Bob remember my hollow bullet AKA wing ring!!

[rsterne]

Nice simulations.... I'm curious why you choose such a high velocity, though, just under Mach 1.... Looking at the first and last drawings as a set shows the relationship between velocity and pressure inside the venturi very well.... higher velocity means decreased pressure and vice versa.... The velocity (drawing #1) at the constriction is choked, so right at Mach 1 (yellow = Mach 0.95-1.14).... The pressure drawing (#4) shows the effect of choking the flow at the constriction.... If you compare the pressure at the entrance (green, 166-198 KPa) ) to the exit (medium blue, 70-101 KPa) you can see the 47% or more reduction of pressure that must occur across the choke point.... ie exit pressure is about half entrance pressure....

I would like to see how the flow compares at about Mach 0.80 (275 m/s which is 900 fps).... I would still expect the flow to choke at the venturi, but would love to see what your program says....

Bob

[Finn]

Why 340 m/s? I wanted to compare bullet drag and see what happens when bullet fired over mach1 drops just below mach1.

.22 cal. V=275 m/s t=20 C, everything else is the same
Cut plots are easier to look at.

[Finn]

For comparison JSB Exact Jumbo Express .22  V=275 m/s. Drag force 0.746N, flow stays under mach 1.

[rsterne]

Thanks for the comparison.... If I am reading it correctly, the flow still chokes inside the venturi?....

Is the number at the top of the line graph the drag force in Newtons?.... ie 0.747 N for the JSB and 0.944 N for the wing ring?.... and for the wing ring at Mach 0.99 it is 2.36 N ?.... Can't that force be applied to the mass of the object to ascertain the deceleration at that instant?.... What are the masses of the two objects, assuming pure lead of SG = 11.3 g/cc ?.... (Oops, I see the pellet, it has a mass of 0.93 grams)....

I have dimensioned drawings of my BBTs in .22 cal from 30 gr. to 75 gr. if you would like to run any of them for comparisons.... PM me your email and I will send them to you if you like....

Bob

[rsterne]

Please correct me if I have the wrong methodology or units.... but here is what I get for the 14.3 gr. JSB Express pellet at 275 m/s....

Mass = 14.3 / 15.43 = 0.927 grams = 0.000927 kg
Force = 0.747 N
Deceleration = F / m = 0.747 / 0.000927 = 806 m/s²
Velocity loss after 0.01 sec = 8.06 m/s, which is about 26.4 fps.... In that time the pellet would have travelled just under 9 ft.... That appears to be out by roughly a factor of 2, compared to ChairGun with that pellet, it says about 5-6 yards to drop that much velocity, not 3 yards (15.4 fps in 3 yards).... but comparisons may still be possible....

The SD of this pellet is 14.3 / 7000 / 0.22² = 0.0422.... I realize that is in Imperial units, not Metric, but comparisons will remain valid.... The SD for other .22 cal JSB pellets is....
15.9 gr.... 0.0469
18.1 gr.... 0.0534
25.4 gr.... 0.0750
34.0 gr.... 0.100

Bob

[Finn]

Yes the number at the top is drag force in newtons, I used the ring bullet design from Reply #18 from first page where the mass is stated 0,00282 pounds or 1.279 grams. After a couple of beers at 0:20 AM I refrain myself from checking any mathwork especially when there is imperial units mixed in, at least the online calculator agrees but the decelerating force is not really constant so there is a small error to begin with.
 I will make proper simulation setup with rotating bullets and double check every setting if someone is interested in more accurate results, setting the program for speed rather than accuracy sometimes changes a lot.

I measured the jsb pellet just roughly with digital caliper, might not be accurate enough for precise predictions. I calculated the Cd from drag and it was 0.677 and Reynolds number of 92900, not absolutely sure about the value for L in the Re equation for this case.

[subscriber]

Interesting Albert,

So the conclusion is that a 20 grain diabolo .22 pellet has less drag than a 20 grain cylinder with a hole though it?

