Long Range Shooter

The Eotvos effect is caused by the rotation of the earth but not to be confused with Coriolis effect. While Coriolis is related to the effects caused by the earth it is on a horizontal plane. Eotvos effect is a vertical change in target position that at long distances could cause a miss on a target. The fowling examples explain the Eotvos effect.

Notice that when shooting eastwards that the effect causes the impact to move up. But while shooting westwards the impact has a tendency to move down.

When the velocity of a rifle bullet fired at supersonic muzzle velocity approaches the speed of sound it enters the transonic region. In the transonic region, an important thing that happens to most bullets, is that the centre of pressure (CP) shifts forward as the bullet decelerates. That CP shift affects the (dynamic) stability of the bullet. If the bullet is not well stabilized, it can not remain pointing forward through the transonic region (the bullets starts to exhibit an unwanted coneing motion that, if not dampened out, can eventually end in uncontrollable tumbling along the length axis). However, even if the bullet has sufficient stability (static and dynamic) to be able to fly through the transonic region and stays pointing forward, it is still affected. The erratic and sudden CP shift and (temporary) decrease of dynamic stability can cause significant dispersion (and hence significant accuracy decay), even if the bullet’s flight becomes well behaved again when it enters the subsonic region. This makes accurately predicting the ballistic behaviour of bullets in the transonic region very hard. Because of this marksmen normally restrict themselves to engaging targets within the supersonic range of the bullet used.

Posted by Sean in Effects on Ballistic • Comments (4)

The vertical angle (or elevation) of a shot will also affect the trajectory of the shot. Ballistic tables for small calibre projectiles (fired from pistols or rifles) assume that gravity is acting nearly perpendicular to the bullet path. If the angle is up or down, then the perpendicular acceleration will actually be less. The effect of the path wise acceleration component will be negligible, so shooting up or downhill will both result in a similar decrease in bullet drop

Air temperature, pressure, altitude and humidity variations make up the ambient air density. Decreased air density will result in a decrease in drag, and increased air density will result in a rise in drag. Humidity has a counter intuitive impact. Since water vapor has a density of 0.8 grams per litre, while dry air averages about 1.225 grams per litre, higher humidity actually decreases the air density, and therefore decreases the drag.

Wind has a range of effects, the first being the effect of making the bullet deviate to the side. From a scientific perspective, the “wind pushing on the side of the bullet” is not what causes wind drift. What causes wind drift is drag. Drag makes the bullet turn into the wind, keeping the centre of air pressure on its nose. This causes the nose to be cocked (from your perspective) into the wind, the base is cocked (from your perspective) “downwind.” So, (again from your perspective), the drag is pushing the bullet downwind making bullets follow the wind. A somewhat less obvious effect is caused by head or tailwinds. A headwind will slightly increase the relative velocity of the projectile, and increase drag and the corresponding drop. A tailwind will reduce the drag and the bullet drop. In the real world pure head or tailwinds are rare, since wind seldom is constant in force and direction and normally interacts with the terrain it is blowing over. This often makes ultra long range shooting in head or tailwind conditions hard.

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 Earth is rotating. For small arms, this rotation 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. 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) swinging to the left which produces this result. The opposite will seem to happen in the southern hemisphere. The Coriolis effect is latitude dependent and 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).

Even in complete calm air, with no sideways air movement at all, a bullet will experience a spin induced sideways component. For a right hand (clockwise) direction of rotation this component will always be to the right. This is because the bullet’s longitudinal axis 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 generally points to the right and a little bit upward with respect to the direction of the velocity vector. 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.