# Progressive Expansion T-Factor Horns

In this post I would like to describe a method that I have been using since some time to get more flexibility with regard to different horn profile slopes. The fact that slow expansion profiles like the exponential or spherical wave horn provide very good loading but suffer somewhat with respect to directivity control inspired me to look for an algorithm that influences the given specific horn expansion function. I ended up with a modification of the well known wave front surface area expansion formula for hyperbolic (hypex) horns which is given by:

\tag{1a}S_z = S_0\cdot \left( cosh(\frac{m}{2}\cdot z) + T \cdot sinh(\frac{m}{2}\cdot z) \right)^2
\tag{1b}m=\frac{4\pi \cdot f_c}{c_s}

I will not go into more detail but with T=1 we get exactly the well known exponential horn for a two dimensional surface area expansion. This formula can also be used for the spherical wave horn with it’s assumed spherical wave fronts and will put out the same SWH profile already described on this site. Equation (1) is extremely flexible because whenÂ  T \lt 1 an hyperbolic profile is the result and when T \to \infty the horn profile becomes conical. This is the reason why I switched to this formula as it gives me the flexibility to produce horn shapes with different slopes only by changing one parameter. Up to here nothing new but what if we make T a variable function that depends on a reference point somewhere on the horn axis z_{off} and the distance from or to this offset?

# DrBA Calculator and BEM Simulation

DonVK’s second article deals with the verification of the DrBA spherical wave horn calculator and BEM simulation model construction. Only the round mouth spherical wave horn was initially used for comparison to published works. Additionally, the effect of adding a roll-back section or even more a merge of the roll-back section with the inner horn wall will be discussed. As already mentioned in the original patents, the continuation of the horn profile beyond the mouth plane has positive effects and leads to more even results.

# BEM Simulation for a Freestanding Horn

After I had finished my first horn profiles as 3D models, the question arose whether it is possible to perform a proof of concept by simulation. Doing some research on the web, I soon discovered the simulation software ABEC3 (http://www.randteam.de/ABEC3/Index.html). Fortunately, by a lucky coincidence, I was able to make two contacts through a DIY forum, which were far ahead of me in this area and have supported me with discussions and simulations. In particular, I would like to thank Don for his tireless support in creating and visualizing the respective ABEC3 scripts for the further development of respective horn profiles. Without Don’s involvement in my projects and the encouraging results, I would hardly have pushed the programming and, of course, the creation of this website with this commitment. I was able to motivate Don to summarize his findings in a few articles and I am pleased to present them in this context.

In particular, I would also like to thank Joerg Panzer, who has provided us with free non-commercial ABEC3 licenses. Thus, it was possible that we could easily exchange the results and work much more efficiently.

The challenge was from the beginning that the horn profiles should work especially as free-standing horns. This requires the simulation of specific measures and configurations. Don wrote an article that I would like to publish here.

The BEM simulations shown in this article took several hours to solve on our workstations which are on a quite actual performance level. It should be mentioned that especially the high frequency part beyond 10 kHz is a special challenge and the results still show some artifacts which are clearly related to the underlying model.