signs a pellet is transonic

[MicErs]

. There is an effective limit on the SD that we can drive with an airgun (with decent velocity), which means that particularly in the larger calibers we need a much slower twist rate.... Unfortunately, for the most part, the airgun manufacturers have been slow to realize that....  FX has figured it out with their Smooth Twist barrels.... So did Sean Pero and I when we came up with our .30 cal barrel with only a 26" twist, which recently won the Extreme Bench Rest match.... The same thing applies to our .357 barrel, which shoots bullets up to 158 gr. perfectly with only a 26" twist....
Bob

Thanks for your efforts in this area.  We can only hope they learn from your successes.

[TCups]

RE: twist rates
did some searching and find references saying "most" are 1/16" twist.

Tom Gaylord did comparison testing for accuracy, PCP's at various power settings, ranges 10 to 50 yards for barrels of 1/10", 1/12",  1/16" and 1/22" twist.  Results discussed in the 2012 blog here:

https://www.pyramydair.com/blog/2012/11/how-does-rifling-twist-rate-affect-velocity-and-or-accuracy-part-1/

All performed well at 10 meters.  Biggest differences in accuracy at 50 meters (no surprise).  Haven't converted his posted group sizes to MOA at the various ranges, which would be a more interesting relative comparison than just group size, I should think.

Measured the twist of my HW-30 .177 tonight - 1/16"

RE: Gyroscopic stabilization and precession:
Posted the physics question regarding the potential differences in angular momentum, head vs. skirt, affecting precession in the Physics Forum, here:

https://www.physicsforums.com/threads/precession-of-an-air-rifle-pellet-in-flight.815987/

As yet, no answers. 

RE: Optimum barrel length:

Though it seems I can no longer absolutely trust the Cardew brothers, they did perform an ingenious test by drilling a barrel  with multiple side holes, tightly plugged with an insulated fitting that let very small wire contacts be moved inward, slightly. into, or pulled back out of the bore, such that by inserting the wires at various lengths up the barrel, the barrel-to-pellet-to-wire contact closed an electrical circuit, allowing the time of travel and instantaneous velocity at each incremental distance up the barrel to be measured. 

There results say for a .22 springer, with a limited, fixed volume of air driving the pellet, max velocity is attained at ~ 6 inches down the barrel, and that critical air flow through the port into the expanding volume behind a pellet moving down a barrel no longer accelerates the bullet.  For pneumatics, as with powder burners, with much larger volumes of gas propellent available, longer barrels = higher velocity.  I suspect that modern magnum springers and perhaps gas ram guns increase the potential air volume per shot and lengthen the effective barrel length. 

[Can-o-cide]

There is no difference in angular momentum between the head and skirt of a pellet, unless the pellet had a swivel at its waist! There is one and only one angular momentum vector of a pellet. Sure, a lead atom in the skirt contributes more to the angular momentum than an atom in the center of the head (after being shot, usually) but that doesn't change the fact that there is only one commonly accepted meaning of "angular momentum of a rigid body".

It appears that the Cardew brothers are the only ones anyone references about pellet ballistics. Even Tom gaylord mentions them exclusively. I'm fixing my broken hatsan and am going to make a carbine out of it. Part of the process will be cutting the barrel down. That's why I'm interested in barrel length. I'll do my own experiment.

[MicErs]

I'm fixing my broken hatsan and am going to make a carbine out of it. Part of the process will be cutting the barrel down. That's why I'm interested in barrel length. I'll do my own experiment.

You will do fine.  Just take it in sections.

[TCups]

There is no difference in angular momentum between the head and skirt of a pellet, unless the pellet had a swivel at its waist! There is one and only one angular momentum vector of a pellet. Sure, a lead atom in the skirt contributes more to the angular momentum than an atom in the center of the head (after being shot, usually) but that doesn't change the fact that there is only one commonly accepted meaning of "angular momentum of a rigid body".

