Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference . It appears to be directed radially away from the axis of rotation of the frame. The magnitude of the centrifugal force F on an object of mass m at the distance r from the axis of a rotating frame of reference with angular velocity ω is: F = m ω 2 r {\displaystyle F=m\omega ^{2}r}
157-721: 1 × M2HB .50 caliber (12.7 mm) machine gun (bow) The Hurricane Aircat was an airboat used as a riverine patrol boat by the US Army and South Vietnamese Army (ARVN) during the Vietnam War . It was used to conduct various counterinsurgency (COIN) and patrol missions in riverine and marshy areas where larger boats could not go. The Viet Cong (VC) insurgents, one of the US Army's main enemies in Vietnam, relied heavily on motorized and paddled sampans to move troops and supplies throughout
314-424: A " fictitious force " arising in a rotating reference. Centrifugal force has also played a role in debates in classical mechanics about detection of absolute motion. Newton suggested two arguments to answer the question of whether absolute rotation can be detected: the rotating bucket argument , and the rotating spheres argument. According to Newton, in each scenario the centrifugal force would be observed in
471-694: A .30 caliber Browning machine gun in each compact one-man turret on M113 APCs used by the Royal Australian Armoured Corps in South Vietnam. The M2HB has been in service with the Israel Defense Forces since its establishment and has served in all of Israel's wars, operations, and conflicts . In 2012, the IDF upgraded its M2HB machine guns to the M2HQCB model, with a heavy quick-change barrel. Today
628-579: A December 1964 accident in which an airboat carrying 11 ARVN soldiers sank in the Mekong River, drowning five. Observers at the scene believed that the overloading of the boat contributed to the accident. Normal roles for the five-soldier crew were one commander/operator, one machine gunner, one radio operator /assistant gunner, and two riflemen . Aircat airboats in American and South Vietnamese service operated in units of six boats. In use by special forces units,
785-619: A VC platoon embarked on sampans in Kien Tuong province, considered "a classic instance of successful employment of an airboat unit" by the Army Concept Team in Vietnam (ACTIV), ramming attacks were responsible for about half of VC casualties and sampan losses. No Viet Cong survived the battle. A downside of the Aircat was the level of additional training that it demanded from operators, gunners, and repair personnel. Almost every aspect of operating
942-513: A beating from bushes, trees, and other obstacles. Testing by the 5th Special Forces Group found that the noise issue could be overcome by using the radio with a CVC tanker's helmet and that the antenna vulnerability issue could be fixed by using a vehicular radio and antenna such as the AN/VRC-12 or AN/VRC-16 . Nevertheless, radio problems persisted at least through 1968–69. During the Vietnam War
1099-452: A centripetal acceleration. When considered in an inertial frame (that is to say, one that is not rotating with the Earth), the non-zero acceleration means that force of gravity will not balance with the force from the spring. In order to have a net centripetal force, the magnitude of the restoring force of the spring must be less than the magnitude of force of gravity. This reduced restoring force in
1256-542: A co-rotating frame. However, the Lagrangian use of "centrifugal force" in other, more general cases has only a limited connection to the Newtonian definition. In another instance the term refers to the reaction force to a centripetal force, or reactive centrifugal force . A body undergoing curved motion, such as circular motion , is accelerating toward a center at any particular point in time. This centripetal acceleration
1413-403: A dedicated M2 version was developed called the ".50 Browning AN/M2" or the "12.7 mm AN/M2". The "AN" stands for "Army/Navy", since the gun was developed jointly for use by both services. The AN/M2 designation was also used for other aircraft guns and therefore it is important to write the caliber before the designation. The 12.7 mm AN/M2 had a cyclic rate of 600–800 rounds per minute, with
1570-489: A fixed developed for use on the M6 Heavy Tank designated Browning Machine Gun, Cal. .50, M2, HB, Fixed, and a "turret type" whereby "Flexible" M2s were modified slightly for use in tank turrets. The subvariant designation Browning Machine Gun, Cal. .50, M2, HB, TT was only used for manufacturing, supply, and administration identification and separation from flexible M2s. A number of additional subvariants were developed after
1727-426: A flash, report, and smoke on contact, useful in detecting strikes on enemy targets; they were primarily intended to incapacitate thin-skinned and lightly armored vehicles and aircraft, while igniting their fuel tanks. Current ammunition types include M33 Ball (706.7 grain) for personnel and light material targets, M17 tracer, M8 API (622.5 grain), M20 API-T (619 grain), and M962 SLAP-T. The latter ammunition along with
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#17330856339321884-500: A frictional force against the seat) in order to remain in a fixed position inside. Since they push the seat toward the right, Newton's third law says that the seat pushes them towards the left. The centrifugal force must be included in the passenger's reference frame (in which the passenger remains at rest): it counteracts the leftward force applied to the passenger by the seat, and explains why this otherwise unbalanced force does not cause them to accelerate. However, it would be apparent to
2041-614: A heavily sandbagged tripod, the M2HB proved very useful in either a defensive role or to interdict or block road intersections from use by German infantry and motorized forces. Hearing the sound of an M2 could often cause enemy infantry to take cover. There are numerous instances of the M2 Browning being used against enemy personnel, particularly infantry assaults or for interdiction or elimination of enemy artillery observers or snipers at distances too great for ordinary infantry weapons. The M2HB
2198-485: A larger-caliber machine gun. Pershing asked the Army Ordnance Department to develop a machine gun with a caliber of at least 0.50 inches (12.7 mm) and a muzzle velocity of at least 2,700 feet per second (820 m/s). Around July 1917, John Browning started redesigning his .30-06 M1917 machine gun for a larger and more powerful round. Winchester worked on the cartridge, which was a scaled-up version of
2355-568: A light naval mine mounted on the end of a bamboo pole and piano wire strung between wooden poles that held fishing traps, used to decapitate or injure airboat drivers and gunners. The change in VC tactics exposed a major weakness of the Aircat: the fiberglass hull offered no protection against gunfire or shrapnel. Standard defensive tactics for the Aircat were to "avoid becoming decisively engaged," i.e. to dodge enemy fire and perform offensive actions. The Aircat
2512-498: A maximum effective range of 2,000 metres (2,200 yd) when fired from the M3 tripod . In its ground-portable, crew-served role as the M2HB, the gun itself weighs 84 pounds (38 kg) and the assembled M3 tripod another 44 pounds (20 kg). In this configuration, the V-shaped "butterfly" trigger is located at the very rear of the weapon with a "spade handle" handgrip on either side of it and
2669-449: A mounting bracket of his own design, Hathcock could quickly convert the M2 into a sniper rifle, using the traversing-and-elevating (T&E) mechanism attached to the tripod . When firing semi-automatically, Hathcock hit man-size targets beyond 1,800 metres (2,000 yd)—twice the range of the standard-caliber sniper rifle of the time (a .30-06 Winchester Model 70 ). Hathcock set the record for
2826-448: A new slotted flash suppressor that reduces muzzle flash by 95 percent, fixed headspace and timing, a modified bolt, and a manual trigger block safety. When a standard M2 had a barrel change, the headspace and timing had to be manually set. Improper adjustment could damage the weapon and cause serious injury to the user. Fixed headspace and timing reduces risk, and the carrying handle allows the barrel to be switched in seconds. In June 2011,
2983-669: A note of the obstacle, and then returning in Aircats and proceeding over it. These characteristics made the Aircat invaluable during the rainy monsoon season , as it could easily cross flooded rice paddies and jump dikes between paddies. The Aircat was very fast relative to other patrol boats, being capable of speeds up to 42 knots (48 mph; 78 km/h) in deep water and 65 knots (75 mph; 120 km/h) on shallow water or rice paddies. Its speed made it ideal for reconnaissance, providing flank security for riverine assault boats, and special forces use. The Aircat's speed and maneuverability
