Optimisation?
Iand wrote: "After a lot of tweaking I've come up with what I think are 2 closely optimised designs, one tapped horn and one reflex, which have almost identical performance but need very different drivers."
Could it be that the TH optimisation has found a good solution but missed the best one (local optimum rather than global one)? In particular there seem to be a lot of TH responses that are only a little worse in frequency response flatness (which I'm not sure should be weighted quite as highly) with a much wider range of drivers than you imply. (I tried the BMS in hornresp and quickly got a TH that, with a modestly up-tilted response, would work well in my room, for example.)
My point? Not sure, but perhaps choosing a slightly different set of constraints will result in a very different outcome in this case. You could optimise for low excursion and see what the response is like (and whether it is correctable by filtering - as is the case for the high power handling "high kp" reflex designs).
It would be useful to state the design constraints more clearly (e.g. flat response from xx to yy Hz +/- z dB, total volume less than qq l ).
Ken
edit - forgot to say that your post was very thought provoking!
Iand wrote: "After a lot of tweaking I've come up with what I think are 2 closely optimised designs, one tapped horn and one reflex, which have almost identical performance but need very different drivers."
Could it be that the TH optimisation has found a good solution but missed the best one (local optimum rather than global one)? In particular there seem to be a lot of TH responses that are only a little worse in frequency response flatness (which I'm not sure should be weighted quite as highly) with a much wider range of drivers than you imply. (I tried the BMS in hornresp and quickly got a TH that, with a modestly up-tilted response, would work well in my room, for example.)
My point? Not sure, but perhaps choosing a slightly different set of constraints will result in a very different outcome in this case. You could optimise for low excursion and see what the response is like (and whether it is correctable by filtering - as is the case for the high power handling "high kp" reflex designs).
It would be useful to state the design constraints more clearly (e.g. flat response from xx to yy Hz +/- z dB, total volume less than qq l ).
Ken
edit - forgot to say that your post was very thought provoking!
Hi iand, for your argument it would be better to operate with fictive, optimum drivers. Since you want to show, that br is at least as good as th, you need the optimum drivers for both cases. I doubt you wanted to make claims about an individual drivers performance in such enclosures. A better driver which may even cost less could be released every day, which would bring your argument down.
Then it would be good to state the criteria for success more clearly. It cannot be about price vs maximum spl, as the price is not a physical value like motor strength or volume etc and is only up to the marketing of the manufacturer. If it is about enclosure volume vs maxspl, then the ideal fictive driver thing may also help, as your case shows very different volumes and doesnt allow to draw conclusions about this.
Good luck with the further argumentation
Then it would be good to state the criteria for success more clearly. It cannot be about price vs maximum spl, as the price is not a physical value like motor strength or volume etc and is only up to the marketing of the manufacturer. If it is about enclosure volume vs maxspl, then the ideal fictive driver thing may also help, as your case shows very different volumes and doesnt allow to draw conclusions about this.
Good luck with the further argumentation
Re: Optimisation?
Thanks for the compliment -- it's possible I've missed the optimum design for a tapped horn, however I've tried *lots* of different drivers in *lots* of different tapped horns, and for a given size box (say around 400l) and a given LF cutoff (say 32Hz) the average sensitivity across the passband (say 32-100Hz) always comes out about 100dB when ripple is smoothed out (and the response for the PA-5100 was the flattest of any design -- mine or anyone else's -- that I've seen)
And the result for 2 drivers (same size as 1 tapped horn driver) in a reflex box usually comes out about the same, including Xmax requirements. I'm saying that this is Hoffman's Iron Law in action for both boxes, because they're both resonator-based systems and the same physics applies to both.
Tom said that for a given driver the tapped horn gives up to 9dB improvement in sensitivity (3x reduction in cone excursion) compared to a direct radiator, which is undoubtedly true for long-excursion high-mass 12" drivers like he uses in the DTS20. For higher-efficiency lower-mass drivers like the B&C TBX he uses in the TH-115 the improvement is about 6dB/2x, which corresponds exactly with my figures.