Agreed.  Only one angular momentum for a rigid body. But if the mass is not evenly distributed along the axis of a rotating rigid body (i.e., the rigid body is not a sphere) and the mass is rotating, and if the distribution of the mass on one end of the axis is spherical and on the other end is cylindrical . . .



Then, if an axel had a disk wheel on one end and a rimmed wheel on the other, or say a spherical wheel on one end and cylindrical wheel on the other, and I put it in a vacuum with no external forces  acting on it (i.e.,no wind resistance gravity, etc) and spin it, it spins on its axis and stays centered.  But if I apply a force to one end or the other, is the resulting perturbation the same? 

Think of it this way -- you and a friend are standing on the right and left side of a road.  A road - sized barbell is rolling  toward you and will hit you both at the same time.  On the left end of the barbell, the wheel is a solid lead ball, diameter 3 ft.  On the right end of the barbell is a spoked cylindrical rimmed wheel, diameter 3 ft.  Hypothetically,both the sphere and the cylinder, as you face them, have roughly the same presenting, visible surface area.  Irrespective of the center of gravity of the rolling (cylinder)--------(sphere)  about to smack both of you -- the COG won't be the centerline of the road, but far closer to the more massive sphere, of course -- which side of the road would you prefer to be standing on when this thing hits both of you?  And if you and your buddy, say, have equal mass, the impact is not only going to perturb both of you, but also perturb the rolling   (cylinder)----(sphere),  then which end of the  (cylinder)-----(sphere) has the greater momentum and is less affected?



And now, imagine the rolling (cylinder) ---- (sphere) is a JSB diabolo pellet proceeding down range at -- pick a velocity -- 800 fps in a 90-degree crosswind from the left at 10 mph.  Are the force of the wind resistance on the leading face of the sphere and the drag resistance on the tailing edge of the pellet equal?  I think not.  Is the force of the cross wind on the side of the pellet designed, roughly we will say, to have the same surface area presenting to the crosswind?  Is the crosswind force an equal vector force (lb/inch*inch) applied to the presenting surface areas of the head and skirt (roughly equal), and therefore, an asymmetrically applied force relative to the center of mass (much closer to the pellet head)?  If angular momentum must be conserved for the rigid body, how does the asymmetric force perturbation affect the motion of the pellet?  Does it move straight sideways, or does the force acting on the skirt push it askew more than the head, rotating the pellet on it's center of mass (like a weather vane)?  And if begins to precess, such that the less massive skirt is now swinging in a wider arc than the more massive head, then wouldn't angular momentum still be conserved, even though the pellet is no longer spinning on the same axis as the trajectory?  Do JSB's with their shallow-holed underskirt and more sphere-like head fare better than pellets with deeper holes?  Does the secant ogive of the JSB fare better than the tangent ogive of Crossman Premier where drag and BC are concerned, analogous to the ogive's effect on a rifle bullet?  Inquiring minds want to know.

And I don't know -- I am only speculating and asking questions, but I would bet 50¢ that diabolo pellets are inherently dynamically unstable when spun, and that conservation of energy and momentum, about the center of mass far forward of the skirt vs. asymmetry of typical ballistic external forces affects head and skirt much differently; that diabolo pellets vs. bullets are much more likely to be affected in odd ways by external forces -- wind, air resistance, drag, and maybe even gravity, compared to a more uniform cylindrical solid.  I think that diabolo pellets must have to pay a significant price in rotational stability (in the ballistic sense) for having to have a skirt that is necessary for a proper seal in an air rifle and drag in excess of the head.  But again, I've been wrong before and may be wrong now.

It appears that the Cardew brothers are the only ones anyone references about pellet ballistics. Even Tom gaylord mentions them exclusively. I'm fixing my broken hatsan and am going to make a carbine out of it. Part of the process will be cutting the barrel down. That's why I'm interested in barrel length. I'll do my own experiment.

Excellent!  We learn by doing.  You will have to re-crown the barrel carefully and decide if losing the barrels choke (if any) is a significant problem.

