Introduction

Ballistics is the study of the firing, flight, and effect of ammunition. A fundamental understanding of ballistics is necessary to comprehend the factors that influence precision and accuracy and how to account for them in the determination of firing data. Gunnery is the practical application of ballistics so that the desired ejects are obtained by fire. To ensure accurate predicted fire, we must strive to account for and minimize those factors that cause round-to-round variations, particularly muzzle velocity. Ballistics can be broken down into four areas: interior, transitional, exterior, and terminal. In this course, we will discuss interior ballistics. Even though there have been very large technical advances in the field of artillery, our projectiles still resemble large metal rockets when loaded but whence fired, they get their stream of light form.

Interior Ballistics Overview

Interior ballistics is the science that deals with the factors that affect the motion of the projectile within the tube. The total effect of all interior ballistic factors determines the velocity at which the projectile leaves the muzzle of the tube, which directly influences the range achieved by the projectile. This velocity, called muzzle velocity (MV), is expressed in meters per second (m/s). Actual measurements of the muzzle velocities of a sample of rounds corrected for the effects of nonstandard projectile weight and propellant temperature show the performance of a specific weapon for that projectile family-propellant type-charge combination. The resulting measurement(s) are compared to the standard muzzle velocity shown in the firing table(s). This comparison gives the variation from standard, called muzzle velocity variation (MVV), for that weapon and projectile family-propellant type-charge combination. Application of corrections to compensate for the effects of nonstandard muzzle velocity is an important element in computing accurate firing data. The following equation for muzzle velocity is valid for our purposes:

MVV (m/s) = SHOOTING STRENGTH OF WPN + AMMUNITION EFFICIENCY

Tube wear, propellant efficiency, and projectile weight are the items normally accounted for in determination of a muzzle velocity. Other elements in the equation above generally have an effect not exceeding 1.5 m/s. As a matter of convenience, the other elements listed below are not individually measured, but their effects are realized to exist under the broader headings of shooting strength and ammunition efficiency.

Shooting Strength of Weapon Ammunition Efficiency:

• Tube Wear
• Propellant Efficiency
• Manufacturer tolerances
• Projectile Efficiency
• Reaction to recoil
• Projectile Weight(fuzed)
• Constuction Of:
  • Rotating Band
  • Bourrelet
  • Obturating band

Nature of Propellant and Projectile Movement

A propellant is a low-order explosive that burns rather than detonates. In artillery weapons using separate-loading ammunition, the propellant burns within a chamber formed by the obturator spindle assembly, powder chamber, rotating band, and base of the projectile. For cannons using semifixed ammunition, the chamber is formed by the shell casing and the base of the projectile. When the propellant is ignited by the primer, the burning propellant generates gases. When these gases develop enough pressure to overcome initial bore resistance, the projectile begins its forward motion.

