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How to estimate flared port's effective radiating surface

dominikz

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The question in the title relates to quasi-anechoic loudspeaker measurements where we do a gated far-field HF measurement, and splice it with nearfield LF measurements of woofers and ports. I've mentioned this already in another thread, but thought it's maybe better suited to a dedicated discussion.

To build the loudspeaker LF response we first need to scale measured frequency responses based on the ratio of effective radiating surfaces or each radiating element (be it a woofer or a port).
This is actually where my question ties in. If the port is a simple cylinder, it is easy to calculate the radiating area. However, often "flared" ports are used, and sometimes the difference in diameter between extremes of the flare can be quite large - e.g. on Revel M16 the narrow part of the port ("throat") is 4,5cm in diameter whereas the widest part of the port ("mouth") is 7,5cm in diameter.

So my question is which port diameter do we use as an 'effective' radiating diameter: port 'throat', 'mouth' or something in between?

The measurements I did so far seem to show fairly good agreement with existing measurements if I use the port 'mouth' diameter when calculating the port radiating surface, but my sample size is extremely small (two speakers so far) and I would love to see some references and/or guidelines for this.

Hope some of you with more experience can provide guidance to this loudspeaker-measuring rookie :) Thanks!
 

Justin Zazzi

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Great question! I'm curious too. I think you're right that the effective radiating surface might be larger than the surface area of the pipe. I wonder if you could apply a correction to the surface area, similar to how you apply an end correction to the effective length of the port due to flush mount, unbaffled, flared, etc.
 

MusicNBeer

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Try measuring with the mic at the inner side of the flare. See if the SPL is higher by a factor of the flare outside to inside diameters. Interesting question.
 

napilopez

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The question in the title relates to quasi-anechoic loudspeaker measurements where we do a gated far-field HF measurement, and splice it with nearfield LF measurements of woofers and ports. I've mentioned this already in another thread, but thought it's maybe better suited to a dedicated discussion.

To build the loudspeaker LF response we first need to scale measured frequency responses based on the ratio of effective radiating surfaces or each radiating element (be it a woofer or a port).
This is actually where my question ties in. If the port is a simple cylinder, it is easy to calculate the radiating area. However, often "flared" ports are used, and sometimes the difference in diameter between extremes of the flare can be quite large - e.g. on Revel M16 the narrow part of the port ("throat") is 4,5cm in diameter whereas the widest part of the port ("mouth") is 7,5cm in diameter.

So my question is which port diameter do we use as an 'effective' radiating diameter: port 'throat', 'mouth' or something in between?

The measurements I did so far seem to show fairly good agreement with existing measurements if I use the port 'mouth' diameter when calculating the port radiating surface, but my sample size is extremely small (two speakers so far) and I would love to see some references and/or guidelines for this.

Hope some of you with more experience can provide guidance to this loudspeaker-measuring rookie :) Thanks!

I struggled with this as well when I started making measurements. I got the best results using the end of the throat, right before the flare begins. As long as you are scaling the SPL right for the area(using the diameter of the throat), you should be okay.

I also wouldn't worry about it too much. We've seen slightly different results from anechoic chambers vs the Klippel NFS vs ground plane at times here, so don't stress too much over it.

A quick and dirty trick for SPL scaling, btw, is to simply to scale the port measurement until its tail matches the woofer below 20hz. It's usually on the money, or pretty close to it
 

restorer-john

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I struggled with this as well when I started making measurements. I got the best results using the end of the throat, right before the flare begins. As long as you are scaling the SPL right for the area(using the diameter of the throat), you should be okay.

I also wouldn't worry about it too much. We've seen slightly different results from anechoic chambers vs the Klippel NFS vs ground plane at times here, so don't stress too much over it.

A quick and dirty trick for SPL scaling, btw, is to simply to scale the port measurement until its tail matches the woofer below 20hz. It's usually on the money, or pretty close to it

Just out of interest, how would you go about port measurements on my current pair of main speakers I am using, the Jamo 507a?

Layout cutaway:
1606355875729.png


Twin internal 6.5" woofers operating push-pull into a sealed and a reflex compartment, exiting from the rear through a large diameter, flared port. They are rated to 150Hz and cover one octave from 40-115Hz. They are intended to be placed near to the rear wall. How do you account for speakers such as these where an quasi anechoic or free field type test on the midbass/midranges (2x4") is so far away from the port and the port is producing all the deep bass, not just augmented like a normal relex port?

I would see these as a nightmare for the Klippel.

The midbass drivers run from 150Hz up to 3KHz where the 25mm dome tweeter takes over.
 
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dominikz

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Thanks to everyone for your inputs, much appreciated!

