Curved Cabinet Volume calculation?

[Hdale85]

I'm working up a cabinet design for a new speaker and I want to do curved sides. I don't think this has been brought up before but how do you figure the volume of the cabinet? Are there any CAD programs that will tell me the volume inside something that I've drawn out? I don't think Sketchup will do it. I know I want a 48" tall cabinet that is 8" wide. Not sure about depth but I know I want it to be a relatively sharp curve so the rear baffle will be quite a bit smaller then the front. Possibly do something like the new Klipsch's

[impala454]

Might be a longshot but did you ever take any calculus? If so you can just make up a fairly simple equation that would describe the curve, then use an integral to calculate the area of the cross section. If you have some exact measurements I can help.

[Hdale85]

Nope no calculus but I'll gladly take you up on your offer. Give me a little while and I'll boot into windows and install an app and draw some stuff up and get some dimensions.

[impala454]

If your app will give you the equation for the curve your'e using that'd be great, otherwise if you can get a top view with detailed dimensions and two axis that should work too.

[Hdale85]

You mean like a radius? I think Solidworks does that not sure about sketchup.

[impala454]

well if it's a semicircle that's mega easy to calculate. lets just see what kinda drawing you can post up. would be easiest if you can put the face of the speaker on the x-axis, and have the y or z-axis go straight through the center of the curve.

[Hdale85]

Yeah I'll try that I'm pretty sure I can get you enough information though. Going to boot up into windows now.

[Deward Hastings]

Two simple old techniques that probably give answers good enough for speaker use are:

Draw the curved profile on graph paper and count the squares. Accuracy depends on the granularity, but the approximation converges very quickly. You can get the bounds by first counting "entirely in" and then counting "in and not entirely out".

Or, if you have a decent scale, cut a piece of cardboard into a rectangle of the same front and depth dimensions, and weigh it. Next, cut it to your desired curve and weigh it again. The ratio of the weights is the same as the ratio of the areas.

The new way is to draw the curve in your favorite CAD program and click on "calculate enclosed area" (if your favorite CAD program has that function). It will probably be using some version of method one, above.

[Hdale85]

Not sure if solidworks does that. I have to find my CD first though and then install it which will take like........a while :B.

[David_D]

Hi Doug,
If you have a volume you are trying to hit. Solidworks will help. It does area calulations on the fly. I could make up a quick model if your interested.

[Hdale85]

Ok I'll figure it out here in a few I found my disc this morning and just have to install it.

[David_D]

Hey Doug,
Are you going for a translam or slit & bent walls?

[Hdale85]

Slit and bent walls. Forget all that trans slam kind of silly since I'm just going to veneer over it Either that or I'll use like 1/4" bendy board. But more then likely it will be a couple layers of 1/2" MDF with slits cut in it.

Well I finally got Solidworks installed but I have some errands to run now so when I get back I'll start working on this.

[Rolex]

If you draw your cross section in autocad, that will generate the area for you. Then just multiply by height to get your volume. That is what I do.. I did take calculus (4 semesters) but autocad is WAY easier!

[impala454]

well if it just *happened* to have a pretty quadratic shape (which it looks like most of these do), it'd be easy

but yeah... software would still be easier

[Hdale85]

Well one of the problems is that I want the top to slope down like it does on the Klipsch's as well.

[Saurav]

That's not too hard, I think. But this isn't easy to describe in words

The area of a right angled triangle is 1/2 the area of the equivalent rectangle. Imagine you didn't have that slanted top surface, but it was horizontal. Now, looking at the cabinet from the side, draw a small rectangle that matches your intended slanted top, i.e. the line for the slanted top would be a diagonal for this rectangle.

The volume of this portion is the cross section area, times the height of that portion, so if you slant the top you've cut the volume of that segment in half.

Something like this, looking from the side...

.......
|\    .
| \   .
|  \  .
|   \ .
|____\.
|     |
|     |
|     |

The diagonal line is your slanted top. The dotted portion shows the volume you would have had without the slanted top. So the dotted portion is what you're removing, which will be half the volume of the portion enclosed in the rectangle.

Hope that made some sense

[impala454]

This wouldn't work with the curved cabinet. The cutout piece would not be half the volume of the remaining piece. That math would work if the cabinet were completely round or completely square, but only half of the cabinet is rounded. The sliced off piece would be less than half the remaining piece. Think of if you sliced through a mailbox. The curved section has less volume to begin with than the squared section.

The math of adding in the slant gets much more complex (yay differential equations), but I'd imagine if your software will calculate volume it should be able to do this no problem.

[Saurav]

LOL. You're right of course.

