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A simple way to improve use of air volume without a longer barrel

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#1 Darthrambo

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Posted 22 December 2011 - 05:53 PM

This is a simple but seriously tedious mod for the vulcan belt, but the principal can be used for tons of other blasters.

It's just a little e-tape around the inside of the back of the dart chamber. While I know there are much more elegant ways of doing this I just wanted to get it done without buying any materials to see the result.

Posted Image
Posted Image
(sorry for the poor quality, it was impossible to get a good shot of the tape ring)

I was thinking of how make use of plunger tube volume (or air volume in general) without the use of a longer barrel.

What I came up with is the concept that with a stronger hold on the chamber has on the dart, the more pressure would build up before the dart is fired which would result in better ranges. This concept is the same as the system used in ball blasters like the reactor.. With ball guns, the speed at which the plunger tube is compressed doesn't really matter much because the ball is only fired once enough air pressure it built up to compress the ball a little and push it past the choke point at the tip of the barrel.

This is the same principal, but for darts. More force acting to hold the dart in place allows more pressure to build up which results in the dart being fired only when greater air pressure is reached. The added friction is all at the back of the dart so to reduce the amount of friction it experiences when it actually starts moving.

No concrete range tests done but if I had to guess it's getting about and added 5-10ft which is pretty amazing for such a simple mod. Not sure how accurate those numbers are because really hard to tell with all the variables with individual darts, and chambers but none the less there is a definite improvement in range. I compared the taped chamber shots to the not taped chamber shots. (The vulcan I was using was stock but the belt had pegs drilled out.)

So the same thing can be done with other blasters. All you need to do is create a better hold for the dart chamber. So for instance, if you had a brass breach, All you would need to do is put a crimped ring at the back end of the breech so when the dart tooth pushed the dart into the chamber it would get shoved in snugly the crimped ring.

This mod however will not work nearly as well, if at all for blasters that use turrets like mavericks, with poor turret to plunger seals.

If I'm not mistaken this mod does the kind of the same thing as a spring upgrade in that it increases the pressure at which the dart is fired.

Edited by Darthrambo, 22 December 2011 - 05:59 PM.

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#2 Buffdaddy

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Posted 22 December 2011 - 06:07 PM

This mainly amounts to an extension of the "telescoping brass barrel" concept (first few inches tight, then looser) used with stefans, although I like your idea of doing this for stock darts. Obviously, as you mentioned, there are variables, most importantly the sealing of the chain to the plunger tube, that would mess with results.

In any case, an interesting take, and one that doesn't require much beyond tape and a large amount of patience.
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#3 Darthrambo

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Posted 22 December 2011 - 06:38 PM

Oh the plunger to belt seal is really good with vulcans, that and the fact that it was easy to access the part of the tube where I wanted to put the tape is why I chose it. You might already know this but when the vulcan fires the tube actually comes forward and presses up against the chain with a o-ring on the front of the tube before the spring is released making a really good seal.

Yeah its the same reason why people use a tight fit on breeches but this concept is slightly different since its only the back 1/2in that gets the tight fit as oppose to the entire length of the dart which reduces friction after the dart starts moving.
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#4 Langley

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Posted 22 December 2011 - 06:58 PM

Yeah its the same reason why people use a tight fit on breeches but this concept is slightly different since its only the back 1/2in that gets the tight fit as oppose to the entire length of the dart which reduces friction after the dart starts moving.

I think you misunderstood. The idea of making the first dart-length of a barrel tighter has been around for a while, in the form of 'telescoping brass barrels' and 'tightening rings'. If you search on those terms, you'll find what I'm talking about. This is probably the first time it's been done with a Vulcan though, I never would have thought the Vulcan makes a good enough seal for this. Cool.

Edit:whoops. Read your post as "entire length of the barrel" instead of "entire length of the dart". Still, it's pretty much the same idea, and you should still search on 'telescoping barrel' because I think a few people have done a lot of research and testing with that method.
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#5 Darthrambo

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Posted 23 December 2011 - 04:29 AM

I think you might be missing some of what I'm trying to say.

Specifically that the reason why this kind of tighter fit is good is because in a way it negates the need for a barrel. This is why I wanted to try it out on a vulcan, which can't have a barrel.

