Range Report 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 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

 

[Maple One]

Re: Epicyclic motion of a bullet (video)

Good info. Very interesting. Thanks for posting.

 

[bigwheeler]

Re: Epicyclic motion of a bullet (video)

Thanks for the post. Wish some high tech lab would high speed camera and actual
bullet for us. I shoot an 7 stw that is a 5.5 pound gun and it is 3/4 at a 100 and as
often as not 3/4" groups at 300. Always bought into the theory but would sure like
to see it in slow mo.

 

[lrs50bmg]

Re: Epicyclic motion of a bullet (video)

Bryan,

The video was great. Nice to see an animated version of what Bob McCoy was trying to describe with the diagram in his book. Easier to visualize the damping with the video. Thanks for posting!

Scott

 

[Terry Cross]

Re: Epicyclic motion of a bullet (video)

Brian,

Very neat graphic. Thanks for posting.

I have a dumb question. I think I understand about the pitch and yaw cycles being the attitude of the bullet axis in relation to the line of flight/bullet path. Is that correct?

If that is correct, how does this graphic relate to the flight path? Does the flight path cycle similar to the yaw/pitch cycles?

Many say that the flight path cycles like that and then tightens into a tighter path further down range. I cannot see what would consistently bring it back to it's orininal flight path. Please help me get this settled in my head.

Thanks again,
Terry

 

[BryanLitz]

Re: Epicyclic motion of a bullet (video)

Terry,
Not a dumb question at all!
In fact your concern has been a common reaction to the video posted on other sites. I have added to the original video in an attempt to make it more comprehensive.

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

 

[esorensen]

Re: Epicyclic motion of a bullet (video)

Right twist barrel? Bryan, check your PM's.

 

[Terry Cross]

Re: Epicyclic motion of a bullet (video)

Bryan, (ha spelled your name correctly this time)

I understand that the intersection of the two axis on the first graphic would be the CG/CM of the bullet with the plot representing maybe the tip of the bullet as it is yawing around it's center of gravity?

I'm not getting the 2nd graphic. Can't figure out what is happening with the bullet path. I'm probably making this harder than it really is. Sorry.

The reason I am interested in this is that I have always wanted to debate the idea of a bullet (especially VLDs) shooting larger MOA groups at closer ranges then "going to sleep" and shooting smaller MOA down range. I am soooo not sold on that.

I can buy into your graphic and explanation about the yaw and pitch of the bullet calming down and stabilizing or dampening to a closer relation to the exact forward vector or line of flight.

What I cannot reason is how a projectile could deviate from a normal ballistic flight path, expecially in a spiral or oscillating motion and then settle uniformly back into that original flight path. Everything tells me that once it's direction of motion changes, it will continue in that direction until something else effects that motion.

I know that these projectiles are approaching 200,000 rpms and a lot of things happen with those spin rates, velocities and aerodynamic compressions but I would like your opinion on the smaller MOA thing at longer distances.

Thanks,
Terry

 

[Austan]

Re: Epicyclic motion of a bullet (video)

Terry- I don't think it is showing that the bullet is actually deviating from the flight path. It is just showing that the bullet wobbles as it comes out of the barrel then begins to settle down in to a tight spiral. I think of it as a football. Put a football on the floor on its nose and spin it good. It will wobble a bit (bullet as it leaves the bore) then spin in a nice spiral (bullet as it "goes to sleep") then as it slows it will wobble again before it falls (bullet making transonic/subsonic transition). This is the best analogy I can think of. I don't buy into someone saying there rifle shoots 2" goups at 100 and 1.5" groups at 200. But I do believe a rifle that shoots an inch at 100 could also shoot an inch at 200. Maybe thats not what Bryan is getting at. Thats just what I thought the video was showing. I could be wrong.

Austan

 

[Terry Cross]

Re: Epicyclic motion of a bullet (video)

Austan,
I understood that. The first graphic (the one on the left) shows what you are describing. I'm all about that. No issue. Per my 2nd post, it is his follow up graphic I'm lost on.

