Projectile Stabilization for Increased Distance and Accuracy
Balance Flight is a new design approach for projectile (bullet) – in all calibers manufacturing. In order to obtain maximum performance from the design, the projectile must be fired through a barrel with special lands and groove configurations. Cartridges with these projectiles are more accurate and travel farther than ordinary cartridges. This design is patent protected.
A projectile begins its trajectory once it emerges from the bore and from the accompanying expanding gases. The signature of the projectile’s trajectory in flight is influenced by a number of factors – some associated with the projectile itself, some associated with the atmosphere in which the projectile translocates and some associated with the earth’s gravitational forces.
To present a complete picture of a projectile’s trajectory in flight, one should integrate all three factors. In this particular case, we shall focus on the projectile itself with only passing reference to the atmosphere and to the earth’s gravitational forces.
A projectile’s mass, diameter, shape as well as axial spin rate are characteristics that influence its trajectory signature in flight. These characteristics are only important when viewed in relation to a defined speed of the projectile in flight.
If the projectile travels far enough without first hitting a target, it will experience three speed zones: supersonic, transonic and subsonic. Conditions in the atmosphere affect speed. It is considered to be a fluid with varying characteristics including its density, temperature, viscosity and wind direction. Speed in flight is measured as a value called Mach (M).
Projectiles with a Mach speed less that 0.8 are considered to be subsonic, while those greater than 1.2 are considered to be supersonic. The range between the two values is known as transonic.
In a vacuum, gravity is the only force acting on the projectile in flight. However in the atmosphere, the projectile encounters resistance called drag or drag force. Drag depends on the forward speed of the projectile – at high speeds it is the dominant force influencing the projectile. Drag has a major influence in modifying the trajectory signature during the early part of the trajectory arc and minor influence occurring during the latter part of the trajectory arc.
There are five factors that separately contribute to drag force.
- Skin friction
- Pressure drag
- Base drag
- Wave drag
- Yaw-dependent drag
Skin friction results from the viscosity of the fluid. Viscosity is defined as the resistance of the shearing motion of the fluid. When a projectile moves through the atmosphere, molecules immediately adjacent to the surface cling firmly to the surface while those adjacent to the surface flow parallel to it. So there is an area where shearing occurs; i.e., boundary layer. This contributes to pressure drag.
Generally, the average static pressure at the front of a projectile is greater than that found at the end of the projectile. This is called pressure drag. Pressure drag can be reduced if the front of the projectile is pointed and the base is tapered. Even so, a base drag can develop as a result of the fluid moving around it to form a wake. These characteristics are pronounced at subsonic speeds and greatly reduced at supersonic speeds.
Note pressure & tail wakes
Another drag appears at supersonic speeds; i.e., wave drag. This is due to the shock waves generated by the projectile traveling through stationary air at a speed greater than the speed of sound. If the shape of the projectile changes dramatically from its forward tip, an additional shock wave will be produced resulting in an additional drag.
Generally a projectile will not travel with its axis aligned to the direction of flight. A measurement called the yaw angle is the angle between the projectile axis and the direction of the flight. Causes are numerous, but this results in a force impinging upon the side of the projectile, which contributes to drag. The level of drag is related to the angle of yaw.
The total drag is the sum of all drags. Taking into effect the air density and forward speed of the projectile, a value without units can be determined. This is drag coefficient. Drag coefficient is used as a measurement of projectile efficiency during flight depending upon the speed of the projectile.
On the other hand, the rate at which projectile velocity decays against a standard is called ballistic coefficient. The ballistic coefficient is expressed as a measure of mass per unit frontal area of a projectile times a drag efficiency factor. The projectile deceleration is inversely proportional to it. The larger the ballistic coefficient means the smaller the deceleration.
The stability of a projectile in flight is related to its ability to overcome disturbances. For example, a projectile subjected to yaw disturbances will define its stability. The projectile might have a tendency to tumble when the center of pressure is forward to the center of gravity. The projectile cannot return to a stable state. Other examples of instability exist.
There is an important correlation in the distance between the center of pressure and the center of gravity and its relation to the stability of the projectile. This is called static stability of the projectile.
As a general rule, most projectiles are aerodynamically unstable in flight. This can be overcome however, by the incorporation of axial spin. For example, if a projectile is experiencing a nose upward motion resulting in an increased yaw angle, a projectile spin – assuming it is fast enough, will cause the nose to move to a stable position or back to its original yaw.
There is a second motion present – one in which superimposes the first. This is gyroscopic motion known as nutation. This motion of a projectile in flight is determined by the dynamic stability of the projectile.
Upper and lower limits exist for the rate of spin. Too much spin results in a projectile flying at a larger yaw angle, which results in lost of the distance traveled and accuracy.
Spin rates with projectiles with small diameters are high. In addition, a longer projectile is more difficult to spin versus a shorter projectile. Finally, projectiles entering tissues will become directionally unstable and will tumble. This assumes that they retain their original shape.
Balance Flight
It is clear that a projectile being able to retain stability throughout its flight will go farther and will be more accurate.
Conditions were identified that could be translated into projectile design, which would exhibit very long distance accuracy. The concept is called Balance Flight and is patented (6,629,669).
Working with PRODAS software, projectiles were designed in multiple calibers, where the linear drag on a projectile is matched to its rotational drag. In other words, forward rate of deceleration and an axial rate of deceleration are balanced. The gyroscopic stability remains constant resulting in the projectile remaining on its original trajectory path.
Non-balance flight occurs when a projectile’s spin is too great, thus leading to an “over spin” of the projectile. Over spin leads to projectile destabilization — first expressed as projectile yaw, then to projectile tumbling, then to the projectile leaving its original trajectory path and finally the projectile falling to the ground.
An important component of Balance Flight is the design of the barrel lands and grooves. A ratio of a total surface of the projectile to a total surface area of the physical feature in the range of to 3.00:1 to 4.00:1 is critical.
As a result of projectile and barrel land / groove design, the drag coefficient is reduced to a range of 0.100 to 0.250. In addition, the bearing surface of the projectile has a depth equal to 1% of the caliber of the projectile and a ratio of a total surface area of projectile to the total surface of the physical feature in the range of to 3.00:1 to 4.00:1. The purpose is to impart an ideal axial surface friction upon launching, which during flight produces a trajectory characterized by a continuously decreasing rate of axial deceleration.
Balance Flight is best associated with the .408 CheyTac® caliber. However, Balance Flight was first designed in 30 caliber, which resulted in major improvements over existing projectiles in this caliber.
Balance Flight’s improvements of projectiles in the 40 caliber went far beyond expectations. Could a Balance Flight improve the 50 caliber projectiles? The answer is yes, but for reasons not as yet known, the 40 caliber is the caliber best served by Balance Flight.
Combined with the CheyTac® cartridge case, the .408 projectile has found an ideal launching platform. This platform represents the best long-distance cartridge to date – in all ballistic characteristic, including kinetic energy.
John D. Taylor, Ph.D.
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