@napilopez That's interesting, I seem to be getting best agreement with existing measurements if I use port mouth diameter rather than port throat diameter to calculate the SPL scaling. Here's some examples:
Revel M16 - port scaling vs LF response.png

As you can see, here I get very close match if I use the trick to match port and woofer <20Hz response (great tip BTW, thanks a lot!) vs if I use port mouth diameter to calculate the SPL scaling - and both match ASR measurement nicely. Note that Revel M16 has a very large flare, so differences are quite large depending on what diameter you choose to calculate the scaling.
Another example:
JBL LSR305 - port scaling vs LF response.png

Here it is not so clear-cut for a few reasons: 1) vendor spin is digitized from very low quality image, 2) port flare is much smaller than on the Revels (port throat dia ~3.4cm, port mouth dia ~6cm). Anyway, again port mouth has reasonable agreement to the vendor spin, as does the flare mid-point diameter. Here I couldn't use the <20Hz match trick as I didn't measure this speaker that low :(

Edit: Note that in the above two diagrams I haven't applied baffle step correction to the nearfield LF measurement - that is why there is a mismatch to full-range measurements >~100Hz. Please disregard that.

@MusicNBeer That's a good tip, I'll try that too when I catch some time to remeasure.

@Justin Zazzi If such a correction factor existed, that would be ideal! I haven't found anything so far, unfortunately.

@Wombat Thanks for the links! Though it seems to me these focus on calculating port properties when designing a vented box - I'm definitely lacking some knowledge, but I don't see how to apply this to find the port effective radiating diameter for purpose of nearfield measurements of a finished loudspeaker. If you have some ideas any help is much appreciated!
 
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Wombat

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The main characteristic of ports is volume of port relative to enclosure volume(Hemholtz). Length to cross section is important. End shape/termination configuration is employed to reduce air-to-air discontinuities which produce distortion. There is some interaction. Flared radiating surface area is not so important as such.

The WWW has practical sites with rule-of-thumb guidelines. Homework time, I guess.

After much research, I used standard port termination on my 14 cu.ft. BR enclosures because I was not constrained by space constraints and could have low pressure ports.

I can't condense my past research into a thread post or two specifically related to a wide range of cabinet choices, thus my previous post contents.
 
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andreasmaaan

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Hope some of you with more experience can provide guidance to this loudspeaker-measuring rookie :) Thanks!

That's a very interesting question :) I don't know if there's a straightforward or general answer.

According to the original Keele paper:
For distances from the piston less than 0.75a^2/L, plane waves are radiated which are contained essentially within a cylinder of diameter 2a. For distances beyond 2a^2/L approximately spherical divergence is found to hold, where the pressure falls inversely as the
distance [increases].

Note that in the above quote, a = piston radius and L = wavelength.

If that's to be taken at face value, depending on the depth of the flare, you may still be within 0.75a^2/L of the cylindrical section, suggesting the internal diameter is the correct one to base the calculation on.

Having said that, your experimental results suggest the mid-point or somewhere between the mid-point and the outer diameter best tracks the ASR measurements.

FWIW, Keele's formulae are based on the assumption that the radiating surface is a rigid circular piston. I know that assumption doesn't hold true with regard to velocity of air exiting a port; I guess it probably doesn't hold true with regard to pressure, either...
 
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dominikz

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That's a very interesting question :) I don't know if there's a straightforward or general answer.

According to the original Keele paper:


Note that in the above quote, a = piston radius and L = wavelength.

If that's to be taken at face value, depending on the depth of the flare, you may still be within 0.75a^2/L of the cylindrical section, suggesting the internal diameter is the correct one to base the calculation on.

Having said that, your experimental results suggest the mid-point or somewhere between the mid-point and the outer diameter best tracks the ASR measurements.

FWIW, Keele's formulae are based on the assumption that the radiating surface is a rigid circular piston. I know that assumption doesn't hold true with regard to velocity of air exiting a port; I guess it probably doesn't hold true with regard to pressure, either...

Thanks a lot! And I agree - it seems to me flaring the port wouldn't make much functional sense in the first place if the air from the port throat acted as a piston with port throat diameter when captured at the port mouth.

I think the next experiment I'll do will be to measure port output at port throat, mouth and in-between them - and then to see where I get when scaling the SPL based on port diameter at the exact mic position. Along the lines of the proposal from @MusicNBeer. Then I will also compare how that matches with visually matching the <20Hz roll-off.

Hopefully it will provide a bit more insight :)
 

andreasmaaan

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Thanks a lot! And I agree - it seems to me flaring the port wouldn't make much functional sense in the first place if the air from the port throat acted as a piston with port throat diameter when captured at the port mouth.

Actually, the flare does begin to effectively expand the diameter of the port at high velocities. You can see this experimentally where, as you measure the output of a flared port at increasing SPLs, the port tuning begins to rise.

This was demonstrated here, for example. (Let me know if you can't get behind that paywall, it's an incredible paper if you're interested in ports.)

No flare:

1606470568343.png


Massive flare:

1606470607413.png


The paper was interested in compression, so that's the main effect you see there, but you can also see how the flared port's tuning rises more steeply with SPL compared with the non-flared port's.