[David_D]

Well one of the problems is that I want the top to slope down like it does on the Klipsch's as well.

As a machine designer, I find myself trying to figure how one might cut, bevel, mount the top to the sides. Not an easy deal, compound angles with degenerating curves to boot. If you had the tops CNC cut with all the compound bevels, then one could inset the top into the sides but then how to trim it. Maybe if the whole enclosure minus the top was cut with one swipe on an industrial miter saw then the tops set inside & glued flush.
Not something for the faint of heart.
This all sounds very intriging. I would love to help.
I forsee lots of bondo in your future, Doug.

[JoshK]

I don't think you need diff eq for the slanted top problem, but I'd have to think about it some. I think you can do it with an extra integral. However, there is also an easy numerical solution that works well with computers.

Take your object and fit a box around it so that the entire object is inside the box. Note the height h, width w, and length l.
Generate n times 3 uniformly distributed (0,1) random variables.
Multiply the n x 3 sets of random variables by (h,w,l) so that the r.v.'s are now distributed along intervals (0,h), (0,w) and (0,l). Have your proceedure count have many of the n points (h_i, w_i, l_i) are inside your object.
Multiply the resulting proportion of the n points by the volume h*w*l, the answer is a numerical approximation of the volume of your object. As you let n grow sufficiently large the approximation converges to your theoretical volume.

The above proceedure sounds much more complicate than it really is. I'd probably use visual basic in excel to do it if I didn't have matlab or some other software.

[Hdale85]

Having issues drawing this out. I was drawing a cross brace and then it dawned on me that I drew it out to the dimensions of the box that I want. There for it is 8" wide at the front and 4" wide at the back which with adding on the sides and what not would bring it to something like 9" wide in the front and 5" wide in the back roughly. Must still be a bit tired lol have to start over it seems. Maybe I should just draw up the whole cabinet.

[Hdale85]

Anyone know how to get the part drawing sort of layout in solidworks? To where it shows top side and all the dimensions and what not? Been quite a while since I played with this.... and even then I don't have much training in it . My friend bought it and ended up using something else he got it with some sort of education discount but anyways he gave it to me.

[David_D]

Anyone know how to get the part drawing sort of layout in solidworks? To where it shows top side and all the dimensions and what not? Been quite a while since I played with this.... and even then I don't have much training in it . My friend bought it and ended up using something else he got it with some sort of education discount but anyways he gave it to me.

That's what I was offering to you.
Send me some dims (ones I can and cannot change), angle of top & estimated volume, and I'll work you up something.

[Hdale85]

Ah ok well I drew up this is Sketchup but I can't get the top parts to come off without the whole side coming off....



Basically what I'm looking for is 49.5" high in the front 39.5" high in the back 8" wide in the front 4" wide in the back. front top and bottom will be 1.5" thick rest is 3/4" thick including the braces. The woofer area needs to be at least 55L more is better up to about 80L (not trying to get this high lol) I was thinking about 17" deep maybe 18" at the most. The midrange chamber up top needs like 10L maybe? I'm not completely sure I PM'd my friend about it but something like that. It's for 2 W4's. The only thing thats really changeable is the depth because of the size of a sheet of MDF.

[Hdale85]

I just can't get solid works to do what I want. What else do you guys use? I think I tried autocad and it was harder to use then Solidworks. I might have to give it a try though see if it works better. Somethings gotta work the way I want.

[Hdale85]

Well I'm drawing it all up as parts now, I just need to figure out the angle that the top and bottom need to be cut at to get the top slanted like that. I like the look I did in that picture which had the front 49.5" tall and the back 39.5" tall which is 10" shorter.

[David_D]

Sorry Doug,
I got a plastic chip in my eye and just got back from the ER.
I got your dims. I'll work something up & send it along.
It will take a day or two.

[Hdale85]

Plastic chip yikes! Did it scratch at all? What did the chip come from? In case you want to cut out the driver holes the drivers being used are in an MTMWWWW configuration and will use W4-1337SA mids Hivi D6.8 woofers and Vifa XT25 tweeter the new double magnet one. I'm still working with solid works as well just figuring stuff out again but I'm doing pretty good.

[David_D]

I was maching a block of polypropylene for a custom part on a machine I am building. My eyes are getting a little bad with age and I have a tendency to peer over the tops of my lenses. I little sliver flew out of the milling machine and into my eye.
No worrys, all better now. My own fault, I need to break out the goggles. Believe me my rear hurts more from the new hole my wife tore into me.

[Hdale85]

Haha...they can do that David do you have any idea on what that angle is? Sketchup doesn't tell me much of anything and I'm trying to draw out parts in sketchup.