We also agree that the driver parameters needed are different for a tapped horn and a reflex, so it's not sensible to compare the same driver in both cases to show that a tapped horn is better -- it's just as easy to find cases where the reflex is fine and the tapped horn has huge ripple which can't be removed.
It's also true that the optimum driver parameters needed for either type of enclosure may be difficult to achieve, but this works both ways; for a reflex box to match the DTS20 drivers with lower BL and Mms with the same Xmax would be needed, which could be difficult; for the tapped horn I quoted to match 2xBMS18N50V2 it's very difficult to build a driver (like the PA-5100) with enough BL and long throw.
The relative cost depends on how much extra it costs to build the optimum driver for a tapped horn; if this needs higher BL then a bigger magnet is needed, which needs a taller top plate, which needs a longer voice coil, which increases Mmd, which needs a bigger magnet... and if this process spirals out of control you end up with a $800 driver like the PA-5100.
Or you could look at it the other way; if the tapped horn needs a 1000W driver with a heavy-duty 4" voice coil, stiff cone, and a given Xmax (say 9mm for Tom's case), a reflex might need 2 500W drivers with 2.5" voice coils and lighter cones but the same Xmax -- these might not cost half as much, but certainly won't cost double.
Basically, the tapped horns needs drivers with a higher power density than a reflex, which shouldn't come as any surprise to anyone. Whether this means the 2 drivers for an equivalent reflex cost the same or more is a case-by-case basis, but what is obvious is that the tapped horn box is a lot more complicated and expensive to make than a reflex, and much harder to get right (as I'm sure Tom will agree
Port choking in a reflex is an issue if the port isn't big enough; there are cases where this is true (small low-tuned boxes) because the port can't be made big enough, but I don't see that this is the case for tapped-horn size boxes (which are not small in this sense), the usual problem is people just plain don't make the ports big enough.
As I said, each BMS driver in a 140l box needs a 200mm diameter port 500mm long, which is huge by normal standards but still only occupies 16l, or about 10% of the total box volume.
A DTS20-sized box tuned to below 20Hz would need a big port -- but then the box is pretty huge anyway, so I think it would still fit no problem.
All this is saying is that it's horses for courses, the optimum drivers needed for tapped horns and reflex boxes are likely to be very different, and it's easy to find cases which show that one or the other is better for a given driver.
What nobody's shown so far (including Tom is that my hypothesis was wrong -- that even though a reflex needs more drivers (with similar Xmax) than a tapped horn, it can achieve the same maximum SPL/cutoff/distortion in a given size box for the same money (including box) which after all is what the customer cares about
(assuming that suitable drivers exist or can be made in both cases)
If anyone (including Tom can show otherwise then I'll be very happy!
So here's the challenge (2xBMS18N850V2 in 280l reflex tuned to 32Hz):
-- net volume 320l
-- -3db at 32Hz, flat from 40Hz-100Hz (negligible ripple)
-- 100dB/W in half space (2pi)
-- power handling 2400W anywhere in the passband without exceeding Xmax
( mathematical Xmax defined as (Hc-3Hg/4)/2 )
Cheers
Ian
P.S. The tapped horn is still a great idea -- even though it's not really a horn...
kstrain said:
Thanks for the compliment -- it's possible I've missed the optimum design for a tapped horn, however I've tried *lots* of different drivers in *lots* of different tapped horns, and for a given size box (say around 400l) and a given LF cutoff (say 32Hz) the average sensitivity across the passband (say 32-100Hz) always comes out about 100dB when ripple is smoothed out (and the response for the PA-5100 was the flattest of any design -- mine or anyone else's -- that I've seen)
And the result for 2 drivers (same size as 1 tapped horn driver) in a reflex box usually comes out about the same, including Xmax requirements. I'm saying that this is Hoffman's Iron Law in action for both boxes, because they're both resonator-based systems and the same physics applies to both.
