Conical Horn Geometry
I’m often asked how horns differ from one another, and also how different types of horns differ in sound and design, such as exponential, tractrix, and new versions of these which carry the names of their designers. I’ve put together some observations, backed up by actual frequency response curves and measurements, so that people can decide for themselves what types of horns would work best for them.For the past 30 years I have designed loud speakers for professional applications and more recently for home HiFi. While designing at Yorkville Sound and in the course of my career, have built and tested numerous exponential and tractrix horns. This includes hybrid profiles using a tractrix and a conical which were created to fulfill specific tasks. In professional audio, horns have to work as intended. They cannot be of unlimited size - in fact, there exists an obvious commercial advantage to building the smallest horn to do a given job well. Tractrix or exponential horns are rarely used in professional applications where clarity and coverage are an issue.
In the early 80's I built a four sided conical prototype to be converted to a bi-radial design. I was astounded by how good it sounded so I measured and tested it. This opened the door to the study of conical horns. Some of the characteristics of conical horns are….
- Good directivity or power response - the hallmark of the conical horn.
- Conicals keep the sound wave at 90 degrees to the wall of the horn at all times as the wave exits the horn.
...After Hughes (Peavey, Also Morse)
(this defines a conical.) The sound wave is not disrupted by the walls of the horn. For these reasons, conical horns have the best sound of any horns for home HiFi Use.
The accidental conical horn
The tractrix profile has been used in commercial products and in DIY. All exponential, and tractrix horns tend to beam as they go higher in frequency due to the squeezing of the side wall of the horn. This results in a "honky" sound and some of the high frequency information is lost, when listening off axis. This is the case no mater what type of mouth correction you might use. The tractrix profile itself is a form of mouth correction.
My first tractrix in production 1989
I have experimented extensively with all types of horns, using absorbing materials, mouth geometry, adding a foam ring at the horn’s mouth, cutting slots, and also with acoustical lenses. (see photo) I have discovered that these devices have, at best, an ameliorating effect, often redistributing the anomalies they try to correct to other places in the passband instead of eliminating them. The acoustic lens holds the most promise.
It is interesting to note that RCA acoustic laboratories analyzed the conical horn flare and mouth termination issues in the 1950's. I am lucky to be in possession of the very lab sample test horns, of which my work is based. See picture.
In listening tests, the rollback using pink noise is very slight. Few individuals have the time, money, space, and technical ability to build and compare using state of the art hardware and software. (I use a TEF analyzer, ATB B&K ,AKABAK, AJ horn software, etc).
I can, however, suggest a simple way to make some experiments for yourself, to see how horns differ from each other in a very rudimentary way. Choose a compression driver, and make a number of very short horns of only 4-5 inches in length ---really horn adapters-- for your driver.
The most critical part of a horn is the first few inches. This is often over looked. Start with a section of straight pipe. Listen to that. It will be very loud, and very colored. Next, try an exponential horn of the same length, then a tractrix - they will be progressively less colored. Finally, try the conical section. It will be the most natural sounding and uncolored.
Musical instruments such as trumpets and trombones are not conical. They are designed to produce harmonics, the very thing we try to avoid in a sound reproducing device. The more the horn is squeezed, the more the harmonics. On the other hand, voice producing devices such as megaphones are always conical.
Horn design is always a game of balancing the factors of length, angle, directivity, low frequency cutoff. There are many ways to tweak a horn’s response. One is to add an exponential throat adapter to a conical horn. This colors the sound, but improves the measurements. Another is to add a secondary flare to a conical to deal with the internal reflection issues.
One other area which deserves discussion is the crucial issue of the beginning of the horn- the throat- and the drivers being used. Compression drivers all have a horn beginning within the driver which you cannot see. The internal geometry of the driver and its phase plug has a direct relationship with the horn.
Sometimes a small exponential throat will be of benefit, sometime it will not. Once again it is a question of degree, and audibility.
If a driver has an exit a half inch, you will likely get to 12kHz, but a driver with a 2 inch opening will be lucky to reach 8kHz. Directivity decreases as the throat diameter increases. Also, if a 2 inch exit diameter driver is being used on a horn expected to go up high, the issue of mouth reflections coming back into the horn pales compared to the very real problem of high frequencies getting “stuck” across the 2 inch throat opening of the horn
As you can see, designing horns is actually a very complex equation involving parameters that all need to be addressed so that an optimal design results. There is no such thing as an “ideal” horn. But certain basic flare profiles work vastly better than others if the best sound quality is the most desired result.
Some general horn examples under test.
I have hundreds of pictures, hundreds of horns, but this is enough for now.
Itawa horn, and odd drivers I use to cover a complete range of drivers when testing a horn
Also A multiple flare horn after Olson
We stand on the shoulders of giants...
Olson
Holland and Newell
I built the Holland horn soon after his paper came out. the gray one was cut down from a 24" mouth version
Morse
Geddes
Here is 90 deg conical with and without rollback. Also a tractrix, and a tractrix mouth coupled to a conical throat
Danley
Keele
RCA
Western Electric
The US Navy
A battle annonce speaker with special articulation drivers. 119dB 1w/1m!
...and many others.