I think the next experiment I'll do will be to measure port output at port throat, mouth and in-between them - and then to see where I get when scaling the SPL based on port diameter at the exact mic position. Along the lines of the proposal from @MusicNBeer. Then I will also compare how that matches with visually matching the <20Hz roll-off.

Sounds good :)
 

napilopez

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Thanks to everyone for your inputs, much appreciated!

@napilopez That's interesting, I seem to be getting best agreement with existing measurements if I use port mouth diameter rather than port throat diameter to calculate the SPL scaling. Here's some examples:
View attachment 95928
As you can see, here I get very close match if I use the trick to match port and woofer <20Hz response (great tip BTW, thanks a lot!) vs if I use port mouth diameter to calculate the SPL scaling - and both match ASR measurement nicely. Note that Revel M16 has a very large flare, so differences are quite large depending on what diameter you choose to calculate the scaling.
Another example:
View attachment 95929
Here it is not so clear-cut for a few reasons: 1) vendor spin is digitized from very low quality image, 2) port flare is much smaller than on the Revels (port throat dia ~3.4cm, port mouth dia ~6cm). Anyway, again port mouth has reasonable agreement to the vendor spin, as does the flare mid-point diameter. Here I couldn't use the <20Hz match trick as I didn't measure this speaker that low :(

Edit: Note that in the above two diagrams I haven't applied baffle step correction to the nearfield LF measurement - that is why there is a mismatch to full-range measurements >~100Hz. Please disregard that.

@MusicNBeer That's a good tip, I'll try that too when I catch some time to remeasure.

@Justin Zazzi If such a correction factor existed, that would be ideal! I haven't found anything so far, unfortunately.

@Wombat Thanks for the links! Though it seems to me these focus on calculating port properties when designing a vented box - I'm definitely lacking some knowledge, but I don't see how to apply this to find the port effective radiating diameter for purpose of nearfield measurements of a finished loudspeaker. If you have some ideas any help is much appreciated!

Thanks for looking into this! It definitely merits some further investigation.

Just to be clear, in the comparison you posted, is each port measurement a different measurement, or are you scaling the same measurement to different SPL levels? It should be the former.

My testing led me to use the throat, but I don't have those measurements in any organized fashion, nor was I being especially rigorous as this was when I was just starting out. I do think that simply lining up the port and woofer response at very low frequencies gives "good" enough results, as you seem to have found here! But as you likely do, I have that itch for doing things a little more mathematically.

I do recall a Klippel paper (PDF) that says to measure ports at the baffle, but it's not clear if it gives any consideration to flared ports at all.

It's been surprisingly difficult to get a definitive answer, which is why I've been hoping to compare my results to ground plane measurements, but it's unfortunately rather difficult to find a place in the city I can bring my speakers for an extended period of time and have a good 10 meters away from non-floor boundaries.

I believe @DDF uses nearfield summations, perhaps he has some insight? @ctrl I don't know how you do bass but tagging you here too =] Either of you have any insight?
 
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dominikz

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Just to be clear, in the comparison you posted, is each port measurement a different measurement, or are you scaling the same measurement to different SPL levels? It should be the former.
The above comparison is a single measurement of port output, measured at center of port, flush with the baffle. This response is then scaled as calculated with different values of port diameter ("throat", "mouth" and in-between) when summing with the driver nearfield response - to illustrate how different the result can be depending on which diameter is chosen.
Next experiment I'll do will be to take multiple measurement of port response at different point in the flare (as described in my previous post) - I'll report back once I find the time to do it.

It's been surprisingly difficult to get a definitive answer, which is why I've been hoping to compare my results to ground plane measurements, but it's unfortunately rather difficult to find a place in the city I can bring my speakers for an extended period of time and have a good 10 meters away from non-floor boundaries.
Yes, seems like a non-trivial issue indeed. I was also thinking about trying the ground-plane method to compare with, but am faced with similar challenges as you to make that happen :)
Thanks for your comments!
 

napilopez

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The above comparison is a single measurement of port output, measured at center of port, flush with the baffle. This response is then scaled as calculated with different values of port diameter ("throat", "mouth" and in-between) when summing with the driver nearfield response - to illustrate how different the result can be depending on which diameter is chosen.
Next experiment I'll do will be to take multiple measurement of port response at different point in the flare (as described in my previous post) - I'll report back once I find the time to do it.


Yes, seems like a non-trivial issue indeed. I was also thinking about trying the ground-plane method to compare with, but am faced with similar challenges as you to make that happen :)
Thanks for your comments!

Ah, understood! SPL level will likely vary with distance from the throat, so that alone might account for the discrepancies you are seeing.

I'm actually in the process of measuring the KEF LS50W Meta so I'll do the same for another point of data, although that one's a bit more complicated as the port is not round.
 
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