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C1

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
The Problem of Exterior Ballistics
Exterior ballistics involves an analysis of the forces which act on the projectile and affect its course during flight from gun muzzle to target. Exterior ballistics is also concerned with the practical problem of laying a gun (setting it in elevation and train) to incorporate ballistic corrections and enable a projectile fired from it to hit the target. The discussion in this section will be limited to the factors involved in solving the problem of hitting a fixed target from a fixed positionno relative motion between gun and target.
If there were no forces acting on a projectile during its flight to the target, fire control would be a simple matter. All that would be necessary to score a hit on a fixed target from a fixed position would be to aim the gun directly at the target and fire.
When a projectile is fired from a gun, its momentum, resulting from the projectile I. V. , tries to keep it on a course in line with the gun bore. Many forces act on it, however, before it reaches the target. The earth's gravity pulls it down; air resistance, due to the friction of the projectile pushing through the air, slows it down; wind and air currents force the projectile off its original course; and the spinning of the projectile tends to make it drift off course. All of these factors greatly alter the projectile's course and must be considered in determining how to elevate and train the gun in order to score a hit.
You will learn in the next few sheets about the effect of each of these forces.

C2

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Analysis of the Vacuum Trajectory
If it were possible to remove all of the air from around the gun and the target, the only force which would act on a projectile fired into the resulting vacuum would be the downward pull of gravity. If the gun were aimed perfectly horizontal and a projectile fired at the same instant that an identical projectile was dropped vertically from the level of the gun muzzle, both projectiles would hit the ground at exactly the same instant.
This illustrates that the force exerted on a projectile by gravity is always the same for a given projectile, regardless of its speed or direction of travel.
If the gun were pointed up at some angle and a projectile fired, its initial velocity could be resolved into horizontal and vertical components. There is no opposition offered, in a vacuum, to the horizontal velocity component so this remains constant during the projectile's flight. Gravity, however, exerts a constant downward force which opposes the vertical velocity component.

C3

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Analysis of the Vacuum Trajectory (continued)
As the projectile continues its flight from gun to target, gravity continues to oppose and reduce the vertical velocity of the projectile until it becomes zero at the midpoint of the flight. From this point onward gravity causes the projectile to attain a downward vertical velocity which continues to increase until the projectile hits the target. Thus the force exerted on the projectile by gravity causes it to follow a curved path from gun to target. This path is called the projectile's "trajectory."
At the midpoint of the trajectory, gravity has acted on the projectile for a time sufficient to reduce the vertical velocity to zero. The time required for the projectile to travel from the trajectory midpoint to the target is the same as is required to reach the midpoint from the gun. Therefore, since the force exerted by gravity is constant, the downward velocity due to gravity attained by the projectile when it reaches the target will equal the vertical component of the I. V. The total velocity of the projectile when it strikes the target, then, will equal the initial velocity since the horizontal component has not changed during the projectile's flight.

C4

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Analysis of the Vacuum Trajectory (continued)
The trajectory of a projectile fired in a vacuum has a regular curved shape as shown below. The projectile reaches its highest travel at a point midway between gun and target.
The projectile leaves the gun along the line of departure and approaches the target along the line of fall. These lines make equal angles with the horizontal, so that the angle of departure (elevation angle Eg) equals the angle of fall. In the case illustrated, when the gun and target are at the same level the line of sight (L. O. S.) from gun to target is horizontal. You saw from the projectile velocity analysis on the preceding sheet that the velocity of the projectile when it strikes the target equals its initial velocity when it leaves the gun muzzle.
It is not possible, of course, to create a vacuum between gun and target. But if you understand the vacuum trajectory it will be easier for you to understand the effects on projectile trajectory of air resistance, wind and projectile spin. The effect of gravity on a projectile's course of flight is constant, in a vacuum or in air, and if it were the only factor to consider fire control would still be a simple problem. It is primarily the other exterior ballistics factors which require elaborate consideration before the fire control problem can be solved.

C5

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
How Initial Velocity Affects Projectile Range
The initial velocity and direction of a projectile determine where it will fall. These are the only properties which can be imparted to a projectile by a gun, and if they could not be controlled the gunner would have no control of his weapons. Once the projectile has left the gun he can't tell it where to go. It is vitally important, then, that we know exactly how a projectile will travel after it leaves the gun at a known speed and in a known direction, so that we can adjust these factors as necessary to make the projectile hit the target.
If a projectile is fired at a fixed elevation angle in a vacuum and the initial velocity is varied, the range will increase as the initial velocity increases. Since the vertical component of velocity is larger, it takes longer for the constant force of gravity to overcome the projectile's upward travel. This allows the horizontal velocity component to carry the projectile farther from the gun, resulting in increased range.
In guns using bag ammunition it is possible to change the initial velocity by using larger or smaller propelling charges. Certain semifixed ammunition intended for beach bombardment uses special low I. V. powder for the propelling charge. In guns using fixed ammunition, however, no control of range is possible by varying initial velocity since the I. V. of such guns is fixed for a certain gun using given ammunition.

