# Ballistics

views updated May 18 2018

# Ballistics

Free-falling bodies

Projectile motion without air resistance

Projectile motion with air resistance

Resources

Ballistics is the scientific study of the motion of bodies projected through space. A projectile is an object that has been launched, shot, hurled, thrown, or by other means projected, and continues in motion due to its own inertia. Such objects can include projectiles fired from cannons or small arms, bombs dropped from airplanes, or powered rockets. The path of the projectile is determined by its initial velocity (direction and speed) and the forces of gravity and air resistance. For objects projected close to Earth and with negligible air resistance, the flight path is a parabola. When air resistance is significant, however, the shape and rotation of the object are important and determining the flight path is more complicated. Ballistics influences many fields of study ranging from analyzing a curve ball in baseball to developing missile guidance systems in the military.

## Free-falling bodies

In order to understand projectile motion it is first necessary to understand the motion of free-falling bodiesobjects that are simply dropped from a certain height above Earth. For the simplest case, when air resistance is negligible and when objects are close to the Earths surface, Italian astronomer and physicist Galileo Galilei (15641642) was able to show that two objects fall the same distance in the same amount of time, regardless of their weights. It is also true that the speed of a falling object will increase by equal increments in equal periods of time. For example, a ball dropped from the top of a building will start from rest and increase to a speed of 32 ft (9.8 m) per second after one second, to a speed of 64 ft (19.6 m) per second after two seconds, to a speed of 96 ft (29.4 m) per second after three seconds, and so on. Thus, the change in speed for each one second time interval is always 32 ft per second. The change in speed per time interval is known as the acceleration and is constant. This acceleration is equal to 1 g (commonly pronounced: one gee), where g stands for the acceleration due to the force of gravity (g). By comparison, a pilot in a supersonic jet pulling out of a nose dive may experience an acceleration as high as 9 g (nine gee). (Of course, a jet is not in free fall but is being accelerated by its engines and gravity.)

The acceleration of gravity, g, becomes smaller as the distance from Earth increases. However, for most earthbound applications, the value of g can be considered constant (it only changes by 0.5% due to a 10 mi [16 km] altitude change). Air resistance, on the other hand, can vary greatly depending on altitude, wind, and the properties and velocity of the projectile itself. It is well know that skydivers may change their altitude relative to other skydivers by simply changing the shape of their body. In addition, it is obvious that a rock will fall more quickly than a feather. Therefore, when treating problems in ballistics, it is necessary to separate the effects due to gravity, which are fairly simple, and the effects due to air resistance, which are more complicated.

## Projectile motion without air resistance

The motion of projectiles without air resistance, can be separated into two components. Motion in the vertical direction where the force of gravity is present, and horizontal motion where the force of gravity is zero. As English physicist and mathematician Sir Isaac Newton (16421727) proposed, an object in motion will remain in motion unless acted upon by an external force. Therefore, a projectile in motion will remain with the same horizontal velocity throughout its flight, since no force exists in the horizontal direction, but its velocity will change in the vertical direction due to the force of gravity. For example, if a cannon ball is fired in the horizontal direction, the velocity of the ball will remain constant in the horizontal direction but will accelerate toward the Earth in the vertical direction with an acceleration of 1 g. The combination of these two effects produces a path that describes a parabola. Since the vertical motion is determined by the same acceleration that describes the motion of objects in free fall, a second cannon ball that is dropped at precisely the same instant as the first cannon ball is fired, will reach the ground at precisely the same instant. Therefore, the motion in the horizontal direction does not affect the motion in the vertical direction. This fact can be confirmed by knocking one coin off the edge of the desk with a good horizontal whack, while a second coin is simultaneously knocked off the desk with a gentle nudge. Both coins will reach the ground at the same time.

By increasing the amount of gunpowder behind the cannon ball, one could increase the horizontal velocity of the cannon ball as it leaves the cannon and cause the cannon ball to land at a greater distance. If it were possible to increase the horizontal velocity to very high values, there would come a point at which the cannon ball would continue in its path without ever touching the ground, similar to an orbiting satellite. To attain this orbiting situation close to the Earths surface, the cannon ball would have to be fired with a speed of 17,700 mph (28,500 km/h). In most instances, projectiles, like cannon balls, are fired at some upward angle to the Earths surface. As before, the flight paths are described by parabolas. (The maximum range is achieved by aiming the projectile at a 45° angle above the horizontal.) Angles equally greater or less than 45°will produce flight paths with the same range (for example, 30° and 60°).