[Hdale85]

Ok Jed just told me the midrange part should be around 11.38L

[Jed]

Dougie, those cabinets are going to look amazing. Looks like a pain to build though.

[Hdale85]

Nah it won't be hard to build but man drawing them out in CAD is a real pain.

[Hdale85]

Well I got the baffle drawn out and everything. I think I finally got the angle right for the top, we'll find out when I draw the other pieces and put them together. Unfortunately it appears I'll have to cut the woofer holes after the cabinet is together. Here are 2 pics of the baffle though I'll work on this more tomorrow and maybe can have a completed cabinet.

[Hdale85]

Ok last update of the night! I got some of it assembled in Solidworks. The angle on the rear baffle is wrong it seems so have to work on that. Looks like I may have my old speakers sold so these might be moving along very quickly here. Anyways here's what I got.

[Brian Bunge]

Doug,

That looks great! Why do you think you'll have to cut the driver holes after the baffle is mounted? It doesn't look like the recess goes past the edges of the baffle's width. Or is it so close that it'll be paper thin? If so, I'd suggest cutting the through holes, cutting the relief on the backs, and then using a rabbeting bit to cut the recesses after the sides are on.

BTW, there's no hole in the back for a binding post plate!

[David_D]

OK Doug,
Based on your measurements, I drew a Raw External Shape. (Doug-001)
Then I removed the appropiate wall thickness as you spec'd. What is left is the Max Internal Volume. (Doug-002) Last I drew up a quick Internal Brace. (Doug-003) Which of course will have to be subtracted from Max Internal Volume.
I hope the drawings make sense.
I did not hunt down your driver and checked thier displacment, nor your ports.
It looks like you are getting the swing of Solidworks. If I can help on that front, I have been using SW for about 3 yrs.

[David_D]

OK.
Too early in the morning.
I just noticed that I had your angled top in the wrong direction.
Attached are all update drawings. Disregard previous ones.

[Hdale85]

I don't quite understand. Is the second picture the internal volume? I'm guessing thats the case. 87 liters means after the braces and the mid section I should have something like 60L or maybe a bit more.

[Hdale85]

Well Brian if you look at this picture:



There is very little space something like .13" it might be enough but I'm not sure.

[Hdale85]

Hey David just another question On the internal width of the front and rear baffle wouldn't it be the same as the brace? On this image it says 3.30 and 7.06 Just curious how it would be larger? Probably something I'm just not thinking about.

[David_D]

I don't quite understand. Is the second picture the internal volume? I'm guessing thats the case. 87 liters means after the braces and the mid section I should have something like 60L or maybe a bit more.

Hi Doug,
Yes, Solidworks wont measure negative space, so the second pic is a solid rendering of the Max Internal Volume (87.133 L)
YMWV on the design of any internal bracing. But, the I sketched up is .876 L
Also, to answer your question on the dimention issue. Look at the last set of drawings posted. It is corrected there.

[Hdale85]

Ok so I'm guessing you have it so the baffle goes on last then? Still doesn't seem quite right..... the sides are 3/4" thick each thats 1.5" thats why I have my brace as 2.5" for the rear then the front is 1.5" thick and the rear is 3/4" thick that would bring the brace down to 14.75. Maybe I'm just guessing all this wrong or something? But thats what I get out of it. What do you think about that slant do you think its to steep? I guess it looks pretty good just can't decide lol. Anyways thanks for those they help a lot! How do you get tech stuff like that from assemblies you make?


Edit just realized this didn't make much sense. My calculations are like your first brace drawing which is 2.5" rear width and then 6.5" front width and 14.75" deep for the braces.

[David_D]

Ok so I'm guessing you have it so the baffle goes on last then? Still doesn't seem quite right..... the sides are 3/4" thick each thats 1.5" thats why I have my brace as 2.5" for the rear then the front is 1.5" thick and the rear is 3/4" thick that would bring the brace down to 14.75. Maybe I'm just guessing all this wrong or something? But thats what I get out of it. What do you think about that slant do you think its to steep? I guess it looks pretty good just can't decide lol. Anyways thanks for those they help a lot! How do you get tech stuff like that from assemblies you make?


Edit just realized this didn't make much sense. My calculations are like your first brace drawing which is 2.5" rear width and then 6.5" front width and 14.75" deep for the braces.

Whoops,
I just noticed that you did call out a 1.5" baffle, my bad.
I will re-design later. Unfortunatly, I have to concentrate on work and get this machine I'm building futher along. I work on this after 5pm. But it does look like you are in the ball park for the volume you were shooting for. Next time I will give you the volume in the slanted area and the crosssectional area of the lower portion. From there, practically anything can worked out on paper.