Another look at C:B ratios

[dongfang]

I´m beginning to believe it is a mistake to consider the often cited 0.7:! the "best" C:B ratio for combustions. It´s the best in analysis all right, but not in design.

The figure comes from experiments, where someone built a cannon with an absurdly long barrel, and then sawed it off piecewise until he found the length that gave the best performance (velocity). That is, finding the point beyond which further extending the barrel is of no use.

But really, I consider the barrel length the #1 "cost" that I want to have value for, not the volume of the chamber. And, with a 0.7:1 C:B, I get almost no value for quite some length of my barrel - just slightly better than if I had saved the cost and cut the barrel shorter. In fact, the "ideal" here is in finding a barrel where there is no more acceleration at the muzzle end (nice for making a quiet gun anyway).

I would rather find the best chamber to drive my barrel than the other way around. Anyway, when I design a gun, I first decide on caliper and barrel length (what kind of gun am I designing?). So
Generally: Which C:B ratio has the best velocity per barrel length unit ?

I have tweaked Burnt Latke´s figures a little - divided his velocities by his barrel lengths - see attached images.

The result from this little division experiment seems to be that the 1.5" cannon performed the best with a 1.2:1 C:B ratio, there is no peak for the 2.5" cannon but the curve seems to be about to flatten out at the large-chamber end, and for the 0.75" gun, the most length-efficient barrels are the absurdly short ones (that nobody would want to use anyway).

Just an idea anyway: If you want to match a chamber with your barrel that will give the best performance for the length of the barrel, it appears that 1.2:1 is a good figure overall. Or, put differently again: Below 0.7:1 is a waste of barrel. With a barrel of a reasonable length, above 1.2:1 could be a waste of fuel and may actually degrade performance.

Regards
Soren

[jimmy101]

I may be miss-interpreting your analysis but ...

You say a CB of 1.2 would be optimal because the d(Velocity)/d(length) is maximum for that CB? Latke's data for the 1.5" puts the dV/dL at 7.3 for that ratio.

But, that ratio under performs the gun with the optimal barrel (513 fps vs. 485 fps).

I guess what you are saying is that over a certain range the cost in muzzle velocity for shortening the barrel is fairly minimal. In this case, cutting the barrel length in half only lowered the muzzle velocity by a small amount.

Code: Select all

CB   Barrel L(")   Velocity (fps)
1.2     66.5           485
0.6     132             513

A completely reasonable way to look at the problem. In fact, I've been thinking about a similar way of looking at it. I call it the "10% Rule". If you want to keep the barrel as short as possible you might ask the question "How short can the barrel be such that the decrease in muzzle velocity is less than 10% of the optimal muzzle velocity?" It is really surprising how much barrel you can chop of and still keep the muzzle velocity within 10% of the velocity you get with the optimum barrel. (I choose 10% as the cutoff since that was the shot-to-short variablity that Latke saw using spuds as ammo.) For my combustion model, it looks like the "10% barrel" is roughly half the length of the optimal barrel. Using Latke's 1.5" data the drop in velocity is only 5% for the half length barrel.

With more data and thought we might be able to declare a "Spud Law" on your observation.

[BC Pneumatics]

It was stated when the tests first came about that this was the ideal barrel length for a fixed chamber, but that for a fixed barrel, a cannon would benefit from a larger chamber. Old news, and pretty much common knowledge, but at least someone around here is thinking. Good job!

[boilingleadbath]

What you are noticing is, essentially, that the pressure in the bore decreases as the projectile moves down it.

Also, as a couple of notes:
1) The last few data points of the 1.5" data arn't very good.
2) You really should graph these - your assumption that the curve reaches a maximum doesn't look right. (and that includes the 1.5" curve.)

[dongfang]

Hi,

Jimmy, I think you found what I was looking for: The C:B ratio to use when accepting a velocity, or a kinetic energy, or whatever, xx% below optimum.

It may sound strange to design for less than optimum, AND get guns that perform better compared to their size. That´s one of the little marvels of engineering.

I have read that the engineers building those ion accelerator rocket engines also go for less than the best specific impulse they can get, even though good specific impulse is the major reason for using such an engine in the first place. The reason is the same again: If they maximized, the engine would become so heavy that the overall performance in moving the payload would get worse...

Regards
Soren

[BC Pneumatics]

It may be that it is 5:30am and I just got off work, but isn't this just very simply the point of diminishing returns?
Maybe I'm crazy, but it hardly seems like a revolutionary concept.

[dongfang]

It is. And it is not. And I didn´t say so much abt revolutionizing ... just that it´s a little funny how people sometimes take the c:b as a gospel, and ignore that a large part of the barrel will do virtually nothing for them.

But of course everybody may decide for himself.

Regards
Soren

[BC Pneumatics]

Perhaps a little elaboration on how it is not?

I see with the ion accelerator rocket analogy as a tad bit flawed. They get to a point where that added mass is a larger burden than is relived by the increased impulse (as you mentioned), however the C:B ratio that is in common usage does not place any additional net burden on the projectile, as the increased drag from friction is less than the performance increase. (Within the parameters of the test, of course)
The analogy only becomes valid when the increased resistance is of a greater force than the increased thrust transfered to the projectile, which occurs at a much lower C:B ratio than is commonly advised.
So, within the commonly used C:B ratio, the point just doesn't seem valid. (To me at least, but I already explained my condition)

When you say "it´s a little funny how people sometimes take the c:b as a gospel, and ignore that a large part of the barrel will do virtually nothing for them. " does not the addition of "virtually" make it the point of diminishing (not counter-productive) returns?

[boilingleadbath]

Sure, it's a case of diminishing returns when viewed as <i>only</i> changing barrel length.

But in the case that you change barrel length and chamber length to get the most performance from a set launcher length, that extra non-productive barrel is counterproductive.

If one wishes to use simplistic modeling to find the optimum c:b ratio for the second case, one may use EVBEC, provided they realize that the predicted c:b ratios are probably (a bit) on the high end - EVBEC doesn't account for increased combustion time.

[BC Pneumatics]

But in the case that you change barrel length and chamber length to get the most performance from a set launcher length, that extra non-productive barrel is counterproductive.

In my first post, this is what I said was fairly common knowledge. Right after Latke's tests, it was mentioned (by "Boogieman" IIRC) that the 0.8:1 C:B ratio was only optimum for a set chamber length, and not for a set launcher length, or barrel length.

[jimmy101]

But in the case that you change barrel length and chamber length to get the most performance from a set launcher length, that extra non-productive barrel is counterproductive.

In my first post, this is what I said was fairly common knowledge. Right after Latke's tests, it was mentioned (by "Boogieman" IIRC) that the 0.8:1 C:B ratio was only optimum for a set chamber length, and not for a set launcher length, or barrel length.

... or chamber diameter, or barrel diameter, or projectile, or number of spark gaps, or fuel, or ...

For the three guns and two ammos (IIRC) Latke tested the optimal CB was different for each configuration.

[BC Pneumatics]

Jimmy, all we are discussing is the .8:1 C:B right now.

[jimmy101]

BC, exactly, but the "optimal 0.8 C:B" is dependent on a lot of things besides chamber length.

I was just continuing/completeling your thought with the real story.

that the 0.8:1 C:B ratio was only optimum for a set chamber length, and not for a set launcher length, or barrel length.
... or chamber diameter, or barrel diameter, or projectile, or number of spark gaps, or fuel, or ...

[BC Pneumatics]

Jimmy, true or not, we do not have any comparative numbers on any of the things you mentioned, so we cannot begin to discuss them in this topic, sadly.