Tom said that for a given driver the tapped horn gives up to 9dB improvement in sensitivity (3x reduction in cone excursion) compared to a direct radiator, which is undoubtedly true for long-excursion high-mass 12" drivers like he uses in the DTS20. For higher-efficiency lower-mass drivers like the B&C TBX he uses in the TH-115 the improvement is about 6dB/2x, which corresponds exactly with my figures.
We also agree that the driver parameters needed are different for a tapped horn and a reflex, so it's not sensible to compare the same driver in both cases to show that a tapped horn is better -- it's just as easy to find cases where the reflex is fine and the tapped horn has huge ripple which can't be removed.
It's also true that the optimum driver parameters needed for either type of enclosure may be difficult to achieve, but this works both ways; for a reflex box to match the DTS20 drivers with lower BL and Mms with the same Xmax would be needed, which could be difficult; for the tapped horn I quoted to match 2xBMS18N50V2 it's very difficult to build a driver (like the PA-5100) with enough BL and long throw.
The relative cost depends on how much extra it costs to build the optimum driver for a tapped horn; if this needs higher BL then a bigger magnet is needed, which needs a taller top plate, which needs a longer voice coil, which increases Mmd, which needs a bigger magnet... and if this process spirals out of control you end up with a $800 driver like the PA-5100.
Or you could look at it the other way; if the tapped horn needs a 1000W driver with a heavy-duty 4" voice coil, stiff cone, and a given Xmax (say 9mm for Tom's case), a reflex might need 2 500W drivers with 2.5" voice coils and lighter cones but the same Xmax -- these might not cost half as much, but certainly won't cost double.
Basically, the tapped horns needs drivers with a higher power density than a reflex, which shouldn't come as any surprise to anyone. Whether this means the 2 drivers for an equivalent reflex cost the same or more is a case-by-case basis, but what is obvious is that the tapped horn box is a lot more complicated and expensive to make than a reflex, and much harder to get right (as I'm sure Tom will agree
Port choking in a reflex is an issue if the port isn't big enough; there are cases where this is true (small low-tuned boxes) because the port can't be made big enough, but I don't see that this is the case for tapped-horn size boxes (which are not small in this sense), the usual problem is people just plain don't make the ports big enough.
As I said, each BMS driver in a 140l box needs a 200mm diameter port 500mm long, which is huge by normal standards but still only occupies 16l, or about 10% of the total box volume.
A DTS20-sized box tuned to below 20Hz would need a big port -- but then the box is pretty huge anyway, so I think it would still fit no problem.
All this is saying is that it's horses for courses, the optimum drivers needed for tapped horns and reflex boxes are likely to be very different, and it's easy to find cases which show that one or the other is better for a given driver.
What nobody's shown so far (including Tom
is that my hypothesis was wrong -- that even though a reflex needs more drivers (with similar Xmax) than a tapped horn, it can achieve the same maximum SPL/cutoff/distortion in a given size box for the same money (including box) which after all is what the customer cares about (assuming that suitable drivers exist or can be made in both cases)
If anyone (including Tom
can show otherwise then I'll be very happy!So here's the challenge (2xBMS18N850V2 in 280l reflex tuned to 32Hz):
-- net volume 320l
-- -3db at 32Hz, flat from 40Hz-100Hz (negligible ripple)
-- 100dB/W in half space (2pi)
-- power handling 2400W anywhere in the passband without exceeding Xmax
( mathematical Xmax defined as (Hc-3Hg/4)/2 )
Cheers
Ian
P.S. The tapped horn is still a great idea -- even though it's not really a horn...
cowanaudio said:
Sorry I also forgot this one -- the key is "with the same motor" which means BL is the same.
The numbers I posted show that BL has by far the biggest influence on both tapped horn and reflex ripple, which again should be expected:
-- at impedance minima the cone doesn't move so Mmd and Cms have no effect, driving force is proportional to BL, drive pressure (SPL) is inversely proportional to cone area ==> SPL = BL/Sd
-- at impedance maxima (resonance) the cone travel is limited only by back EMF so Mms and Cms have no effect, travel is inversely proportional to BL, SPL (displacement) is proportional to cone area ==> SPL = Sd/BL
Since the required BL is very different for tapped horn and reflex it's impossible for one driver to be optimum for both.
