calculations for spherical enclosure.
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 6th October 2018, 11:24 PM #21 Galu   diyAudio Member   Join Date: Apr 2018 Call me mathematically challenged, but I don't understand that lens volume calculator! Last edited by Galu; 6th October 2018 at 11:42 PM.
 6th October 2018, 11:34 PM #22 Galu   diyAudio Member   Join Date: Apr 2018 This one's better - click on Sphere Radius 'r' & Chord 'AB' Spherical Cap Calculator Last edited by Galu; 6th October 2018 at 11:37 PM.
tsmith1315
diyAudio Member

Join Date: Jul 2003
Location: Doerun, GA
Quote:
 Originally Posted by Galu Call me mathematically challenged, but I don't understand that lens volume calculator!
Your link is indeed easier to see and use, but in case anyone is interested in alternative shapes...

That lens calculator describes a biconvex lens with a cylindrical middle section between the two convex surfaces.

r1 - describes the radius of curvature for the (spherical) convex surface on the left
r2 - describes the radius of curvature for the (spherical) convex surface on the right
rc - describes the radius of the cylinder that intersects the two convex surfaces
hc - describes the length of the cylinder between the two convex surfaces

In the case of the OP, we want the volume under one spherical convex surface cut off by a plane.
The plane intersects as a circle with whatever radius the OP wants as his opening.

As an example, let's use a 14" diameter sphere with an 8" speaker. Ignore baffle size, kerf, etc for the sake of demonstration and assume we want a hole with an 8" diameter.

So we want the intersection in our case to be flat circle, a cylinder with a height of 0 and diameter of the speaker. This gives us:
hc = 0, and
rc = 4

Using the left convex side as our spherical cap to be removed, which is being cut off the 14" sphere, giving us:
r1 = 7

We want the right surface to be flat, not convex. So the radius of the right side should be infinity, or high enough to be of little consequence. Let's use:
r2 = 10000

Inserting these values into Richidoo's link gives us 32.609 for the volume of the spherical cap to be removed from the OP's sphere.

In Galu's link, using r=7 and chord = 8 finds a spherical cap volume of 32.589 that's pretty good agreement.

The lens calculator does bring up the thought of alternative enclosure shapes employing spherical baffles.
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Galu
diyAudio Member

Join Date: Apr 2018
Quote:
 Originally Posted by tsmith1315 Inserting these values into Richidoo's link gives us 32.609 for the volume of the spherical cap to be removed from the OP's sphere. In Galu's link, using r=7 and chord = 8 finds a spherical cap volume of 32.589 that's pretty good agreement.
A 'pretty good' agreement? To three significant figures the two calculated volumes are identical (32.6)!

 7th October 2018, 12:15 PM #25 Galu   diyAudio Member   Join Date: Apr 2018 P.S. No offence intended to Richidoo and tsmith1315! While the Spherical Cap Calculator better fits the needs of the OP, I take the point that the Lens Calculator is more comprehensive. Spherical Cap Calculator Last edited by Galu; 7th October 2018 at 12:18 PM.
Aucosticraft
diyAudio Member

Join Date: Nov 2009
Location: Pune
Quote:
 Originally Posted by Richidoo The formula you want is simple arithmetic, but it requires that you inquire with the driver manufacturer to find out the driver displacement (volume of portion of the driver that is behind the driver mounting flange.) Mfgs know this but it is often not published. You could also make a close enough estimate yourself. Call this displacement volume "D." Then you need to determine the volume between the driver mounting plane cut into the sphere and the concave surface of the portion of the sphere that is removed. This is a lens shaped volume, so you can determine that volume using this online calculator. Be sure to use the "thru hole" dimension for the diameter of this volume, not the overall flange rabbet diameter that is cut into the sphere walls. Call this lens volume "L" If you make the speaker ported, then also subtract the volume of the port from the box volume - the outer port tube dimensions and the space inside it. Call this port volume "P" Volume of a sphere is 4/3*pi*r^3. call this "S" Your formula for the net volume remaining inside the sphere when you cut the driver hole and install the driver (enclosure working volume) is: V = S - (L + D + P) There are some sources of acrylic and polystyrene foam spheres of various sizes online. When choosing the diameter of your sphere, also consider how it will affect the baffle step for your filter and EQ designs. Spheres have a lot of volume inside that will usually exceed what you need for good bass alignment. So you can build a more traditional box shape inside the sphere to minimize internal sound reflections acting on the driver. Non parallel walls, etc. You can make these from thin plywood, then just glue them to the inside of the sphere then fill the void with expanding urethane foam through some holes in the plywood. Make a lot of holes so the foam can expand easily, then cut it flat after foam hardens. Or you can just spray the foam in blobs, measure the volume with sand and cut away to achieve the volume you want. Or use liquid concrete to make the walls, etc. If you're doing a sealed speaker the volume is not too critical, but a ported speaker box volume (Vb) is critical.
Yes, My primary intention for using spherical enclosure is to get smooth diffraction curve. There is nothing we can do to avoid it completely. And it holds true even for different axis response. This makes easy to correct the diffraction electronically or electronically.

This design is going to be a sealed enclosure. And can work till 80Hz down. They can be used as Satellite speakers with subwoofer or as a standalone bookshelf. (Although not going down to 30Hz.)

The link you shared "True Audio TechTopics: Diffraction Loss" was referred. But i had found more detailed measurement document where they provided detail plot. Unfortunately I am not able to find it again. My bad , Should have bookmarked it.

I soon would need something that would calculate (simulate) diffraction for sphere. If you know any please help.
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Last edited by Aucosticraft; 7th October 2018 at 03:36 PM.

Aucosticraft
diyAudio Member

Join Date: Nov 2009
Location: Pune
Quote:
 Originally Posted by scottjoplin Don't forget the volume the driver occupies
Yes Driver displacement should be to Vb during calculations.
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Aucosticraft
diyAudio Member

Join Date: Nov 2009
Location: Pune
Quote:
 Originally Posted by Galu P.S. No offence intended to Richidoo and tsmith1315! While the Spherical Cap Calculator better fits the needs of the OP, I take the point that the Lens Calculator is more comprehensive. Spherical Cap Calculator
I understand , everyone here has put best efforts to get the solution.
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 7th October 2018, 07:54 PM #29 Patrick Bateman   diyAudio Member     Join Date: Oct 2006 Location: San Diego I've been able to achieve VERY nice polars by using elliptical enclosures: The Advantages of a Diffractionless Enclosure They sound really great too. Highly recommended, and easy to make.
hollowboy
diyAudio Member

Join Date: Jul 2007
Location: 'straya
Quote:
 Originally Posted by Aucosticraft Yes, My primary intention for using spherical enclosure is to get smooth diffraction curve.
If that is the primary intention, then a bigger sphere = better.

If you want go for the biggest and/or smoothest practical enclosure for optimal diffraction, there's not much point in calculating the volume to 3 decimal places.
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