel. fps9881000 P21.8828.57 IPSC PF153200
The 40 S&W is high-lighted because this is the only caliber where the target velocity of 1000 fps was not exceeded at the selected minimum charge and bullet weight. The next lower bullet weight would normally be selected to prevent an advantage here. I left it because this one really needs an average position between this and the next lower weight position. The value difference is quite small. It is sitting next to it's big brother, the 10mm Auto so it needs every nudge it can get.
The next table represents what I have been referring to as the true magnum calibers. These calibers are very difficult to load subsonic. It can be done using what would be termed “Gallery” loading but such loads are not useful for this comparison. Remember that these loads are considered the safe starting minimum for each caliber.
Supersonic Calibers
Cal.22 WMR5.7x29 FN327 Mag357 Mag41 Mag44 Mag454 Casull Mass gr.4040100110170180225 Charge7 gr4.3 gr8.9 gr17.8 gr24.1 gr29 gr33.9 gr Vel. fps1500150015001568158215411657 P8.578.5721.4324.6438.4239.6355.63 IPSC PF6060150172268277389
All 22 caliber rim-fire data is highlighted since the criteria for selection cannot apply to the rim-fires. Due to the design of the case, it is weaker at the base than any center-fire. This limits the pressure the case can be loaded for in order to prevent the base from blowing out. These cases are not considered available loads for hobbyists and all factory loads are based upon keeping load pressure below the reduced strength fail-pressure for the case. Data shown for the 22 calibers is based upon best estimates from several sources listed in the reference section.
Load data for the new Federal 327 Magnum was taken from the source listed in the reference section.
All data listed was obtained using barrel lengths of between 4 and 5 inches except for 25 ACP which used 2 inches, 32 ACP which used 3 inches, 380 ACP which used 3.5 inches, 44 Russian which used 6.5 inches, 45 Colt which used 7 inches, and 454 Casull which used 6 inches. Since the barrel lengths for the exceptions were varied based upon what tends to be available on the market for those calibers, I believe the final data is better for this.
The 454 Casull is unlikely to be a self-defense handgun choice due to the high penetration qualities and heavy recoil of this caliber. It is included as the upper boundary sanity check for the calibers listed. Likewise, the rim-fire 22 short is unlikely to be a self-defense handgun choice due to the lack of penetration qualities and despite its negligible recoil. It is included as the lower boundary sanity check for the calibers listed.
The bar chart plots in the main text come from the above data tables using the IPSC data row as the y axis and the Caliber row as the x axis. Replacing the y axis with the momentum (P) values gives identical bar charts but with lower y axis grid values. Instead of repeating the charts here I will demonstrate this with a “bonus” for those who read this appendix.
Here is the “bonus” chart for the Appendix sample bar charts.
The Monsters
(and these are MINIMUM loads)
Cal.460 SW Mag480 Ruger475Linebaugh50 AE500 S&W Mass gr.300325325325400 gr Charge34 gr27.1 gr31.2 gr31.2 gr35.8 gr Vel. fps17981503159213001607 P77.0669.7873.9760.3691.83 IPSC PF539488517422642
First, plotting momentum (P) versus caliber gives the true momentum plot as this:
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CHART 7
Note the relationship of the bars to each other and how that relationship will not change when the IPSC PF row is used for the y axis. The relationship is preserved because IPSC uses a whole number multiple of momentum to stretch the y axis grid.
These calibers, as is the 454 Casull, were intended for hunting large game with a handgun. They are not suited for concealed carry due to size and weight. They are not suited for self defense due to excessive penetration. The latter argument means that in a self defense situation, these calibers are most likely to continue through the target while still retaining lethal force down range.
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CHART 8
The tables list charge weight in grains which has not yet been discussed. The momentum values in the tables will be used in Appendix B along with the charge weight. The charge weight is retained in both Appendixes for consistency.
All loads shown, exception for rim-fire as noted above, are minimum safe loads that should be safe in any gun, new or used. The minimum was chosen since it was far easier to do than to compare the maximum loads and get into a discussion of +p and the +p+ loads and what the standards for those are. Plus the potential to improve every caliber listed is easy. The so called “hot” loads or defense loads on the market will come much closer to full SAAMI pressure levels than the loads listed here. While there are SAAMI standards for some +p loads, use caution and the manual with your firearm. Some manuals caution against this. There are currently no SAAMI pressure standards for +p+ loads. The best safety caution I can make is that you are on your own with those. My research indicates that +p+ loads would fall somewhere between +p levels and factory “Proof” test loads.
Appendix B
A Direct Method to Compare Bullet Caliber Recoil
Data from Appendix A will be used for the calculations in this Appendix. Appendix A contains the momentum calculation (P) for each caliber plus the associated charge weight used for the data listed.
Consider the point in time when a firearm is triggered. The primer in the caliber case goes off, contributing its chemical energy to igniting the powder charge, which generates the expansive pressure against the base of the bullet necessary to launch it down the barrel. At the same time, this same pressure is exerted against the firearm's chamber. From the Conservation of Momentum, these must be equal since the net momentum at the start is zero for the reference frame considered. The momentum of the gun, however, is equal to the total momentum imparted to the bullet PLUS the momentum generated by the charge gases and anything else that goes out, like wads or sabots, which also exits the barrel. Recoil relates to Conservation of Momentum, and “free recoil” relates to the energy associated with the gun when the gun is fired. It can be derived from the gun's momentum using several methods. The method chosen for this appendix is known as the “Momentum Short Form” which comes from the classical mathematical relationship between momentum and energy.
