Arai horn design

Introduction


Arai 290 and 480 horns are Hyperbolic Constant Directivity 95° horn so this opening is coherent between 2.5m to 6m listening distance, further you will need a 60° horn.

The coherence of a speaker is when we are are close to a 50/50 ratio between direct field (what go out of the speaker directly to your hears) and the reverberant field (the direct that touch a wall and go to your hears). More information about this :
http://hyperphysics.phy-astr.gsu.edu/hbase/Acoustic/reverb.html

As the horn use fins, it maintain an open directivity upper, fins are really important in this design with these opening coverage and allow a Constant Directivity pattern. Each fin create a horn cell by division, each horn cell must be identical, symmetrical and have the same point of origin.

Yuichi made Arai horn without fins but mainly for mid-range application as he said, for full range it doesn't make sense, specially for the big A290. Due to her smallest size the A480 is less impacted, but still impacted, to fins removal.

The throat adapter is round to square so there is no compression, no pinch are present at the throat.
The consequence is that at 0°, in front of the horn, you will need EQ but once you have EQ the off-axis measurement haven't any noticeable accidents.

The brain merge direct and reverberant field but know the difference due to timing, because reverberant arrive later, so even if you listen on-axis in a room, you need the better off-axis behavior possible for a room listening.

Differences and behavior compared to TAD TH4001


The TAD TH4001 is the closest cousin of the Arai 290. The TH4001 barely don't need EQ due to round to rectangle (it's a pinch so a compression) throat  adapter but have an audible accident as a resultant. This accident will be off-axis and moving in upper frequencies according to the measurement angle, he will impact reverberant field, not in a very good way.

The Arai sound large at all frequency and the TH4001 tightens in high frequencies, the result is that feel that the Arai 290 sound more natural and neutral at upper frequency and are globally more coherent than TH4001 in a room without acoustics treatment on side walls, in a pro studio environment it will be less (or even not) the case.

These two horn look the same but by listening side by side in a room they have in fact a different behavior due to the compression on the TH4001.

Here is the original design content based of the Arai 290 wrote by Yuichi Arai, I have added some observations in red:


This is not a perfect design guide, but gives you some idea to generate the Horn contour. Originally I wanted to build a good Horn speaker. Unfortunately I could not find out good design guide which matches to my willing. So, I made may own calculation system long time ago. However, the Horn system exists still in the high end market today. Which means that there is still some DAY funs in this space. This is the reason why I summarize how to design the horn from my book which was published long time ago. Please refer the idea how to generate the horn design such as A-290 but not to look at details. I have no confidence about the consistency in detail numbers.

The horn expands its horn space (S) from the throat position (So) to the mouth (Sm). "How it expands"? depends upon the equation which is so called horn type. Which includes the "Exponential", "Hyperbolic", "Cone" and "Tractric". Since the Tractric horn expands its horn space up until the infinite baffle, its horn length is limited. Other horns have unlimited horn length. Therefore, we cut the horn length intentionally because we can not make it.

Here, we discuss about the hyperbolic horn which has nicer capability than the exponential horn. In reality, the exponential horn is one of the hyperbolic horn. In any way, left fig. shows the naming of each part of the horn.


Where x=Horn Length from the throat

You can find out the equation of the hyperbolic contour in the text book such as above. In the equation I assumed as follows to make it simple.
Horn width = Horn Height
Fc=200Hz, T=0.6 (flat frequency response) T=1 generates the exponential horn.
The calculation is as shown in the left. First the Horn space is calculated to the horn length. The horn length is endless. However, there is conventional equation to cut the horn length which came from Fc (cut off frequency Hz) or wave length. In this case the horn length is 48cm or the mouth space 2668 cm^2. This size creates the minimum impacts of the acoustic impedance from the mouth area. We call this as a full size horn.
Now we can design the horn system.
The reason why the A-290 has several fins inside is as follows. Without fins the high frequency sound over 8KHz concentrates in the center of the horn. Therefore, the separator is important to have flat frequency response to provide wider service area in front of the Horn. Just thin separators will creates some problems. Therefore, the fins has to be reasonably robust.
Then,.....we assumed that the A-290 type horn consists of several Horn cells or sub horns as illustrated in the left fig.
So, from now on, we consider to calculate single horn cell. The summation of horn cells follow the equation (S). How many horn cells we I have, is totally up to us, but there is not so much freedom available. So, we have to do "cut and try" many times on the computer.

