As early as 1900 Edison had 11-sided horns made for his gramophones. These are continuously expanding, extruded polygons. Each side of the polygon consists of a flat piece of sheet metal that is forced into a curve when the sides are joined. Essentially the same method is used here, although the materials differ radically.

General Procedure

Use whatever program you have to compute the horn's contour in the usual way. At that point, convert the circular areas to 12 sided polygons. Then draw the horn curve as well as an extruded side of the polygons in a CAD program and make cardboard templates from the CAD drawings.

If you don't already have a CAD program, see if you can find an inexpensive one with automatic and aligned dimensioning.  

Printing the Templates

To print out these - and larger - templates on a small printer, you can separate the templates at any given line for the distance at x, then print them out and tape them together. For reference, don't forget to include the same distance line in each part of the drawing. Refer to the 80Hz horn page for an example.

If you intend to copy this horn, you will only need the information in Tables 1 to 3, and Templates 1 and 2 on the Computations page. The construction of the horn and its fixture are described here.

The terms "m" and "x" refer to the exponential equation on the Computations page. X is always the straight line distance through the horn. M is the horn constant.

For those who want to reverse engineer this project, I used 0.65 for m. Usually this is an arbitrary number and lies somewhere between 0.5 and 0.6. As this horn isn't intended for low frequencies, I used a slightly higher number for m. If you need a flatter rolloff on the low end, you can use a smaller number for m and get a longer horn. That may or may not affect directionality. On the other hand, if you to build an exponential horn as short as a tractrix horn, try using 0.85 for m at your own risk. It's too short to support most diaphragms and squelches low frequencies without contributing anything to the highs or to dispersion.

Because this horn was intended for use above 800 Hz, I selected 400 Hz as the cutoff frequency. My driver necessitated a 1.5 inch throat. If you need a smaller throat, inexpensive adapters for 1 inch throats are available. I computed this horn as shown in Table 1.

TABLE 1

Distance at x in inches	Radius in inches	* 0.988	New Radius in inches
0	0.75		0.7414
1	0.8543		0.8446
2	0.9883		0.9770
3	1.1566		1.1435
4	1.3652		1.3497
5	1.6212		1.6028
6	1.9336		1.9117
7	2.3132		2.2869
8	2.7732		2.7417
9	3.3296		3.2918
10	4.0017		3.9563
10.5	4.3883		4.3386
11	4.8129		4.7583
11.5	5.2793		5.2194
11.6	5.3779		5.3169

You can identify the surface areas using the radii. The factor 0.988 is explained on the Computations page.

FLANGES AND STIFFENERS

Cut out four or eight parts similar to the one shown below. For its curve, use TEMPLATE NO. 1. Aside from stiffening the horn, this part should push down on the stiffening ring and up against the driver flange to keep these parts flat.

Cut this stiffening ring out of the same material you use for the horn. Its dimensions are not very important. Mine has the same outside diameter as the flange below.

The driver flange also serves to hold the sides together at the throat. Cut the opening so it fits tightly over the material you use for the horn. Like the horn, this flange only serves as a form for the actual flange: several layers of roving and resin.

Making the Fixture 

Computing and drawing the templates are described in detail on the Computations page.

TEMPLATE NO 1 shows the horn's flare. Note that opposite the curve a 1/2 inch has been removed so that all 12 stiffeners would fit on the baseboard of the fixture.

Glue the uncut printout of template No. 1 to a piece of poster paper, as paper of normal thickness tends to slide while being cut. After gluing, cut out the template by cutting through the lines with a multipurpose knife.

With a sharp pencil or scribe draw the template on a 1/4 inch Masonite sheet. You will need 12 of these for the fixture. You can cut Masonite with a saber saw and a saw blade for metal.

Bevel the straight "backs" opposite the curve with a multipurpose knife. You need to do this because there is not much space when these supports are mounted on the base.

At the throat end of each support cut out a 1/8" x 1/8" notch. On the remaining material peel away about 1/10^th of an inch with a multipurpose knife. This supports the throat end of the fixture with the notched disk shown below.

This disc consists of two pieces of 1/8th inch cardboard matting. Cut them out, then glue them together with wood glue. This piece maintains the angles and distances between the supports.

You only have to push this disc into the notches at the ends of the supports after you have put the fixture together. Do not glue it.

All dimensions are in inches.

Out of a 5/8^ths square wood strip cut 12 pieces, each 2 9/16^ths long. About 1 1/4 from one end drill a 3/16^ths hole in each piece. Use wood glue to glue these strips to the mouth ends of the fixture supports. The holes have to point up. The end of the wood strip should just touch the curve. The bottom of the strip just touches the bottom (mouth end) of the fixture support. (Refer to the inset in the above picture.)

The holes are set back so you can have room for your hands and tools.

The mounting surface or base board is a 24 x 16 inch sheet of plywood. It also serves as a work surface and should not be much thicker than 1/2 inch to keep the stove bolts short. If your plywood is warped, you can bolt angle iron underneath it.