The kinetic energy of an object can be computed from its momentum by the relationship:
http://www.concealcarrychat.com/forums/../formula_01.pngKinetic Energy equals the object's momentum value squared and divided by twice the mass of the object. P of the gun = (mass of bullet times velocity of bullet) + (mass of other ejecta times ejecta velocity)
The Momentum Short Form takes the above two equations together as follows:
Momentum short form: Etgu = 0.5 · [{(mp · vp) + ( mc · vc)} / 1000]2 / (mgu)
Where:
Etgu is the translational kinetic energy of the firearm as expressed by the joule (J).
mgu is the weight of the firearm expressed in kilograms (kg).
mp is the weight of the projectile expressed in grams (g).
mc is the weight of the powder charge expressed in grams (g).
vp is the velocity of the projectile expressed in meters per second (m/s).
vc is the velocity of the powder charge expressed in meters per second (m/s).
1000 is the conversion factor to set the numerator equal to kilograms.
“0.5”is taking the 2 in the denominator of the first equation above and converting 1/2 to 0.5
Etgu, as the translational kinetic energy of the gun, is also known as the “free recoil” energy of the gun. What we would most like to do is calculate the “net energy” of the gun, known as “felt recoil”. Trying to figure the net recoil energy of a firearm is a near futile endeavor. Even if you can calculate the recoil energy loss due to a muzzle brake, recoil operated action, gas operated action, mercury recoil suppression tube, recoil reducing butt pad and hand grip, shooting vest and gloves, the human factor remains subjective.
Thus we need a subjective method to relate what we can calculate to that which we cannot calculate. Once free recoil is tabulated, a speculative technique should give a logical inference between this and “felt recoil”. With that available, this appendix should yield the data necessary to plot a gun's weight versus felt recoil for candidate calibers. Since our computations are based upon minimum loads in Appendix A, we have the best case to look at, which is minimum recoil energy from each caliber.
It is a simple conversion exercise to change the table data in Appendix A to metric data for use in the Momentum Short Form. The end result will be a computation for each caliber and for each gun weight ranging from 4 to 40 ounces (also converted to grams). The final data list will show free recoil in Joules. For those who prefer the SI system of measure, the conversion is:
1 Joule = 0.737562 ft ·lbf
Here is a sample calculation which will also show how the computations were formatted in the spread sheet.
22 short25 ACP32 ACPEtc.. Enter Bullet Mass (grams)1.883.243.88
Enter Bullet Vel. (meters/sec)199.2236.1295.2
Enter Charge Mass (grams)0.260.050.17
Enter Charge Vel. (meters/sec)158515851585
Enter Gun Mass 39 oz (1.11Kg)1.111.111.11
Numerator (Pbullet + Pcharge)786.5844.11415
Div by 1000 (grams to Kg)0.790.841.41
(Total P) Squared0.620.712 Divide P squared by 2 x gun mass (ounces to Kgs, 39 oz = 1.106Kg) Result is free recoil Joules for a gun mass of 39 oz.0.280.320.91
Multiply this computation for every caliber and for every gun mass from 4 to 40 ounces.
Data for the low subsonic calibers, the high subsonic, and Magnum data:
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CHART 9
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CHART 10
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CHART 11
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CHART 12
Three-D plots from these data tables are in the main text and not reproduced here. As a bonus for anyone that makes it this far, there is another way to compare free recoil that would involve fun iterations and probably be even more useful. Given that all the data sheets compute and compare apples to apples (Joules), it would be possible to calculate the area under each curve to arrive at a percentage ratio between the curves computed. To make it work would require a big data sheet with every caliber listed and plotted together. Then each curve area would ratio directly between calibers. I will do a simple one for the magnum calibers, but the only way to percentage recoil with the other calibers is to plot them all in the same area/percentage computation. Here is the sample bonus chart that ratios only the magnums to each other.
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CHART 13
Appendix C
Reference List
Hardcover References
Lyman Pistol and Revolver Handbook, Third Edition
Lyman Reloading Handbook, 49th Edition
Internet Reference Link List
Myth of muzzle energy
http://www.chuckhawks.com/myth_muzzle_energy.htm
Muzzle momentum
http://terra.gg.utah.edu/guns/energy.pdf
chuck hawks cartridge chart (unfortunately, sites Marshall and Sanow poor study)
http://www.chuckhawks.com/handgun_power_chart.htm
Powder in 22 WMR mag is 7 grns
http://www.gun-tests.com/performance/apr96reloading.html
free recoil of 327 and other 32's
http://www.chuckhawks.com/327_federal.htm
powder charge of 327
http://www.shootingtimes.com/ammunition/ST_reloadingthe327_200902/index1.html
momentum over energy
http://www.gsgroup.co.za/articlemomentum.html
Excellent: Great bullet debate
http://personal.palouse.net/joeh/pages/BulletDebate.htm
IPSC Rules (downloaded the handgun rules)
http://www.ipsc.org/pdf/RulesHandgun.pdf
IPSC (International Practical Shooting Confederation)
http://www.ipsc.org/whatipsc.htm
SAAMI max pressures by cartridge
http://www.leverguns.com/articles/saami_pressures.htm
SAAMI standards site
http://www.saami.org/
unsafe firearm combinations
http://www.saami.org/Unsafe_Combinations.cfm
computing free recoil energy
http://en.wikipedia.org/wiki/Free_recoil
laws of motion
http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton.27s_third_law:_la w_of_reciprocal_actions
physics of firearms
http://en.wikipedia.org/wiki/Physics_of_firearms
22 rimfire
http://www.chuckhawks.com/history_rimfire_ammo.htm
http://www.chuckhawks.com/22_rimfire_cartridges.htm
http://www.chuckhawks.com/22mag.htm
http://www.gunnersden.com/index.htm.rimfire-rifles.html
http://www.gunblast.com/Paco_22AutoMag.htm
[For the complete Article, Visit: http://www.concealcarrychat.com/index.php?pageid=self-defense-guide]
This review was the September Contest Winner!