[K.O.]

I think each pellet has its own very complex mix of aerodynamics , Center of gravity, alloy/specific gravity and length so that once out of the barrel causes it to ask for a certain speed range at X twist rate.  I feel very small details can make a big difference...

The RWS Superdomes have that ridge(parting line?) around the edge of the head I think it has a huge effect on the .177s and not so much on the .22s... on the .177 it compared to the size of the pellet is large causing a much larger area of low pressure and to lower speeds...

so at high velocity it sheds velocity very quickly and it goes from acting more like a gyroscopically stabilized bullet to a drag/gyroscopically stabilized pellet rather quickly...

why do I think it acts more like a bullet at high speed... because the skirt is riding in a low pressure area created by the head... physics says
double the speed quadruple the drag also... so the flatter the head and the higher the fps the more abrupt the transition to drag stabilization at the skirt... effectively a shift in the apparent  COG towards the rear of the pellet...

then there is the twist rate the faster you spit the pellet at the higher the initial rpm of pellet...

I have been getting .5-.75 groups at 30 yards with the .177 superdomes out of a 20" 1:15 twist barrel (trying to catch lulls in the wind) and I think it has to do with both of the above...

Why? 

I think the ~430 fps the Daisy 953 sends them out at keeps the skirt in a condition where the it's drag is consistent and though the Stability calc (SF of about 4)  say it is way over stabilized there is no shift in apparent cg... and the cq is forward enough to prevent wallowing..?

and

sending it at 430 fps imparts a spin of about 21,000 rpm out of a 1:15 twist barrel...

where as

sending it at 850 fps imparts a spin of about   38,000 rpm out of a 1:16 twist barrel... and that makes it more susceptible to any imbalance in the pellet (caused by the barrel, production or handling ).

and of course I think it is more complex than the above in reality...

[TCups]

I think each pellet has its own very complex mix of aerodynamics , Center of gravity, alloy/specific gravity and length so that once out of the barrel causes it to ask for a certain speed range at X twist rate.  I feel very small details can make a big difference...

The RWS Superdomes have that ridge(parting line?) around the edge of the head I think it has a huge effect on the .177s and not so much on the .22s... on the .177 it compared to the size of the pellet is large causing a much larger area of low pressure and to lower speeds...

so at high velocity it sheds velocity very quickly and it goes from acting more like a gyroscopically stabilized bullet to a drag/gyroscopically stabilized pellet rather quickly...

I was looking critically at several pellets last night, critically, with a lighted magnification.  The separation line you refer to implies a cast bullet, correct?  That was what I thought when I saw it.  it also appears that the Superdome skirt may have been swaged onto a mandrel to form the cavity for the bolt tip, whereas pellets with a more conical skirt cavity seem in most cases to have been drilled or reamed. The Superdome's heads also appear to have been polished (possibly a simultaneous operation with skirt swaging?), but the finish on the rest of the pellet is indeed somewhat rough.

Had a rather odd idea last night, and I am going to try it out tonight -- dropping a handful of pellets into my now little-used vibratory tumbler (switched to a wet, rotary tumbler) with some corncob media to see what happens if I try to polish some pellets that way.  It may ding the skirts too much, don't know yet.  I suspect that it would depend on the number of pellets in the tumbler at one time and how long they were left tumbling.  In the past, I have also added NuFinish car wax to cotton patches and put them in with the tumbling media to give brass a really shiny finish that doesn't tend to tarnish when stored.  Wondering if a wax job might lubricate the pellets and potentially do some good as well.  If I get really industrious, I will measure the test pellets before and after, and shoot some test groups.

[K.O.]

Me I am stuck on playing with twist rates right now and need to get busy getting the work done...

