Bob remember my hollow bullet AKA wing ring!!

[oldpro]

I hope oldpro does not think I am trying to steal his idea; or claim credit for it.  However, it should be obvious by now that I am perfectly capable of generating "unusual" ideas all by myself. 

My impression when looking at patents is that almost anything I can think up has already been thought up.  While this can be frustrating, it is also a validation of sorts.  I happen to have more than a dozen US patents, with another handful in the pipe.  None of them relate to lead slinging, so I am not competing with any of you here.

The through-flow "nozzle" design below is closer to one of my original ideas; hatched about April last year.    The nozzle shaped internal cavity could be swaged; but good luck casting it with a conventional mold.

I would love to see someone make the wing ring projectile and I mean anybody. I love the knowledge being shared and truly believe with my limited testing something good will come of it.

[subscriber]

Bob,

You bring up a very good point about chocked flow in a nozzle. 

What I remember from thermodynamics class in 1981 was that any given nozzle would reach maximum flow when the velocity in the throat reached the speed of sound.  After that, increasing the pressure differential across the nozzle would not add any flow. 

Now, pressure differential depends on the inlet and exhaust pressure.  If both inlet and exhaust pressures are increased, the absolute pressure throughout the nozzle would increase.  That would raise the density of the air, and the speed of sound along with it.  I think this may be the crux of what enables you to reach 2000+ FPS with your airguns.  In a nutshell; you are operating at several atmosphere of pressure, so the speed of sound in your flow ports are above 1100 FPS throughout much of the "power stroke".

Anyway, for an airgun projectile, the average base pressure is at most one atmosphere. Significantly less, with a flat base projectile and as speed increases - the very problem that we want to address.

By virtue of this through flow passage, the maximum inlet pressure should be a lot less, than if the projectile were a simple flat closed cylinder (wad-cutter).

Perhaps your admonition for minimum throat diameter is all that needs to be considered.  Well, almost all.  If the divergent section of the nozzle is made with too steep an angle, the flow will break away and result in a virtual choke.  Now, considering that an 8 degree (per side) boat tail works pretty well in an open flow path, I don't see why the inside would have to be made to a shallower angle than that. It could be; but should not have to be.

The simplest flow-through projectile would look like a length of thin walled pipe, with the leading a trailing ends rounded slightly.  This would provide an almost full caliber flow path with a very high effective sectional density.  The question is if such a projectile would carry enough mass to be useful? 

Now, the normal metrics for "heavy enough for long range" may have to be thrown out; precisely because such a light projectile should have the drag of a sub-caliber sabot round, combined with the terminal performance of a full caliber wad-cutter.  One that does not rely on expansion to cause significant damage.





Anyway, a nozzle shaped flow passage would be very difficult to manufacture; especially in smaller calibers. As such, parallel passages are probably the best bet for experimentation.  These could be drilled.

Below are some potential through flow projectiles; including more conventional looking ones.   

The .30 caliber boat tail secant nose slug has a .2" meplat with a tapering core pin to enable NOE molding.

[subscriber]

Are you guys familiar with "base bleed" shells?  https://en.wikipedia.org/wiki/Base_bleed

If so, then the idea that all the air in front of the "wing ring" has to pass through it, for the through-flow ventilation to add significant range, would seem debunked.    Even if the flow through the passage is choked, the reduction in base drag should be very significant.

Some air is going to flow around the outside anyway.  If you can just halve the vacuum at the projectile's base (or double the absolute pressure), that would make a huge difference in drag, compared to conventional projectiles.

[rsterne]

You state that a flow through projectile will have a high SD, but that (for a lead projectile of constant cross section) will depend solely on the length.... If the length is a constant, it doesn't matter if you have a 1/4" cylinder, a 1" cylinder, or a 1/2" OD tube with a 1/4" ID.... all will have the very same SD.... Pick any dimensions you choose and do a few examples, and you will see what I mean.... Once you fix the length, the volume (and hence the weight) is proportional to the cross sectional area.... Increasing both by the same proportion means the SD is a constant....

