This section contains brief discussions of various ballistics and shooting related topics as requested by correspondents. If you have a question you have been trying to find an answer to (keep 'em ballistics and shooting relatedsee your minister for the mysteries of life) email me by clicking here and I'll do my best to find the answer for you and if it is of general interest, publish it here. If you can contribute additional input to one of the answers I'd would appreciate hearing from you too.
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On this page:
What is +P and +P+ ammunition?
What are the current SAAMI pressure specifications for
ammunition?
How are proof pressures determined?
What is the Hatcher Formula?
Q. What is +P and +P+ ammunition?
A. "Plus P" and "Plus P Plus" ammunition is simply ammunition loaded to higher than normal SAAMI (Sporting Arms & Ammunition Makers Institute) pressure specifications. "Plus Ping" was first done with law enforcement pistol ammunition in an effort to wring the last bit of power out of a cartridge. For most rounds the gain in performance is minimal and leads to increased wear and tear on the firearm. The +P+ ammunition is loaded to even higher pressure levels than +P. +P+ loadings are generally limited to "law enforcement sale only." The SAAMI pressures for pistol ammunition are given below. Note that there are no SAAMI specifications for +P+ loads, but by general industry agreement they are about 15 percent greater than +P. Note that there are no SAAMI specifications for +P pistol loads other than those shown below. (The .38 Super is frequently listed as "+P" but that is just to differentiate between the "Super" round and the original .38ACP round.)
The table below gives an idea of what some common +P and +P+ loads do. (Velocity data varies with manufacturer. I have chosen to use the high end figures.) Pressures are given as PSI (piezo transducer).
Standard Load  +P Load  +P+ Load (Not SAAMI)  Proof Pressure  
Approximate Velocity  Pressure (PSI) (Max Avg) 
Approximate Velocity  Pressure (PSI) (Max Avg) 
Approximate Velocity  Pressure (PSI) (Max Avg) 
Minimum Allowable PSI 
Maximum Allowable PSI 

9 mm 115 gr 9 mm 125 gr 
1220 1140 
35,000  1280 1200 
38,500  1335 1250 
42,000  52,000  55,000 
.38 SPL 125 gr .38 SPL 158 gr 
850 780 
17,000  945 910 
18,500  1000 950 
22,000  25,000  27,500 
.45 ACP 185 gr .45 ACP 230 gr 
960 850 
21,000  1140 990 
23,000  n/a  n/a  31,000  33,000 
257 Roberts 110 gr 257 Roberts 115 gr 
2880 2630 
54,000  2980 2760 
58,000  n/a  n/a  77,500  83,000 
Pressure data per SAAMI
Q. What are the current ANSI/SAAMI pressure specifications for ammunition?
A. The tables below give the current maximum average pressure specifications for common commercial cartridges. Note that these specification may differ from previous ones because, unless specified otherwise, they are now based on Piezo transducer PSI measurements and not copper crusher (CUP) measurements. Piezo measurements tend to read slightly higher than copper crusher measurements as they more accurately read pressure peaks. The standards are set in the following SAAMI publications. Not all specifications have been changed to piezo measurement. The standards are available in printed format at the prices below.
#205 ANSI/SAAMI Centerfire Pistol & Revolver, Z.299.3 1993  $30.00
#206 ANSI/SAAMI Centerfire Rifle, Z.299.4 1992  $35.00
#208 ANSI/SAAMI Rimfire, Z.299.1 1992  $20.00
#209 ANSI/SAAMI Shotshell, Z.299.2 1992  $25.00
#203 ANSI/SAAMI Ammunitions Standard CRROM  $90.00 (the complete set)
They can be ordered from
ANSI  SAAMI
11 Mile High Rd
Newton, CT 06470
2034261320
Contact Coleen Swayne and ask for the ANSI Ammunition Specification publications.
The tables below were excerpted from those publications.
Under ANSI/SAAMI procedures, for bottlenecked cases the center of the transducer is located .175" behind the shoulder of the case for large diameter (.250") transducers and .150" for small diameter (.194") transducers. For straight cases the center of the transducer is located onehalf of the transducer diameter plus .005" behind the base of the seated bullet. Small transducers are used when the case diameter at the point of measurement is less than .35".
The rest of the world uses the Commission Internationale Permanete (CIP) standards for ammunition. Under CIP standards a drilled case is used and the measuring device will be positioned at a distance of 25 mm from the breech face when the length of the cartridge case is between 30 and 40 mm, including limits. When the length of the cartridge case is less than 30 mm, pressure measurement will take place between 5 mm and 25 mm from the base of the case depending on the size of the case. (6.35 mm for the Hornady 17 Mach 2, and 25 mm for most rifle cartridges) The difference in the location of the pressure measurement gives different results than the SAAMI standard
I am currently working on putting together a table of CIP pressure specifications.
ANSI/SAAMI Rifle Pressure
Specifications (Maximum Average pressure) 

