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Single Pipe C:B Ratio

Post questions and info about combustion (flammable vapor) powered cannons here. This includes discussion about fuels, ratios, ignition systems, safety, and anything else relevant.
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Single Pipe C:B Ratio

Unread postAuthor: sgort87 » Fri Mar 20, 2009 1:44 pm

I started a big discussion on this a long time ago, and as far as I know, nothing became of it. I'm looking to see if anyone has did any tests using a single pipe for the barrel and chamber with reliable results of a C:B ratio for the shot with the fastest velocity.

Before anyone says .7 or .8 to 1, think again. That is for matching a barrel volume to a set chamber volume. You can add even more chamber to that same barrel to get a more powerful shot, up to a certain point. My goal is to find the point in a set LAUNCHER volume to separate the chamber and barrel to give the best results in terms of ve-locity, not efficiency.

(Yes, I messed with EVBEC with no success. I also searched the forum, but the search is actually not working at all for me now, and turns up no results for anything.)
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Unread postAuthor: psycix » Fri Mar 20, 2009 1:50 pm

I believe HGDT should have a function for this called "gun optimizer". I am sure that GGDT has it, but I bet HGDT has it too.
If you pick "keep overall length constant" (fixed length) HGDT will search for the most powerful ratio.


EDIT:
Crap, I just tried it, and HGDT does not have that function.
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Unread postAuthor: starman » Fri Mar 20, 2009 1:59 pm

Have you loaded HGDT and fiddled with modelling different chamber sizes?

I'm not sure there is a definite optimum chamber to barrel size for velocity as you can almost always add more chamber and get more velocity. It will just get to the point that so much energy is getting wasted as heat and noise behind and already ejected projectile. I believe that's why the c:b efficiency ratio has stuck around and still has some relevance.

It also ties into the burst disk conversations that have been taking place around here of late. I believe a burst disk can go a long way toward harnessing more of the otherwise wasted energy problems with "inefficient" c:b barrel lengths.

psycix wrote:EDIT:
Crap, I just tried it, and HGDT does not have that function.


Did you look under Tools/Sensitivity Studies? There is a way to model various chamber length and diameter and graph the results. There is also the gun scaler tool.
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Last edited by starman on Fri Mar 20, 2009 2:08 pm, edited 1 time in total.
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Unread postAuthor: Ragnarok » Fri Mar 20, 2009 2:07 pm

Now, I reasonably sure something got posted about about this on Spudtech - all based on Latke's results.

Ah ha! Yes there is... and crap, the image link to the data table is dead.
Still, the post text quotes 1.25:1 C:B ratio was the end estimate for a fixed volume launcher's ideal C:B ratio.

Make of the summary of the table what you will.
joannaardway wrote:In summary:
Where Barrel Volume (BV) is based on Chamber volume (CV):
The famous .8:1 ratio is the best bet.

Where CV is based on BV:
The ratio of .8:1 is the most efficient ratio (and probably your best bet), but if you want a bit more power and don't care about cost of your propane,a larger C:B ratio will result in a higher muzzle velocity, but exceeding 2:1 C:B gives diminishing returns. There is some truth in the 1.5:1 figure, but only when CV is based on BV

For fixed volume launchers:
The ideal ratio for highest muzzle velocity for a fixed volume launcher should be about 1.25:1 - or the barrel taking up 44% of the length of the launcher.
The most efficient ratio in terms of muzzle energy to propane used should be about .66:1 or the barrel being 60% of the length of the launcher.

I should note that the rest of the topic mentions that the 0.66:1 ratio is an oddity, but it is the most efficient one in terms of muzzle energy to propane of a fixed volume launcher - but that it shouldn't be used over 0.8:1, because with a 0.66:1 launcher, just truncating the barrel slightly will actually improve power.
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Unread postAuthor: sgort87 » Fri Mar 20, 2009 2:15 pm

That is exactly what I am looking for. Thank you.
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Unread postAuthor: starman » Fri Mar 20, 2009 2:16 pm

Ragnarok wrote:I should note that the rest of the topic mentions that the 0.66:1 ratio is an oddity, but it is the most efficient one in terms of muzzle energy to propane of a fixed volume launcher - but that it shouldn't be used over 0.8:1, because with a 0.66:1 launcher, just truncating the barrel slightly will actually improve power.


