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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.
A 'pretty good' agreement? To three significant figures the two calculated volumes are identical (32.6)!
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
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
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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.
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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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.
The Advantages of a Diffractionless Enclosure
They sound really great too. Highly recommended, and easy to make.
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.
I agree with "The bigger the better". But this is kinda satellite / bookshelf design.
So, do you know any simulator tool that can help me simulate spherical enclosure's Baffle edge diffraction?
Hi no need of simulator: 115/ diameter in meter.
Eg: if your external diameter is 11,5cm, 115/0,15:1000hz.
You use a high shelf with fc 1khz and attenuate until it sound good/natural to you ( if you have headphone take them as reference and do it by ear).
This is exactly same situation as for a rectangular enclosure except the attenuation profile is smoother with spherical ( you don't have the typical bounce followed by dip around fc encountered with rectangular shape) so a shelf is an (even) better approximation of what happen in the transition zone from 2pi to 4 pi.
Eg: if your external diameter is 11,5cm, 115/0,15:1000hz.
You use a high shelf with fc 1khz and attenuate until it sound good/natural to you ( if you have headphone take them as reference and do it by ear).
This is exactly same situation as for a rectangular enclosure except the attenuation profile is smoother with spherical ( you don't have the typical bounce followed by dip around fc encountered with rectangular shape) so a shelf is an (even) better approximation of what happen in the transition zone from 2pi to 4 pi.
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For a bookshelf speaker, the concept of minimising diffraction is nearly irrelevant because there will be so many boundaries and reflections near the speaker.
Only a free standing speaker, distant from objects and room boundaries, gets the full diffraction benefit of being in a spherical (or smoothly curved) enclosure - see page 15 and fig 3.8 of the linked pdf.
Nope, but Dr Geddes has written a lot on the topic, so Googling him plus key words like "diffraction" will probably be a good start, e.g. this:
http://www.gedlee.com/downloads/AT/Chapter_3.pdf
My personal take on it (assuming finite resources + normal listening room that is used for other purposes) would be to either:
1) use a found object that is good enough. e.g. Google [ Ikea bowl speaker ]
and make a stand-mounted (or pendant hung) satellite speaker that you can move well away from room boundaries during listening sessions.
2) build the closest thing to a soffit mount that you can manage. e.g. make the truncated pyramid shown in post 2 of this discussion, and mount it on a wall.
Diffraction
Krivium, Thanks.
I tried couple of days to understand if I can implement it. Sorry. I think I will need more help from you. Is there any video or something that can practically show. I could not understand how"You use a high shelf with fc 1khz and attenuate until it sound good/natural to you".
I think Google [ Ikea bowl speaker ] should help me.
Probably , these speakers would be suspended down from ceiling. And would not be mounted on the corners or fixed on wall.
Thanks for the help/
Hi,
This will help:
True Audio TechTopics: Diffraction Loss
SBIR calculator
Once you've got your fc for baffle step compensation (1000hz in my previous example) you'll have a choice to make: either you 'boost' your low end, either you 'cut' the high end.
Two things have to be taken into account in the choice you'll make:
_first is headroom: if you boost low end frequency you'll loose headroom in the low which may be an issue as low are usually high crest factor signal ( think about a kick drum: no or low sustain but high impact thus high transient, this is the reason in PA you'll have kwatts amplifier dedicated to low end too: high transients to take care of...),
_second we (our brain) are less sensitive to phase rotation implied in cut eq than in boost.
So for bsc the logical choice for me is to use an eq in high shelf mode where fc is 1khz and attenuate the high end by an amount up to -6db. This value is a worst case scenario ( in free field with the loudspeaker mounted on a 6meter pole) and you'll usually have something within 2 to 4 db range of attenuation in a real room ( you have room gain and boundary conditions which come into play).
You can use any high shelf eq on your source material ( if your source is a computer this is easy) cause you'll cut the high freq ( much less chance to saturate the source as you cut) and then you can either move away to listen to your music or if you plan a passive bsc circuit you'll have the attenuation needed for your speakers.
I hope this is clearer.
Anyway, what is the outside diameter of the ball you plan to use? We will do the math here.
