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Study of a Dipole/Cardioid Bass Horn
Study of a Dipole/Cardioid Bass Horn
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Old 5th July 2014, 05:36 PM   #1
xrk971 is offline xrk971  United States
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Study of a Dipole/Cardioid Bass Horn
Default Study of a Dipole/Cardioid Bass Horn

This topic started originally in the Hornresp thread here: Hornresp and interest in it continues. Being OT from David McBean's excellent thread devoted to Hornresp, I am creating a new thread here to fully discuss this topic.

Legis asked if a very simple V-horn with dual drivers and an open back could be simulated in Hornresp. The sketch provided by Legis looked like this:

Click the image to open in full size.

I proceeded to model it using Akabak. It is quite simple to model as a 2-segment linear horn with the backs of the drivers acting as open faced radiators. The drivers are Eminence Deltalite II 15 inchers. The script is here:

Code:
| ### Model of Legis open back dual driver 1 m x 1m x 50 cm high horn with Dual Deltalite 15's
| by xrk971
| July 3, 2014

System 'Legis Horn'

Def_Const
 
{  

| ### input parameters ###

| ### Define exterior physical size of speaker

Width = 1.00  ;   | width at mouth in meters
Height = 0.50 ;   | height of speaker in meters
Depth = 1.00  ;   | depth of speaker from cusp to mouth in meters

Speaker_pos=0.25;  | Speaker height above floor in meters
Dist_wall=2.0;     | Speaker distance from back wall in meters

| Horn geometery 

S0=0.01    ;  |width of vertex in meters (small value)
S1=0.173   ;  |width at driver center assuming 200 mm center to edge distance for driver in meters
L01=0.173  ;  |distance from vertex to driver on centerline cos(30deg)*200mm=173mm
S2=1.00    ;  |width at mouth in meters
L12=0.827  ;  |distance from driver at centerline to mouth in meters

}

Def_Driver  'Deltalite15'  | Eminence Model Delatalite II 15  4.8 mm xmax, 99.2dB, Qts 0.38
  SD=856.3cm2   |Piston
  fs=42Hz
  Mms=72g
  Qms=4.56
  Qes=0.41 
  Re=5.29ohm 
  Le=1.15mH
  Bl=15.7Tm
  Vas=204L 


| Speaker with horn axis CL at Speaker_pos above floor and Dist_wall away from back wall 
Def_Reflector  HorizEdge
Bottom={Speaker_pos}  Top={Dist_wall+Depth}
HAngle=0  VAngle=0

Filter 'HighPass' |Highpass filter -12dB/oct BW
fo=75Hz vo=1
{b2=1; 
a2=1; a1=1.414214; a0=1; }


| Define driver to be used and wired in parallel (left driver when viewed from front
Driver Def='Deltalite15' 'Driver 1'
Node=1=0=11=201

| Right driver when viewed from front
Driver Def='Deltalite15' 'Driver 2'
Node=1=0=11=202

| Backside of drivers are radiators angled at 30 deg back - left driver angled left back
Radiator  'Rear_Rad1'  Def='Driver 1'    Node=201
    x=-0.173m  y=0  z=-0.827m  HAngle=-30  VAngle=0 
    WEdge={Width/2}  Hedge={Height/2}  Reflection
Label=10

| Right driver back radiator angled back right
Radiator  'Rear_Rad2'  Def='Driver 2'    Node=202
    x=0.173m  y=0  z=-0.827m  HAngle=30  VAngle=0 
    WEdge={Width/2}  Hedge={Height/2}  Reflection
Label=20

| ### HORN WAVEGUIDE 

Waveguide 'Horn Seg 1'  | From vertex to driver at node=11 (both drivers excite node 11
Node=10=11
STh={S0*Height} 
SMo={S1*Height} 
Len={L01}

Waveguide 'Horn Seg 2'  | From driver injection point to mouth
Node=11=12
STh={S1*Height} 
SMo={S2*Height} 
Len={L12}

| ### Main horn mouth radiator    
Radiator  'Horn Mouth'  Def='Horn Seg 2'    Node=12
    x=0  y=0  z=0  HAngle=0  VAngle=0 
    WEdge={Width/2}  Hedge={Height/2}  Reflection
Label=30
This code produced a response which looks like this (no wall effects with horn on floor in 2 pi space):

Click the image to open in full size.

