Projectile

A projectile is any object thrown into space by the exertion of a force. Although any object in motion through space may be called a projectile, the term more refers to a ranged weapon. Mathematical equations of motion are used to analyze projectile trajectory. An object projected at an angle to the horizontal has both the vertical and horizontal components of velocity; the vertical component of the velocity on the y-axis given as Vy=USin while the horizontal component of the velocity Vx=UCos. There are various terms used in projectiles at specific angle teta 1. Time to reach maximum height, it is symbolized as, the time taken for the projectile to reach the maximum height from the plane of projection. Mathematically, it is give as t=USin/g Where g=acceleration due to gravity U= initial velocity teta= angle made by the projectile with the horizontal axis. 2. Time of flight: this is the total time taken for the projectile to fall back to the same plane from which it was projected. Mathematically it is given as T=2USin/g 3.

Maximum Height: this is the maximum height attained by the projectile OR the maximum displacement on the vertical axis covered by the projectile. It is given as H= U²Sin²/2g 4. Range: The Range of a projectile is the horizontal distance covered by the projectile. Mathematically, R= U²Sin2/g; the Range is maximum when angle teta= 45° I.e Sin2=1. Blowguns and pneumatic rifles use compressed gases, while most other guns and cannons utilize expanding gases liberated by sudden chemical reactions. Light-gas guns use a combination of these mechanisms. Railguns utilize electromagnetic fields to provide a constant acceleration along the entire length of the device increasing the muzzle velocity; some projectiles provide propulsion during flight by means of a rocket jet engine. In military terminology, a rocket is unguided. Note the two meanings of "rocket": an ICBM is a guided missile with a rocket engine. An explosion, whether or not by a weapon, causes the debris to act as multiple high velocity projectiles.

An explosive weapon, or device may be designed to produce many high velocity projectiles by the break-up of its casing, these are termed fragments. Many projectiles, e.g. shells, may carry an explosive charge or another chemical or biological substance. Aside from explosive payload, a projectile can be designed to cause special damage, e.g. fire, or poisoning. In projectile motion the most important force applied to the ‘projectile’ is the propelling force, in this case the propelling forces are the muscles that act upon the ball to make it move, the stronger the force applied, the more propelling force, which means the projectile will travel farther. See pitching, bowling. A projectile that does not contain an explosive charge or any other kind of payload is termed a kinetic projectile, kinetic energy weapon, kinetic energy warhead, kinetic warhead or kinetic penetrator. Typical kinetic energy weapons are blunt projectiles such as rocks and round shots, pointed ones such as arrows, somewhat pointed ones such as bullets.

Among projectiles that do not contain explosives are those launched from railguns and mass drivers, as well as kinetic energy penetrators. All of these weapons work by attaining a high muzzle velocity, or initial velocity up to, collide with their targets, converting their kinetic energy into destructive shock waves and heat. Other types of kinetic weapons are accelerated over time by gravity. In either case, it is the kinetic energy of the projectile; some kinetic weapons for targeting objects in spaceflight are anti-satellite weapons and anti-ballistic missiles. Since in order to reach an object in orbit it is necessary to attain an high velocity, their released kinetic energy alone is enough to destroy their target. For example: the energy of TNT is 4.6 MJ/kg, the energy of a kinetic kill vehicle with a closing speed of 10 km/s is of 50 MJ/kg. This saves costly weight and there is no detonation to be timed; this method, requires direct contact with the target, which requires a more accurate trajectory.

Some hit-to-kill warheads are additionally equipped with an explosive directional warhead to enhance the kill probability. With regard to anti-missile weapons, the Arrow missile and MIM-104 Patriot PAC-2 have explosives, while the Kinetic Energy Interceptor, Lightweight Exo-Atmospheric Projectile, THAAD do not. A kinetic projectile can be dropped from aircraft; this is applied by replacing the explosives of a regular bomb with a non-explosive material, for a precision hit with less collateral damage. A typical bomb has a speed of impact of 800 km/h, it is applied for training the act of dropping a bomb with explosives. This method has been used in Operation Iraqi Freedom and the subsequent military operations in Iraq by mating concrete-filled training bombs with JDAM GPS guidance kits, to attack vehicles and other "soft" targets located too close to civilian structures for the use of conventional high explosive bombs. A Prompt Global Strike may use a kinetic weapon. A kinetic bombardment may involve a projectile dropped from Earth orbit.

