External Ballistics Part II – Flight to Target

Thank you for returning to continue our study of ballistics. In this article, I will pick-up where we left off from our previous discussion of External Ballistics and focus solely on the projectile’s flight to target. Before introducing the key concepts of kinetic energy, gyroscopic stability and ballistic coefficient, I will provide a brief review to fully set the stage.

During our discussions on Internal Ballistics, we focused on firearm function, reliability, safety and mechanical precision. The complex sequence of interactions that initiate a projectile’s movement from the cartridge case to the end of the barrel. Essentially, it helped us understand how “our” interaction with the firearm affects its function and the start of the projectile’s travel to target.

During our first discussion on External Ballistics, we focused on the principles of Newtonian Physics and the short period of projectile instability caused by Yaw, Precession and Nutation as the projectile transitions from controlled force and rotation in the bore to environmental forces (gravity and air resistance) during free rotation. As we continue this discussion on External Ballistics and analyze the factors that affect the projectile’s flight to target, we need to concede that “our” part as a shooter has ended and all of the forces acting on the projectile are out of our control.

We need to understand these external forces, however. They allow us to “back plan” by choosing the correct firearm, cartridge, aiming solution, etc. Understanding the principles in this second article on External Ballistics will not only set-up the following articles on Trajectory and Terminal Ballistics, it will allow you to make the right mental and physical preparations to consistently place the projectile on target with the desired ballistic effect.

Regardless of the shooting discipline (target shooting, competition, hunting, self-defense, etc.), the terminal ballistic effect can only be accomplished if the projectile arrives where it is intended and with sufficient energy. Target and competition shooters need to ensure their projectile retains enough velocity and stability to optimize their accuracy with the firearm’s mechanical precision. Hunters and those using a firearm for self-defense need to ensure their projectiles retain enough energy to expand and produce the desired terminal ballistic effect.

So, let’s continue with our discussion on External Ballistics.

Velocity and Kinetic Energy

I’ve grouped these two measurements together due to their interrelated nature and role they play in terminal ballistic performance.

Velocity: This is the measure of an object’s change in position relative to time… or how fast a projectile is traveling in a specific direction. Since it is a measure of position and time, velocity can be expressed in many different units of measure, such as feet per second, miles per hour, kilometers per hour, etc. The most common measure of velocity in regard to ballistics is feet per second (ft/s).

• With the right devices and instrumentation, velocity can be measured accurately anywhere along a projectile’s trajectory from its initial velocity (or muzzle velocity), summit velocity (at the highest point in its trajectory), and striking velocity (projectile velocity as it impacts the target). Note that I used the term striking velocity instead of the more commonly used “terminal velocity.” Terminal velocity has an exact and specific meaning which describes the greatest velocity that an object can acquire by falling freely through the air.
• Although velocity can be measured anywhere along the trajectory, it is costly andimpractical to take this measurement anywhere beyond the muzzle. Many shooters will use a chronograph placed just a few feet in front of the muzzle to measure a projectile’s initial velocity. Chronographs are rather simple devices that are made up of sensors and timing devices. As the projectile passes over the first sensor, the clock “starts” and runs until the projectile passes the last sensor which “stops” the clock. Since the sensors are placed at a known distance, the time measured between the first and last sensor calculates the velocity. Chronographs are commercially available for between $100 and $600.
• Applicability: Measuring initial velocity is required to calculate other important ballistic factors such as kinetic energy and bullet drop. Also, since consistency and repeatability are key factors in mechanical precision, measuring initial velocity can demonstrate how consistently (or inconsistently) a specific cartridge performs in a specific firearm.
  

Kinetic Energy: All objects in motion have kinetic energy. Newton’s fundamental law of Conservation of Energy states that energy can neither be created nor destroyed. Since all objects in motion possess kinetic energy, this energy must be transferred from the projectile into the target on impact. By measuring the kinetic energy of a projectile at the muzzle, we can calculate how much energy will be transferred into the target at a certain distance.

• Kinetic energy is simply calculated by multiplying ½ times the mass of the projectile times the square of the velocity… or KE = ½ * MV^2.
• While projectile velocity is typically measured in feet per second (ft/sec), Kinetic Energy is typically measured in foot-pounds. For those interested in calculating kinetic energy for themselves, KE = ((projectile weight in grains)*(velocity in feet per second)²)/(450,400). The number 450,400 combines the conversion from grains to pounds with the ½ required to calculate kinetic energy.
• For example, I recently chronographed a few of my hand-loads in my rifles and pistols. In my Remington 700 in .308cal, I fired a series of 175 grain hollow point boat tail projectiles and calculated an average muzzle velocity of 2,762.4 ft/s. Using the formula for kinetic energy above, KE = ((175)*(2762.4)²)/(450,400) = 2,964.92 ft/lbs of kinetic energy.I conducted the same test with my AR-15 in .223 and my 1911 in .45ACP. In the AR-15, the 62gr projectiles averaged 3,036.80 ft/s and resulted in 1,269.48 ft/lbs of energy. In the 1911, the 230gr projectiles averaged 772 ft/s and resulted in 304.34 ft/lbs of energy.
• The important concept here is that velocity plays a greater role than projectile weight when it comes to kinetic energy. Notice how the .45cal bullet is clearly the largest projectile fired in my test, but its low velocity resulted in the lowest kinetic energy. Also note how the weight of the .223 projectile was just over one-third the weight of the .308 round, but due to the fact that it was nearly 300 feet-per-second faster than the .308 round, it possessed just under one-half of the kinetic energy at the muzzle.
• For a very loose comparison, scientists have “estimated” that a professional boxer’s punch delivers 330 ft/lbs of kinetic energy. (note, this is a very rough estimate because the boxer’s fist is attached to the body which is not “limp” on impact. A boxer can continue to “thrust” a punch following impact whereas a firearm projectile is left with only resultant mass and velocity). For the purposes of this argument, compare the 330 ft/lbs of a boxer’s punch to the muzzle energy of the 175gr .308 (2,762.4 ft/lbs), 62gr .223 (1,269.48 ft/lbs), and 230gr .45ACP (304.34 ft/lbs).
• Applicability: Even with the considerable kinetic energy of the 175gr .308 projectile, there is really no such thing as “knock-down power” in regard to human or large animal targets. Granted the projectile’s kinetic energy will puncture paper or knock-down certain steel or wooden targets that are designed to fall, the energy transferred from a projectile into a human or large animal target will not knock it down from impact alone. The kinetic energy transferred will, however, contribute to penetration and/or expansion. Therefore projectile performance and shot placement play the greatest role in ending the threat or taking down the game animal. This will be discussed in greater detail in my forthcoming articles on Terminal Ballistics.

