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Yaw of Repose and Spin Drift

HappyHellfire

Silver $$ Contributor
Is spin drift important for your long range shooting? How do you know how important spin drift is to say Coriolis or cross wind? I'm going to try to explain what spin drift is and how to estimate it.

Bullets do not fly perfectly straight. Even the best, most stable bullet will have what we call epicyclic motion or bullet wobble. The nose of the bullet wobbles up and down (pitch) and left and right (yaw) as it flies. We have the math to study this motion, its called Linear Projectile Theory. If we solve for a spin stabilized bullet fired horizontal, we get a pretty little pattern.
1720438045146.png
This is for a 168 grain Sierra fired at a Mach 2.4 (2700 fps) from a 1:10" barrel. The center of this shape is slightly offset to the right for right hand rifling and produces a tiny average force that pushes the bullet to the right. With a good bit of math we can estimate how much the spin drift is by the equation:

1720438252030.png
This is one of the only good reasons not to over-spin a bullet. If the bullet is stable at a 1:10 twist and you fire the same bullet out of a 1:8 twist, the increase spin (p in the equation) will increase the spin drift. For a well designed rifle and bullet combo, the spin drift will only be about half of the Coriolis drift and the Wind drift will dominate the cross range motion of the bullet.

If you like the math, I have a link to my book on external ballistics on my website https://www.aerospikebullets.com/the-bullet-guy . Don't buy it unless you have a good bit of advanced calculus under your belt, it will be a waste of money but if you are weird like me you might find it interesting.
 
As I understand it, the yawning behavior only occurs when the bullet leaves the barrel when there is a crosswind to disturb it.
 
“This is one of the only good reasons not to over-spin a bullet.”
Not true. The best reason not to over spin a bullet is because when you do, the will explode mid flight. I’ve seen this happen with my own eyes and many great shooters on this site have seen the same thing. “Extra” spin drift caused by over spinning your bullets should be the least of your concerns, whether or not your bullet hits the target as a single bullet or in multiple pieces.
Dave
 
As I understand it, the yawning behavior only occurs when the bullet leaves the barrel when there is a crosswind to disturb it.
It always occurs to some extent. Even if the bullet leaves the barrel perfectly symmetrical (no angle of attack) the bullet will start to wobble like a top. The larger the asymmetry (the bigger the jump from the gun) the more pronounced it is.
 
“This is one of the only good reasons not to over-spin a bullet.”
Not true. The best reason not to over spin a bullet is because when you do, the will explode mid flight. I’ve seen this happen with my own eyes and many great shooters on this site have seen the same thing. “Extra” spin drift caused by over spinning your bullets should be the least of your concerns, whether or not your bullet hits the target as a single bullet or in multiple pieces.
Dave
Yep, bullet integrity is another reason. Also for fuse activated warheads the direction the nose is pointed really matters. Finally, for really high angle trajectories like artillery and anti-aircraft the bullets fired with too much spin they can actually flip at the top of the trajectory (apogee) and hit the ground ass first.

For y'all and accuracy, over spin mostly just increases spin drift.
 
Yep, physics can sometimes suck. You can do a little experiments to see this. Get a top and try to place it spinning on a smooth surface as perfectly upright as possible. It will start to wobble immediately. The equation for a top and a spin stabilized bullet end up being almost exactly the same.

For a really cool science fair project. Make a pencil into a top and start it spinning on a clean sheet of paper. You will see the same flower pattern.
 

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