3140-404: A range of 250 yd (230 m). Winchester improved the .50 caliber round to have similar performance. Ultimately, the muzzle velocity was 2,750 ft/s (840 m/s). Efforts by Browning and Fred T. Moore resulted in the water-cooled, .50 caliber M1921 Browning machine gun and an aircraft version. These guns were used experimentally from 1921 until 1937. They had lightweight barrels and
3297-574: A rate of fire of approximately 800 rounds per minute and was used singly or in groups of up to eight guns for aircraft ranging from the P-47 Thunderbolt to the B-25 Mitchell bomber, which in the last J-version of the Mitchell could have up to fourteen M2s firing forward for ground attack missions – eight in a solid metal-structure nose, four more mounted in a pair of conformal twin-gunned gun pods on
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#17330856339323454-711: A reaction to a centripetal force in some scenarios. From 1659, the Neo-Latin term vi centrifuga ("centrifugal force") is attested in Christiaan Huygens ' notes and letters. Note, that in Latin centrum means "center" and ‑fugus (from fugiō ) means "fleeing, avoiding". Thus, centrifugus means "fleeing from the center" in a literal translation . In 1673, in Horologium Oscillatorium , Huygens writes (as translated by Richard J. Blackwell ): There
3611-439: A rectangular hull 17 feet (5.2 m) long with 7.25 feet (2.21 m) beam . The draft varied with speed but was no more than four inches (100 mm). At top speed, the Aircat could draw as little as a single inch (25 mm) of water. The hull was made from five layers of molded fiberglass and was semi- catamaran fore and flat-bottomed aft. This unique hull shape helped the Aircat surmount higher obstacles. The Aircat
3768-425: A rotating reference frame because it rotates once every 23 hours and 56 minutes around its axis. Because the rotation is slow, the fictitious forces it produces are often small, and in everyday situations can generally be neglected. Even in calculations requiring high precision, the centrifugal force is generally not explicitly included, but rather lumped in with the gravitational force : the strength and direction of
3925-403: A stationary observer watching from an overpass above that the frictional force exerted on the passenger by the seat is not being balanced; it constitutes a net force to the left, causing the passenger to accelerate toward the inside of the curve, as they must in order to keep moving with the car rather than proceeding in a straight line as they otherwise would. Thus the "centrifugal force" they feel
4082-509: A subject about which I have more to say than I am able to do at present. But, in order that those interested in these things can sooner enjoy these new and not useless speculations, and in order that their publication not be prevented by some accident, I have decided, contrary to my plan, to add this fifth part [...]. The same year, Isaac Newton received Huygens work via Henry Oldenburg and replied "I pray you return [Mr. Huygens] my humble thanks [...] I am glad we can expect another discourse of
4239-507: A variety of ships and watercraft including the soft mount and fixed type versions. The fixed types fire from a solenoid trigger and come in left- or right-hand feed variants for use on the Mk 56 Mod 0 dual mount and other mounts. Huaqing Machinery has made a clone of the M2HB known as the CS/LM6, which was released publicly in 2010 at foreign weapons expo conventions. It was made with a picatinny rail on
4396-862: A vehicle weapon and for aircraft armament by the United States since the 1930s. It was heavily used during World War II , the Korean War , the Vietnam War , the Falklands War , the Soviet–Afghan War , the Gulf War , the Iraq War , and the War in Afghanistan . It is the primary heavy machine gun of NATO countries and has been used by many other countries as well. U.S. forces have used the M2 longer than any other firearm except
4553-588: Is a heavy machine gun that was designed near the end of World War I by John Browning . While similar to Browning's M1919 Browning machine gun , which was chambered for the .30-06 cartridge, the M2 uses Browning's larger and more powerful .50 BMG (12.7 mm) cartridge. The design has had many designations; the official U.S. military designation for the infantry type is Browning Machine Gun, Cal. .50, M2, HB, Flexible . It has been used against infantry, light armored vehicles, watercraft, light fortifications, and low-flying aircraft. The gun has been used extensively as
4710-401: Is a stationary frame in which no fictitious forces need to be invoked. Within this view of physics, any other phenomenon that is usually attributed to centrifugal force can be used to identify absolute rotation. For example, the oblateness of a sphere of freely flowing material is often explained in terms of centrifugal force. The oblate spheroid shape reflects, following Clairaut's theorem ,
4867-478: Is another kind of oscillation in addition to the one we have examined up to this point; namely, a motion in which a suspended weight is moved around through the circumference of a circle. From this we were led to the construction of another clock at about the same time we invented the first one. [...] I originally intended to publish here a lengthy description of these clocks, along with matters pertaining to circular motion and centrifugal force , as it might be called,
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5024-406: Is based upon the idea of an inertial frame of reference, which privileges observers for which the laws of physics take on their simplest form, and in particular, frames that do not use centrifugal forces in their equations of motion in order to describe motions correctly. Around 1914, the analogy between centrifugal force (sometimes used to create artificial gravity ) and gravitational forces led to
5181-411: Is made, fictitious forces, including the centrifugal force, arise. In a reference frame rotating about an axis through its origin, all objects, regardless of their state of motion, appear to be under the influence of a radially (from the axis of rotation) outward force that is proportional to their mass, to the distance from the axis of rotation of the frame, and to the square of the angular velocity of
5338-451: Is no net force acting on the object and the force from the spring is equal in magnitude to the force of gravity on the object. In this case, the balance shows the value of the force of gravity on the object. When the same object is weighed on the equator , the same two real forces act upon the object. However, the object is moving in a circular path as the Earth rotates and therefore experiencing
5495-438: Is often applied to rotating devices, such as centrifuges , centrifugal pumps , centrifugal governors , and centrifugal clutches , and in centrifugal railways , planetary orbits and banked curves , when they are analyzed in a non–inertial reference frame such as a rotating coordinate system. The term has sometimes also been used for the reactive centrifugal force , a real frame-independent Newtonian force that exists as
5652-401: Is provided by a centripetal force, which is exerted on the body in curved motion by some other body. In accordance with Newton's third law of motion , the body in curved motion exerts an equal and opposite force on the other body. This reactive force is exerted by the body in curved motion on the other body that provides the centripetal force and its direction is from that other body toward
5809-408: Is removed (for example if the string breaks) the stone moves in a straight line, as viewed from above. In this inertial frame, the concept of centrifugal force is not required as all motion can be properly described using only real forces and Newton's laws of motion. In a frame of reference rotating with the stone around the same axis as the stone, the stone is stationary. However, the force applied by
5966-505: Is required. These fictitious forces are necessary for the formulation of correct equations of motion in a rotating reference frame and allow Newton's laws to be used in their normal form in such a frame (with one exception: the fictitious forces do not obey Newton's third law: they have no equal and opposite counterparts). Newton's third law requires the counterparts to exist within the same frame of reference, hence centrifugal and centripetal force, which do not, are not action and reaction (as
6123-463: Is sometimes erroneously contended). A common experience that gives rise to the idea of a centrifugal force is encountered by passengers riding in a vehicle, such as a car, that is changing direction. If a car is traveling at a constant speed along a straight road, then a passenger inside is not accelerating and, according to Newton's second law of motion , the net force acting on them is therefore zero (all forces acting on them cancel each other out). If
