Acoustic Horn Design – The Easy Way (Ath4)

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Please could someone check this LEM script if this is enough to define a direct radiating driver (like the 5" Faital above)? I'm still a bit helpless.
Code:
Def_Driving
  Value=2.83 IsRms

Def_Driver 'Drv1'
  dD=103mm
  Mms=10.5g
  Cms=0.57e-3m/N
  Rms=0.52Ns/m
  Bl=6.9Tm
  Re=5.4ohm
  fre=35kHz ExpoRe=1
  Le=0.1mH ExpoLe=0.618

System 'S1'
  Driver 'D1' Def='Drv1' Node=1=0=10=20
 
  // Rear volume
  Enclosure 'Eb' Node=20
    Vb=5e-3m3 Qb/fo=0.1

  RadImp 'Throat' Node=10 DrvGroup=1001
 
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The whole sentence is "The above formula provides a simple closed-form expression for a very general horn profile that smoothly terminates into a flat baffle" and that is true. Rollback is not integrated into the formula (can't be). It would be nice to have some simple parametric expression for the curve including the rollback but I doubt it's possible.
 
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that insert seems like really good idea. It will be very easy to make it on lathe machine (and probably more precise than 3D printing).
It will make entry angle 0 for all CDs where is applicable so, as I understand, naturally better for the flat wavefront.
To not squeeze the exit to much maybe will be the best to take 1.4" CD and implement such insert

Why not take a driver without a conical exit section?
 

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With a suitable 1.4" driver with an open enough throat extension one could get the HF directivity of a 1" driver but with the low frequency extension of a 1.4" driver. At least that's the idea. The same principle holds for any driver size. Also the loading would be a little better with the decreased throat angle.

Driver without a conical exit section doesn't offer this possibility.
 
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This is the Le Script that I used for a model of the 15PR400

Code:
//*****************************************************************************
//
// ABEC3 Lumped Element File
// Project:sealed woofer
//
//*****************************************************************************


// Thiele-Small parameter of electro-dynamic driver

Def_Driver '15PR400'		// 15inch paper woofer
  Re=5.1ohm				// datasheet
  Le=0.75mH				// datasheet
  Mms=56.8g  			// datasheet
  Cms=0.24e-3m/N		// datasheet
  Bl=16.7Tm				// datasheet
  Qes=0.34				// datasheet
  Qms=6.0				// datasheet
  Rms=3.11Ns/m		// use HornResp to derived
  Fs=35Hz				// datasheet
  //SD=857cm2			// datasheet
//fre=3.1kHz			// 
//ExpoRe=0.824			// 
  ExpoLe=0.3			// 



Def_Driving "Driving"
  DrvValue=2.83V		// assumption is gnd=node "0" and output is node="1"
  IsRms


// Lumped element network
  
System 'Woofer'
 
    //Filter 'WooferLR4LP' f0=700Hz V0=1 Order=4 LR Lowpass;		// implicit input

    Driver  'Drv1'
    Def='15PR400'
    Node=2=0=111=112		// connected woofer to LP filter, lowest node# is input
//    DrvGroup=1011,1012		// front,rear of woofer 2 port
	DrvGroup=1011		// front only,
	
  	RadImp 'WooferFront'	// rad imped,  a different object
    Node=111				// connect drive source node
    DrvGroup=1011			// the DrvGroup links the LE to BE

//  	RadImp 'WooferRear'		// rad imped, a different object
//  	Node=112          	
//    DrvGroup=1012

	Enclosure "WooferRearChamber"	// using a lumped compliance model with damping
	Node=112	// connect to drive source node
	Vb=60L		// rear chamber volume
	//Lb=10cm		// rear chamber length
	etaB=2.7e-2	// medium damping

Looks pretty much the same on a quick view. Watch the length of the rear chamber, I found leaving it out was the better option.


Please could someone check this LEM script if this is enough to define a direct radiating driver (like the 5" Faital above)? I'm still a bit helpless.
Code:
Def_Driving
  Value=2.83 IsRms

Def_Driver 'Drv1'
  dD=103mm
  Mms=10.5g
  Cms=0.57e-3m/N
  Rms=0.52Ns/m
  Bl=6.9Tm
  Re=5.4ohm
  fre=35kHz ExpoRe=1
  Le=0.1mH ExpoLe=0.618

System 'S1'
  Driver 'D1' Def='Drv1' Node=1=0=10=20
 
  // Rear volume
  Enclosure 'Eb' Node=20
    Vb=5e-3m3 Qb/fo=0.1

  RadImp 'Throat' Node=10 DrvGroup=1001
 
Like with most of my "brilliant" ideas, there is a fly in the ointment - how does the shape of the slot affect the polar characteristics of the woofer. Is there a way to model that?
The benefit of having both woofer and waveguide being axisymmetric and of similar sizes is that their directivities will be similar and give a good polar match both horizontally and vertically.

Slot loading the woofer will create a bandpass chamber that will cause a peak in the response before it rolls off much earlier than normal. The long thin exit will not be a good polar match at 500Hz or above which are the likely crossover points, the effect can be simulated in Hornresp or with greater precision in ABEC/Akabak.

Edit: Seems like the post I responded to vanished.
 
Here is the last one (free standing) with the Faital 5FE100 (5") - absolute SPL at 1m/2.83V. Of course first one would have to get rid of the resonance, this is totally non-optimized...

Maybe usable to 200 Hz (?). That's not bad, IMHO.

maybe you could even add a bandpass design to create an aggressive roll-off

that would mean that the drivers harmonic distortion would be suppressed. could be a good trick to make it sound even cleaner...
 
it is depend of the length of throat exit. If it is short enough it will be possible to incorporate it in OS throat profile of WG. Otherwise we need an insert if want to follow the WG profil from pp

This probably also depends on the type of diaphragm and the specific design of the phase plug.
The outer slit of a 3 slit annular phaseplug may, or may not interfere with a throat insert.
The same may be true for some ring radiators in which the wave front is directed past a centrally located plug.
 

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it is depend of the length of throat exit. If it is short enough it will be possible to incorporate it in OS throat profile of WG. Otherwise we need an insert if want to follow the WG profil from pp
Pure OS throat (k=1) most probably wouldn't fit to any extension, for any reasonable coverage angle. The whole point is to start a curvature-continuous WG profile at a smaller throat. Then even for k>1 the performace would be better than a pure OS throat starting at the exit of the extension. At least this stems from the simulations. Starting at a smaller throat is always an improvement. Making the profile smoother (without the curvature change) is another improvement.