"Ath" is a freeware acoustic horn/waveguide design tool.
Constant directivity waveguides of various shapes and sizes were never so easy to design and test.
Create your own model and examine it with BEM analysis using R&D Team's ABEC (*).
Ath will generate all the necessary files for you with just a few keystrokes.
Following Dr. Earl Geddes' footsteps, state-of-the-art waveguide formula was developed, extending and improving what is known as oblate spheroidal (OS) waveguide:
OS-SE formula in Desmos calculator
(For more details about the formula please see the Appendix in the User Guide)
Recommended diyAudio threads: Theory & Design | Practicalities
(*) Since ABEC changed to AKABAK in the meantime and there seem to be some compatibility issues, you may still want to use the old version of ABEC 3 until the issue is resolved.