Posted on Leave a comment

Ballistic Coefficient

The ballistic coefficient (BC) of a bullet is a measure of a bullets ability to overcome air resistance during its flight. This flight is inversely proportional to the negative acceleration: a high number indicates a more streamlined bullet.

Mathematically, the BC calculation is the sectional density of the bullet divided by the form factor. This definition emerges from the physics of ballistics and is used in mathematical analysis of bullet trajectories.

The History

The science of Ballistics goes back many years. From the invention of firearms man needed to know how the projectile would travel.

In 1537, Niccolo Tartaglia discovered that firing a bullet at around 45 degrees gave you maximum range and that the trajectory was a continuous curve.

In 1636 Galileo Galilei discovered that gravity had a consistent acceleration on a falling body (terminal Velocity). This allowed him to prove that a bullets trajectory was a curve.  

1665 Sir Isaac Newton discovered the law of air resistance. Newton established this through his experiments on drag through air and in fluids: drag increases proportionately as the air or fluid density increases. As speed increased the drag increase was the square of the speed. One needs to remember in the 1600s there were no high velocity rifle cartridges.

1800s with the advent of artillery and serious government backing as wars were extremely common in Europe and America, the science of ballistics grew rapidly. By the end of the 1800s the basics had all been done and it was now just a question of refining the process. 1718, John Keill challenges the continental maths of the day. He said that air resistances increases exponentially as the velocity of the projectile increases. However he could not prove this claim. Enter John Bernoulli who picked up this challenge and in a fairly short time solved the problem and this is now known as the Bernoulli equation.

1742, Benjamin Robbins invented the ballistic pendulum (the first chronograph). It was a simple mechanical device that would measure a projectile’s velocity. Robbins, in his book, New Principles of Gunnery found that air resistance varied according to velocity with a major change coming at the speed of sound. He used numerical integration to prove this. This initiated the standard projectile which evolved into the Standard G1 and G7 projectile as we know them today.

1753, Leonhard Euler perfected the maths and it was now possible to theoretically calculate trajectories. He used Bernoullis equation to formulate air resistance.

1844, the Electro-ballistic chronograph was invented. By 1867 the chronograph was accurate to within one ten millionth of a second. This is the forerunner of the chronograph we use today.

The Bernoullis definition emerges from the physics of ballistics and is used in mathematical analysis of bullet trajectories. In a practical sense, this definition is not satisfactory to most people for at least two reasons.

The first is the question of a bullet’s form factor. The form factor is a property of the shape of the bullet design, but it is no easier to explain than the BC.

The second reason is that this mathematical definition can lead to an erroneous conclusion. Assume for the moment that the form factor is just a constant property of the bullet design (not always true). The sectional density of a bullet is its weight divided by the square of its diameter. So, to get a large BC we need a large sectional density. It appears from the mathematics that a bullet with a very small diameter should have a very large sectional density because its weight is divided by a very small number, and this should give it a very high BC. In other words, this line of reasoning would lead us to expect that small caliber bullets should have very large BC values. But this is not true because when the diameter of the bullet is small, the volume also is small. The weight of the bullet then is small and the sectional density is necessarily small also. The net result is that small calibre bullets generally have lower BC values than larger calibre bullets.

Before the end of the 19th century, pointed bullets and boat-tail bullets were developed which significantly improved ballistic performance. For their improvements to be beneficial it became imperative to understand a bullets trajectory which would make it possible to reliably engage targets out at longer ranges. Shooting at longer ranges necessitated the development of graduated sights.

The second half of the 19th century and the early part of the 20th century was a period of very intensive development in the science of ballistics. These developments in ballistics were driven by technological advances for warfare in guns, projectiles, propellant ignition and propellants. Governments were eager to fund research, development and manufacturing of improved guns and gunnery and battles were often decided by the forces that had the superior arms.

As warfare grew in intensity and mobility it became necessary to understand the physics of bullet flight. It was now necessary to find methods of calculating bullet trajectories as well as the changes in those trajectories caused by changes in bullets, muzzle velocities, firing and atmospheric conditions.

BC Today

We now see that the ballistic coefficient is a scale factor. The BC standard drag is used to compare nonstandard bullets against this standard. The higher the BC numbers, the more streamlined or aerodynamic the bullet is. BC’s are normally given in the G1 scale when large calibre low drag bullets are measured and their values inserted in as a G1 value. It is possible to have a BC value greater than 1.0—this is seen in the .50BMG. BC’s that are just given as a BC and no indication of wither the value is a G1 or G7 will be a G1 value. On the more modern, low drag type bullets the manufacturers are now giving G1 and G7 values. G7 values are better suited and more closely follow the trajectory of a Spitzer shaped boat tail bullet. Sierra bullets have an interesting way of dealing with the problem—they supply multiple G1 BC’s at different velocities.

G1 and G7 both refer to aerodynamic drag models based on a “standard projectile” (see Figure 1 and Figure 2) which is used to establish the drag model. The G1 shape resembles the flat based bullet–the Ogive is only 2 times diameter making it not very aerodynamic. As can be seen the G7 shape is very different, and closely duplicates the geometry of a modern long-range boat tail bullet. When choosing a drag model, G1 is better suited to flat-based bullets and the G7 is better fit for longer streamlined, boat-tailed bullets.

Used for sporting and target-shooting purposes, BC’s are generally easy and inexpensive to measure. On the other hand measuring the bullets drag to establish form factors are complexed and the equipment to do the measuring is expensive. The BC values quoted by all producers of commercial bullets refer to G1 and when referencing G7 the manufacturer will specify. It is important to note that BC values quoted by commercial producers should be used only with the same drag model. If you insert a G1 value in as a G7 value on an app or ballistic program the values generated will not be correct.

Formula for calculating a Ballistic Coefficient

Where:

  • BC =  ballistic coefficient
  • m = mass of bullet
  • d = measured cross section (diameter) of projectile
  • i = Coefficient of form or form factor.

In closing

The better ballistics Apps allow the user to select either G1 or G7 Ballistic Coefficient values to calculate the bullet’s flight path. The BC of a bullet is its ability to overcome air resistance during its flight. As you have probably seen G7 values are numerically lower around 50% lower than the G1 values for the same bullet. Do not substitute G7 values with G1 values as your bullet’s flight path will be totally off.

A bullet that is not 100% stable will not achieve its advertised BC as excessive YAW will impose more air drag on the bullet which will not allow the bullet to fly with its designed freedom—especially over longer distances.

G1 drag models are very speed sensitive so over longer shots the bullet drop might not be accurate.

Leave a Reply

Your email address will not be published. Required fields are marked *