6280-407: Is the result of a "centrifugal tendency" caused by inertia. Similar effects are encountered in aeroplanes and roller coasters where the magnitude of the apparent force is often reported in " G's ". If a stone is whirled round on a string, in a horizontal plane, the only real force acting on the stone in the horizontal plane is applied by the string (gravity acts vertically). There is a net force on
6437-463: The .45 ACP M1911 pistol , which was also designed by John Browning. The M2HB (heavy barrel) is manufactured in the U.S. by General Dynamics , Ohio Ordnance Works, U.S. Ordnance , and FN Herstal for sale to the U.S. government and other nations via Foreign Military Sales . Machine guns were heavily used in World War I, and weapons of larger than rifle caliber began appearing on both sides of
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6594-579: The Coriolis force − 2 m ω × [ d r / d t ] {\displaystyle -2m{\boldsymbol {\omega }}\times \left[\mathrm {d} {\boldsymbol {r}}/\mathrm {d} t\right]} , and the centrifugal force − m ω × ( ω × r ) {\displaystyle -m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})} , respectively. Unlike
6751-461: The M4 Sherman , M7 Priest , M8 Greyhound , or M10 tank destroyer variously used by British, Canadian, Australian, South African, and New Zealand units. Nevertheless, the heavy Browning's effectiveness was praised by many British and Commonwealth soldiers in infantry, armored, and ordnance branches. Many commanders thought that the .50 Browning was the best weapon in its class, certainly the best of
6908-628: The Mobile Strike Force Command (MIKE Force). US Navy personnel, including Navy SEALs , helped US Army Special Forces train these irregulars. Many Aircats returned to the United States, where they became widely used by civilians for recreation, commercial jobs, and environmental conservation. Aircats have been used by individuals for fishing, hunting, and personal travel and by companies for tours, geophysical surveying and oil exploration , mosquito control, and transporting workers to oil rigs and construction sites in marshlands. Estimating
7065-477: The US Fish and Wildlife Service . Some Fish and Wildlife Aircats are military surplus, while others are civilian models purchased new. Aircats have proved particularly valuable for bird banding , allowing researchers to band more birds and bird species than was possible using bait-trapping or other methods, although the loud noise of their engines can scare off wildlife. Some civilian Aircats have made their way outside
7222-658: The US Pacific Command ( CINCPAC ) approved the request on June 19, 1964, and ordered six airboats from two commercial manufacturers—the Hurricane Fiberglass Products Company of Auburndale, Florida and Susquehanna Danville Airport of Danville, Pennsylvania —to evaluate and test them and then select a winner. The Susquehanna airboats were a joint venture between Ken Burrows-owned Danville Airport of Danville and Mari-Mar Industries of Port Trevorton, Pennsylvania . The two models of airboats evaluated were
7379-845: The USAAF and the F4F , F6F , and Vought F4U Corsair for the US Navy . For bombers, the AN/M2 was used in both flexible and fixed positions for both offensive and defensive use. In flexible defensive positions, the Boeing B-17G Flying Fortress heavy bomber was armed with 13x AN/M2 guns in both turreted and flexible positions. In fixed offensive configurations, like on the North American B-25 Mitchell , commonly carried 6 to 12 fixed guns for strafing. Centrifugal force This fictitious force
7536-428: The equivalence principle of general relativity . Centrifugal force is an outward force apparent in a rotating reference frame . It does not exist when a system is described relative to an inertial frame of reference . All measurements of position and velocity must be made relative to some frame of reference. For example, an analysis of the motion of an object in an airliner in flight could be made relative to
7693-402: The vector cross product . In other words, the rate of change of P in the stationary frame is the sum of its apparent rate of change in the rotating frame and a rate of rotation ω × P {\displaystyle {\boldsymbol {\omega }}\times {\boldsymbol {P}}} attributable to the motion of the rotating frame. The vector ω has magnitude ω equal to
7850-472: The vis centrifuga , which speculation may prove of good use in natural philosophy and astronomy , as well as mechanics ". In 1687, in Principia , Newton further develops vis centrifuga ("centrifugal force"). Around this time, the concept is also further evolved by Newton, Gottfried Wilhelm Leibniz , and Robert Hooke . In the late 18th century, the modern conception of the centrifugal force evolved as
8007-409: The .30-06. Winchester initially added a rim to the cartridge because the company wanted to use the cartridge in an anti-tank rifle, but Pershing insisted the cartridge be rimless. The first .50-caliber machine gun underwent trials on 15 October 1918. It fired at less than 500 rounds per minute, and the muzzle velocity was only 2,300 ft/s (700 m/s). Cartridge improvements were promised. The gun
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#17330856339328164-467: The .50 BMG cartridge, which offers longer range, greater accuracy, and immense stopping power . The closed bolt firing cycle made the M2 usable as a synchronized machine gun on aircraft before and during World War II, as on the early versions of the Curtiss P-40 fighter. The M2 is a scaled-up version of John Browning's M1917 .30 caliber machine gun . The M2 has varying cyclic rates of fire, depending on
8321-477: The 5th Special Forces Group Company D eventually found that the using the AN/PRC-25 radio and CVC tanker's helmet sufficiently reduced noise to the point where the radio was usable. However, noise problems persisted at least through 1968. Field research conducted from 1964 to 1966 led to the development of tactics that could minimize the boats' noise level. These tactics combined with the low silhouette and high speed of
8478-470: The 5th Special Forces Group mount operations and establish CIDG bases deep into territory previously under the control of the Viet Cong. These gains were not without cost, however: 55 Special Forces and 1,654 Vietnamese were killed during 1967, as well as an estimated 7,000 Viet Cong. The 5th Special Forces Group found that the Aircats were most effective when used in combined arms operations with gunships , as
8635-482: The Aircat often operated with a crew of three: commander/pilot, gunner, and radio operator/grenadier. A rifle platoon could be transported in 6–8 boats. Initially, Aircats were able to operate with impunity, as they were faster and sturdier than any enemy vessels. Their dominance of the Mekong Delta led the Viet Cong to develop dedicated anti-airboat tactics and introduce several dedicated anti-airboat traps, including
8792-426: The Aircat proved to require substantial training. Learning the basics of operating an Aircat took two weeks, although ARVN troops often took longer to reach the desired level of competence. Learning to sail in formation and execute tactical maneuvers would take ARVN troops an additional three weeks. Gunners and riflemen also had to receive training in firing at moving targets while moving towards, laterally, and away from
8949-548: The American weapons, including the M1 Garand and M1 Carbine . In North Africa, after Commonwealth units began to obtain sufficient parts, manuals, gauges, and ammunition for the new weapon, the .50 Browning was increasingly used, eventually replacing the 15 mm Besa, but in Italy it was often deleted from top turret mountings because the mount exposed the operator to low branches and enemy fire. All LRDGs , and some SAS units used
9106-483: The Army began conversion of M2HB machine guns to M2A1s. The M2A1 was named one of the greatest Army inventions of 2011. As of 30 November 2012, 8,300 built or converted M2A1s had been fielded by the U.S. Army; the program will upgrade the Army's entire M2 inventory of more than 54,000 guns. The U.S. Marine Corps plans to upgrade all of their ground-mounted M2s to M2A1 standard from 2016 to 2018. The first phase of conversions
9263-465: The Browning was used with standard ball, armor-piercing (AP), armor-piercing incendiary (API), and armor-piercing incendiary tracer (APIT) rounds. All .50 ammunition designated "armor-piercing" was required to completely perforate 0.875 inches (22.2 mm) of hardened steel armor plate at a distance of 100 yards (91 m) and 0.75 inches (19 mm) at 547 yards (500 m). The API and APIT rounds left
