theoretically ideal horn design?

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hi everyone

I am very new to this world and still looking for alot of answers to simple questions.so here is my question of the day.

After seeing that many people are building horn speakers(i hope my wording is correct),is a horn speaker by deffinition a encolure that is tapering and spiraling?if so what are the benifits of this design?
The horns that i have been looking at are very angular internally is this on pupose or to simplify the building procces?is somthing like the nautilus the ideal shape for a horn.And lastly does any one know of a source for the equations to figure the internal shape of something like a nautilus?

Thank you all for looking and please respond with ANY info,i mean it when i say that i have alot of learning to do.
Thanks
Yosh
 
Here is one...
 

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Actually there is an ideal shape and that is having a straight center line which is only common with mid range and higher frequency horns like those pictured above. Straight bass horns are uncommon due to the required lengths involved. The folded horns that you've seen are for bass and maybe even midbass frequencies since the folds have less of an effect in the lower frequencies. The best expansion rate (flair rate) is a matter of preference and debate and seems to be frequency dependant.

A nautilus shell has a "golden ratio" rate of expansion. See http://www.camerahobby.com/Ebook-GoldenRatio_Chapter16.htm . If made large enough, it might make a great bass horn.

Here's some good basics about horn theory:
http://www.volvotreter.de/downloads/Dinsdale_Horns_1.pdf
http://www.volvotreter.de/downloads/Dinsdale_Horns_2.pdf
http://www.volvotreter.de/downloads/Dinsdale_Horns_3.pdf
 
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