Ian
As far as what the "optimum" drivers are, my guess is as follows
tapped horn : single driver, high BL, high mass, high power, large Xmax
reflex : dual driver, same Sd, lower BL (70%?), lower mass (70%?), lower power (50%), same Xmax (100%)
==> tapped horn needs higher power density driver (higher BL, Mmd, Pe per unit of Sd)
For some boxes (like the ones I posted) it's difficult to make the optimum tapped horn driver with high enough BL and Xmax, I can't actually find anything else as good as the TC PA-5100 would have been. I suspect the B&C drivers Tom uses are Xmax limited before they're thermally limited (Tom, is this the case?)
For some low-tuned boxes (like the DTS20 and TH-50) it's difficult to make the optimum driver for a dual reflex box with large Xmax and relatively low BL and Mmd -- actually it shouldn't be so difficult, but hardly anyone makes such drivers because there's no demand (the McCauley 6174 is the only one that springs to mind, and it *certainly* isn't cheap).
Cheers
Ian
tapped horn : single driver, high BL, high mass, high power, large Xmax
reflex : dual driver, same Sd, lower BL (70%?), lower mass (70%?), lower power (50%), same Xmax (100%)
==> tapped horn needs higher power density driver (higher BL, Mmd, Pe per unit of Sd)
For some boxes (like the ones I posted) it's difficult to make the optimum tapped horn driver with high enough BL and Xmax, I can't actually find anything else as good as the TC PA-5100 would have been. I suspect the B&C drivers Tom uses are Xmax limited before they're thermally limited (Tom, is this the case?)
For some low-tuned boxes (like the DTS20 and TH-50) it's difficult to make the optimum driver for a dual reflex box with large Xmax and relatively low BL and Mmd -- actually it shouldn't be so difficult, but hardly anyone makes such drivers because there's no demand (the McCauley 6174 is the only one that springs to mind, and it *certainly* isn't cheap).
Cheers
Ian
Hi Iand, guys
I am not sure you can reach the target you specified, a quick model of that combo suggests that with 320L and two of those drivers, the best one can get is about 98.6dB sensitivity with a –3 at about 33Hz.
Then, if one models “at power” one finds that at 100 Watts (the level the measured curves for the Tapped horns were taken), that even with a 12 inch diameter port the port losses have raised the –3 dB point to 37Hz. At 1600Watts input (800 ea), that the –3dB point is about 50Hz. Ports are not good, even if you made one large enough in area, its length then produced pipe organ resonances.
This is not including power compression, just port nonlinearity.
Also, if one had a vented box and Tapped horn with the same response shape, they would not have the same acoustic phase, the Tapped horn is not a vented box, it is a horn who’s dimensions are too small to provide constant loading and that is accommodated by the variable addition of the front and back radiations.
One can see this if you stack multiples together.
For example, a group of 4 of the TH-115’s have a 1w1m sensitivity of 109 to 111dB above 40Hz, you couldn’t make a pile of vented boxes that was that high in efficiency (mutual coupling gain has an upper limit of about 20-25% efficiency)
Best,
Tom
I am not sure you can reach the target you specified, a quick model of that combo suggests that with 320L and two of those drivers, the best one can get is about 98.6dB sensitivity with a –3 at about 33Hz.
Then, if one models “at power” one finds that at 100 Watts (the level the measured curves for the Tapped horns were taken), that even with a 12 inch diameter port the port losses have raised the –3 dB point to 37Hz. At 1600Watts input (800 ea), that the –3dB point is about 50Hz. Ports are not good, even if you made one large enough in area, its length then produced pipe organ resonances.
This is not including power compression, just port nonlinearity.
