FN FAL Rifle

Ballistic Coefficient
When shooting at a range of 1,000 yards (about the same as 1,000 meters) or more there are a number of corrections to the aiming point that need to be made.
Wiki has a section titled "Long Range Factors" on their External Balistics web page. Wiki also has web pages for:

Internal ballistics
Trajectory of a projectile

I've ordered the book "New Exact Small Arms Ballistics: The Source Book for Riflemen" by Arthur J. Pejsa (Wiki: Pejsa Model)
The key idea is that the "Ballistic coefficient" (BC) (Wiki) was developed in antiquity and has a problem at some bullet Mach numbers.

In addition it turns out that the Coriolis Effect (Wiki) is very important at 1000 yards (more important than some of the more common ideas).
The Eötvös effect (Wiki) may also be important (don't remember it being in the book). Both of these are because the Earth is rotating.
For example where a bullet goes depends on the azimuth the gun is pointing.

Pejsa points out that the stability of a projectile is improved if the center of gravity (Cg) is at the same location as the center of pressure (Cp). When these are at different locations the projectile is less stable. Is there a commercial .308 round where these are at the same location? Let me know.
From the gyroscopic discussion below I would expect that if the Cp was far behind the Cg, like an arrow, that would lead to higher stability.
Does someone make a shotgun round that contains a cross bow bolt (Wiki, Projectiles)? Some engineering would be needed to balance the weight of the bolt and the amount and type of gunpowder. In addition the cg location, shaft length and fin area also need to be optimized. The goat would be to get the arrow to have an angle of attack that is parallel to its trajectory. That minimizes wind resistance, minimizing flight time and maximizing accuracy.

Gyroscopic Instability
While learning about gyroscopes I read (Gyroscope Reference 3, 1913) that (1) the purpose of rifling in a gun barrel is to slow down the bullet so the (black) powder has more time to burn and develop higher pressure and that (2) at long ranges the spinning of the bullet makes it less accurate. The second effect comes about because the bullet is gyroscopically stabilized and it's centerline stays parallel to the centerline of the barrel throughout the trajectory. That means that as soon as the trajectory bends the bullet is no longer pointing along it's path but instead pointing to one side. The larger the angle difference between the barrel centerline and the trajectory the more the bullet is pointing the wrong way. Note that an arrow is aerodynamically steered so that it always points in the direction of travel. If a bullet was made like an arrow with a tail that could keep it pointing forward it would be much more stable (accurate). Note the gyroscope book reference 3 is about 100 years after the below papers on Gunnery and Rifled Barrels.

The Mk44 Bushmaster II (Wiki, Alliant Techsystems) is demonstrated on Future Weapons Season 3 (Netflix streaming video). The interesting thing is that after using a laser range finder to determine the distance to the target then programming the shell to explode either just prior to the target, at the target or after going some distance behind the target. This is similar to the capability of the XM 25mm grenade rounds that are being developed. The Mk44 does this by measuring the Earth's magnetic filed and using that to count the rotation of the round. Patent 5497704 Multifunctional magnetic fuse explains how it works. Note the fuse includes an impact sensor, time delay, turn counting, magnetic (proximity) sensor . After the programmed number of turns the shell explodes. The muzzle velocity is about 1,000 meters/second so for 1 meter stability the rifling pitch is about 1 turn per meter. Trivia: A similar method was used in the Kettering Bug where propeller turns were counted.

The CheyTac Intervention (Wiki, ) fires the .408 Chey Tac (Wiki) round which includes the patented (6629669) Balanced-flight controlled-spin projectile concept. The outline of the .408 is very similar to the Barrett .416 (Wiki) (I wonder if Barrett copied the .408 but made it a little different?). The Barrett Optical Ranging System (BORS) is based on the old fashioned BC idea and includes left-right tilt which Pejsa has shown to be a faulty idea.

Accuracy International (Wiki) makes sniper rifles in various calibers but not the .408 or .416.
Trijicon CCAS Continuously computed aiming solution 50 - 2000 meter auto ranging, baro pressure, inclination,
4806007 Optical gun sight, Glyn A. J. Bindon, Armson, Inc., Feb 21, 1989, 359/424, 42/122, 359/429, 359/431
7676137 Optical sight, Darin W. Schick, Newton Quan-Chung Kwan, Timothy H. Miller, Jerry Glen S. Elpedes, Trijicon, Inc., Mar 9, 2010, 385/147, 385/134, 42/111, 33/298, 42/132, 33/297 - has provision for digital data in field of view. - What is model number of just scope with data display?
The Kestrel 5700 is mechanically and electrically identical to the Kestrel 5500 Fire Weather meter, except it has firmware for Ballistics.