If you profile the outside, or the inside, or both, you will reduce the SD because the maximum cross sectional area stays the same, but the volume (and hence the weight) decreases.... You are trading off decreased SD against a hopefully lower FF.... If you use a less dense material, the SD will also decrease, of course.... For simplicity, let us consider a cylinder, or a tube, both of lead.... If you use a tubular section for your bullet, you can get the same SD with a cylinder of the same length, if you use a smaller caliber.... For example, a .25 cal tubular bullet of constant cross section with a 0.20" hole through it would have a cross sectional area (0.0177 sq.in) the same as a .15 cal solid cylindrical bullet.... and indeed the same weight, and hence SD, if they were the same length.... The SD is only one of the two factors that determine the BC, the other is the Form Factor, by the equation BC = SD/FF.... So, of course even if the SD is the same, the wing ring MAY have a better BC, if the FF is less (or it may not).... but stating that just because you drill a hole down the middle of a bullet increases the SD is incorrect.... If you keep the same length and material.... that is not likely the case.... and would certainly NOT be the case if you compare a tube to a cylinder, both of the same length....

While you are correct that a tubular projectile should have less drag than the corresponding cylinder it came from, it will also have less mass to counteract that drag.... and in fact the only way to prove whether it is better or worse from a ballistics point of view is testing.... I have serious doubts about possible gains in "Exterior Ballistics", however there are two areas where gains may be possible.... "Interior Ballistics" (the ability to accelerate a given mass with a give pressure) and "Terminal Ballistics", which is how the projectile performs when it hits the target....

Interior Ballistics.... The ability to accelerate a conventional (solid) bullet in a PCP to a given velocity is governed by its SD.... There is a limiting SD for any given combination of pressure and barrel length if you wish, for example, to reach 950 fps.... If the SD is too high, you will not reach that velocity.... The exception, of course, is if you use a Sabot, so that the area that the expanding air is acting on is larger than the cross sectional area after the sabot detaches.... You are in effect lowering the SD during the acceleration phase.... while maintain a higher SD during the flight phase.... In this respect, a wing ring is similar to a sub-caliber bullet launched by a sabot....

Terminal Ballistics.... I don't have good enough grasp of what might happen when a tube hits meat to give a realistic answer.... but logic would seem to imply that the damage from a tube would be greater than the same weight cylinder hitting at the same velocity and hence energy.... If both were launched by the same diameter sabot, since the weight was the same, they should have the same MV.... and if they were the same length, the same SD and close to the same exterior ballistics.... and so both arrive at the target at the same velocity and energy.... An argument could be made that since penetration is the product of SD and velocity, they should have the same penetration.... however I think the drag of creating a "meat worm" would likely slow the wing ring faster than a smaller diameter cylinder.... so I would expect the wing ring to have a wider, but shorter wound channel.... much like what you see with an expanding hollowpoint bullet....

My personal opinion is that the wing ring has many of the same advantages as a sub-caliber projectile launched with a sabot, and many of the same disadvantages as well.... Just as you can profile the inside of the wing ring to reduce drag (ignoring the effects of choking for the moment), so can you profile the outside of a sub-caliber bullet to reduce its drag as well.... In both cases, you have to have a reliable and consistent release from the sabot for consistency, accuracy and repeatability.... The available shapes for a sub-caliber projectile are well developed and documented, and the ballistics readily available.... the wing ring, not so much.... I am not trying to discourage its development in any way.... merely trying to point out some alternative ways of thinking about it.... and trying to clear up the idea that it increases the SD, which I do not view to be the case.... To increase the SD in any given caliber, in reality, requires an increase in the length (or density) of the projectile.... All bullet design is trying to trade off a decrease in SD for an decrease in FF.... If the FF drops faster than the SD, you have improved the BC.... If not, you haven't.... The SD remains one of the two dominant factors in how a bullet loses velocity and energy as it travels to the target.... The other is the FF or Cd.... The key to the success of the wing ring will, IMO, lie with the ability to reduce the FF below what is found in a conventional projectile....

