Why do bullets precess in the opposite direction from gyroscope diagrams?

Question

1. Bullet spin causes a bullet to become a gyroscope. Specifically, bullets have their center of pressure in front of their center of mass. Therefore, when pressed, gyroscopic forces cause a bullet to spin 90 degrees instead of tumble. See this diagram:

2. The precession does not cause the bullet to point into the direction of movement, but the direction of apparent incoming wind. That means that if there is a crosswind of 20mph, the bullet will turn slightly to point towards the incoming wind while traveling straight forward. See this diagram:

3a) As a bullet drops, there is apparent wind coming from the downward direction. Apparent wind occurs when there is a differential between the object and the surrounding medium. Therefore, the bullet turns down as it drops. See this diagram below.

3b) Importantly, gravity accelerates, so there is always an increasing apparent wind as the bullet falls. This accelerating vertical apparent wind causes continuous forward rotation of the bullet.

4a) Air resistance forces to the front of the bullet and those to the side of the bullet cause different behavior. Air resistance to the front causes the bullet to reorient into the direction of the incoming force. (See the first image.)

4b)Air resistance to the side of the bullet (i.e., from the left, up, down, or right directions) pushes the bullet to point 90 degrees clockwise to the incoming air. So left-to-right crosswind cause aerodynamic jump down and a or right-to-left crosswind causes aerodynamic jump up. (Note the horizontal defection in this image is due to the crosswind, which is distinct from spin drift.) See this diagram:

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5. Therefore, intuitively, when a bullet rotates down due to being in a falling trajectory with gravity, it points to the right if it has a right-hand twist:

6. But every diagram I see of a gyroscope has the gyroscope rotating the opposite direction.

7. I can’t figure out why the bullet gyroscope rotates in the opposite direction of other gyroscopes. This is not Magnus effect! From Modern Exterior Ballistics, McCoy, “Although the Magnus force acting on a spinning projectile is usually small enough to be neglected, the Magnus moment must always be considered.” Note in the diagram that the Magnus moment points down, and not the to left or right. See these diagrams:

8. In contrast, spin drift is related to the pitching moment, which does point left or right. See this diagram:

9. Something to note is that the traditional depiction of bullet rotation may be somewhat inaccurate. (I cannot confirm.) Traditionally bullets are depicted as rotating around the center or mass. Instead, they may rotate around an independent axis. See this diagram:

Thanks so much for the help!

I have reedited this question to be more understandable. 02 Dec 2023

Answer 1

About gyroscopic precession: there is a 2012 answer by me in which I present an explanation of gyroscopic precession using diagrams. (In that explanation I do not use the angular momentum vector. Instead the explanation takes advantage of symmetry.)

I won't repeat that explanation here; to give you an idea: the space in which the gyro wheel is rotating is divided in 4 quadrants that are not co-rotating with the gyro wheel. The explanation tracks the motion of sections of the gyro wheel as those sections of the gyro wheel are moving through the quadrants.

I verified with my gyroscope:
When as seen from my perspective the gyro wheel is turning clockwise, and I pitch nose down, then the gyro wheel turns to the left. (And it follows of course that when rotating counterclockwise as seen from my perspective a nose down pitching will have the gyro wheel turning to the right.

According to the description you copied: after the bullet exits the muzzle the bullet quickly developes a motion pattern where the spin axis of the bullet is sweeping out a cone. According to the description: over time the amplitude of that cone becomes smaller.

According to the description: for the pitch angle there is an 'angle of repose'. The bullet tends to settle onto that angle of repose. (According to the description: a cross wind will tend to mess with that.)

I emphasize: this 'angle of repose' is a dynamic state that the bullet tends to settle on, it is not an instantaneous thing.

According to the description there is also a 'yaw of repose'.

This is important: in external ballistics one must be aware of the distinction between 'response to pitching motion' which is instantaneous gyroscopic effect, and 'yaw of repose' which is analogous to the angle of repose of pitching motion of the bullet.

I get the impression that you are totally overlooking that distinction.

Answer 2

This is a new answer, following a renewed request.

My aim is to discard unnecessary complexity.

I think the following property is essential: when a (spin stabilized) bullet in flight starts to precess then that precessing motion leads to a turbulence pattern that tends to dissipate the energy of the precessing motion.

As an aside, let me discuss a particularly simple example of energy dissipation: a bowl with a marble in it, rolling back and forth. The moving marble experiences air friction, so it is losing velocity all the time. Whatever the initial motion pattern, the motion will become smaller and smaller, and eventually the marble ends up motionless at the bottom of the bowl.

In the case of a bullet in flight and turbulence:
So the observation is that if a bullet in flight experiences a cross wind the orientiation of the bullet tends to change, and the bullet tends to end up in such an orientation that it no longer experiences a cross wind. In effect: the bullet-in-flight has a tendency to turn into the wind.

The essential factor, it seems to me, is that once the bullet is moving into the wind it no longer has opportunity to dissipate energy through precession induced turbulence.

So the fact that the bullet tends to turn into the wind is inevitable, just as inevitable as the marble ending up at the bottom of the bowl.

Let me return to the turbulence factor.
So we have:
-The Center Of Pressure is ahead of the Center Of Mass
-A cross wind will tend to push the front of the bullet-in-flight out of alignment
-Due to the spin of the bullet that out-of-alignent tendency turns into precessing motion

The thing is: while that cross wind can induce some measure of precessing motion we observe that that precessing motion does not accumulate. The turbulence depletes the precessing motion faster than it can be induced.