Prepared by:
Larry S. (aka sinclair from Conceal Carry Forum)
Introduction
I have made a decision to obtain a gun for self defense. I know several others who have done so and I have discussed this many times. I have also taken an excellent self-defense course and am familiar with basic gun safety. In fact, I am very familiar with firearms but like anyone else who is new to this topic, I am faced with a personal dilemma. Where do I begin and what do I need ? Everybody has an opinion but I do not want to make a selection by consensus. Before I start looking at what is available, I would like to know how the choices relate to each other and which choices might be right for me. I would also like that information to be as free from opinion and salesmanship as I can get. When I look at candidates, can the different calibers be related so I understand them better ? If I really like the large, ugly gun, will it take my hand off when I shoot it ? If I have an understanding of these things, then I believe I shall have no trouble finding one I like and want.
First, then, is how to relate the gun calibers to each other. The approach I finally decided upon is discussed in Appendix A. For those technically inclined, feel free to offer improvements upon it. While I believe this to be my own work and not a duplication of the efforts of someone else, I also believe it to be a good approximation and should give a genuine grasp of what is out there. In Appendix A, I discuss why I believe that most common calibers will fall in three distinct velocity ranges. For ease of presentation, I will show these in three graphs. Low Subsonic, High Subsonic, and Magnum performance. With that brief introduction, lets take a look using the IPSC (International Practical Shooting Confederation) modified method for calculating bullet momentum.
Caliber Comparison
First, the Low Subsonic category.
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CHART 1
As discussed in Appendix A, these calibers are grouped together because it is difficult to load them to High Subsonic levels without pushing safe pressure limits established by the Sporting Arms and Ammunition Manufacturer's Institute (SAAMI). The IPSC (International Practical Shooting Confederation) Power Factor was chosen as the best and most useful technique to display bullet momentum. All calibers shown are compared at MINIMUM SAFE LOAD starting levels.
Next, the High Subsonic calibers.
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CHART 2
For those more technically inclined, I believe by now you may have noticed something you would have a disagreement about, specifically, these power factors seem too low. If so, Appendix A is for you. For everyone else, I hope you can see that these charts are intended to help you scale the difference between calibers. Each chart is adding higher values to the IPSC Power Factor, which is itself a simple multiple of a bullet's momentum.
Now for the highest values yet.
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CHART 3
The above chart also represents the true magnum calibers. No matter how you load them, it is a stretch to get them subsonic. For the purists out there, the 32 H&R magnum is in the middle chart because that is where it calculates. The Appendix, remember ? One surprise I did not expect was the new (mid 90's) FN developed 5.7 x 28 FN, which has been appearing in the Five-seven pistol and others. It is a center-fire cartridge with ballistics equal to the rim-fire 22 WMR. I did not include the 7.62 Tokarev as a separate entry because it is identical to the 30 Mauser, and the dimensions are so close that those cartridges can be interchanged and fired in either caliber gun, with identical ballistics. Another ballistic twin, although they cannot and should not be interchanged in each gun caliber (the bullet diameters are too different), is the 9mm Makarov and the 380 Auto. The first chart does not show this because the 9mm Makarov is the only center-fire caliber I could not find “jacketed” bullet load data for, which is one of the criteria used for all the others. The best equivalent load data was for “lead” which creates a slight disadvantage in the computation for it. I believe the calculation should be the same as the 380 ACP but it is shown where the “lead” data places it.
I keep reminding myself to leave the technical in the Appendix and stay with the generic purpose here, which is to give a sense for how the properties of a bullet/caliber can be related to one another. What we have with the IPSC Power Factor serves more than one purpose. It represents a physical property of a bullet, a specific multiple of the bullet's momentum, in the same manner that an automobile has a momentum property when it is moving. With the different types and sizes of automobiles, one way to compare their momentum properties would be to get them moving at the same speed. With a bullet, it is a bit more involved but the details; yes, see the Appendix. It is in the appendix where the method for comparison is chosen to be the minimum safe loads for each caliber.
Another purpose for the IPSC Power Factor would be for that category of competitive shooting. Many who enjoy the sport of shooting either attend or become involved with the competitive aspects of the sport. IPSC is such a sport which can greatly enhance not only shooting skills, but self-defense skills as well. By measuring the relative momentum property by caliber, using the IPSC version, you already understand the basic technique for determining how your own self-defense gun can compare to the pistol categories used by IPSC.
Free Recoil Comparison
Before selecting something from these charts, there is another consideration to look at. This one will be fun. How do the gun calibers relate to recoil, and which ones might not be fun to shoot ? To answer that, another bit of data is very important. How much does the gun weigh ? With a knowledge of the gun caliber (bullet momentum), and how much the empty gun weighs (including empty magazine weight for automatics), the “free recoil” of the gun can be calculated. Is this useful ? Another analogy applies to this one. Suppose the outside temperature shows as 68 degrees F. We can all agree that the temperature reading is correct, but some of us will feel comfortable outside while others will feel cool and need a jacket. Likewise for “free recoil”. It is different from “felt recoil” which tends to be every bit as subjective as how we “feel” temperature. Relating these things is what Appendix B is all about. For those less technically inclined, lets just take a look at the recoil relationships.
Free Recoil is the Translational Kinetic Energy imparted to the gun as a result of the powder charge in the bullet case expending it's chemical energy. Everything that goes out the barrel has a momentum property that, when totaled, must equal the momentum of the gun. (Newton's Third Law of Motion anyone ?) By computing safe load bullet momentum to derive our first charts, the only thing we need add is the momentum of the powder exhaust gas since the charge weight for each safe load is also known.
