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Miscellaneous Questions #11
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 P-ing" 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+ commercial 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 CR-ROM - $90.00 (the complete set)
They can be ordered from
ANSI - SAAMI
11 Mile High Rd
Newton, CT 06470
203-426-1320
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 one-half 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 |
.30-30 Winchester |
42,000 |
| .17 Rem | 52,000 cup |
.30-06 Springfield |
60,000 |
|
.22RF Short |
21,000 |
.30-30 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 |
|
.22-250 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 |
.32-20 | 16,000 cup |
|
.25-06 Remington |
63,000 |
.32-40 | 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 BR-REM | 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 |
.38-40 Win | 14,000 cup |
|
7mm Mauser |
51,000 |
.38-55 Win | 30,000 cup |
|
7mm Rem Magnum |
61,000 |
.416 Remington Magnum |
65,000 |
|
7mm Weatherby Mag |
65,000 |
.444 Marlin |
44,000 cup |
|
7mm-08 |
61,000 |
.45-70 Government |
28,000 |
| 7-30 Waters | 45,000 |
.458 Winchester Magnum |
53,000 cup |
|
7.62x39 |
45,000 |
.470 NE | 35,000 cup |
|
.30 Carbine |
40,000 |
|
|
| .30-40 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 | .44-40 | 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 |
| .38-40 | 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 R2 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 R2 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 used 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 in2
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 in2
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 Semi-wadcutter | 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 (in2) |
| .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 |