Draw the mouth opening on the plywood. Start with the radii at 30 degrees to each other, then draw the sides of the polygon. Center the fixture supports on the radii so their tips just touch the lines for the sides. Mark through the holes in the wood strips. Number the holes in the supports and on the mounting board so all the holes fit after drilling them. Drill 12 3/16ths holes in the mounting board. File them lightly towards the inside and outside for a minimum of play. Then bolt the fixture supports to the mounting surface. (I used M4 x 35 stove bolts.) 

Adjusting the Supports

Tighten the bolts of two opposite pairs. With wood glue or five-minute epoxy, glue pieces of 1/8th inch thick Masonite between the pairs and as near to the throat end as possible. Make sure the throat diameter is correct when the supports are tightened and glued (Refer to the pictures).

Supports Around the Mouth

Hold a piece of material you will use for the sides of the horn (see below) against a support and against the mounting board. The edge of the material covers the lines for the mouth opening. (Refer to the drawing below.)

Mark the new outside edge of the mouth.

To keep the sides from sipping off the fixture, I used 12 3/4 x 1/2 plywood strips as shown below. Cut these strips slightly shorter so that you can move them back and forth.

1) Drill 1/8th holes at each end, align these supports on the mounting board and mark the holes.

2) Remove the stiffeners and drill the holes.

3) Cover the markings you made for the mouth opening with 2 inch wide Scotch tape so the lines run down the middle of the tape.

4) Fold a piece of tape over the top, bottom and inside of the supports. Run a small piece of Scotch tape over the butt ends of the mouth supports so resin can't glue them together. Slice open all the holes with a multipurpose knife.

5) Rebuild the fixture.

The Scotch tape is necessary to keep resin from adhering to the mounting board and the mouth supports. Bolt the mouth supports with M4 x 30 stove bolts.

The mouth supports do three things.

1) They prevent the sides of the horn from slipping off the fixture.
2) They maintain the angle of the sides while they are being glued (see below).
3) They also act as a form, as resin flows down and collects around the mouth opening. This results in a thick stiffener around the mouth that is    almost invisible from the front of the horn.

Sides

TEMPLATE NO. 2

This is the extruded side of the horn. Note how the distances are "stretched" to fit onto the curve.

You can use just about anything except sheet metal and plexiglass because resin won't stick to either. So-called "foam boards" won't work because resin turns the foam into black smoke.

Cork, veneer, or Formica might work. The latter two are so thin that they will be hard to glue at their edges. Cork is easy to glue, but hard to surface smoothly.

The cardboard used for matting in picture frames seems to work best. It absorbs resin and becomes very hard. Besides its dampening values are high because its core stays soft, as the picture indicates.

Some varieties of cardboard have a smooth or shiny surface and can't be used in this project because resin will not seep into the material. You can buy raw matting in art supply stores.

Cutting the Sides

Before you use Template No. 2, glue it to a sheet of posterboard, then cut it out, always cutting through the lines. Use this template to mark the matting. If you don't have a saber saw, cut out the sides with a multipurpose knife. Just remember that the marked side will become the inside of the horn, that is, the side you see from the front and the computed side of the polygon. As the drawing above implies, you might cut the sides at 90 degrees and still be able to get a small horn like this one together. The purpose of cutting the sides exactly is to keep glue from running into the horn. The only thing you must avoid is cutting the angle too steep and leaving gaps on the inside of the horn. The angles can be cut exactly with a saber saw. Black & Decker offers a knife-like saw blade for cutting soft materials.

Fit the sides to the fixture. All 12 must fit. If one doesn't fit, usually none do. Find the "worst" side and sand its edges with #150 paper. The edges don't need to fit exactly, as they are joined at an angle on a curve so that errors are almost invisible when one looks into the mouth of the horn.

Gluing the Sides

You cannot use contact cement. Resin dissolves it. Use 5-minute epoxy. This is actually viscous resin and can be used to fill up small holes between the sides without running down into the horn.

Glue two sides, starting at the mouth. From there, run a narrow bead of glue about 4 inches up the horn as the marks in the picture indicate. The epoxy hardens faster if you mix it thoroughly.

Press the sides together and against the supports as shown to create the required curve. Make sure the edges touch the mouth supports so that the sides don't slip and the angle at the mouth is correct. Glue the remaining sides. Then glue the sides up to the throat and drop the stiffening ring over the horn. Don't glue it yet.

Push the flange over the throat.

As the flange should fit tightly, you will only need a spot of glue to hold it temporarily.

Glue the stiffeners (that you may have cut out of Masonite) onto the flange and throat. The stiffeners straighten the flange and push down the stiffening ring. Glue the ring. The form for the horn is finished. Leave it on the fixture. If some edges have gaps, you can fill them with epoxy. Just don't let the epoxy run into the horn.

