The Effect of Gravitational Attraction and Air Resistance on a Projectile

The study of exterior ballistics is based primarily on the understanding and application of principles of physics. In their book, Shooting Incident Reconstruction, authors Michael G. Haag and Lucien C. Haag discuss the physics and application of exterior ballistic forensics. In this blog post we will review the two primary parameters associated with a bullet’s flight and review the equation responsible for expressing the slowing of a projectile.
The study of exterior ballistics is based primarily on the understanding and application of principles of physics. In their book, Shooting Incident Reconstruction, authors Michael G. Haag and Lucien C. Haag discuss the physics and application of exterior ballistic forensics. In this blog post we will review the two primary parameters associated with a bullet’s flight and review the equation responsible for expressing the slowing of a projectile.

During an investigation where bullets are present, there are likely a number of unknown pieces of information. Fortunately, in exterior ballistics, there are a number of parameters that are either constant or readily measurable with modern instrumentation. The primary parameters that must be taken into account are the gravitational attraction and air resistance.

The first and most obvious of these parameters is gravitational attraction. Gravitational attraction, is described as a force manifested by acceleration toward each other of two free material particles or bodies or of radiant-energy. Its effect on the bullet is constant and predictable. The average sea level value for the earth’s gravitational acceleration is 32.174 fps/s (9.807m/s/s). A bullet, regardless of its muzzle velocity, will be acted on immediately after it leaves the muzzle and will ultimately fall to the ground.

Atmosphere, in the form of air resistance, is the other major force acting on a projectile. Air resistance, also called drag, is described as the forces that are in opposition to the relative motion of an object through the air. While there are a number of weaker and more subtle force acting on a bullet in flight, gravity and drag are the two most important.

Air resistance slows the bullet down and gravity pulls it back to earth. At high velocities, deceleration as a result of air resistance is quite substantial. The slowing of a projectile in can be expressed in the following equation:

F = -½ρV2 ACd

In this equation F is the deceleration force of drag, a ρ (rho) is the density of the atmosphere, which depends on barometric pressure, altitude, temperature and humidity. The International Civil Aviation Organization (ICAO) standard on sea-level value for the density air is 0.076474 pounds per cubic foot (0.01226 grams per cubic centimeter.) The standard atmosphere is 59 degrees F, 78% relative humidity and pressure of 29.53 in Hg (750 mm Hg). V in the equation is the velocity, A is the cross sectional area of the projectile, and CD is the drag coefficient, which is not considered a constant and varies as a result of velocity as well as the properties of the projectile, including its stability in flight.

While many unknowns are likely to persist during an investigation involving the presence of bullets, there are some parameters of exterior ballistics that are either constant or readily measurable with modern instrumentation. Once private investigators and forensic scientist are able to determine these parameters, this information can then be applied to the investigation efforts and ideally lead to a greater understand of the situation and evidence at hand.
blog comments powered by Disqus