The corresponding SPL at xmax of 4.8mm and 55v (with high pass filter at 75 Hz) is quite impressive:

Click the image to open in full size.

If you place the horn 2 m in front of a back wall, the wall reflections make the output at 0deg in front look like this:

Click the image to open in full size.

Legis then asked if either a sealed chamber behind the drivers could be added, say 30 liters, or maybe a leaky box with a resistive vent to produce a cardioid response. I proceeded to model that and produced the following results:

Case (a) open back:

Click the image to open in full size.

Case (b) sealed 30 liter back chamber with Q=0.5:

Click the image to open in full size.

Case (c) 30 liter back chamber with 4 in dia x 10 in long vent:

Click the image to open in full size.

What I noticed that was interesting was that the open back case actually loads the cone better than the sealed back chamber, as can be seen from the cone excursion plots of each case at 55 volts (the drive voltage needed to hit xmax for the open back case):

Case (a) cone excursion for open back:

Click the image to open in full size.

Case (b) cone excursion for sealed back (30 liters):

Click the image to open in full size.

Case (c) cone excursion for 30 liter chamber with 4 in dia x 10 in long vent:

Click the image to open in full size.

Here are the polar responses for 100 Hz, 200 Hz, and 500 Hz at 4 meters away for the above cases:

Open back polar:

Click the image to open in full size.

Sealed 30 liter chamber closed back polar:

Click the image to open in full size.
Vented back polar:

Click the image to open in full size.

I am now working on the effects of a resistive vent back similar to the one posed by Legis as illustrated here:

Click the image to open in full size.

If you "Synergize" this with a compression chamber and injection port for each driver (still open back) and the addition of a B&C DE-250 CD XO at 1600Hz at the vertex you get this:
Click the image to open in full size.

More info in post #156: Study of a Dipole/Cardioid Bass Horn
Attached Images
File Type: png Legis-horn-displ-open-back.png (26.1 KB, 2785 views)
File Type: png Legis-horn-displ-sealed-back.png (24.4 KB, 2776 views)
File Type: png Legis-horn-displ-vented.png (26.3 KB, 2764 views)
File Type: png Legis-horn-Polar-open-back.png (27.8 KB, 2762 views)
File Type: png Legis-horn-Polar-vented-back.png (26.9 KB, 2767 views)
File Type: png Cardioid-horn-diag.png (5.8 KB, 2762 views)
File Type: png Legis-horn-Polar-sealed-back.png (24.4 KB, 2763 views)

Last edited by xrk971; 23rd July 2014 at 01:27 AM.
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Old 5th July 2014, 06:17 PM   #2
NEO Dan is offline NEO Dan  United States
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Hi,
I might be wrong but I thought when you enter height and width, the values are converted to a 1D area, and Akabak is limited to conic and exponential expansion? What is the default expansion? See attached examples.

As a result I think you are modeling something more like this?
Attached Images
File Type: png Akabak.png (14.5 KB, 166 views)
File Type: png para.png (36.4 KB, 211 views)
File Type: png coinc.png (36.4 KB, 174 views)
File Type: png exp.png (36.2 KB, 154 views)
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Last edited by NEO Dan; 5th July 2014 at 06:35 PM. Reason: Add expansion examples
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Old 5th July 2014, 06:56 PM   #3
xrk971 is offline xrk971  United States
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Study of a Dipole/Cardioid Bass Horn
Quote:
Originally Posted by NEO Dan View Post
Hi,
I might be wrong but I thought when you enter height and width, the values are converted to a 1D area, and Akabak is limited to conic and exponential expansion? What is the default expansion? See attached examples.

As a result I think you are modeling something more like this?
I believe there are three types of waveguides in AkAbak: linear where the area expands linearly as a function of distance along the waveguide (no specifier), conical where the area expands quadratically like a pyramid ("conical" specifier), and exponential where the expansion follows an exponential function set with a "T" value. I have built linear horns based on an AkAbak sims and the result is quite accurate.