Gyroscopic Stability

If you recall our discussion in External Ballistics Part I, there is a moment when the projectile transitions from controlled movement in the barrel to free-rotating travel outside of the barrel when Yaw, Precession, and Nutation cause it to “wobble” in a helical pattern.  You may also recall how these forces quickly dampen the “wobble” into a predictable and stable flight.  This is due to the fact that All spinning objects possess gyroscopic properties.  In a firearm projectile, these gyroscopic properties contribute to a principle called “rigidity in space” which creates the gyroscopic inertia required for the projectile to travel along a predictable trajectory.

• In general, a heavier projectile is more resistant to disturbing forces than a light mass… i.e. heavier projectiles maintain a greater gyroscopic stability and are less affected by wind, and incidental contact than lighter projectiles.
• The higher the rotational speed (i.e. faster rifling twist), the greater the rigidity, gyroscopic inertia, and resistance to deflection (wind).
• Applicability: in theory, a heavier projectile with a higher rotational speed will maintain its gyroscopic stability better than a lighter projectile with a lower rotational speed.

Ballistic Coefficient

As we covered in External Ballistics Part I, gravity and air resistance immediately exert force on a projectile the moment it leaves the barrel. So far in this article, we’ve covered muzzle velocity, kinetic energy, and gyroscopic stability en route to understanding our goal - how to ensure a projectile retains as much muzzle velocity as possible for both predictable ballistic flight and to ensure effective terminal ballistic performance. This leads us to the term Ballistic Coefficient, which is a measure of how well a projectile can overcome air resistance and maintain flight velocity. Mathematically calculating the characteristics of projectile weight, diameter, and shape, the ballistic coefficient measures the projectile’s ability to conquer air resistance. This mathematical equation produces a number between zero and one. The higher (closer to one) ballistic coefficient is preferable as this indicates it will maintain its velocity better than a projectile with a lower ballistic coefficient (closer to zero).

• Shape - the third factor in determining ballistic coefficient is the shape from theprojectile tip through the ogive to the surface area of maximum diameter combined with the shape of the base. In general terms blunt tips with flat bases have the least efficient form factors whereas sharp tips with long ogives and boat-tails have the most efficient form factors.
• Weight and diameter - These two measurements combine to determine sectional density of a projectile. Sectional density is measured by dividing the weight by the square of the diameter. SD=w/d². Heavier projectiles possess greater gyroscopic stability and resistance to wind. Large diameters, however, incur greater air resistance. Therefore, the most proficient projectiles are those that are the heaviest in proportion to their diameter (caliber).
• Applicability: the most common way to design a heavier projectile of the same caliber is to make it longer.

• Applicability: A projectile with a high ballistic coefficient will travel to the target with a flatter trajectory, will spend less time in flight, and be less influenced by air resistance and wind deflection… therefore, it will arrive at the target with the greatest amount of residual velocity and kinetic energy.

Wow, that was quite a ride. Just remember: measuring muzzle velocity allows you to determine the consistency of your cartridge selection and calculate bullet drop and kinetic energy; velocity has a greater effect on kinetic energy than projectile weight; heavier projectiles with a higher rotational velocity are more stable and less affected by wind; long, heavy, and sleek projectiles with boat tail bases travel along a flatter trajectory, spend less time in flight, and arrive at the target with the greatest amount of residual velocity and kinetic energy.
With all of this knowledge in hand, we will be ready to discuss bullet drop, wind drift, and trajectory calculations in the next article. Until then, stay safe and shoot straight!

About Author

- Howard Hall 

Range Master

Howard has served for nearly 20 years in the Marine Corps. He has served as a Platoon Commander, Company Commander, Battalion Executive Officer, Regimental Operations Officer, and Battalion Commander. He has multiple combat tours to include serving as a military transition team member in Fallujah. He is an NRA Certified handgun instructor and holds numerous Marine Corps training credentials.  An active competitor in action pistol (United States Practical Shooting Association), long range rifle (NRA F-Class), and shotgun (Amateur Trapshooting Association, National Skeet Shooting Association), howard has earned numerous accolades and medaled during DoD competitions with the 1911 platform in bulls-eye shooting.

Source: http://aegisacademy.com/community/external-ballistics-part-ii/