Let my try to explain myself.

Longer barrels give the pressure more time to accelerate the dart, and the perfect barrel would be the length at which the pressure has accelerated the dart to its maxim speed.

To contrast let me explain the perfect "tight ring"

Tighter rings give pressure more time to build up before the dart starts moving. The perfectly "tight ring" would hold the dart in place until the instant full compression of the tube and maximum pressure was achieved. The instant that the dart left the ring, it would instantly be accelerated to the maximum speed the tubes volume was capable of producing.


The concept I am referring to is impulse.

Impulse = Force x Time

In this case pressure is the force.

The barrel increases the time the force acts on the dart I= f x T
The ring increases the force (pressure) that the dart is pushed by I=F x t

Theoretically either way you could get the maximum output for your air volume.



Also the only tightening rights I'm familiar with are the ones that act as dart teeth on things like angel breeches. The problem with this is that you have to force the entire dart through the rings and the choke point is after the breech meaning you have the possibility of losing air pressure through the breech.
What I was talking about in the original post would be the same thing but in the chamber part of the breech instead of in the barrel. As said before this should negate the need for a long barrel and you could just use the existing dart tooth on CS blasters to push the darts into the ring.
If this has been done before I'd like it if someone could point me in the direction of the thread. I've seen tightening rings after the breech, I've seen snug barrels, what I haven't seen is anyone do a brass breech with a stock barrel using a tighter ring to allow more pressure to build before the dart started moving.

Edited by Darthrambo, 23 December 2011 - 04:44 AM.

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#6 cheyner

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Posted 23 December 2011 - 10:05 AM

I think you are missing what everybody is telling you, on multiple sites.

So with your super awesome magical tape method, the rest of the "barrel" now has absolutely no effect on the dart? Shit, I guess everybody has been wrong all along, we should be using 1/2" long, super tight barrels on everything.

Yes, tightening rings do work exactly like this, so does sticking say a 1/2" long stub of 17/32 brass into Petg.

I have the feeling you have no idea how an Angel breach works, so you probably should not use it as an example. The tightening rings are there to build up more pressure, shockingly like your super innovative tape. What use would they be as a dart tooth? Considering a dart tooth would stop the dart from moving, notice how it moves out of the way on stock CS blasters after you load a dart? Pretty sure you can't take those rings out after you load a dart. If anything would be a dart tooth in this mod, it would be the 1/2" and 17/32" brass that pushes the dart into the rings.
But in the end, considering tightening rings are optional pretty much destroys any argument you have for them being a dart tooth.

Also, technically a Vulcan does have a barrel, 25 of them stock to be exact. Following your train of thought, pretty much every Nerf blaster that doesn't use streamlines doesn't have a barrel.

But yeah, Merry Christmas.
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#7 Nerfomania

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Posted 23 December 2011 - 11:40 AM

Thanks cheyner, Reading his post just about made my head want to explode.

This is interesting but is the same concept we have all been saying.
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#8 Langley

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Posted 23 December 2011 - 11:59 AM

Stuff


Yes, we are on the same page about the effect you are going for. Here is an example of a very early discussion of the effect. In practice, people have typically just used a dart-length of tighter barrel material, and not the 3-stage design outlined in that article. More recently the effect has been used by the U3 with 'optimal barrels' Which start with a short length of CPVC that leads to the more loose Sched80 PVC. I'm not trying to give you a hard time for arriving at the same theories as other nerfers that came before you, especially since you seem to have a better grasp of the physics behind it than most.

There's been some debate about the efficacy of telescoping barrels/tightening rings, over whether the increased friction of a tighter barrel significantly increases the force required to overcome the static friction of the dart, and there is also some question as to whether it is best for the pressure in the barrel to peak before the dart starts moving. If you want to experiment further with this, I would definitely be interested to hear about your results. You might want to talk to Doom and Dan Beaver, who've taken a more scientific approach to this sort of thing.
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#9 Darthrambo

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Posted 23 December 2011 - 04:29 PM

I think you are missing what everybody is telling you, on multiple sites.