Interesting, that number is suspiciously close to nature's "Golden Ratio" of 0.618054.
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Unread postAuthor: Ragnarok » Fri Mar 20, 2009 2:33 pm

@sgort: No problem. Just bear in mind, it's a mathematical analysis of Latke's fixed chamber volume tests, not a direct set of tests itself. It shouldn't be way out, but I don't expect it'll be right on the money.

Would I be right in saying you were planning on doing tests on fixed volume launcher ratios at some point, or was that someone else?

starman wrote:Interesting, that number is suspiciously close to nature's "Golden Ratio" of 0.618054.

As far as I know, that's complete coincidence, unless there's some bizarre unknown force at work.
It just so happens that 0.66:1 is when the savings in input energy from having a smaller chamber are offset by the losses in output energy from the barrel being too long for the chamber to maintain.
It is however oddly less powerful than a launcher with the same chamber volume but where the barrel half has been cropped back to nearer 0.8:1

This odd "most efficient, but less efficient than it can be" ratio only exists for the fixed-volume combustion, because of the fact that the volume of chamber and barrel are dependent on each other.

Truly bizarre.

EDIT: On the note of that link of yours, it's quite wrong when it says "Not only are the figures after the decimal point identical in both, but each is the reciprocal of the other - These are the only two numbers that demonstrate this property".
The numbers 2.414213562 and 0.414213562; 3.302775638 and 0.302775638; 4.236067977 and 0.236067977; etc; etc...

There are an infinite series of numbers with an integer difference (i.e. they share the number sequence after the decimal point, but where one is the reciprocal of the other. Indeed, the simplest number of this form is 1. (Integer difference of 0)

EDIT #2: Now I look closely, the larger of number of each pairing follows the format: (X + SQRT(X<sup>2</sup>+4))/2 ; where X is any integer. The lesser number is simply the reciprocal of that.
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Unread postAuthor: starman » Fri Mar 20, 2009 3:21 pm

Ragnarok wrote:As far as I know, that's complete coincidence, unless there's some bizarre unknown force at work.



Probably...maybe...However, there are many seemly unrelated phenomena that do respond to golden ratio rules....like audio speaker box dimensions. They have long been known to best perform when, at least roughly, are dimensionally designed to conform to the ratio. It wasn't until relatively late where modern materials can be used to negate the affects of less optimally dimensioned box.

I wouldn't completely rule it out as a factor.

FWIW, Wiki has a fairly in-depth look at the golden ratio.
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Unread postAuthor: jimmy101 » Fri Mar 20, 2009 5:16 pm

HGDT (0.3.0):
burst disk at 0 PSI
single ignition point
2" diameter pipe
50" total length
80g spud
10 PSI friction
turbulance
insulation "none"

Puts the optimum at ~CB 0.67 (20"L chamber, 30"L barrel).

Max velocity 212 FPS. The CB range that keeps the velocity within 10% of the maximum velocity is 0.4~1.2. So the guns performance it fairly insensitive to the CB over a fairly wide range.

Of course, if you actually make a "mono" gun you can measure the optimal CB pretty easily.
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Unread postAuthor: sgort87 » Fri Mar 20, 2009 5:37 pm

How much difference would it make if the projectile was one of those tiny vortex balls? I'm not sure on the weight and friction of it. I don't actually have one yet, but I hope you may know the right numbers for it.
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Unread postAuthor: jimmy101 » Sat Mar 21, 2009 2:38 pm

The lighter the ammo and the lower the friction ...

Probably want a smallish sized chamber so it has a chance to actualy burn a significant fraction of the fuel, and hence reach a decent pressure, before the ammo exits the barrel.
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