5 mm RFM  37,000 
.3030 Winchester 
42,000 
.17 Rem  52,000 cup 
.3006 Springfield 
60,000 
.22RF Short 
21,000 
.3030 Winchester (Saboted) 
38,000 
.22RF Long & LR  24,000 
.300 Savage 
47,000 
.22WRF  19,000 
.300 Weatherby Magnum 
65,000 
.22WRM 
24,000 
.300 H&H Mag  54,000 cup 
.22 Hornet 
43,000 cup 
.300 Win Mag 
64,000 
.218 Bee  40,000 cup 
.303 British 
49,000 
.22250 Remington 
65,000 
.307 Win  52,000 cup 
220 Swift  54,000cup 
.308 Winchester 
62,000 
.222 Remington 
50,000 
.308 Winchester (Saboted) 
52,000 
.222 Rem Mag  50,000 cup 
.32 Win Special 
42,000 
.223 Remington 
55,000 
.32 Rem  37,000 cup 
.243 Winchester 
60,000 
.3220  16,000 cup 
.2506 Remington 
63,000 
.3240  30,000 cup 
.250 Savage  45,000 cup 
8mm Mauser 
35,000 
.256 Win  43,000 cup 
8mm Rem Magnum 
65,000 
.257 Roberts 
54,000 
.338 Win Mag 
64,000 
.257 Roberts +P  58,000  .348 Win  40,000 cup 
.264 Win Mag 
64,000 
.35 Remington 
33,500 
.270 Winchester 
65,000 
.351 Win SL  45,000 cup 
.280 Remington 
60,000 
.35 Whelan  52,000 cup 
.284 Winchester 
56,000 
.350 Rem Mag  56,200 cup 
6mm Remington 
65,000 
.356 Win  52,000 cup 
6 mm BRREM  52,000 cup  .358 Win  52,000 cup 
6.5x55 
46,000 cup 
.375 H&H 
62,000 
6.5 Rem Mag  56,200 cup  .375 Win  52,000 cup 
7mm BR Rem 
52,000 cup 
.3840 Win  14,000 cup 
7mm Mauser 
51,000 
.3855 Win  30,000 cup 
7mm Rem Magnum 
61,000 
.416 Remington Magnum 
65,000 
7mm Weatherby Mag 
65,000 
.444 Marlin 
44,000 cup 
7mm08 
61,000 
.4570 Government 
28,000 
730 Waters  45,000 
.458 Winchester Magnum 
53,000 cup 
7.62x39 
45,000 
.470 NE  35,000 cup 
.30 Carbine 
40,000 

.3040 Krag  40,000 cup 
ANSI/SAAMI Pistol Pressure
Specifications (Maximum Average pressure) 