So with your super awesome magical tape method, the rest of the "barrel" now has absolutely no effect on the dart? Shit, I guess everybody has been wrong all along, we should be using 1/2" long, super tight barrels on everything.


Translation: "I counter physics and and scientific theory with my opinion". Address what I actually said I=FxT, don't just assert that it's wrong or doesn't apply because you think so. If you think that basic principals of physics are wrong then then please enlighten the world and claim your Nobel prize.

And yeah, that's what physics seems to say (minus the derisive tone). You can reduce barrel length and still achieve max ranges with use of tightening rings.

Seriously, I never claimed that putting tape in something is anything impressive, or that the idea of using a tight fit is something new. I just wanted to discuss that the math says that holding the dart in place longer allowing pressure to build up does effectively the same thing as a longer barrel. This can be useful in guns like a Vulcan that can't have a longer barrel or if you wanted an alternative to making a sealed breech and having a longer barrel.

Because:
Impulse= Froce x Time
Longer barrel increases the time the force acts on the dart, tighter fit increases the force acting on the dart before it moves. Using either method or a combination of the two can give you the maximum impulse possible for a given air volume.

If you want to discuss this great. If you want to just say it's wrong because that's not what everyone else says/does, please move on. I really don't want to waste time with someone that doesn't understand why that kind of argument isn't valid. If you think what I'm saying is incorrect, say why.

Also, technically a Vulcan does have a barrel, 25 of them stock to be exact. Following your train of thought, pretty much every Nerf blaster that doesn't use streamlines doesn't have a barrel.

Try asking anyone who knows anything about guns if a revolver has 6 barrels and see what they say. By this logic every bullets shell casing is its own barrel. If you want to say that I guess it's true on some level but it's not really effective terminology imo.



@ Langley

Thanks for the link,
I've seen similar stuff before about barrel length and different ID barrel material.

What I'm talking about specifically though is related but not the same. What I'm trying to discuss is the relationship between "tightening rings" and barrel length which I haven't seen anywhere. What I'm trying to say is that they are inversely proportional in that the more pressure achieved by a tightening ring before the dart starts moving, the shorter barrel you would need to still get optimum speed.

Where those guys talking about that kinda stuff as well?

Edited by Darthrambo, 23 December 2011 - 04:30 PM.

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#10 cheyner

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Posted 23 December 2011 - 07:07 PM

My bad, didn't realize you totally think Nerf guns are the same thing as a real gun, and that anything dealing with firearms can totally be related directly to Nerf.
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#11 Darthrambo

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Posted 23 December 2011 - 07:17 PM

Yup, that's about the level of response that I was expecting from you. Please move on, I'm done with you.

Edited by Darthrambo, 23 December 2011 - 07:18 PM.

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#12 mysterio

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Posted 23 December 2011 - 07:41 PM

Darthrambo, the reason why a super-short, yet very tight, barrel will not work on blasters is because the weight on a dart is concentrated in the front, and a large amount of sudden pressure from the back will cause the dart to fling out and go nowhere. The reason why everyone keeps mentioning telescoping barrels is because of this fact.
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#13 cheyner

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Posted 23 December 2011 - 08:18 PM

I actually had a few other things to say, but was trying to not sound like a dick. But you are clearly a douche so why should I worry?

Nobody has said that your math is wrong, its what you are saying that is wrong. Pretty much every example you have given in defense has been wrong.

Yeah, how about I ask somebody your revolver question, then show them a Maverick and a Mustang 6 and watch their head explode.

You say that this is useful on something like a Vulcan because it can't have a longer barrel, yet this morning you said it can't even have a barrel, which is it? But wait! If we use that along with your revolver question, how the fuck does a Vulcan even work in the first place then? Could it possibly be because it has 25 "barrels" in the form of a chain?

Like I basically said on NRev, suck up your pride and realize what people are saying so we can move onto the actual mod and its applications.

Now lets move on from all of that, and get back to the actual mod.

Did you measure the length of tape you used? Have you tried different lengths?
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#14 Darthrambo

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Posted 23 December 2011 - 11:11 PM

I actually had a few other things to say, but was trying to not sound like a dick. But you are clearly a douche so why should I worry?