9420-468: The Coriolis force in particular, it is independent of the motion of the particle in the rotating frame. As expected, for a non-rotating inertial frame of reference ( ω = 0 ) {\displaystyle ({\boldsymbol {\omega }}=0)} the centrifugal force and all other fictitious forces disappear. Similarly, as the centrifugal force is proportional to the distance from object to
9577-455: The Earth. This is due to the large mass and velocity of the Sun (relative to the Earth). If an object is weighed with a simple spring balance at one of the Earth's poles, there are two forces acting on the object: the Earth's gravity, which acts in a downward direction, and the equal and opposite restoring force in the spring, acting upward. Since the object is stationary and not accelerating, there
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#17330856339329734-646: The Hurricane Aircat and the Susquehanna Skimmer. Each Aircat and Skimmer cost about $ 6,000 each in 1964 (equivalent to about $ 49,000 in 2018). The Army finished its evaluation by the end of 1965. The Aircat was found to be more durable, maneuverable, and have greater obstacle crossing capabilities than the Skimmer, although the Skimmer outperformed the Aircat in deep water. As such, the Army opted to begin purchasing Aircats in early 1966. The Hurricane Aircat had
9891-555: The Hurricane Aircat was used by US Special Forces and ARVN to patrol and attack in riverine and marshy areas where larger boats could not go. Aircats were used primarily in the 15,000 square miles (39,000 km) of the Mekong Delta and Plain of Reeds though they also saw action in the Bảy Núi mountains near the Cambodian border. Its most important contribution to the American war effort
10048-595: The M1921A1 and M1921E2). With support from the Navy, Colt started manufacturing the M2 in 1933. FN Herstal (Fabrique Nationale) has manufactured the M2 machine gun since the 1930s. General Dynamics, U.S. Ordnance and Ohio Ordnance Works Inc. are other current manufacturers. A variant without a water jacket, but with a thicker-walled, air-cooled barrel was designated the M2 HB ( HB for Heavy Barrel ). The added mass and surface area of
10205-509: The M2 Browning, i.e. they would fire continuously at suspected points of ambush while moving through areas still containing enemy forces. One vehicle would fire exclusively to the right, the following vehicle to the left, the next one to the right, and so on in order to cover both flanks of the advancing convoy. Besides vehicle-mounted weapons, the heavy weapons companies in a World War II U.S. Army infantry battalion or regiment were each issued one M2 Browning with tripod (ground) mount. Mounted on
10362-527: The M2 in a ground role, exposing him to return fire. Units in the field often modified the mountings on their vehicles, especially tanks and tank destroyers, to provide more operator protection in the anti-vehicular and anti-personnel role. The weapon was particularly hated by the Germans, whose attacks and ambushes against otherwise helpless stalled motor convoys were frequently broken up by .50 caliber machine gun fire. Vehicles would frequently "recon by fire" with
10519-492: The M2 serves as an infantry crew-served heavy machine gun, as a remote-controlled external coaxial gun on Merkava main battle tanks , as the main weapon on the Samson RCWS , and as a secondary weapon on Israeli Sea Corps gunboats and missile boats . Nigerian troops have extensively deployed the 50 caliber Browning, mounted on Otokar Cobra APCs, Panhard VBL M11s and Landcruiser gun-trucks in counterinsurgency operations in
10676-399: The M2 was the only adjustable headspace weapon in the U.S. inventory. With rising reports of injuries from improperly headspaced weapons, the U.S. military held a competition for a quick change barrel conversion kit with fixed timing and headspace in 1997. Three companies offered kits and Saco Defense won the competition. However, funding was lost before the design could be fully evaluated and
10833-456: The M903 SLAP (Saboted Light Armor Penetrator) round can perforate 1.34 inches (34 mm) of FHA (face-hardened steel plate) at 500 metres (550 yd), 0.91 inches (23 mm) at 1,200 metres (1,300 yd), and 0.75 inches (19 mm) at 1,500 metres (1,600 yd). This is achieved by using a 0.30-inch-diameter (7.6 mm) tungsten penetrator. The SLAP-T adds a tracer charge to the base of
10990-623: The Military Assistance Command, South Vietnamese forces, or parties in the continental United States, by March 1971. However, some Aircats remained in US service until 1972. Following their service in Vietnam, Aircats were either transferred to other militaries or to civilian use. Starting in 1969, the US Army began to transfer Aircats to the South Vietnamese Army (ARVN). US forces began training ARVN troops to operate Aircats soon after
11147-616: The Niger Delta, N.E Nigeria, the Jos Plateau, and in Mali. The M2 machine gun has also been used as a long-range sniper rifle when equipped with a high-powered telescopic sight . Soldiers during the Korean War used scoped M2s in the role of a sniper rifle, but the practice was most notably used by US Marine Corps sniper Carlos Hathcock during the Vietnam War. Using an Unertl telescopic sight and
11304-748: The US and South Vietnamese militaries disagreed, however. In spring of 1964, US Special Forces advisers to ARVN forces in South Vietnam expressed a need for fast, shallow-draft boats. In response, the Commander of the Military Assistance Command in Vietnam , ( COMUSMACV ) stated an operational requirement in June 1964 for shallow-draft boats capable of carrying 4-5 troops plus crew-served weapons that could negotiate aquatic plants and other obstacles abundant in marshes and rice paddies at speeds of at least 20 miles per hour (32 km/h). The Commander-in-Chief of
11461-791: The United States, where they have found use in 28 countries around the world. Outside the United States, Aircats have been used by civilians to transport lumberjacks in Pakistan , bring sick people to missionary clinics in East Pakistan (modern Bangladesh ), control weeds on the Panama Canal , herd livestock in Venezuela , and transport animal specimens in Colombia . References Bibliography M2 Browning machine gun The M2 machine gun or Browning .50 caliber machine gun (informally, " Ma Deuce ")
11618-468: The Viet Cong" and turned the flood season into a tactical advantage for US forces. The use of Aircats, increases in troop strength, and introduction of other tactics allowed the 5th Special Forces Group to take the fight to the VC and capture territory in the Delta, helping to make the 50% of territory and CIDG bases that were previously too overrun with Viet Cong to enter safe enough to operate in. It also helped
11775-437: The ability to be fired from an electrically operated remote-mount solenoid trigger when installed as a fixed gun. Cooled by the aircraft's slip-stream, the air-cooled 12.7 mm AN/M2 was fitted with a substantially lighter 36-inch (91 cm) length barrel, reducing the weight of the complete unit to 61 pounds (28 kg), which also had the effect of increasing the rate of fire. The full official designation for this weapon
11932-652: The absolute angular velocity of the rotating frame is ω then the derivative d P /d t of P with respect to the stationary frame is related to [d P /d t ] by the equation: d P d t = [ d P d t ] + ω × P , {\displaystyle {\frac {\mathrm {d} {\boldsymbol {P}}}{\mathrm {d} t}}=\left[{\frac {\mathrm {d} {\boldsymbol {P}}}{\mathrm {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {P}}\ ,} where × {\displaystyle \times } denotes
12089-502: The absolute acceleration d 2 r d t 2 {\displaystyle {\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}} . Therefore, the observer perceives the extra terms as contributions due to fictitious forces. These terms in the apparent acceleration are independent of mass; so it appears that each of these fictitious forces, like gravity, pulls on an object in proportion to its mass. When these forces are added,
12246-3224: The absolute acceleration of the particle can be written as: a = d 2 r d t 2 = d d t d r d t = d d t ( [ d r d t ] + ω × r ) = [ d 2 r d t 2 ] + ω × [ d r d t ] + d ω d t × r + ω × d r d t = [ d 2 r d t 2 ] + ω × [ d r d t ] + d ω d t × r + ω × ( [ d r d t ] + ω × r ) = [ d 2 r d t 2 ] + d ω d t × r + 2 ω × [ d r d t ] + ω × ( ω × r ) . {\displaystyle {\begin{aligned}{\boldsymbol {a}}&={\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}={\frac {\mathrm {d} }{\mathrm {d} t}}{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}={\frac {\mathrm {d} }{\mathrm {d} t}}\left(\left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times {\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\\&=\left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times \left(\left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]+{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}+2{\boldsymbol {\omega }}\times \left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})\ .\end{aligned}}} The apparent acceleration in
