The 3D-Spiral Horn Speaker Building
Why 3D-Spiral Horn?
Revised on 4 Apr. 2006

gifbuild
When I had hit upon a 3D spiral horn concept several years ago, my intention had been to improve a folded rear horn.
A rear horn utilizes the sound radiated from the back of driver to enhance effectively bass sound. A folded rear horn made of plywood is difficult to build because of its complicated structure. Moreover, its sound quality is degraded by unwanted resonance originated from its angular sound passage.
I had thought a 3D spiral horn might solve these problems by its relatively simple structure and by its curved surface.

After numerous trials, I have reached an understanding that the rule of thumb applicable to a rear horn had not stood up for a 3D spiral (horn.)
My experiences have been a history of struggle for freeing myself from common senses about rear-loaded horn.
This may imply that a 3D-spiral (horn) is a new type of loudspeaker, which belongs neither to a rear-loaded horn nor to a ordinary bass-reflex (vented box).

A 3D spiral horn has a relatively short three-dimensional spiral sound passage that looks like a conch shell.
Its structure is comparatively simple. It can be built using standard PVC pipes and fittings. Therefore, you do not need a high degree of technical skills to build.
The most prominent peculiarity of 3D spiral (horn) is that its lower frequency region extends to 50 Hz using 3" full range driver without booming and without decline of SPL. (Please see frequency response of Helix-H75)
Sound degenerations are minimal because a 3D spiral horn has a smoothly expanded sound passage and because there is no parallel plane, which may produce standing wave. Recent examination has indicated a constant pitch spiral gave an equivalent frequency response with an expanded spiral. (See VC75)
If you bring the ear close to the horn mouth, you can hear very clear sounds although bass sounds are much emphasized. This means the distortion inflicted through a 3D spiral horn is minimal.
linear model
conch shell
A Japanese conch shell is shown left, and here is a sound sample. Buddhist monk practicing asceticism in the mountains blows on a conch shell of the present age.
The rules of thumb applicable to a 3D spiral horn are:
  1. Air-chamber volume must be big enough. But, a too big air-chamber or too low fh compared with Fs may not come to a good result. The optimum fh may be (Fs/2) Hz.
  2. Optimum rotation number of spiral (horn) may be 1.0 to 2.0. (Relatively short horn length may be desirable.)
  3. Drivers with high Qts (over 0.40) are favorable.
A 3D spiral (horn) system is same as a bass-reflex (vented box) at least in principle, and its behavior can be explained with Helmholtz resonance.
3D spiral (horn) is not only a method for making a longer port, but also a method for getting a high quality deep bass lower than Fs.
Helmholtz resonance frequency fh may be given by

helmholtz
Where
c: velocity of sound
S: cross-sectional area of throat
V: volume of air chamber = box inside volume - (horn volume + volume of reinforcements)
L: maximum length of spiral
L = nπD + Lt/(n + 1)
n : rotation number of spiral horn
D : inside diameter of tube
Lt: length of tube
throat

There is some contradiction between previous rules of thumb and the equation. The equation indicates small S, large V and long L are better for lower fh. It seems rational to say that a way of obtaining higher SPL at bass region should compromise with a way of obtaining lower fh.
energy

The contradiction may be explained by the above figure in which the sound energy conservation law is showed.
For example, the deep-bass region is raised in compensation for lowering the mid-bass region at too low fh compared with Fs (red line.) Thus, the sound energy is coserved.
Helix
models
V
liters
S
cm2
L
cm
fh
(calculated)
Hz
fh
(observed)*
Hz
L152 20.4 56.7 107 28 25
H125 12.4 45 50 46 45
H88 3.6 17 32 65 60
* Location of the first frequency peak measured by mouth output.

Although a horizontal model makes me hesitate to use a word "horn" because a 3D spiral horn is too short as a horn, I will continue to use it.
Measurements of the impedance characteristic
From the following measurements of impedance characteristic of the 3D spiral horn systems, conclusions are as below.

(1) There are two impedance peaks, and the frequency of the first impedance peak is about half of Fs. This is similar to an ordinary bass-reflex (vented box).

(2) The most prominent feature of a 3D spiral horn system is that the low end extends flatly to the first impedance peak frequency. This may be the reason of the far extended low end compared to ordinary bass-reflex (vented box).

(3) The frequency of the first impedance peak is nearly equal to fh, but vary with Fs.

comparison

Impedance measurements
config
Helix
models
Drivers Fs
(specification)
Hz
First impedance peak
(observed)
Hz
fh
(calculated)
Hz
fh
(observed)
Hz
L152 GW-S650/8 55 20 28 25
H125 FW168HP-X 70 38 46 45
H88 FE88ES-R 106 48 65 60

l152 Vertical axis has an arbitrary linear scale and is proportional to the impedance of the driver.
Resolution 5.383Hz


Impedance characteristic of Helix-L152 and naked GW-S650/8.
h125 Impedance characteristic of Helix-H125 and naked FW168HP-X.
h88 Impedance characteristic of Helix-H88 and naked FE88ES-R.
L152/FW168-GW
FW168/H125-L150

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