Horn resp for beginners

I was sent this guide to Horn resp a long time ago, thought i would post it up for you guys to read..............

Hornresp Kickstart


Introduction
The Hornresp 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. Furthermore Hornresp's abilities keep growing steadily. Hence the reason for this guide.



Entry guide


ANG:

Here you indicate where the horn is located. In a nutshell, enter 0.5 for optimal 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 Hifi
2 Ground only 1/2 space On ground outdoors or middle of room Typical PA Sub/bass cabinets
4 Full space Full space Suspended high over the ground Large PA Mid/high cabinets


Low-frequencies are omni-directional, radiating in all directions. This full sphere is known as 4 Pi space. When placed on the ground, the sphere is cut in half and the ground forms an acoustic mirror which effectively doubles the size of the horn mouth compared to full space. As a result you can make the mouth smaller when placed on the ground. This is called half space. When the horn is against another wall, the hemisphere is divided in half again, quarter space. Where there are two walls and a floor, we have a corner, 1/8 space. Each time the radiation angle is cut in half, the required mouth size is halved, hence it is recommended to place the horn in a corner to reduce the necessary physical size of the horn.

In most cases, except very large PA, subs are ground stacked and thus are best simulated in half space. Tops are usually flown or placed upon standards or subs (to get the high frequency drivers horn mouth above the crowd). As the height of placement and/or the frequency rises, loading will go from half space towards full space. This is accelerated by the horns increased directivity at higher frequencies (they aren't strictly omni-directional any more and thus are less affected by boundary loading). PA tops in general therefore should be simulated in full space.
Note: Loading into half the previous space (i.e. 4 Pi --> 2 Pi) gives a maximum increase of ~ 5 dB according to Hornresp (6 dB in theory), this is however based upon a very solid boundary. Thin/ wooden walls, ceilings or floors might not present such a solid boundary and thus show a smaller actual increase in SPL then predicted.
In worst case scenario's (often high SPL/low frequencies) a wooden floor/ wall might actually act as a bass-absorber as it vibrates (converting sound energy into movement and heat).

VEL / DEN:

Note: In later versions of Hornresp VEL/DEN were replaced with EG and RG

The velocity of sound in air at a given temperature and pressure (at standard conditions) / Density of air at a given temperature and pressure - Unless you know the precise conditions of the location your horns will be used at, keep this at the default value (VEL - 34400 cm/s / DEN – 1.205 g/litre)


EG:
Amplifier RMS Voltage (Volts) - Effectively the input power, when it's squared and divided by impedance (see the electrical impedance tab). In Hornresp you're not working with Watts (like WinISD Pro) but with voltage. This tab will influence the SPL and cone excursion and enables you to get an indication of the maximum SPL performance based on the excursion limits of the driver.
Hornresp has a calculator (appearing upon double click in the tab) 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.

U = I x Z --> 40.00 / 8 = 5 A --> P = U x I --> 40 x 5 = 200 W (= U^2 / Z) {U = voltage, I = current, Z = impedance, P = power}


RG:

Amplifier output resistance (ohms) - This includes the resistance from the cables (from amplifier to speakers) too. The next values ought to give you a start: Cable from amplifier to speakers (10 meters long, 2.5 mm^2 on average) ~0,3 Ohm, amplifier itself ~ 0,04 Ohm.

CIR:

Free space normalised horn mouth circumference in flare cut off frequency wavelengths - CIR is only visible when either the last horn segment is Exponential or the first and only horn segment is either Exponential or Hyperbolic-exponential. If this is not the case CIR is replaced by FTA (ahead).

As you might know, Hornresp simulates the horn (mouth, throat and segment) area's as if those are circular. To give optimum efficiency at the cut off frequency of the horn, the circumference of the circular mouth area needs to be the same length as the wavelength, corresponding with that cut off frequency (in 4.0 Pi). You have achieved this when CIR is 1.0
For 2.0 Pi you can get optimum efficiency for a certain cut off frequency with a smaller mouth area. In 1,0 Pi this mouth area can be made smaller again, etc.
In most modern horn designs the actual mouth area is smaller than the optimum mouth area (most often a compromise between gigantic size and actual performance needed). About the reasoning behind this you can find more information in the Speakerplans FAQ's and general horn theory found on the www. In short you can get away with a CIR smaller than 1.0 without degrading performance to much if designed correctly.