## Projectile motion with air resistance

If projectiles were only launched from the surface of the moon where there is no atmosphere, then the

### KEY TERMS

Acceleration of gravity The vertical downward acceleration equal to 32 ft (9.8 m) per second per second experienced by objects in flight close to Earth.

Air resistance The drag force on an object in flight due to the interaction with air molecules.

Free falling body A falling object in one dimensional motion, influenced by gravity when air resistance is negligible.

Gyroscope A device similar to a top, which maintains rotation about an axis while maintaining a constant orientation of that axis in space.

Inertia The tendency of an object in motion to remain in motion in a constant direction and at a constant speed, and the tendency of an object at rest to remain at rest.

Projectile An object that is projected close to Earth and whose flight path is determined by gravity, air resistance, and inertia.

effects of gravity, as described in the previous section, would be sufficient to determine the flight path. On Earth, however, the atmosphere will influence the motion of projectiles. As opposed to the situation due to purely gravitational effects, projectile motion with air resistance will be dependent on the weight and shape of the object. As one would suspect, lighter objects are more strongly affected by air resistance. In many cases, air resistance will produce a drag force that is proportional to the velocity squared. The effects of increased air drag on an object such as a cannon ball will cause it to fall short of its normal range without air resistance. This effect may be significant. In World War I, for instance, it was realized that cannon balls would travel farther distances if aimed at higher elevations, due to the decreased air density and decreased drag.

More subtle effects of air resistance on projectile motion are related to the shape and rotation of the object. Clearly, the shape of an object can have an effect on its projectile motion, as anyone has experienced by wadding up a piece of paper before tossing it into the waste can. The rotation of an object is important, too. For example, a good quarterback always puts a spin on a football when making a pass. By contrast, to produce an erratic flight, a knuckle ball pitcher in baseball puts little or no spin on the ball. The physical property that tends to keep spinning objects spinning is the conservation of angular momentum. Not only do spinning objects tend to keep spinning but, also, the orientation of the spin axis tends to remain constant. This property is utilized in the design of rifle barrels that have spiral grooves to put a spin on the bullet. The spinning of the bullet around its long axis will keep the bullet from tumbling and will increase the accuracy of the rifle. This property is also utilized in designing guidance systems for missiles. These guidance systems consist of a small spinning device called a gyroscope, which keeps a constant axis orientation and, thus, helps to orient the missile. Small deviations of the missile with respect to the orientation of the gyroscope can be measured and corrections in the flight path can be made.

## Resources

### BOOKS

Hewitt, Paul. Conceptual Physics. Englewood Cliffs, NJ: Prentice Hall, 2001.

Munson, Bruce, et al. Fundamentals of Mechanics. 4th ed. New York: John Wiley and Sons, 2002.

Young, Hugh D. Sears and Zemanskys University Physics. San Francisco, CA: Pearson Addison Wesley, 2004.

Kurt Vandervoort

# Ballistics

views updated May 21 2018

# Ballistics

Ballistics is the study of projectile motion . A projectile is an object that has been launched, shot, hurled, thrown, or by other means projected, and continues in motion due to its own inertia. The path of the projectile is determined by its initial velocity (direction and speed) and the forces of gravity and air resistance. For objects projected close to Earth and with negligible air resistance, the flight path is a parabola . When air resistance is significant, however, the shape and rotation of the object are important and determining the flight path is more complicated. Ballistics influences many fields of study ranging from analyzing a curve ball to developing missile guidance systems.

## Free-falling bodies

In order to understand projectile motion it is first necessary to understand the motion of free-falling bod ies—objects that are simply dropped from a certain height above Earth. For the simplest case, when air resistance is negligible and when objects are close to the earth's surface, Galileo Galilei (1564-1642) was able to show that two objects fall the same distance in the same amount of time , regardless of their weights. It is also true that the speed of a falling object will increase by equal increments in equal time periods. For example, a ball dropped from the top of a building will start from rest and increase to a speed of 32 ft (9.8 m) per second after one second, to a speed of 64 ft (19.5 m) per second after two seconds, to a speed of 96 ft (29.4 m) per second after three seconds, and so on. Thus, the change in speed for each one second time interval is always 32 ft per second. The change in speed per time interval is known as the acceleration and is constant. This acceleration is equal to 1 g, which stands for the acceleration due to the force of gravity. By comparison, a pilot in a supersonic jet pulling out of a nose dive may experience an acceleration as high as 9 g (of course, a jet is not in free fall but is being accelerated by its engines and gravity).