Fins and sides is disposed in a circle with a precise common origin, so the sides are barely an extended fin. That is very important for off axis behavior.


Left fig. shows a model of single horn cell. In this case, above horn consists of five small horn cells. A horn cell consists of two horn space expansion mode, S1 and S2.

S1 and 2 is two space expansion but it still the same mathematical expansion law with the same surface origin (So).

The horn cell starts from throat space (So) with height (H). The height (H) stays the same until the end of the Fin. In this area Horn space (S1) belongs to radial expansion of both side wall minus thickness of the fins.

After the end of the fin location, the Horn space (S2) follows the radial expansion of side walls and expansion of the height (HD*2). So, the S1 and S2 expand the space in deferent ways. Smooth transition between S1 and S2 is important. So, thicker fin is good for mechanical point of view but not good for acoustic point.

Here x²+y²=R² is true for a 90° horn that is composed of five 18° sub cell, but the Arai is 95° (5*19°) so the formula is not very accurate and will provoke a shift.

This is the top view of single horn cell or a sub horn. Each horn cell is to be aligned with angle AN. The center horn cell starts from X2. And each throat of the horn cell is located on circle R. It is easy to understand the factors of horn space expansion horizontally. The contribution factors are the radial expansion and the thickness of the fins up until the end of the fin area.

This is the side view of the horn cell or the sub horn. It is easy to understand the factors of horn space expansion vertically. In the fin area, the contribution to the horn space is horizontal only because the height (H) stays the same. After the fine ended, displacement of the horn height (HD) complement the radial expansion to keep S2.

This is the cross section of the fin. On this chart, "T" means half of the fin thickness. Therefore, T*2 is the thickness.

This is the calculation of single cell where...
HL=Horn Length, HS=Horn Space, HH=Horn Height, HD=Horn Height Displacement, W=Width, T*2=thickness of the Fin, FL=Fin Length

The Fin Length longer than 19.26 is invalid because the fin thickness (T*2) becomes zero.

The length of the horn cell is 37cm. This does not 100% match to the horn length. This is because of mismatch between throat positions of the horn cell and the horn.


Consequence of the previous formula (see upper), 23mm is a rounded value and fins is too close, they are aligned as in a 90° horn, Arai is 95°.

Above is the calculations. To do this, I cared about available size of wood materials, possibility of process, thickness of the fin, the mouth contour, side wall contour, angle of the horn, and other factors.

One other thing is how to fix the driver with square (four corners) mouth. It usually use the cast in the professional world. But for DAY way it is not applicable.

So, another "Try and error" processes contributed to generate the drawings. So, the size does not perfectly match to the calculations for smooth matching to the air at the mouth area and others.

As upper, there is a shift so it's not really 200mm too, it's a little bit more.

This is the side view of the horn. The thickness of the wood material at the mouth location keep 1cm to minimize vibration. The throat of the horn cell is located 1cm inside of the horn throat. This came from the drawing of the top view.

Four mounting holes are provided to fix the throat adapter.

This is the drawing of the throat adapter. There are two requirements to this component.

One is to convert 5cm diameter driver space to 5cm x 5cm horn throat. This space expansion requires 2.5cm length of the horn. Therefore, I used 2.5cm thick hard wood.

One other purpose is to mechanically fixes the driver to the horn.

To perform these objectives, the throat adapter is designed.

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