FTA:

Flare tangent angle (in degrees) – Only visible if CIR is not (see CIR).
When the FTA is zero, the horn is a straight tube, the 90 degree maximum is a (close to infinite) expansion/ flare rate: I.e. S1 is much smaller than S2 and/or L12 is very small. See also the schematic diagram.

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 for normal horns.

Compression ratio
The compression ratio is Sd/S1 (except for tapped/offset horns). 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 mid-bass 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). 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.

Footnote: For tapped and offset horns Sd/S2 sets the compression ratio.

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, h, 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. 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 multiple conical parts.
Mid/high and band pass horns can be made much shorter and frequently consist of just one horn segment. With a band pass horn the throat and rear chamber become more important (more on that later). However, all horns are band pass 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).

T:

Note: In earlier Hornresp models this parameter was known as FLA.

Hyperbolic (-exponential) horn flare parameter - This controls how fast the horn flairs as you get towards the mouth. Press H when the length tab is highlighted. You can only use the input boxes for the first segment now (S1, S2 and L12).


T = 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 horn mouth, 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:
T =1 (exponential)
An exponential horn will give more gain in the low-frequency reproduction of the bass horn 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:

T = 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 double-click 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) - Table: Typical Sd values for different diameters. Footnote: 1 sq inch = 6.45 cm^2.


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 ( times the length of voice coil wire in that flux (L), and thus the units are Tesla-meters. Sometimes it's stated as Newton/ Ampere's, read here why that's the same but different.

CMS:

Driver diaphragm suspension mechanical compliance (m/Newton) - Compliance is the inverse of stiffness. 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 litres (cubic dm / dm3).
Footnote: 1 cubic ft ~28.32 litre.

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 usually not by much. Note: How Mms is derived might differ amongst manufacturers, Mmd can be calculated.

LE:

Driver voice coil inductance (Milli-Henry's / mH) - This parameter can't be calculated from other T/S-parameters. The Le will have a large influence on the high frequency roll-off of the horn in some cases. A higher voice coil inductance will limit upper usable 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, for a “4 ohm driver” around 3 ohm.

... end of T/S-parameters

ND:

Number of drivers in the loudspeaker enclosure - Input parameters --> Tools --> Multiple drivers. As Nd doubles so should horn parameters such as S1, S2, VTC, VRC, AP, ATC, etc. to keep the horn(s) the same as before. The horn length will remain (approximately) the same.

VRC:

Rear compression chamber volume (litres) - This is the horn's rear chamber (in case of a front loaded 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 horn sub 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 power handling (Xmax is reached with a lower power input).
◦A horn sub that is meant to be used in stacks generally has a smaller rear chamber. These kind of subs trust more on the horn loading 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.
◦Band pass 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 80 litres (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 horn length will increase slightly due to a larger end correction from the larger mouth area, thus lowering the cut-off 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. As the LRC becomes larger, these resonances will be lowered in frequency. 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 (and off course it will).

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 necessarily used in sub horn rear chambers, so you can 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.

AP:

Rear chamber port cross-sectional area (sq cm) – Ap and Lpt (see next) characterise the port dimensions (Helmholtz resonator) in the rear chamber. On default FR and TAL are shown, upon double click on either the VRC, LRC, FR or TAL tab, FR and TAL make place for Ap and Lpt (and vice versa). The tuning frequency can easily be spotted in (amongst) the SPL response and diaphragm displacement-window as the bottom of a steep/sharp dip in the response.
For the combined frequency response of the driver and port, use Tools --> Combined Response --> (Difference in cm) --> Enter. See also Port assisted horns (ahead).

Ap en Lpt can also be used to specify a port in a tapped horn system with throat chamber. The port enters the tapped horn at S2, whereas the throat chamber is located between the driver and the port.

LPT:

Rear chamber port tube length (cm) – See AP (above) and Port Assisted Horns (ahead).

VTC:

Volume Throat Chamber (in cm3) - The volume of the front chamber. Notice that you'll have to use a factor of 1000 here to get the number in litres. In principle you will almost always have a front chamber 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.

A large VTC will limited the upper frequency response. In high frequency drivers it's downsized by using a phase plug /phase bung. In a BPH the VTC is generally quite large (making the BPH look like a 4th order band pass, 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.


Some handy tools:
The tools that you can use/pick depend on the current Window you're viewing. The tools listed below are the ones I used/needed most frequently in the first months (and still). Tools are listed per Window.