12403-660: The action fully. The adapter is very distinctive, attaching to the muzzle with three rods extending back to the base. The BFA can often be seen on M2s during peacetime operations. The M2 .50 Browning machine gun has been used for various roles: At the outbreak of the Second World War, the United States had versions of the M2 in service as fixed aircraft guns, anti-aircraft defensive guns (on aircraft, ships, or boats), infantry (tripod-mounted) guns, and as dual purpose anti-aircraft and anti-vehicular weapons on vehicles. The .50 AN/M2 light-barrel aircraft Browning used in planes had
12560-507: The aircraft (AN/M2) version of the gun, while beam/waist-mounted and turret-mounted Brownings were used later in the war in such aircraft as the Short Sunderland and Lancaster bomber . After World War II, the .50 Browning continued to see action in Korea and other theaters, in aircraft, tripod (ground), ground AA (hip-ring), and vehicle mounts. One of its most notable actions in a ground role
12717-494: The airliner, to the surface of the Earth, or even to the Sun. A reference frame that is at rest (or one that moves with no rotation and at constant velocity) relative to the " fixed stars " is generally taken to be an inertial frame. Any system can be analyzed in an inertial frame (and so with no centrifugal force). However, it is often more convenient to describe a rotating system by using a rotating frame—the calculations are simpler, and descriptions more intuitive. When this choice
12874-719: The ammunition fed only from the left side. Service trials raised doubts about whether the guns would be suitable for aircraft or for anti-aircraft use. A heavy barrel M1921 was considered for ground vehicles. John M. Browning died in 1926. Between 1927 and 1932, S.H. Green studied the design problems of the M1921 and the needs of the armed services. The result was a single receiver design that could be turned into seven types of .50 caliber machine guns by using different jackets, barrels, and other components. The new receiver allowed right or left side feed. In 1933, Colt manufactured several prototype Browning machine guns (including what would be known as
13031-464: The ammunition. This ammunition was type classified in 1993. When firing blanks, a large blank-firing adapter (BFA) of a special type must be used to allow the recoil-operated action to cycle. This functions on the principle of a recoil booster , to increase the recoil force acting on the short recoil action. This is the exact antithesis of a muzzle brake . Without this adaptor, the reduced-charge blank cartridge would develop too little recoil to cycle
13188-429: The axis of rotation of the frame, the centrifugal force vanishes for objects that lie upon the axis. Three scenarios were suggested by Newton to answer the question of whether the absolute rotation of a local frame can be detected; that is, if an observer can decide whether an observed object is rotating or if the observer is rotating. In these scenarios, the effects attributed to centrifugal force are only observed in
13345-509: The balance between containment by gravitational attraction and dispersal by centrifugal force. That the Earth is itself an oblate spheroid, bulging at the equator where the radial distance and hence the centrifugal force is larger, is taken as one of the evidences for its absolute rotation. The operations of numerous common rotating mechanical systems are most easily conceptualized in terms of centrifugal force. For example: Nevertheless, all of these systems can also be described without requiring
13502-592: The boat's introduction in 1964, and ARVN troops began crewing Aircats as early as 1967. In addition to regular ARVN troops, civilian irregulars crewed Aircats. These irregulars were paid by the South Vietnamese government to perform counterinsurgency and patrol missions along the Mekong River, especially in the Mekong Delta and surrounding area. These irregulars included forces from the Civilian Irregular Defense Group (CIDG) and Nung militiamen from
13659-630: The boats enabled the Aircats to occasionally be highly stealthy and suitable for operations like surprise attacks, special operations insertions, and reconnaissance. In August 1970, the 5th Special Forces Group reported to the Military Assistance Command in Vietnam that its Aircats were "excess", indicating that they wanted to dispose of them, as a response to decreased operational requirements caused by President Richard Nixon 's Vietnamization policy. The 5th Special Forces Group began turning in its Aircats in December 1970 and finished transferring its Aircats to
13816-488: The body in curved motion. This reaction force is sometimes described as a centrifugal inertial reaction , that is, a force that is centrifugally directed, which is a reactive force equal and opposite to the centripetal force that is curving the path of the mass. The concept of the reactive centrifugal force is sometimes used in mechanics and engineering. It is sometimes referred to as just centrifugal force rather than as reactive centrifugal force although this usage
13973-529: The bolt release can be unlocked into the up position resulting in single-shot firing (the gunner must press the bolt latch release to send the bolt forward). Unlike virtually all other modern machine guns, it has no safety (although a sliding safety switch has recently been fielded to USMC armorers for installation on their weapons and is standard-issue for the U.S. Army for all M2s). Troops in the field have been known to add an improvised safety measure against accidental firing by slipping an expended shell casing under
14130-407: The bolt release in the center. The spade handles are gripped and the butterfly trigger is depressed with one or both thumbs. Recently, new rear buffer assemblies have used squeeze triggers mounted to the handgrips, doing away with the butterfly triggers. When the bolt release is locked down by the bolt latch release lock on the buffer tube sleeve, the gun functions in fully automatic mode. Conversely,
14287-408: The bore within a few thousand rounds, necessitating replacement. In addition to full automatic, the M2HB can be selected to fire single shots, fire slowly at less than 40 rounds per minute, or fire rapidly for more than 40 rounds per minute. Slow and rapid firing modes use 5–7 round bursts with different lengths of pause between bursts. The M2 has an effective range of 1,830 metres (2,000 yd) and
14444-472: The butterfly trigger. The upgraded M2A1 has a manual trigger block safety. Because the M2 was designed to operate in many configurations, it can be adapted to feed from the left or right side of the weapon by exchanging the belt-holding pawls, and the front and rear cartridge stops (three-piece set to include link stripper), then reversing the bolt switch. The operator must also convert the top-cover belt feed slide assembly from left to right-hand feed as well as
14601-542: The canals, streams, swamps, and rivers abundant in Vietnam, particularly in the Mekong River delta . The boats used by US forces prior to the Aircat's 1964 introduction relied on screw-propellers, which would become fouled by aquatic plants and thus rendered useless. US forces sometimes used paddled sampans to avoid this problem, although these sampans had the same speed as the VC ones and so were unable to effectively pursue and defeat them. Because US boats had trouble navigating
14758-420: The car enters a curve that bends to the left, the passenger experiences an apparent force that seems to be pulling them towards the right. This is the fictitious centrifugal force. It is needed within the passengers' local frame of reference to explain their sudden tendency to start accelerating to the right relative to the car—a tendency which they must resist by applying a rightward force to the car (for instance,
14915-410: The cartridge in the chamber. The round can be too tight in the chamber and the gun would not fire, or be too loose in the chamber, resulting in a stoppage or ruptured cartridge. The other dimension that could not be held closely enough was when the firing pin would fall. The solution to these problems was adjustable timing and headspace ("Timing" is the adjustment of the gun so that firing takes place when
15072-405: The concept of centrifugal force, in terms of motions and forces in a stationary frame, at the cost of taking somewhat more care in the consideration of forces and motions within the system. While the majority of the scientific literature uses the term centrifugal force to refer to the particular fictitious force that arises in rotating frames, there are a few limited instances in the literature of