Bob

[subscriber]

Hi Bob,

The only reason why I kept using .45" for the projectile length is because that is the longest that fits Marauder mags...

My statement about "increased SD" should be pondered in this context:

 A .25 caliber wadcutter weighing 50 grains has a SD of 50 / .25 x .25 = 800 units

A .25 caliber wadcutter weighing 50 grains that has a cylindrical hole through it, of diameter .15", has a SD of
50 / [(.25 x.25)-(.15 x .15)] = 1250 units. 

Obviously the hollow 50 grain projectile of the same OD, has to be longer than the solid one (assuming they are made from the same material).

So, SD has gone up; not because weight went up, but because cross sectional area exposed to drag in flight went down.  Effective area exposed to gas pressure down the barrel are the same, because the hollow projectile relies on a sealing disc that drops away like a sabot.

Even if you "normalize" SD via projectile length, and the ratio of wadcutter to vent area; larger projectiles will perform better than smaller ones.  At least, until the diameter is greater than the projectile length (at which point it will become unstable - like a dropped coin, or leaf).  Allow me to explain:

Consider a projectile with with a uniform circular matrix of ten .01" diameter holes, that run through its length.  Now, compare this with a similar projectile with a single hole of the same nominal area as the ten smaller holes through it. 

The single large hole will flow better than the ten small ones in parallel.  This is because the larger hole has a shorter perimeter, than the combined perimeter of the smaller holes.  The longer the perimeter, the more air molecules cling to the surface around that perimeter.  In turn, these molecules cling to a greater percentage of the cross-section of molecules in each smaller "pipe".  Thus the effective percentage area of a small pipe is much smaller than the effective percentage area of a large pipe; for each pipe respectively.

This boundary layer friction loss also occurs on the outside of the projectile .  Such friction is a function of perimeter length.  Perimeter increases with the diameter, while projectile mass (the ability to carry energy)  increases with the square of the diameter.    So, a .30 diameter projectile will have a better mass to perimeter friction ratio, than a .22 caliber projectile of the same length; despite them both having the same SD.

The point of the above, is that very small, long projectiles with a small vent channel won't work as well as a larger diameter projectile of similar (but reasonable) length. 

Now, rather than get hung up on if this is a SD effect, or a form factor effect, or an edge effect; I predict that larger diameter through flow projectiles will have a higher BC than smaller ones; even at the same calculated sectional density; even with the same shape.

[subscriber]

The main advantage of a hollow cylinder of similar SD to a sub-caliber sabot fired projectile is the elimination of the additional sabot to projectile eccentricity.

Now, it would seem prudent to make the sub-caliber projectile very aerodynamic to preserve the very high initial velocity, as they usually are made lighter than the full caliber projectile.

If the sub-caliber projectile weighed the same as a wing ring of the same length, the sub caliber projectile would required a much faster rifling twist to stabilize it.  Here the "fat" light for caliber wing ring has a clear advantage.

That takes us back to side area and wind drift...  If the only thing that counts is "lag time" then the wing ring should be a winner.

As for terminal performance; if a long thin walled soft lead tube hit significant resistance, it may mushroom uniformly outwards due to centripetal force.  Or it may buckle like a empty Coke can, when you step on it.  It will most likely at least cut a full caliber hole, proportional to its initial outside diameter, mass and velocity.

[subscriber]

Just to confuse things, consider the following .45" long projectiles:

The .30" OD tubular streamlined projectile below has the same section shape as the .05" OD solid spike projectile.  The tubular .30 projectile has the same outside dimensions as the solid .30 projectile.

With respect to relative aerodynamic performance; one should ask how far the average air molecule will have to travel "up, down or sideways" to pass around (or through) the projectile?  The less the air has to be displaced and the less abruptly, the better.  So, the spike wins; with the ring a very good second. 