I have all the parts for a budget 900+ fps w/7.9g cphp at 20 pumps MK1377

I have  3 different twist rates to try on it : Daisy 10 land/groove 1:15 twist, Crosman 10 land/groove 1:16 twist and a Lothar-Walther 12 land/groove 1:17.7 twist(choked)

I wish I could find a Broken BSA Meteor to scrounge the barrel from I found a AoA pdf that says they have a cold forged 12 land/groove 1:19 twist barrel...

Scroll down a bit

https://www.google.com/search?sourceid=navclient&aq=&oq=&ie=UTF-8&rlz=1T4ADFA_enUS508US508&q=bsa+meteor&gs_l=hp..6.41l253.0.0.0.213156...........0.

Cast .177 not likely imo just to hard to avoid voids and such...

I also have thoughts about tweaking the specific gravity #s to account for the missing mass/weight(compared to bullets) when using the twist rate calculator...

http://www.geoffrey-kolbe.com/barrel_twist.htm

in the end ya got what ya got though and just trying different pellets till you find the one that works best for a given powerplant/barrel gets the job done...

but it is very enjoyable to try and figure the whys...

[rsterne]

TCups.... that is an excellent explanation of Moments of Inertia, but as mentioned previously, in a rigid body, all the moments add up to produce ONE moment of inertia acting through the CG.... If the sideways aerodynamic drag acts through the same point (the CP), then there is no torque applied to cause an upsetting yaw.... The sum of all the forces acting in a crosswind and likewise be considered to act through a Center of Pressure, a concept familiar to sailing or flying.... If you read through the link I posted the summary from on page 1 of this thread, you will find the following regarding the interaction of the Magnus Force, acting through that Centre of Pressure, and the Center of Gravity, which causes the "Magnus Moment"....

http://www.nennstiel-ruprecht.de/bullfly/fig11.htm

The key part of this is the following statement....

the Magnus moment will have a stabilizing effect as it tends to decrease the angle of yaw d.

It can be easily shown that this is only true, if the centre of pressure of the Magnus force CPM is located behind the CG. The Magnus force destabilizes the bullet and increases the angle of yaw, if its centre of pressure is located ahead of the CG, which may come true in a specific velocity regime.

What I get from that, is that if the CP is behind the CG the bullet should be dynamically stable (yaw damps out), but if the CP is ahead of the CG it will be unstable.... I would rather assume that Diabolo pellets are designed to have the CP behind the CG, so should be tending towards stability.... but this may come unglued at certain velocities and rates of spin....

Bob

[Slavia]

This is a tangent, but it relates:  Did you ever make one of those 2 liter soda bottle rockets, powered by water and compressed air?  It will be most stable if the addition of fins and other doodads puts the cp behind the cg by 1/2 bottle diameter.

[TCups]

Bob:

 I confess I still haven't read all of your references, yet.  Busy day at work, etc.   I will.  and I will come to grips with the vector graphic animation posted.  I seem to think the 2-D animation shows the principle, but thinking about it in 3-D, I believe I can now more clearly see how and why pellets DO indeed "corkscrew" downrange.  Actually, as it turns out, I explained exactly why and how pellets might fly in a spiral trajectory in my second post on this thread, without realizing it:

"Under a strobe light, in the dark, I have seen a fletched arrow fired from a compound bow wobble and spiral."

and the second statement in that post is probably also still be correct:

"I have never seen evidence that a bullet actually spirals".

Spirals is probably the wrong word -- technically all rifle bullets spiral, but don't usually corkscrew.

I think I have the right concepts here, if not the right technical terminology:

The heavy head and hollow skirt produce a moment of inertia that tends to wobble the long axis of an air rifle pellet.  In my mind, I think of a swivel office chair.  With legs extended, take a spin, then pull your legs in -- you rate of spin increases, like an ice skater tucking into a tight spin.  Energy and angular momentum are conserved.  Angular velocity changes.

