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What is the best cab shape?

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Since, other than a perfect sphere (which would tend to roll off the stage), a geodesic dome has the most internal volume/external size ratio, I am going to go with that. Why not?

Because it's wrong?

A sphere has the greatest volume / surface area ratio, so it makes some sense from a cost efficiency perspective if the material is very expensive.

Since it will effectively use up the space of its enclosing cube, the internal volume / external size ratio will be quite poor.
 
I'm no geometrician, but what enclosing cube are you referring to? I am visualizing a half-sphere sitting on a surface.
A hemispherical or semi-cylindrical rear chamber is a very good shape for strength to weight, resonance control and internal reflection control. The problem with those shapes is the small internal volume relative to the external linear dimensions. That's why you see them used in small hi-fi satelllite midrange speakers that don't need much interior volume, but not in bass cabs that do.
 
I'm no geometrician, but what enclosing cube are you referring to? I am visualizing a half-sphere sitting on a surface.

An enclosing cube (box) is the space you need to allow around the thing so that you're not running into some bit of it (okay, that's entirely too technical <G>). Think of it as the size of the box that you're going to have to use to pack and ship it. If you have a sphere that has a diameter of 4 feet, an enclosing cube will be 4x4x4. If you're going to put it somewhere on stage, that's how much volume you have to allow for it.

It's not an efficient shape in this case because you have to fill the rest of the box with packing peanuts. Or because you're wasting space onstage (footprint) that might be better utilized if the object had the same volume enclosed in a box-shaped space.
 
I was thinking about this question (What is the best cab shape?) when I happened upon the Gallien Krueger 410RBH/4 with the angled back corners.

If build cost was not a factor what would the optimal cab shape be? What is the effect, if any, of the parallel sides and right angle internal corners?

For a bass cab, there's not ordinarily a reason to tilt things back (4x10's get a bit directional, I suppose) or angle interior walls to prevent standing wave buildup.
 
The sphere is best for eliminating internal box reflections/cancellations/standing waves. They also roll off the stage and lose a lot of internal volume in relation to their footprint. The commonly seen cube/box shape makes the most use of internal volume in relation to the space the cab takes up externally.

There is a "golden ratio" of I think .6 to 1 to 1.6 that's supposed to be the best as far as internal cancellations. Bass cab makers for the most part stuff as many drivers in as little box as possible and still sound good enough to sell and the rest be damned.

There was a thread on here a couple/few years ago about somebody making bass cabs out of bass drum shells. That's pretty cool, and has actual sonic benefits to boot.
 
Bass cab makers for the most part stuff as many drivers in as little box as possible and still sound good enough to sell and the rest be damned.

+1

Still sound good enough... well, it depends what your references are.
But, I think as far as stuffing as many drivers in a (ehm, small box) there's only one example that has it's place in the basscommunity, the Ampeg 810. It's by far no high fidelity but for some this is the ticket to nirvana.

About the enclosure shape, depends on what you want to achieve. If you want good control of internal reflections keep the shape as asymetrical as possible. To fight standing waves you could use the golden ratio (as mentioned before) in conjunction with an internal helmholz-resonator to absorb the 1st standing wave. If you want as little defractions as possible on the (outer)edges of the cabinet the "egg" shape is the way to go, this is only a problem in hifi cabinets where you have drivers that have a very broad dispersion.