The charge gas drives the bullet out the barrel, and also exits. We can assume all of it exits for calculation purposes even though a small amount of residue remains. The charge momentum is thus the charge weight (even though it becomes a gas) times the charge velocity. For the purpose of these calculations we shall use single base nitrocellulose at a powder charge velocity of 1585 meters per second (5200 feet per second). With the total momentum of all forward moving items calculated, we have the rear-ward momentum of the gun. If we know the mass of the gun, we can use the classical relationship between momentum and kinetic energy to compute the kinetic energy imparted to the gun. By selecting a weight range for the gun, we can develop data for every caliber and gun weight we choose. This is a summary of Appendix B. From this data we can show several things. The gun weights chosen were 4 ounces to 40 ounces as representative of the majority of concealed carry gun options. Now, looking at our three categories of calibers, we can compare Free Recoil in the following three charts.
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CHART 4
Try as I might, the 9mm Makarov remains hidden between the 38 special and 44 Russian. Plus the graph rotations dislocate the caliber label alignment down and away from the associated color. The 9mm Makarov curve is virtually identical to the 380 ACP curve, which is fully visible. Since these are plotted with increasing bullet diameter, moving it is not an option as it actually is bigger than the 38 special.
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CHART 5
Again, the caliber labels are slightly dislocated down from their proper position on the associated color. This now appears to be an import problem from the spread sheet to this document. The 32 H & R magnum is almost hidden between the 30 Mauser and the 9mm Luger. This reflects the real-world problem with the lack-luster performance of the 32 H&R Mag. It is not a magnum by most definitions.
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CHART 6
There are now three charts that plot the free recoil of most all self defense guns to show the recoil value versus gun weight. Guns that do not exist yet can be compared by the weight they will have. The only problem is how to relate free recoil to what we experience when we shoot the thing. As mentioned when this section began, felt recoil is not unlike felt temperature. These charts represent the thermometer that measures the temperature. While we can disagree about whether 68 degrees F. feels cold or not, we are unlikely to disagree when the temperature is below the freezing point.
For the charts, it is time to examine the extreme conditions. In Chart 4, the least recoil value for any caliber is the 22 short. And the highest value for that caliber occurs at the minimum gun weight of 4 ounces. There is a gun in that caliber with that weight; the NAA 22 short revolver. It has a recoil energy of 2.7 Joules. If a 40 ounce gun were available in that caliber, the recoil energy drops to 0.27 Joules. This is close to a logarithmic relationship. I.E., Ten times the weight gives about one tenth the energy and visa versa. While this sounds like a bad thing (it is) in the 22 short it just is not a problem. That's because 2.7 Joules is a mouse fart compared to what some of the other calibers are doing. The main item to take note of is to compare the 22 short curve to the rest. At four ounces, the curve is just beginning to ramp up, where as most of the others look like a “ski jump”.
The other extreme is in Chart 6, the last curve and caliber being the 454 Casull. Yes, there is a real self defense revolver in that caliber and it weighs just a tad over 40 ounces. It is the Ruger Alaskan in 454 Casull, based upon a Super Redhawk frame with the barrel cut back to 3 inches. Most reviews I have seen indicate that this gun is painful for repetitive shooting. (Wears blisters in the web of the strong hand after one cylinder full) This curve is the calibration point. At 40 ounces, the recoil energy is 52 Joules. Let's call that our freezing point on the thermometer where everyone can agree it is cold or that the recoil is painful. Also notice where that occurs on the slope of the“ski jump”. Adjacent to the 454 Casull is the 44 magnum. 40 ounces is right for some of the 44 mag snubbies available, and that recoil energy is 32 Joules. Most reviews I have seen call the 44 mag snubbies to be “heavy” recoil.
The suggested calibration in the two above paragraphs gives a thermometer that looks like this: Recoil EnergySubjective "Feel" 3 JoulesLight Felt recoil 32 JoulesHeavy Felt recoil 52 JoulesPainful
To use the charts, pick the caliber you like from the first three, then obtain the gun weight and read the approximate recoil from that caliber at that gun weight. Look at the above thermometer and see where it reads. If you desire light recoil, then the closer you get to 3 Joules and the further away from 32 Joules, the better you will be. (Also avoid the high part of the “ski slope”, where recoil is shooting the moon.)
Caution: These charts are based upon minimum safe loads. Full power loads and +P loads will increase recoil energy significantly. Warning: Any +P+ loads are likely to double the recoil energy as well as cause potential damage and/or excess wear to the gun.
Selection Process
The best way to test any guide is to try to use it. A selection from each caliber category should do the trick. Selecting from the low supersonic category seems the best place to pick from the center. No particular reason except that I am aware that the lowest entry, the 22 short, is the oldest caliber still in production. It began as a self defense derringer cartridge but rapidly fell out of favor for that use. My inclination is to up the power factor a bit from there. The highest power factors on Chart 1 are around 160. The half way point is a power factor of 80. I see the 380 ACP is right on the money. Next, from Chart 4, I see that the 380, even at the lightest weight tops out at 15 Joules, half way between Light and Heavy felt recoil. I think that 4 ounces would be a small gun with a real snap to it so I would want the gun weight to go up a bit from 4 ounces. I would prefer a real joy to shoot and not be bothered by recoil on my first self defense gun. I see that at a weight of 20 ounces, the 380 ACP recoil energy is 3 Joules. Great, made to order. In real life, and very recently, I went through the true experience of looking at available 380 “Auto's” as they are called and found the closest in the shop to my target weight. I purchased the Bersa Thunder 380 which is 23 ounces, dripping wet, with empty magazine. I have not fired the weapon yet, but I am confident that I know exactly what to expect.
