This thread is to share information about the shape and performance of the various horns and waveguides that may be of interest to DIYers. This follows on from my thread “Handmade Ersatz M9500 Speakers”, which my be found at:
The above thread generated some spirited discussion, and provided some useful information on Horns and Waveguides. Hopefully, that can be continued here.
To get things rolling, I am attaching two graphs which compare the contours of Conical, Exponential, Hyperbolic, Tractrix, and Hughes (Peavey) horns / waveguides. Some information on these types may be found in the above thread, including a paper by Charles Hughes on his “combination” waveguide.
It is important to note that with the exception of the Tractrix, all of these contours have 3 degrees of freedom. This means that one may choose a throat diameter, a mouth diameter, and a length (i.e. depth), and a solution may be calculated. Of course, extremely shallow (i.e. short) horns will have extreme “flare factors”, but they will nevertheless be part of that family of contours. However, the Tractrix only has 2 degrees of freedom. Therefore, if one chooses the throat diameter to start, then only one other choice remains. If a particular length is selected, then the mouth diameter is defined by the equation. Or, one can select a desired mouth dimension, and end up with the length specified by the Tractrix formula. This paragraph is the reason for the two graphs, as will be seen below.
My favorite horn dimensions are 2” throat diameter, 15.5” mouth diameter, and a length (depth) of 6”. This allows the horn (waveguide) to “match” a standard 15” bass driver in size, have the same bolt hole pattern, and perhaps even be retro-fitted into an existing “dual 15” cabinet. I used this configuration in my M9500 speakers described in the above referenced thread. Therefore, the first graph below follows these dimensions. My actual horn is exponential, and the others are calculated using the same parameters. The hyperbolic has a “degree of hyperbolic expansion” (M) of 0.4. (M is an additional parameter in the hyperbolic equation that can be used to shape that family of contours.) However, since we have defined the length (depth) of this horn at 6”, the Tractrix will probably not have the same mouth diameter as the others. It doesn’t – it’s 9.5” diameter at the mouth, instead of 15.5”. This is not really a “fair” comparison for the Tractrix, so the second graph shows a Tractrix with a throat of 2” dia, a mouth of 15.5”, and an equation-calculated length (depth) of 13.52”. All the other contours, on the second graph, are then calculated to these dimensions. Such a deep horn is not practical for my application, but it does compare all the contours with identical parameters.
Here are couple of interesting facts about the Tractrix horn. The Tractrix curve was discovered in the 1600’s, when a gentleman placed his pocket watch on a table, and pulled it along by running the other end of the chain along the straight table edge. The name, Tractrix, is derived from the Latin verb “to pull”. In 1927, P. Voight was granted a UK patent for using the Tractrix curve to produce a hemispherical wave front horn.
Finally, there are two competing German companies, www.acapella.de and www.avantgarde-acoustic.com , that both market “spherical horns” that they claim to have “invented” in the 1970’s. Their descriptions sound like a Tractrix horn (patented in 1927!). Does anyone know if their horns are different, or is the name just a marketing ploy? Inquiring minds want to know!