Ballistics - Calculating the Distance and Trajectory of a Bullet - Essay Example

? Ballistics involves the study of firearms. The study of ballistics concerns itself with the path in which the bullet from a gun moves through the air, to a target location. In the criminal justice system, ballistics is used to identify and match bullets recovered from the crime scene, to the specific firearm used during the commission of a criminal action (Kieser and Taylor, 2013). There are two types of ballistics, interior and exterior ballistics. Interior ballistics concerns itself with the thermodynamics and chemistry that occurs in a guns barrel. Exterior ballistics concerns itself with the motion of a bullet that comes from a gun. This paper concerns itself with the mathematics that occurs from the exterior ballistics. This paper seeks to identify how mathematics helps to determine the distance and trajectory of a bullet. Coupland and Rothchild (2011) denote that motion is of two types, that is natural motion, and violent motion. Natural motion faces resistance from air or water, basically because it occurs in such kind of a medium. An example of a natural motion is the falling of a stone, or the rising of a smoke. Violent motion on the other hand occurs as a result of an application of force. An example of a violent motion is the movement of a bullet from a firearm. Coupland and Rothchild (2011) denote that the weight of the object and the force in which an individual applies to a motion object will determine the distance and the speed in which the motion object under consideration will move (Pender, 2012).Before determining on how to use mathematics to determine the distance and trajectory of a bullet, it is important to understand that a trajectory determination does not identify and reveal the occurrences prior to an individual holding the gun (McCoy, 2012). It only identifies the distance, and the nature of the weapons used by the criminals. In calculating the distance and trajectory of a bullet, it is important to denote that a bullet under motion faces two types of forces, that is the force of gravity, and the natural force brought by the air around which the bullet flies. In calculating a distance that a bullet covers, it is important to denote that bullets have a ballistic coefficient of G1 (Pender, 2012). The ballistic coefficient of a bullet (G1) allows an individual to scale the bullets drag to the standard projectile established by the Gavre Commission. The standard ballistic coefficient of a bullet established by the Gavre commission was 1.000 (Warlow, 2012). This standard allows an individual to calculate how many feet’s a projectile will lose a given number of velocities in comparison to a distance a standard projectile will cover, after losing the same amount of velocity, under similar atmospheric environment. For example, a G 1 standard projectile drops approximately 2904 to 3000 fps over a distance of 100 yards. This is at a standard meteorological condition. If the bullet under consideration will have a ballistic coefficient of 0.5, the bullet will drop from 3000fps to 2904 fps in a distance of 50 yards (Kieser and Taylor, 2013). This distance is calculated in this manner,100 yards multiply by 0.5= 50 yards. From these calculations, we can denote that when the ballistic coefficient of a bullet is big, the weight and shape of the bullet have a lesser drag. The bullet will also lose its velocity in a slower manner, and the rate of its deflection by the wind is minimal. This calculation will mostly affect artilleries made in the standard shapes of the 1800s, in which the Gavre commission established the bullets ballistic coefficient (Warlow, 2012). However, in the current century, manufactures have different shapes of a projectile which also have a different G1standard.On this basis, different G I standards, and Ballistic coefficients work over a limited number of velocities. On this basis therefore, modern bullets have a specified ballistic coefficient, over a given and different velocity range. This is because the shapes emanating from their drag curve is not identical with that of an old bullet at the different velocity ranges. Because of differences in the ballistic coefficient of a bullet, and G1 measurements of modern projectiles, other methods of measuring the distance and trajectory of a bullet have emerged (Warlow, 2012).One of the methods of calculating the distance and trajectory of a bullet is by using the pejsa model. This model has the capability of determining the distance and trajectory of a bullet over 1000 yards. The size of the bullet must be within 0.5mm and its velocity must be within 0.3m/s. This method uses the standard G1 coefficient of a bullet, it thereafter incorporates this coefficient into a coefficient function of Pejsa retardation. The intention of incorporating the standard G1 coefficient of a bullet into the coefficient function of Pejsa retardation is to model the retardation characteristics of the projectile under consideration (McCoy, 2012).On this basis, the Pejsa method uses a drag coefficient that is modeled as an analytic function of a Mach number. This Mach number is developed from the drag profile of a projectile. For a ballistic expert to come up with this number, he or she needs to test the various bullets under consideration, and thereafter develop the Mach number that fits the profile of the drag projectile.The Pejsa model also has a constant slope factor that accounts for a change in the retardation rate of the sizes and rates of different bullets and ammunitions (Kieser and Taylor, 2013). This constant factor ranges from 0.1 to 0.9, but it depends on the size and shape of the bullet under consideration. If ballistic experts do not know this deceleration constant factor, then they will use a constant of 0.5 for purposes of predicting the flight behavior of a bullet. With this mathematical model, a ballistic expert can identify the drag behavior of a particular projectile. On this basis, it is possible to predict the distance and the trajectory of a bullet over a range of 547 yard, or 500 meters. Another mathematical method of calculating the distance and the trajectory of a bullet is the use of the use of the point mass method (Kieser and Taylor, 2013). This method uses the x, y and z axis of a travelling projectile, and uses a table of cd vs. Mach of bullet of any size and shape. For example, at every 0.001 of the motion of a bullet, a program looks into the cd table to identify the exact value at that instant, therefore solving the distance and trajectory of the bullet at the time. On this basis, the point mass method is effective in identifying the distance and trajectory of a fired bullet (Pender, 2012). In conclusion, a valuable method of calculating the distance and trajectory of a bullet has to meet three conditions. It must be practical, robust and accurate. Under accuracy, the method must be able to identify the specific distance and trajectory of the bullet. On this note, it is important to denote that all firearms shoot to a specific area, and not point (McCoy, 2012). The distance should therefore be calculated in terms of the area that the bullet covered. Under robust, the method of calculating the distance and trajectory of the bullet must factor in a wide range of input values and conditions without compromising the accuracy of its predictions. A mathematical method that cannot use different non-standard conditions, and drag functions can create problems in accurately predicting the distance and trajectory of a bullet. Finally, the practicality of the mathematical method under use is of great importance. The method under use must have the ability to treat in a similar manner the different drag functions that exist while calculating the distance and trajectory of a bullet. This is because different bullets come with different measurements of their ballistic coefficients. References: Coupland, R. M., & Rothchild, M. A. (2011). Wound ballistics basics and applications (Transl. of the rev. 3. German ed.). Berlin: Springer Medizin. Kieser, J., & Taylor, M. (2013). Forensic biomechanics. Chichester, West Sussex, UK: Wiley- Blackwell. McCoy, R. L. (2012). Modern exterior ballistics: the launch and flight dynamics of symmetric projectiles ([Rev. 2nd ed.). Atglen, PA: Schiffer Pub.. Pender, H. (2012). Ballistics science. Delhi: University Publications. Warlow, T. A. (2012). Firearms, the law, and forensic ballistics (3rd ed.). Boca Raton, FL: CRC Press. Read More