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15th March 2006, 02:13 AM  #1 
diyAudio Member
Join Date: Aug 2002
Location: NY

Minimum Port Diameter
I'm trying to calculate minimum port diameter, and I'm getting different results.
First, in searching around the web, I have found a few different equations. So I'm trying them all to see if one gives me an answer near what I expected. The sub I'm working on this for is the Ascendant Audio 12" Assassin. My first question  what is effective diameter of the cone? Is this the distance measured straight across from where the surround meets the cone? I'm guessing this is between 10 and 10.5" on a 12" speaker (I don't have the sub on hand to measure). Second  what equations do you use? I've tried a few that I've found around the web, and I get different answers with each. Some involve unit conversions, some do not, and I'm sure that's where the problem comes in. Finally, if someone could calculate this and tell me what they get, I'm shooting for 20Hz, Xmax is 15.5mm, and as I said above, I don't know effective cone diameter. Those seem to be the three pieces of information that all the equations use. The most realistic result I'm getting is a minimum of about 5". Other than that, I'm getting results close to 11". Anyone have any insight? Is 5" realistic? I've built a few sealed boxes, but this is the first ported, so I haven't gotten into this before... Thanks in advance. 
15th March 2006, 03:55 AM  #2 
diyAudio Member

There's no way you'll need 11 inches. I would guess a pair of 4 inch flared ports or a singled flared 6 would do the trick.
Did you know that Ascendant has a support forum? http://forum.carstereos.org/forumdisplay.php?f=50 tell 'em we sent you....
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Ports rule! 
15th March 2006, 06:27 AM  #3 
diyAudio Member
Join Date: Nov 2004
Location: Québec, Québec

Even a single 4" dual flared port would be enough. A pair would be better but usually problematic because they are too long.
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15th March 2006, 11:38 AM  #4 
diyAudio Member
Join Date: Aug 2002
Location: NY

Thanks for the responses, but the engineer in me needs to know HOW to calculate this.
I know 11" is a lot, but I can't figure out why I'm getting that as an answer. I suspect the 5" is closer to what it should be. Going to the carstereos.org forum is only going to get an answer to one of my three questions (or none, I may just get guesses from people who have used the sub). 
15th March 2006, 06:39 PM  #5 
diyAudio Member

to the engineer in all of us.....
To know how big your port has to be, you need to model the airspeed in the port. The easiest way to find this is to use a speaker design program. I'm partial to WinISD pro, which gives you a graph of port airspeed at different frequencies. See my short writeup at: http://www.users.bigpond.com/bcolliso/WinISD.htm If your airspeed is too high, you will get "chuffing" from the port. This can be controlled by using flares, but there is still a limit to how fast you can go. I've got some recommendations at: http://www.users.bigpond.com/bcolliso/portflares.htm If you want a small box tuned low, you'll find that the port is very long, leading to problems with "pipe mode" resonance. The way around this is to move to a passive radiator design. I'll have to hand you off to others if you go down that road.... regards Collo
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Ports rule! 
16th March 2006, 08:17 PM  #6 
diyAudio Member
Join Date: Feb 2004
Location: Stockholm

As you may know the first thing to make right is the tuning of the port, which is given by wh=c*sqrt(S/(LV)). Thus a given box volume tells us that thew ratio between the crosssectional area S and the effective length L must be
S/L=(wh/c)^2*V So, we are free to choose S and calculate L or the other way around, for a given wh. The choice is the engineer's. It is a balance between mainly port overloading and pipe resonances in the tube. The air velocity is a major factor determining the tendency to overload. The way to find reasonable port dimensions is usually to simulate. If you find an equation for the port size with respect to overload it is almost certainly based on some sort of rule of thumb. While such equations may seem exact, ports still overload gradually, so the equations can be expected to give varying results depending on the grounds they are based on. Another comment on port overloading. If a large crosssectional area is needed, it is better to split it in several ports than a single large one. In a large tube, turbulence starts at a lower flow rate. Also, a slit are less inclined to give turbulent flow than a circular port, if the slit has a high width/height ratio. There is a limit in the other end too, dimensions shoul not be smaller than a few centimetres. You might find old postings by me on this forum stating the contrary, but I have changed my views on this. And yes, flared ends are good. There should be a flare also in the inner end of the port, and possibly even a baffle. Otherwise strange high level effects can occur; there will be a DC flow component in the port due to the assymetry, and this will lead to a DC pressure inside the box, forcing the membrane out of its equilibrium position. 
16th March 2006, 11:04 PM  #7 
diyAudio Member
Join Date: Jan 2005
Location: Rotterdam, NL

If you need help with WinISD Pro, this guide might help (there is also a guide in the diy wiki):
http://www.speakerplans.com/forum/fo...TID=1314&PN=10 @Collo: Nice site! Especially the parts on making flares/ PVC sheets (gotta find an excuse to use that). Wkr Johan
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17th March 2006, 12:09 PM  #8 
diyAudio Member
Join Date: Aug 2002
Location: NY

Thanks for the information.
I'm doing ok with WinISD, I think. At least for basic modeling, the builtin help seems to be very good. Collo, Nice website. I liked the case study. I found the air velocity in WinISD, and graphed it, but I'm not sure exactly what I'm looking at. I've been looking at your projects and I noticed you are designing for home theater, which is my application as well. I was planning on tuning at 20Hz. Does this sound reasonable for home theater? Should I try to go lower? I'm also trying to go for as flat as possible... Have you found that peaks in certain places work well for home theater? Svante, It sounds like what you're saying is I should not worry so much about the calculations. I should focus on the simulation, and take a look at the air velocities chart. Ok, so I have my graph of "rear port  air velocity". It shows a peak of about 5.4 ft/s at around 19 Hz. What does this mean for me? That's with (2) 4" diameter ports. What kind of air velocity is too high? 
17th March 2006, 01:18 PM  #9 
diyAudio Member
Join Date: Jun 2002
Location: USA, MN

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 55 feet per second.
I derived the following equation 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 27/8" (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.
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17th March 2006, 08:15 PM  #10 
diyAudio Member
Join Date: Aug 2002
Location: NY

Reading that made me realize I was looking at my plots with a signal input of 1W.
So, I adjusted it to 100W, which gives me an SPL of about 108dB at the frequencies it matters. I went back to my plots and 2 4" ports show a maximum air velocity of about 54 ft/s. That gives me a total cross sectional area of 25.132 in^2. Or, 2 5cm ports, velocity of 16.5 m/s, cross sectional area of 157 cm^2. The result is an 18" long port, which is something I could do. Ron E, I will throw the numbers in some of your equations later this evening. Thanks 
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