SHORT-N-SASSY Wrote:Using the retained Kinetic Energy of that round, at 300 meters (538 ft. lbs.), as a parameter, I compare the following cartridges (all, based on velocites from 16" barrels): MK262, 77-grain, BC- 0.362, MV - 2650 fps.; .300 AAC Blackout, 125-grain, BC - 0.330, MV - 2215 fps; 6.8 SPC, 140-grain Berger VLD, BC - 0.487, MV - 2401 (NOTE: This load is approx. 5,000 PSI above the SAAMI 6.5 Grendel, and has a Cartridge Overall Length of 2.315" vs 2.260" for the Grendel); 6.5 Grendel, 144-grain Lapua FMJBT, BC - 0.636, MV - 2275 fps:

M855 - 538 ft.lbs. @ approx. 328 yards (300 meters);
MK262 - 538 ft.lbs. @ approx. 394 yards;
.300 AAC Blackout - 538 ft.lbs. @ approx. 388 yards;
6.8 SPC - 538 ft.lbs. @ approx. 760 yards;
6.5 Grendel - 538 ft.lbs. @ approx. 925 yards.

Texas Wrote:As a matter of fact, my first military issue weapon was a well worn M1. What I was referring to is Col Hatchers formula which takes into account form factor:
The Hatcher formula was originally developed in the 1930s when Major General Hatcher was working in the US Army's Ordnance department. It uses the bullet mass, velocity, frontal area of the bullet and also a 'form factor' which depends on the type of bullet. Unlike the Taylor KO factor and Thorniley Stopping Power formula which only consider the diameter of the bullet in their calculations, the Hatcher formula uses the bullet cross-sectional area in its calculation. It also uses the bullet momentum formula (we studied this three posts back) as part of its equation. Additionally, unlike all the other formulae we have studied until now, this one includes the bullet type (jacketed, non-jacketed, flat point, round nose etc.) as part of its calculation. The Hatcher Formula is:
RSP = M/(2*g) * A * F

where:
RSP = Relative Stopping Power
M = Momentum of the bullet in foot-pounds/sec (momentum = mass * velocity where mass is in lbs and velocity is in feet/sec)
g = Acceleration due to gravity in feet/sec2.
A = Frontal area of the bullet in square-inches
F = A bullet form factor that depends on the type of the bullet (see notes below)

In General Hatcher's original paper, he quotes the formula as RSP=M*A*F and prints a table of the calculated RSP values for a variety of common handgun bullet types. However, he calculates the momentum incorrectly as (kinetic energy/velocity), which ends up calculating a value of 1/2 of the actual momentum (since kinetic energy = 1/2 * mass * velocity2). He also incorrectly divides by g (acceleration due to gravity) when converting grains to lbs (no need to, because grains are a units of mass, not weight). Therefore I've updated the original formula to match the numbers on his original table and translated the equation to M/(2*g)*A*F.

The values for bullet form factor for some bullet types are defined as:
F Bullet Type
700 Fully Jacketed Pointed
900 Fully Jacketed Round Nose
1050 Fully Jacketed Flat Point
1100 Fully Jacketed Flat Point (Large flat)
1000 Lead Round Nose
1050 Lead Flat Point
1100 Lead Flat Point (Large Flat)
1000 Jacketed Softpoint (unexpanded)
1350 Jacketed Softpoint (expanded)
1250 Lead Semi-wadcutter
1100 Hollow Point (unexpanded)
1350 Hollow Point (expanded)

In an earlier version of this article, your editor had accidentally quoted the numbers as 0.7, 0.9, 1.05 etc. instead of 700, 900, 1050 etc. Apologies for that and thanks to reader Nathaniel Fitch for pointing it out in the comments below (boy, do I have egg on my face now :-))

Because the type of bullet is part of the calculation, cartridges of a particular caliber meant for a single firearm can have different RSP values because they have different bullet types. For example, for a .45 ACP bullet which has a mass of 185 grains and moving at 1000 feet/sec, we compute a RSP value of 65.661 if the bullet is a Lead Round Nose bullet, but 88.642 for a Hollow Point (expanded) bullet. How do we get these numbers, you ask?
Weight of bullet = 185 grains.
We know that 1 lb = 7000 grains.
Therefore, mass of bullet in lbs = (185/7000) = 0.0264285 lbs approximately
Velocity of the bullet = 1000 feet/sec
Therefore, Momemtum of the bullet (M) = 0.0264285 * 1000 = 26.4285 foot-lbs/sec

Diameter of the bullet = 0.451 inches. Therefore, radius of the bullet = 0.451/2 = 0.2255 inches
Frontal area of bullet (A) = pi * r2 = 3.1415927 * 0.22552 = 0.160 inches2 approximately

Now, let's assume acceleration due to gravity (g) = 32.2 feet/sec2 approximately.

For a lead round nose bullet, the form factor bullet F = 1000 from the table above.
Therefore RSP for this bullet is calculated as:
RSP = M / (2*g) * A * F = 26.4285 / (2 * 32.2) * 0.160 * 1000 = 65.661

For a hollow point (expanded) bullet, the bullet form factor F = 1350 from the table above.
Therefore RSP for this bullet is calculated as:
RSP = M / (2*g) * A * F = 26.4285 / (2 * 32.2) * 0.160 * 1350 = 88.642

Special thanks go out to reader Nathaniel Fitch for pointing out the errors in an earlier version of the article. His comments are posted below. Give him a big round of applause folks!