Next stop is Chart 2. Here is where I should have picked from the center. One caliber is centered numerically and almost by power factor, too. I am pleased so far with the 380 choice so maybe I can get lucky again. Thus I will pick the 9mm Luger. From Chart 5, and actually reading from the data tables in Appendix B, the 9mm Luger looks to be a caliber with a wide range of weights for low recoil, but it will most likely exceed the recoil of my choice from the first group. It also appears that around 10 to 12 ounces would be the point that recoil begins to be a worry. Thus my choice for a 9mm that I like will be at least 15 ounces or more. Nothing less. Since I do not purchase a gun very often, it is on my list for purchase with lots of time to find something that feels good in the hand and appeals to the eye. I will not look at anything that weighs less than 15 ounces.
On to Chart 3. If I ever wanted a small derringer style revolver, something like the NAA (North American Arms) Black Widow in 22 Magnum, and at 6 ounces looks pretty good. After putting these charts together, it seems to me that a center-fire derringer in 5.7 x 28 FN is going to show up sooner or later. If so, that caliber is capable of firing heavier weight bullets that the 22 Magnum, and might be a very interesting palm sized weapon. What really catches my attention is the 327 Magnum. The power factor compared to the 357 Magnum is good, and the comparative recoil from Chart 6 is even better. From the data in Appendix B, I see that the 357 Magnum looks like a heavy hand-hammer at 15 Ounces and 32 Joules, while the 327 at that gun weight is still at 18 Joules, about half the 357 recoil. Most of the magnum calibers are best applied in revolvers, which would likely range in the 30 ounce area. Both of my first two selections have been automatic pistols, so a good revolver will be a pleasant change. There are not many around in this new caliber, which was a joint effort by Federal and Ruger. Research indicates this caliber was designed specifically for the Ruger SP 101. It is a good firearm with reliable history, weighs in at 28 ounces (3 inch barrel), which gives 9 and a half Joules of free recoil. Looks to be a pleasant shooter for a magnum caliber, and though it is not the equal of the 357, it does come close. Put it on my list of three choices using the criteria in this guide.
Closing Comments
Preparing this document was a fun and learning experience. I was motivated to do something like this for a long time because age and a broken wrist (strong hand) has resulted in a reduced tolerance for recoil in many of the firearms I have enjoyed. The first to go was a NAA 454 Casull. I suspect it would have gone anyway as I never enjoyed shooting it. Still, the hand cannon is an experience to be remembered.
The choices made as an example above are easy to defend. The 380 auto is capable of shooting the same bullet weight and velocity as the old Colt 1851 Navy, the gun that made Colt's reputation and was winning the west long before the 45 Colt appeared on the scene. The 9mm Luger is as venerable and classic as the 45 Auto with an equal history. The 327 Magnum may fade as soon as it has appeared, but the gun it was designed for, particularly in a stainless version, would quickly become a collector, thus an easy trade-up in caliber.
Appendix A
A Heuristic Method to Compare Bullet Caliber
http://www.thefreedictionary.com/heuristic
"relating to a usually speculative formulation serving as a guide in the investigation or solution of a problem."
Momentum P = m * v (mass times velocity)
The goal is to make as unbiased, fair comparison of bullet calibers as possible, and base this as firmly on sound principles and reasoning as can be found. There are heuristic methods in abundance in the gun world. Most of them are used to compare the relative striking power of a bullet. Naturally, that opens a debate which can be quite heated. To minimize that debate, the selection of gun physics, and in particular, Conservation of Momentum, will allow for computing properties of the gun, and bullet in a more exact form. To avoid the most heated debates, a comparison of the momentum properties of a bullet will not be used to predict the effectiveness of that bullet on specific targets.
In the main text, a physical comparison between different makes of automobiles was suggested as an analogy. To get a good momentum comparison between the different cars, the easiest method is to have each car travel at the same speed. Obviously, the heaviest car will have the highest momentum, and there would be no need for obtaining momentum. Just weigh the cars and the heaviest is the one that will always have the most. That is not where the analogy breaks down. It perfectly illustrates the property of momentum. When objects have the same velocity, the heaviest mass will have the most P. Likewise, when objects have the same mass, the highest velocity object will have the most P. With bullets, the lighter bullets travel faster with the same charge and tends to break the weight dependency for momentum, and each caliber can be loaded with multiple weights which can break the velocity dependency. Our comparison problem is no longer trivial nor weight/velocity dependent, and really compounded when trying to get this diversity to comparable weights or velocities.
Therein lies the insight to begin a comparison. There is a growing popularity with subsonic loads for pistols. One reason would be for sound suppression. The less obvious but more important reason is because most pistol calibers can break the sonic barrier but not enough to maintain that velocity all the way to the target (say 25-50 yards). As they slow down, the sonic wave can catch up and disturb the bullet, seriously impacting accuracy. Subsonic loads are becoming more popular with competitive shooters for this reason. Many ammunition manufacturers are beginning to aim for this “subsonic” market. Around 1150 feet per second, depending on altitude and atmospheric factors, is the rough sonic barrier. To stay subsonic independent of the variable factors, the load target is usually between 1030 and 1050 feet per second. This reminds me of another insight. IPSC Shooting competitions determine the shooting class (Major or Minor for pistol) based upon a modification to the bullet momentum. That modification is very interesting for what this Appendix is about. In a way, IPSC rules almost set a speed limit for bullets in this sense: If you multiply bullet momentum (bullet mass in pounds time velocity in fps) by seven (7) you get the IPSC Power Factor (Yes, I know that is not how it is calculated by IPSC, but the math is there). Now remember our car analogy. If they travel at the same speed, just weigh the car ? If you can get your loads at 1000 feet per second, no need to calculate either momentum, or IPSC Power. The IPSC Power Factor = bullet weight (in grains) AT THAT SPEED. And the bullet momentum is equal to the IPSC Power Factor divided by seven. (except that IPSC rounds down on Power Factor, meaning that 124.999 does not equal 125. It stays 124)
I like that “magic” number (1000 fps). The problem now is how can it be used fairly with every caliber on the market ? The first problem is that some calibers cannot be safely loaded to even reach 1000 fps. The next problem is that all calibers that can reach that velocity are also capable of exceeding it. Finally, some calibers, even in mild loadings, will stay supersonic. This is where ammunition liability laws come to assist this effort. Standard factory loads, economy loads, or bulk ammunition is assembled considering the “worst” clunker-gun out there. The ammunition liability creates a need to market loads that will be safe in most anything. How this is done is hard to find and most likely proprietary information. There is another source. More ammunition is loaded in this country by “hobbyists” than is produced by the factories. The way the “hobbyists” do this is common knowledge, not proprietary. They work up loads for each individual gun to determine what loads are safe for that gun. The “rule of thumb” is to reduce the maximum powder charge by ten percent and gradually move up to the full charge that approximates the SAAMI caliber pressure standard. What better way to compare calibers ? Reduce all caliber loadings to the hobbyist's safe starting loads and measure them. Each and every load is then compared at starting pressure levels where all guns should safely work, and every measurement level for every caliber has the potential to be improved with full pressure loads, or even the so called +P and +P+ loads which need not be addressed at all.