A hypothetical kinetic weapon that travels at a significant fraction of the speed of light found in science fiction, is termed a relativistic kill vehicle (RKV

Sabot

A sabot is a structural device used in firearm or cannon ammunition to keep a sub-caliber flight projectile, such as a small bullet or arrow-type projectile, in the center of the barrel when fired, if the bullet has a smaller diameter than the bore diameter of the weapon used. The sabot component in projectile design is more than the thin and deformable seal known as a driving band or obturation ring needed to trap propellant gases behind a projectile, keep the projectile centered in the barrel, when the outer shell of the projectile is only smaller in diameter than the caliber of the barrel. Driving bands and obturators are used to seal these full-bore projectiles in the barrel because of manufacturing tolerances. Driving bands and obturator rings are made from material that will deform and seal the barrel as the projectile is forced from the chamber into the barrel. Small caliber jacketed bullets do not employ driving bands or obturators because the jacket material, for example copper or gilding metal, is deformable enough to serve that function, the bullet is made larger than the barrel for that purpose.

Sabots use driving bands and obturators, because the same manufacturing tolerance issues exist when sealing the saboted projectile in the barrel, but the sabot itself is a more substantial structural component of the in-bore projectile configuration. Refer to the two APFSDS pictures on the right to see the substantial material nature of a sabot to fill the bore diameter around the sub-caliber arrow-type flight projectile, compared to the small gap sealed by a driving band or obturator to mitigate what is known classically as windage. More detailed cutaways of the internal structural complexity of advanced APFSDS saboted long rod penetrator projectiles can be found at reference 2; the function of a sabot is to provide a larger bulkhead structure that fills the entire bore area between an intentionally designed sub-caliber flight projectile and the barrel, giving a larger surface area for propellant gasses to act upon than just the base of the smaller flight projectile. Efficient aerodynamic design of a flight projectile does not always accommodate efficient interior ballistic design to achieve high muzzle velocity.

This is true for arrow-type projectiles, which are long and thin for low drag efficiency, but too thin to shoot from a gun barrel of equal diameter to achieve high muzzle velocity. The physics of interior ballistics demonstrates why the use of a sabot is advantageous to achieve higher muzzle velocity with an arrow-type projectile. Propellant gasses generate high pressure, the larger the base area that pressure acts upon the greater the net force on that surface. Force, pressure times area, provides an acceleration to the mass of the projectile. Therefore, for a given pressure and barrel diameter, a lighter projectile can be driven from a barrel to a higher muzzle velocity than a heavier projectile. However, a lighter projectile may not fit in the barrel. To make up this difference in diameter, a properly designed sabot provides less parasitic mass than if the flight projectile were made full-bore, in particular providing dramatic improvement in muzzle velocity for APDS and APFSDS ammunition.

Seminal research on two important sabot configurations for long rod penetrators used in APFSDS ammunition, namely the "saddle-back" and "double-ramp" sabot was performed by the US Army Ballistics Research Laboratory during the development and improvement of modern 105mm and 120mm kinetic energy APFSDS penetrators, permitted by the significant recent advancement in the computerized Finite element method in structural mechanics at that time. Upon muzzle exit, the sabot is discarded, the smaller flight projectile flies to the target with less drag resistance than a full-bore projectile. In this manner high velocity and slender, low drag projectiles can be fired more efficiently; the weight of the sabot represents parasitic mass that must be accelerated to muzzle velocity, but does not contribute to the terminal ballistics of the flight projectile. For this reason, great emphasis is placed on selecting strong yet lightweight structural materials for the sabot, configuring the sabot geometry to efficiently employ these parasitic materials at minimum weight penalty.

The purpose of the sabot is to allow a smaller diameter flight projectile to be launched at greater muzzle velocity than if the flight projectile alone were fired from a gun of equal caliber. Firing a smaller-sized projectile wrapped in a sabot raises the muzzle velocity of the projectile. Made of some lightweight material; the sabot consists of several longitudinal pieces held in place by the cart

Euler angles

The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They can represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra. Any orientation can be achieved by composing three elemental rotations, i.e. rotations about the axes of a coordinate system. Euler angles can be defined by three of these rotations, they can be defined by elemental geometry and the geometrical definition demonstrates that three rotations are always sufficient to reach any frame. The three elemental rotations may be intrinsic. Euler angles are denoted as α, β, γ, or φ, θ, ψ. Different authors may use different sets of rotation axes to define Euler angles, or different names for the same angles. Therefore, any discussion employing Euler angles should always be preceded by their definition. Without considering the possibility of using two different conventions for the definition of the rotation axes, there exist twelve possible sequences of rotation axes, divided in two groups: Proper Euler angles Tait–Bryan angles.

