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## 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.

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## Twist Rates & Bullet Stability

Why are barrels rifled?

Why not use a smooth bore? It would certainly simplify things for the barrel manufacturer and lower costs for everyone.

The answer is that bullets will not fly straight unless you spin them. The rifling grips the bullet by the jacket and forces it to spin at a high rate as it is pushed down the bore by propellant gasses. Rifling ensures bullets will be stable.

The spin applied to a bullet by the rifling is called the twist rate. This is expressed as one complete turn (revolution) in a given number of inches or millimetres. The longer a projectile is the faster it must be spun to stabilize or remain point first in flight.

SAAMI has established standard twist rates for most cartridges which are chambered by firearms manufactures. These standard twist rates will stabilize standard-for-caliber bullet weights. Military and long range target shooters have gone to heavy-for-caliber bullets to increase ballistic coefficient for extreme long range shooting. The same applies to monolithic bullets as due to the lower specific gravity (SG) these bullets are long for caliber. These long bullets require faster twist rates in order to properly stabilize. If these heavy-for-caliber or long-for-caliber bullets are shot in standard twist-rate barrels, they will wobble or tumble going through the target sideways—known as “key-holing”.

As shooters we are interested in two types of bullet stability—gyroscopic stability and dynamic stability. For a bullet to be stable you need to meet both of these conditions:

A bullet that is gyroscopically stable but dynamically unstable is not stable – it will tumble.

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When one looks at and compares Monolithic bullets to Copper jacketed lead core bullets one of the biggest factors are the different materials Specific Gravity (SG). Typically lead has a SG of 11.34,   copper has a SG of 8.9 and brass has a SG of 8.1. Jacketed lead core bullets have an SG of around 10.4 (this varies slightly according to jacket thickness. We can therefore see that on average solid copper bullets are 16% lighter than copper lead core bullets and brass bullets are around 20% lighter. What this means that in the exact same profile, length and diameter jacketed bullets will always be 16% to 20% heavier. (Most jacketed bullets have guilding metal jackets, not copper jackets. Guilding metal is copper with 5% to 10% of Zinc added to harden the copper.)

The next problem we need to look at is the manufacturing processes. Most monolithic bullets are turned on CNC lathes—the advantage of this method of manufacture is that set up is quick and relatively cheap which allows for smaller production runs. The process of turning has a further added benefit in that all components are always concentric which aids with the bullets accuracy.

Jacketed bullets are swaged. You have two components that are swaged individually and then combined and a final swaging operation will be swaging the combined jacket and core into the final shape. There are several problems that can occur during these processes, one of them being you are working with two different metals and linear coefficient of thermal expansion. Essentially this states that when an object is heated or cooled, its length and diameter changes by an amount proportional to the to the original length and diameter to the change in temperature. The factor for Copper is 16 and the factor for Lead is 29. A secondary problem is Springback, the geometric change that happens to a component at the end of the swaging process when the part has been released from the forces of the forming tool. The dimensional accuracy of a finished part is this affected, which makes it difficult to produce the part. As a result, the bullet manufacturer is faced with some real problems: Firstly, prediction of the final part geometry after springback and secondly, appropriate tools must be designed to compensate for these effects. The spring back between lead and copper are different and therefore makes it difficult to keep the two together at exacting sizes with no air gaps. In bullet manufacturing when boattails or rebated boattails are been swaged the possibility of springback is at its highest.