Gyroscopic precession of a spin-stabilized bullet

[johnlpmark]

TL;DR Summary

Why does the gyroscopic precession of a spin-stabilized bullet cause drift in the same direction as the spin?

Hi!

I am trying to understand the physics behind the gyroscopic phenomenon called spin drift. Spin drift occurs to bullets that are spin-stabilized over the course of their flight.

Spin drift starts with an induced rotation in a spin stabilized bullet. As a bullet flies through the air, gravity causes the apparent direction of the incoming air to change as the bullet flies in a parabolic trajectory. The bullet tips into the direction of the incoming air (called weather-vaning). From the perspective of the bullet, this is a forward rotation.

Gyroscopic precession occurs when the bullet translates this forward rotation 90 degrees due to gyroscopic precession. Thereby, the bullet translates some of the downward tipping into sideways tipping. When tipped sideways, lift forces cause the bullet to change the direction of travel into whatever direction the bullet is pointed. That is, the reverse of weather-vaning occurs: instead of drag causing a change in orientation, lift causes a change in travel vector.

In sum, spin drift causes a bullet to always turn to the right and go right when fired with a right or clockwise (from the perspective of the shooter) spin. And a bullet left for a left twist. "Precession 90 degrees in the direction of spin. The gyroscopic force translates that nose-up, tail-down torque on the fast-spinning bullet into a nose-right yaw on the bullet because most rifling is to the right (clockwise ) from the shooter’s perspective." As far as I can tell, spin drift should occur to the opposite direction of spin, but that is not the case.My question is not on why spin drift or gyroscopic precession occurs, but rather why it occurs to the right or left. The problem I have is that spin drift occurs in the same direction of spin. That is, right spinning bullet (a clockwise spinning bullet when viewed from the rear) turns right. This is well-attested empirically. However, whenever I view diagrams and explanations, or experiment with a gyroscope myself, a right spin should force a forward rotation to induce a left turn.

One possible explanation is that there are two axes of spin. The first axis is the center of mass of the bullet itself. The second and larger axis is the axis of travel. When bullets travel, they do so in a helix pattern, and not a straight line. If a right-spinning bullet creates a left-spinning helix, it could explain why spin drift occurs in the same direction as the spin. But I don't really know.

I've searched everywhere! Please help me understand. I am not a phyisist, and do not understand nor have any need for equations. This paper probably explains how it works, but I can't read it well enough to understand this one particular aspect. A Coning Theory of Bullet Motions | James A. Boatright | Revised: March 2018 . Also, if it is relevant, for bullets the center of pressure (COP) is always ahead of the center of gravity (COG).Thanks so much for your help!

Here are some pictures to help understand what I am talking about

Gyroscopic Precession​

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Weather-vaning​

Coning Theory of Bullet Travel​

Helical travel​

Spin Drift​

 

[Bystander]

https://en.wikipedia.org/wiki/Magnus_effect

 

[Baluncore]

Why does the gyroscopic precession of a spin-stabilized bullet cause drift in the same direction as the spin?

Gyroscopic precession does not cause the spin drift or walk.

I've searched everywhere! Please help me understand. I am not a phyisist, and do not understand nor have any need for equations.

As a clockwise, right spinning, projectile follows its trajectory, the fall of the projectile causes an apparent rising airflow that applies a pressure to the bottom of the body. That results in aerodynamic lift, with a higher pressure below the projectile, and lower pressure above. The projectile walks to the right due to the higher drag below than above the body.

As the projectile follows the arc of the trajectory, that extra tail force lifts the tail and lowers the nose. That causes the projectile to gyroscopically precess slightly to the left, but due to the very gentle arc, is not sufficient to overcome the walk to the right.

 

[johnlpmark]

This is very incorrect and misleading. Spin drift is caused by gyroscopic precession and this is well documented.