1. Several parts of the cannon tube affect interior ballistics.
   • The caliber of a tube is the inside diameter of the tube as measured between opposite lands.
   • The breech recess receives the breechblock. The breech permits loading the howitzer from the rear.
   • The powder chamber receives the complete round of ammunition. It is the portion of the tube between the gas check seat and the centering slope.The gas check seat is the tapered surface in the rear interior of the tube on weapons firing separate-loading ammunition. It seats the split rings of the obturating mechanism when they expand under pressure in firing. This expansion creates a metal-to-metal seal and prevents the escape of gases through the rear or the breech. Weapons firing semifixed ammunition do not have gas check seats since the expansion of the ease against the walls of the chamber provides a gas seal for the breech. The centering slope is the tapered portion at or near the forward end of the chamber that causes the projectile to center itself in the bore during loading.
   • The forcing cone is the tapered portion near the rear of the bore that allows the rotating band to be gradually engaged by the rifling, thereby centering the projectile in the bore.
   • The bore is the rifled portion of the tube (lands and grooves). It extends from the forcing cone to the muzzle. The rifled portion of the tube imparts spin to the projectile increasing stability in flight. The grooves are the depressions in the rifling. The lands are the raised portions. These parts engrave the rotating band. All United States (US) howitzers have a right-hand twist in rifling.
   • The bore evacuator is located on enclosed, self-propelled howitzers with semiautomatic breech mechanisms. It prevents contamination of the crew compartment by removing propellant gases from the bore after firing. The bore evacuator forces the gases to flow outward through the bore from a series of valves enclosed on the tube.
   • The counterbore is the portion at the front of the bore from which the lands have been removed to relieve stress and prevents the tube from cracking.
   • The muzzle brake is located at the end of the tube on some howitzers. As the projectile leaves the muzzle, the high-velocity gases strike the baffles of the muzzle brake and are deflected rearward and sideways. When striking the baffles, the gases exert a forward force on the baffles that partially counteracts and reduces the force of recoil.
2. The projectile body has several components that affect ballistics. Three of these affect interior ballistics--the bourrelet the rotating band and the obturating band.
   • The bourrelet is the widest part of the projectile and is located immediately to the rear of the ogive. The bourrelet centers the forward part of the projectile in the tube and bears on the lands of the tube. When the projectile is fired, only the bourrelet and rotating band bear on the lands of the tube.
   • The rotating band is a band of soft metal (copper alloy) that is securely seated around the body of the projectile. It provides forward obturation (the forward gas-tight seal required to develop pressure inside the tube). The rotating band prevents the escape of gas pressure from around the projectile. When the weapon is fired, the rotating band contacts the lands and grooves and is pressed between them. As the projectile travels the length of the cannon tube, over the lands and grooves, spin is imparted. The rifling for the entire length of the tube must be smooth and free of burrs and scars. This permits uniform seating of the projectile and gives a more uniform muzzle velocity.
   • The obturating band is a plastic band on certain projectiles. It provides forward obturation by preventing the escape of gas pressure from around the projectile.
3. The sequence that occurs within the cannon tube is described below.
   • The projectile is rammed into the cannon tube and rests on the bourrelet. The rotating band contacts the lands and grooves at the forcing cone.
   • The propellant is inserted into the chamber. The propellant explosive train is initiated by the ignition of the primer. This causes the primer, consisting of hot gases and incandescent particles, to be injected into the igniter. The igniter burns and creates hot gases that flow between the propellant granules and ignite the granule surfaces; the igniter and propellant combustion products then act together, perpetuating the flame spread until all the propellant granules are ignited.
   • The chamber is sealed, in the rear by the breech and obturator spindle group and forward by the projectile, so the gases and energy created by the primer, igniter, and propellant cannot escape. This results in a dramatic increase in the pressure and temperature within the chamber. The burning rate of the propellant is roughly proportional to the pressure, so the increase in pressure is accompanied by an increase in the rate at which further gas is produced.
   • The rising pressure is moderated by the motion of the projectile along the barrel. The pressure at which this motion begins is the shot-start pressure. The projectile will then almost immediately encounter the rifling, and the projectile will slow or stop again until the pressure has increased enough to overcome the resistance in the bore. The rotating band and obturating band (if present) or the surface of the projectile itself, depending on design, will be engraved to the shape of the rifling. The resistance decreases, thereby allowing the rapidly increasing pressure to accelerate the projectile.
   • As the projectile moves forward, it leaves behind an increasing volume to be filled by the high-pressure propellant gases. the propellant is still burning, producing highpressure gases so rapidly that the motion of the projectile cannot fully compensate. As a result, the pressure continues to rise until the peak pressure is reached. The peak pressure is attained when the projectile has traveled about one-tenth of the total length of a full length howitzer tube.
   • The rate at which extra space is being created behind the rapidly accelerating projectile then exceeds the rate at which high-pressure gas is being produced; thus the pressure begins to fall. The next stage is the all-burnt position at which the burning of the propellant is completed. However, there is still considerable pressure in the tube; therefore, for the remaining motion along the bore, the projectile continues to accelerate. As it approaches the muzzle, the propellant gases expand, the pressure falls, and so the acceleration lessens. At the moment the projectile leaves the howitzer, the pressure will have been reduced to about one sixth of the peak pressure. Only about one-third of the energy developed pushes the projectile. The other two-thirds is absorbed by the recoiling parts or it is lost because of heat and metal expansion.
   • The flow of gases following the projectile out of the muzzle provides additional acceleration for a short distance (transitional ballistics), so that the full muzzle velocity is not reached until the projectile is some distance beyond the muzzle. The noise and shock of firing are caused by the jet action of the projectile as it escapes the flow of gases and encounters the atmosphere. After this, the projectile breaks away from the influence of the gun and begins independent flight.
   • This entire sequence, from primer firing to muzzle exit, typically occurs within 15 milliseconds but perhaps as much as 25 milliseconds for a large artillery howitzer.
4. Pressure travel curves are discussed below.
   • Once the propellant ignites, gases are generated that develop enough pressure to overcome initial bore resistance, thereby moving the projectile. Two opposing forces act on a projectile within the howitzer. The first is a propelling force caused by the high-pressure propellant gases pushing on the base of the projectile. The second is a frictional force between the projectile and bore, which includes the high resistance during the engraving process, that opposes the motion of the projectile. The peak pressure, together with the travel of the projectile in the bore (pressure travel curve), determines the velocity at which the projectile leaves the tube.
   • To analyze the desired development of pressure within the tube, we identify three types of pressure travel curves:
     1. An elastic strength pressure travel curve represents the greatest interior pressure that the construction of the tube (thickness of the wall of the powder chamber, thickness of the tube, composition of the tube or chamber, and so on) will allow. It decreases as the projectile travels toward the muzzle because the thickness of the tube decreases.
     2. A permissible pressure travel curve mirrors the elastic strength pressure travel curve and accounts for a certain factor of safety. It also decreases as the projectile travels through the tube because tube thickness decreases.
     3. An actual pressure travel curve represents the actual pressure developed during firing within the tube. Initially, pressure increases dramatically as the repelling charge explosive train initiated and the initial resistance of the rammed projectile is overcome. After that resistance is overcome, the actual pressure gradually decreases because of the concepts explained by Boyle's Law. (Generally, as volume increases, pressure decreases.) The actual pressure should never exceed the permissible pressure.
        • Initial Excessive Pressure. This is undesirable pressure travel curve. It exceeds the elastic strength pressure and permissible pressure. Causes of this travel curve would be an obstruction in the tube, a dirty tube, an "extra" propellant placed in the chamber, an unfuzed projectile, or a cracked projectile.
        • Delayed Excessive Pressure. This is an undesirable pressure travel curve. It exceeds the elastic strength pressure and remissible pressure. Causes that would result in this travel curve would be using wet powder or powder reversed.
        • Desirable Pressure Travel Curve. This curve does not exceed permissible pressure. It develops peak pressure at about one-tenth the length of the tube.
   • The following general rules show how various factors affect the velocity performance of a weapon projectile family-propellant type-charge combination:
     1. An increase in the rate of propellant burning increases the resulting gas pressure developed within the chamber. An example of this is the performance of the multiperforated propellant grains used in white bag (WB) propellants. The result is that more gases are produced, gas pressure is increased, and the projectile develops a greater muzzle velocity. Damage to propellant grains, such as cracking and splitting from improper handling, also affect the rate of burn and thus the muzzle velocity.
     2. An increase in the size of the chamber without a corresponding increase in the amount of propellant decreases gas pressure; as a result, muzzle velocity will be less (Boyles Law).
     3. Gas escaping around the projectile decreases chamber pressure.
     4. An increase in bore resistance to projectile movement before peak pressure increases the pressure developed within the tube. Generally, this results in a dragging effect on the projectile, with a corresponding decrease in the developed muzzle velocity. Temporary variations in bore resistance can be caused by excessive deposits of residue within the cannon tube and on projectiles and by temperature differences between the inner and outer surfaces of the cannon tube.