Air meeting the middle of the .30 solid's .25" diameter meplat has to travel a long way, nearly perpendicular to the projectile's long axis before it can make it around the sides.  Air also has to change direction abruptly at the front, and then again at the rear, to fill in the low pressure wake of the .30 solid. 

As such; .30 solid should have a lot more drag than the other two projectiles, even though its sectional density is actually a bit higher than the other two  (the solid has lost proportionately less material to form its nose and tail shape).  The Spike should have the least drag, but has the lowest SD of the three. 

The ring would seem to combine good form with good SD.  It should be a practical projectile that is stable at regular twist rates (but, requires a sealing disc to shoot).  It is no wonder the ring looks like a jet turbine engine cowling

The spike is completely unpractical.  Too little area for air pressure to act on inside the barrel, without using a sabot.  It would also require a ridiculously fast rifling twist to stabilize...
 

[rsterne]

So, SD has gone up; not because weight went up, but because cross sectional area exposed to drag in flight went down.

I would argue that the SD has increased because the length has increased....

It is interesting that you bring up the surface area in respect to the multiple holes, compared to a single hole of the same area.... The total drag of the wing ring (or any object) is a sum of several types of drag.... In ballistics calculations, such as those done in the McDrag program, they are broken down into nose drag, base drag, boattail drag, driving band drag, and skin drag.... Of these, the base drag and the skin drag are the greatest in Subsonic flow, and in fact for boattail bullets below Mach 0.6, the skin drag dominates.... In simpler terms, for most aerodynamics, we use form drag, surface drag, and parasite drag, plus induced drag if lift is being created.... It there is compressibility occurring in the flow (shock waves), then the form drag includes that component.... Any object that is being "streamlined" to reduce the form drag by increasing the length/diameter ratio will have an increase in surface drag, because there is more area subject to skin friction.... This is, most obviously, the case for a wing ring, because for the same length, it will have MUCH more surface area along which the boundary layer of air will create friction.... You are trading a reduction in base drag for an increase in skin drag.... I would argue that a single, slim projectile can have an equal or better form drag than the wing ring, although it would have to be sabot launched to achieve the same velocity for the same weight and SD....

Like with any conventional projectile, increasing the "slimness" ratio to reduce form drag increases the surface area and increases the surface drag.... This creates an "optimum" length/diameter ratio, beyond which total drag increases.... For projectiles like bullets, I would suggest that optimum is around 4:1 or 5:1*, otherwise we would see longer bullets commonly used in long range shooting.... As an example, we don't see .25 caliber bullets that are 1.5" long.... This is despite the fact that as the projectile gets longer, the SD increases.... If they had less total drag, or even a higher BC, we would use faster twist barrels to stabilize them, don't you think.... along with long barrels and slow burning powders to launch them?.... Of course the wing ring has no such stability problem, because its overall length/diameter is low, and it also has a high moment of inertia due to the concentration of mass at the outside edge.... That does greatly increase the stability, and actually would lower the required twist rate, compared to the same length solid projectile....

Your argument about twist rate is valid, but only if the required twist rate for the sub-caliber sabot launched projectile is unobtainable.... Using your example of a .30 cal with a 0.20" hole (cross sectional area = 0.0393 sq.in), and a length of 0.45", while the profile shape of the ring may be the same as that of a 0.05" solid spike, that is not really a valid comparison, because they have totally different weights and SDs.... A sub-caliber bullet with the same SD would be 0.224 caliber, and 0.45" long.... At a length/diameter ratio of only 2, there would be no difficulty in stabilizing that.... If for simplicity we reduce the projectiles to a cylinder and a straight walled tube, both 0.45" long... the surface area of the sides of the .224 cylinder is 0.317 sq.in.... while that of the tube is 0.707 sq.in (over twice as great).... I have left off the area of the ends, because that creates mostly nose drag and base drag.... and is in any case the same, since the cross sectional areas are identical....

