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Epicyclic motion of a bullet,video)

Bryan Litz Ballistics

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Just playing around with the 6 Degree Of Freedom simulation and learning how to make video's from the output.

click here to view video

The link is to a dynamic plot of the pitching and yawing motion of a bullet fired with an initial yaw rate of 25 radians per second,about 1,433 degrees per second). You can watch the bullet damp the yaw cycles from a maximum of over 3 degrees to less than 1 degree at 200 yards. This is the process commonly referred to as the bullet 'going to sleep'.

As for how realistic/common a 25 rad/s initial yaw rate is, I can't say. The motion produced by such a 'tip-off' rate only acts to reduce the effective BC by less than 1% in the first 100 yards, and not at all beyond that. A shot with 25 rad/s initial yaw rate only strikes about 0.75" from a bullet launched with no yaw at 100 yards. If the initial yaw were randomly oriented, this would produce a radius of dispersion of 0.75", and a 1.5" c-t-c group. However, if the initial yaw rate is always in the same direction, then the shots could form a group much smaller than 1.5".

I suspect that thinner, lighter weight 'whippier' barrels would tend to produce higher levels of initial pitch/yaw than a heavy bull barrel like we use in competition.

-Bryan
 
I can't see that the diameter of the barrel has much, if any, effect on yaw and pitch. The center of gravity, mass, spin and form for the bullet along with the alignment of the bullet to the axis of the barrel I would think to have a more significant effect.
 
Bryan,

The simulation is very interesting and really illustrates the dynamic stability that the bullet exhibits as the yards traveled increases.

What effect,if any) does bullet runout in the case have on this stability?

RGDS

Bob
 
I was thinking about the severity of muzzle movement when the bullet exits. I suspect this would be worse for lighter barrels that have more 'whip' than heavier barrels.
You're right, there are many other factors that can influence the level of initial 'tip off' rate.
-Bryan
 
bsl,
Can you list the six degrees of freedom that are being simulated? I'm trying to get a handle what a "degree of freedom" describes in an n-dimensional world. Thanks.
 
Winchester,
3 degrees of translation in the X, Y, and Z directions,front-back, left-right, up-down)

and 3 degrees of rotation on the pitch, yaw, and roll axis.

Most ballistics programs only give you the trajectory in 3,translational) degrees of freedom. Getting the rotational degrees of freedom is a lot harder, and requires aerodynamic and mass properties data for the bullet that's not easily obtained.

The only dynamics that the 6 DOF simulation can't account for is the 'flexibility' of the bullet. In other words, if the bullet bends in reaction to it's motion,like an arrow or a javelin), the 'rigid body' assumption of the 6-DOF simulation would be invalid. In general, the rigid body assumption is good for small arms bullets.

-Bryan
 
Bryan,

I figured you were talking about barrel whip but I can't figure out how it would translate into yaw or pitch. The only effect should be to add a velocity component in the direction of the whip. The transverse wave that travels down the barrel like a balloon might allow axial misalignment. What does a .0001" tilt from front to rear translate too?
 
Bryan,

IN trying to understand the dynamic stability issue, it seems like:

the bbl is moving,vibrating) as the bullet makes it way down the bore. As the bullet exits the bore, the muzzle is "whipping" due to the vibrations. The bullet is sent on it's merry way with a certain amount of movement in these six axies. The spinning of the bullet,gyroscopic stability) begins to dampen these movements with respect to time,or distance) and eventually begins to "Fly Straight". Is this correct?

Can you state simply, why flat based bullets "go to sleep" faster than boat tail bullets? Is it because the bearing surface is usually longer and therefore the bullet starts down it's flight path with less tendencies for oscillation?

Bob
 
As a bullet spins in the barrel, it will spin about the axis of the bore. Once it exits the barrel, it will spin about it's center of gravity, so beyond barrel whip, any difference between the axis of the barrel and the CG of the bullet will cause a kick to the bullet as it releases from the muzzle.

Of course, crown is also important here. As the high pressure gasses escape as the tail end of the bullet leaves the muzzle, any non-uniformity of gas flow will provide a kick to one side on the rear of the bullet, increasing initial yaw.

Art
 
The original video has stirred up quite a bit of discussion on this and other sites about the dynamics of a bullets flight. Unfortunately, there's been a common misunderstanding that the plot is showing the bullet path.

In fact the original video shows the pitch and yaw angles. The scale showing the size of 1 degree is in the bottom left of the plot.

Anyway, in an attempt to clear up the confusion, I've created another video. This one shows the original yaw-pitch plot, and right beside it shows the actual bullet path from the shooters point of view, so you can see the minor effect of the pitch-yaw angles on the trajectory. The 25 rad/s initial yaw rate causes about a 1 MOA deflection in the opposite direction of the initial yaw, but the actual 'corkscrew' of the trajectory is very small.

Considering the actual bullet path, it's hard to say that such levels of pitching and yawing could be responsible for smaller MOA groups at longer range.

Here's a link to the new video.

-Bryan
 
Amazing. It would be neat to see a series of these graphs comparing a range of rifles like a factory barrel, heavy custom
barrel, one with a poor crown versus a good crown etc. Thanks
for posting this graph.
 
Bryan,
First of all thank you for posting these. How about a little more clarification for those of us who are mentally challenged?

In your first video, I am assuming the shooter is behind the bullet or at the intersection of the X-Y axis,0,0) and observing the bullet going down range. As it goes down range toward contact with target, it is gyroscopically stabilizing or 'going to sleep'. Am I correct so far? If not pleae explain.

In your second video, I don't understand the part about the shooter's point of view. Is the shooter's point of view still at the intersection of the X-Y axis,0,0) and what you are depicting is the bullet's travel from below the shooter's line of sight to contact with the target? In other terms, the video is describing the typical parabolic arc,trajectory) from below line of sight to the target? Inquiring mind,s) would like to know.

Lou Baccino
 
Lou,
The biggest thing to remember is that the first video,left side of the new video) is a plotting the angle of the bullets axis with respect to it's flight path in degrees. It's not showing the path of the bullet.
The right hand side of the second video is showing the bullets actual flight path, in inches, from the shooters point of view. The 'crosshairs' in the video can be thought of as the scope view. The trajectory originates from below the crosshairs because the bore is below the scope. You are watching the bullet fly away from you, arcing up to about 2" above the line of sight at 100 yards, and falling back down to a vertical zero at a distance of 200 yards. The bullet is hitting about 2" to the left at 200 yards due to the initial yaw rate that sets up the dynamics.

Sorry for the incomplete explanation before, I hope this helps.

-Bryan
 

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