The acceleration of gravity, g, becomes smaller as the distance from Earth increases. However, for most earthbound applications, the value of g can be considered constant (it only changes by 0.5% due to a 10 mi [16 km] altitude change). Air resistance, on the other hand, can vary greatly depending on altitude, wind , and the properties and velocity of the projectile itself. It is well know that sky divers may change their altitude relative to other sky divers by simply changing the shape of their body. Also, it is obvious that a rock will fall more quickly than a feather. Therefore, when treating problems in ballistics, it is necessary to separate the effects due to gravity, which are fairly simple, and the effects due to air resistance, which are more complicated.

## Projectile motion without air resistance

The motion of projectiles without air resistance, can be separated into two components. Motion in the vertical direction where the force of gravity is present, and horizontal motion where the force of gravity is zero . As Isaac Newton (1642-1727) proposed, an object in motion will remain in motion unless acted upon by an external force. Therefore, a projectile in motion will remain with the same horizontal velocity throughout its flight, since no force exists in the horizontal direction, but its velocity will change in the vertical direction due to the force of gravity. For example, a cannon ball is fired in the horizontal direction. The velocity of the cannon ball will remain constant, in the horizontal direction, but the ball will accelerate toward the Earth, in the vertical direction, with an acceleration of 1 g. The combination of these two effects produces a path which describes a parabola. Since the vertical motion is determined by the same acceleration that describes the motion of objects in free fall, a second cannon ball that is dropped at precisely the same instant as the first cannon ball is fired, will reach the ground at precisely the same instant. Therefore, the motion in the horizontal direction does not affect the motion in the vertical direction. This fact can be confirmed by knocking one coin off the edge of the desk with a good horizontal whack, while a second coin is simultaneously knocked off the desk with a gentle nudge. Both coins will reach the ground at the same time.

By increasing the amount of gun powder behind the cannon ball, one could increase the horizontal velocity of the cannon ball as it leaves the cannon and cause the cannon ball to land at a greater distance. If it were possible to increase the horizontal velocity to very high values, there would come a point at which the cannon ball would continue in its path without ever touching the ground, similar to an orbiting satellite . To attain this orbiting situation close to the earth's surface, the cannon ball would have to be fired with a speed of 17,700 MPH (28,500 km/h)! In most instances, projectiles, like cannon balls, are fired at some upward angle to the earth's surface. As before, the flight paths are described by parabolas. (The maximum range is achieved by aiming the projectile at a 45° angle above the horizontal.) Angles equally greater or less than 45° will produce flight paths with the same range (for example 30° and 60°).

## Projectile motion with air resistance

If projectiles were only launched from the surface of the moon where there is no atmosphere, then the effects of gravity, as described in the previous section, would be sufficient to determine the flight path. On Earth, however, the atmosphere will influence the motion of projectiles. As opposed to the situation due to purely gravitational effects, projectile motion with air resistance will be dependent on the weight and shape of the object. As one would suspect, lighter objects are more strongly affected by air resistance. In many cases, air resistance will produce a drag force which is proportional to the velocity squared. The effects of increased air drag on an object such as a cannon ball will cause it to fall short of its normal range without air resistance. This effect may be significant. In World War I, it was realized that cannon balls would travel farther distances if aimed at higher elevations, due to the decreased air density and decreased drag.

More subtle effects of air resistance on projectile motion are related to the shape and rotation of the object. Clearly, the shape of an object can have an effect on its projectile motion, as anyone has experienced by wadding up a piece of paper before tossing it into the waste can. The rotation of an object is important also. For example, a good quarterback always puts a spin on a football when making a pass. By contrast, to produce an erratic flight, a knuckle ball pitcher in baseball puts little or no spin on the ball. The physical property that tends to keep spinning objects spinning is the conservation of angular momentum . Not only do spinning objects tend to keep spinning but the orientation of the spin axis tends to remain constant. This property is utilized in the design of rifle barrels that have spiral grooves to put a spin on the bullet. The spinning of the bullet around its long axis will keep the bullet from tumbling and will increase the accuracy of the rifle. This property is also utilized in designing guidance systems for missiles. These guidance systems consist of a small spinning device called a gyroscope , which keeps a constant axis orientation and thus helps to orient the missile. Small deviations of the missile with respect to the orientation of the gyroscope can be measured and corrections in the flight path can be made.

