EXTRACT from EXTERNAL SITE
BOLD ITALIC UNDERLINED section may explain
Magnus force and Magnus moment
Generally, the wind force is the dominant aerodynamic force. However, there are numerous other smaller forces but we want to consider only the Magnus force, which turns out to be very important for bullet stability.
With respect to the figure , we are looking at a bullet from the rear. Suppose that the bullet has right-handed twist, as indicated by the two arrows. We additionally assume the presence of an angle of yaw d. The bullet's longitudinal axis should be inclined to the left, just as indicated in the previous drawings.
Due to this inclination, the flowfield velocity has a component perpendicular to the bullet's axis of symmetry, which we call vn.
However, because of the bullet's spin, the flowfield turns out to become asymmetric. Molecules of the air stream adhere to the bullet's surface. Air stream velocity and the rotational velocity of the body add at point B and subtract at point A. Thus one can observe a lower flowfield velocity at A and a higher streaming velocity at B. However, according to Bernoulli's rule (see elementary physics textbook), a higher streaming velocity corresponds with a lower pressure and a lower velocity with a higher pressure. Thus, there is a pressure difference, which results in a downward (only in this diagram!) directed force, which is called theMagnus force FM (Heinrich Gustav Magnus, *1802, died 1870; German physicist).
This explains, why the Magnus force, as far as flying bullets are concerned, requires spin as well as an angle of yaw, otherwise this force vanishes.
If one considers the whole surface of a bullet, one finds a total Magnus force, which applies at its instantaneous center of pressure CPM (see figure ). The center of pressure of the Magnus force varies as a function of the flowfield structure and can be located behind, as well as in front of the CG. The magnitude of the Magnus force is considerably smaller than the magnitude of the wind force. However, the associated moment, the discussion of which follows, is of considerable importance for bullet stability.
You can repeat the steps that were followed after the discussion of the wind force. Again, you can substitute the Magnus force applying at its CP by an equivalent force, applying at the CG, plus a moment, which is said to be the Magnus moment MM. This moment tends to turn the body about an axis perpendicular to its axis of symmetry, just as shown in the figure .
However, the gyroscopic effect also applies for the Magnus force. Remember that due to the gyroscopic effect, the bullet's nose moves into the direction of the associated moment. With respect to the conditions shown in the figure , the Magnus force thus would have a stabilizing effect, as it tends to decrease the yaw angle, because the bullet's axis will be moved opposite to the direction of the yaw angle.
A similar examination shows that the Magnus force has a destabilizing effect and increases the yaw angle, if its center of pressure is located in front of the CG. Later, this observation will become very important, as we will meet a dynamically unstable bullet, the instability of which is caused by this effect.
Another Extract from another site
The Magnus effect in external ballistics, also known as 'spin drift'
The Magnus effect can be found in advanced external ballistics. A spinning bullet in flight is often subject to a sideways wind. In the simple case of horizontal wind, the Magnus effect causes an upward or downward force that depends on the direction of the wind which affects the projectiles point of impact. Even in completely calm air, a bullet will experience a small sideways wind component. This is because bullets have a yaw motion that causes the nose of the bullet to point in a slightly different direction from the direction in which the bullet is actually traveling. This means that the bullet is "skidding" sideways at any given moment, and thus experiences a small sideways wind component. (yaw of repose) All in all, the effect of the Magnus force on a bullet is not significant when compared to other forces such as drag. However, 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. This means that the Magnus force affects 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 flowfield structure, in other words, it depends on whether the bullet is in super-sonic or sub-sonic 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, twisting it either towards the axis of flight (stabilizing) or away from the axis of flight (destabilizing).