C6

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
How Elevation Angle Affects Projectile Range
If a projectile is fired in a vacuum with a fixed initial velocity, its range will depend only on the elevation angle (Eg)the angle between the gun bore and the horizontal. As Eg is increased from zero to 45 degrees, the range increases since it takes longer for gravity to overcome the projectile's vertical velocity and during this time the projectile travels farther from the gun.
As the vertical velocity increases due to increased elevation, the horizontal velocity decreases. As the gun is elevated higher than 45 degrees, the time the projectile is traveling continues to increase, but the horizontal velocity will be so reduced that even in the longer time the projectile won't go as far.
You can see that for any range there are two possible elevation anglesone greater and one less than 45 degrees. To keep the time of flight to a minimum, elevations less than 45 degrees are used for fire against surface targets. Elevations greater than 45 degrees are ordinarily used only for antiaircraft fire.

C7

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
The Effect of Air Resistance on Trajectory
So far we have considered the flight of a projectile in a vacuum and you have seen how gravity, initial velocity and elevation affect the projectile's trajectory when air resistance is neglected. We cannot, of course, create a vacuum in the combat area so we must determine, understand and compensate for the effects of air resistance on the projectile's course if we hope to score a hit on the target.
The effect of gravity on a projectile is constant, regardless of whether the projectile travels in air or in a vacuum. Gun elevation and initial velocity still affect the projectile's trajectory in the same manner. Hence the discussion on the preceding sheets of these effects in a vacuum also applies
to the flight of the projectile in air.
As a projectile travels through air, the air is forced out of the projectile's path just as a ship forces the water from in front of it as it moves through the sea. As the air is moved aside, it exerts a force on the projectile which opposes its motion.
Just as the force of gravity opposes the vertical component of projectile velocity, the force due to air resistance always acts in opposition to the total velocity of the projectile (sum of vertical and horizontal components). Air resistance varies depending on projectile size and projectile velocity.

C8

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
The Effect of Air Resistance on Trajectory (continued)
The faster a projectile moves through the air, the faster it must force the air out of its path. The more rapidly the air is moved out of its original position, the greater the force it exerts on the projectile. Thus, air resistance has a greater effect on projectiles traveling at high velocities than it does on slowmoving projectiles.
As long as a projectile is in flight, air resistance continues to reduce its velocity. Thus the projectile travels much more slowly as it approaches the target than it did when it left the gun muzzle. Also, the longer a projectile remains in flight, the more slowly it travels, which results in a shortening of the trajectory at the far end and a great reduction in range as shown below. The trajectory high point is no longer at the midpoint as it was in a vacuum, but will be nearer the point of impact than it is to the gun. The angle of fall is greater than the angle of departure and the striking velocity (projectile velocity when it hits the target) is less than the initial velocity.
In the above illustration, initial velocity, elevation angle and size of projectile are the same.

C9

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
The Effect of Air Resistance on Trajectory (continued)
Any projectile fired in a vacuum at an elevation of 40 degrees and with an I. V. of 2500 fps will attain a horizontal range of 192, 000 yards (almost 100 miles). At the same elevation in air, a 16inch projectile will attain a range of only 42, 000 yards, a 5inch projectile 17, 000 yards and a 1.1inch projectile only 7000 yards.
The illustration shows how projectile size radically affects its range in air. Large projectiles have more initial energy and will travel farther against air resistance.
Because of air resistance, maximum projectile range is not attained when the elevation angle equals 45 degrees as is true in a vacuum. In air, maximum range occurs when the elevation angle is slightly more or less than 45 degrees, depending on the characteristics of the gun and the projectile. For instance, the maximum range of the 5inch gun is obtained when Eg = 44 degrees 35 minutes, just a little less than 45 degrees.
You can see that the presence of air greatly complicates the fire control problem, and that careful adjustments are required to compensate for its effects.