Now, think of a double decker office chair on a single, long pedestal -- if you and I start out at the same rate of rotation, on the same axis in each of the chairs, you above and me below, but now, suddenly, you tuck in and I throw my legs out, what happens?  We cannot spin at different rates (angular velocity).  We haven't changed the center of gravity or the total energy of the mechanical system.  But each of us has changed our moment of inertia.  Something has to give.  The pedestal (axis) has to begin to wobble to conserve angular momentum.

At nominal velocities, even without spin to stabilize a pellet, skirted pellets fly a relatively straight trajectory, because, like that arrow, the skirt acts like the fins of an arrow to stabilize the trajectory.   .

If the pellet's skirt tries to swing outward and wobble while the pellet is still flying fast enough, it just gets pushed back in line by wind resistance.  But as, down range, the linear velocity decays faster than the angular velocity, then the pellet can begin to swing it's skirt outward, and the pellet wobbles - precessing about it's center of gravity, and  yes, at one and only one angular velocity, and at one and only one  total angular momentum,  but to conserve its total angular momentum, the moment of inertia (is that the right term for the vector force that tips the axis of precession?) is not constant. 

Even wobbling, the pellet is still flying down range, and still flyiing with its skirt, wobbling or not, acting like a finned projectile -- an arrow.   And the rotational precession of the pellet's "fin", its skirt, steers the direction of the pellet's flight. 

For a finned projectile, spiraling yaw (precession) + fins = corkscrew trajectory

For an un-finned projectile, spiraling yaw occurs, too, but the bullet projectile's center of pressure, forward of the COG, makes the bullet tumble and keyhole, and yes perhaps even spiral slightly, but nothing like a finned projectile.

Down range, spinning bullets tend to "go to sleep", become more gyroscopically stable and behave well in most cases.
Down range, spinning pellets tend to "wobble" and fly like a wobbling finned projectile -- in an ever increasing spiral, as forward velocity decays and angular momentum begins to dominate, inducing a rotational torque on the skirt that overpowers wind resistance against the skirt and steers a corkscrew trajectory.

It seems to me that the farther and faster air gunners try to shoot skirted pellets, the more the get screwed.

PS:  Here's an counter intuitive afterthought.  If one were to swage a LH twist rifling into the skirt of a pellet flying out of a RH twist barrel, then as the linear velocity of the pellet decays, and the skirt begins to yaw and swing outward into the air stream, steering a corkscrew, might the counter twist on the skirt begin to increase drag on the skirt, and to slow the angular velocity of the pellet's spin, helping to reduce the tendency to yaw, and helping to minimize corkscrewing, albeit at the cost of a faster decay in terminal linear velocity.?

[rsterne]

The pedestal (axis) has to begin to wobble to conserve angular momentum.

Sorry, don't see it.... if the total change in moment of inertia is zero, nothing changes.... If the MOI increases, the angular velocity decreases to conserve angular momentum, and vice versa.... This is because the axis connecting you and I is rigid, and the body (in either state) must be considered one rotating body.... If there is no external torque applied, why would it wobble?....

I'm not so sure of your definition of spiraling not being corkscrewing.... I would agree that wobbling (precession and/or nutation) is not corkscrewing, but once the CG is describing a helical path, I would call that both spiraling or corkscrewing, I would use the terms interchangeably....

I think your generalization about (all) pellets spiraling more downrange while bullets do not is vastly oversimplified.... You really need to read and study that reference and the diagrams showing varying modes of Dynamic (In)Stability.... and in particular the part that say that for the most part it is not possible to predict it because many of the variables are difficult or impossible to measure or predict....

Bob

[TCups]

Yes, on my reading list for this weekend, I promise.  But isn't angular momentum a vector quantity?  Even if the total angular momentum is conserved, its vector can change --  has to changes -- if an external force is causing a deviation of the original axis of rotation.  No more posts hijacking the thread for now.  Sorry.  I have a lot of reading to do, so I may be a while getting back. In the final analysis, though, yes, pellets do spiral and seem to behave, potentially, like a wobbling, finned arrow in flight under the right circumstances.   Thanks.