If you were trying not to sound like a dick, you failed at that in your original post. Seriously, go look at the tone of your original post and ask yourself who is being the d-bag. Which is why I really have no interest in talking with you about this.


Nobody has said that your math is wrong, its what you are saying that is wrong. Pretty much every example you have given in defense has been wrong.


Please tell me what I have said that was wrong other than the one post where I there was a typo from not reading though after revising where I said the rings in an angel breech act as dart teeth when I meant to say was rings where the dart teeth would be.

You say that this is useful on something like a Vulcan because it can't have a longer barrel, yet this morning you said it can't even have a barrel, which is it? But wait! If we use that along with your revolver question, how the fuck does a Vulcan even work in the first place then? Could it possibly be because it has 25 "barrels" in the form of a chain?

So you really don't understand that not being able to have a barrel and not being able to have a longer barrel are not contradictions?

No it can't have an effective barrel, which would mean that it also couldn't have a longer barrel because it can't have any kind of barrel.

If you want to call the dart chambers or chain links or what ever barrels, fine, but this is a matter of semantics which really doesn't matter. Like I said I just don't feel that its effective terminology because they can mean 2 distinct things but if you want to, like I said before it's not wrong.
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#15 Ice Nine

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Posted 23 December 2011 - 11:29 PM


Yup, that's about the level of response that I was expecting from you. Please move on, I'm done with you.





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#16 Langley

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Posted 24 December 2011 - 12:29 AM

Darthrambo:
This is turning into a pattern with you. You've got to start explaining things more clearly, or be less defensive about it when someone misunderstands.

I don't even know what you two are supposed to be arguing about. You're on a fucking Nerf forum attacking each other over....what? Barrel design...or something? If you're going to disagree, just explain the case you're trying to make and back it up. If someone's attacking you personally in an argument over nerf.....do I really have to tell you to rise above it?
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#17 Darthrambo

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Posted 24 December 2011 - 03:54 AM

I agree with you Langley

This is why I tried to explain that there was a misunderstanding even though he insisted there wasn't. When the nerd rage came out I just said I was done. As for the personal attack thing, it's foam darts, I really could not care less if someone wants to insult me over the internet.

As for not explaining things clearly I see your point but sometimes when things make complete sense to you, it makes it harder in a way to understand what it takes to explain it to someone who doesn't know what you are talking about. I'll try to edit my original post to make it more clear.

To me it still really seems that people were just ignoring the first line after the pictures which says:
"I was thinking of how make use of plunger tube volume (or air volume in general) without the use of a longer barrel."

But maybe I needed to emphasize that this is what I was talking about, not just the tightening ring but the effect it has on optimal barrel length.

Edited by Darthrambo, 24 December 2011 - 11:18 AM.

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#18 hamoidar

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Posted 24 December 2011 - 01:03 PM

I belive that darth is right. Let me give an example that I think brings darths point across. Lets say you have a two foot piece of 1/2 inch pvc, you also have a 3 inch piece of 1/2 in cpvc. If you were to put the cpvc in, say, a Snap. The cpvc would hold the dart tightly, and when the gun is fired quite a bit of pressure builds up before the dart is released. With the pvc, hardly any pressure would build up before the dart begins to move. With the long barrel, the air has more time to accelerate the dart,but with the cpvc barrel, the dart starts out from the get-go at high speed; eleminating the need for a long barrel. Both the pvc and cpvc fire the dart with pretty good ranges, although the longer barrel out-performs the cpvc, for certain aplications the cpvc is more practical. By putting E-tape were the dart is held, darth increased the amount of preasure needed to get the dart out of the belt, therefor increasing dart speed and range. This mod is useful because puting long barrels on a vulcan belt would be impossible. I don't know that E-tape is the best thing to use, but it works.
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#19 Daniel Beaver

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Posted 24 December 2011 - 01:57 PM

I'm not quite sure why this thread blew up. The physics presented are not controversial - what Darthrambo is talking about is basically correct, and has been understood for years now. For a blaster like the Vulcan, adding a tight section to the base of the barrel does help. The only reason these sorts of tricks are not more widely implemented is that we lack methods of measuring the physical parameters of system, and so we necessarily resort to guesswork when designing barrels. Theoretical models are not very useful if you can't measure the inputs.

