Folded horn length

[Don Snyder]

Calculating the length of the bends in a folded horn is confusing.
Figures 1, 2 & 3 are the most common bends. For low frequency waves,
they are nearly identical, with a small edge given to figure 3. The
green squiggle in figure 1 represents turbulence.

Figure 4 would seem to be the way to go, until you consider that
the outer part of the bend (the green area) has 3 times the area
that the inner (red) part has. Also, the length of the dividing
line is WAY below (30% below) the experimental data.

In figure 5, the "center" line is moved from 50% of the duct width
to 70%. Now, the green area is equal to the red area, and the
length of the line dividing the red from the green agrees within
a few percent of experimental data.

Figure 6 is nearly as good, and a lot less trouble. Just draw a
diagonal line in each corner, and connect the center points of each
line. The length of that line is within a few percent of the horn
length as calculated using figure 5.

[Don Snyder]

Here is an example.

[MaVo]

I used nr.6 in all my horns and it allways worked. But, once the diameter rises, the error of this method rises too. For near the mouth, the something between 4rth and 5th may be better.

[Don Snyder]

Tom Danley said: "A word about folding, one mistake made in horn folding is to make the horn passage significantly less volume
that it was when straight. The air in a bend has a rotary motion and so momentarily has rotational properties, the effect of this is
that the air has slightly more mass (inertia? DS) than in a straight section. This in turn allows a small reduction in acoustic length for that section but it is small. When I lay out a bend I usually try to keep the total volume close to that of a straight horn. With increasing frequency, a bend's dimension will have an impact on the sound. At the point where the difference in acoustic path length around
the inside and outside of the bend reaches 1/2 wavelength, there will be a deep notch in the response. Above this frequency
will be a pattern of notches and so on as the dimensions are N 1/2 wavelengths. If you have to make a bend, make it where the dimensions are small, make the angle as small as possible."