## Resources

### books

Armenti, Angelo Jr. The Physics of Sports. New York: American Institute of Physics, 1992.

Hewitt, Paul. Conceptual Physics. Englewood Cliffs, NJ: Prentice Hall, 2001.

Munson, Bruce, et al. Fundamentals of Mechanics. 4th ed. New York: John Wiley and Sons, 2002.

Kurt Vandervoort

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acceleration of gravity

—The vertical downward acceleration equal to 32 ft (9.8 m) per second per second experienced by objects in flight close to Earth.

Air resistance

—The drag force on an object in flight due to the interaction with air molecules.

Free falling body

—A falling object in one dimensional motion, influenced by gravity when air resistance is negligible.

Gyroscope

—A device similar to a top, which maintains rotation about an axis while maintaining a constant orientation of that axis in space.

Inertia

—The tendency of an object in motion to remain in motion in a constant direction and at a constant speed, and the tendency of an object at rest to remain at rest.

Projectile

—An object that is projected close to Earth and whose flight path is determined by gravity, air resistance, and inertia.

# Ballistics

views updated Jun 08 2018

# Ballistics

When a forensic investigation involves a shooting, ballistics becomes an important facet of the investigation. Ballistics is a term that refers to the science of the flight path of a bullet. The flight path includes the movement of the bullet down the barrel of the firearm following detonation and its path through both the air and the target.

Tracing the path of a bullet is important in a forensic examination. It can reveal from what direction the bullet was fired, which can be vital in corroborating the course of events in the crime or accident.

It is an obvious truism that the distance that a bullet can travel depends on its speed. A higher speed imparts more energy to the bullet. The frictional resistance of the air and the downward pull of gravity will take longer to slow the bullet's flight, as compared to a bullet moving at a lower initial velocity.

Generally, a bullet fired from a rifle will carry more energy than a bullet fired from a handgun. This is because the stronger firing chamber of a rifle is able to withstand the increased explosive power of a larger quantity of powder that would likely rupture the barrel of the handgun. Detonation of the powder in a rifle or handgun supplies the thrust to propel the bullet down the barrel.

Expansion of the exploding gunpowder generates pressure, which is measured as the force of the explosion that pushes on the area of the bullet's base. This area is essentially the diameter of the barrel of the firearm, which remains constant. Thus, the explosive energy that passes to the bullet depends on the mass of the bullet multiplied by the force of the explosion multiplied by the time that the force is applied (i.e., the time the bullet is in the barrel). A longer barrel will produce a faster moving bullet.

Once a bullet leaves the rifle or gun barrel, the aforementioned frictional and gravitational forces begin to slow its speed, producing a downward arc of flight. The frictional force is affected by the bullet's shape. A blunt shape will present more surface area to the air than will a very pointed bullet.

Another factor that affects the flight of a bullet is called yaw. As in an orbiting spacecraft or a football tossed through the air, yaw causes a bullet to turn sideways or tumble in flight. This behavior is decreased when the object spins as it moves forward (the spiraling motion of a football). The barrel of a rifle or gun contains grooves that cause the bullet to spin. More damage results from a bullet that is tumbling rather than moving in a tight spiral.

The shape of a typical bulletmuch like a football with one end blunt instead of taperedis a compromise that reduces air resistance while still retaining the explosive energy that allows the bullet to damage the target.

The composition of a bullet is also important. Lead is commonly used to form the core of bullets. However, because it tends to deform, the blending in of other metals (typically antimony and copper) produces a bullet that can withstand the pressure of flight and impart high energy to the target upon impact.

Copper is often used to jacket the inner lead core of a bullet. However, some bullets are deliberately made without this full metal jacket. Instead, the bullet has a tip made of lead or a tip that is hollow or very blunt. These bullets deform and break apart on impact, producing more damage to the target than is produced by a single piece of metal. This is because the bullet's energy is dissipated within a very short distance in the tissue.

Forensic and medical examiners are able to assess the nature of tissue damage in a victim and gain an understanding of the nature of the bullet used.

A bullet produces tissue damage in three ways. First, a bullet can shred (lacerate) or crush tissue or bone. Bullets moving at relatively low velocity do most of their damage this way. Fragmentation of bone can cause further damage, as the bone shards themselves become missiles.

The second form of damage is known as cavitation. This damage is produced by the forward movement of air or tissue in the wake of the bullet. The wound that is produced by the bullet is destructively broadened by the force of the moving air or tissue. In a tissue, this produces even more structural damage.

