Optimal throat size = 0.5 or 0.7 Sd ?

[lowtherdream]

Need some advise from the experimented back loaded horn designers out there

I have been playing with a design of a back loaded horn using a Fostex FE207E driver. From all the reading I have done in the past 2 months, I have not been able to decide which contour is best and what are the best sizes for the throat and compression chamber.

I have been playing in Autocad with the hyperbolic contour and formulas I have found on Dominique Petoin's site in France. Now that I am comfortable with the tools, I would like to tackle the throat size issue.
With my current design, it will be easy to play with the compression chamber size, but not the throat size, so it is essential that I find the best estimate for the throat area.

I have found multiple ways to calculate throat area:
0.5 x the piston area (smaller then Sd)
0.5 x Sd
0.7 x Sd
between 0.5 and 0.7 Sd
1 x Sd

This is all very confusing

Does anybody have practical experience with the throat sizing and the Fostex FE207E or FE206E ? Any practical info about throat shape and location ?

I am also trying to find a good source of information about the shape of the sound waves generated by a loudspeaker. Were there ever any tests performed under water to simulate the wave propagation in front behind the driver ?

If it is of some importance ... the design is similar to the Little Big Horn from Carfrae ( http://www.carfrae.com )

[AndrewT]

Hi,
I thought piston area=Sd.

the throat to Sd ratio deteremines a number of characteristics of the horn.
two that spring to mind are efficiency and distortion.
I think these two go in opposite directions, so that determines the first compromise.

A high ratio i.e. throat<<Sd can only be driven by some drivers.
Can someone tell us whether those Fostek models come into that range?
0.5 (Sd/St=2) should work for most decent drivers. You should not need to go as far as 0.7 (Sd/St=1.4) and certainly not 1.

[Scottmoose]

Ah, throat area. Interesting subject. I'm not surprised you're confused though.

OK, getting back to the basic physics, believe it or not, & contrary to what most people expect, driver Sd is actually pretty much immaterial to the throat area per se. So don't get too hung up on it -Sd is more a convenient measure than anything else. Have a gander at these:

Single Driver site on horn throats & general design:
http://melhuish.org/audio/horndesign.html

Leach's horn design paper: http://users.ece.gatech.edu/~mleach/.../HornPaper.pdf

Not many mentions of Sd...

Martin King's site is also required reading, but IIRC, he does not prescribe a method for selecting the ~ideal throat CSA. http://www.quarter-wave.com/Horns/Horn_Theory.html

You might find this interesting too: Olson's original patent for adding a filter chamber to a horn (note -the room is the compression chamber for a BLH). Still makes interesting reading: http://www.google.com/patents?vid=US...+olson#PPA3,M1

Best
Scott

[lowtherdream]

Using the "Single Driver" website recipe ...

Fostex FE207E Fostex FE206E
Fs= 39 Hz 39 Hz
Zn= 8 Ohms 8 Ohms
Sd= 0.0261 m2 0.0261 m2
Qts= 0.26 0.18
Vas= 56.25 L or 0.05626 m3 54.53 L or 0.05453 m3
Mms= 15.02 g 15.35 g
Xmax= 1.5 mm 1.5 mm
Re= 6.73 Ohms 6.69 Ohms
Qms= 3.86 3.73
Qes= 0.28 0.18
BL= 9.41 Tesla/m 11.82 Tesla/m
Cms= 0.00094 mm/N 0.00091 mm/N

At=(2pi*Fs*Qts*Vas)/c

At is the area of the throat (m2)
FS is the nominal air resonance of the driver
QTS is the total Q of the driver (note, some formulas use QES, the electrical Q here - Bruce Edgar for one)
VAS is the equivalent volume suspension (m3)
c is the speed of sound (344 m/s)

Fostex FE207E At= (2pi*39*0.26*0.05626)/344 = 0.01041981778047 m2 = 104.198 cm2 = 16.15 sq in

Fostex FE206E At= (2pi*39*0.18*0.05453)/344 = 0.006991897470698 m2 = 69.919 cm2 = 10.84 sq in

Using the piston area for both drivers:
0.5 x Sd = 103.5 cm2 = 16.04 sq in
0.7 x Sd = 144.27 cm2 = 22.36 sq in

Very similar result with 1/2 the piston area on the FE207E but does not work with the FE206E.

You are probably right saying that Sd is not needed in the calculation, but there is an indirect relationship. It is somewhere in the Q and Vas of the driver.

Let me play with the Leach formulas, and I will post the results.

Any thoughts on the throat shape and position ?

[Scottmoose]

Position of the throat in the back chamber will noticably affect the response. That's where Martin's MathCad worksheets come in, so you can model your intended enclosure. Martin charges a nominal $25 fee for the full set, which is an outright bargin given what they let you do, and the expensive mistakes they can save you from making.

For example, here's a horn (it's not an optimised box!) with the throat positioned at the opposite end of the back chamber to the driver:

[Scottmoose]

And here's the same horn, back-chamber & driver, but with the throat moved to the same end of the back-chamber as the driver. Makes quite a difference doesn't it?

As I say, this is where the software helps you select an optimal location for the throat, which will in turn affect how you fold the thing, because AFAIK, there are no formulas etc written down for establishing the best place for it -you either have to build a couple of prototypes, and measure them, or model it. The latter usually works out quicker, and a heck of a lot cheaper.

[lowtherdream]

I always have difficulty with the interpretation of models.
In this case, I see an added dip in the 350HZ zone when the throat is at the back of the compression chamber.

In a real model, we would have to take into consideration the turbulance the the compression chamber, the fluidity of the access to the throat of the horn, the damping material and position, etc ...

Where can I get more nfo on Martin's worksheets ?

[Scottmoose]

Oh yes. All of which are accounted for in the above, and can be adjusted in MathCad. Nope -I'm not joking.

It all comes back to QW theory & standing waves generated by an enclosure. Martin's work & software is derived from this, which he's advanced our knowledge of massively in recent years. See his site at www.quarter-wave.com I cannot recommend it highly enough. Required reading, and purchase IMO. Every speaker I have designed has been modelled & optimised in his worksheets. Their staggering accuracy is proven. They can't design a cabinet for you, but they're probably the most powerful tool available to the DIY speaker designer.

[lowtherdream]

Thanks for all the info !
I will take a look at the documentation and run a sample model.

[AndrewT]

Originally posted by lowtherdream
Qts= 0.26 . . . . . . . 0.18
BL= 9.41 Tesla/m . . . . . .11.82 Tesla/m
Fostex FE207E At= 16.15 sq in

Fostex FE206E At= 10.84 sq in

Using the piston area for both drivers:

now take the two recommended throat areas and compare them to Sd.
the 207 comes out @ ~=2
the 206 @ ~=3.2

Both these compression ratios are just about in the range that most/many drivers can live with.
Note that the 206 with the much stronger damping (stronger magnet?) can accept the higher compression ratio.

I suspect compression ratio may have been invented to avoid the maths, that you went through, to get to 16.2 & 10.8 sq in.

The smaller throat of the 206 may give a slightly higher efficiency at the expense of slightly higher distortion.
That's where prototyping comes in where you can compare different horns trying to find the ONE that appeals to the designer the most.