Fiberglass Roving

I used a liter of resin and a package (two square feet) of fine, 6.5-ounce fiberglass roving (not mat!) that I found at an automotive supply store. The roving is easy to cut with scissors and can be laminated over sharp angles and rounded corners. One package is enough for two horns.

If you continue the way I did, you will need another two square feet of 18 ounce roving. It is very thick and easiest to cut with a multipurpose knife. If you decide not to use it, you will need at least four layers of the fine roving mentioned above, or another two square feet. Either way, the amount of resin stays the same.

Cut roving for two horns. Per layer you will need:

20 strips                  ca. 18x6 cm
24            "              ca.  8x6 cm
20            "              ca.  6x4 cm

For the lower half of the horn, i.e. the mouth, you will need for two horns six pieces of roving that you can cut with the help of Template No. 2. Copy the lower 15 cm of the template onto typing paper four times. Tape the four copies together as in the picture.

They don't fit very well, but do result in a flat figure that will fit the curved surface of the mouth. Use a felt-tipped pen to copy this template to the roving. Then cut the roving. Where the roving tapers toward the throat make 1.5 cm deep cuts about 1 cm apart. This way you can easily laminate the upper end of this piece under the stiffening ring.

If you are using 18 ounce roving, you will need:

20 pieces ca. 10x10 cm
8   pieces ca. 15x5   cm
12 pieces ca.   6x4   cm.

This is easiest to cut with a multipurpose knife. For straight cuts, press a board or piece of angle iron onto the roving and cut along the edge. Don't try to cut pieces much smaller than the ones given above, as this roving tends to fall apart when there isn't enough warp and weft to hold it together.

Resin

Only mix as much resin and hardner as you can use quickly. The largest amount that you will need for this project is about 200 cc, or half a pint. Use a white plastic bowl to mix your resin so you can judge its color as it begins to react with the hardner. When some brands turn medium brown it's time to work fast. Use a paint brush to stir the resin and hardner.

Warning: the resin available in hobby shops and parts stores is usually extremely old stuff that is hard to mix and often hardly mixes at all. Often the container for the hardner is not graduated so you never know what you're doing. You are always well advised to buy your resin from vendors who use it themselves. But then you have to buy more.

Resin hardens fastest where you find the most of it. That means it hardens first in the mixing bowl and a half hour later on the work piece. For this reason, start with the largest surfaces first. Always laminate small parts last.

Use a paint brush to press the resin into the roving. You only paint on the cardboard.

Laminating

You need a paint brush with natural bristles. (Synthetic bristles don't hold enough resin and slow down your work, but not the hardening time of the resin.) Paint the entire horn.

Place the 8x6 cm Strips around the mouth so that their long sides butt against the visible edge of the mouth. Touch an end of the strip with resin, then put on another strip with an overlap of about 1.5 cm. Continue all the way around the mouth, always pushing resin into the roving.

Lay the piece of roving you cut with the template onto the horn so that it touches the edge of the mouth. As this piece is too long, press it against the horn so that it covers the under side of the stiffening ring. Then let resin run down the sides and overlap the second piece of roving. Do the same with the third piece.

At this point you should have used about 200 cc's of resin. Mix another 100 cc's. With luck you will be able to use the same paint brush, as the new mixture softens the brush.

Laminate about eight 18x6 cm strips down the throat and over the stiffeners. These pieces are a bit too long and should run from the lower edge of the flange to the outer edge of the stiffening ring.

After you've covered the entire horn with thin roving, either repeat the process, or start with the 15 x 5 cm pieces of 18 ounce roving. Laminate these four pieces onto the throat so that they cover part of the vertical stiffeners. At this point you will have to mix another 100 cc's of resin. Then laminate the ten 10 x 10 pieces around the mouth.

You can use as much roving as you want. So that the horn looks smooth from the outside, laminate scrap from the fine roving over any ends of the 18 ounce roving that may be sticking out. Paint the driver side of the flange with resin.

Let the horn dry for two to three hours. Then pull it straight off the fixture. Turn it over and paint its inside with resin before you laminate the 6 x 4 strips around the flange. If you are using 18 ounce roving, laminate the 6 x 4 strips around the flange as well.

I taped three strips of wide Scotch tape onto the baseboard and set the wet horn down on the tape so I could laminate the flange. Don't forget to cover the edges with resin.

As the resin remains reactive for two to three days, you can make repairs on dried surfaces without running the risk that the new roving breaks off. For this reason, you can repaint the inner surface of the horn two days later.

After four or five hours you can correct any irregularities within the horn. Generally these would be fibers from the matting that tend to stand up when the resin dries. Sand them off with No. 100 or 150 paper.

To save paint brushes, laminate the second horn. Then repaint the insides of both horns at the same time. You shouldn't need more than five paint brushes.

Resand the insides with No. 150 paper. If necessary, use auto body spackling to fill any minor depressions or cracks. To paint a project of this size you can use spray cans. Auto lacquer works the best for me. You will need one small can of primer, one small can of a color of your choice, and a large can of clear.