I realize I am comparing the wing ring to a sub-caliber, sabot launched projectile, but since the wing ring does need a sabot of some kind to take advantage of the decreased SD during acceleration, so that it can have a higher SD during flight, I think that a fair comparison.... Using the numbers above, we are comparing a .30 cal wing ring to a .22 cal boattail of the same weight, length and SD.... It would be interesting to see how the total drag of the two compares at various velocities.... as that is really the bottom line, IMO....

Once again, I am not trying to discourage experimentation and development in any way.... Nor am I (hopefully) just being argumentative.... I am attempting to point out alternate ways of looking at the problem, so that we don't ignore certain basics along the way....

Bob

* As a footnote, I spent 30 years of my life designing and manufacturing R/C Racing Yachts, which use a fin & bulb keel.... Packaging the weight of the lead ballast in the lowest drag shape was of paramount importance.... I did a great deal of studying of length/diameter ratios, and the streamlined shape of "bodies of revolution" (of which bullets are one type), and determined that a length of 6-7 times the diameter was the optimum.... Shorter, fatter shapes (eg. 3:1 or 4:1) had greater form drag, while longer, slimmer shapes (eg. 8:1 or 10:1) had more wetted surface drag.... The total drag was minimized when the thickness was about 15% of the chord.... Interestingly, if you look at the nose and tail of nuclear submarines, they have almost exactly the same shape, joined by a tube as the most efficient way of packaging the contents within a structurally strong vessel.... The NACA Laminar Flow airfoils of the 6-series were the best shapes, with the 63-015 having the least sensitivity to pitching, through the 66-015 which had the lowest drag in smooth conditions.... I settled on a body of rotation based on the 64-015 as the best compromise.... Bullets generally have a truncated base, but just looking at the shapes of long range bullets and artillery shells indicates to me that a similar drag minimum occurs, and at a slightly shorter length/diameter ratio.... Bullets that are more than 5 calibers long are rare indeed....

[subscriber]

As usual, Bob, you make a lot of sense.

I think that optimizing one factor until it compromises others to the point of a significant total loss, is probably taking thinks too far. 

I wonder if the wing ring's extra skin drag can be reduced by micro dimples, small driving band "spoilers", or texture; as is the case with shark skin?  I realize that such texture will most likely increase the Magnus effect.

Now, getting back to oldpro's opening statement; what if a wing ring somehow did not produce a supersonic crack until it was driven well above 1100 FPS?  After all, if any region of air flow is forced to travel faster than the speed of sound, that region produces a snapping sound, as heard from a stationary position.

Perhaps the supersonic flow occurs only on the inside of the wing ring, and that makes the sound very directional.  Or, due to the reduced air compression, suppresses it entirely.   My point is that the wing ring may have other perceived advantages not usually on the list; beyond accuracy, retained energy, flatness of trajectory, wind drift, cost and availability.


Speaking of long bullets that do not look particularly "streamlined"; the very long bearing surface of the 6.5×52mm Carcano always struck me as odd:  (Left to right) 8mm Mauser (also called 7.92mm Mauser), 6.5mm Carcano, and 7.35mm Carcano




Fired 6.5×52mm Carcano:

[rsterne]

I'm glad you are taking my arguments in the light they are offered.... I am enjoying debating stuff like this with you.... we seem to have the ability to challenge each other's thought process without it becoming a $%&#ing contest.... 

Textured surfaces are generally there to trip the boundary layer from laminar to turbulent, which reduces the size of the wake zone by making the flow stay attached and "wrap around" into the base area more.... If combined with backspin (like a dimpled golfball) they can also create lift, not something you really want (if causes spin drift) in a bullet.... Besides, I think the grooves from the rifling on a spinning bullet pretty much guarantee turbulent flow on the outside.... Inside the tubular cavity you may or may not want to trip the flow to turbulent, I think it might increase the drag (it does inside a pipe)....

