which taper ratio for TL?

[mondogenerator]

basically, i have nearly finished my design of latest speaker. It is going to be a tapered TL using a 5 inch driver, Fs 40Hz, Qts 0.43, and Vas 11 litres.

I have chosen to taper the TLine in order to shorten it and negate the need for any bends.

I have 2 options:

1: Sl= 4.5Sd tapering down 20:1 ratio, So=0.25Sd, line length about 900mm

2: Sl= 4.5Sd tapering down 10:1 ratio, So=0.4Sd, line length about 1050mm

Presently I am considering design #1, as i figure that if i need to tune the pipe slightly higher for any reason, then i can increase the vent area a little. Indeed i may be able to increase it up to the same So as design #2 if necessary. As i cant see much in the way of size difference, it occured to me..."Why dont i just build the 10:1 taper instead".

Now im confused ..hehe

my question is this:

which design would be preferable and why?

[h@kan]

I'm curious on your box geometries.

A roughly one meter long line tapered 20:1 without any internal bends?
A triangular prism?

Regards H@kan

[mondogenerator]

Originally Posted by h@kan

I'm curious on your box geometries.

A roughly one meter long line tapered 20:1 without any internal bends?
A triangular prism?

Regards H@kan

Yes, a triangular prism. Most likely built within a 'normal' rectangular box, with the cavity filled with sand. Or maybe rear panel perforated and filled with absorbent.

[pkitt]

Your 10:1 tapered line will have a 1/4-wavelength resonant frequency around 50 Hz, but your driver's combination of Fs and Qts will likely fair better if the line's resonant frequency is at or a little below the driver's Fs of 40 Hz. Now the 20:1 tapered line will have a bit lower resonant frequency, but it still might not be low enough for the flattest, smoothest overall response, and you have to be careful about potential terminus air velocity at larger and larger tapers with smallish beginning line areas (you may be okay starting at 4.5 Sd, however). Of course a benefit of larger taper ratios is that they will smooth out the overall response.
Paul

Originally Posted by mondogenerator

basically, i have nearly finished my design of latest speaker. It is going to be a tapered TL using a 5 inch driver, Fs 40Hz, Qts 0.43, and Vas 11 litres.

I have chosen to taper the TLine in order to shorten it and negate the need for any bends.

I have 2 options:

1: Sl= 4.5Sd tapering down 20:1 ratio, So=0.25Sd, line length about 900mm

2: Sl= 4.5Sd tapering down 10:1 ratio, So=0.4Sd, line length about 1050mm

Presently I am considering design #1, as i figure that if i need to tune the pipe slightly higher for any reason, then i can increase the vent area a little. Indeed i may be able to increase it up to the same So as design #2 if necessary. As i cant see much in the way of size difference, it occured to me..."Why dont i just build the 10:1 taper instead".

Now im confused ..hehe

my question is this:

which design would be preferable and why?

[mondogenerator]

Originally Posted by pkitt

Your 10:1 tapered line will have a 1/4-wavelength resonant frequency around 50 Hz, but your driver's combination of Fs and Qts will likely fair better if the line's resonant frequency is at or a little below the driver's Fs of 40 Hz. Now the 20:1 tapered line will have a bit lower resonant frequency, but it still might not be low enough for the flattest, smoothest overall response, and you have to be careful about potential terminus air velocity at larger and larger tapers with smallish beginning line areas (you may be okay starting at 4.5 Sd, however). Of course a benefit of larger taper ratios is that they will smooth out the overall response.
Paul

yes a smoothening of passband ripples is the intention, hence the initial idea of a 20:1 ratio taper...both lengths quoted here are approx. as i dont have the drawings to hand, but the intended Fb is about 45-50Hz, as i figure stuffing will lower that a small amount, plus with a Qts of .43, i would like to aim for a finished line QWfrequency of 45Hz.

These figures are approx and especially as i have just measured Fs on both drivers and the average is actually about 46Hz with 40hrs of run in. However, in a ported system the port area works out to be very small, in fact a 1.5" tube, and i would be happier with a minimum of 2" so an area of .25Sd or about 3 in³ would meet that criteria. I was more worried about over attenuating the vent output. though that being said, wouldnt a smaller vent are also decrease the acoustic LP frequency of the vent; thus keeping more mids from being radiated from the vent?

[pkitt]

I'm not sure I follow your logic entirely but in a vented system, as well as in an ML-TL that uses a port, making the port's diameter smaller will lower the tuning frequency which will, indeed, reduce the frequency of signals that are allowed to exit the port. If you want, I'd be happy to model the expected performance of your TL, just give me the proposed line dimensions and all of these driver's T/S values: Fs, Re, Le, Bl, Vas, Sd, Qes and Qms.
Paul

Originally Posted by mondogenerator

yes a smoothening of passband ripples is the intention, hence the initial idea of a 20:1 ratio taper...both lengths quoted here are approx. as i dont have the drawings to hand, but the intended Fb is about 45-50Hz, as i figure stuffing will lower that a small amount, plus with a Qts of .43, i would like to aim for a finished line QWfrequency of 45Hz.

These figures are approx and especially as i have just measured Fs on both drivers and the average is actually about 46Hz with 40hrs of run in. However, in a ported system the port area works out to be very small, in fact a 1.5" tube, and i would be happier with a minimum of 2" so an area of .25Sd or about 3 in³ would meet that criteria. I was more worried about over attenuating the vent output. though that being said, wouldnt a smaller vent are also decrease the acoustic LP frequency of the vent; thus keeping more mids from being radiated from the vent?