Edited by Daniel Beaver, 24 December 2011 - 01:57 PM.

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#20 Doom

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Posted 24 December 2011 - 03:14 PM

I call the effect you all are discussing the "static friction effect" because it really is only about static friction. Spud gunners and Nerfers have independently reinvented this idea and called it "telescoping barrels", "tightening rings", "detents", or other things I don't remember. I wanted a single name, so I describe the physics.

I have characterized Nerf guns before based on a "dimensionless dart mass". For "heavy" darts (guns with dimensionless dart masses higher than the "critical dimensionless dart mass"), the gun performs as if the flow restrictions offered no resistance (or equivalently, as if the pressure was independent of spatial location). Increasing static friction is one way to lower the critical dimensionless dart mass.

What I'm trying to say is that they are inversely proportional in that the more pressure achieved by a tightening ring before the dart starts moving, the shorter barrel you would need to still get optimum speed.


Your conclusion is wrong. You incorrectly extrapolate from a few examples. But you are right that static friction can improve performance.

Nerf guns see diminishing returns in performance from increasing static friction. With enough static friction the dart won't move because of the tight fit. But in a certain range of static pressure the dart will act as if the flow restrictions offered no resistance.

And if the gun had no flow restrictions we can calculate the ideal barrel length. So ignoring the dart plugging up the system, increasing static friction makes the ideal barrel length approach the ideal barrel length of a gun without flow restrictions. The ideal barrel length won't continue to shorten beyond that.

Edited by Doom, 25 December 2011 - 03:41 PM.

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#21 Darthrambo

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Posted 24 December 2011 - 10:58 PM

Your conclusion is wrong. You incorrectly extrapolate from a few examples.

Nerf guns see diminishing returns in performance from increasing static friction. With enough static friction the dart won't move because of the tight fit. But in a certain range of static pressure the dart will act as if the flow restrictions offered no resistance.

And if the gun had no flow restrictions we can calculate the ideal barrel length. So ignoring the dart plugging up the system, increasing static friction makes the ideal barrel length approach the ideal barrel length of a gun without flow restrictions. The ideal barrel length won't continue to shorten beyond that.

Cool, someone who addresses the physics of this!

Can you give me some equations that specifically show that greater pressure before the static friction is overcome wouldn't shorten barrel length? If I'm wrong I like to know why.

If the force of pressure is greater then the acceleration would be greater when the static friction is overcome. Because of this the way I'm looking at the physics, it seems that this would take less time for the dart to reach full potential acceleration meaning it would need less barrel length.

In terms of the barrel length equation the way I was looking at it is that Pc would increase by the tightening ring since it takes more pressure to overcome the static friction.

I do like physics but I am no expert. With that being said, for that equation it does seem like the pressure of Pc is 1atm to for V1 but once the tube starts to compress boyle's law should be accounted for shouldn't it? This would mean that the Pc should be P2 of V1Pv=V2P2. Where V1 is the Vc + dead space in the equation and P1 is 1 atm. V2 how ever should be the volume of the tube at the point in compression when the dart starts to move + dead space and the pressure can be at this point can be found because it is the only unknown variable.

Maybe I'm misinterpreting the definitions of the variable in that equation
Dead volume is dead space between the dart and tube right?
Pf is static friction or the friction of the barrel?
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#22 Kanashimi

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Posted 25 December 2011 - 12:30 AM

I had thought that the mechanics of spring powered nerf guns worked like this.

1: Trigger is pulled, catch releases plunger, plunger begins movement.
2: Plunger increases air pressure behind the dart, static friction holds the dart in place
3: Air pressure behind dart exceeds static friction, dart begins acceleration
4: Dart accelerates along the barrel. Two main forces at work, air pressure behind the dart and kinetic friction between the dart and barrel
5. Dart leaves barrel

Nerfers working on these ideas is pretty apparent. We use stronger springs to increase air pressure, thus having a greater force push the dart. Barrels with a proper fit allows high pressure to be built up before the dart is launched, and nearly zero kinetic friction as the dart is accelerating. Barrels of a proper length allow the dart to achieve maximum velocity when they exit the system.