Can you post what HR predicts for the same V horn? It may be that I have this sitting on the floor and that acts as an extension of the horn as a plane of symmetry reflection surface. In HR when you set 2 pi does it assume that the mouth exits a plane wall acting as the 2 pi boundary? Also, are you looking at power or pressure? AkAbak is showing pressure along 0 deg axis at a height of the centerline of the horn or 0.25 meters above the ground. The ground plane makes a difference. I could turn off all reflections and plot it in 4pi steradian space and that maybe something that is easier to compare to?

AkAbak has a tough steep learning curve, but the ability to place a radiator from a vent, waveguide, or cone arbitrarily at any x,y,z location angled at theta, phi, psi, that is, 6 deg of freedom is very powerful and needed if one is looking at the effect of multiple horns, vents, or cones as in dipoles and cardioids. Also the effect of floor and wall reflections are easily implemented.

Last edited by xrk971; 5th July 2014 at 07:14 PM.
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Old 5th July 2014, 07:19 PM   #4
NEO Dan is offline NEO Dan  United States
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It looks like the default expansion is exponential when not specified:

Quote:
Originally Posted by Akabak Manual PDF page 195
Parameter
Waveguide Keyword
'...' Identifier
Node=s=t Network node of the Waveguide. The volume velocity at the entrance - the funnel throat - 'flows' from pole s to ground and at the outlet - the funnel mouth - from pole t to ground.
T= (Optional) Parameter of horn function (Eqs. 1,2), as described for the element Horn.
If T is not entered, the program sets T=1, thus specifying a purely exponential horn function.
If the keyword Conical has been entered, the value of T is ignored.
range: 0<=T<=100
T= 0 catenoid
0 < T < 1 cosh
T= 1 exponential (default)
1 < T < 100 sinh Conical (Optional) If entered, the horn function describes a conical horn profile (see above). If the parameter T has been entered, it is ignored.
I don't think parabolic expansion is supported:?
Attached Images
File Type: png expansion.png (34.3 KB, 340 views)
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Dan

Last edited by NEO Dan; 5th July 2014 at 07:30 PM.
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Old 5th July 2014, 07:35 PM   #5
xrk971 is offline xrk971  United States
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Study of a Dipole/Cardioid Bass Horn
NEODan,
Thanks for pointing that out. Hmm... a linear expansion can be approximated by exponential for short distances - and you may be right about why the HR is different. When specifying conical isn't that the same as parabolic? As conical horns follow a quadratic or parabolic expansion.
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Old 5th July 2014, 07:44 PM   #6
NEO Dan is offline NEO Dan  United States
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I removed the back chamber volume to illustrate the difference in volume between the expansions. Also you can see the resulting area at S2 is quite different.

If Akabak could do parabolic I'd be very familiar with it...
Attached Images
File Type: png exp2.png (30.0 KB, 316 views)
File Type: png coinc2.png (30.1 KB, 119 views)
File Type: png para2.png (30.1 KB, 124 views)
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Old 5th July 2014, 07:48 PM   #7
sine143 is offline sine143  United States
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xrk. we had this discussion a short while ago (for the who knows what time). Con expands with a linear radius expansion (think traffic cone). PAR expands with a linear AREA expansion. thus, Par can be built out of straight plywood, with 2 "sides" parallel to each other. Con can not be built in this fashion.
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Old 5th July 2014, 08:08 PM   #8
NEO Dan is offline NEO Dan  United States
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Like so:
Attached Images
File Type: png 3m example.png (31.5 KB, 467 views)
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Old 5th July 2014, 08:11 PM   #9
mwmkravchenko is offline mwmkravchenko  Canada
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Study of a Dipole/Cardioid Bass Horn
Yeah!

What Dan said.

31n23oVcOfL._SY445_.jpg
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Old 5th July 2014, 08:15 PM   #10
NEO Dan is offline NEO Dan  United States
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They really are parabola heads after all... eh
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