Yes, I've been caught by the  Horn's Virus too... :)

I've found a lot in the web about  horns. Now I'm experimenting with tractrix 'cause
this way of expansion has many advanteges compared to others  (conical, hyperbolic, exponential).
In details, the tractrix is a curve derived from exponential but preferreable  because it has a shorter
lenght  while mantaining low distortion.

I don't want add more details  than this. A lot can be found in these two very nice sites:
http://home.sol.no/~ketilp/bigfunht.htm
http://members.tripod.com/~Fusaro/Trombe.htm
The following part is mainly based on the equations that can be found there.

Now My little contibution: Everybody knows that The tractrix's expansion formula is:

Where:
 

x is the distance from the "mouth" of the horn
a is the radius at the mouth
r is the radius at the distance x from the mouth

To solve the equations i've used a numerichal approach: I've written a little macro in excel's basic
using the binary search algorithm.
Here follows the "pseudo-basic" code:

Function tractrix(r; a)

x = a * Log((a + Sqr(a * a - r * r)) / r) - Sqr(a * a - r * r)
tractrix = x

Fuction  finder(xx; aa)
a = 0
b = aa
eps = 0,001
maxit = 10000
it = 1
x = 10000

Repeat

x = (a + b) / 2
z = xx - tractrix(x; aa)

    if z < 0  then
        a = x
       else
        b = x
    endif
    it = it + 1
    if  it > maxit then
        exit 
    endif

Repeat until Abs(a - b) < eps
finder = x
End function

The sheet contains a group of formulae to calculate the main paramters of the horn, including back volume, ideal lenght and Fs.  Input data and parameters are in blue:

Here is the table with the main data of the horn:

That's all folks. It's possible to dowload the spreadshet by clicking here    while holding
the "Shift" key pressed. 

ENJOY! and please let me know of any improvements/problems you'll  find with.
 
 
 

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