Design of rectangular ports for Bass reflex box

[endrek]

Hi,
i've been looking for some information of how to calculate, and desing a bass reflex speaker. But all books i look, they only talk about diameter, only of cilindrical ports.

But what about if i want to design a speaker with a rectangular port? wich formulas do i have to use?? Or is it a cut & try solution only?

how can i calculate, or estimate if you want to put one, two, four or how many ports you want? Or i can put as many as i want aslong as they verify they formulas???

i found this, can anyone verify this is correct? haven't seen it in any of the 3 books i looked

Port Length
The port length required to tune a volume of air to a specific frequency can be calculated by using the following equation: Lv = (23562.5*Dv^2*Np/(Fb^2*Vb))-(k*Dv)

where,
Dv = port diameter (cm)
Fb = tuning frequency (Hz)
Vb = net volume (litres)
Lv = length of each port (cm)
Np = number of ports
k = end correction (normally 0.732)

==================================================
i have this formula from a good book, but for circular ports:

Lv=2340*(dv^2/fb^2*Vab) - 0'73dv

looks like it....but..... still not sure :S :S :S



thanks for your help in advance!!
keep up this cool forum )

[Ron E]

Originally Posted by endrek

Hi,
i've been looking for some information of how to calculate, and desing a bass reflex speaker. But all books i look, they only talk about diameter, only of cilindrical ports.

But what about if i want to design a speaker with a rectangular port? wich formulas do i have to use?? I found...
Lv = (23562.5*Dv^2*Nv/(Fb^2*Vb))-(k*Dv)

where,
Dv = port diameter (cm)
Fb = tuning frequency (Hz)
Vb = net volume (litres)
Lv = length of each port (cm)
Nv = number of vents
k = end correction (normally 0.732)

i [also] have this formula from a good book, but for circular ports:

Lv=2340*(dv^2/fb^2*Vab) - 0'73dv

The second formula is for measurements in mm and volume in liters.
The Nv business is to correct the area for multiple ports, so if you take it out and allow for a factor of 10, for mm vs cm, you will see the formulas are essentially the same except for the constant. I think the correct value for the constant should be about 23610 in the first and 2361 in the second, but you often see values between 2340 and 2350, so there might be a "fudge factor" worked in. Small suggested to use 2350 - so 23500 for the first formula..

I think the first formula has an error in that it doesn't correct for the end correction properly - should read:
Lv = (23500*Dv^2*Nv/(Fb^2*Vb))-(k*Dv*sqrt(Nv))

This is for cylindrical ports. Remember the area of a circle Av=pi*Dv^2, so Dv^2=Av/pi and Dv=sqrt(Av/pi) so to convert the formula for area you get
Lv=(23500*Av*(Nv/pi)/(Fb^2*Vb))-(k*sqrt(Av*Nv/pi))

For a rectangular port, you get Av=Wv*Hv (width times height), so:
Lv=(23500*Wv*Hv*(Nv/pi)/(Fb^2*Vb))-(k*sqrt(Wv*Hv*Nv/pi))

...assuming I didn't make any substitution errors.

Have fun!

[Arty]

The Subwoofer DIY Page - Port Calculations

That should help.
But do notice, cross sectional area will be the same, but since You are using rectangular ports.
The difference is simply, that the rectangular port needs bigger cross sectional area than a cylindrical one. It is couse of different flow of air.
Allso, You should notice that no calculation will ever yield what You get in real life.
In other words, You may do Your math as best as it can be, but when You build it, it will be not realy accurate.
Calculations are just to give a starting point. Suposedly cylindrical pots can be made to be adjustable in lenght with ease.
It has the benefit to be adjusted after building the whole box, so You can set Your desired tuning freqvency.
vent tuning
while this article has its own flaws, it does verifys (correctly) that calulcations and real life are 2 different things.

Usualy the simulation/calculation toosl just give a nice starting point.
Goal is to get the largest possible crossectional area You can fit into the box, get a more or less close tuning freqvency, then mesure What You done and adjust Your port till You get what You where looking for.
The process of mesuring the tuning feqvency is not hard. a simple multimeter can do the job.
As tuning freqvency will have an impedance peak.

Port placement has its own effects too, specialy for the non-cylindrical ports.
They can act as if they where a LOT longer than they are actualy.
That is realised as a lower tuning freqvency then expected.
Good news is, they can be cut down to size with ease, and that is what You need to do in order to get a higher tuning freqvency.

My absolute not scientific approach is simply using the maximal crossectional area regardles if its cylindircal, or not.
Allso, in my calculations value of k = end correction (normally 0.732) is just 0.7
I done that by experience. MAny times I got it closer with 0.7 end correction to real life, many times close enough to simply not worth the effort to trimm it a bit shorter.
-> notice, the k value i use is not at all verifyd by anyone, not even me. it is just my personal practice.