I think the shape of the 6.5 Carcano bullet is merely to get the highest possible SD (ie weight) within an overall length limitation.... and a cylinder with a round nose is the best way to do that and not have the extreme drag of a full wadcutter nose....

The only way to find out the advantages (and disadvantages) of the wing ring is to test it.... I have perhaps been a bit unfair in comparing it to a sub-caliber saboted bullet, but I was trying to make a point about the relationship between SD and length, and the ULTIMATE total drag of a projectile of a given weight and length.... The sabot/disc required to accelerate a wing ring is much simpler than a sabot for a sub-caliber projectile (after all, really just a flanged plug in the back).... and if a relatively loose fit should detach upon exit from the muzzle as soon as the pressure on the front exceeds that on the back.... As you said, it might wreak havoc on baffles inside a suppressor, but in Canada, where those are illegal that is not a concern.... I hope that you and/or Travis develop and test it thoroughly, although I would not worry about Supersonic performance because of the large drag increase (and corresponding increase in wind drift) in the Transonic region.... Good Luck !!!

Bob

[subscriber]

we seem to have the ability to challenge each other's thought process without it becoming a $%&#ing contest.... 

I thought that was the point.    Even if someone says something "wrong", or suggests something silly; that may trigger an objective observer to notice that, "if you turn this upside down and cut that bit off, you may have something of value".

Inside the tubular cavity you may or may not want to trip the flow to turbulent, I think it might increase the drag (it does inside a pipe)....

I think it is a matter of scaling the "roughness" of the texture appropriately to the type of fluid and its expected velocity.  Gross turbulence reduces effective flow area because a significant amount of the fluid volume is "flowing backwards"; or at least sideways, reducing average forwards velocity.

Small scale eddies near the surface of the "tube" act like a field of little "ball bearings" (in my mind's eye, anyway); uncoupling and thinning out the stagnant boundary layer, to useful effect.

Water is incompressible, and has much higher density and viscosity than air.  I think air "needs" and can stand much rougher surfaces to flow over.  Strong evidence for my "ball bearing" eddy theory, is that expert tuners "porting and polishing" inlet manifolds and cylinder heads have found by experience that a mirror finish reduces flow (and therefore performance), compared to a slightly textured surface.

Exhaust manifolds may be mirror polished to reduce carbon adhesion because they operate at much higher pressure than inlet manifolds.  The latter spend a lot of time flowing at partial vacuum; and hardly ever exceed one ATM pressure, except with turbo chargers.

[rsterne]

If you really want to bother (I don't) there are formulas for the critical Reynold's Number which will give you a maximum chord (distance along the bullet from the leading edge in this case) where the flow will trip from laminar to turbulent regardless of surface finish.... The distance will decrease if you ask the flow to suddenly change direction (through roughness or excess curvature), and can be extended slightly if the pressure gradient is "goldilocks right", like in the 6x-xxx series NACA airfoils (the second digit is where the laminar flow should extend to, 30-60% of chord) under perfect conditions.... There are also equations to give the thickness of the boundary layer (which decreases as you travel aft).... and any roughness greater than that thickness will trip the flow to turbulent....

On the outside, I think the transition will occur on a spinning projectile at the first hint of a mark caused by the rifling.... On the inside, you're on your own.... 

and yes, in a previous lifetime I also ported and polished many race engines.... 

Bob

[MJP]

I hope oldpro does not think I am trying to steal his idea; or claim credit for it.  However, it should be obvious by now that I am perfectly capable of generating "unusual" ideas all by myself. 

My impression when looking at patents is that almost anything I can think up has already been thought up.  While this can be frustrating, it is also a validation of sorts.  I happen to have more than a dozen US patents, with another handful in the pipe.  None of them relate to lead slinging, so I am not competing with any of you here.

The through-flow "nozzle" design below is closer to one of my original ideas; hatched about April last year.    The nozzle shaped internal cavity could be swaged; but good luck casting it with a conventional mold.