15229-528: The conflict. The larger rounds were needed to pierce the armor that was being introduced to the battlefield, both on the ground and in the air. Germany introduced the Junkers J.I aircraft, whose armor could render ineffective aircraft machine guns that used conventional rifle ammunition such as the .30-06. Consequently, the American Expeditionary Force 's commander General John J. Pershing asked for
15386-564: The end of World War II. The M2 Heavy Barrel, M48 Turret Type was developed for the commander's cupola on the M48 Patton tank. The cupola mount on the M48A2 and M48A3 was thoroughly disliked by most tankers, as it proved unreliable in service. An externally mounted M2 was later adopted for the commander's position on the M1 Abrams tanks. Three subvariants were also developed for use by the U.S. Navy on
15543-455: The engine block or fuel tanks of a German Bf 109 fighter attacking at low altitude, or perforate the hull plates and fuel tanks of a German half-track or light armored car . It could even penetrate the sides and rear of the Panzer I , Panzer II , Panzer III , and Panzer IV tanks. While the dual-purpose mounting was undeniably useful, it did normally require the operator to stand when using
15700-1212: The equation of motion has the form: F + ( − m d ω d t × r ) ⏟ Euler + ( − 2 m ω × [ d r d t ] ) ⏟ Coriolis + ( − m ω × ( ω × r ) ) ⏟ centrifugal = m [ d 2 r d t 2 ] . {\displaystyle {\boldsymbol {F}}+\underbrace {\left(-m{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}\right)} _{\text{Euler}}+\underbrace {\left(-2m{\boldsymbol {\omega }}\times \left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]\right)} _{\text{Coriolis}}+\underbrace {\left(-m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})\right)} _{\text{centrifugal}}=m\left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]\ .} From
15857-572: The fact that the individual M2HB's rate of fire (450–550 rounds per minute) was low for an effective anti-aircraft weapon. Towards the end of the war, as Luftwaffe attacks became less frequent, the quad .50 (nicknamed the Meat Chopper or Krautmower ) was increasingly used in an anti-personnel role, similarly to the earlier-introduced (1940) and more powerful—but much more difficult to keep well-fed with ammunition when in action—German 20 mm Flakvierling . Snipers firing from trees were engaged by
16014-408: The forces be zero to match the apparent lack of acceleration. Note: In fact, the observed weight difference is more — about 0.53%. Earth's gravity is a bit stronger at the poles than at the equator, because the Earth is not a perfect sphere , so an object at the poles is slightly closer to the center of the Earth than one at the equator; this effect combines with the centrifugal force to produce
16171-457: The frame. This is the centrifugal force. As humans usually experience centrifugal force from within the rotating reference frame, e.g. on a merry-go-round or vehicle, this is much more well-known than centripetal force. Motion relative to a rotating frame results in another fictitious force: the Coriolis force . If the rate of rotation of the frame changes, a third fictitious force (the Euler force )
16328-682: The gunships would locate and engage the enemy while the Aircats would use their speed and maneuverability to seal off escape routes. The Aircat was also valuable to special forces because it could be easily transported by Chinook helicopter , allowing for flexible operations across southern Vietnam . In addition to special warfare use, Aircats were used by the South Vietnamese government for transporting important officials and by Vietnamese police forces for inspecting fishing boats. Crew sizes varied greatly by mission. The Aircat could carry as many as 12, although it generally carried no more than six. Crew sizes were reduced to an average of 5–6 in response to
16485-450: The heavier .50 caliber (12.7 mm) M2HB machine gun to increase the boat's firepower, though the M2HB often proved too powerful for the flimsy vessel. While the gunner fired, the pilot had to pull forward to offset the gun's recoil or risk the boat being blown about or even capsized. The 57mm M18 recoilless rifle was test fired from an Aircat and proved impractical owing to its extensive back blast . The 106mm M40 recoilless rifle
16642-499: The heavy barrel compensated somewhat for the loss of water-cooling, while reducing bulk and weight: the M2 weighs 121 lb (55 kg) with a water jacket, but the M2 HB weighs 84 lb (38 kg). Due to the long procedure for changing the barrel, an improved system was developed called QCB (quick change barrel). The lightweight "Army/Navy" prefixed AN/M2 "light-barrel" version of the Browning M2 weighing 60 pounds (27 kg)
16799-544: The introduction is Browning Machine Gun, Cal. .50, M2, with others as described below. The development of the M1921 water-cooled machine gun which led to the M2, meant that the initial M2s were, in fact, water-cooled. These weapons were designated Browning Machine Gun, Cal. .50, M2, Water-Cooled, Flexible. There was no fixed water-cooled version. Improved air-cooled heavy barrel versions came in three subtypes. The basic infantry model, Browning Machine Gun, Cal. .50, M2, HB, Flexible,
16956-449: The local " gravity " at any point on the Earth's surface is actually a combination of gravitational and centrifugal forces. However, the fictitious forces can be of arbitrary size. For example, in an Earth-bound reference system (where the earth is represented as stationary), the fictitious force (the net of Coriolis and centrifugal forces) is enormous and is responsible for the Sun orbiting around
17113-405: The local frame (the frame in which the object is stationary) if the object is undergoing absolute rotation relative to an inertial frame. By contrast, in an inertial frame, the observed effects arise as a consequence of the inertia and the known forces without the need to introduce a centrifugal force. Based on this argument, the privileged frame, wherein the laws of physics take on the simplest form,
17270-409: The longest confirmed kill at 2,250 metres (2,460 yd), a record which stood until 2002, when it was broken in Afghanistan by Canadian Army sniper Arron Perry . Licensed historic production: Current production (2023): The basic M2 was deployed in U.S. service in a number of subvariants, all with separate complete designations as per the US Army system. The basic designation as mentioned in
17427-436: The lower cockpit sides, and two more if the forward dorsal turret's pair of M2 guns were also aimed straight forward. The later A-26 bested this with up to a maximum of 16/18 machine guns, 8 in the nose, four more per wing in flush-mount pods, plus 2 guns in the dorsal turret. In the dual-purpose vehicle mount, the M2HB proved extremely effective in U.S. service: the Browning's .50 caliber AP and API rounds could easily penetrate
17584-403: The model. The M2HB air-cooled ground gun has a cyclical rate of 450–575 rounds per minute. The early M2 water-cooled AA guns had a cyclical rate of around 450–600 rpm. The AN/M2 aircraft gun has a cyclic rate of 750–850 rpm; this increases to 1,200 rpm for AN/M3 aircraft guns. These maximum rates of fire are generally not achieved in use, as sustained fire at that rate will wear out
17741-477: The motion is described in terms of generalized forces , using in place of Newton's laws the Euler–;Lagrange equations . Among the generalized forces, those involving the square of the time derivatives {(d q k ⁄ d t ) } are sometimes called centrifugal forces. In the case of motion in a central potential the Lagrangian centrifugal force has the same form as the fictitious centrifugal force derived in
17898-561: The number of military Aircats that ended up being transferred to civilians is difficult because Hurricane produced several civilian versions of the Aircat alongside the military model. Between the military and civilian models, over 800 Aircats were built. Some civilian Aircats are still in use today. Aircats are used widely for wildlife monitoring, biological sampling, and other activities in marshy wildlife preserves, especially in National Wildlife Refuges where they are operated by
18055-401: The object's local frame (the frame where the object is stationary) only if the frame were rotating with respect to absolute space. Around 1883, Mach's principle was proposed where, instead of absolute rotation, the motion of the distant stars relative to the local inertial frame gives rise through some (hypothetical) physical law to the centrifugal force and other inertia effects. Today's view
18212-449: The observed weight difference. For the following formalism, the rotating frame of reference is regarded as a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame denoted the stationary frame. In a rotating frame of reference, the time derivatives of any vector function P of time—such as the velocity and acceleration vectors of an object—will differ from its time derivatives in
