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The Ballistic Coefficient

In this age of Field Firing Solutions such as SORD™ and ballistic calculation software that sits on your phone, not to mention the capability of precision weapons such as the EDM Windrunner M96 or the THOR M408, the BC or Ballistic Coefficient is a term that is hard to escape in shooting these days, especially in long range shooting, but there is also a considerable amount of confusion as to what the term actually means and what various numeric classifications denote.

So to start, where did the ballistic coefficient begin and how has it progressed over time to what we understand it to be today.

The first projectile analysis came from Galileo way back in 1636 when he published his analysis of projectile trajectories.  At that time Galileo incorrectly thought that air drag was minimal compared to the impact of gravity on a projectile.  To be fair to Galileo this was primarily due to the fact that the firearms of the time had muzzle velocities that were much less that the speed of sound.

These models underwent fundamental revision in 1742, when Benjamin Roberts, an English mathematician, invented the Ballistic Pendulum, that made the direct measurement of bullet velocities possible.  The Ballistic Pendulum immediately identified two fundamental shifts away from Galileo’s original suppositions.  First, the muzzle velocities of bullets were much higher than predicted and second, bullets slowed down in flight much faster than originally thought.

Projectile theory progressed over the following century as theoretical developments in mathematics and physics also progressed but it wasn’t until around 1870 that a real leap forward came when the Reverend Francis Bashforth, another English mathematician and experimenter, invented an early type of chronograph and established the concept of a “standard bullet”.

His concept was that a cylindrical flat-based bullet of a certain diameter, weight, length and point shape could be defined as a standard and from that a scalar deviation factor could be calculated as the actual bullet’s weight and diameter changed.  By establishing a standard drag for a standard bullet it meant a multiplier could be used against that standard rather than having to measure the drag of each and every individual bullet.  This was a huge step forward and was the first steps towards the ballistic coefficient, as we know it today.

Initially this value was named the drag scale factor and Bashforth based his formula on a bullet diameter of 1 inch and a bullet weight of 1 pound for his standard bullet that simplified the equation still further but ultimately a problem developed as experiments proved that the drag scale factor was giving the incorrect answer.  Unknown to Bashforth or others at the time small changes in the size or shape of a bullet will cause different air flow around the bullet and therefore change the drag on the bullet.  We know this today as the form factor and it is usually denoted in the equation as the letter “I” giving us the drag scale factor equation of:

Drag scale factor = [ I * dact bullet^2/wact bullet]

In turn as it was felt that “bigger is better”,  the ballistic coefficient became the inverse of the drag scale factor giving us an equation as follows:

Ballistic Coefficient =[1/drag scale factor]=[ wact bullet/(I * dact bullet^2)]

By taking this approach, when comparing two bullets the one with the larger ballistic coefficient has the lessor amount of drag of the two and is therefore more efficient in the air and has the higher performance.

That was not the whole story however when it came to the Ballistic Coefficient.  Again through experimentation it was found that the standard drag on a bullet is not consistent at all velocities and therefore the ballistic coefficient calculated using the standard drag could not be calculated as being consistent across all velocities.  In order to make scaling of the drag factor to work, therefore, the ballistic coefficient must be able to change in value across different velocities or a new standard bullet that is more appropriate for the actual bullet must be found.

If the former approach is taken a single drag model is applied, such as G1, in addition to velocity regions spanning the full velocity range.  This is not unusual today where bullet manufacturers supply the G1 across a number of ranges.

The second approach is increasing however as more research goes into bullet design and they move further away from the original Basforth standard bullet we are seeing the use of additional “G” numbers that are a truer reflection of the bullet design itself.

Chosen in honour of the French Gavre Commission, which existed in the late 19th Century and performed firing tests and analysis, the “G” designation was given to denote the drag function (or G function) of a given bullet design.  G1 was given to the original Basforth standard bullet with the other G numbers representing other bullet shapes as follows:

  • G1 :     Flat based pointed
  • G2 :     Conical Point Banded
  • G5 :     Low-base Boat Tail
  • G6 :     Flat-base Spire Point
  • G7 :     VLD Boat Tail
  • G8 :     Flat-base Secant Nose

G1 and G7 are the most common that we see in use today for commercial bullets however it is important to remember that the ballistic coefficient of a bullet is measured in relation to a particular G function.  They are not interchangeable so if your entering information into your ballistic computer and you’ve entered a drag function such as G7, make sure it’s the G7 number that is entered else the calculations will be wrong.

So whatever your shooting demands a good understanding of the ballistic coefficient and how it effects your shooting will only help improve your ammunitions performance and hopefully your scores.

This and other blogs on long range shooting are available at the Figure14.com website http://www.figure14.com.  Figure14 is a partner of Knesek and THOR Global Defense importing EDM and THOR rifles into the UK.

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John Mason is a Director an co-founder, along with Larry Knesek of Figure 14 Limited. Figure 14 is a UK based firearms dealer specialising in precision weapon systems from EDM and THOR
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  • Drag is another misnomer. Drag sis pulling something behind or dragging behind.Four forces acting on a moving projectile, shape, friction, air resistance on its nose and diameter and and vacuum behind. The first three factors increase to the square of the velocity, but the latter is a function of a constant force (vacuum above sound barrier) which affects retardation and is dependent on flight time. In modern (and metric) ballistics this is expressed as the RFD%. A slower bullet is losing less velocity from forces acting on the nose, but relatively more velocity due to a constant force of vacuum acting longer on the base of the bullet when flight time is longer. Author of 17 books on fire arms and ballistics.