Horn Response Help
<Paul Spencer, Rademakers & John Sheerin>
Introduction
The Horn Response program, written by David McBean
? and based on Olson's horn model, is a very easy to use horn simulation program. David wrote the original version in the early 1970's in Fortran IV and ran it on a room-sized IBM mainframe computer. Some people call it a bass horn simulation program as it does not have enough input information to always simulate higher frequencies accurately, but the model is accurate for predicting power response at higher frequencies as well (more on this later). But if it's so easy, why write a guide? While it's easy to use, it has some abbreviations and terms which will remain a mystery to many, even after reading the built-in help file. Hence the reason for this guide.
Entry guide
ANG:
Here you indicate where the horn is located. In a nutshell, enter 0.5 for typical hifi corner loading, or 2 for PA outdoors use where you will have a floor but may not have a rear wall.
| INPUT | INPUT DENOTES | SPACE | DESCRIPTION | Typical Application | Comments |
| 0.5 | Corner loading | 1/8 space | Placed in a corner | Hifi | Horn can be made smaller |
| 1 | Floor & Wall | 1/4 space | On floor with one wall | | |
| 2 | Ground only | 1/2 space | On ground outdoors or middle of room | Typical PA | |
| 4 | Full space | Full space | Suspended high over the ground | Large PA | |
Low-frequencies radiate omni-directional, this means that the sound radiates from the cabinet in all directions. This way the sound forms a sphere surrounding the cabinet with the cabinet/speaker/source being at it�s centre position. This full sphere is known as 4 Pi space.
4 Pi is fullspace
It means that the cabinet is flown high (relative
to the length of the wavelength) above the ground.
2 Pi (or 1/2 space)
usually means on the floor, but it could also be interpreted as against a wall (only one). With 2,0 Pi the sound that would have been radiated down in fullspace is now constrained to go forwards or upwards. It�s like there is a mirrored cabinet beneath the floor. Because there are now (virtually) double the amount of cabinets present, the horns will couple and by this also extend the low frequency response. So the smaller the number in front of Pi the louder and deeper the horn will reach with the same input.
1 Pi (1/4th space)
usually would be on the floor and against a wall.
0.5 Pi (1/8th space)
is also called cornerloaded, so on the floor and against 2 walls. If the horn mouth is not truly in the corner, you might get some cancellations based on the distance the mouth is from the corner (but this is not simulated in Hornresp)
0 Pi for infinite horns.
This is a good way to look at theoretical situations.
VEL
The velocity of sound in air at a given temperature and pressure (at standard conditions). Unless you know the precise conditions of the location your horns will be used at, keep this at the default value - 34400 cm/s.
DEN
Density of air at a given temperature and pressure. See VEL.
S1
This is the area at the beginning of the horn (or throat area), the end closest to the driver. It's ratio to the driver's area sets the compression ratio.
Compression ratio
The compression ratio is Sd/S1. So if Sd is 1220 cm2 and S1 is 610 cm2 the compression ratio is 2. What the compression ratio will be is up to you, but there are some boundaries you should take into account. 10:1 is what some high frequency compression drivers use - this is considered high for midrange and bass horns. 4:1 is more typical of the range used in midrange and midbass horn, with 2:1 to 6:1 being pretty standard. Because there is no published parameter yet for the strength of the cone (hint to manufacturers ;), it�s not easy to figure out what a safe compression ratio is other than figuring it out in practice (too high a compression ratio could cause the cone to break due to high pressures generated at the throat of the horn). Thus if you are designing for home hi-fi use, this is usually not as important. If you are designing for pro-sound levels, it becomes much more important.
S2
This is the horn segment 1 ending area and horn segment 2 beginning area. So you don�t have to type this again in S2 at the beginning of the second horn segment (because S2 = S2), Hornresp will do this for you.
L12
The (axial) length of horn segment 1 (in cm). You can choose CON (conical), EXP (exponential), HYP (hyperbolic-exponential), TRA (tractrix) by typing c,e,y, or t while your cursor is in the length box.
Many horns are built out of several conical segments, which together can come close to approximating the shape of an exponential expansion (for example).
Keep this part in mind when designing your horn (if you ever intend to build one). It�s not easy to build a true exponential (and still solid) sub/bass horn. This is the main reason why most horns consist of conical parts.
