Horns are used in acoustic and antenna
applications. Typically it is optimal for the horn to taper
outward not linearly, but as an exponential function of the
horn's length. A logarithmic horn having a rectangular cross
section everywhere is not a developable surface: it is not
possible to make one by cutting and then bending or folding
a sheet of paper. It is, however, possible to make the horn
out of four sheets of paper.
This will generate a readytoprint PDF template for any kind
of rectangular logarithmic horn, given its dimensions. Just
cut out the four pieces, and join them along their edges.
All dimensions are in mm.
The `shape factor' goes from zero to infinity; it determines how
nonlinear the horn's taper is. One is a good value to start. In
the limit, a value of zero corresponds to a linear horn.
The actual expression for the exponential curve is
$MinLength +
(($MaxLength  $MinLength)/
(exp(($ShapeLength/$MaxHeight)*$MaxHeight)1)) *
(exp(($ShapeLength/$MaxHeight)*$height)  1)
This expression describes the taper of the assembled horn. It
does not (necessarily) describe any of the curves on the
paper templates; the taper of the horn gets distorted when
it is `flattened out.'
Nov 2005, Cambridge
