Minimum Port Diameter

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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.
 
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).
 
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/port-flares.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
 
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 cross-sectional 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 cross-sectional 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.
 
Thanks for the information.

I'm doing ok with WinISD, I think. At least for basic modeling, the built-in 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?
 
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 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.
 
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
 
By choosing an input level that gave me an output of 108dB (a lot of volume), am I going to notice any negative affect when I am listening with the volume lower? With an output of, say, 90dB?

Or is more that if it gets louder than 108dB, I will start to hear noise?

In which case, maybe I should go for something higher...
 
Narcisse91 - When you tune for 20hz, it usually costs you SPL in the 25 - 35hz range.
If WinISD is telling you 108dB, I would suggest that you don't have enough to squander.

Tuning a bit higher, say 25 -27hz will give you a bit more punch for movies in the range where most of the content lives.

Tuning higher also moves the peak in port velocity to a higher frequency, where your port works better.

17 m/s is fine provided you flare both ends - the Precision ports have a 30mm flare, which is good up to 17m/sec above 26hz.

Listening at levels lower than the 108dB you modelled, won't have any negative effects.

RonE - that's a handy formula - a lot simpler than doing a full workup in WinISD if you only need to answer the one question!

Rademakers - I'm glad you liked the site. Heating the ends of PVC pipe to get up to 25mm flares works very well.

Unfortunately I can't report the same success with the flat sheet idea. I did some more work recently and found that the sheet rips before it can be stretched enough to make a decent flare.

I think DIY large flares are probably restricted to fibreglass over a mold. (maybe my next project)

regards
Collo
 
I have my plots on a different computer, so I can't quote exact numbers, but the farthest anything dipped below my peak output was less than -2dB, until you got below 20Hz. Think that will be too much of a dip? I can't remember what total output is at peak power, I just chose 100W because I think 108dB is a pretty reasonable max output before I turn it down. I think at full power, it was closer to 120dB, which is pretty loud.

However, if that 2dB dip around 25 to 30 Hz (you're right, it is lower there) is going to hurt me, instead of tuning higher, I think I would rather go with a different sub. I modelled the new Dayton hifi 12" was showing me a very flat curve down to 20Hz, in a much smaller encloser (almost half the size).
 
Well, for a subwoofer, you can allow a rolloff to take into account the room gain.

I use a -3 dB per octave of rolloff to achieve a flat response in room. Some people allow more.

For example, I did a subwoofer that looked like this :
-0 dB at 80 Hz
-2 dB at 40 Hz
-5 dB at 20 Hz

It's near -3 dB per octave and in a room it looked like this :
 

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Old thread I know but ...
I see some constants in the equations offered and was wondering if anyone could tell me where they come from. :)

"Sp_min=0.24*10^(SPL_max/20)/(Fb*up_max)"
The "0.24" times 10 to the power of Y looks like a lovely number.
Any idea where it came from?
and the "20" in "SPL_max/20" is that the 5% of Mach that he was talking about?

Lv=2360*Dv^2/(Fb^2*Vb)-0.73*Dv
The "0.73" seems to be another nice number.
I note that Brian Steele uses "0.732" in his spreadsheet but I was just curious as to where they got it. :)
Now in the spreadsheet Brian is using 23562.5 instead of 2360 but if you convert from cm to mm they are essentially the same number.
Anyone know what that number represents?
 
Old thread I know but ...
I see some constants in the equations offered and was wondering if anyone could tell me where they come from. :)

"Sp_min=0.24*10^(SPL_max/20)/(Fb*up_max)"
The "0.24" times 10 to the power of Y looks like a lovely number.
Any idea where it came from?
and the "20" in "SPL_max/20" is that the 5% of Mach that he was talking about?

Lv=2360*Dv^2/(Fb^2*Vb)-0.73*Dv
The "0.73" seems to be another nice number.
I note that Brian Steele uses "0.732" in his spreadsheet but I was just curious as to where they got it. :)
Now in the spreadsheet Brian is using 23562.5 instead of 2360 but if you convert from cm to mm they are essentially the same number.
Anyone know what that number represents?

IIRC, it represents rho-naught*c^2

Air density times speed of sound squared, in appropriate units. I think, lol.
 
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