Epicyclic motion of a bullet (video)

[BryanLitz]

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

 

[Michael Eichele]

Thanks for sharing that.

This is a similar concept of what that ex sniper instructor was saying about why some bullets group better at longer range than close. He explained it like looking down a spiral wire in a spiral bound notebook. He said that the binding is still heading in a straight line. Now envision a bullet following a similar but more exagerated course. It is still headed for the target just in a corkscrew fasions. As it reaches its optimum stability factor it goes to sleep and the corkscrewing motions will settle down and tighten up. As the bullet goes to sleep, goes away alltogether.

I was fixing to line up 2 or 3 targets by use of a laser and a small hole in the middle from proper alignment and fire some groups that I know are unsettled for several hundred yards to see if the bullets would appear on both sides of the middle on sperate targets versus staying off course and stying on one side or the other. It looks like your video will save me a TON of time!

Thanks again!

 

[Buffalobob]

It appears that there are three lobes to the orbit. Does a different initial yaw produce different numbers of lobes or would it be a function of the spin?

 

[BryanLitz]

Bob,
It's a strong function of spin rate and independent of amplitude.

Mike,
Before you jump to a conclusion...
It's true that the pitching and yawing motion causes what's known as 'epicyclic swerve', which is exactly what you described. However, given the short period of the orbits, and the fact that the bullet doesn't generate much lift, the radius of the 'corkscrew' trajectory is very small, like less than 1 caliber. See this write up:

Homepage of Bryan Litz - A Bravenet.com Hosted Site

for a more thorough investigation into epicyclic swerve.

I would still be interested in your test. I've actually done the test you described, but for different reasons and with rifles that were not known to create smaller MOA groups at longer range. It's a stunt to pull it off. Take your time, and don't punish yourself by trying to do it on a windy day (the targets get pushed around and mess up the measurements.)

-Bryan

 

[Michael Eichele]

It's a stunt to pull it off. Take your time, and don't punish yourself by trying to do it on a windy day (the targets get pushed around and mess up the measurements.)

-Bryan

LOL!

Yeah I was contemplating how I was going to accomplish this earlier. I think I will set up a target frame and backer at 300 yards with a spot target in the middle. Have a laser leveled at the bench project a laser beam on center of the 300 yard target. Set up another target at 250 yards with a big square cut out of the backer with thin paper over the cut out and a .5" hole cut in the middle and set it up so the laser projects through the hole. The paper would have one verticle and one horozontal line intersecting the hole. I would repeat the process in 50 yard increments to 100 yards. The rifle would be centered over the laser.

Fortunatly we are having a very clear high pressure system latley which at least in Anchorage hasnt generated any wind. It would still take quite some time to set it all up. Give me a couple weeks and I will see what I can do.

 

[BryanLitz]

Awesome.
I hope you can pull it off.
I think your laser idea would work very good, provided you can see it 'at distance' in the daylight.

In my test, I zeroed at 1000 yards and placed a target ~55" above the line of sight at 200 yards leaving a 'window' under the 200 yard target that I could look thru to see the 1000 yard target. I had a surveying partner to help me measure the proximity of the 200 yard target to the line of sight.

Good luck, I'm looking forward to hearing how it goes.

-Bryan

 

[Michael Eichele]

Awesome.
I hope you can pull it off.
I think your laser idea would work very good, provided you can see it 'at distance' in the daylight.

You're in luck!! Daylight hours right now are not only short, the sun never gets high enough to hit my 300 yard target range! Even on these clear days, it isnt very bright where I am shooting.

 

[eddybo]

That is exactly as I envisioned it, that is cool. I have banged my head against the wall trying to explain this to a guy. Maybe this will help, thanks for sharing.

 

[davewilson]

thanks for posting. i always thought the path was more circular, with a constantly decreasing radius until it went to sleep.

is it true that, generally speaking,short per caliber bullets have a greater radius of yaw but go to sleep quicker than long VLD type of bullet that might not have as great a radius of yaw but need more time of flight or distance to go to sleep?

 

[BryanLitz]

I think the magnitude of yaw and how much time it takes to go to sleep after a given initial tip-off rate depends mostly on the gyroscopic stability of the bullet. You could get a long bullet to damp oscillations faster than a shorter bullet by spinning it way faster.

In general, shorter bullets have greater gyroscopic stability from a given twist barrel which would lead to quicker dampening.

-Bryan

 

[BryanLitz]

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 was showing 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