Lowther PM6A In Back-Loaded Horns

Driver parameters for hornresp program.

There were some difficulties in settling on some of the parameters.

pm6a is not available in full specs; we derive and interpolate some by looking at EX, DX, etc. Also, Lowther site's T?S params are shaky at best.

1.   Driver Diaphragm Piston Area SD, sm^2

This seems easy yet sources vary. Lowther is 23 sm diameter, with 14.5 sm as physical paper-cone diameter; yet its "effective" radius is bigger than 14.5/2 = 7.25, though, something like 8 or a bit more. What is the "right" radius is not very clear, since a part of the cone suspension also moves, and in the frequencies we're concerned with the radius is larger than paper cone radius.

Lowther claims 210 sm^2

Area A = Pi * R ^ 2: 


  R, sm    SD. sm 
======================
  8.00     201.1 
  8.05     203.6 
  8.10     206.1 
  8.15     208.7 
  8.20     211.2 
  8.25     213.8 
---------------------
We'll assume SD = 210 sm^2.

Sept'05: Note that [1] is more conservative and puts SD = 260 for DX* series.

2.   BL, tesla * meter

This is merely a product of Driver magnetic flux density B, Tesla, and voice coil conductor length L, meter.

For most Lowthers, B is 1.75 to 2.4 Tesla. Coil length? 3 to 5 meters.

From various sources, for PM6A BL can be set between 7 and 11. [1] sets BL for DX* Lowthers as 9, 9.3, 10.4.

We use BL = 8

3.   Driver Diaphragm suspension mechanical compliance CMS, meter/newton.

Some Lowther evidences 

DX3: .91 mm/N == 9.1e-1 mm/N == 9.1e-4 m/N
DX2: 1.8  mm/N == 1.8e-3 m/N

[dx3 is 2x stiffer? interesting]

ex2-4: .993 mm/N == 9.93e-4

from various sources.
We can attack this from the fundamntal principles.

xhttp://www.birotechnology.com/articles/mass.html

What is Vas for pm6a? Sources claim Vas from 50 to 85 liters for pm6a, and ~100 for pm2a Lowther's site gives 15 liters for Dx/Ex (too low?).

This varies Cms from ~.9 to ~ 1.8 e-3 


  Vas, L      Cms, m/N
============================
  50.00       8.990133e-004
  60.00       1.078816e-003
  70.00       1.258619e-003
  80.00       1.438421e-003
  90.00       1.618224e-003
  100.00      1.798027e-003
---------------------------
We use CMS = 1.2e-3 m/N for pm6a. hornresp's result for values 1..2 makes little difference.

4.   Driver Diaphragm and voice coil dynamical mechanical mass MMD, Grams

Hornresp clarifies also that it is MMS minus air load. Lowther provides 11g of effective moving mass - is it supposed to be MMS or MMD? Some other sources quote MMS for Lowther in 6 to 9 g range. Would MMD be lower yet? How much?

On another hand, In [2], for the "generic driver" MMD is 14g.

We can attack this from the fundamntal principles. http://www.birotechnology.com/articles/mass.html 

(let* (
       (c 325)  m/s
       (po 1.180) kg/m^3
       (Vas 60)  liters for pm6a. for pm2a - 100
       (Sd (* pi .082 .082)) m^2
       (Fs 59) Hz
       (Cms (* (/ Vas (* po c c Sd Sd)) .001)) m/N
       (Mms (/ 1 (* 2 pi Fs 2 pi Fs Cms)))   kg
       (Mml (/ (* 8 Sd Sd Sd po) 3))
       (Mmd (- Mms (* 2 Mml)))
       ) 
  (list Mms Mmd)) (0.006745107471751414 0.006685785788226833)
we use MMD = 7, which may be a bit low.

5.   RMS, Nm/s

So far the most confusing. Newton * sec / meter, or NS/M

For starters, many sources provide RMS in KG/S. 

1 kg/s = 1000 g/s
assuming N = G * M / S^2, we get 1 G/S = 1 N * S^2 / M * S = N * S / M.

Thus, 1 kg/s = 1000 Ns/m

But this is not all yet, as some sources provide Rms in Kg/s and some - Rme in N*s/m, and these do differ, yet not by the factor of 1000. Various sources claim Lowther RMS as .4 to .5 KG/S. What to do? when RMS = 400 entered in hornresp, SPL curve is clearly bad.