The 2nd graphic (the one on the right) is suppossed to show <span style="font-weight: bold">"the actual bullet path from the shooters point of view" </span>per Bryan. Why does that plot start below the origin? Why does it pass through the X-axis and then come back down, all the while moving further left from the Y-axis?

<span style="font-weight: bold">You said,"But I do believe a rifle that shoots an inch at 100 could also shoot an inch at 200."</span>Why? That would have to do with deviations from the original flight path and a return to that "home" trajectory later. Not talking about pitch. Not talking about yaw. Not talking about the bullet settling down. Regardless of its attititude in relation to the flight path, you are saying that it can cycle out of that flight path and then come back into it later and then stay there till destabilizing or impact.

I say no. Even if the model calculated a theoretical bullet path cycle that would come back to a uniform path (= good group again), the amplitudes and frequencies of those cycles would have to be very uniform. If they were uniform, the group would still be there at any closer range, it would just be offset from the intended flight path by the distance of it's amplitude from the base.

Keep in mind, I'm not a ballistician and can't prove it doesn't. It's just that it goes against what I thought I was taught in college.
What I really think is that I am too inbred to undertand it.

 

[Terry Cross]

Re: Epicyclic motion of a bullet (video)

Does anybody have Stephen Hawking's cell number?

 

[BryanLitz]

Re: Epicyclic motion of a bullet (video)

Terry,
You understand the first (left) graph perfectly. It's showing the angle, in degrees, of the bullets axis, not its flight path.

The right hand side of the new video is showing the bullets actual flight path, in inches, from the shooters point of view.

The 'crosshairs' in the right hand side plot 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.

It may seem strange at first that the deflection is to the left when the initial yaw rate is to the right. If you look closely at the first few cycles, you can see that the bullet reaches it's max average angle 180 degrees from the original yaw direction. In other words, the precession causes the bullets nose to swing left after a disturbance to the right. After the first max yaw cycle (180 deg from original tip off), the amplitudes are smaller, so the bullet doesn't ever 'correct the damage' (leftward deflection) that was done in that first cycle. The result is about 1 MOA of left deflection for a 25 rad/s nose <span style="font-style: italic">right</span> initial yaw rate.

As for the idea of bullets grouping smaller MOA at longer ranges...

There's too much anecdotal evidence on this to ignore it. The epicyclic swerve depicted in my videos <span style="font-style: italic">might</span> be a possible mechanism for it if the initial yaw amplitudes were high enough. However, in the video I posted, there was only a 25 rad/s initial yaw rate. The resulting 'corkscrew' flight path that results from that is very 'mild', as you can see in the trajectory plot. In other words, by the time the bullet gets to 100 yards, the radius of the spiral trajectory is less than one caliber. You can see a little 'wiggle' at the very beginning of the bullet path, but after that it settles out very nice.

I have tried, using this simulation, to create a combination of initial conditions that would cause a spiral trajectory severe enough to produce 1.5" groups at 100 yards and 2" groups at 200. No matter how I varied the initial conditions I was not able to create a series of shots that exhibited such dispersion. It would be very bold of me to say that epicyclic swerve is not the culprit for the common observation (of smaller MOA at longer range). I can say that I haven't been able to produce the effect in simulation with epicyclic swerve.

I believe that it is possible to shoot smaller MOA groups at longer range, but I don't know how. Some have suggested aiming errors like scopes not properly adjusted for parallax at close range as a possible reason and that sounds reasonable. So far, to my knowledge, there is not a proven explanation. If someone knows please tell us!

-Bryan

 

[Lindy]

Re: Epicyclic motion of a bullet (video)

Bryan: I admire a person who admits to gaps in his knowledge.

Evidence of smaller groups at greater distances is going to be anecdotal without some kind of way of tracking bullet path at more than one distance without affecting the path.

I suspect that this question might well be answered by doppler radar data, but I haven't access to that data.

I was trained as an engineer, so my orientation is that if it can't be measured, it doesn't exist.