C10

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Why Projectiles Drift
You learned when you studied gun construction that the bores of Navy guns are rifled by cutting a series of twisted grooves on their interior surfaces. You also learned in the section which dealt with ammunition and projectiles that projectiles are provided with a rotating band which engages the rifling of the bore and gives the projectile a spinning motion as
it travels through the bore. Now let's see why it is necessary that a projectile spin during flight and what the effects of that spinning motion are.
As the projectile travels through the air its spinning action makes it behave very much like a spinning top or hoop. That is, it tends to resist any force which tries to change the position of the axis about which it is spinning. This tendency on the part of a rapidly spinning object is known as "gyroscopic action." In the case of the spinning projectile, gyroscopic action tends to keep the projectile on course, making it possible to predict the course of the missile and hence achieve accuracy of fire.
If the projectile did not spin it would tumble or "wobble" during its flight and would not maintain a predictable course, making accurate fire control impossible.

C11

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Why Projectiles Drift (continued)
During its flight, the spinning projectile attempts to align its axis of spin with the tangent to the projectile's trajectory. Since the trajectory is curved downward, the nose of the projectile must move down as the projectile moves forward. This downward motion of the projectile's nose is opposed by air resistance, as is the projectile's forward velocity. Thus an upward force is exerted on the projectile's forward end.
Suppose now that we consider one point on the surface of the projectile in flight. It has a velocity AB in the illustration below due to the spin of the projectile. The force of air resistance acts upon the front of the projectile and attempts to impart a motion AC to the point. The resulting motion is along the line AD. In order for the point to move along AD, the axis of spin of the projectile must rotate clockwise in a horizontal plane as shown, thus pointing the projectile to the right. This movement along AD is called "precession " and is characteristic of all gyroscopes or other spinning objects.

C12

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Why Projectiles Drift (continued)
As the projectile's axis of spin rotates to the right, the trajectory curves to the right. This horizontal deflection of the projectile during flight due to the combined actions of gravity, gyroscopic action and air resistance is called "drift. "
Drift is not appreciable at short ranges but increases rapidly for a given gun as the range becomes greater. Since projectiles always drift to the right, the gun must be aimed to the left of the target by an amount depending on the range if a hit is to be scored.
For a given range, the drift of small projectiles will be greater than that of large projectiles. For instance, at a range of 15, 000 yards a 5inch projectile drifts about 250 yards, whereas a 16inch projectile drifts only 50 yards. The amount which a projectile will drift at a given range has been determined experimentally, and accurate information is available to assure that the necessary corrections to the gun traverse settings can be made.

C13

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
The Effects of Cross Wind and Range Wind
If you have ever played football on a windy day, you are familiar with the effects of wind on an object in flight. Depending on the wind direction and velocity, your wellaimed "forward pass" may have curved to the right or left, or fallen short of or beyond the point where you wanted it to land.
Wind has exactly the same effect on a projectile in flight. If the wind blows from the left the projectile's trajectory will turn to the right and vice versa. If the projectile is headed into the wind its range will be decreased, and if it travels with the wind the range will be increased. You can see that the effects of wind must be considered in the solution of the fire control problem.

C14

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
The Effects of Cross Wind and Range Wind (continued)
If the wind is blowing at right angles to the projectile's line of fire it is called a "cross wind;" if it is blowing along the line of fire, either with or against the projectile, it is called "range wind." Corrections for cross wind are made to the train angle separately from those for drift; range wind is compensated for by increasing or decreasing the elevation angle.

C15

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
The Effects of Cross Wind and Range Wind (continued)
If the wind were cooperative enough to blow at all times either in line with or at right angles to the projectile's line of fire (L. O. F.), it would be a relatively simple matter to compute the corrections required when the wind velocity is known. Usually, however, the wind blows at some angle to the L. O. F. In order to correct for range and cross winds, it is necessary to resolve the true wind into components in line with and perpendicular to the L. O. F. When this is done, each component can be treated individually and the proper gun setting adjustments made.
When the projectile is first fired, it is traveling at such a high speed that the wind does not affect its flight very much. As the projectile slows down during its flight, the wind affects its course more and more. Hence the longer a projectile remains in flight, the more its course will be altered by the wind, so that wind deflection increases with range.
Two other factors which affect the amount the projectile deflects are wind speed and projectile size. Obviously the greater the wind velocity, the greater its effect on the projectile. Also, as was true for deflection due to drift, large projectiles have more initial momentum (weight x velocity) and can resist the effects of wind better than small projectiles.