Next, a selection method that favors no caliber but will provide all the data needed.
All calibers will use jacketed bullets, since lead bullets tend to move slower at the same weight/charge levels. All caliber data will use only recommended safe starting load levels from the same source. Two exceptions shall be allowed; rim-fire cartridges and the new 327 Federal Magnum.
The heaviest weight bullet in each caliber that can achieve the target velocity of 1000 fps with minimum load levels will be selected. All such calibers will be placed in the category of “High Subsonic”.
When there is no load for a given caliber that can reach the target velocity, the highest velocity available for any bullet in that caliber at minimum load levels shall be selected. All such calibers will be placed in the category of “Low Subsonic”, even if their full SAAMI pressure loadings can attain the target velocity.
The first three methods fail when encountering the true magnum calibers (other than the 32 H&R Magnum) since even minimum magnum load data is supersonic. This means that magnum calibers will be biased by our criteria. Thus they are separated and the criteria adjusted as follows: The heaviest weight bullet in each magnum caliber that can achieve a target velocity of 1500 fps at minimum load levels will be selected. This modified velocity recognizes the nature of a true magnum and selects a velocity that will still be supersonic at target ranges (25-50 yards), thus addressing the accuracy problem imposed by the subsonic criteria on all other calibers.
To apply this selection criteria using a single center-fire cartridge loading source, I have selected the Lyman Reloading Handbook, 49th edition, Published by Lyman Products Corporation. The 22 Rim-fire sources are discussed and cited below the tables since this selection criteria cannot apply to rim-fire.
The new 327 Federal Magnum load data is scarce and I will use the only source I have found for it.
Using this selection criteria on the sources gives the following results:
Low Subsonic Calibers Part 1
Cal.22 Short25 ACP32 ACP32 SWL380 ACP38 SW38 Spl Mass gr.2935608595150110 Charge4 gr1.2 gr2.7 gr2.5 gr2.4 gr2.8 gr4.1 gr Vel. fps653774968842861688875 P2.713.878.310.2211.6914.7413.75 IPSC PF182758718110396
Low Subsonic Calibers Part 2
Cal.9mm Mak44 Russian44 Special45 ACP45 GAP45 Colt Mass gr.95180180185185185 Charge3.2 gr4.9 gr7.3 gr7.4 gr6.3 gr10.8 gr Vel. fps672776823917923876 P9.1219.9521.1524.2424.3923.2 IPSC PF63140148169170162
The tables are almost self explanatory; the Capitol “P” is Momentum in Lb-Feet/Sec and the IPSC PF is the Power Factor from IPSC competition, in accordance with the current rules of the IPSC that can be downloaded from http://www.ipsc.org/pdf/RulesHandgun.pdf
The charge is the powder weight for the bullet mass and velocity combination taken from the primary source. Powder brand is not listed and not needed for computations.
To convert grains into pounds, divide by 7000 (grains/pound) for momentum calculation.
IPSC Power Factor is computed by multiplying bullet weight in grains times velocity, the total then divided by 1000.
The 22 calibers will be addressed after the tables are presented. The 9mm Makarov is a sample to show that the selection criteria has a problem when it cannot be adhered to. In particular, the primary source does not have metal jacketed loads, only lead for this caliber. I suspect this is due to the shortage of components for this caliber. If jacketed were available, this column would most likely be identical to the 380 ACP column because the velocity would be nearly the same as well as identical bullet weights. The next table will also be in two parts.
High Subsonic Calibers Part 1
Cal.22 LR30 Luger30 Mauser32 HR Mag9mm Luger38 Super357 Sig Mass gr.40939371125147147 Charge5 gr4.5 gr6 gr4.5 gr7 gr8.3 gr6.2 gr Vel. fps1000100010421000100010471030 P5.7113.2913.8410.1417.8621.9921.63 IPSC PF40939671125153151
The 22 calibers will be addressed after the tables are presented. Note that according to the selection criteria the 32 H&R Magnum is magnum in name only. It does not meet magnum performance selection criteria.
Whenever a listed velocity is very close to 1000 fps, that is the listed table velocity provided the actual velocity does not significantly change the momentum. When it does the actual velocity is used, as for example the 1030 fps of the 357 Sig.
High Subsonic Calibers Part 2
Cal.40 S&W10mm Auto Mass gr.155200 Charge7.2 gr6.3 gr Vel. fps9881000 P21.8828.57 IPSC PF153200
The 40 S&W is high-lighted because this is the only caliber where the target velocity of 1000 fps was not exceeded at the selected minimum charge and bullet weight. The next lower bullet weight would normally be selected to prevent an advantage here. I left it because this one really needs an average position between this and the next lower weight position. The value difference is quite small. It is sitting next to it's big brother, the 10mm Auto so it needs every nudge it can get.
