Internal ballistics

Internal Ballistics

1. SUBMITTED BY –ADITI TRIPATHI SUBMITTED TO – KETAN SIR INTERNAL BALLISTICS

2. INTRODUCTION It is the particular field which deals with the motion of projectiles in the bore of the weapon. It commences as soon as the 1 st gain of the propellant is ignited and subsists till the projectile leaves the muzzle of the weapon. SOME TOPICS ARE EXPLAINED HERE :- 1.] Muzzle velocity & factors affecting it. 2.] Le Due’s formula Velocity , Space curve 3 .] All burnt point

3. Muzzle velocity Muzzle velocity is the speed of a projectile at the moment it leaves the muzzle of a gun. [1] Muzzle velocities range from approximately 120 m/s (390  ft /s) to 370 m/s (1,200  ft /s) in black powder muskets, [2] to more than 1,200 m/s (3,900  ft /s) [3] in modern rifles with high-performance cartridges such as the .220 Swift and .204 Ruger , all the way to 1,700 m/s (5,600  ft /s) [4] for tank guns firing kinetic energy penetrator ammunition Projectile velocity :- The velocity of a projectile is highest at the muzzle and drops off steadily because of air resistance. Projectiles traveling less than the speed of sound (about 340 m/s (1,100  ft /s) in dry air at sea level) are subsonic, while those traveling faster are supersonic and thus can travel a substantial distance and even hit a target before a nearby observer hears the "bang" of the shot

4. Factors affecting muzzle velocity The quantity of the powder The quality of the powder Barrel length Twist rate Bullet fit Dimension of the throat

5. Velocity V = FT/M Faster rounds not only get to the target quicker, but they are also less prone to environmental factors that can slow down and throw off the trajectory and flight path of the bullet.

6. Difference between the two rounds

7. Factor affecting velocity Propellant: The amount of propellant and the type of propellant will determine the ultimate range of the projectile.  Muzzle Length: In accordance with propellant, determines the muzzle velocity of the projectile. A general rule of thumb is, the longer the muzzle, the higher the muzzle velocity. Projectile Type: As in it's shape. A baseball is not going to fly as far as an artillery shell, even if thrown at the same speeds, due to the drag it creates. Atmospheric Pressure: Affects how dense the air is, determines how much drag the projectile will have to fly through, affecting it's range. Temperature: Same as atmospheric pressure. Wind: Depending on the speed and direction, can result in the projectile arriving in places it has no business being in. Humidity: Same as atmospheric pressure, but also if a projectile has to travel through a particularly humid area when the conditions are just right and if the projectile is in the air long enough, it can accumulate ice, affecting it's shape, increasing drag and increasing it's weight. Spin of the Earth, or The Coriolis Effect: Shows it's effects most at the West-East, and vice versa, directions. Can be negligible in short distances, such as when a pistol is fired or a ball is thrown. Will become more noticeable as the range increases and will need corrections to aiming such as when firing a sniper rifle at long range or artillery fire. Projectiles fired

8. Le duc empirical formula Le Duc Empirical Model   The Le Duc method of internal ballistics originated from a course of lectures by Captain Le Duc published in 1905. The method was adopted as a standard for the U.S. Navy well into WW1. The system is almost entirely empirical and is based on a simple equation that approximates the velocity-space curve for a projectile in a gun.   V = a*x/( x+b )   x is the distance of bullet travel   v is the velocity of the bullet   a, and b are parameters of the model.   This model is about as far as the usual gun magazines get into internal ballistics. It is convenient to use the model to figure the effect of gun barrel length on the bullet velocity given 2 velocity - distance points that can be used to determine the parameters a and b. It is also possible to solve for the parameters given a peak pressure, velocity, and distance point, since the above equation can be differentiated to give the acceleration which is proportional to pressure. dv/ dt = v*dv/dx = a^2*b*x/( x+b )^3   The peak acceleration/pressure point can be deduced by taking the derivative and setting it to 0.

9.   V'' = (a^b^2 - 2*a^2*b*x)/( x+b )^4   so x = b/2 when v'' = 0. This means peak pressure occurs at x = b/2.   Substituting b/2 for x in the equation for v' gives v' = 4*a^2/(27*b) at peak pressure. From F=ma we write   Ps*A = m*v'   where Ps is the pressure on the base of the shot (bullet) and A is the area of the bore, and m is the bullet mass. The relationship between bullet pressure and gun breech pressure is Pb (breech) = (1+C/(2*m))*Ps as derived in the classical theory section, where C is the powder charge mass. The expression for breech pressure, adding in bore friction Fr would then be:   Pb = (1+C/(2m))*m/A*[a^2*b*x/( x+b )^3 + Fr ] and the peak pressure at x=b/2 would then be:   Pb (max) = (1+C/(2m))*m/A*[4*a^2/(27*b) + Fr ]   This equation coupled with the original velocity equation makes it possible to tabulate v vs. x given a peak pressure and velocity/distance point. Consult the program section of the home page to pick up a free LECUC program which does this. Once you know a and b, it is possible to graph the pressure-space curve for the system with the above equation for Pb as below for a typical .223 Rem load.  

10. Brunt point   3. All Burnt - The point during a projectile's travel up the gun barrel where all of the propellant charge has been consumed. In most instances, propellant charges are designed such that the propellant has been consumed by the time that the projectile is about one half to two thirds of the way up the barrel. For example, the standard charge in a 5"/54 (12.7 cm) Mark 67 cartridge achieves All Burnt between 115 to 125 inches (290 to 320 cm) of shot travel, depending upon the amount of propellant loaded in the lot of charges being fired. Shot travel in the 5"/54 is 235 inches (597 cm), which means that the All Burnt point is about half-way up the barrel. There are a few exceptions where the All Burnt point is further up the barrel, but these are usually for rounds developed after the gun entered service where the charge developers are trying to obtain the highest possible muzzle velocity

11. To correct this the load can be altered by either quantity of powder, using different weight bullets or by using a faster or slower burning powder. Doing this safely whilst not exceeding the safe pressures the gun can routinely handle should not be undertaken without knowledge and experience