Tractrix midrange horn (Pt I)

This is the story of the round, midrange horns pictured and their (part) DIY construction in Fibreglass.

The midrange horns with Lowther PM4 drivers, sitting atop Mauhorn IVs:

“It remains hard to convince people, including acoustical engineers, that the midrange is where we live, and it is in the midrange that distortion is the most annoying and where amplitude response errors are most prominently evident. i have spent more man-hours of R & D time on the midrange than on the bass.”

Paul Klipsch, 1971

Horns are ‘acoustic transformers’… they give the driver a good load to drive and allow the high sound pressure produced by the driver diaphragm to be gradually and smoothly ‘transformed’ down to room air pressure level.  The power and efficiency of the driver is increased.

This midrange horn was originally made for Lowther drivers, but has been used also with Field Coil drivers & currently in use with SEAS FA22RCZ drivers.

Lowther PM2C & Lowther PM4

‘Old Brown Dog’ Field Coil drivers & SEAS FA22RCZ

I was attracted to the sound of ‘full-range drivers’ (‘wide-range’ would be a better description):

• I like the transparent sound of minimal-crossover in the important midrange.
• I like the ‘speed’ of lightweight paper cones driven by a strong magnet.
• The high sensitivity of these drivers (94-96dB/W typically) allows the use of low power, elegantly simple, short signal path, amplification (eg. triodes).

However, these drivers typically have rising frequency response, with stronger output in the upper midrange-low treble. (‘Whizzer’ cones also have problems – but that’s another story!)

SEAS FA22RCZ – typical response of a “full range” driver.

Midrange  horn-loading boosts the lower midrange frequencies (depending on horn size), gives an enhanced sense of scale and effortless, open, macro and micro dynamics.  The driver does not struggle to ‘throw’ a sound wave into the room.

HornResp simulation – SEAS FA22RCZ in 140Hz Tractrix horn with rear chamber loading.

Lowther PM4 in 140Hz mid horn – rough 1/3 octave response plots at listening seat, showing off-axis response with reduction of upper midrange peak.

My chosen design cut-off frequency (Fc) was 140Hz – LF roll-off often starts at 1/3 to 1/2 octave higher, eg. around 200hz.

The 140Hz Tractrix horn – compared with 150Hz Tractrix and 130Hz Tractrix profiles

The choice of the Tractrix horn flare profile was influenced by many things, including:

•  J Dinsdale, “Horn Loudspeaker Design” in Wireless World 1974, concluded, “…both theoretical considerations and very careful listening tests by the author and others tend to support the claims that the tractrix is the optimum horn contour.“
• Dinsdale claimed that the Tractrix contour “…combined the excellent low frequency characteristics of the exponential curve with the spherical wave propagation characteristics of a conical horn“. (Bruce Edgar, “The Tractrix Horn Contour”, Speaker Builder, 2/81)
  

  From “Horn Loudspeaker Design”, by J. Dinsdale, Wireless World, Mar 1974.

• The Tractrix profile “launches spherical waves that can yield excellent stereo imaging effects”  (Bruce Edgar, “The Edgar Midrange Horn”, Speaker Builder, 1/86)
• “The tractrix’s reduced length compared with conical or exponential horns of the same frequency range gives the advantage of being smaller than other horn contours.” ( Bruce Edgar, “The Tractrix Horn Contour”, Speaker Builder, 2/81)
• The Tractrix curve is generated from the mouth (not from the throat like most other horn profiles, except Le Cleac’h) and so, mouth-room termination is more gentle, more ideal & more efficient, in air-pressure terms. The Tractrix horn mouth terminates when curve tangent is 90° to the horn axis. “Keele found that beaming effects of conical and exponential horns can be minimized by doubling the flare at the mouth.”  ( Bruce Edgar, “The Tractrix Horn Contour”, Speaker Builder, 2/81)

Dr Bruce Edgar (Edgar Horn previously) has been responsible for much modern development in horn loudspeaker implementation, understanding and remedying colourations and addressing shortcomings that were typical of horn loudspeakers previously.  (I was fortunate enough to spend most of a day with this learned and generous man, on a visit to LA in the mid ’90s.)

Dr Bruce Edgar’s drawing – from his “An Interview with P.G.A.H. Voigt – Pt 1”, Speaker Builder, 3/81.

From “Horn Loudspeaker Design”, J Dinsdale, Wireless World, Mar 1974.

Some history: The Tractrix horn contour was developed by the German-born, British audio-inventor P.G.A.H. (Paul) Voigt in 1926 (patented in 1927). We should pay some respect to Paul Voigt.  Just a few of his innovations:

• He designed a loudspeaker driver in the mid-1920s, with ultra-light paper cone & ultra-high magnet strength coil (originally electromagnet field coil) – specifications still currently marketed by Lowther and others.
• Voigt invented the twin-cone loudspeaker, which was licensed to Wharfedale and Goodmans.
• Voigt patented  the Tapered Quarter Wave Pipe (TQWP) enclosure concept for loading speakers.
• He developed horn loudspeakers for domestic and cinema use.

My Tractrix horn was to be cast in Fibreglass, so a mould needed to be made first.  The easiest options were to use Polyurethane foam or Extruded (XPS) or Expanded (EPS) Polystyrene foam – Expanded Polystyrene (Styrofoam) was most economical.

The horn curve template cut from MDF sheet.

80mm thick polystyrene foam layers glued together, with Tractrix curve template.

Rough-cutting the Styrofoam, with a bread-knife.

Shaping the ‘mouth-roll’ with a curved sandpaper block.

The Styrofoam mould is finished to shape and smoothed simply with sandpaper.

Detail of the throat-driver flange end.

I had no experience in Fibreglass, so I took advice from a Fibreglass workshop (Allied Fibreglass in Auckland).  They hard-coated my Styrofoam mould, recoated and spray primer-coated it – for me to do all the simple, laborious hours of sanding and sanding and sanding….

The Styrofoam has been hard-coated by the Allied Fibreglass workshop, ready for more sanding, by me.

The final sandable spray coating has been applied, fine-sanded and minor imperfections filled with fine epoxy-filler before more fine-sanding.

The almost-finished mould – not perfect smoothness yet but looking very good.

Completed Fibreglass Tractrix horns – cast with white ‘gel-coat’ and increased layer thickness near mouth to reduce resonances:

The first completed horn, with integral driver flange, cast on my mould by Allied Fibreglass:

A later version with separate throat-driver flange, makes it more compact for shipping….

Removable flange version, stacked, ‘nested’ together.

Throat-driver flanges can be epoxy-glued on later.

Finally, a nice pic of….

Horns made for Jonathan who took them to Sydney, Australia.

Useful links:

• Tractrix Horn Calculator
• “Horn Loudspeaker Design” Pts 1 – 3, by J. Dinsdale, Wireless World 1974 – http://wp.volvotreter.de/dl-section/articles/
• “The Edgar Midrange Horn”, Bruce Edgar, Speaker Builder 1/86 – http://wp.volvotreter.de/dl-section/articles/

(Thank you, Volvotreter.)

Any comments welcome!

Update March 2016:  Tractrix Midrange Horn – Drive Units