Aerodynamic Drag Stabilization (Ballistic Application)

[turbo1889]

Okay, I've been working on designing a custom mold cut for a 410-gauge shotgun slug and need some help with the principle of "Drag Stabilization". Many shotguns are smooth bores and thus shotgun slugs in order to dependably fly straight must have a drag-stabilized design. They can not depend on any rotational spin imparted by rifling for stabilization, which is the normal method of bullet stabilization in flight used by most firearms. So I've been lathe cutting prototypes and testing them for stability in flight, but need to have a few questions straightened out:


1~ For a slug design made entirely out of a single material (cast lead alloy in this case) is it correct that a test model which is cut to the exact same dimensions but made entirely out of a different material (hard-wood in this case) will exhibit similar behavior in flight. Problem I'm having is that when dropped from about ten feet up in random positions into a bucket full of soft putty my lead prototypes give no consistent or interpretable data as to whether they land nose first. Wooden prototypes on the other hand show definite results. I believe that the lower density material model is behaving at low velocity how the higher density material model would behave at higher velocity --- Is that line of thinking correct?

2~ To more thoroughly test my high density (lead) prototypes I am considering constructing an apparatus consisting of a clear plastic pipe of a diameter of about 3-4 inches with a fixture to hold a prototype at its center of mass inside so that the prototype can be rotated via. Finger pressure within the tube and force feedback in the form of touch sensation on the finger can be felt. A high volume gas engine powered water pump (such as those used to pump out ditches, basements, ect., in the construction trades -- one of which I happen to own) would be attached to one end of the pipe and a continuous closed loop of water flow would be achieved via. a return pipe and a water reservoir consisting of a 40 gallon trash can. I'm thinking that the water flow as opposed to airflow will simulate the projectile’s flight through the air at much higher velocity then the water flow in the apparatus. I know that some boat hauls are designed using wind tunnels so I'm thinking the opposite might work as well in order to simulate higher velocities with low velocity experimental apparatus.

3~ All the drag stabilized factory slug designs I have examined (cutting open factory loaded ammunition and retrieved the slug) have clearly shown that a drag stabilized design must be "nose-heavy" and usually hollow base. Surely there is a little more too it then that. What other factors come into play?

 

[FredGarvin]

- Drag is dependent on the geometry of the object. So you should be fine in the use of another material as long as it maintains it's shape and has roughly (pardon the pun) the same surface finish.

- Using a water tunnel is a good idea. You do have to make adjustments for using a different fluid though. Also realize that you'll probably need a way to cool the water if you use a continuous loop. That pump will put a fair amount of work into the water. Holding the temperature constant will keep the fluid properties constant which will give better test results.

- I don't know a thing about shot gun shells other than which way is the front. I'll have to do a little self educating before I tackle that question.

 

[turbo1889]

- Drag is dependent on the geometry of the object. So you should be fine in the use of another material as long as it maintains it's shape and has roughly (pardon the pun) the same surface finish.

- Using a water tunnel is a good idea. You do have to make adjustments for using a different fluid though. Also realize that you'll probably need a way to cool the water if you use a continuous loop. That pump will put a fair amount of work into the water. Holding the temperature constant will keep the fluid properties constant which will give better test results.

- I don't know a thing about shot gun shells other than which way is the front. I'll have to do a little self educating before I tackle that question.

1~ Glad to have that one answered.

2~ Good input. Is my reasoning correct that "to simulate higher velocities with low velocity experimental apparatus" use water instead of air (thicker fluid) ?

3~ For assistence in the self education process in the form of pictures of cut open slug-loads, descriptions and measurements of the internal components, etc. go here: http://mcb-homis.com/slug_410/index.htm

 

[minger]

2. You are correct. You can test dynamically similar conditions if an important non-dimensional parameter known as the Reynolds number is held constant. It is VL/v, where V is the velocity of the flow, L is a characteristic length (diameter is common), and v is the viscosity of the fluid. Since your length will stay common, you will dynamically similar conditions if V/v stays constant. Since the viscosity of much smaller than 1, that must increase to give the same same value (dividing by a much smaller number less than 1 will give a greater result).

 

[jim mcnamara]

I do not know much about shotgun slugs, but the muzzle velocity of most shotgun ammunition is well below Mach I.

Since you seem to want a lethal round, that leaves out bean-bag stabilization.
That leaves fin drag stabilization, flare drag stabilization and what you already mentioned, I guess we can call it the miniball method -- what slugs like that were called long ago.

A fin is just what you imagine. On heavy projectiles the fin deploys when the projectile is outside the muzzle; looks like what you've already probably seen on other ordinance. In your case, I guess a sabot will work to cover the fins.

Flare stabilization works better for higher velcocities, circa Mach I and higher. Since you have to provide a sabot for the front 75% of the projectile(or so), the mass of the projectile is lower, muzzle velocity higher, assuming the same chamber pressure. The area behind the flare is hollow. You may want to check that method as well.

We used to measure the following to get at what you seem to want... We never tried to emulate anything with a slow moving projectile for a lot of reasons - among them erosion and destabilization of the projectile, and other oddities that develop because of firing.