For self-defense purposes, the Hatcher scale recommends that the RSP be between 50-55 for effective stopping power. Values of RSP beyond 55 lead to diminishing returns, as the increase in stopping power is offset by the extra recoil strength that must be managed by the user. Per the Hatcher scale, values below 30 give a user a 30% chance of stopping the target in one shot. For values between 30 and 49, the chance of a one-shot stop rises to 50%. For values above 50, the chance of a one-shot stop rise to 90% per the Hatcher scale. Most .45 ACP cartridge types have a RSP value over 50, while 9 mm. Luger cartridges are mostly between 30 and 40. This means Hatcher's formula tends to favor .44 Magnum and .45 ACP over 9 mm. Luger for stopping power.

While the Hatcher formula does not consider factors such as bullet penetration, it is considered a fairly decent formula to determine the effectiveness of pistol ammunition.

grayfox Wrote:Not an expert in any of those platforms so this may be a bit too elementary, but instead of looking at a 1930's work (which doubtless was a great one for its day, and still might be useful), for today's fmj's usually flat based or slightly boat-tail, why not use available ballistics and look for a point where ke falls below some minimum...

Lemonaid Wrote:Found this (a portion only) on wikipedia about the M24 Sniper Weapon System.
My take on it is that Maximum Effective Range as a military standard is only about accuracy. So if you want a Grendel MEF, start with an accepted standard of accuracy and you will be able to calculate or test what it's MEF is.

Lemonaid Wrote:Found this (a portion only) on wikipedia about the M24 Sniper Weapon System.
My take on it is that Maximum Effective Range as a military standard is only about accuracy. So if you want a Grendel MEF, start with an accepted standard of accuracy and you will be able to calculate or test what it's MEF is.


They were rigorously tested before being approved by Remington and the military.
A U.S. Soldier training with a M24

Accuracy: According to MIL-R-71126(AR), 3.15.7 Targeting and Accuracy, The rifle shall achieve the dispersion set forth below when fired from a Government approved machine rest. The average mean radius shall be less than or equal to the values stated below. The minimum rate of fire for conducting this test shall be three rounds per minute.[3]

Range / Average Mean Radius (AMR) — Mean Radius (MR) expresses the average distance of all the shots from the center of the shot group. AMR averages the MR of several shot groups.

200 yards (183 m): 1.3 inches
273 yards (250 m): 1.4 inches
300 yards (274 m): 1.9 inches

The radial distance from the calculated center of impact of the first target compared to the calculated center of impacts of the subsequent targets shall be less or equal to 1.086 MOA (3.3 inches @ 300 yards, 2.2 inches @ 200 yards, 2.4 inches @ 200 meters) on an average basis.

The actual rifle requirements for accuracy were .35 MOA from a machine rest and according to Major John Mende (ret.) this accuracy had to be maintained to 10,000 rounds. He stated, "Interesting side note was there was a 10,000 round requirement for the barrel to maintain the original accuracy. In fact after some 10,000 round tests we discovered the accuracy improved. A few barrels were tested past 20,000 and accuracy never went below the original accuracy requirement."[8]

Maximum effective range is given as 800 meters (875 yd), but record shots have been made with the M24 at over 1,000 meters (1,094 yd). Meanwhile, the standard optical sight has a maximum elevation adjustment of 1,000 meters (1,094 yd).

LR1955 Wrote:Lemonaid:

Take if from a guy who has fired thousands of rounds of M-118 Special Ball out of M-24's. M-14 service and super match, the M-14 EBR, and a couple of Model 70 Match rifles.

I have never seen any of them hold one minute at 300 yards when firing issued M-118 Special Ball. I have seen them hold that when firing M-852 Match. The lots of M-118 LR that I used and witnessed being used were hit or miss in quality at the time they came out so can not comment on them.

As for 800 meters being the max effective range for the M-24 and an average trained Sniper team of the 1980's and 1990's using the 24, a 10X fixed mil dot reticle, M-118 Special Ball, at unknown distances to 1000 meters, I think a 50% chance of a first round hit on a E-Sil at around 800 meters is pretty damn good. The problem is, guys who do not shoot true unknown distance ranges, while laying in the prone, with a spotter in the prone using a M-49 scope, firing M-118, have no clue what so ever of the pure luck that goes into some of the longer shots with that particular equipment that is now obsolete.

I am sure what you cited is a requirement written sometime in the late 70's or early 80's when the 24 was being developed. Sounds right but never quite got there.

Not sure why you even cited this requirement. It reflects the technology of US Army sniping in the late 70's and into the 80's. It is obsolete today.

LR55

stanc Wrote:The accuracy standards you cite are for a bolt-action sniper rifle with 24" barrel, firing match grade ammo. It would seem reasonable to use those standards as a basis for a 6.5 Grendel sniper rifle, but they are totally inapplicable to determining the maximum effective range of a service grade 6.5 Grendel carbine with 16" barrel, firing service grade ball ammo.

You need to use the standards for 5.56 M855A1 Ball. The weight range of hypothetical EPR bullets has practical limits of around 95 gr at the low end, to about 125 gr at the high end. Considering the probable BC and MV of such loads, the max effective range seems likely to not differ greatly from that of 5.56 ball ammo.

Lemonaid Wrote:Interesting that you mentioned a grendel sniper rifle, I didn't find much about this on the forum (search term "grendel sniper" ).

Texas Wrote:Do you mean Max effective range or relative stopping power calculation?
M1 carbine max effective range 300 yards
M1 Garand max effective range 400 yards
M14 max effective range 500 yards
M16 max effective range 600 yards
At 600 yards the M1 has the highest relative stopping power.