[Finn]

In this case yes, but not all hollow bullets are equal of course and the weight of the projectile is irrelevant when comparing drag alone.

[rsterne]

OK, so 19.74 gr., which is 1.279 grams.... Using the drag of 0.944 N at 275 m/s we get....

Deceleration = 0.944 / (1.279 / 1000) = 738 m/s².... so it is slowing less rapidly than a 14.3 gr. pellet, which might be expected because the SD (even based on the whole .22 cal diameter) is 38% higher at 0.0583.... Velocity loss at 0.01 sec. would be 7.38 m/s which is 24.2 fps....

It might be educational to compare it to the 18.1 gr. JSB Exact Heavy, which is closer in weight.... According to ChairGun, the BC of the 18.1 gr. is 0.036, compared to 0.028 for the 14.3 gr.... That is 29% higher, almost exactly the same as their difference in weight (SD) which is 27%.... Since the shapes are very close, and the FFs (BC/SD) are within a couple of percent.... if we assume the drag of the 18.1 gr. JSB is the same at 275 m/s as the 14.3 gr..... we can calculate the velocity loss by using the pellet drag of 0.747 N at 275 m/s and the weight of 18.1 gr. = 1.173 grams....

Deceleration = 0.747 / (1.173 / 1000) = 637 m/s².... for a velocity loss in 0.01 sec. of 6.37 m/s or 20.9 fps.... Therefore, based on the flow/drag calculations, the theoretical gain in SD from the hollow core isn't there.... Mind you, you are comparing a round-nosed pellet, which are notorious for ice-pick like penetration.... to the wing ring which should hit more like a wadcutter....

It would appear that the only way to be sure is going to be testing a wing ring to determine its BC....

Bob

[Finn]

Well lets do it then. We should maybe determine by simulation what design is the best to start with before machining and casting a set of bullets. My largest caliber airguns are currently only .22 so I would have to stick with that. First few examples may be best to turn with lathe and then make a mold if they show promise. My pcp rifles have magazine length restrictions of 10,5 mm max, not sure if that is a problem, break barrels can be used for long bullets but the speed will be lower.

[oldpro]

 Please do your drag simulation with the actual wing ring design instead of a hollow bullet design I think things will change dramatically. We really got off on a tangent from the original wing ring idea.

[subscriber]

  We really got off on a tangent from the original wing ring idea.

Where is that?  This video, or something else?

[Finn]

Not sure what the "original" design is but heres .22 10 mm long airfoil bullet at 275 m/s, weight 1,02grams and reasonably low drag of 0.257N.

[rsterne]

I don't remember seeing a drawing of the original.... perhaps Travis can point us to one?....

Bob

[Bill G]

Very interesting Albert.  What is this simulator that you are using? 

[lloyd-ss]

VERY interesting discussion. I read through most of it and got a bit bogged down with the theoretical discussions, although I realize that they are vital in avoiding false starts in application, but the concept is very intriguing.

I would like to give this a try, too, but have a few questions for those who can help me, shall we say, bypass the theory. I sometimes enjoy playing the lab tech who has to construct the models and run the tests to tell the engineer that his ideas either worked, or failed miserably, or somewhere in between.

1. If this concept were to be applied in such a manner as to be practical in an airgun sense, hunting or otherwise, what might be the advantages and/or disadvantages over a conventional cast bullet?

2. Instead of using a solid  drive disk or a sabot, what about using a solid rod (possibly carbon fiber or Ti tube) fixed into place in the center of the barrel bore? The airflow reduction might not be significant and it seems that the launch might be efficient. Let's not worry about the "how to do it", just yet.

3. Assuming that the projectile needs to be sealed on the O.D. and I.D., what might be some optimal configurations with  internal and external drive bands and whatever tapers that seem to make sense.  Don't worry about bullet manufacture just yet, either. This would just be a proof of concept exercise.