 

[Austan]

Re: Epicyclic motion of a bullet (video)

Terry, what I was getting at is people saying that they shoot smaller groups at a further distance. My example was a 2" group becoming a 1.5" group further out. That would mean that the bullet deviates from its path and somehow comes back to certain point. I don't buy that. I know plenty of people that say they shoot better at 2-300 yards than 100 yards. It has nothing to do with the actual bullet path but everything to do with the way they shoot. Or a combination of the way they shoot and things such as optical parallax or aiming errors like Bryan mentioned. The shot cone is called a cone for a reason. You can't cheat physics.....or the wind. Although the vld sure tries hard!

 

[TiroFijo]

Re: Epicyclic motion of a bullet (video)

In Bryan's site there is an explanation of the epicyclic motion and its influence on group size at vaeious ranges.

What is surprising for me in this animation is the large amount of horizontal deflection at 100 and 200 yds... the horizontal difference in POI is almost 1" between 100 and 200 yds. In my experience this is much smaller, very difficult to notice sometimes. Perhaps this is because I'm using other bullets, or ??? I would like to see a similar animation with a 0.308" 175 SMK or a 150 FMJBT similar to NATO ball.

 

[Lindy]

Re: Epicyclic motion of a bullet (video)

The animation is based on a computer model.

The output of computer models is suspect until confirmed by other data. Is there such data to validate this model?

 

[eric long]

Re: Epicyclic motion of a bullet (video)

I was told by a friend/gunsmith that "it is well known" that boattail bullets do not "settle down" for 200+ yards. He says that you often shoot larger groups at closer range with the BT bullets. That looked like what I was seeing, of course cataracts could be clouding my vision.

 

[Lindy]

Re: Epicyclic motion of a bullet (video)

Well, my AI regularly groups Sierra 175s into a half MOA at 100 yards. It doesn't do that at 200 or further out, alas. Perhaps it's just that I can't shoot.

 

[Terry Cross]

Re: Epicyclic motion of a bullet (video)

I too have seen what appears to be said phenomenon. Our SO range is a bitch to get a group at 200yds. 100 and 300 on the same sitting is cool with the 300 sometimes getting around 1" or so on the group. At first, I would say that my rifle is not performing at 200yds. Then I take it to another range and, boom, it's shooting small at 200yds. If this ballistic anomoly was a function of the bullet stabilization, it should be consistent and repeatable. It is only consistent on that range and then not 100%. Poor mental or physical technique on my part or squirrely light/wind conditions have to be the culprit.

So I agree with you Bryan about the anecdotal evidence. However, I will continue to scratch my head as to the causes all the while fully believing that it is NOT because of the flight path coming unraveled and then falling back into place at some point further down range.

I am also totally convinced that me getting off my ass in front of this computer and shooting my rifle will make me a better performer and help me predict impacts more efficiently. I do however like to ponder the "why" sometimes. I appreciate Bryan and the other brainiacs that put the time and expertise into getting hard, documentable results.

Then again, I can get totally mesmerized by any small shiney object.

TC

 

[Terry Cross]

Re: Epicyclic motion of a bullet (video)

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Bryan Litz</div><div class="ubbcode-body">It may seem strange at first that the deflection is to the left when the initial yaw rate is to the right. If you look closely at the first few cycles, you can see that the bullet reaches it's max average angle 180 degrees from the original yaw direction.
-Bryan</div></div>

Bryan,

Your model shows the initial yaw to the right. Was that a starting point chosen by your input? How repeatable is the initial direction of yaw? Would velocity deviations from shot to shot cause pressure/rpm/acceleration variances that would alter the direction of initial yaw?

Ditto for barrel length. If you had a 24" barrel and load with zero velocity SD, wouldn't a change in the barrel length cause a change in the initial yaw direction?

Same question for a different bullet style with the CG at a different point in relation to the overall length of the bullet? For example a 190gr Berger VLD vs a 190SMK.

 

[One_Feather]

Re: Epicyclic motion of a bullet (video)

OH....