The next table represents what I have been referring to as the true magnum calibers. These calibers are very difficult to load subsonic. It can be done using what would be termed “Gallery” loading but such loads are not useful for this comparison. Remember that these loads are considered the safe starting minimum for each caliber.
Supersonic Calibers
Cal.22 WMR5.7x29 FN327 Mag357 Mag41 Mag44 Mag454 Casull Mass gr.4040100110170180225 Charge7 gr4.3 gr8.9 gr17.8 gr24.1 gr29 gr33.9 gr Vel. fps1500150015001568158215411657 P8.578.5721.4324.6438.4239.6355.63 IPSC PF6060150172268277389
All 22 caliber rim-fire data is highlighted since the criteria for selection cannot apply to the rim-fires. Due to the design of the case, it is weaker at the base than any center-fire. This limits the pressure the case can be loaded for in order to prevent the base from blowing out. These cases are not considered available loads for hobbyists and all factory loads are based upon keeping load pressure below the reduced strength fail-pressure for the case. Data shown for the 22 calibers is based upon best estimates from several sources listed in the reference section.
Load data for the new Federal 327 Magnum was taken from the source listed in the reference section.
All data listed was obtained using barrel lengths of between 4 and 5 inches except for 25 ACP which used 2 inches, 32 ACP which used 3 inches, 380 ACP which used 3.5 inches, 44 Russian which used 6.5 inches, 45 Colt which used 7 inches, and 454 Casull which used 6 inches. Since the barrel lengths for the exceptions were varied based upon what tends to be available on the market for those calibers, I believe the final data is better for this.
The 454 Casull is unlikely to be a self-defense handgun choice due to the high penetration qualities and heavy recoil of this caliber. It is included as the upper boundary sanity check for the calibers listed. Likewise, the rim-fire 22 short is unlikely to be a self-defense handgun choice due to the lack of penetration qualities and despite its negligible recoil. It is included as the lower boundary sanity check for the calibers listed.
The bar chart plots in the main text come from the above data tables using the IPSC data row as the y axis and the Caliber row as the x axis. Replacing the y axis with the momentum (P) values gives identical bar charts but with lower y axis grid values. Instead of repeating the charts here I will demonstrate this with a “bonus” for those who read this appendix.
Here is the “bonus” chart for the Appendix sample bar charts.
The Monsters
(and these are MINIMUM loads)
Cal.460 SW Mag480 Ruger475Linebaugh50 AE500 S&W Mass gr.300325325325400 gr Charge34 gr27.1 gr31.2 gr31.2 gr35.8 gr Vel. fps17981503159213001607 P77.0669.7873.9760.3691.83 IPSC PF539488517422642
First, plotting momentum (P) versus caliber gives the true momentum plot as this:
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CHART 7
Note the relationship of the bars to each other and how that relationship will not change when the IPSC PF row is used for the y axis. The relationship is preserved because IPSC uses a whole number multiple of momentum to stretch the y axis grid.
These calibers, as is the 454 Casull, were intended for hunting large game with a handgun. They are not suited for concealed carry due to size and weight. They are not suited for self defense due to excessive penetration. The latter argument means that in a self defense situation, these calibers are most likely to continue through the target while still retaining lethal force down range.
http://www.concealcarrychat.com/forums/../selfdefenseguide/chart_08.gif
CHART 8
The tables list charge weight in grains which has not yet been discussed. The momentum values in the tables will be used in Appendix B along with the charge weight. The charge weight is retained in both Appendixes for consistency.
All loads shown, exception for rim-fire as noted above, are minimum safe loads that should be safe in any gun, new or used. The minimum was chosen since it was far easier to do than to compare the maximum loads and get into a discussion of +p and the +p+ loads and what the standards for those are. Plus the potential to improve every caliber listed is easy. The so called “hot” loads or defense loads on the market will come much closer to full SAAMI pressure levels than the loads listed here. While there are SAAMI standards for some +p loads, use caution and the manual with your firearm. Some manuals caution against this. There are currently no SAAMI pressure standards for +p+ loads. The best safety caution I can make is that you are on your own with those. My research indicates that +p+ loads would fall somewhere between +p levels and factory “Proof” test loads.
Appendix B
A Direct Method to Compare Bullet Caliber Recoil
Data from Appendix A will be used for the calculations in this Appendix. Appendix A contains the momentum calculation (P) for each caliber plus the associated charge weight used for the data listed.
Consider the point in time when a firearm is triggered. The primer in the caliber case goes off, contributing its chemical energy to igniting the powder charge, which generates the expansive pressure against the base of the bullet necessary to launch it down the barrel. At the same time, this same pressure is exerted against the firearm's chamber. From the Conservation of Momentum, these must be equal since the net momentum at the start is zero for the reference frame considered. The momentum of the gun, however, is equal to the total momentum imparted to the bullet PLUS the momentum generated by the charge gases and anything else that goes out, like wads or sabots, which also exits the barrel. Recoil relates to Conservation of Momentum, and “free recoil” relates to the energy associated with the gun when the gun is fired. It can be derived from the gun's momentum using several methods. The method chosen for this appendix is known as the “Momentum Short Form” which comes from the classical mathematical relationship between momentum and energy.
The kinetic energy of an object can be computed from its momentum by the relationship:
http://www.concealcarrychat.com/forums/../formula_01.pngKinetic Energy equals the object's momentum value squared and divided by twice the mass of the object. P of the gun = (mass of bullet times velocity of bullet) + (mass of other ejecta times ejecta velocity)
The Momentum Short Form takes the above two equations together as follows:
Momentum short form: Etgu = 0.5 · [{(mp · vp) + ( mc · vc)} / 1000]2 / (mgu)
Where:
Etgu is the translational kinetic energy of the firearm as expressed by the joule (J).
mgu is the weight of the firearm expressed in kilograms (kg).
mp is the weight of the projectile expressed in grams (g).
mc is the weight of the powder charge expressed in grams (g).
vp is the velocity of the projectile expressed in meters per second (m/s).
vc is the velocity of the powder charge expressed in meters per second (m/s).