This aside, we can attack this from the fundamntal principles.

http://www.birotechnology.com/articles/mass.html 

(let* (
       (c 325)  m/s
       (po 1.180) kg/m^3
       (Vas 60)  liters for pm6a. for pm2a - 100
       (Sd (* pi .082 .082)) m^2
       (Fs 50) Hz
       (Qms 3)
       (Cms (* (/ Vas (* po c c Sd Sd)) .001)) m/N
       (Mms (/ 1 (* 2 pi Fs 2 pi Fs Cms)))   kg
       (Mml (/ (* 8 Sd Sd Sd po) 3))
       (Mmd (- Mms (* 2 Mml)))
       (Rms (/ (* 2 pi Fs Mms) Qms)) Ns/m
       ) 
  Rms) 0.983516174156132
For now, we use Rms = .9

6.   Le, mH.

We use 0.9

7.   Re

We use 7

8.   Throat chamber volume VTC (cc)

Possibly tricky. What is cc??

VTC *does* affect high-freq resonsnce patterns. See [2] for explanation.

For various Lowther enclosures, this is from 6 to 11 liters.

9.   ATC

We assume this is area normal to the horn axis. It would be more interesting to specify the area behing the driver and the lenght behind it, Unfortunately, the relevant data seems to be the area normal to the throat, regardless of how the driver is oriented. Should we isntead assume the driver is normal to the throat? Or asume it is not very important?

After some considereations, we assume it is area NORMAL to the horn axis,

10.   Horns

once the driver parameters are set, we can start modeling various back loaded horn enclosures. Hornresp feels a bit tricky at first but one can get used to it.

Each horm described here is built from comical segments and the conical mode was used in Hormresp

For each horn, s1-s5, segment length were computed from the enclosure plans.

10.1   Jericho 

s1: (* 36.0 2.8) 100.8
s2: (* 36.0 5.6) 201.6
s3: 424
s4: (* 36.0 30) 1080.0
s5: (* 36.0 50) 1800.0

(+ 70 70 85 31) 256

vtc 5L atc 400
pm6a-jericho-in.gif
pm6a-jericho-hr.gif

Diaphragm displacement is under 1mm above 30hz which is pretty good.

10.2   Fidelio 

---------------
w: (- 28 4.4)    23.6

s1: (* 24 2.4)   57.59
s2: (* 24 4.6)   110.39
s3: (* 24 11)    264
s4: (* 24 41)    984

l: (+ 52 (+ 54 24) 62 89)   281
vtc: (- (* 24 25 10) 2)     5998
atc (* 10 24)               240
pm6a-fidelio-in.gif
pm6a-fidelio-hr.gif

Diaphragm displacement is <1mm above 32hz.

10.3   Mauhorn XII 

s1: (* 25.6 2.5)
s2: (* 25.6 (- 65.0 58))
s3: (* 25.6 11.1)
s4: (* 25.6 13.5)
s5: (* 25.6 72.5)
(+ (- 115.0 2.2 2.2 61) 70 85 31)
VTC: (- (* 13.0 29.0 25.6) 1500)

atc?? (* 25.6 20)
pm6a-mauhorn-xii-in.gif
pm6a-mauhorn-xii-hr.gif

Diaphragm displacement is <1mm above 33hz.

10.4   Medallion II (1996) 

(* (* 2.54 3) (* 2.54 20) 31)

(* 2.54 3)

w: (* 2.54 12.5) 31.75 

s1: (* 32 (* 2.54 3)) 243.2
s2: (* 32 (* 2.54 5.2)) 422.656 
s3: (* 32 (* 2.54 11)) 894.08
s4: (* 32 (* 2.54 15))  1219.2
s5: (* 32 (* 2.54 17.5)) 1422.4
s5no2: (* 31 63)

len: (+ (* 2.54 19.5) (* 2.54 22)(* 2.54 14)(* 2.54 3))

atc??  (* (* 2.54 2.85) (* 2.54 12.5)) 229.83825
VTC: (- (* (* 2.54 2.85) (* 2.54 20) (* 2.54 12.5)) 1500)
pm6a-medallion-in.gif
pm6a-medallion-hr.gif

Excursion tops 1mm under 55 hz.

11.   References

[1] M.J. King on Lowther Parameters

[2] M.J. King, Back Loaded Horn Design