Standard Muzzle Velocity

Applicable firing tables list the standard value of muzzle velocity for each charge. These standard values are based on an assumed set of standard conditions. These values are points of departure and not absolute standards. Essentially, we cannot assume that a given weapon projectile family-propellant type-charge combination when fired will produce the standard muzzle velocity.

Velocities for each charge are indirectly established by the characteristics of the weapons. Cannons capable of high-angle fire (howitzers) require a greater choice in the number of charges than cannons capable of only low-angle fire (guns). This choice is necessary to achieve range overlap between charges in high-angle fire and the desired range-trajectory combination in low-angle fire. Other factors considered are the maximum range specified for the weapon, the maximum elevation and charge, and the maximum permissible pressure that the weapon can accommodate.

Manufacturing specifications for ammunition include a requirement for velocity performance to meet certain tolerances. Ammunition lots are subjected to test firings, which include measuring the performance of a tested lot and comparing it to the performance of a control (reference) lot that is tested concurrently with the same weapon. An assumption built into the testing procedure is that both lots of ammunition will be influenced in the same manner by the performance of the tube. This assumption, although accurate in most instances, allows some error to be introduced in the assessment of the performance of the tested lot of propellant. In field conditions, variations in the performance of different projectile or propellant lots can be expected even though quality control has been exercised during manufacturing and testing of lots. In other words, although a howitzer develops a muzzle velocity that is 3 meters per second greater (or less) than standard with propellant lot G, it will not necessarily be the same with any other propellant lot. The optimum method for determining ammunition performance is to measure the performance of a particular projectile family-propellant lot-charge combination (calibration). However, predictions of the performance of a projectile family-propellant lot-charge group combination may be inferred with the understanding that they will not be as accurate as actual performance measurements.

Factors Causing Nonstandard Velocities

Nonstandard muzzle velocity is expressed as a variation (plus or minus so many meters per second) from the accepted standard. Round-to-round corrections for dispersion cannot be made. Each of the following factors that cause nonstandard conditions is treated as a single entity assuming no influence from related factors.