For simplified explanations, see:
https://appliedballisticsllc.com/wp-content/uploads/2021/06/Gyroscopic-Drift-and-Coriolis-Effect.pdf
https://en.wikipedia.org/wiki/External_ballistics#Gyroscopic_drift_(Spin_drift)From "Calculating Yaw of Repose and Spin Drift -A novel and practical approach for computing the Spin Drift perturbationJames A. Boatright & Gustavo F. Ruiz":

"For spin-stabilized bullets, this small rightward yaw attitude bias creates the well known rightward Spin Drift displacement. The small horizontally rightward yaw of repose angle causes a small rightward aerodynamic lift force which, in turn, causes a slowly increasing horizontal velocity of the bullet."
This is not the magnus effect."The projectile walks to the right due to the higher drag below than above the body....That causes the projectile to gyroscopically precess slightly to the left, but due to the very gentle arc, is not sufficient to overcome the walk to the right."

I'm sorry, but I don't follow. Why would an air-pressure differential above and below the bullet cause a bullet to "walk"? Again, I understand the magnus effect but that is not a significant cause of spin drift and is in fact a separate effect.

Thanks very much.

 

[Baluncore]

This is very incorrect and misleading. Spin drift is caused by gyroscopic precession and this is well documented.

You yourself have observed that cannot be the case, because it gives the negative of the effect witnessed.

Cut the hostility, and open your mind to the fact that those simple gyroscopic explanations might all be lost sheep, following each other on the internet, far away from the righteous path.

Hitting it with a bigger hammer will not reverse the effect. Read some mathematical textbooks on "exterior ballistics", where body lift is analysed.
Robert L. McCoy - Modern Exterior Ballistics - Schiffer Publishing, Ltd. (2012)
Klimi, George - Elements of Exterior Ballistics - Long Range Shooting - Xlibris US (2016)

 

[johnlpmark]

You yourself have observed that cannot be the case, because it gives the negative of the effect witnessed.

Cut the hostility, and open your mind to the fact that those simple gyroscopic explanations might all be lost sheep, following each other on the internet, far away from the righteous path.

Hitting it with a bigger hammer will not reverse the effect. Read some mathematical textbooks on "exterior ballistics", where body lift is analysed.
Robert L. McCoy - Modern Exterior Ballistics - Schiffer Publishing, Ltd. (2012)
Klimi, George - Elements of Exterior Ballistics - Long Range Shooting - Xlibris US (2016)

I have read McCoy 2012. As far as I can tell, he covers drift on page 198 of Chapter 9: "For a right-hand twist...the bullet's nose points to the right of the flight path, in a small, steady-state yaw of repose.... The yaw of repose has one significant effect on the trajectory; it produces the right-hand deflection referred to by ballisiticians as drift [sic italics]. Drift is illustrated...in Figure 9.8."

I am open to explanations, but I'm afraid I cannot parse your explanation. It seems to be contradicted by the textbook you cited.

Regarding "You yourself have observed that cannot be the case, because it gives the negative of the effect witnessed." There are other possible explanations. For example, the fact that there is precession and nutations together could explain the difference instead of precession alone.

I appreciate you spending time on this post. I'm afraid I either misunderstand your explanations or they are wrong. Spin drift is caused by a yaw of repose which is caused by gyroscopic precession which is caused by spin stabilization. This is undisputed in the literature. If that is agreed upon, then I do not understand what you are telling me and I would gladly receive another explanation. Much appreciated,
John

 

[Baluncore]

Spin drift is caused by a yaw of repose which is caused by gyroscopic precession which is caused by spin stabilization.

Where exactly do you get that misconception from?

 

[johnlpmark]

Where exactly do you get that misconception from?