Also, if one had a vented box and Tapped horn with the same response shape, they would not have the same acoustic phase, the Tapped horn is not a vented box, it is a horn who’s dimensions are too small to provide constant loading and that is accommodated by the variable addition of the front and back radiations.
One can see this if you stack multiples together.
For example, a group of 4 of the TH-115’s have a 1w1m sensitivity of 109 to 111dB above 40Hz, you couldn’t make a pile of vented boxes that was that high in efficiency (mutual coupling gain has an upper limit of about 20-25% efficiency)
Best,
Tom
Tom Danley said:
Hi Tom
Your "small-signal" figures look very close to mine (phew!) -- 98.6dB vs 99dB (100dB was a typo which I corrected), 33Hz vs 32Hz the differences are probably the resolution which I could read off Hornresp plots.
Your info about port nonlinearity is very interesting, and much more severe than I would have expected for decent-sized ports (20cm diameter per driver) -- how did you calculate these numbers? This is exactly the kind of large-signal effect that's ignored by most speaker modelling software (but obviously not yours
Pipe organ resonances won't be a problem for a 50cm long port at the frequencies we're talking about here, obviously if you stuff higher frequencies into a sub you're asking for trouble -- and I'd have to point out that the tapped horn resonances at 130/190Hz are probably much worse than port pipe resonances (unless you start using tuned resonators to remove them like in the DTS-20).
I admit I'm ignoring acoustic phase -- until someone shows that this actually matters at these frequencies I feel happy with this...
If you do stack a pile of tapped horns together then I can believe that the efficiency goes up faster (and to a higher limit) than reflex boxes -- for example a pair of horns can gain 6dB in efficiency where a pair of direct radiators only gain 3dB, though I'm not sure this applies to tapped horns -- is this the case or not?
But I have to point out that most people (amateurs like me!) don't use big stacked arrays, which is why I was comparing a single tapped horn with a dual 18" reflex -- 133dB at 1m from a 320l box is enough for the likes of me
Please don't think I'm knocking the tapped horn concept, I've been following your work for years with great respect (and came up with some of the same ideas -- but it's a hobby for me, not business, which is why many of them never turned into hardware) -- which is why I've been *very* frustrated to find that I can't seem to do any better with a single driver tapped horn (according to Hornresp) than I can with a optimised dual driver reflex box!
So, ignoring the port nonlinearity issue (which if correct invalidates most ported speaker designs
-- can you do better with a tapped horn in the same size box? (99dB/W, 33Hz, 320l net, 2400W before Xmax limit, 133dB maximum ignoring power compression)And if you can, with what driver specification?
Cheers
Ian
P.S. On the issues like proper engineering-backed frequency response and sensitivity specifications and making measurements at realistic drive levels you're so far ahead of most of the rest of the industry that it's laughable -- maybe someday they'll catch up.
P.P.S. Oh yes I forgot, this might make them look bad. Shame...
Re: TH v. Bass Reflex
If I could find an easy way of grabbing a snapshot of the Hornresp results window and posting this to the forum I'd be glad to do so -- any advice on the best way to do this?
tb46 said:iand: Hi Ian, would you mind posting the Input Parameter pages for your optimized designs? This would make it easier to duplicate your line of thought. Anyway, it might help a feeble mind like mine.
If I could find an easy way of grabbing a snapshot of the Hornresp results window and posting this to the forum I'd be glad to do so -- any advice on the best way to do this?
Chris8sirhC said:
I don't know, I haven't been targeting this region.
It's quite possible that as frequency goes down it gets easier to build optimised drivers for a tapped horn and harder to build them for a reflex, I wouldn't like to say -- but I'll bet that Tom can
All I know is that in the parameter space I've been looking at (32-100Hz single box ~320l) I haven't been able to come up with a tapped horn that beats a reflex (with twice the number of drivers), at least according to Hornresp -- which may be ignoring some of the large-signal issues that Tom has raised, but that's true for everyone using small-signal tools to design speakers.
Hopefully Tom can do better, he's got *way* more knowledge than me in this area...
Ian