1. Velocity trends. Not all rounds of a series fired from the same weapon and using the same ammunition lot will develop the same muzzle velocity. Under most conditions, the first few rounds follow a somewhat regular pattern rather than the random pattern associated with normal dispersion. This phenomenon is called velocity trends (or velocity dispersion), and the magnitude varies with the cannon, charge, and tube condition at the time each round is fired. Velocity trends cannot be accurately predicted; thus, any attempt to correct for the effects of velocity trends is impractical. Generally, the magnitude and duration of velocity trends can be minimized when firing is started with a tube that is clean and completely free of oil.
2. Ammunition lots. Each ammunition, projectile, and propellant lot has its own mean performance level in relation to a common weapon. Although the round-to-round variations within a given lot of the same ammunition (ammo) types are similar, the mean velocity developed by one lot may differ significantly in comparison to that of another lot. With separate-loading ammunition, both the projectile and propellant lots must be identified. Projectile lots allow for rapid identification of weight differences. Although other projectile factors affect achieved muzzle velocity (such as, diameter and hardness of rotating band), the cumulative effect of these elements generally does not exceed 1.5 m/s. As a matter of convenience and speed, they are ignored in the computation of firing data.
3. Tolerances in new weapons. All new cannons of a given caliber and model will not necessarily develop the same muzzle velocity. In a new tube, the mean factors affecting muzzle velocity are variations in the size of the powder chamber and the interior dimensions of the bore. If a battalion equipped with new cannons fired all of them with a common lot of ammunition a variation of 4 meters per second between the cannon developing the greatest muzzle velocity and the cannon developing the lowest muzzle velocity would not be unusual. Calibration of all cannons allows the firing unit to compensate for small variations in the manufacture of cannon tubes and the resulting variation in developed muzzle velocity. The MVV caused by inconsistencies in tube manufacture remains constant and is valid for the life of the tube.
4. Tube wear. Continued firing of a cannon wears away portions of the bore by the actions of hot gases and chemicals and movement of the projectile within the tube. These erosive actions are more pronounced when higher charges are fired. The greater the tube wear, the more the muzzle velocity decreases. Normal wear can be minimized by careful selection of the charge and by proper cleaning of both the tube and the ammunition.
5. Nonuniform ramming. Weak ramming decreases the volume of the chamber and thereby theoretically increases the pressure imparted to the projectile. This occurs because the pressure of a gas varies inversely with volume. Therefore, only a partial gain in muzzle velocity might be achieved. Of greater note is the improper seating of the projectile within the tube. Improper seating can allow some of the expanding gases to escape around the rotating band of the projectile and thus result in decreased muzzle velocity. The combined effects of a smaller chamber and escaping gases are difficult to predict. Weak, nonuniform ramming results in an unnecessary and preventable increase in the size of the dispersion pattern. Hard, uniform ramming is desired for all rounds. When semifixed ammunition is fired, the principles of varying the size of the chamber and escape of gases still apply, particularly when ammunition is fired through worn tubes. When firing semifixed ammunition, rearward obturation is obtained by the expansion of the cartridge case against the walls of the powder chamber. Proper seating of the cartridge case is important in reducing the escape of gases.
6. Rotating bands. The ideal rotating band permits proper seating of the projectile within the cannon tube. Proper seating of the projectile allows forward obturation, uniform pressure buildup, and initial resistance to projectile movement within the tube. The rotating band is also designed to provide a minimum drag effect on the projectile once the projectile overcomes the resistance to movement and starts to move. Dirt or burrs on the rotating band may cause improper seating. This increases tube wear and contributes to velocity dispersion. If excessively worn, the lands may not engage the rotating band well enough to impart the proper spin to the projectile. Insufficient spin reduces projectile stability in flight and can result in dangerously erratic round performance. When erratic rounds occur or excessive tube wear is noted, ordnance teams should be requested to determine the serviceability of the tube.
7. Propellant and projectile temperatures. Any combustible material burns more rapidly when heated before ignition. When a propellant burns more rapidly than would be expected under standard conditions, gases are produced more rapidly and the pressure imparted to the projectile is greater. As a result, the muzzle velocity will be greater than standard and the projectile will travel farther. Table E in the tabular firing tables lists the magnitude of change in muzzle velocity resulting from a propellant temperature that is greater or less than standard. Appropriate corrections can be extracted from that table; however, such corrections are valid only if they are determined relative to the true propellant temperature. The temperature of propellant in sealed containers remains fairly uniform though not necessarily at the standard propellant temperature (70 degrees Fahrenheit [F]). Once propellant has been unpacked, its temperature more rapidly approaches the air temperature. The time and type of exposure to the weather result in temperature variations from round to round and within the firing unit. It is currently impractical to measure propellant temperature and apply corrections for each round fired by each cannon. Positive action must be taken to maintain uniform projectile and propellant temperatures. Failure to do this results in erratic firing. The effect of an extreme change in projectile or propellant temperature can invalidate even the most recent corrections determined from a registration.
   • Ready ammunition should be kept off the ground and protected from dirt, moisture, and direct rays of the sun. At least 6 inches of airspace should be between the ammunition and protective covering on the sides, 6 inches of dunnage should be on the bottom, and the roof should be 18 inches from the top of the stack. These precautions will allow propellant and projectile temperatures to approach the air temperature at a uniform rate throughout the firing unit.
   • Propellant should be prepared in advance so that it is never necessary to fire freshly unpacked ammunition with ammunition that has been exposed to weather during a fire mission.
   • Ammunition should be fired in the order in which it was unpacked.
   • Propellant temperature should be determined from ready ammunition on a periodic basis, particularly if there has been a change in the air temperature.
8. Moisture content of propellant. Changes in the moisture content of propellant are caused by improper protection from the elements or improper handling of the propellant. These changes can affect muzzle velocity. Since the moisture content cannot be measured or corrected for, the propellant must be provided maximum protection from the elements and improper handling.
9. Position of propellant in the chamber. In fixed and semifixed ammunition the propellant has a relatively fixed position with respect to the chamber, which is formed by the cartridge case. In separate-loading ammunition, however, the rate at which the propellant burns and the developed muzzle velocity depends on how the cannoneer inserts the charge. To ensure proper ignition of the propellant he must insert the charge so that the base of the propellant bag is flush against the obturator spindle when the breech is closed. The cannoneer ensures this by placing the propellant flush against the Swiss groove (the cutaway portion in the powder chamber). The farther forward the charge is inserted, the slower the burning rate and the lower the subsequent muzzle velocity. An increase in the diameter of the propellant charge can also cause an increase in muzzle velocity. Loose tie straps or wrappings have the effect of increasing the diameter of the propellant charge. Propellant charge wrappings should always be checked for tightness, even when the full propellant charge is used.
10. Weight of projectile. The weights of like projectiles vary within certain zones (normally termed square weight). The appropriate weight zone is stenciled on the projectile (in terms of so many squares). Some projectiles are marked with the weight in pounds. In general terms, a heavier-than-standard projectile normally experiences a decrease in muzzle velocity. This is because more of the force generated by the gases is used to overcome the initial resistance to movement. A lighter-than-standard projectile generally experiences an increase in velocity.
    