This will help:
True Audio TechTopics: Diffraction Loss
SBIR calculator
Once you've got your fc for baffle step compensation (1000hz in my previous example) you'll have a choice to make: either you 'boost' your low end, either you 'cut' the high end.
Two things have to be taken into account in the choice you'll make:
_first is headroom: if you boost low end frequency you'll loose headroom in the low which may be an issue as low are usually high crest factor signal ( think about a kick drum: no or low sustain but high impact thus high transient, this is the reason in PA you'll have kwatts amplifier dedicated to low end too: high transients to take care of...),
_second we (our brain) are less sensitive to phase rotation implied in cut eq than in boost.
So for bsc the logical choice for me is to use an eq in high shelf mode where fc is 1khz and attenuate the high end by an amount up to -6db. This value is a worst case scenario ( in free field with the loudspeaker mounted on a 6meter pole) and you'll usually have something within 2 to 4 db range of attenuation in a real room ( you have room gain and boundary conditions which come into play).
You can use any high shelf eq on your source material ( if your source is a computer this is easy) cause you'll cut the high freq ( much less chance to saturate the source as you cut) and then you can either move away to listen to your music or if you plan a passive bsc circuit you'll have the attenuation needed for your speakers.
I hope this is clearer.
Anyway, what is the outside diameter of the ball you plan to use? We will do the math here.
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Here is one that has some clear (honest) measurements and commentary.
Ikea Bowl Speakers TB W4-657D - Album on Imgur
Regarding this - I could not understand how"You use a high shelf with fc 1khz and attenuate until it sound good/natural to you".
If you look at the 1st graph (6th picture) in the link above, you'll see how the response falls off below 150-200Hz (with a 20cm sphere). If you built something similar, that's where you'd put the high shelf (equalisation) if you wanted to use the speakers full range.
Since you're talking about a sub / satellite system, you could cross over to the subwoofers at about 150Hz, and not worry about attenuation.
The frequency you set the high shelf to depends on the size of the sphere. If you used a 40cm sphere, you could probably set the shelf or crossover to about 75Hz.
Hi Hollowboy,
https://www.diyaudio.com/forums/multi-way/328293-calculations-spherical-enclosure-4.html#post5568386
True Audio TechTopics: Diffraction Loss
I suppose the plots you talk about does already have a bsc applied either by an electronic circuit or built in the natural frequency response ( like in some Markaudio driver (alpair 7 gen1 4")i have which being fullrange does not really produce bass below 80hz closed and typical 300/700hz 'bump' in fr which correspond more or less to bsc of 20cm width faceplate approximately. ). The loss i see in the 150/200hz is more probably related to the box alignement/type choosen, but i may be wrong.
The point is i use the same formula (115/width in meter) with my own threeway which are 54cm wide and the bsc fc IS located around 225hz so i can not see a 20cm diameter box having it at 150hz. (Olson locate it at 190hz for a 24" sphere)
https://www.diyaudio.com/forums/multi-way/328293-calculations-spherical-enclosure-4.html#post5568386
True Audio TechTopics: Diffraction Loss
I suppose the plots you talk about does already have a bsc applied either by an electronic circuit or built in the natural frequency response ( like in some Markaudio driver (alpair 7 gen1 4")i have which being fullrange does not really produce bass below 80hz closed and typical 300/700hz 'bump' in fr which correspond more or less to bsc of 20cm width faceplate approximately. ). The loss i see in the 150/200hz is more probably related to the box alignement/type choosen, but i may be wrong.
The point is i use the same formula (115/width in meter) with my own threeway which are 54cm wide and the bsc fc IS located around 225hz so i can not see a 20cm diameter box having it at 150hz. (Olson locate it at 190hz for a 24" sphere)
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None taken... glad to help.
EDIT: There's perfectly smooth and predictable diffraction cancellation with a sphere. You don't need a simulator to tell you that. It's about a 3-4dB per octave attenuation toward the low freq. If you know the center freq of the baffle step then you can easily flatten it perfectly with a simple filter, active or passive. The center freq is solely determined by the diameter of the sphere.
Another resource for understanding baffle step diffraction is Rod Elliott.
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Good point.
The article doesn't show any bsc, so I guess the bit I underlined is the correct explanation.
It looks like it has a ~5dB droop from 1 to 5kHz.
Tang Band W4-657D | Loudspeaker Database
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