[pkitt]

Mondo, I got the automated email from this forum containing the T/S values for your driver but for some reason, your post didn't end up being posted in this thread. Anyway, I did some modeling. I don't know exactly what kind of driver you're using but for the sake of modeling I assumed it was a ~5-inch fullrange type. So, I ended up with a line tapered at 15:1 and 42" long, starting at 4.13 Sd and ending at 0.276 Sd. Dimensionally the starting area was 7.5" square and the ending area was 7.5"W x 0.5"D. The terminus would be 7.5"W x 0.5"H. I placed the driver's center 8" from the beginning of the line. I used a stuffing density of 0.75 lb/cu.ft., stuffing with a total of ~7.5 ounces in the first 28" of the line. I've attached the system response graph (red line). I used Martin's ML-TQWT worksheet which allows modeling a tapered line, too. As you will see on the response graph, F3 is ~39 Hz and the ripples in the response are acceptably low. If the stuffing density and/or length were to be increased, the ripples would be diminished but at the expense of a higher F3. The terminus air velocity with this 2.83-volt modeling input was under 1% of the speed of sound.
Paul

Edit: The peak of the terminus air velocity occurs at ~32 Hz. Without stuffing, the system's tuning frequency is 40 Hz, and with stuffing it's ~38 Hz.

[mondogenerator]

many thanks...basically im working nights and at work. The figures i gave were approximate and after checking them in the excel sheet i used previously i couldnt get them to tie up quite the same. So i deleted the post, with the intention of posting the figures i have on my home spreadsheet calculations i did from my measurements. I think for the most part the numbers are accurate enough though, but BL maybe 0.1 or so higher or lower, whatever difference that would make!!

FR graph does indeed look really quite acceptable, i was expecting somewhat higher F3 given that the driver is fairly low Qts. And this is tuned to 40Hz unstuffed...given that FR graph, coupled with room modes etc, maybe tuning slightly lower WOULD give subjectively better results...

Thanks very much again..hopefully i remembered all my numbers ok!!! If theres any glaring errors then ill be sure to repost them, correctly. As a guideline design i think maybe the 10:1 or your comprimise between my 2 ideas, the 15:1 taper may both be pretty good starting places.

P.S. the driver is Visatons AL130 aluminium cone mid bass driver. Never played with rigid cones before, but it impresses and has a nice smooth midband. Obvious main breakup mode at about 7 kHz but the crossover im using rolls that out of audibility way before you get that high. Cone resonance seems very well damped, considering the metal cone. Would recommend highly to anyone.compared to my past project; audax HDA 130mm 2 way in SBB4, their resolution and tonal balance is awesome. Strangley that what i thought when i built the audax's, going from paper to HDA cones.

[pkitt]

I can always model again with different T/S values just to be sure, and I can see whether tuning the line lower will give you something you'd prefer. Also, I didn't model with any d.c. resistance assumed to be in series with it, like that from a series crossover inductor, and we really ought to incorporate that, too. BTW the Qts isn't particularly low and if we add in this series resistance, it will be higher yet. What tweeter are you planning on using with this Visaton driver? Based on my modeling the tweeter would be located above the Visaton.
Paul

Originally Posted by mondogenerator

many thanks...basically im working nights and at work. The figures i gave were approximate and after checking them in the excel sheet i used previously i couldnt get them to tie up quite the same. So i deleted the post, with the intention of posting the figures i have on my home spreadsheet calculations i did from my measurements. I think for the most part the numbers are accurate enough though, but BL maybe 0.1 or so higher or lower, whatever difference that would make!!

FR graph does indeed look really quite acceptable, i was expecting somewhat higher F3 given that the driver is fairly low Qts. And this is tuned to 40Hz unstuffed...given that FR graph, coupled with room modes etc, maybe tuning slightly lower WOULD give subjectively better results...

Thanks very much again..hopefully i remembered all my numbers ok!!! If theres any glaring errors then ill be sure to repost them, correctly. As a guideline design i think maybe the 10:1 or your comprimise between my 2 ideas, the 15:1 taper may both be pretty good starting places.

P.S. the driver is Visatons AL130 aluminium cone mid bass driver. Never played with rigid cones before, but it impresses and has a nice smooth midband. Obvious main breakup mode at about 7 kHz but the crossover im using rolls that out of audibility way before you get that high. Cone resonance seems very well damped, considering the metal cone. Would recommend highly to anyone.compared to my past project; audax HDA 130mm 2 way in SBB4, their resolution and tonal balance is awesome. Strangley that what i thought when i built the audax's, going from paper to HDA cones.

[mondogenerator]

Thank you for the offer. Maybe you could model the response with a line tunes to 35Hz or 30 Hz instead of 40, to see what difference it would make as im probably just as interested in F10 as F3, so here are my reviewed figures:

Qms 4.75
Qes 0.45
Qts 0.4118
Re 5.6
DCR L1=0.25 Ohm
So assume 0.4 Ohm with wiring

Vas 10.82 litres
Sd 79cm²
Bl 5.78

with your 15:1 ratio, well 0.08 is the nearest i can do on excel sheet:
Sl=49in²
So=3.7in²
length=48in

Oh and im using the visaton g20sc tweeter, due to its very flat response graph on their site, the waterfall looks pretty clean too. The only thinh that lets it down for me at least is the 'average' Fs, lower would be nice, but we cant always have it all!

Again thanks alot.