Rifling (Gyroscope)

New Principles of Gunnery 1805 (Free Google Book) has papers from the prior 50 years. The first 380 pages are about interior and exterior ballistics of round projectiles fried from black powder guns (3/4" lead balls and 24 pound iron balls). In those pages he shows that air resistance greatly reduces the range you would get in a vacuum and so the trajectory is far from parabolic. I expect this is also true of dumb bombs, that's to say the trajectory is far from parabolic.

In the section titled On the Nature and Advantage of Rifled Barrel Pieces the reasons those on the continent (Europe) said were it's advantages are:

that the inflammation of the powder was greater by the resistance, which the bullet thus forced into the barrel gave thereto, and that hereby the bullet received a much greater impulsion, than it would have done from the same quantity of powder in a common (smooth bore) piece, or

that the bullet by the compounding of its circular and revolving motion did, as it were, bore the air, and thereby flew to a much greater distance, than it would otherwise have done ; or

that by the same boring motion it made its way much easier through all solid substances, and penetrated much deeper into them, than if discharged in the common manner.

The projectile was a round lead ball, either forced into and down the barrel where the lead deformed to match the barrel or in a leather patch where the lead was not deformed. The latter had much higher muzzle velocity because there was much lower friction, but still for the same powder charge used with the smooth bore the velocity was lower than a smooth bore.

The author then makes that case that the main advantage is that the effect of air resistance on a ball with any defects (in Cg or aerodynamics) will be averaged because of the rotation of the ball. (This is the stability improvement provided by rifling, not the gyroscopic effect which is destabilizing)
But, he also says "And in the first place I must observe, that though the bullet impelled' from them keeps for a time to its regular track with sufficient nicety; yet; if its flight be so far extended, that its track is much incurvated, it will then of ten undergo considerable deflections. This, according to my experiments, arises from the angle at last made by the axis, on which the bullet turns, and the direction in which it flies; for that axis continuing nearly parallel to itself, it must necessarily diverge front the line of the flight of the bullet; when that line is bent from its Original direction; and when it once happens; that the bullet whirls on an axis, which no longer coincides with the line of its flight; then the unequal resistance described in the former papers will take place, and the deflecting' power hence arising will perpetually increase, as the track of the bullet, by having its range extended, becomes more and more incurvated."

Note in none of the above arguments (both European & English) is improved accuracy a benefit of rifling. In the case of the English analysis it helps accuracy at short ranges by averaging imperfections in the ball but at longer ranges causes a lot of problems (because of gyroscopic action).

But he didn't do any experiments relating to the amount of powder that's useful in rifled barrels. Remember with black powder that once the bullet leaves the muzzle any unburned powder is pushed out and will fall on the ground (easy to detect if a white bed sheet is on the ground). I expect that you can use more power to useful effect in a rifled barrel, confirming the first bullet above leading to higher muzzle velocity.

Wiki: Alfred George Greenhill, formula for rifling twist for stability
Wiki: Miller twist rule - supposed to me more accurate than the Greenhill formula.

Smooth Bore
It may be the case that a modern smooth bore gun using a round made from material with uniform properties throughout would be more accurate. That in fact is the case for modern long range artillery (Wiki: Gerald Bull, Project HARP, Super High Altitude Research Project, Other web pages: Operation Plumbbob (Scroll to Test: Pascal-B), Learning to Contain Underground Nuclear Explosions)
note that G. Bull (Wiki: SRC, Base Bleed, Fineness ratio, GC-45 Howitzer, G5 Howitzer) developed long range accurate artillery by using a smooth bore
Torpedo: Range & Accuracy, Big Gun Disconnect
3886009 Projectile containing pyrotechnic composition for reducing base drag thereof, Walter J Puchalski, US Army, App:1973-12-13
4213393 Gun projectile arranged with a base drag reducing system, Nils-Erik Gunners, Rune V. Hellgren, Torsten Liljergren
4807532 Base bleed unit, Kurt G. Andersson, Nils-Erik Gunners,Yngve L. Nilsson, 1989-02-28, -
SE507777C2 Artillery shell firing method, Foersvarets Forskningsanstalt, 1998-05-28
Note Pascal-B was the second underground nuclear test where the ground level cover (a 4' diameter 4" thick steel plate (about 1 ton weight) was blown off at about "Six times the escape velocity from the earth."
This was caused by many tons of concrete that were vaporized by the explosion that went up the shaft and propelled the cover. The cover vaporized like a meteor.

