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Old 3rd May 2006, 03:29 PM   #1
jwatts is offline jwatts  United States
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Default 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.
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Old 3rd May 2006, 05:11 PM   #2
sreten is offline sreten  United Kingdom
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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.
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Old 3rd May 2006, 11:04 PM   #3
Ron E is offline Ron E  United States
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Default Re: Port Diameter

Quote:
Originally posted by jwatts
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.
They are usually derived by calculating the air velocity through the port. It depends on which minimum port diameter equations you mean. Post a couple.

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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Old 4th May 2006, 10:06 PM   #4
Notax is offline Notax  Montenegro
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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 bass-reflex enclosures.
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Old 5th May 2006, 03:02 PM   #5
Ron E is offline Ron E  United States
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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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Old 5th May 2006, 04:47 PM   #6
Notax is offline Notax  Montenegro
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Quote:
Originally posted by Ron E
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.
I wrote "corections of T/S". I use some of known formulas, some that I corected, and some of mine formulas or correction coeficients.

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).
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Old 5th May 2006, 05:04 PM   #7
AndrewT is offline AndrewT  Scotland
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Hi,
Jwatts said
Quote:
pressure exerted on the port
none of you have considered pressure.

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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Old 8th May 2006, 11:53 PM   #8
Ron E is offline Ron E  United States
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Quote:
Originally posted by AndrewT
none of you have considered pressure.

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?
I considered pressure in my response.

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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Old 9th May 2006, 12:07 AM   #9
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There's some good stuff in this white paper from the guys behind Soundeasy that makes interesting reading.
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Old 9th May 2006, 01:32 AM   #10
Ron E is offline Ron E  United States
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Quote:
Originally posted by pinkmouse
There's some good stuff in this white paper from the guys behind Soundeasy that makes interesting reading.
Yup. Bohdan's a smart guy. So what? Are you suggesting we all go out and buy soundeasy becasue we cannot possibly cope without it?

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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