Window 1 (Input parameters):
Driver arrangement (multiple drivers) - Normal: With this Hornresp calculates the new T/S-parameters as they would be for a single driver when you replace multiple (of the same) drivers. For simulating multiple driver subs like the Labhorn or mulitple horns when stacked.
Driver arrangement – Offset: Newer feature to calculate a horn where the drive isn't firing straight down the horn but rather starts further down the horn from the sides. I.e. the 1850 horn, CV-style fold, Punisher, etc. S1 – S2 = horn before (the middle of the) driver, S2 -S3, etc. = horn after driver. Compression ratio = Sd/S2.
Driver arrangement – Tapped Horn: For simulating tapped horns (no prompt before calculating). See also Tapped Horns (ahead).
System design (hypex-designer) – With driver: For calculating the optimal hyperbolic exponential horn based on the T/S-parameters of the driver and the needed low-and-high frequency roll-off. Subs calculated these way for PA use aren't very functional in handling, size and weight (and the name “monster horn” quickly comes to mind). The normal route for PA use is to design 4 or 6 cabs that in total will have the same mouth area and horn length as one of these monsters. This way it does show that you need to have realistic demands when it comes to both SPL and low frequency response.
With the use of the "compare"-function (ahead) you can easily reverse engineer this “monster horn” to a more usable size and weight.
System design – From specifications: Newer option, S1 and VRC are fixed, nice for a quick mid/topdesign.
Find: Easy to find a record if you have too many already (you'll), just select and close (or double click). For an easy way to keep the active record list short, see Hornresp Merge (Updates).

Window 4:
Multiple speakers: For calculating the response from multiple cabs (stacked).

Impulse response: Calculate the impulse response. A good impulse response shows a sharp peak with little dips and peaks afterwards.

Window 3,4,5,6,7:
Sample: Depended on Window-type this gives a sample at a certain frequency. For example at Window 6) it will tell you the excursion the driver has to make at a specific frequency, so you can see what power your driver will handle.


Window 4,5,6,7:
Compare: Compare the current calculation with the previous. This way you can find the horn parameters that will suite you, by comparing each step with the previous while changing one (or more) parameters each time. Also enables you to compare the influence of the drivers T/S-parameters. You can also use Control + C, to capture the current result.


Window 1 t/m 7:
Options: Throat chamber and rear compression chamber resonances: Here you can tell Hornresp if it should mask the resonance coming from the VRC and VTC or not, it can also prompt you for each calculation.
Options: Default result window: SPL response (4) is regular.


Export:

Export allows you to view the data showed in Hornresp with programms other than Hornresp.

Window 1: Export the input parameters as an AkAbak-script. Ang must be 2,0 Pi.
Window 2: Exports the schematic diagram as an text-file. The text opened in a program such as notepad shows the horn parameters (such as horn area, height, depth, angle) for every cm horn path from the throat to the mouth. In the input pad opened, you can input the height at S1, S2,... by dividing the corresponding area by the internal width of the cabinet. An increment of 1 will show the values per 1 cm horn path length.
Window 3 t/m 7: Exports as a text-file, showing the specific parameter of that window against frequency.


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 modelled 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 directivity index (DI) at that frequency. The DI is a number in dB giving the gain over what the level of the power response is.


Tapped Horns:

Hornresp 16.xx and higher are suitable for tapped horn simulation. This very old yet recently rediscovered technique allows you to design a (sort of) back loaded horn with a relatively small mouth area but still decent efficiency at low frequencies in comparison to normal horns. In return the frequency/ phase response higher up is ruined, so it's primarily use is as a sub/bass horn. Lots of information on tapped horns can be found on the World Wide Web, for instance here and here. The text below will just focus on getting your tapped horn simulations started and hopefully in the right direction.
A standardised tapped horn model consists of three horn segments and no front or rear chamber. Characteristic for the tapped horn is that the rear of the driver is loaded near the beginning of the horn and the front of the driver is loaded near the horn mouth (I'm saying front and rear but inverted placement of the driver doesn't change it’s overall effectiveness). So both sides are loaded by the horn as opposed to a normal back loaded horn, where only one side of the driver is loaded by the horn.
◦The 1st segment (S1, S2, L12) starts at the closed end of the horn (S1) and ends at the rear of the driver (S2).
◦The 2nd segment (S2-S3, L23) starts at the rear of the driver and ends at the front of the driver.
◦The 3rd segment (S3, S4, L34) starts at the front of the driver and ends at the horn mouth.
Usually the 1st and 3rd segment are relatively short, while the 2nd segment is by far the longest. In the simplest, single folded design (see example) the 1st and 3rd segment have approximately the same horn length but changing this can be used for “fine tuning” the design. The 1st and 3rd segment in the example have a length of at least half the diameter of the driver. Hornresp has a “Tapped horn wizard” which can be used to change the driver location without altering the overall horn length, the horns expansion rate must be constant.