Cartridge  Pressure (Max Avg)  Cartridge  Pressure (Max Avg) 
.221 Rem Fireball  52,000 cup  .38 Colt  12,000 cup 
.22 Jet  40,000 cup  .357 Magnum  35,000 
.25 ACP  25,000 cup  .357 Maximum  40,000 
.30 Luger  28,000 cup  .40 S&W  35,000 
.32 ACP  20,500  10 mm  37,500 
.32 S&W Long  15,000  .41 AE  35,000 
.32 H&R Mag  21,000 cup  .41 Magnum  36,000 
.380 ACP  21,500  .44 Special  15,500 
9 mm Luger  35,000  .4440  13,000 cup 
9.mm Luger +P  38,500  .44 Magnum  36,000 
9 mm Win Mag  45,000 cup  .45 Auto Rim  15,000 cup 
.38 Auto  26,500  .45 ACP  21,000 
.38 S&W  14,500  .45 ACP +P  23,000 
.38 Special  17,000  .45 Colt  14,000 
.38 Special +P  18,500  .45 Colt (Ruger)  25,000 cup 
.3840  14,000 cup  .45 Win Mag  40,000 cup 
.38 Super +P  36,500  .454 Casull  50,000 cup 
.38 S&W  13,000 cup  .50 AE  35,000 
ANSI/SAAMI Shotgun Pressure
Specifications (Maximum Average Pressure in PSI) 

Cartridge  Maximum Average pressure 
10 gauge  11,000 (all) 
12 gauge  11,5000 (all but 3 1/2" mag) 
12 gauge 3 1/2" mag  14,000 
16 gauge  (11,500 (all) 
20 Gauge  12,000 (all) 
28 gauge  12,500 (all) 
.410 Bore 2 1/2"  12,500 
.410 Bore 3"  13,500 
New statistical data analysis suggests that for most cartridges ANSI/SAAMI Maximum Average Piezo (PSI) and Maximum Average copper crusher (CUP) can be related by the following formula which has an R^{2} value (a statistical measurement of certainty) of .927.
(1.51586 * CUP)  17902.0 = PSI
While the relationship is generally within 3Kpsi (it assumes that the CUP was determined using ANSI/ SAAMI standards) one should not rely on this conversion for absolute maximum loads. This conversion is only applicable to rifle ammunition.
Comparison of Pressure
Specifications Between 

Max Average Pressure  Max Probable Lot Mean 
Max Probable Sample Mean 

Copper Units of pressure (CUP)  52,000  53,300  55,300 
PSI (Piezo)  62,000  63,600  66,000 
PSI Converted from CUP  60,922     
Interestingly the correlation between the European CIP CUP measurements and Piezo measurements has an even better correlation with an R^{2} of .997. The formula for the CIP conversion is
(1.20911 * CIPCUP)  2806.88
The same warning about using this conversion for maximum load work and its being applicable to rifle ammunition only applies to this formula. too
For a detailed analysis of the origin of these formulas see the article "Correlating CUP and PSI" on RSI's Tech Information Page at www.shootingsoftware.com.
Q. How are proof pressures determined?
A. US commercial proof pressures are set by SAAMI specifications while Europe uses the CIP standards. The current standards for proof pressures are shown below. Military proof load standards are set by the arsenals and government specification and may or may not be the same as SAAMI.
SAAMI 
CIP 