[Brian Steele]

Originally Posted by Ron E

I think the first formula has an error in that it doesn't correct for the end correction properly - should read:
Lv = (23500*Dv^2*Nv/(Fb^2*Vb))-(k*Dv*sqrt(Nv))

That would make the end correction subject to the number of vents being used, rather than just the vent's diameter. I remember reviewing this formula some time ago (years, LOL), and having an end-correction that was independent of the number of vents in use was judged to be more "accurate".

[Brian Steele]

Originally Posted by Arty

vent tuning
while this article has its own flaws, it does verifys (correctly) that calulcations and real life are 2 different things.

I suspect that the formula breaks down as vent volume approaches box volume. But you're correct - the calculated lengths should be considered a starting point, with some trimming likely required to get the target Fb.

[Brian Steele]

Originally Posted by Brian Steele

I suspect that the formula breaks down as vent volume approaches box volume. But you're correct - the calculated lengths should be considered a starting point, with some trimming likely required to get the target Fb.

Further to this, I tried comparing the results of my vent length equation against the predictions of another program that's used a lot here for speaker design - HornResp. I simmed a 80 litre volume that's being tuned to various frequencies with a 140cm^2 vent.

This first table shows the predicted lengths using my vent calculation:

20 Hz - 121.5 cm
30 Hz - 48.6 cm
40 Hz - 23.4 cm
50 Hz - 11.2 cm
60 Hz - 4.8 cm
70 Hz - 0.9 cm


This second table shows the lengths predicted by HornResp

20 Hz - 118.0 cm
30 Hz - 51.6 cm
40 Hz - 27.0 cm
50 Hz - 15.0 cm
60 Hz - 8.8 cm
70 Hz - 5.2 cm


It looks like HornResp is predicting longer vents are required to achieve the same Fb (except for 20 Hz). The difference between the lengths seems to vary from 4.3 cm down to 3.0 cm @ 30 Hz, suggesting that the end-correction factor that HornResp is not only slightly different, but also somewhat frequency-dependent.

Curiously enough, if my equation is predicting vent lengths that are longer than required (the linked site in a previous message suggests just under 20% too long), that means that the vent lengths predicted by HornResp might even more inaccurate...

[Ron E]

Originally Posted by Brian Steele

That would make the end correction subject to the number of vents being used, rather than just the vent's diameter. I remember reviewing this formula some time ago (years, LOL), and having an end-correction that was independent of the number of vents in use was judged to be more "accurate".

Hi Brian,
The theory is that the shape of the vent doesn't matter (or that it is multiple) only the areas, so the correction I posted is more "mathematically correct" than yours.

I seem to remember an old argument on the bass list where this was discussed and the person who posted wrote me later that upon testing he found I was right - in THAT case anyway

In real life, vents are not the ideal creatures envisioned in theory, and in practice the environment near the port makes a difference. Most empirical studies I have seen show lower tuning frequencies than predicted. This makes the formula conservative, in that you can always cut the port shorter, but it is harder to add material....

Note: Troels Gravesen has some port investigations on a site somewhere where he gives results from empirical study. [edit - Ah, I see it is linked above]

Regards,
Ron

[Brian Steele]

Originally Posted by Ron E

Hi Brian,
The theory is that the shape of the vent doesn't matter (or that it is multiple) only the areas, so the correction I posted is more "mathematically correct" than yours.

That was actually the crux of the argument - that the calculated length referred to the length of each vent, not the length of a "summed" vent that consisted of N vents of the same area, and it was therefore incorrect to apply the end correction in the manner your equation suggested.

If I remember the discussion correctly (it WAS a long time ago), it concerned an analysis of JL Audio's suggested approach for vent calculations - see JL Audio - Car Audio Systems. My equation gives results that are in close agreement with JL's for multiple vents.

In any case, the results of the calculations seems to be quite conservative, to the tune of 15~20%, and the vents will likely need to be trimmed a bit to achieve target Fb.

[Ron E]

Originally Posted by Brian Steele

In any case, the results of the calculations seems to be quite conservative, to the tune of 15~20%, and the vents will likely need to be trimmed a bit to achieve target Fb.

The end correction is for the area, though, and not the diameter of a single vent. So regardless of JL's info I would stand by my correction.

Troels results for undamped boxes give approx 19000 for the first constant and 0.57 for the end correction constant if fitted to the same equation. Might be interesting to measure a vented box and see.

--
Ron

[Brian Steele]

Originally Posted by Ron E

Troels results for undamped boxes give approx 19000 for the first constant and 0.57 for the end correction constant if fitted to the same equation. Might be interesting to measure a vented box and see.

Some quick measurements with a vented speaker I have on hand suggest that even that might be conservative, e.g.

Box size = 5.1 litres
Vent = 4.5cm diameter, 9.5 cm long
Measured Fb = 67.8 Hz

My equation:
Calculated L (67.8 Hz) = 16.7 cm

Troels' adjustment
Calculated L (67.8 Hz) = 13.5 cm

The box does have a little bit of damping in it, which might be skewing Fb down a bit.