C16

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
The Effects of Cross Wind and Range Wind (continued)
Corrections for the effects of wind are only approximate because wind speed and direction are usually different at various levels. For instance, the wind might be blowing from the north on the surface of the ocean and from the south at an altitude of 6000 feet. In such a case the projectile's course will be affected differently as it is acted on by the wind at various levels of its flight.
HOW WIND MAY VARY WITH ALTITUDE
Wind conditions at different elevations are determined by observations from an airplane or by observing the movements of a small balloon. If it is found that the projectile's trajectory will take it through winds which move in opposite directions, a "weighted ballistic wind" must be used to compute gun setting corrections. This ballistic wind makes allowance for variations in wind velocity and direction and for variations in air density at different levels.
If the projectile's trajectory is low and passes through winds of one direction only, surface wind is used to compute corrections.
In the upper air, winds blow up and down as well as horizontally. These vertical winds can lift the projectile or push it down and thus lengthen or shorten the range. Because these winds are extremely difficult to measure and have little effect, they are never considered in fire control computations.

C17

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
The Meaning of Projectile Dispersion
If a battery of guns is fired at the same instant with the same elevation and traverse settings, the projectiles will not all fall at the same point. This variation in the fall of projectiles fired simultaneously from a battery of guns is called "projectile dispersion." A certain amount of dispersion is expected from guns no matter how carefully they are aimed. For instance, for a certain battery of guns firing at a range of 10, 000 yards, it is considered fairly good if the projectile "range dispersion" is only 50 yards. This dispersion is illustrated below.
Dispersion is the result of variations in certain factors of interior as well as exterior ballistics. Variations in powder temperature, structure of the projectile, density and manner of loading, and extent of erosion produce different I. V. 's among the several guns, thus affecting their ranges. Equally important, unpredictable variations in air currents affect the projectiles' trajectories and hence the ranges.
"Deflection dispersion, " in which the projectiles fall to one side or the other of the target, also occurs in battery fire and is due to the same causes as range dispersion.

C18

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Other Factors Affecting the Flight of the Projectile
Thus far in your study of the problem of hitting a fixed target from a fixed position you have learned of the effects on the flight of the projectile of gravity, air resistance, initial velocity, drift and wind. These are the most important factors which affect the projectile's trajectory and they require the largest corrections to gun elevation and traverse settings. There are several other factors, however, which affect the projectile's flight and which should be mentioned.
We have thus far assumed that the sight telescope, gun and target are all in the same horizontal plane and that the line of sight from gun to target is in that plane. Actually these conditions do not usually hold. First of all, the line of sight from director to target is not parallel to the gun L. O. S. This necessitates a correction for "vertical parallax" to allow for the vertical distance between gun and director aboard ship. In addition, while the gun is located some distance above the water line, fire is directed at the target's waterline (for surface targets) and thus the gun line of sight is depressed slightly below the horizontal. This "position angle" correction is very minor, however, and is normally neglected for fire against surface targets.

C19

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Other Factors Affecting the Flight of the Projectile (continued)
Just as vertical parallax requires a correction to gun elevation to compensate for the vertical distance between gun and director aboard ship, the horizontal distance between gun and director requires a correction to gun deflection to compensate for "horizontal parallax."
If the gun's L. O. F. were parallel to the director's L. O. S. , the fired projectile would miss the target by the horizontal distance between gun and director, as shown below.
In order to correct for horizontal parallax, the guns must be trained through an angle greater or smaller than that through which the direction is trained, so that the director L. O. S. and the gun L. O. F. would intersect at the target before corrections for other factors. In the illustration below, the forward gun must be trained through an angle greater than the director train angle, while the aft gun must be trained through an angle less than the director train angle.

C20

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Other Factors Affecting the Flight of the Projectile (continued)
Because the earth's surface is curved, the target is not in the horizontal plane which is tangent to the earth at the gun. The greater the range, the farther the target falls below the horizontal and the line of sight is depressed below the horizontal. If the elevation angle were set to hit a target at the measured range in the horizontal plane, the projectile would fall beyond the target. Hence the elevation angle must be slightly reduced (depending on range) to correct for curvature of the earth.
Tabulated information is available on the correction to elevation angle required for various values of range. This correction is small for short range fire, but becomes appreciable as range increases.
When fire is directed against shore installations the target may be above the gun, in which case the line of sight will make an anglecalled "target elevation angle"with the horizontal. The vertical angle between L. O. S. and L. O. F. (bore axis) to compensate for curvature of trajectory due to the effect of gravity is known as the "superelevation angle."