Thank you all,
Lloyd

[rsterne]

I think the primary advantage of using a sabot (besides that you can use an existing airgun) is that the "launch" SD is lower than the "flight" SD, enabling lower external drag (better ballistics) than what could be obtained by a bullet of similar energy.... or rather putting more energy into a bullet that has a given external drag.... If you use an annular barrel, by placing a rod down the center, you no longer have the advantage of that lower internal SD, because your base area (which governs the force) is the same as the frontal area of the bullet (which governs the drag).... As an example, using a .25 cal bullet with a .15" hole through it that weighs 25 grains, with and without sabot we have the following....

Base (annular) area = 0.0314 sq.in.... force at 3000 psi = 94.2 lbs....

Sabot area = 0.0491 sq.in.... force at 3000 psi = 147.3 lbs.... force at 2000 psi = 98.2 lbs....

Therefore, neglecting any additional friction from the "rod" down the center of the bore, you can get more velocity at 2000 psi using a sabot than at 3000 psi using an annular barrel.... Once in flight, both projectiles are identical, so would have the same downrange ballistics....

Bob

[lloyd-ss]

I think the primary advantage of using a sabot (besides that you can use an existing airgun) is that the "launch" SD is lower than the "flight" SD, enabling lower external drag (better ballistics) than what could be obtained by a bullet of similar energy.... or rather putting more energy into a bullet that has a given external drag.... If you use an annular barrel, by placing a rod down the center, you no longer have the advantage of that lower internal SD, because your base area (which governs the force) is the same as the frontal area of the bullet (which governs the drag).... As an example, using a .25 cal bullet with a .15" hole through it that weighs 25 grains, with and without sabot we have the following....

Base (annular) area = 0.0314 sq.in.... force at 3000 psi = 94.2 lbs....

Sabot area = 0.0491 sq.in.... force at 3000 psi = 147.3 lbs.... force at 2000 psi = 98.2 lbs....

Therefore, neglecting any additional friction from the "rod" down the center of the bore, you can get more velocity at 2000 psi using a sabot than at 3000 psi using an annular barrel.... Once in flight, both projectiles are identical, so would have the same downrange ballistics....

Bob

But wouldn't the same be true whether shooting a bullet with a sabot, or a ring with a sabot? Both would use a lighter weight projectile compared to a non-sabot projectile of similar barrel bore dia.
I probably missed it, but what is the advantage of the ring over a bullet, other than possible higher velocity from the sabot?

[oldpro]

I think the primary advantage of using a sabot (besides that you can use an existing airgun) is that the "launch" SD is lower than the "flight" SD, enabling lower external drag (better ballistics) than what could be obtained by a bullet of similar energy.... or rather putting more energy into a bullet that has a given external drag.... If you use an annular barrel, by placing a rod down the center, you no longer have the advantage of that lower internal SD, because your base area (which governs the force) is the same as the frontal area of the bullet (which governs the drag).... As an example, using a .25 cal bullet with a .15" hole through it that weighs 25 grains, with and without sabot we have the following....

Base (annular) area = 0.0314 sq.in.... force at 3000 psi = 94.2 lbs....

Sabot area = 0.0491 sq.in.... force at 3000 psi = 147.3 lbs.... force at 2000 psi = 98.2 lbs....

Therefore, neglecting any additional friction from the "rod" down the center of the bore, you can get more velocity at 2000 psi using a sabot than at 3000 psi using an annular barrel.... Once in flight, both projectiles are identical, so would have the same downrange ballistics....

Bob

But wouldn't the same be true whether shooting a bullet with a sabot, or a ring with a sabot? Both would use a lighter weight projectile compared to a non-sabot projectile of similar barrel bore dia.
I probably missed it, but what is the advantage of the ring over a bullet, other than possible higher velocity from the sabot?

No Sonic boom or deflection from going beyond sonic.

[lloyd-ss]

 No Sonic boom or deflection from going beyond sonic.

Got it. Thank you!