One issue with your idea is that you don't take into account anything past step three. While the initial acceleration of the dart is important, the acceleration along the barrel is just as important, if not more. After the maximum air pressure is reached and the dart begins movement, the air pressure behind the dart still accelerates it, as it is a force on the dart that is greater than the forces in the opposite direction. Ideally, the dart exits the barrel when acceleration is zero (the force from air pressure behind the dart and kinetic friction between the dart and barrel are equal)*, which is when it has its maximum velocity.

So, the issue boils down to a greater maximum air pressure does not really imply that the dart needs a shorter track to accelerate on. It simply implies that the dart will be faster.

Something I feel I need to note. I don't have many gripes with you. However, I must ask that you use commas in sentences and explain your variables. The lack of commas make your sentences near unreadable to me, and the fact that physics is the subject makes it worse. Not explaining what your variables mean also makes it so I can not comment on your response.

Kanashimi

*In another thread, Doom states that the acceleration of the dart must be 0, and jerk must be negative. I don't quite understand this, so if Doom can explain in this thread, that'd be most helpful.
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#23 Darthrambo

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Posted 25 December 2011 - 04:46 AM

*In another thread, Doom states that the acceleration of the dart must be 0, and jerk must be negative. I don't quite understand this, so if Doom can explain in this thread, that'd be most helpful.



What he means by 0 acceleration is that the dart is no longer gaining speed. Acceleration is the change in speed or direction. Jerk or jolt is the rate of change in acceleration, and negative jerk means that the dart has changed from gaining speed to losing speed.

Sorry for not defining variables, I was kind of talking directly to Doom who seems to know about physics and Boyle's law is really basic stuff.

One issue with your idea is that you don't take into account anything past step three. While the initial acceleration of the dart is important, the acceleration along the barrel is just as important, if not more. After the maximum air pressure is reached and the dart begins movement, the air pressure behind the dart still accelerates it, as it is a force on the dart that is greater than the forces in the opposite direction. Ideally, the dart exits the barrel when acceleration is zero (the force from air pressure behind the dart and kinetic friction between the dart and barrel are equal)*, which is when it has its maximum velocity.


No you are missing the point entirely.

What I'm saying is the dart accelerates faster when it's pushed by greater force from the greater air pressure build up. This means it will reach its max velocity faster. This means it will take less barrel length to reach a higher velocity.

The only problem is that with higher acceleration is the more distance the dart will travel in a shorter time so it would spend less time in a barrel of a given length. Maybe it would be more accurate to say that that tightening rings increase the velocity for barrels shorter than optimum length.

Edited by Darthrambo, 25 December 2011 - 04:49 AM.

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#24 Doom

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Posted 25 December 2011 - 11:47 AM

1) Can you give me some equations that specifically show that greater pressure before the static friction is overcome wouldn't shorten barrel length?

2) In terms of the barrel length equation the way I was looking at it is that Pc would increase by the tightening ring since it takes more pressure to overcome the static friction.

3) With that being said, for that equation it does seem like the pressure of Pc is 1atm to for V1 but once the tube starts to compress boyle's law should be accounted for shouldn't it?

4) Dead volume is dead space between the dart and tube right?
Pf is static friction or the friction of the barrel?


1) You missed my point. Static friction can increase the maximum pressure, which can shorten ideal barrel length. What I disagree with is that you can trade one for the other (i.e., they are inversely related). The ideal barrel length won't continue to decrease as static pressure increases. It has a limit which corresponds to the unrestricted flow case.

Are you asking why the ideal barrel length won't decrease below the ideal barrel length for the unrestricted flow case (which is the case for the equation I posted)? The unrestricted flow case has the highest physically achievable barrel pressures (without changing gas chamber pressure). So the ideal barrel length can't decrease further.

2) P_c is the pressure at time zero (i.e., right before the trigger is pulled) in the gas chamber of a pneumatic gun. Everything in that equation is independent of time.

3) Boyle's law does not apply here. You can use adiabatic/isentropic process relationships for perfect gases (i.e., constant entropy, not constant temperature as in Boyle's law) if the barrel pressure is approximately equal to the gas chamber pressure (with the gas chamber being an air tank or spring-piston chamber). This occurs when the valve/constriction doesn't obstruct the flow much as characterized with a "heavy" (as defined earlier), slow moving dart.