Note that in contrast to a normal horn where Sd/S1 sets the compression ratio, for a tapped horn Sd/S2 sets the compression ratio. Again a compression ratio of 2:1 is considered safe for larger (horn suited) drivers (15” plus), smaller drivers might take a higher ratio.
For most tapped horns, the total horn length (S1 – S4) is quite long compared to normal rear and front loaded BPH. Some input parameter examples for drivers/tapped horns located on the diyaudio.com forum: [1], 2, [3].

As a newer option you can include a throat chamber into the tapped horn, this chamber might also be ported (Ap, Lpt and Vtc). The port enters the tapped horn at S2, whereas the throat chamber is located between the driver and the port.

Footnote: The Fs of the driver used might actually be higher (1.414x) than the cut-off you're aiming for. Up till date the consencus is that an actual measurement will show a (much) flatter frequency reponse and lower sensitivity than the Hornresp simulation.


Port Assisted Horns:

Port assisted horns contain a Helmholtz resonator (port) inside the rear chamber. The port is generally tuned at or below the cut-off of the horn for three main reasons:
◦Tuning within the pass band of the horn usually leads to nasty interference; A peaky response or partially less gain then without port.
◦At the tuning frequency the cone excursion is (theoretically) reduced to zero, so it can be used for keeping cone excursion under control as this is the highest right below /at the horns cut-off point. Below the tuning frequency however the driver becomes unloaded and the cone excursion (again) quickly rises. For this reason it’s advisable to use a high pass filter at or around the tuning frequency.
◦For horns that are used as singles or small stacks, the port can be used to extend the low frequency response in the same way as a bass reflex can extend the low frequency response over a closed box. In a non-ported horn the driver is only loaded by the (small) closed box below the horn cut-off, which is quite inefficient (especially with low Qts drivers) at lower frequencies. Below the tuning frequency, the roll-off will be steeper in comparison with a closed chamber (~24 dB/octave instead of ~12 dB/octave).
Because horns generally have relatively small rear chambers the vent needs to be quite long in order to tune it low enough. Too long and the port will develop a ¼ wave resonance in the intended frequency range. Too short and the port area may become too small, which leads to chuffing aka port-noise, especially at high power inputs.
For this reason you might want to check the “port velocity” in programs such as WinISD Pro or Bass Box Pro 6, to ensure that it stays below 34 m/sec. Simulate the rear chamber/port as a normal reflex enclosure and apply the maximum power input in the signal tab. A high pass slope can than be added in the “filter tab” as this will result in a significant decrease in port velocity.


Building the horn
Simulated vs. actual volume
When you model a horn, the net volume appears in the schematic diagram. Add the volume occupied by the driver, panels, bracing and such and you'll get the actual volume. Knowing the ratio between the simulated and actual volume gives some advantages:


◦It allows to take an existing design and quickly determine what it's capable of or should be like, based upon Hoffman's iron law and a handful parameters.
◦Simulating randomly and having a good view on what it would look like when actually build.
◦Designing a cabinet with pre-determined volume and/or dimensions.
◦Knowing that what you simulate corresponds to what you build and vice versa.
Made out of 15 mm or 18 mm ply, most cabinets fall within a 1.2 – 1.35 ratio between actual and simulated volume. Generally the 1.2 ratio means a simple design, with few folds (and thus few inside panels) and none or very little occupied spaces (like corner deflectors). The 1.35 ratio should safely build you about any modern horn.

Actual volume vs. dimensions

This method is used to arrive at the dimensions based upon the actual volume and vice versa. Just as Hornresp, it's based upon the metric system. Footnote: 10 centimetre = 1 decimetre = ~4” = 0.1 metre = ~0.1 yard.