For emphasis I repeat: the energy loss to turbulence is so rapid that it it will always prevent accumulation of precessing motion.

Also: dissipation of energy is non-directional. You don't have to think about direction of motion, that factor averages out

For sure the dissipation of the energy of precessing motion is a key factor. In order to succeed at explanation of the phenomenon of angle of repose that dissipation must be a part of the presented explanation.

Once the bullet has ended up flying head on into the wind: at that point the air load is symmetric, and with that symmetry there is no longer a net force available that would tend to induce precession.

Answer 3

Not an answer, just an idea...

...It looks like precession (the conical movement of the main spin axis) does not start immediately, so while it speeds up to compensate aerodynamic force, the mentioned "bullet drift" is quietly (mentioned by you, but not explained well in books, huh) somehow occurring.

Answer 4

This is the best explanation that I have come up with, if someone would be kind enough to help me verify or refute:

The first concept is the center of mass. The center of mass is the average location of mass of an object. The center of mass does not have to be within the bounds of the object, as in a donut or hollow-point bullet, where the center of mass may be in an interior area that is vacant.

The second concept is the aerodynamic force. For the purposes of this issue, this is the force that is generated on a solid object when it collides with gas. This is conceived of as the solid object traveling through the gas; however it is only the differential in velocity that matters. Whether from the perspective of the observer the solid object moves through a stationary gas or whether a moving gas goes around a stationary, solid object, the same force occurs.

Lift and drag are perpendicular components of the aerodynamic force, and not independent forces. The partial vertical component of the aerodynamic force is lift, which the horizontal component is drag. Specifically, lift is defined as being parallel to gravity while drag is perpendicular to gravity.

The third concept is the center of force. This is the average location of force acting on an object. Special cases of the center of force include the center of gravity (technically gravity is not a force, but here it is treated as one) and the center of pressure. The center of gravity is identical to the center of mass when gravity is the same along an entire object. The center of pressure is the average location of the aerodynamic force on an object. Bullets taper at the front where the air impacts them, therefore bullets have a center of pressure in front of the center of mass.

In the context of ballistics, lift is also called the overturning force. As a bullet travels, the bullet naturally does not point straight into the air; it is always slightly eschew. Therefore, one side of the bullet it hit harder by the air and receives more force. This force differential between the top and bottom, combined with the fact that the center of pressure is in front of the center of mass, leads to an overturning torque on the bullet would cause the bullet to overturn and tumble if not for spin stabilization.

The fourth concept is spin axis. When an object rotates, the axis about which it rotates is called the spin axis. An object wants to rotate around the center of mass; however, they actually rotate around the average center of mass. Rotating around a spin axis creates gyroscopic stability, which is the principle that a spinning object tends to maintain its rotational axis. This stability is a result of the conservation of angular momentum, a fundamental concept in physics. When an object spins, it resists changes to its orientation due to the angular momentum generated by its rotation.

Pulling the previous concepts together, when bullets spin, they rotate their average center of mass around the spin axis. This spinning maintains the center of pressure in front of the center of mass. In doing so, the tapered end of the bullet stays pointed forward, maintaining the bullet in an aerodynamic orientation.

The mechanism by which spinning maintains the center of pressure in front of the center of mass is called gyroscopic precession. Precession is a phenomenon that redirects force (y axis) that is perpendicular to the spin axis (x axis) to be perpendicular to both (z axis). For example, when an upright, clockwise-spinning wheel is suspended in the air by a string on one side and nothing on the other, the force of gravity pulls down, and the wheel rotates to the left.

Curiously, bullets at first would appear to rotate in the opposite direction of the aforementioned wheel. When bullets pitch down, they turn to the right. However, this is not actually a difference in how force is redirected in the horizontal direction, but the vertical direction. First, bullets turn right instead of left because the net overturning torque pushes the tip of the bullet upwards. This is in contrast to the wheel, where the net force of gravity attempts to pull the unsupported side of the wheel down. Upward pitching torque causes a right turn and a downwards pitching torque causes a left turn.

Notably in both cases, without friction and point connections and with infinite angular momentum, precession would be perfect and no vertical movement would occur at all. However in the real world, gyroscopically stabilized objects do still rotate parallel to an applied force. That means there is actually a second spin axis about which the first spin axis rotates. Referring back to the wheel example, although it does rotate left, gravity also still rotates the unsupported side of the wheel down. Curiously though, bullets also pitch down! For the wheel the explanation is simple: the force of gravity pulls the wheel down. But the way that a bullet defies the net overturning torque to actually turn into the torque is explained by a concept called dynamic stability.

Dynamic stability is the ability of a gyroscopically stabilized object to align the spin axis with the force vector. (In more technical, ballistic terms, dynamic stability is when yawing motions and radii of nutation and precession decrease over time.) A good demonstration of dynamic stabilization is a spinning top. Watch any video of a spinning top and no matter the initial orientation of the spin axis, they immediately orient themselves directly upwards and align with the gravitational force vector. Once angular velocity drops so too does dynamic stabilization and the spin axis slowly deviates from the force vector. Spinning wheel and gyroscope demonstrations usually do not demonstrate dynamic stability because they initialize the spin axis too far (often perpendicular) to the force vector for alignment to occur. That is, the direction about which the first spin axis rotate depends on whether precession can overcome the applied torque vector to rotate into the torque vector.