[MicErs]

Let me ask the obvious here.  What if a pellet is not concentric on it's axis?  What if the skirt is say 0.001 shorter on one side than the other?  What if the central axis of the skirt is two degrees different from the central axis of the head?  How much actual distance is that?  IRL (In Real Life).

We have problems with pellets.  It might cost those of us who care five cents a pellet to fix these problems, but WE DO have problems with pellets.

I am probably about to be bludgeoned here... so just count this post as the rambelings of an idiot and continue to march.

There are really only two reasons why they can fly poorly.  Either they are poorly stabilized, or the vendors are giving us pellets which will not fly.  It could be both.

All of the rest is icing on a cake.  The cake is where we need to work.  In my mind we should eliminate the variables which have anything to do with stabilization first.  That might be by addressing rifling rates.  That might be by addressing the quality of our pellets.  But these two areas come to the top of the list.  Fix one first, does not matter which, then fix the other.

This is how industry works.  It is somewhat like science but CHEAPER.  First solve the CHEAPEST problem.  If that does not result in a satisfactory solution then solve the more expensive problem.

This is just an opinion.  Nothing more.

[rsterne]

I agree 100%.... The less perfect the pellet, the more chance it will be Dynamically Unstable if it's spun too quickly.... So, you can either convince the pellet manufacturers to up their game and produce perfect pellet (which might easily cost 10 - 100 times as much).... or try a slower twist.... Benchrest shooters have know this for years, they were flirting with slowing the twist down to the verge of unstable for the Static Stabilty.... The Military use a Stabilty Factor of 1.5 - 2.5, and the BR guys were flirting with 1.2 (1.0 or below is unstable).... Then they found out that when you go below 1.5 the bullet, although it isn't keyholing, is wobbling enough that the BC is reduced.... JBM has a calculator on their website that deals with that.... Current thinking is that we should be as close as possible to that 1.5 SF as we can.... When the SF gets up into the 3.5-4.0 and over, then we can see Dynamic Instability occurring in SOME bullet designs, and it certainly starts to emphacize any imperfection in the bullet....

None of the available Twist Calculators are set up for Diabolo pellets.... The best you  can do is use the dimensions for a round nose bullet of the same length and caliber, and possibly make some correction for the reduced weight.... Even that is very difficult to use, as the calculators assume a uniform bullet density.... so how do you determine the rotational Moment of Inertia of a pellet (with a waist and a hollow skirt) and compare that to a solid round nosed cylinder?.... At what stability factor is a pellet overspun, and therefore more susceptible to Dynamic Instability?.... Would that be at 3.0 and above?.... 2.0 and above?.... 1.0 and above?.... or is the answer to spin the pellet extremely slowly, like the FX Smooth Twist barrel, where I have seen spin rates listed of as low as 1 turn in 13 FEET?.... If the cure for Dynamic Instability and pellet Spiralling is too fast a twist rate, then the Smooth Twist barrels should never show it, WITH GOOD PELLETS, regardless of range of velocity....

I don't have all the answers by any means.... However, my gut is telling me that if you see Pellet Spiralling developing at longer ranges you have too fast a twist rate for that pellet....

Bob

[MicErs]

or is the answer to spin the pellet extremely slowly, like the FX Smooth Twist barrel, where I have seen spin rates listed of as low as 1 turn in 13 FEET?.... If the cure for Dynamic Instability and pellet Spiralling is too fast a twist rate, then the Smooth Twist barrels should never show it, WITH GOOD PELLETS, regardless of range of velocity....

I don't have all the answers by any means.... However, my gut is telling me that if you see Pellet Spiralling developing at longer ranges you have too fast a twist rate for that pellet....

Bob

I don't know but I think it would not hurt to test a lot of different pellets in the FX barrel.  If the data suggests that we are vastly over stabilizing then we have an answer.  If it doesn't then we have an answer.  =)

Either way, I thank you for your work.  It really is brilliant.