Tait–Bryan angles are called Cardan angles. Sometimes, both kinds of sequences are called "Euler angles". In that case, the sequences of the first group are called proper or classic Euler angles; the axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, Y, Z. The geometrical definition begins by defining the line of nodes as the intersection of the planes xy and XY. Using it, the three Euler angles can be defined as follows: α is the angle between the x axis and the N axis. Β is the angle between the Z axis. Γ is the angle between the X axis. Euler angles between two reference frames are defined. Intrinsic rotations are elemental rotations that occur about the axes of a coordinate system XYZ attached to a moving body. Therefore, they change their orientation after each elemental rotation; the XYZ system rotates. Starting with XYZ overlapping xyz, a composition of three intrinsic rotations can be used to reach any target orientation for XYZ. Euler angles can be defined by intrinsic rotations.

The rotated frame XYZ may be imagined to be aligned with xyz, before undergoing the three elemental rotations represented by Euler angles. Its successive orientations may be denoted as follows: x-y-z, or x0-y0-z0 x′-y′-z′, or x1-y1-z1 x″-y″-z″, or x2-y2-z2 X-Y-Z, or x3-y3-z3 For the above-listed sequence of rotations, the line of nodes N can be defined as the orientation of X after the first elemental rotation. Hence, N can be denoted x′. Moreover, since the third elemental rotation occurs about Z, it does not change the orientation of Z. Hence Z coincides with z″; this allows us to simplify the definition of the Euler angles as follows: α represents a rotation around the z axis, β represents a rotation around the x′ axis, γ represents a rotation around the z″ axis. Extrinsic rotations are elemental rotations that occur about the axes of the fixed coordinate system xyz; the XYZ system rotates. Starting with XYZ overlapping xyz, a composition of three extrinsic rotations can be used to reach any target orientation for XYZ.

The Euler or Tait–Bryan angles are the amplitudes of these elemental rotations. For instance, the target orientation can be reached as follows: The XYZ system rotates about the z axis by γ; the X axis is now at angle γ with respect to the x axis. The XYZ system rotates again about the x axis by β; the Z axis is now at angle β with respect to the z axis. The XYZ system rotates a third time about the z axis by α. In sum, the three elemental rotations occur about z, x and z. Indeed, this sequence is denoted z-x-z. Sets of rotation axes associated with both proper Euler angles and Tait–Bryan angles are named using this notation. There are six possibilities of choosing the rotation axes for proper Euler angles. In all of them, the first and third rotation axes are the same; the six possible sequences are: z1-x′-z2″ or z2-x-z1 x1-y′-x2″ or x2-y-x1 y1-z′-y2″ or y2-z-y1 z1-y′-z2″ or z2-y-z1 x1-z′-x2″ or x2-z-x1 y1-x′-y2″ or y2-x-y1 Angles are defined according to the right-hand rule. Namely, they have positive values when they repre

Driving band

In an artillery shell, the driving band or rotating band is a band of soft metal near the shell's bottom made of gilding metal, copper, or lead. When the shell is fired, the pressure of the propellant swages the metal into the rifling of the barrel and forms a seal; the shell is stabilized for yaw in the barrel by a smaller bourrelet band near the front of the projectile. This band doesn't engage the rifling; as shell weight increases, it becomes more difficult to engineer a driving band that prevents propellant gases from either blowing past it, or blowing it off the shell. Some weapons that operate at high rates of fire, such as the GAU-8 Avenger Gatling cannon, use plastic driving bands instead of soft metal. Using plastic as a swage material reduces wear on the barrel's rifling, extends the life and average accuracy of the weapon. In a small-arms rifle, the entire bullet is covered in copper or another soft alloy, making the entire bullet its own driving band. Driving bands pre-cut for the rifling have been used for muzzle loaded weapons.