1. muzzle velocity with a chronograph at 2' and 50' to estimate a drag coefficient

2. fire a fixed weapon at a fixed target 100' with varying speeds of crosswinds and measured deflection - which in your case ought to be low due to projectile mass. Except.
I do know that drag stabilization decreases stabilization in high crosswinds, even for heavy projectiles. This is from research - can't release the particulars.

3. we measured dispersion on a fixed target with zero wind at 100' to estimate stabilization.

From (mostly)#1 and projectile mass and dimensions, it is possible to derive an estimated ballistic coefficient. This is the "drag" you are after.

For slow slugs this is less important, but it seems to be what you want - minimal velocity disspation and low dispersion on target. You also want minimal wind drift, but I think the effective range of slugs is pretty short, pretty much like black powder muskets with miniballs.

 

[turbo1889]

Thanks for the clarification and math for question #2, minger. I've got the water tunnel partially built in the shop as of present.


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Now as to, jim mcnamara, you seem to be addressing question #3. For the particular gauge shotgun ( 410 ) I'm working with shot loads have a muzzle velocity of between 1,350 and 1,000 feet per second depending on the exact load, and slugs have a muzzle velocity range 1,800 - 1,200 fps. depending on the specific slug load. The standard (sea level, standard pressure, standard temp., etc. ) value for Mach-I is 1,128 fps. Which puts shot loads in the transonic range. Light weight, fast slugs are supersonic and heavy, slow slugs (like I'm trying to make a mold for) are transonic.

Fins, are out of the question because the mold will be two piece metallic hinged mold cut either by lathe boring or cheery cutting. Thus the design must be radial symmetrical for each cross section. In other words it must be a design made out of stacked cylinder and cone shaped sections. I can make it wasp-waisted, hollow-base, larger diameter base then head or vica versa., but I can't do complex designs like fins. If I can't cut the prototype with a lathe --- it’s a no-go for a mold as well.

I fully intend to do live-fire prototype testing but intend to weed out bad designs that have no potential for working on the range in the shop via. prototype testing so they never make it to the range in the first place. It doesn't snow, rain, and get dark in the shop. Not so at the range. Loading takes time and effort and firing will almost surly destroy the prototype slug upon impact with the target board so live-fire testing means a lot more lathe time with multiple prototypes of a single design.

Flair Stabilization ---- Okay, that's a new one on me. I'll need to do some research on that one. but I think what your talking about is a cone shaped back end to the projectile that is larger diameter then the main body like on a blow gun dart?

 

[jim mcnamara]

No - the butt end is larger - a flare, the front end is inside a sabot. Not a cone, more like a blowgun dart with a hollow end (bad analogy but the best I can do right now, sorry). Your miniballs are halfway to a flare already. Flares are often cast with three longitudinal valleys which act more like fins - see below on fins.

I used to work on large projectile modeling - like I said I don't know much about shotgun slugs. I worked with projectiles that weighed Kg not mg.

With those muzzle velocities your slugs are likely not pure lead, it would probably deform too much unless impulse (J) for some reason is lower or it's already ball ammo.

I don't see your objection to fins. A fin set has the same outer diameter as the projectile, with a core that is like 70% diameter. The fins can be "fat". They look like somebody had a cylinder and with a round gauge and carved away material about 1/4 of the way from the bottom of the projectile leaving three or four fat longitudinal ridges- they are not like bomb or torpedo fins. What you are doing is greatly increasing air resistance on the butt end of the slug when any tumbling starts. Since you are probably using an antimony hardened slug, the fins will not deform with the acceleration (impulse) and gass pressure if you have wadding to reduce heating and blowby. Fins probably would not deform even if your slug was pure lead.


In looking this stuff up - There is also a 1/5 ounce (~86 grain) Foster type rifled slug load available for the .410 shotgun. Muzzle energy is about 1020 J and ~1750-1850 fps MV.

Why not consider a rifled slug? These guys think its good. I would not know.

I guess the part I don't get: references say the effective range of slugs is 50 yards max and maybe suitable for jack rabbits or some such small animal under 20lbs. You cannot use slugs for clay pigeons, although H&R makes a model fitted out with a telescopic sight (H&R ultra slug gun). Does this make it a target weapon?

Why are you going thru this drill, there doesn't seem to be a gleaming light at the end of the tunnel? What the heck do you do with an 86 grain slug that drops off the edge of the Earth at 50 yards?

 

[turbo1889]

No - the butt end is larger - a flare, the front end is inside a sabot. Not a cone, more like a blowgun dart with a hollow end (bad analogy but the best I can do right now, sorry). Your miniballs are halfway to a flare already. Flares are often cast with three longitudinal valleys which act more like fins - see below on fins

. . . . .

I don't see your objection to fins. A fin set has the same outer diameter as the projectile, with a core that is like 70% diameter. The fins can be "fat". They look like somebody had a cylinder and with a round gauge and carved away material about 1/4 of the way from the bottom of the projectile leaving three or four fat longitudinal ridges- they are not like bomb or torpedo fins. What you are doing is greatly increasing air resistance on the butt end of the slug when any tumbling starts. Since you are probably using an antimony hardened slug, the fins will not deform with the acceleration (impulse) and gass pressure if you have wadding to reduce heating and blowby. Fins probably would not deform even if your slug was pure lead.