The reason Boyle's law does not apply here is because the temperature of the gas in a Nerf gun varies significantly. There is little heat transfer to the gas. Boyle's law implicitly assumes that heat transfer maintains the temperature constant. Adiabatic process relationships are built around the idea that there is no heat transfer.

I derived the ideal barrel length equations for air guns and springers using adiabatic process relationships under the assumption that the flow is unrestricted between the barrel and gas chamber. Without flow restrictions, the process relationships can be used because all of the pressurized gas in the Nerf gun is at the same pressure.

If the barrel pressure was different than the gas chamber pressure because of flow restrictions, or worse, if you can't define a single barrel or gas chamber pressure (as is the case for many spud guns), then you can not use these simplified models. In short, you need to write a computer simulation for this case.

4) Dead volume is the volume between the valve/flow obstruction and dart at time zero. P_f is dynamic friction force divided by the barrel cross sectional area (so that you get a pressure --- this simplifies the equations). Unfortunately, I have not had the time to properly document everything I have developed.

1) So, the issue boils down to a greater maximum air pressure does not really imply that the dart needs a shorter track to accelerate on. It simply implies that the dart will be faster.

2) In another thread, Doom states that the acceleration of the dart must be 0, and jerk must be negative. I don't quite understand this, so if Doom can explain in this thread, that'd be most helpful.


1) This is true. Greater maximum barrel pressure does not necessarily imply that the ideal barrel length is shorter. But it does not necessarily imply that the muzzle velocity will increase either. Both usually are true, but they are not necessarily true.

2) Darthrambo has it right, but I'll offer my explanation anyway.

The time derivative of acceleration (jerk) must be negative for maximums. If it was positive, then you have a minimum. If it was zero, you have an inflection point, which we don't care about.

This page explains this better than I could. Note that they're talking about the derivative of velocity (i.e., acceleration) and the second derivative of velocity (i.e., jerk).

Edited by Doom, 25 December 2011 - 01:41 PM.

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#25 Darthrambo

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Posted 25 December 2011 - 06:46 PM

1) You missed my point. Static friction can increase the maximum pressure, which can shorten ideal barrel length. What I disagree with is that you can trade one for the other (i.e., they are inversely related). The ideal barrel length won't continue to decrease as static pressure increases. It has a limit which corresponds to the unrestricted flow case.

Oh yeah, totally, I never meant to imply that you should make a 2in super tight barrel. This was just meant as a possible way to shorten barrel length without sacrificing performance. They are inversely related but to a reasonable point. I didn't mean you could swap out a barrel for a super tight ring and get the same effect.

I know you say that you disagree that they are inversely related but you also just said they were.
"Static friction can increase the maximum pressure, which can shorten ideal barrel length"
i.e., More static friction = Less barrel length.
This is what I meant by inverse relationship. What you are saying is the the relationship isn't linear, and we are in agreement.

3) Boyle's law does not apply here. You can use adiabatic/isentropic process relationships for perfect gases (i.e., constant entropy, not constant temperature as in Boyle's law) if the barrel pressure is approximately equal to the gas chamber pressure (with the gas chamber being an air tank or spring-piston chamber). This occurs when the valve/constriction doesn't obstruct the flow much as characterized with a "heavy" (as defined earlier), slow moving dart.

The reason Boyle's law does not apply here is because the temperature of the gas in a Nerf gun varies significantly. There is little heat transfer to the gas. Boyle's law implicitly assumes that heat transfer maintains the temperature constant. Adiabatic process relationships are built around the idea that there is no heat transfer.


Significantly?
I understand this in terms of theory but for this application I really don't think it's necessary to take temp change into consideration.
You really think the temperature change of the gas in the chamber is really going to effect anything to a degree where it should even be considered?

Even if it does change to an amount that should factor in then fine, use PV=NRT. You still end up with the same effect. The pressure increase in with a tightening ring before it overcomes static friction, regardless of if the temp changes a little.

Edited by Darthrambo, 25 December 2011 - 07:00 PM.

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