    Note: Copperhead projectiles are not marked with weight in pounds. The precision manufacturing process used guarantees a weight of 137.6 pounds.
    
    
11. Coppering. When the projectile velocity within the bore is great, sufficient friction and heat are developed to remove the outer surface of the rotating band. Material left is a thin film of copper within the bore and is known as coppering. This phenomenon occurs in weapons that develop a high muzzle velocity and when high charges are fired. The amount of copper deposited varies with velocity. Firing higher charges increases the amount of copper deposited on the bore surfaces, whereas firing lower charges reduces the effects of coppering. Slight coppering resulting from firing a small sample of rounds at higher charges tends to increase muzzle velocity. Erratic velocity performance is a result of excessive coppering whereby the resistance of the bore to projectile movement is affected. Excessive coppering must be removed by ordnance personnel.
12. Propellant residue. Residue from burned propellant and certain chemical agents mixed with the expanding gases are deposited on the bore surface in a manner similar to coppering. Unless the tube is properly cleaned and cared for, this residue will accelerate tube wear by causing pitting and augmenting the abrasive action of the projectile.
13. Tube conditioning. The temperature of the tube has a direct bearing on the developed muzzle velocity. A cold tube offers a different resistance to projectile movement and is less susceptible to coppering, even at high velocities. In general, a cold tube yields more range dispersion; a hot tube, less range dispersion.
14. Additional effects in interior ballistics. The additional effects include tube memory and tube jump.
    • Tube memory is a physical phenomenon of the cannon tube tending to react to the firing stress in the same manner for each round, even after changing charges. It seems to remember the muzzle velocity of the last charge fired. For example, if a fire mission with charge 6 M4A2 is followed by a fire mission with charge 4 M4A2, the muzzle velocity of the first round of charge 4 may be unpredictably higher. The inverse is also true.
    • Tube jump occurs as the projectile tries to maintain a straight line when exiting the muzzle. This phenomenon causes the tube to jump up when fired and may cause tube displacement.