Epicyclic motion of a bullet (video)

B

bsl135

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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 the 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
 
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'.
Click to expand...
Brian, this is passing strange. The plots I've seen of pitch versus yaw in McCoy's work don't show this degree of dampening, and both the plots and the verbal descriptions have have the fast arm damping, but the slow arm never really does. On this model, "going to sleep" either means "damping of primary (pitch and) yaw, or "old wives tale No. 742."

What gives?
 
Charles

In McCoy's book and some of his papers on epicyclic motion and dynamic stability, he usually uses the .30 caliber 168 grain Sierra MatchKing to demonstrate the various aspects of stability (fast vs slow arm dampening, lack of the latter, etc). As we know, this particular bullet is a unique anomaly in terms of dynamic stability which makes it a good model for demonstrating academic points, but is not representative of typical bullets in this class. Most normal bullets are perfectly capable of damping both the fast and slow arms of epicyclic motion and achieving very small levels of average yaw.

The magnitude of the first max yaw due to a given initial yaw rate and how quickly the bullet damps the resulting pitching/yawing motion depends mostly on the gyroscopic stability of the bullet at the muzzle. Greater gyroscopic stability (faster twist rates) results in lower first max yaw angles and faster damping.

Hope this clears it up.
-Bryan
 
bullet yaw

Bryan,great demonstration..... I`ve been involved in this discussion many times in many shooters circles.I`ve saved your work for reference...
Thanks:
Bill Larson
 
Bryan, thanks for taking the time to post this. Just a couple of points to maybe get some discussion going, if you don't mind?

-It's interesting that with a 1.44 sg, the model shows the majority of damping occuring just a bit past the 100 yd. mark. This coincides with the 1.5 sg number that is considered to be 'perfect' for accuracy work.

-As to the yaw rate, I have to wonder if the 25 rad/sec rate isn't a bit more than what we actually have in most situations? I know this is virtually impossible to measure and we need to assign it some sort of reference number. But if the Real World yaw is even just 75% of the reference number of .25 rad/sec...I imagine the plot would look quite a bit different. and give almost total damping at 100 yds.

These two things together....a 1.5 sg and a bit less yaw....would seem to coincide with the accuracy results we're seeing at 100 yds. in Real World situations.

Thanks again. :) -Al
 
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Video post

Bryan,
Thank you for posting this; certainly helps helps to frame the term 'going to sleep'.

Lou Baccino
 
Al, even more things to discuss from a "real world" perspective:

1. As long as pitch & yaw are damping, why does it matter how fast they dampen?

2. Since (as I understand it), the ideal situation is reasonably high Sg with as slow a twist as possible, what can be done to move the bullet's center of mass forward while still retaining a high BC?

Here, I'm thinking of Vaughn with his plastic cylinder in the bullet's base, or even Robinett, who has been known to get away with running the lead waaay up in the bullet's nose. And for a subplot, if strength is an issue, what about thicker jackets, since us competition shooters don't have to worry about bullet expansion?

I guess what I'm saying is that discussions of compromise in bullet design always seem to start with the basic bullet as already manufactured. What kinds of compromises would we face if we took different performance/manufacturing parameters for bullets? For barrels? etc. After all, it's winter, and not all the answers would be "unobtainium."
 
Al,
To clarify, the initial yaw rate was 25 rad/s, not .25 rad/s.
As stated in the original post, such an initial yaw rate would cause about 0.75" of deflection at 100 yards compared to a bullet fired with zero initial yaw rate. I used to think that the fact that we routinely shoot groups under 1.5" at 100 yards is clear evidence that initial yaw rates are less than 25 rad/s. However, that belief is based on the assumption that the initial yaw rate is random in direction.
What if the initial yaw rate is systematic in direction? In other words, something like barrel whip, or an imperfect crown always 'tips-off' the bullet in the same direction, at more or less the same rate. This would allow for 'typical' 25 rad/s initial yaw rates AND groups under 1.5".
I honestly don't know the answer to this, but there seems to be some evidence that barrels, especially thinner ones, have a significant amount of whip which might induce great amounts of initial yaw. For example, short range measurements of BC sometimes result in lower measured BC from thin barrels than heavy barrels. In order to measure a lower BC, you would need way more than 25 rad/s initial yaw. For the Berger 180 VLD, 100 rad/s results in 10 degrees first max yaw, 7.5% lower BC over the first 100 yards, and 4" shift in POI at 100 yards. I don't think it's that bad out of my med contour match barrel, but could it be that bad from a soda straw barreled hunting rifle? I think it's possible.
Also, consider the drastic shift in POI you can expect between a 150 vs 220 grain .308 bullet from a light barreled hunting rifle. The POI shift is way more than can be expected from just gravity drop alone. What I don't know is how much of the POI shift is due to the muzzle simply 'pointing' in a different direction when the bullet exits, and how much is due to the amount of 'tip-off' the bullet receives?
As for increasing the Sg to hasten the damping... I'm not sure how that would play out. I suspect you may have less deflection due to the swerving motion from an initial tip-off rate, but you would have more dispersion from bullet imperfections (spinning an offset cg faster).
I'm working on another clip that will show the bullet path that results from the pitch and yaw.
Stand by,
-Bryan
 
Thank you Bryan! I wish I would have had access to this for the past 10 years when people told me guns can't shoot better at longer distances (in Moa) and I was an idiot for thinking so. But after seeing it several hundred times from several hundred guns, I knew it existed. Of course, I had read many studies on it and they were there for others to read but you know what happens when you suggest to someone that they need to do more homework!:eek:
 
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