 

[eddief]

Re: Epicyclic motion of a bullet (video)

You guys are too smart for me, I'm going to watch cartoon network now and see how the acme rockets yaw is in flight!

On a real note, I hope people realize the engineering that people (like Bryan) put into products that we just shoot and have fun with.

Makes the price for a box of bootlits seem a little less trivial.

Thanks guys!

 

[aggiesig]

Re: Epicyclic motion of a bullet (video)

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">I believe that it is possible to shoot smaller MOA groups at longer range</div></div>

I totally agree, I've seen it. I always blamed bullet stabilization, like the opposite of what happens when you shoot a bow that isn't tuned well.

It is very apparent at close ranges.

I've got a 16.5" '94 chambered in 32 winchester special (barrel had a bulge when I bought it so I cut it down) It shoots 3" groups at 15 yards, and 1.5" groups at 50 yards. Same shooter, same bench, same ammo.

granted the velocities, ranges, and bullet weights/coefficients are drastically different than the topic at hand, but the same physics apply

 

[SoOutlaws]

Interesting! Thanks for posting

 

[KYpatriot]

Bryan: I admire a person who admits to gaps in his knowledge.

Evidence of smaller groups at greater distances is going to be anecdotal without some kind of way of tracking bullet path at more than one distance without affecting the path.

I suspect that this question might well be answered by doppler radar data, but I haven't access to that data.

I was trained as an engineer, so my orientation is that if it can't be measured, it doesn't exist.

This right here. Someone who owns one of these mythical rifles that shoot tiny groups at distance but large ones at 100 needs to agree to a test. Shoot the rifle at a distant enough target that the bullet rises fairly far above the line of sight. Calculate how far above the line of sight the bullets must go at 100, 200, 300, etc and place cellophane or some very thin paper there to record the groups as the bullets pass through to the distant target. I predict you will find, when you have a small group at the target that satisfies this shooter, than there will be even smaller groups on the tissue paper on the way.

 

[KYpatriot]

Terry, what I was getting at is people saying that they shoot smaller groups at a further distance. My example was a 2" group becoming a 1.5" group further out. That would mean that the bullet deviates from its path and somehow comes back to certain point. I don't buy that. I know plenty of people that say they shoot better at 2-300 yards than 100 yards. It has nothing to do with the actual bullet path but everything to do with the way they shoot. Or a combination of the way they shoot and things such as optical parallax or aiming errors like Bryan mentioned. The shot cone is called a cone for a reason. You can't cheat physics.....or the wind. Although the vld sure tries hard!

Exactly. I am not saying people haven't seen this, but the bullet isn't responsible for it, they are. Also, the 7mm 180 Berger has one of the best form factors on the planet and is probably a fairly extreme example of this phenomenon, given the fast twist and high velocities...I suspect this simulation was run at 7mm Rem mag velocities to accentuate the high RPM to maximize the effect. The already small dispersion due to swerve is maximized in those conditions, meaning that it is even less of a factor in "lesser" bullets at more moderate velocities and twists.

Besides, as you point out, while swerve may cause dispersion to be less linear with TOF than it otherwise would be, there is no way in which it could actually correct a group and make it smaller than a closer group. Out of curiosity I would like to know why shooters are seeing this, but I'd eat my hat if its the bullet.

 

[KYpatriot]

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">I believe that it is possible to shoot smaller MOA groups at longer range</div></div>

I totally agree, I've seen it. I always blamed bullet stabilization, like the opposite of what happens when you shoot a bow that isn't tuned well.

It is very apparent at close ranges.

I've got a 16.5" '94 chambered in 32 winchester special (barrel had a bulge when I bought it so I cut it down) It shoots 3" groups at 15 yards, and 1.5" groups at 50 yards. Same shooter, same bench, same ammo.

granted the velocities, ranges, and bullet weights/coefficients are drastically different than the topic at hand, but the same physics apply

Yes its possible, but its you doing it, not the bullet. If it was the bullet, it would be repeatable, would happen every time, with any good shooter. Is that what you are seeing, or did this happen once and you just thought it must be the gun/bullet combo causing it?