1000 is the conversion factor to set the numerator equal to kilograms.
“0.5”is taking the 2 in the denominator of the first equation above and converting 1/2 to 0.5
Etgu, as the translational kinetic energy of the gun, is also known as the “free recoil” energy of the gun. What we would most like to do is calculate the “net energy” of the gun, known as “felt recoil”. Trying to figure the net recoil energy of a firearm is a near futile endeavor. Even if you can calculate the recoil energy loss due to a muzzle brake, recoil operated action, gas operated action, mercury recoil suppression tube, recoil reducing butt pad and hand grip, shooting vest and gloves, the human factor remains subjective.
Thus we need a subjective method to relate what we can calculate to that which we cannot calculate. Once free recoil is tabulated, a speculative technique should give a logical inference between this and “felt recoil”. With that available, this appendix should yield the data necessary to plot a gun's weight versus felt recoil for candidate calibers. Since our computations are based upon minimum loads in Appendix A, we have the best case to look at, which is minimum recoil energy from each caliber.
It is a simple conversion exercise to change the table data in Appendix A to metric data for use in the Momentum Short Form. The end result will be a computation for each caliber and for each gun weight ranging from 4 to 40 ounces (also converted to grams). The final data list will show free recoil in Joules. For those who prefer the SI system of measure, the conversion is:
1 Joule = 0.737562 ft ·lbf
Here is a sample calculation which will also show how the computations were formatted in the spread sheet.
22 short25 ACP32 ACPEtc.. Enter Bullet Mass (grams)1.883.243.88
Enter Bullet Vel. (meters/sec)199.2236.1295.2
Enter Charge Mass (grams)0.260.050.17
Enter Charge Vel. (meters/sec)158515851585
Enter Gun Mass 39 oz (1.11Kg)1.111.111.11
Numerator (Pbullet + Pcharge)786.5844.11415
Div by 1000 (grams to Kg)0.790.841.41
(Total P) Squared0.620.712 Divide P squared by 2 x gun mass (ounces to Kgs, 39 oz = 1.106Kg) Result is free recoil Joules for a gun mass of 39 oz.0.280.320.91
Multiply this computation for every caliber and for every gun mass from 4 to 40 ounces.
Data for the low subsonic calibers, the high subsonic, and Magnum data:
http://www.concealcarrychat.com/forums/../selfdefenseguide/chart_09.png
CHART 9
http://www.concealcarrychat.com/forums/../selfdefenseguide/chart_10.png
CHART 10
http://www.concealcarrychat.com/forums/../selfdefenseguide/chart_11.png
CHART 11
http://www.concealcarrychat.com/forums/../selfdefenseguide/chart_12.png
CHART 12
Three-D plots from these data tables are in the main text and not reproduced here. As a bonus for anyone that makes it this far, there is another way to compare free recoil that would involve fun iterations and probably be even more useful. Given that all the data sheets compute and compare apples to apples (Joules), it would be possible to calculate the area under each curve to arrive at a percentage ratio between the curves computed. To make it work would require a big data sheet with every caliber listed and plotted together. Then each curve area would ratio directly between calibers. I will do a simple one for the magnum calibers, but the only way to percentage recoil with the other calibers is to plot them all in the same area/percentage computation. Here is the sample bonus chart that ratios only the magnums to each other.
http://www.concealcarrychat.com/forums/../selfdefenseguide/chart_13.gif
CHART 13
Appendix C
Reference List
Hardcover References
Lyman Pistol and Revolver Handbook, Third Edition
Lyman Reloading Handbook, 49th Edition
Internet Reference Link List
Myth of muzzle energy
http://www.chuckhawks.com/myth_muzzle_energy.htm
Muzzle momentum
http://terra.gg.utah.edu/guns/energy.pdf
chuck hawks cartridge chart (unfortunately, sites Marshall and Sanow poor study)
http://www.chuckhawks.com/handgun_power_chart.htm
Powder in 22 WMR mag is 7 grns
http://www.gun-tests.com/performance/apr96reloading.html
free recoil of 327 and other 32's
http://www.chuckhawks.com/327_federal.htm
powder charge of 327
http://www.shootingtimes.com/ammunition/ST_reloadingthe327_200902/index1.html
momentum over energy
http://www.gsgroup.co.za/articlemomentum.html
Excellent: Great bullet debate
http://personal.palouse.net/joeh/pages/BulletDebate.htm
IPSC Rules (downloaded the handgun rules)
http://www.ipsc.org/pdf/RulesHandgun.pdf
IPSC (International Practical Shooting Confederation)
http://www.ipsc.org/whatipsc.htm
SAAMI max pressures by cartridge
http://www.leverguns.com/articles/saami_pressures.htm
SAAMI standards site
http://www.saami.org/
unsafe firearm combinations
http://www.saami.org/Unsafe_Combinations.cfm
computing free recoil energy
http://en.wikipedia.org/wiki/Free_recoil
laws of motion
http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton.27s_third_law:_la w_of_reciprocal_actions
physics of firearms
http://en.wikipedia.org/wiki/Physics_of_firearms
22 rimfire
http://www.chuckhawks.com/history_rimfire_ammo.htm
http://www.chuckhawks.com/22_rimfire_cartridges.htm
http://www.chuckhawks.com/22mag.htm
http://www.gunnersden.com/index.htm.rimfire-rifles.html
http://www.gunblast.com/Paco_22AutoMag.htm
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