Rotating bands can be used to reduce the spin imparted to the round as is preferable for HEAT warheads or fin-stabilised projectiles fired from general-purpose rifled barrels. Gerald Bull worked extensively on ways to eliminate the driving band, leading to the development of his Extended Range, Full Bore ammunition using an inversion of the pre-cut rifling for his GC-45 howitzer, now replacing older artillery worldwide. Swaging Obturate Rotating gas-check Big Bullets for Beginners

Baltimore

Baltimore is the largest city in the state of Maryland within the United States. Baltimore was established by the Constitution of Maryland as an independent city in 1729. With a population of 611,648 in 2017, Baltimore is the largest such independent city in the United States; as of 2017, the population of the Baltimore metropolitan area was estimated to be just under 2.808 million, making it the 20th largest metropolitan area in the country. Baltimore is located about 40 miles northeast of Washington, D. C. making it a principal city in the Washington-Baltimore combined statistical area, the fourth-largest CSA in the nation, with a calculated 2017 population of 9,764,315. Baltimore is the second-largest seaport in the Mid-Atlantic; the city's Inner Harbor was once the second leading port of entry for immigrants to the United States. In addition, Baltimore was a major manufacturing center. After a decline in major manufacturing, heavy industry, restructuring of the rail industry, Baltimore has shifted to a service-oriented economy.

Johns Hopkins Hospital and Johns Hopkins University are the city's top two employers. With hundreds of identified districts, Baltimore has been dubbed a "city of neighborhoods." Famous residents have included writers Edgar Allan Poe, Edith Hamilton, Frederick Douglass, Ogden Nash, H. L. Mencken. During the War of 1812, Francis Scott Key wrote "The Star-Spangled Banner" in Baltimore after the bombardment of Fort McHenry, his poem popularized as a song. Baltimore has more public statues and monuments per capita than any other city in the country, is home to some of the earliest National Register Historic Districts in the nation, including Fell's Point, Federal Hill, Mount Vernon; these were added to the National Register between 1969–1971, soon after historic preservation legislation was passed. Nearly one third of the city's buildings are designated as historic in the National Register, more than any other U. S. city. The city has 33 local historic districts. Over 65,000 properties are designated as historic buildings and listed in the NRHP, more than any other U.

S. city. The historical records of the government of Baltimore are located at the Baltimore City Archives; the city is named after Cecil Calvert, second Lord Baltimore of the Irish House of Lords and founding proprietor of the Province of Maryland. Baltimore Manor was the name of the estate in County Longford on which the Calvert family lived in Ireland. Baltimore is an anglicization of the Irish name Baile an Tí Mhóir, meaning "town of the big house." The Baltimore area had been inhabited by Native Americans since at least the 10th millennium BC, when Paleo-Indians first settled in the region. One Paleo-Indian site and several Archaic period and Woodland period archaeological sites have been identified in Baltimore, including four from the Late Woodland period. During the Late Woodland period, the archaeological culture, called the "Potomac Creek complex" resided in the area from Baltimore south to the Rappahannock River in present-day Virginia. In the early 1600s, the immediate Baltimore vicinity was sparsely populated, if at all, by Native Americans.

The Baltimore County area northward was used as hunting grounds by the Susquehannock living in the lower Susquehanna River valley. This Iroquoian-speaking people "controlled all of the upper tributaries of the Chesapeake" but "refrained from much contact with Powhatan in the Potomac region" and south into Virginia. Pressured by the Susquehannock, the Piscataway tribe, an Algonquian-speaking people, stayed well south of the Baltimore area and inhabited the north bank of the Potomac River in what are now Charles and southern Prince George's counties in the coastal areas south of the Fall Line. European colonization of Maryland began with the arrival of an English ship at St. Clement's Island in the Potomac River on March 25, 1634. Europeans began to settle the area further north, beginning to populate the area of Baltimore County; the original county seat, known today as "Old Baltimore", was located on Bush River within the present-day Aberdeen Proving Ground. The colonists engaged in sporadic warfare with the Susquehanna, whose numbers dwindled from new infectious diseases, such as smallpox, endemic among the Europeans.

In 1661 David Jones claimed the area known today as Jonestown on the east bank of the Jones Falls stream. The colonial General Assembly of Maryland created the Port of Baltimore at old Whetstone Point in 1706 for the tobacco trade; the Town of Baltimore, on the west side of the Jones Falls, was founded and laid out on July 30, 1729. By 1752 the town had just 27 homes, including two taverns. Jonestown and Fells Point had been settled to the east; the three settlements, covering 60 acres, became a commercial hub, in 1768 were designated as the county seat. Being a colony, the Baltimore street names were laid out to demonstrate loyalty to the mother country. For example King George, King and Caroline streets. Baltimore grew swiftly in the 18th century, its plantations producing grain and tobacco for sugar-producing colonies in the Caribbean; the profit from sugar encouraged the cultivation of cane in the Caribbean and the importation of food by planters there. As noted, Baltimore was as the county seat, in 1768 a courthouse was built to serve both the city and county.

Its square was a center of community discussions. Baltimore established its public market system in 1763. Lexington Market, founded in 1782, i