I got it from the the textbooks I read, including McCoy. Brian Litz has a great explanation in his book Applied Ballistics For Long Range Shooting 3rd Edition-Applied Ballsitics LLC (2015), page 95-96:

"A Brief Explanation of Spin Drift
Spin drift is a unique consequence of spin stability. Spin stability works because the spin axis of the bullet is rigid, and that rigidity is stronger than the aerodynamic overturning torque that's applied to the bullet's nose. The fact that the bullet axis maintains rigidity is mostly a good thing, but on long range trajectories, it causes a little bit of a problem. Imagine a bullet launched at a small initial upward angle towards a distant target. If the axis of the bullet remained absolutely rigid, it would not be able to trace, or weather-vane along the trajectory, and would impact the target in the same nose high orientation that it was launched at. Part of the fundamental definition of stability (fin or spin stability), is that the projectile stays pointed into the oncoming air flow. That's why if you shoot an arrow at a high angle, the arrow weather-vanes along its trajectory and sticks in the ground point first. Bullets that are spin stabilized will do the same thing, but the rigidity of the bullets spin axis resists the tendency of the projectile to naturally weather-vane with the trajectory. This resistance of the spin axis to bend with the trajectory is what starts the process that results in spin drift.

The exact interaction between the inertial and aerodynamic effects that result in the epicyclic motion of spin stabilized projectiles is outside the scope of this book. Suffice it to say that when the spin axis of the bullet is forced to weather-vane (trace) with the trajectory, it reacts by pointing its nose slightly to the right for right twist barrels, and to the left for left twist barrels. The spin stabilized bullet is tracing with the trajectory because it's stable, but unlike a fin stabilized projectile, it reacts with this slight out of plane angle which is known as the yaw of repose. The fact that the yaw of repose points to the right for right twist barrels causes the bullet to steer itself in that direction. Keep in mind that the yaw of repose for long range trajectories is typically less than 0.1 degrees, so the steering effect isn't very strong at any particular point. However, the steering effect is persistent and builds to significant levels over long range trajectories."

Note that when he says "steer itself in that direction," he is referring to the lift force interacting with the yaw of repose.

 

[Baluncore]

Nowhere in that quote from Brian Litz does it mention gyroscopic forces.

"Suffice it to say that when the spin axis of the bullet is forced to weather-vane (trace) with the trajectory, it reacts by pointing its nose slightly to the right for right twist barrels, and to the left for left twist barrels."

My question is not on why spin drift or gyroscopic precession occurs, but rather why it occurs to the right or left. The problem I have is that spin drift occurs in the same direction of spin. That is, right spinning bullet (a clockwise spinning bullet when viewed from the rear) turns right. This is well-attested empirically. However, whenever I view diagrams and explanations, or experiment with a gyroscope myself, a right spin should force a forward rotation to induce a left turn.

And it doesn't force a left turn, so it isn't caused by gyroscopic precession.

To weather-vane, and so get its nose down, the projectile must expose more of the bottom to the virtual wind. That surface is spinning left, so the surface drag rolls the projectile to the right. The top of the projectile, spinning right, has less drag than the bottom, the drags do not cancel, so the projectile moves a little bit to the right.

A projectile, flying with the nose high, has aerodynamic lift. Pressure above the body is reduced by the lift, which explains the differential drag, that causes the drift.

 

[hmmm27]

Sorry if this seems a bit too basic, but...

The stabilization keeps it from fully weathervaning.

The lack of weathervaning means the bottom of the bullet is pushing into the wind (like the bottom of the spaceshuttle wings glowing red coming back into the atmosphere).

The grooves in the bullet catch the wind, and the bullet sideslips/walks to the right, just like if you drop a spinning object onto the ground or on top of the water. It's not pointing to the right (actually tending to point left thanks to precession)

Does that sound correct ?

 

[A.T.]

The bullet tips into the direction of the incoming air (called weather-vaning). From the perspective of the bullet, this is a forward rotation.
...
.... a right spin should force a forward rotation to induce a left turn.

You seem to conflate the change of the bullets orientation with the aerodynamic torque acting on the bullet. You call both "forward rotation", but in the second instance you seem to actually mean the aerodynamic torque, and its gyroscopic interaction with the spin.

For fin-stabilized-projectiles this aerodynamic torque would indeed act to push the nose down (forward rotation). But for spin-stabilized projectiles this is not necessarily the case, as the diagram you posted shows. Here the drag force R passes above the center of mass C, thus acting to lift the nose (backward rotation):