18369-500: The other two fictitious forces, the centrifugal force always points radially outward from the axis of rotation of the rotating frame, with magnitude m ω 2 r ⊥ {\displaystyle m\omega ^{2}r_{\perp }} , where r ⊥ {\displaystyle r_{\perp }} is the component of the position vector perpendicular to ω {\displaystyle {\boldsymbol {\omega }}} , and unlike
18526-410: The particle, given by: a = d 2 r d t 2 , {\displaystyle {\boldsymbol {a}}={\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\ ,} where r is the position vector of the particle (not to be confused with radius, as used above.) By applying the transformation above from the stationary to
18683-491: The perspective of the rotating frame, the additional force terms are experienced just like the real external forces and contribute to the apparent acceleration. The additional terms on the force side of the equation can be recognized as, reading from left to right, the Euler force − m d ω / d t × r {\displaystyle -m\mathrm {d} {\boldsymbol {\omega }}/\mathrm {d} t\times {\boldsymbol {r}}} ,
18840-546: The program ended. In 2007, the military found money to start a new competition. Saco Defense had since been acquired by General Dynamics , which won the competition. On 15 October 2010, the M2A1 heavy machine gun was type classified by the U.S. Army. Formerly known as the M2E2, the M2A1 incorporates improvements to the design including a quick change barrel (QCB) with a removable carrying handle,
18997-525: The quad gunner at trunk level; the weapon would cut down and destroy the entire tree, and the sniper with it. The M45 Quadmount was still in use during the Vietnam War. The Commonwealth use of the M2 Browning .50 caliber machine gun (known as the .5 Browning in British and Commonwealth service) began in World War II, though from 1942 it was standard armament on US-built AFVs provided under lend-lease such as
19154-465: The rate of rotation and is directed along the axis of rotation according to the right-hand rule . Newton's law of motion for a particle of mass m written in vector form is: F = m a , {\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}\ ,} where F is the vector sum of the physical forces applied to the particle and a is the absolute acceleration (that is, acceleration in an inertial frame) of
19311-407: The receiver in order to have quick installation of various optics. The original M2HB tripod and parts can be used on the CS/LM6. When the M2 was first being designed, John Browning faced two design challenges. With the machine tools available at that time, the dimensions that established the location of the bolt face and the depth of the chamber could not be held tightly enough to control the fit of
19468-418: The recoiling parts are in the correct position for firing; "headspace" is the distance between the face of the bolt and the base of the cartridge case, fully seated in the chamber); the operator had to screw the barrel into the barrel extension, moving the barrel toward the bolt face to reach the proper headspace with simple gauges to allow the operator to adjust to the proper dimensions. By the late 20th century,
19625-424: The rotating frame is [ d 2 r d t 2 ] {\displaystyle \left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]} . An observer unaware of the rotation would expect this to be zero in the absence of outside forces. However, Newton's laws of motion apply only in the inertial frame and describe dynamics in terms of
19782-431: The rotating frame three times (twice to d r d t {\textstyle {\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}} and once to d d t [ d r d t ] {\textstyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]} ),
19939-428: The six original Aircats deployed, one was lost to an accident and the remaining five required considerable engine repair to remain in service by 1965. Another downside was that Aircats could be very loud. The high noise level of the engine and propeller could give away the boats' position. It also made use of radio equipment difficult while the vehicle was in motion, as it was difficult for crews to hear their radios over
20096-482: The sound of the engine. However, the Aircat's noise was found to be both an advantage and a disadvantage, as it was often impossible for enemies to determine how many Aircats were bearing down on them or from where, especially if the boats were used alongside similarly loud helicopters. The high noise level also contributed to the psychological warfare value of the Aircat, and small groups of Viet Cong would freeze in place when attacked by Aircats. Similarly, field tests by
20253-432: The spring and plunger in the feed arm. This will take a well-trained individual less than two minutes to perform. The charging assembly may be changed from left to right-hand charge. A right-hand charging handle spring, lock wire, and a little "know-how" are all that is required to accomplish this. The M2 can be battle-ready and easily interchanged if it is preemptively fitted with a retracting slide assembly on both sides of
20410-399: The spring is reflected on the scale as less weight — about 0.3% less at the equator than at the poles. In the Earth reference frame (in which the object being weighed is at rest), the object does not appear to be accelerating; however, the two real forces, gravity and the force from the spring, are the same magnitude and do not balance. The centrifugal force must be included to make the sum of
20567-433: The stationary frame. If P 1 P 2 , P 3 are the components of P with respect to unit vectors i , j , k directed along the axes of the rotating frame (i.e. P = P 1 i + P 2 j + P 3 k ), then the first time derivative [d P /d t ] of P with respect to the rotating frame is, by definition, d P 1 /d t i + d P 2 /d t j + d P 3 /d t k . If
20724-413: The stone in the horizontal plane which acts toward the center. In an inertial frame of reference , were it not for this net force acting on the stone, the stone would travel in a straight line, according to Newton's first law of motion . In order to keep the stone moving in a circular path, a centripetal force , in this case provided by the string, must be continuously applied to the stone. As soon as it
20881-443: The string is still acting on the stone. If one were to apply Newton's laws in their usual (inertial frame) form, one would conclude that the stone should accelerate in the direction of the net applied force—towards the axis of rotation—which it does not do. The centrifugal force and other fictitious forces must be included along with the real forces in order to apply Newton's laws of motion in the rotating frame. The Earth constitutes
21038-609: The targets. Any engine maintenance required bringing in scarce aircraft mechanics. As ACTIV wrote, "Even the most elementary engine repair work required the attention of a skilled mechanic." Though US and South Vietnamese forces had fiberglass-repair capabilities at the unit level, they lacked the ability to do extensive electrical or engine repair, which was often required because the Aircats were initially built with commercial off-the-shelf electrical and drive system components that did not hold up well in Southeast Asian conditions. Of
21195-477: The term applied to other distinct physical concepts. One of these instances occurs in Lagrangian mechanics . Lagrangian mechanics formulates mechanics in terms of generalized coordinates { q k }, which can be as simple as the usual polar coordinates ( r , θ ) {\displaystyle (r,\ \theta )} or a much more extensive list of variables. Within this formulation
21352-524: The waters of the Mekong Delta, the region quickly became home to many Viet Cong strongholds and logistics bases. In 1961, the US Navy brought airboats and pump-jet boats, neither of which rely on propellers in the water, to Vietnam at the behest of ARVN for testing. The Navy found that airboats outperformed pump-jets and screw-propeller boats in all respects except noise, although they concluded that airboats' noise made them unacceptable for use in counterinsurgency operations. Army special forces and others in
21509-466: The weapon system. This eliminates the need to have the weapon removed from service to accomplish this task. At some point during World War II, the Frankford Arsenal developed a squeeze bore version of the M2HB which reduced the bullet size from .50 to .30 caliber. There are several different types of ammunition used in the M2HB and AN aircraft guns. From World War II through the Vietnam War ,
21666-463: The weapon. Since Finland was already producing 12.7 mm ammunition, the Finnish variant was rechambered to 12.7 mm (.50 BMG). The Finnish variant was designated VKT 12,70 LKk/42 and was produced by Finland. The M2 machine gun was widely used during World War II, and in later postwar conflicts, as a remote or flexible aircraft gun. For fixed (offensive) or flexible (defensive) guns used in aircraft,
