With most horns types (e.g. exponential
and hypex) you have reflections at the mouth which give resonances.
With the tractrix horn, since the waves are hemispherical going
through the horn, they exit with very few reflections. Tractrix
horns therefore have less colorations. HornCalc is a software
that calculates the tractrix contour in seconds.
Contents on this page:
1. Description of
the HornCalc.
2. Tractrix horn history.
3. Design considerations.
4. Software License
Agreement.
5. Ordering.
6. The HornCalc
demo download facility.
1. Description of the HornCalc.
The HornCalc demo version:
The demo version is limited to calculate round section
tractrix horns with a cut off from 300Hz up to a horn super-tweeter.
The demo version may be downloaded free of charge.
The HornCalc full version:
The full version calculates square and rectangular tractrix
horns in addition to the round style and also a very wide range
of sizes. Thus, everything from a 1-Hz infra-bass horn to a horn
super-tweeter may be calculated.
Software and Hardware Requirements:
HornCalc works with Windows 95, 98, ME, Windows NT or
XP on most personal computers.
A hard disk drive with about 1 MB free space is needed.
How to install HornCalc:
HornCalc is distributed as a compressed file. The demo
version is named horndemo.zip and the full version is named horncalc.zip.
You must first uncompress this file into any directory on your
hard disk. This will extract two files; either the "horncalc.exe"
or the "horndemo.exe" and also the "readme.txt"
file.
You can use PKWARE's PKUNZIP or any compatible utility such as
WinZip to do this. To start the HornCalc you double click the
HornCalc icon in the appropriate directory, or make a short cut
placed on the Windows desktop.
How to use HornCalc:
Begin by choosing "Circular" or "Rectangular"
in the "Settings" pull-down menu. After choosing units
and entering your values, press the "Test" button to
get the resultant horn length and mouth size. The display changes
accordingly if at any time you change the units (between mm and
inch) or "Horn size" (between radius and diameter).
Note: the decimal-point format is determined by your computer.
The proper format for your country (a point "." or
comma ",") is used automatically when the numerical
keys are pressed.
The "calculate" button yields the full list of measures
along the horn. Choose the appropriate "Table Increment."
If you do not, the list may become very long and the calculation
time could be increased significantly. The list can be saved
as a text file and edited in any word processor.
2. Tractrix horn history.
The Tractrix horn is designed to produce a hemispherical wave
front and to have less coloration than other horns. In October
5, 1927 P.G.A. Voight got the British patent 278,078 for a horn
based on the tractrix curve.
The following is an excerpt from his patent application:
"In a horn constructed according to this invention, the
taper at any point is as nearly as possible such that the sound
is expanding as if the source was at a fixed distance which is
at least a quarter wavelength, of the lowest frequency at which
full efficiency is required, away." And: "Since according
to this invention, the rate of expansion shall be as if the source
was a fixed distance away, it follows that the length of the
tangent is equal to this distance. The property of this curve
is therefore that the length of tangents is constant. At the
point where the tangent is at right angles to the centre line,
it becomes the radius. I call this point the "mouth"
and prefer either to terminate the curve at this point, or to
continue the plane (baffle) at right angle to the centre line.
The curve whose tangent to the centre is of constant length is
called the "Tractrix", and may be drawn by drawing
a small portion of one tangent after the other. In the case of
a square horn, the tangent to the corners is longer than that
to the middle of the sides and a compromise is unavoidable. I
prefer to make the section correspond to the tractrix. The shortest
tangent is then correct, but the area is 4/pi=1.27 times that
of the corresponding tractrix. If the area is made equal to the
corresponding tractrix, the tangent at the sides will be short,
a defect which is partly compensated for by the excess length
of the tangent to the corners."
And more:
"If the horn is assumed to have a horizontal partition along
the centre which is preferably continued for some distance in
front of the mouth, the sound will still expand perfectly in
each half. When the sound is not required to expand downwards,
as for example in a table gramophone [or a horn placed on the
floor -- Sonic Design], the lower half of the horn can be omitted
and considerable space will be saved."
3. Designing tractrix horns with HornCalc.
HornCalc is based on this formula:
x = a * ln((a + sqrt(a^2 - r^2)) / r) - sqrt(a^2 - r^2)
where;
x is the distance from the mouth of the horn,
a is the radius at the mouth, and
r is the radius at distance x from the mouth.
