Gyroscopic drift (Spin drift)
Even in completely calm air, with no sideways air movement at all, a spin-stabilized projectile will experience a spin-induced sideways component. For a right hand (clockwise) direction of rotation this component will always be to the right. For a left hand (counterclockwise) direction of rotation this component will always be to the left. This is because the projectile's longitudinal axis (its axis of rotation) and the direction of the velocity of the center of gravity (CG) deviate by a small angle, which is said to be the equilibrium yaw or the yaw of repose. For right-handed (clockwise) spin bullets, the bullet's axis of symmetry points to the right and a little bit upward with respect to the direction of the velocity vector as the projectile rotates through its ballistic arc on a long range trajectory. As an effect of this small inclination, there is a continuous air stream, which tends to deflect the bullet to the right. Thus the occurrence of the yaw of repose is the reason for bullet drift to the right (for right-handed spin) or to the left (for left-handed spin). This means that the bullet is "skidding" sideways at any given moment, and thus experiencing a sideways component.[21][22]
The following variables affect the magnitude of gyroscopic drift:
Projectile or bullet length: longer projectiles experience more gyroscopic drift because they produce more lateral "lift" for a given yaw angle.
Spin rate: faster spin rates will produce more gyroscopic drift because the nose ends up pointing farther to the side.
Range, time of flight and trajectory height: gyroscopic drift increases with all of these variables.
Doppler radar measurement results for the gyroscopic drift of several US military and other very-low-drag bullets at 1000 yards (914.4 m) look like this:
Magnus effect
Spin stabilized projectiles are affected by the Magnus effect, whereby the spin of the bullet creates a force acting either up or down, perpendicular to the sideways vector of the wind. In the simple case of horizontal wind, and a right hand (clockwise) direction of rotation, the Magnus effect induced pressure differences around the bullet cause a downward (wind from the right) or upward (wind from the left) force to act on the projectile, affecting its point of impact.[23] The vertical deflection value tends to be small in comparison with the horizontal wind induced deflection component, but it may nevertheless be significant in winds that exceed 4 m/s (14.4 km/h or 9 mph).
Magnus effect and bullet stability
The Magnus effect has a significant role in bullet stability because the Magnus force does not act upon the bullet's center of gravity, but the center of pressure affecting the yaw of the bullet. The Magnus effect will act as a destabilizing force on any bullet with a center of pressure located ahead of the center of gravity, while conversely acting as a stabilizing force on any bullet with the center of pressure located behind the center of gravity. The location of the center of pressure depends on the flow field structure, in other words, depending on whether the bullet is in supersonic, transonic or subsonic flight. What this means in practice depends on the shape and other attributes of the bullet, in any case the Magnus force greatly affects stability because it tries to "twist" the bullet along its flight path.[24][25]
Paradoxically, very-low-drag bullets due to their length have a tendency to exhibit greater Magnus destabilizing errors because they have a greater surface area to present to the oncoming air they are travelling through, thereby reducing their aerodynamic efficiency. This subtle effect is one of the reasons why a calculated Cd or BC based on shape and sectional density is of limited use.
Poisson effect
Another minor cause of drift, which depends on the nose of the projectile being above the trajectory, is the Poisson Effect. This, if it occurs at all, acts in the same direction as the gyroscopic drift and is even less important than the Magnus effect. It supposes that the uptilted nose of the projectile causes an air cushion to build up underneath it. It further supposes that there is an increase of friction between this cushion and the projectile so that the latter, with its spin, will tend to roll off the cushion and move sideways.
This simple explanation is quite popular. There is, however, no evidence to show that increased pressure means increased friction and unless this is so, there can be no effect. Even if it does exist it must be quite insignificant compared with the gyroscopic and Coriolis drifts.
Both the Poisson and Magnus Effects will reverse their directions of drift if the nose falls below the trajectory. When the nose is off to one side, as in equilibrium yaw, these effects will make minute alterations in range.
Coriolis drift
Coriolis drift is caused by the Coriolis effect and the Eötvös effect. These effects cause drift related to the spin of the Earth, known as Coriolis drift. Coriolis drift can be up, down, left or right. Coriolis drift is not an aerodynamic effect; it is a consequence of flying from one point to another across the surface of a rotating planet (Earth).
The direction of Coriolis drift depends on the firer's and target's location or latitude on the planet Earth, and the azimuth of firing. The magnitude of the drift depends on the firing and target location, azimuth, and time of flight.
Coriolis effect
The Coriolis effect causes subtle trajectory variations caused by a rotating reference frame. The coordinate system that is used to specify the location of the point of firing and the location of the target is the system of latitudes and longitudes, which is in fact a rotating coordinate system, since the planet Earth is a rotating sphere. During its flight, the projectile moves in a straight line (not counting gravitation and air resistance for now). Since the target is co-rotating with the Earth, it is in fact a moving target, relative to the projectile, so in order to hit it the gun must be aimed to the point where the projectile and the target will arrive simultaneously. When the straight path of the projectile is plotted in the rotating coordinate system that is used, then this path appears as curvilinear. The fact that the coordinate system is rotating must be taken into account, and this is achieved by adding terms for a "centrifugal force" and a "Coriolis effect" to the equations of motion. When the appropriate Coriolis term is added to the equation of motion the predicted path with respect to the rotating coordinate system is curvilinear, corresponding to the actual straight line motion of the projectile. For an observer with his frame of reference in the northern hemisphere Coriolis makes the projectile appear to curve over to the right. Actually it is not the projectile swinging to the right but the earth (frame of reference) rotating to the left which produces this result. The opposite will seem to happen in the southern hemisphere.
The Coriolis effect is at its maximum at the poles and negligible at the equator of the Earth. The reason for this is that the Coriolis effect depends on the vector of the angular velocity of the Earth's rotation with respect to xyz - coordinate system (frame of reference).[26]
For small arms, the Coriolis effect is generally insignificant, but for ballistic projectiles with long flight times, such as extreme long-range rifle projectiles, artillery and intercontinental ballistic missiles, it is a significant factor in calculating the trajectory.
Eötvös effect
The Eötvös effect changes the apparent gravitational pull on a moving object based on the relationship between the direction of movement and the direction of the Earth's rotation. It causes subtle trajectory variations.
It is not an aerodynamic effect and is latitude dependent, being at its most significant at equatorial latitude. Eastward-traveling objects will be deflected upwards (feel lighter), while westward-traveling objects will be deflected downwards (feel heavier). In addition, objects traveling upwards or downwards will be deflected to the west or east respectively. The principle behind these counterintuitive variations during flight are explained in more detail in the equivalence principle article dealing with the physics of general relativity.
For small arms, the Eötvös effect is generally insignificant, but for long range ballistic projectiles with long flight times it can become a significant factor in accurately calculating the trajectory.
Equipment factors
Though not forces acting on projectile trajectories there are some equipment related factors that influence trajectories. Since these factors can cause otherwise unexplainable external ballistic flight behaviour they have to be briefly mentioned.
[edit]Lateral jump
Lateral jump is caused by a slight lateral and rotational movement of a gun barrel at the instant of firing. It has the effect of a small error in bearing. The effect is ignored, since it is small and varies from round to round.
Lateral throw-off
Lateral throw-off is caused by mass imbalance in applied spin stabilized projectiles or pressure imbalances during the transitional flight phase when a projectile leaves a gun barrel. If present it causes dispersion. The effect is unpredictable, since it is generally small and varies from projectile to projectile, round to round and/or gun barrel to gun barrel.