Cartridge Class  Minimum Proof*  Maximum Proof**  Proof 
Shotshell 
1.55 
1.70 
1.30 
Centerfire Rifle 
1.30 
1.40 
1.25 
Centerfire Pistol 15,000 psi or less  1.40  1.55  1.30 
Centerfire Pistol 15,100  18,000 psi 
1.35 
1.50 
1.30 
Centerfire Pistol 18,100  21,000 psi 
1.30 
1.45 
1.30 
Centerfire Pistol 21,100 psi or greater 
1.30 
1.40 
1.30 
Rimfire 
1.25 
1.40 
1.30 
* Max Probable
Lot Mean is calculated by adding two standard errors to the Max Average
pressure. The "standard error is calculated by the standard
deviation of the sample by the square root of the size of the
sample. For all intents and purposed just use the Max Avg
Pressure. * Min Proof values rounded UP to nearest 500 psi. ** Max Proof values rounded DOWN to nearest 500 psi. 
Q. What is the Hatcher Formula?
A. The Hatcher Formula is a mathematical formula use to evaluate the approximate effectiveness of pistol ammunition in incapacitating a person shot with it. It was developed by Gen. Julian Hatcher in the 1930s and uses the bullet momentum, bullet frontal area, velocity, and a form or shape factor. It was derived from his observations of the effects of pistol ammunition on cadavers and steers. While it does not take into consideration bullet penetration or expansion and is basically an approximation, it is still a good formula to use to give one an idea of how a given round will stack up as a fight stopper.
The original formula was somewhat cumbersome to use and the formula was:
RSP = MB * A * F
where
RSP = Relative Stopping Power Index
MB = Momentum of the bullet in pound feet  (WB/450240) * V
(If you know the kinetic energy and the velocity you can divide the KE by the velocity to get the momentum.)
A = Area of the bullet in in^{2}
F = Form factor derived from the chart below.Note: In the text of Textbook of Pistols and Revolvers the original formula given in the text contained an error in math (he used 240,125 or 1/2 the correct number as the divisor and thus if the text is followed you will get values double the correct ones. The table for the momentum calculations is, however, correct in the book.
A more convenient variation of the original formula which eliminate working with big numbers is:
RSP = (WB * V * A * F) / 1000
where
RSP = Relative Stopping Power Index
WB = the bullet weight in grains
A = Area of the bullet in in^{2}
V = the bullet velocity in feet per second (f/s)
F = Form factor derived from the chart below.
In the form factor table below the entries in red are recent approximations for bullet types not originally listed by Hatcher. For Hatcher's original formula the numbers below should be multiplied by 1000 before using.
Bullet Type 
"F" 
Bullet Type 
"F"  
Fully Jacketed Pointed  .7  Lead Flat Point (Large Flat)  1.1  1.2  
Fully Jacketed Round Nose  .9  Jacketed
Softpoint (unexpanded) 
1  1.1  
Fully Jacketed Flat Point  1.05  Jacketed
Softpoint (expanded) 
1.35  
Fully Jacketed Flat Point (Large flat)  1.1  Lead Semiwadcutter  1.25  
Lead Round Nose  1  Hollow Point (unexpanded) 
1.1  
Lead Flat Point  1.05  Hollow Point (expanded) 
1.35 
Note that the results obtained by this "short form" are not numerically equal to the original formula (they are about half the old formula numbers) but the the comparisons between different cartridges are still valid. With this short form a value of about 14 is considered barely adequate and about 25 or greater highly desirable. With the original formula a value of 30 was considered barely adequate and 50 or greater highly desirable.
There are several "modern" variations of this formula floating around. One variation sometimes seen is to multiple the results by 0.9 if penetration in test media is less than 10" and by 1.1 if penetration is greater than 10". Another one uses the average area of the "expanded" bullet (area of minimum expanded diameter + area of maximum expanded diameter) / 2, as the bullet diameter and no form factor is used.
For your enjoyment the table below lists the frontal area of common pistol calibers.
Bullet Caliber  Area (in^{2}) 
.22  .039 
.25  .052 
.30  .074 
.32  .076 
9 mm  .099 
.38 / .357  .101 
.40 / 10 mm  .125 
.41  .132 
.44  .146 
.45 ACP  .160 
.45 Colt  .161 
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Disclaimer
As far as I know all the information presented above is correct and I have attempted to ensure that it is. However, I am not responsible for any errors, omissions, or damages resulting from the use or misuse of this information, nor for you doing something stupid with it. (Don't you hate these disclaimers? So do I, but there are people out there who refuse to be responsible for their own actions and who will sue anybody to make a buck.)
Updated 20131023