Different authors on loudspeaker horns have proposed different
ideas about approximating a square or rectangular horn shape
to the tractrix contour. P.G.A. Voight preferred the section
height to equal the diameter of the (round) tractrix. The area
of a square horn is then 1.27 times larger than the tractrix
contour, and the circumference, to which some authors pay great
attention, will be even larger compared to the circular circumference.
To calculate from the circumference, on the other hand, would
yield a smaller area from square horns than the circular tractrix,
and since the square and rectangular shapes are compromises anyway,
it seems safe not to complicate things more than necessary. Consequently
HornCalc calculates the sectional area of square and rectangular
horns based on equal area as a circular horn of the selected
cut off.
The cut-off frequency is determined by the size of the horn,
and the circumference of the mouth should be at least one wavelength
of the lowest reproduced frequency for a free field. The horn
length should be at least 1/4 wavelength of this frequency. If
you have input values that make the length shorter than 1/4 wavelength,
the calculated table will print a warning. But if you are to
add it to another horn, you may ignore the warning.
The cut off is calculated according to this and the formula;
Fc=c/(2*pi*r),
where "c" is the speed of sound, 340m/s, and "r"
is the radius of the horn mouth for the fully expanded tractrix.
This is in line with the articles in Speaker Builder about the
Edgar horns. You may note, however that P.G.A. Voight was of
the opinion that the length of the tangent from the horn flare
to the centre line should be a quarter wave of the lowest frequency
at which full efficiency is required. This tangent is a constant
throughout the horn and finally defines the opening radius. Thus,
P.G.A. Voight can be claimed to calculate: Fc=c/(4*r). His remark
"at full efficiency" may suggest a somewhat different
definition of cut off than -3dB, and this perhaps could explain
the difference.
A ratio of at least one to five between the throat and the mouth
area should be achieved. If this and the length are considered,
the mouth area can be reduced to 1/2 for placement in one wall
(baffle), to 1/4 for placement close to the floor and one wall,
and to 1/8 if the opening is placed in a corner. If the room
walls are not heavy enough, their supporting effect may be lost
and a larger mouth may be necessary.
One cannot simply choose a smaller mouth to get the reduction
of size, since the contour would not become right in that case.
A full-size horn is the base for the calculation of the reduced
horn, and the reduction is done by HornCalc by dividing the full
tractrix horn section into half, a quarter or an eighth, and,
as Voight said about the horn for half space, "The sound
will still expand perfectly in each half".
For midrange and tweeter horns, many of the tractrix horn advantages
are lost if the horn curve is terminated before the full, right-angle
turn is reached. Unwanted edge diffractions would be created
by the sharp edges of such a mouth. Thus no provision is made
for the reduction of circular cross-section horns.
The produced table of the calculations for circular horns has
an interesting feature in the angle column. If you would like
to add a tractrix mouth to an existing horn or compression driver
with a known or measured opening angle, it is possible to make
the start angle fit. Set the throat diameter to fit the preceeding
horn, and try different cut-off frequencies until you get the
desired start angle.
For rectangular horns it is possible to select two flat sides
if you would like the horn to be easier to build. If you make
the distance between sides 1A and 1B equal at both the throat
and the mouth, these sides will become parallel -- this can be
useful when designing folded horns.
The two flat sides may be used to design a horn for constant
directivity with the desired projection angle in one plane.
The produced table, when calculating rectangular horns with two
flat sides, has a column with values for the distance along the
horn measured on the flat side. This will greatly simplify the
construction of the horn sides.
4. Software License Agreement
By using the HornCalc full version or the HornCalc demo version
software on your computer, you accept the terms of the following
License Agreement between you, Almeflo Audio and Sonic Design.
After purchasing your copy of HornCalc you may load it on a single
computer and use it for as long as you like, provided that you
do not violate the copyright and follow these rules:
You may not modify, translate, reverse engineer, decompile, disassemble
(except to the extent applicable laws specifically prohibit such
restriction), or create derivative works based on HornCalc; copy
HornCalc (except for backup purposes); rent, lease, transfer
or otherwise transfer rights to HornCalc; or remove any proprietary
notices or labels on HornCalc.