Knowing that 10 centimetre (cm) times 10 cm times 10 cm = 1 decimetre (dm) x 1 dm x 1 dm = 1 litre, makes it easier to work out the volume of the cab. A cabinet with measurements of 50 x 80 x 80 (cm) is 5 x 8 x 8 = 40 x 8 = 320 litres.
If for example you've an actual volume of 292.3 litre and you've decided on the width of the cab, say 60 cm: 292,3 / 6 = 48,7 So the other two measurements multiplied are 48.7. So 6 x 8 = 48 or 7 x 7 = 49 fall into that category, meaning an approximate 60 cm x 80 cm or 70 cm x 70 cm for height and depth of the cab.
The mouth area is a fixed number that, together with a fixed width gives the minimum height at the front of the cab. In case of a full mouth front, the height is fixed as well, leaving only the depth.


Folding the horn
There several methods to fold a horn. When you know your way in CAD you can use this CAD-based script.

Another way described on the web (still looking for the source) is to draw the horn on paper and cut it into small rectangular bits. The rectangular bits can than be used to form the folding, based upon a drawing of the inner dimensions of the cab. This (and the next) method will show a path length slightly different from the practical path length because the path length in a corner isn't truely axial, however the difference isn't spectaculair.

Personally I find it easiest to draw the cab in a simple drawing program like MS Paint, using a grid. Before that it was the old paper and pencil/pen. Other digital options are Inventor, Sketch up, CAD or Solid Works.
If you have pre decided on the measurements the cab is going to have, it's a matter of making a side view with height and depth. Using the export function in the schematic diagram gives a list of horn area, width, height, etc. per cm of horn length. Determine the height at S1, S2, etc. by dividing the horn area by the inner width of the cabinet. Alternatively use the inner width as the height.
Based upon this data you can draw the horn starting at the mouth all the way to the (inner) back of the cabinet.
In case of a 90 degree bend there is a horn area just before the bend and a horn area just after the bend, the latter usually smaller than the horn area before the bend (seen from mouth to throat). The horn path within the bend is the axial horn path length and equals half the height before the bend + half the height after the bend.

Now it’s time to take an educated guess: At 41 cm from the mouth (so 41 cm from the throat) the height is 19.8 cm. Directly after the bend the height is now 16.4 cm. The axial horn path length in the corner is 0.5 x (19.8 + 16.4) = ~18 cm. The height of 16.4 cm corresponds to an horn path length of 23 cm (41 – 18) seen from the throat.
According to Hornresp the height at 23 cm should be

At 46 cm from the mouth ( 39 cm from the throat) the height is 19 cm. Directly after the bend the height is now 14.4 cm. The axial horn path length in the corner is 0.5 x (19 + 14.4) = ~ 17 cm. The height of 14.4 cm corresponds to an horn path length of 22 cm (39 – 17) seen from the throat.
According to Hornresp this is correct.

Footnote: A 180 degree bend can be seen as 2 times a 90 degree bend as it follows the same guidelines.

Download
The latest version can be downloaded here. As it's as much a hobby to David as it is for us, you'll find an updated version from time to time. Version 8.1 and up have some fairly large changes in SPL readings, compared to 7.x, so an upgrade is advisable.

Updates
◦Hornresp 8.xx: Noticeable changed SPL-model.
◦Hornresp 11.xx: Enables to simulate a ported rear chamber, see also AP, LPT and Ported assisted horns (above).
◦Hornresp 16.xx: Finally!!! The sheer power of tapped horns within your grasp! (sorry for the excitement) For more details see the Tapped Horn section above.
◦Hornresp 16.40: Hornresp now simulates negative expansions, i.e. transmission lines (TL)
◦Hornresp 18.10: Tapped horns can now have a throat chamber.
◦Hornresp 20.00: Offset horns, tapped horns with ported throat chambers.
◦Hornresp 20.10: Bugs fixed.
◦Hornresp 21.00: Simulate compound horns.
◦Hornresp 21.50: Simulate the impulse response
◦Hornresp Merge: Not from David McBean, but an interesting program that allows you to transfer individual Hornresp records between two dat files, whether that is on two separate computers or in an archive file. I.e. would be handy to move the long list of records that you don't use, but also don't want to lose, or speed up your ability to share your designs on the world wide web.
◦Hornresp 24.10: Is able to export Hornresp records as .text-files. These text-files can be imported by other HR-users (put in the import map).

Credits
In random order: Paul Spencer, Johan Rademakers, John Sheerin. Thanks to Reiner, Sabbelbacke and mobiele eenheid