Thanks for the clarification on the "flair stablization" and also on "fins".

. . . . With those muzzle velocities your slugs are likely not pure lead, it would probably deform too much unless impulse (J) for some reason is lower or it's already ball ammo. . . .

Basically I get a mold cut in a aerodynamically feisable design and then can adjust the lead casting alloy to whatever strength is necessary for proper structural integrity of the slug --- the weight will very slightly corosponding to changes in the alloy but not considerably enough to cause problems. I have casting experience with lead alloys including but not limited to, pure (99.97%) lead, 40:1 (lead:tin), 30:1, 20:1, "hardball" (2%-tin 6%-antimony 92%-lead ), and finally "type-metal" (4%-tin 12%-antimony 84%-lead). That gives me a range of alloys that at the bottom end are so soft they are almost guarenteed to squash into a mis-shapen hunk of lead under acceleration load up to so hard that it probably won't even dent when it hits the target.

Actual live fire testing will most likely be done with 20:1 alloy prototypes lathe turned from cast lead cylinders. The mold for making those cylinders is easy enough just a blank mold bored almost all the way through at a diameter of 0.410". The 20:1 alloy is hard enough for successful use in other cartridges with similar balistics and caliber size to a .410-slug and at the same time is fairly soft so structural problems with the design shouldn't go un-noticed.

Oh, yah, wadding as you correctly assumed is an integral part of any shotgun load so gas cutting is usually a minor issue to worry about

. . . . I guess the part I don't get: references say the effective range of slugs is 50 yards max and maybe suitable for jack rabbits or some such small animal under 20lbs. You cannot use slugs for clay pigeons, although H&R makes a model fitted out with a telescopic sight (H&R ultra slug gun). Does this make it a target weapon?

Why are you going thru this drill, there doesn't seem to be a gleaming light at the end of the tunnel? What the heck do you do with an 86 grain slug that drops off the edge of the Earth at 50 yards?

Yes, you are correct the ballistic performance of a standard factory .410-slug load is pretty un-impressive. However, as you might have noticed there is a major difference between the weight of usual .410 shot loads (1/2oz. through 3/4oz.) and factory slug loads (1/5oz. through 1/4oz.). This is where the problem with factory slugs lies --- the .410 does a very efficient job of pushing a (comparatively) heavy load to a moderate velocity but doesn't do very well when pushing a smaller load to a higher velocity. Factory 410-slugs are like trying to race a farm-truck in a NASCAR race. I'm trying to make my slug mold so that even when using the lightest alloy the slug will still weigh at least 1/2oz. Thus, letting the farm-truck continue to do what it does best --- launching a much heavier load at a reduced but much more efficient velocity. The theory has proven to be sound via launching heavy 11/16oz. simple cylinder slugs out of a specially built rifled .410-slug gun. The load is much more effective and retains energy much further down range then a factory slug. In fact taking actual "Chrony" measurements of it's velocity at 70-yards down range (Yes, the "Chrony" was actually set up 70 yards down range and the slug fired from a solid mounted gun so that it would pass through the screens) and then by consulting the "maximum game animal weight calculation formula" from the Lyman 47th edition handloading manual such a "slower but much heavier 410 slug" is able to humanely and ethically take an animal with a maximum weight of up to 130 pounds at that range.

The problem lies with producing a stable projectile in that weight range that can be sucessfuly fired from a smooth bore. I have the necessary equipment and I believe the intuition and experience to attempt to produce such a stable projectile via. the very old method of trial and error. I do, however, need some advice from others with a lot more "book learning" then myself in order to have some sign posts along the way to point in the general right direction.

So far I have had some very good lab (my garage) results from a particular unorthadox design very similar in appearance to a "tadpole" (as in baby frog) with a ring shaped protrusion on the back of the tail.

 

[jim mcnamara]

FWIW - you do know that the burn rate of propellant, like black powder FF vs F,
is one thing you really should consider for a larger slug if you want to improve exterior ballsitic performance.

Assuming a constant chamber pressure, you can diddle the load mixture, add retardants or encapsulate the propellant into larger "beads", then use a slightly larger slug than you are proposing, and get better external ballistics. Do you know how to measure and analyze a "copper pressure" for example? So you don't trash yourself and your barrels.

From what I know about larger projectile history, that was all it was about in the era of 16" guns. More bang for a buck. Except those projectiles leave the atmosphere for longer range targets. 45 degree trajectory for a target 20+ miles away, goes 'way up there - 20+ miles up.

 

[jim mcnamara]

As an afterthought -

You can improve downrange ballistics signifcantly by crafting an ogive onto your projectile. Assuming the flare, fin or whatever gives you stability against tumbling.
Effective ogives usually start in the 1.5 caliber range and go up. For your muzzle velocities, a max of a 2 caliber ogive ought to be reasonable.

The only real problem with this is the size of the chamber vs. the length of the load shell.
You may want to lookat some old papers on the subject, if you are a math person. DTIC has a bunch of WWII era papers on exterior ballistics.

http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0310002