Directivity Index of a Driver by it's Size

The polar maps linked are indeed the directivity behavior you can expect from 6,5" to 15".
These are approximation ( they are simulation based upon SD ( membrane surface) ).

Directivity index is used to determine a horn usually, that said you could derive it from the polar map of direct radiating driver if you want. Take a look at the thread linked, there is a link to a Jbl 2380a horn. In the datasheet you'll see directivity index. But it'll not be the usual way to plot direct radiating drivers for what i've seen.
 
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Thanks for the link. I may have been using the term directivity index improperly. Maybe it's just directivity?
I think DI is more appropriate when you're talking about a specific directivity, and just directivity when speaking casually. And a plot of DI vs say, the DI or a figure of DI whether talking about a single frequency or a range.
 
Generally, yes, as long as you're looking at the drivers when they're operating in without breakup, and the diaphragms are shallow to moderate in depth.

Things start to diverge when you enter breakup or have weird diaphragm shapes.
 
Edge overlays. Spl drop is exaggerated because with mic off-axis also distance gets longer. Mic offset 0, 250, 500 and 1000mm
Baffle diffraction changes too off-axis!
 

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