The US Abrams M1A1 tank (Wiki) uses a German design smooth bore gun (Wiki). I found "Fin-stabilised projectile" while searching for patents where "Rheinmetall" was the assignee. The US M829A2 (Wiki) projectile resembles an arrow.

YouTube: Ballistics: "Fundamentals of Ballistics" 1948 US Army Training Film TF9-1512" 1948 (18:05) - interior, exterior & Terminal, but the gyroscopic effect causing the centerline of the projectile to not align with the trajectory was not mentioned.

Terminal

The ballistic pendulum (Wiki) is not only a way to make measurements of the projectile it's also a way to understand the effect of a projectile striking a target.

Symbol	atomic wt. g/mole
K	39.0983
N	14.0067
O	15.9994
S	32.065
C	12.0107

Round	End of Burn Barrel Len In.	Vel fps	Muzzle Energy ft lbs	Time in Barrel ms
CCI 27 gr. CPHP	9	1100	73	0.68
CCI 29 gr. CPRN	14	1100	78	1.06
CCI 32 gr. CPHP Stinger	13	1500	160	0.72
Remington 33 gr. HVTCHP Yellow Jacket	16	1400	144	0.95
Remington 36 gr. HVTCS Viper	12	1300	135	0.77
Remington 36 gr. Golden BUllet HP	11	1180	111	0.78
CCI 40 gr. CPRN MiniMag	11	1200	128	0.76
Winchester 40 gr. Super XRN	13	1250	139	0.87
CCI 40 gr. CPHP Volocitor	16	1380	169	0.97
Aguila 60 gr. SSS	12	900	108	1.11

Nomenclature	Description	NSN	Link
M4A1	Carbine w/Carrying Handle	1005-01-382-0953
Reflex Sight	Trijicon, RX01M4A1, 1X24, Amber Reticle and Dot	1240-01-435-1916	eBay-Trijicon, Wiki 5653034 Reflex Sight 20040047586 R.S. mult pwr sources
ECOS-N	Aimpoint CompM2 (M68 Close Combat Optic))	1240-01-495-1385	Wiki,
	Trijicon ACOG 4x32, 4X Day Optical Scope	1240-01-412-6608	eBay 7676137 Optical sight 8364002 ACOG
AN/PEQ-5	Insight, Carbine Visible Laser	5860-01-439-5409	Wiki,
AN/PEQ-2	Infrared Illuminator	5855-01-422-5253	L3, Wiki
AN/PVS-17A	Mini Night Vision Sight (replaces the PVS-4)	5855-01-474-8904	eBay, Optics4Birding
	Backup Iron Sight	1005-01-449-6306
PVS14 (Wiki) PVS18 M68	Universal Pocketscope Mount	5855-01-482-6164 5855-01-485-7749 5855-01-465-7755
	Forward Handgrip	1005-01-416-1091
	Visible Bright Light Surefire M952NXM07 Millennium	5855-01-501-3081	eBay, Surefire, KM3 LED
	Sound Suppressor Kit	1005-01-437-0324	patent 6595099 ?
	Rail Interface System	1005-01-416-1089
M203 (Wiki)	9" (40mm) Barrel Assembly	1010-01-410-7422	eBay,
	40mm Grenade Launcher Sight	1010-01-418-4588
AN/PSQ-18A	M203 Day/Night Sight (DNS)	1010-01-516-0953	eBay,

FN FAL Rifle

Background

Markings

Video

Related

Ballistics

Internal

External

References

Time of Flight

Ballistic Coefficient

Gyroscopic Instability

Rifling (Gyroscope)

Smooth Bore

Terminal

Picatinny rail, MIL-STD-1913 rail, 2324 rail, or tactical rail, (Wiki)

Method of Stadia (Range-finding)

Stoner

SOPMOD M4 Accessory Kit

Sights

High Standard 10B Shotgun

Interesting 22LR

22 Reloading

Kel-Tec

Silencers

Fundamental Concepts

Related