Mid/high and bandpass horns can be made much shorter and frequently consist of just one horn segment. With a bandpass horn the throat and rear chamber become more important (more on that later). However, all horns are bandpass devices - the importance of sizing the front and rear chambers depends on the exact characteristics you are trying to design for.
F12
Horn segment 1 flare cut-off frequency in Hz (for exponential, hyperbolic and tractrix)
FLA
Hyperbolic (-exponential) horn flare parameter. This controls how fast the horn flairs as you get towards the mouth. I usually go to the hypexdesigner (double click on any of the input parameter boxes) but you can also go straight to hyperbolic flare (press H when length tab is highlighted). You can only use the input boxes for the first segment now (S1, S2 and L12)
FLA = 0
the horn flare will be catenoidal, this type of horn flare is really nice to integrate in a design since the horn will almost not expand till it�s close to the hornmouth, where it will expand very quickly. You will find that this way it�s easy to fit a long horn in a relative small folded horn enclosure.
Of course there is a downside to this: To get a nice and deep output, you want the horn to expand more quickly like with:
FLA=1 (exponential)
An exponential horn will give more gain in the low-frequency reproduction of the basshorn than a catenoidal horn. However as you might aspect, it�s much harder to fit it nicely into a compact folded horn enclosure.
Luckily you can make it anything in-between 0.00 and 1.00 so that you will get a compromise you�ll like.
These aren�t the only possibilities though, with:
FLA = 99,999.99
You will get a conical horn. A conical horn will be totally straight, from S1 to S2 it will go in a straight line. Conical horns often have a small "hump" (few dB's gain on small frequency-band) before they fall off downwards. In some cases you can use this hump to extend the low-frequency response.
T/S Parameters
Hornresp can calculate BL, CMS, RMS and MMD out of other T/S-parameters. Just doubleclick on the tab and a calculator will appear that will
calculate the mechanical parameters from the T/S-parameters (Fs, Qes, Qms. Vas).
SD
Driver diaphragm piston area (in square cm / cm2)
Typical SD values
| DIAMETER | SD (cm2) |
| 5" | 85 |
| 6.5" | 130 |
| 8" | 230 |
| 10" | 330 |
| 12" | 500 |
| 15" | 780 |
| 18" | 1200 |
BL
Driver's force factor - a measure of motor strength. This is equal to the magnetic flux density in the gap (B) times the length of voice coil wire in that flux (L), and thus the units are Tesla-meters.
CMS
Driver diaphragm suspension mechanical compliance (m/Newton).
Compliance is the inverse of stifness. If you double click on the CMS box, the calculator will ask you if the VEL, DEN, and SD values are correct. Then it will ask for the driver's Vas in liters (cubic dm / dm3).
Footnote: 1 cubic ft ~28.32 liter.
RMS
Driver diaphragm suspension mechanical resistance (Newton.sec/m).
For this parameter to be calculated you need CMS
(so calculate this first if necessary), Fs and Qms.
MMD
Driver diaphragm, voice coil, and other moving parts dynamic mechanical mass.
Mms also takes the weight of the air displaced by the driver
into account. Therefore Mms is higher, but not by much.
LE
Driver voice coil inductance (Milli-Henry's).
This can't be calculated from other T/S-parameters. The Le will have
a large influence on the highfrequency roll-off of the horn in some cases. A higher
voice coil inductance will limit upper useable range, however in a
bass horn other compromises such as bends in the horn and the front chamber volume could impose a more significant limit.
An Adire whitepaper demonstrates an impact on transient response which may be a more significant effect.
RE
Driver voice coil DC resistance.
For an "8 ohm driver" this will generally be around 5 - 6 ohms.
ES
Amplifier RMS Voltage (Volts). Effectively input power when squared and divided by impedance (see the electrical impedance tab).
This will influence the SPL and cone excursion and enables you to get
an indication of max SPL performance based on excursion limits of the driver.
Hornresp has a calculator (appearing once again upon doubleclick)
that can "translate" the amount of Watts, on a specific load (impedance),
to the Voltage required in the tab.