C21

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Other Factors Affecting the Flight of the Projectile (continued)
Suppose that you had a gun at the North Pole which could fire a projectile far enough to reach a target fixed at the equator. Because the earth spins on an axis through the North Pole the gun would be stationary, but the target would be moving at a velocity of about 1000 miles per hour since a fixed point on the equator has that velocity due to the earth's rotation. If you aimed the gun at the target and fired, the target would move several miles during the time the projectile is in flight and the projectile would land where the target had been at the instant of firing.
In order to score a hit it is necessary to "lead" the target, that is, train the gun on the point to which the target will have moved during the projectile's flight. Projectile and target will arrive at this point at the same time.
This condition holds true whenever a projectile's trajectory has a northtosouth component, that is, whenever the gun is at a different latitude than the target. The effect increases as the northtosouth distance between gun and target increases. However, a correction is made for the error introduced by the earth's rotation only on guns larger than 5inch, since the error is negligible in smaller guns.

C22

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Other Factors Affecting the Flight of the Projectile (continued)
You have learned how air resistance affects a projectile's trajectory. You found that the air displaced by the projectile during flight exerts a force on the projectile which opposes its motion and that this force depends on projectile size and speed. Another factor which influences the effects of air resistance, and which also is a factor in the computation of the weighted ballistic wind previously discussed, is the density of the air.
The density of a substance is a measure of how many molecules of the substance occupy a certain volume. A dense material has many molecules in a fixed volume, while a less dense substance has fewer molecules in the same volume.
The density of air varies with altitude. At high altitudes the air pressure is less than on the earth's surface and the air is less dense, since there is less force pushing the molecules together. When the air is less dense, there are fewer molecules of air to be displaced by the moving projectile, hence they exert less force to oppose its motion than does dense air.
As a projectile gains altitude during the first half of its flight, air resistance decreases due to the thin air at high altitudes; as it descends to hit the target, the air resistance again increases due to the dense air near the earth's surface. A correction to the gun elevation angle is made to compensate for variations in air density.

C23

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Review of Range and Deflection Ballistics
Of the various factors previously discussed which affect the flight of the projectile from a fixed gun to a fixed target, some can be classified as "range ballistics" and others as "deflection ballistics."
Range ballistics are those factors which affect how far a projectile will travel from gun to point of impact. Corrections to compensate for the effects of errors introduced by the factors of range ballistics are made by adjusting the elevation angle Eg.
Deflection ballistics are those factors which affect how far a projectile will travel along a line perpendicular to the L. O. F. Corrections to compensate for the effects of errors introduced by the factors of deflection ballistics are made by adjusting the horizontal angle between the L. O. S. and the L. O. F. , which is called sight deflection Ds.
Before learning about the complications to the fire control problem introduced when both target and own ship are moving, let's review the factors of range and deflection ballistics when both gun and target are fixed.

C24

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Review of Range and Deflection Ballistics (continued)
The various range ballistics factors and the quantities which determine these factors are listed in the table below. Each of the range ballistics factors requires a correction to the gun elevation angle Eg.
RANGE BALLISTIC (Corrections to Eg)  QUANTITIES WHICH AFFECT RANGE BALLISTIC 
1. Initial projectile velocity  Interior ballistics 
2. Vertical parallax  Distance from gun to director Range to target 
3. Curvature of earth  Range to target 
4. Rotation of earth  Range to target Latitude 
5. Force of gravity  Projectile weight 
6. Air resistance  Air density Projectile construction Projectile velocity 
7. Range wind  Air density Wind velocity Wind direction Projectile construction 
8. Superelevation of target  Height of target above gun Range to target 
The range ballistics factors only are shown in the illustration below.

C25

THE PROJECTILE IN FLIGHTEXTERIOR BALLISTICS
Review of Range and Deflection Ballistics (continued)
The factors of deflection ballistics and the quantities which affect these factors are listed in the table below. Each of the deflection ballistics introduces a correction to sight deflection Ds.
DEFLECTION BALLISTIC (Corrections to Ds)  QUANTITIES WHICH AFFECT DEFLECTION BALLISTIC 
1. Rotation of earth  Range to target Latitude 
2. Cross wind  Wind velocity Wind direction Air density Projectile construction 
3. Drift  Range to target Projectile size Projectile velocity 
The deflection ballistics factors only are shown in the illustration below.
In this section you have learned about the many factors which affect the flight of the projectile from a fixed gun to a fixed target, and how corrections (called "control ballistics") are made to the gun settings in elevation and traverse to compensate for the errors introduced by these factors. Now you are ready to go on and apply the things you have learned to the study of the problem of hitting a moving target from a moving ship. All of the principles of interior and exterior ballistics which apply to a stationary target and gun also hold true when both own ship and target are moving.