Third, the air at the front and sides of a very fast moving bullet can become compressed. The explosive relaxation of the compression generates a damaging shock wave that can be several hundred atmospheres in pressure. Fluid-filled organs such as the bladder, heart, and bowel can be burst by the pressure.

Recovery of bullets can be a very useful part of forensic ballistics. A variety of bullet designs exist, some that are specific to the firearm. Furthermore, the scouring of a bullet's surface as it encounters the grooves of the firearm barrel can produce a distinctive pattern that enables a bullet to be matched with the firearm. A weapon recovered from a suspect can be test fired and the bullet pattern compared with a bullet recovered from the scene to either implicate or dismiss involvement of the firearm in the crime.

This aspect of ballistics was crucial in convicting John Allen Muhammad and John Lee Malvo of the 10 sniper murders and the wounding of three others in the Washington, D.C. area that occurred during three weeks in October of 2002.

# Ballistics

views updated May 18 2018

# Ballistics

Ballistics is the study of projectile motion. A projectile is an object that has been launched, shot, hurled, thrown, or projected by any other means and that then travels on its own along a ballistic path. For instance, a baseball player throwing a ball from center field to the infield usually throws the ball in a slightly upward direction. The ball's path travels along an arc from the outfield to the infield. Mathematically, the arclike path taken by the ball is known as a parabola.

Ballistics has long been a subject of interest to scientists because bullets, cannon shells, arrows, and other weapons travel in ballistic paths. Military leaders have always valued the information that scientists were able to provide them concerning the proper way in which to aim their guns and bows in combat.

## Projectile motion without air resistance

Consider a bullet fired from a rifle that is held parallel to (in the same direction as but never touching) the ground. The path taken by that bullet is affected by two forces. The first force is the velocity given to the bullet by the force of the rifle. (Velocity is the rate at which an object moves in a specified direction; it is measured in meters per second.) That force tends to make the bullet move in a straight line, out of the mouth of the rifle and parallel to the ground. If there were no air present, there would be nothing to slow the motion of the bullet and it would keep traveling with its original velocity.

A second force also operates on the bullet: the force of gravity. As the bullet travels away from the gun, it is pulled downward by Earth's gravitational field. Instead of traveling in a straight line, then, it travels in a curved path towards Earth's surface. That curved path, typical of projectile motion, is a parabola.

The exact shape of the bullet's path is determined by two factors: the mass of the bullet and the velocity with which it travels. The heavier the bullet is, the stronger Earth's gravitational field will pull on it. And the faster the bullet leaves the rifle, the greater its tendency to travel in a straight line away from the gun.

Finding the path for any kind of projectile is an easy problem in physics. If one knows the mass of the object and the velocity with which it is projected, then its pathway can be calculated by well-known formulas.

The practical importance of this calculation is obvious. If a naval ship fires a rocket at an enemy vessel, the path of the rocket must be known. Otherwise the rocket may travel beyond the enemy ship or fall into the water before reaching it. A rocket scientist has to know the path of a space probe launched to Mars if the probe is to land exactly on target rather than sailing on past its intended destination.

## Other factors affecting projectile motion

Air resistance is another important factor affecting projectile motion. As a rifle bullet travels through the air, it tends to slow down because of friction between the bullet and the air through which it passes. The amount of friction, in turn, is influenced by a number of factors. Among these factors is the shape of the bullet. Most bullets (and other kinds of projectiles) have pointed front endsa feature that reduces air resistance. A bullet with a blunt front end would experience a great deal of air resistance and would slow down rapidly. Rotation affects air resistance as well. A good quarterback always tries to place a spin on a football. This helps the football to travel through the air more smoothly than it would without the spin.

# ballistics

views updated May 18 2018

ballistics Science of projectiles, including bullets, shells, bombs, rockets, and guided missiles. Interior ballistics deal with the propulsion and motion of the projectile within the firing device. Exterior ballistics investigate the trajectory of the projectile in flight. Terminal ballistics involves the impact and effect of the projectile at the target. At each stage, scientists try to maximize the performance of the gun and projectile by improving their design. Ballistic technology has developed alongside artillery, and with the invention of instruments to monitor variables, such as the ignition and burning of the propellant explosive, the stress on a gun barrel, or the effect of air resistance and gravity on the trajectory.

# ballistics

views updated May 21 2018

bal·lis·tics / bəˈlistiks/ • pl. n. [treated as sing.] the science of projectiles and firearms. ∎  the study of the effects of being fired on a bullet, cartridge, or gun.