I would love to see someone make the wing ring projectile and I mean anybody. I love the knowledge being shared and truly believe with my limited testing something good will come of it.

Easy as pie, there is no problem making those bullets. I'll just chuck some of the 20mm bullets in a lathe and give it a go as soon as I'll get to cast some.

Marko

[Bill G]

Bob do you think this could be cast?

Pretty difficult i'd say.  Buuut...... swaged is a different story.  internal punch/ejector has leading edge profile up to the apex of the air foil and external punch carries the aft profile. Lots of care would have to be emphasized on concentricity  and and squareness of the ends of the form punches. Otherwise, you'd have ugly flashing on the inside and it would negate the function. Then the question of sabot or self shedding plug.

Bill G

[Bill G]

  I suppose I should have read the thread to the bottom

[Bill G]

https://patents.google.com/patent/US6647890  Been done.  The US military experimented with an "air foil grenade" (M234 Riot control grenade) one version had CS powder the other just blunt force. more for crowd management than war applications. for obvious reasons, no place for a warhead.  but the range was extended considerably of the typical 40mm M203 or antique M79. 

I would imagine that the length needs to be kept to no more than 1.5X the diameter. Bob points out the rifling marks and that is a good call.  This would be more of a smooth bore application i'd guess.  Shedding the plug could be initiated with a choke on the barrel as long as the intended projectile didn't fit the plug/sabot too tightly. spitballing. 

The lack of sonic boom can be explained.  Check out Busemann's Biplane.

[rsterne]

Bill, thanks for the tip on the Busemann's Biplane, I checked it out, very interesting concept.... It works by reflecting the shock waves internally, with the optimum noise cancellation occurring when the positive pressure shock wave formed by the leading edge hits the point of the internal restriction, which is normally the source of the negative pressure shock wave, like this....



Since the angle of the shock wave to the direction of travel becomes more acute as the speed increases, there is an optimum length for a given diameter, and I haven't seen the data, but logic would tell me that the faster it goes, the longer it needs to be for a given diameter.... The Mach Angles for some velocities are:

Mach 1.0 = 90 deg.
Mach 1.1 = 65 deg.
Mach 1.3 = 50 deg.
Mach 2.0 = 30 deg.

These are approximate, and temperature, air density, etc.etc cause some variation in the angle.... Note the sharp leading edge which is part of the Busemann design.... Roughly speaking, a wing ring about 1 caliber long would have good noise cancellation at maybe Mach 1.2, depending on the ID and OD.... However, it would fall back Subsonic quite quickly (at which point there is no sonic boom/crack.... so this is likely the effect Travis noted with his prototype.... I would think that even non-optimum configurations would have reduced shock waves intensity....

Bob

[Bill G]

wonder what length, diameter and internal profile would retain velocity the longest. The Mass being so low would likely have a lot to do with that.

[rsterne]

If you read my posts above about SD, the longer the bullet the higher the SD.... Since BC = SD/FF, and longer bullets also tend to have a better FF, that is even more reason to have a long bullet to retain velocity and energy.... I can't comment on the internal profile because I haven't a clue, unless you are looking for Supersonic, in which case you want a sharp leading edge and two cones, like the Busemann design.... Some annular projectiles have an airfoil cross section, with the idea being that when launched at an  upwards angle, the spin keeps it on that angle and as gravity pulls it down it acquires an angle of attack, and the airfoil generates lift.... This extends the range compared to a conventional projectile which has little or no lift.... However, the effect for our use would be tiny, because you need an angle of attack for the idea to work.... and at 100 yards we are working with only about 1 degree relative to the air for the last few yards of flight.... You don't get much lift at only 1 degree.... I think the "best" section for subsonic use is the one that produces the least drag at low angles of attack (less than 1 or 2 degrees.... and forget about trying to get lift, or take advantage of the Busemann idea, because of the short time spent Supersonic....

Bob

[Finn]

.22, V =340 m/s