A few noobie Q's about box design

[david_moechnig]

I just picked up a copy of Vance Dickason's Loudspeaker Design Cookbook 6th Edition and have read almost all of it in the last few days. Today I decided to start using the formulas for vented box design whth various dirvers from the Parts Express catalog and came up with a few questions I would like answered.

1) There are two formulas for minimum port diameter. They both yield vastly different results. I.E. Using a Peerless 850146 10" woofer in a SBB4 alignment (Qts=0.36, Vas=144.4L, fs=22.6 Hz, and Vd=.000297 m3) dvmin= 6.36" or 3.18" Which formula is better? More accurate? Or would taking the average be sufficient? How would you all work this?

2) Say the formula for port diamter yields 6.36"==>6.5" (for round number sake) This is a large port, say I want to make 2 ports with the same area. This would make 2 X 4.6" ports. Now we come to the port length formula which takes into account the port radius. If 2 smaller ports are used do you use their radii or the radius of the single large diameter port to calculate length?

3) Lastly (for now at least), the ports take up internal volume. Does enclosure volume include the air inside the port(s) or would you consider that a solid cylinder and modify you cabinent dimensions (L X W X H) to allow for the volume the port displaces?

[mikee12345]

1)use winisd pro vent speed graph,it will show speed,and is tells you what speed to keep it under <18m/s

2)use winisd pro,it quickly shows you the results of these variables changing.

3) the air in the port is NOT usable volume.As is bracing,etc..

www.linearteam.dk

[david_moechnig]

I guess being an engineering student I was looking more for a formula or a description of how it works. If I could see that then I would understand how the WinISD calculates it and then not have to rely completely on the program. I'm not so interested in the end result rather how it was derived and I can have a better understanding of how everything works. If anyone has formulas please chime in. I do appreciate WinISD and the power it yields but I just want to have a deeper understanding on how everything fits together.

[Ron E]

Asking someone to derive such a thing for you is a tall order. Neither of the cookbook formulas I have seen are accurate.

Better to buy JE Benson's "Theory and Design of Loudspeaker Enclosures", or if your library is well stocked, check out Richard Small's articles from the early 70's. IF you understand LaPlace transforms you will get a lot out of that book, otherwise not.

I derived a simple formula based on desired SPL at Fb (rather than power handling or Vd) that I can post for you, it matches my own software (which plots vent air speed) very well. I'll see if I can find it this evening.....

WinISD pro alpha does not calculate port speed or excursion correctly IIRC, it is off by ~10-20% or so, but it may have been fixed since I tried it.. WinISD beta has a lot more errors than that, and I wouldn't recommend it...

[BillFitzmaurice]

There is no simple answer here. A rule of thumb of using a port area of 1/4 to 1/3 of cone area is usually OK, but what works with a watt or two input that results in a millineter of excursion won't be worth much with 300 watts in and 30 millimeters excursion. WinISD will tell you instantly if the port area is absolutely too small, beyond that it's as much experience as anything else. The best rule to use is to make the port area as large as you can without that resulting an a duct length too long to fit inside of your target box size. WinISD calculates the speed of the air going through the vent, and if that goes 'red' it is high enough to be audible. But how much air is going through the vent is also a product of how far the cone is moving. The more air you plan to move the larger the vent has to be to compensate, or not only will you get port noise but you'll also get power compression of the vent output.

[Dave Jones]

Originally posted by david_moechnig
I guess being an engineering student I was looking more for a formula or a description of how it works. If I could see that then I would understand how the WinISD calculates it and then not have to rely completely on the program. I'm not so interested in the end result rather how it was derived and I can have a better understanding of how everything works. If anyone has formulas please chime in. I do appreciate WinISD and the power it yields but I just want to have a deeper understanding on how everything fits together.

Check out www.diysubwoofers.org . In particular, http://www.diysubwoofers.org/prt/ . That web site has formulas.

Finding the information you are looking for can be maddening. It seems everything you find is either dumbed out or assumes you know a quite a lot already. I've been poking around this stuff for several months now, and I'm just scratching the surface.

Ron E is a guru.

[Ron E]

Hello again,

The classic method for determining port size is the port that results in a velocity of 5% of the speed of sound (0.05 Mach) or less, but this rule is often broken to allow the ports to fit in the box. 5% of the speed of sound is ~17 meters/sec, or about 50 feet per second.

I derived the following equation myself, based on the assumption that all the sound at Fb comes from the port, and have found that it works better than any of the rule of thumb equations out there.

Sp_min=0.24*10^(SPL_max/20)/(Fb*up_max)

Sp_min = minimum area of port in cm^2
Fb = port tuning frequency
SPL_max = max desired SPL at Fb
up_max = desired maximum port velocity in m/s

Note that the equation above gives the port velocity at Fb, and the actual peak in port velocity is just below Fb, but it usually isn't too much higher, perhaps 10%, so you could add a fudge factor....

You must select realistic values to get a useful result. up_max must be less than ~30m/s to get a valid result. The equation is quite sensitive to the SPL_max parameter - reducing by 1dB may reduce area quite a lot. The thing that is missing in this equation above is Xmax - you could very easily use an SPL in the formula that is way more than the driver could realistically handle. Modeling with a decent program to begin with to figure out an accurate SPL to enter is a good idea. Or just put in a value that you think is the loudest you will listen. I think that above 100dB, you probably aren't going to hear any port noise anyway due to masking from all the other frequencies....

For an example, I have a 12" woofer tuned to 30Hz at home and I am using it with a 2-7/8" (7.3cm) diameter port for an area of pi*7.3^2/4 = 42 cm^2

I can rearrange the formula to get an idea of max SPL at Fb for a given area and port velocity.
SPL_max = 20*log(Sp*Fb*up_max/0.24)
Assuming a max velocity of 17 meters/second:
20*log(42*30*17/.24) = 99dB
This is the SPL where port velocity equals up_max.

Once you have settled on a diameter - you may calculate port length with:
Lv=2360*Dv^2/(Fb^2*Vb)-0.73*Dv
Dv,Lv are diameter and length of vent in millimeters and Vb is volume in liters.