Title, ownership rights, and intellectual property rights in
and to HornCalc shall remain in Almeflo Audio and Sonic Design.
HornCalc is protected by international copyright treaties. Title,
ownership rights, and intellectual property rights in and to
the content accessed through HornCalc is the property of the
applicable content owner and may be protected by applicable copyright
or other law. This license gives you no rights to such content.
You may copy the demo version of HornCalc to test and demonstrate
the software and its capabilities.
Termination
This agreement is valid as long as the copywright laws protect
the HornCalc software.
The license to use the HornCalc will terminate automatically
if you fail to comply with the limitations described above.
Disclaimer
Users of HornCalc must accept the following disclaimer of warranty:
By using this software you are consenting to and are bound by
this agreement.
HornCalc is supplied "as is." Almeflo Audio and Sonic
Design disclaims all warranties, expressed or implied, including
--without limitation-- the warranties of merchantability and
of fitness for any purpose.
Almeflo Audio, Sonic Design and the licensee are aware that functional
defects in the licensed HornCalc software cannot be totally ruled
out, in the present state of technical knowledge, even if the
very greatest care is taken.
Almeflo Audio and Sonic Design assumes no liability for damages,
direct or consequential, which may result from the use of HornCalc.
Under no circumstances and under no legal theory, tort, contract,
or otherwise, shall Almeflo Audio or Sonic Design be held liable
to you or any other person for any indirect, special, incidental,
or consequential damages of any kind, including, without limitation,
damages for loss of goodwill, work stoppage, computer failure
or malfunction, or any and all other commercial damages or losses.
In no event shall Almeflo Audio or Sonic Design be liable for
any damages in excess of Sonic Design's list price for one license
of HornCalc, even if Almeflo Audio or Sonic Design shall have
been informed of the possibility of such damages, or for any
claim by any other party. This limitation of liability shall
not apply to liability for death or personal injury to the extent
applicable law prohibits such limitation. Furthermore, some jurisdictions
do not allow the exclusion or limitation of incidental or consequential
damages, so this limitation and exclusion may not apply to you.
Governing law
This license shall be exclusively subject to the laws of Sweden.
Severability
In the event of invalidity of any provision of this license,
the parties agree that such invalidity shall not affect the validity
of the remaining portions of this license.
Entire Agreement This is the entire agreement between
you, Almeflo Audio and Sonic Design, which supersedes any prior
agreement or understanding, whether written or oral, relating
to the subject matter of this license.
Trademarks
HornCalc is a trademark of Almeflo Audio, Sweden.
Sonic Design is a registered trademark of Sonic Design, Sweden.
Windows® and Windows NT® are trademarks of Microsoft
Corporation.
PKWARE, PKZIP, and PKUNZIP are registered trademarks of PKWARE,
Inc.
Trademarks of other companies mentioned in this documentation
appear for
identification purposes only and are the property of their respective
companies.
Copyright
Copyright © 1997-2005 Almeflo Audio and Sonic Design, Sweden.
All rights reserved.
5. Ordering.
Ordering the HornCalc full version.
Please make sure you read and understand the Software
License Agreement before you order.
Price for the EU countries of Europe:
EUR 28 or SEK 250 incl. VAT
Price for all other countries:
$25 USD excl. VAT
The software is delivered via e-mail (0.15 MB).
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Required Information:
Company:
Name:
Country:
E-mail address:
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Please e-mail this completed form along with payment to the address
below. State "HornCalc full version".
Sonic Design
Skrytv. 27
SE-820 41 Färila
Sweden
Email: info@sonicdesign.se
Payment:
To be paid in advance.
You may pay with your card via PayPal to: info@sonicdesign.se
Or you could let your bank transfer the payment
to our account no:
IBAN: SE57 9500 0099 6042 0152 1491
BIC: NDEASESS
(with Nordea Bank AB
SE-105 71 Stockholm
Sweden)
Print this page and bring it to your bank and they will have
all the necessary information to assist you.
6. The HornCalc demo download facility.
Please make sure you read and understand the Software
License Agreement before you download the HornCalc demo.
FREE: HornCalc demo
download here.
Back to the Sonic
Design Homepage.