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3rd May 2006, 04:29 PM  #1 
diyAudio Member
Join Date: Jan 2004
Location: Erwin, Tennessee

Port Diameter
Does any body know how the minimum port diameter equations are derived. I have derived a formula based on the pressure exerted on the port and it gives good numbers but they are slightly smaller than what is typically used by the norm. Could some tell how the norm is usually derived.

3rd May 2006, 06:11 PM  #2 
diyAudio Member
Join Date: Nov 2003
Location: Brighton UK

Hi,
the minimum port diameters are determined by the SPL capability and the maximum air velocity allowed. Edit : rereading you post seems this is not what you are asking. Possibly you are not considering a ports length is not its effective length. The effective length is somewhat longer depending on dimensions. /sreten. 
4th May 2006, 12:04 AM  #3  
diyAudio Member
Join Date: Jun 2002
Location: USA, MN

Re: Port Diameter
Quote:
While not impossible, I doubt you have come up with a correct formula without knowing how the derivation is performed  but who knows? While the pressure in a box created by a driver does have something to do with the flow through the port and the sound output of the system, there are other things to be considered. Post your formula or derivation and people can pick it apart. I think I have posted my formula here, which gives air velocity at Fb given SPL and tuning frequency and port diameter. Do a search and use it to check your results. My derivation merely assumes that all sound at Fb comes from the port, and treats the port as a rigid piston.
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4th May 2006, 11:06 PM  #4 
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Join Date: Jun 2004
Location: Belgrade

Xc  calculated excursion
k1=1/(Qts+0.68)*0.68+0.28 Xc=k1*srq(Re)*Sd/BL Fb=h*Fs h=0.382/Qts+0.14*Qts Rt=Dt/2=0.501*sqr(Fb*Xc*Sd) Its minimum Dt(Rt) for not to come to situation that air velocity in port is greater than 1/10 of C (speed of sound), or 34 m/s. This is some of my formulas (corections of T/S) for calculations of bassreflex enclosures. 
5th May 2006, 04:02 PM  #5 
diyAudio Member
Join Date: Jun 2002
Location: USA, MN

I'm not sure that's te hway I would caclulate excursion, but apart from your Xc and h business, the formula:
Dmin=0.5*sqrt(Xmax*Sd*Fb) is well known. I played around with it some time ago and (from memory) it doesn't seem to correlate all that well with port air velocity. Perhaps I mixed up the units?? That is why I came up with my own formula, which matches my actual simulations of port velocity. I like being able to specify SPL and port velocity and have it spit out a diameter.
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5th May 2006, 05:47 PM  #6  
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Join Date: Jun 2004
Location: Belgrade

Quote:
Xc is NOT Xmax. Formula for Xc looks simle, but I got it from more complicated calculations with SPL, Sd and other T/S parameters. Xc is calculated real excursion around Fb, and because of that I got near exact result for Rt(Dt) as in simulation program for port and air velocity. Give me few examples (with all T/S parameters). 

5th May 2006, 06:04 PM  #7  
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Join Date: Jul 2004
Location: Scottish Borders

Hi,
Jwatts said Quote:
But, for a vented cabinet, calculating the pressure might be more than a little difficult. Has he been particularly clever in deriving an alternative method of analysis?
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9th May 2006, 12:53 AM  #8  
diyAudio Member
Join Date: Jun 2002
Location: USA, MN

Quote:
Actually the sound power output from either a vented or sealed box is equal to the power required to compress the air in the box, but in a vented box it is more than just diaphragm displacement, there is a resonance going on. If you ignore diaphragm output and assume it all comes from the port  things simplify and you get my relations. Now for Notax. Consider: Fs 22 Hz Qts 0.38 Qes 0.4 Vas 144 Liters Re 2.7 Ohms Dia 24.5 cm Xmax 15 mm Pe_max 300 Watts Le 0 Henrys P_input 90 Watts@8ohms Box parameters Vb 100 Liters Fb 22 Hz You don't define units, so I assume SI. From your relation I seem to get 42mm diameter From the 0.5*sqrt(Vd*Fb) I get 62mm My equation says, for 107dB and 17m/s at Fb you would need a 135mm diameter vent. For 34m/s you would need 0.7 times that. From my box simulator calculations I get 80m/s at 90Watts input with a 62mm diameter port and 170m/s at 90 watts input with a 42mm diameter port. So in my opinion both of these calculations give ports that are too small. Obviously those are linear predictions and port compression would reduce actual velocity. BTW, when I say 90 watts I actually mean the voltage that would cause 90 watts to be dissipated in an 8 ohm resistor. V=sqrt(90*8)
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9th May 2006, 01:07 AM  #9 
diyAudio Moderator Emeritus

There's some good stuff in this white paper from the guys behind Soundeasy that makes interesting reading.
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9th May 2006, 02:32 AM  #10  
diyAudio Member
Join Date: Jun 2002
Location: USA, MN

Quote:
My formula is not a nonlinear port velocity simulation, it is a linear simulation based on T/S acoustic theory  but it is still closer than the other two formulas we have seen here. I modeled with my formula using the woofer and box specs in the article you cite. Mine suggests ~106mm by inputting 104dB and 17 m/s. Both Notax's and the "conventional formula" give ~56mm diameter This particular alignment is one where velocity below Fb is much more than at Fb  If that is taken into account, my full sim software recommends a diameter of 120mm. This port would need to be more than 36cm (14") long. In practice, port design is more an exercise in what will fit, rather than what is technically best.
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