21823-404: Was "Browning Machine Gun, Aircraft, Cal. .50, AN/M2" (Fixed) or (Flexible). The 12.7 mm AN/M2 was used on many aircraft during WWII , as it served as the main aircraft armament in the US military. Most US fighter aircraft were armed with four, six or eight AN/M2 MGs mounted in the wings. Some examples being the Curtiss P-40 , Republic P-47 Thunderbolt , and North American P-51 Mustang for
21980-491: Was also developed, and became the standard .50-caliber aviation machine gun of the World War II–era for American military aircraft of nearly every type, readily replacing Browning's own air-cooled .30 caliber machine gun design in nearly all American aircraft installations. The Browning M2 is an air-cooled , belt-fed machine gun. The M2 fires from a closed bolt , operated on the short recoil principle. The M2 fires
22137-465: Was also modified to defend against the piano wire traps by welding a large piece of iron to the gun mount that would protect the Aircat crew from the wire. The Aircat's hull was durable otherwise: it withstood ordinary damage and cross-country travel easily. It was also much sturdier than the wooden sampans used by the enemy Viet Cong; Aircats used ramming attacks against sampans to great effect. In one November 1965 battle involving three Aircats battling
22294-788: Was completed in March 2017, with 3,600 M2A1s planned to be fielded by the Marines in total. The Israel Defense Forces adopted the M2-HQCB (the commercial version of the M2A1) in 2012 as a replacement to the M2HB. One derivative of the M2 Browning is the Mitrailleuse d´Avion Browning - F.N. Calibre 13,2 mm , more commonly known as the FN Browning M.1939. The FN Browning M.1939 was a heavily modified M2 Browning for aircraft use designed by FN Herstal for export. Their aim
22451-413: Was designed for this gun. It was of a high explosive type and was designed to take down a small aircraft with a single hit. Tests showed that it was very effective against both cloth and aluminum skinned aircraft. Due to the aforementioned improvements, the gun received interest from numerous nations when it entered the export market in 1939. Due to the start of World War 2 and the invasion of Belgium it
22608-445: Was especially noteworthy for its use of Aircats, operating 84 of the vessels in the Mekong Delta beginning in early 1967. Colonel Francis J. Kelly, commander of the 5th Special Forces Group from June 1966 to June 1967 and author of a book about US Army Special Forces in Vietnam, praised the Aircat for its "speed and firepower," writing that once tactics adjusted to employ the Aircat to maximum effect, Aircats enabled "telling victories over
22765-464: Was exported to only Romania and Sweden . Sweden was able to buy the majority of the weapons along with the blueprints to produce the weapon on their own without paying for a license. In Sweden, the weapon received the designation Automatkanon m/39, short Akan m/39, meaning Autocannon m/39 and was later produced by Ericsson as the Akan m/39A. Sweden also gave the blueprints to Finland so they could produce
22922-406: Was fired off to the side to avoid exposing crew to the back blast. The Aircat enabled bringing the weapon over “terrain where normally a heavy crew served weapon could not be used”. The Aircat was equipped with an AN/PRC-25 radio for short-range communication. The AN/PRC-25 posed challenges because of the difficulty hearing the radio over the engine noise and the fragility long antennas, which took
23079-436: Was heavy, difficult to control, fired too slowly for the anti-personnel role, and was not powerful enough against armor. While the .50-caliber was being developed, some 13.2×92mmSR Mauser 1918 T-Gewehr anti-tank rifles and its ammunition were captured. The 13.2 mm German rounds had a muzzle velocity of 2,700 ft/s (820 m/s), an 800 gr (52 g) bullet, and could penetrate armor 1 in (25 mm) thick at
23236-431: Was important for US Special Forces because they were able to outrun and outmaneuver most enemy vessels. As such, the craft was used widely by special forces for pursuing and assaulting Viet Cong units in flooded areas in the Mekong Delta. That said, the Aircat's speed and maneuverability could also be a disadvantage, as Aircat crews would often get disoriented without constant aerial observation. The 5th Special Forces Group
23393-556: Was in a fierce battle with a nine-man Special Air Service team at the Battle of Mirbat in Oman in July 1972, where the heavy Browning and its API ammunition was used to help repulse an assault by 250 Yemeni Adoo guerrillas, though the more famous weapon from the battle is a 25 pounder gun . The Scots Guards used the weapon in the 1982 Falklands War . A .50 caliber Browning was installed along with
23550-885: Was in allowing American Green Berets to attack previously unassailable Viet Cong (VC) support bases and strongholds in wetlands and swamp forests. Aircats saw combat on many occasions in which they engaged Viet Cong forces, captured enemy documents, weapons, and munitions, and received enemy fire and suffered casualties. The Aircat proved effective at many types of missions: in its 104 missions in 1965, encompassing reconnaissance, flank security, and assaults, it killed 86 VC, destroyed 26 of their boats, and achieved most mission objectives. Aircats were able to clear obstacles that proved insurmountable for other boats. The Aircat could cross 2-foot (0.61 m) high dikes at 20 miles per hour (32 km/h) and there were several examples of US troops encountering obstacles or blockades in other watercraft, such as Swift Boats and river patrol boats , making
23707-516: Was killed during the firefight and was posthumously awarded the Medal of Honor . The M45 Quadmount was a mounting of four .50 M2HB guns with a single gunner situated behind an armored housing. This was used by U.S. anti-air battalions, fitted either on a towed trailer or mounted on a half-track carrier. With 200 rounds per gun in a powered tracking mount, the guns proved very effective against low-flying aircraft. The use of four guns adequately compensated for
23864-519: Was not widely used in the Pacific campaign for several reasons, including the weight of the gun, the nature of infantry jungle combat, and because road intersections were usually easily outflanked. However, it was used by fast-moving motorized forces in the Philippines to destroy Japanese blocking units on the advance to Manila. The quad mount .50 was also used to destroy Japanese emplacements. The M2HB
24021-426: Was powered by a 4-cylinder Lycoming O-360 aircraft engine providing 180 horsepower (130 kW). The engine was hooked up to a 66-inch (1.7 m) diameter aerial propeller. The propeller blades were made from wood and tipped with bronze , which sometimes caused a problem, as three propellers failed during the evaluation period when the wood rotted and the bronze tips were separated by centrifugal force . Steering
24178-450: Was provided by a stick controlling two air rudders aft of the propeller and propeller guard. Counting crew and passengers, the Aircat could carry payloads of up to 2,000 pounds (910 kg). A .30 caliber (7.62 mm) M1919 machine gun was mounted on a pintle mount in the bow. These guns were found to be accurate up to 200 yards (180 m), comparable to the guns of some WWII fighter aircraft. Some crews substituted this gun for
24335-406: Was to make a light, reliable heavy machine gun with the same damage output as a 20 mm autocannon. To achieve this, they raised the firing rate to 1080 rpm and gave it a more powerful cartridge in the form of the 13.2×99mm Hotchkiss . This cartridge was a popular Eurasian analog of .50 BMG developed independently in 1920s with a 13.2 mm bullet (.52 in) and more propellant. A new projectile
24492-499: Was used in Korea and Vietnam, and later in both Operation Desert Storm , the Afghan theater of Operation Enduring Freedom and in Iraq . In 2003, U.S. Army SFC Paul Ray Smith used his M2HB mounted on an M113 armored personnel carrier to kill 20 to 50 enemies who were attacking a U.S. outpost, preventing an aid station from being overrun and allowing wounded soldiers to be evacuated, SFC Smith
24649-495: Was used on airboats “frequently” by the 7th Armored Squadron, 1st Air Cavalry Division , who and “proven very valuable”. Using the 106mm recoilless rifle on an Aircat had little effect on the airboat or on accuracy, but issues arose relating to speed and maneuver (the boat could not attain top speed and was not as maneuverable) and ammunition (only 4 rounds can be carried in the boat with the gun; any additional rounds had to be transferred from other Aircats). The 106mm recoilless rifle
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