2.83 Volts translates into 1 Watt @ 8 ohm. 2.83 would also be 2 Watts into 4 ohm.
For instance if you need 200 Watts into a 8 ohm load, Hornresp calculates 40.00 Volts.
VRC
Rear compression chamber volume (liters). This is the horn's rear chamber
(in case of a frontloaded horn). In most cases it's a closed chamber with the
speaker mounted into one of its walls, like in a standard sealed box system.
A hornsub that is meant to be used in singles generally has a large rear chamber to get a decent output on low frequencies. The downside of a large rear chamber is the accordingly lower mechanical powerhandling (Xmax is reached with a lower power input).
A hornsub that is meant to be used in stacks generally has a smaller rear chamber. These kinds of subs trust more on the hornloading of the stack to get decent output at low frequencies. If a horn like this is used on its own, it will have a relatively large dip in the frequency response (like the LAB horn). By stacking multiple horns together the mouth area will be enlarged. The lower the frequency, the bigger the mouth area needs to be to give good results.
Bandpass Horns (BPH) generally also have large rear chambers, mostly combined with a large VTC (throat chamber). It's hard to define a specific number here but a rear chamber above 60 liters (for an 18" or smaller) would be considered quite large. BPH are also typically meant to be used in multiples. The horn length is too short to be a true horn. By stacking the horns together, the virtual hornlength will increase slightly due to a larger end correction from the larger mouth area, thus lowering the cutoff frequency of the horn compared to a single one.
LRC
Rear compression chamber average length/depth. If you mask the resonance of the rear chamber, this has no influence (Tools, Options: Throat chamber and rear chamber resonances), so you can put here any number you like (i.e. 20 cm). If you don't mask the resonances this parameter can influence where notches and peaks in the high frequency response occur, but in most cases these will be out of the frequency area you will use the sub for. The bigger the LRC, the lower frequency these resonances will be. When you're new to Hornresp you can mask it but keep it in mind when you are finishing up a design that will actually be built.
FR
The airflow resistivity of any stuffing / damping material used in the rear chamber. You can leave it at default if you're using stuffing but don't know any values for it. More typically, stuffing is not used in subhorn rear chambers, so change this to zero.
TAL
The thickness of the used isolating material. You can leave it at default or zero depending once again on whether or not you want to use stuffing.
VTC
Volume Throat Chamber (in cm3). The volume of the frontchamber. Notice that you'll have to use a factor of 1000 here to get the number in liters. In principle you will almost always have a frontchamber because the volume of the air in / directly in front of the cone is acting as a front chamber. The front chamber is the volume of air that is compressed when the cone moves forward as opposed to the air that moves down the horn. Sometimes it is hard to know where the boundary between these two areas is, especially with low compression ratio designs.
In high frequency drivers this volume is downsized by using a phase plug. In a BPH this volume is generally quite large (making the BPH look like a 4th order bandpass, hence the name).
ATC
Throat chamber average cross-sectional area normal to the axis of the horn (in sq cm).
In case you choose to mask resonances (see the LRC comments) this parameter will not influence the results. In the schematic diagram it's easy to see what the ATC is by comparing 2 different value's. In case you don't mask the resonance, you can keep the ATC the same as the Sd of the driver by default, or change it to move the resonances around.
How high can you model before the results become inaccurate?
Hornresp models the power response of the horn. This is different than the on-axis response which you might measure with a microphone. The power response is what you would measure at a point if sound radiated evenly in all directions away from the horn, within the solid angle specified in the ANG input. So the modeled results should be fairly accurate up to the frequency where the horn starts to have directivity - where the polar pattern starts to narrow. This is typically at the frequency where the wavelength falls below the diameter of the horn mouth. Above this frequency, Hornresp will predict lower SPL levels than what you would measure on-axis. Hornresp now includes tools to investigate this effect. Once you calculate the model, go to the SPL Response chart. Under Tools, select Directivity. If you enter a blank input, you will see the power response. If you enter 0, you will see a prediction of the on-axis response. You can also enter other angles. Also under tools, you can look at the Pattern tool. This will predict the polar pattern at the frequency you input and show you the DI, directivity index at that frequency. Directivity index is a number in dB giving the gain over what the level of the power response is.
Credits
Johan (Rademakers) on this forum posted some helpful comments on another forum
which have been incorporated into this help guide:
