How much free air does a dipole line need to stay a dipole?

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I'm trying to figure out a design problem with a baffleless dipole line array design. I live in an apartment and so it's a bit difficult to get outside to do true free air polar measurements. My design goal includes good power response, not just good on-axis response.

Anyone know how to calculate how much free air space between two baffleless dipole lines is required at a given frequency for each line to still operate, more or less, like the other line isn't there?

Details of my challenge:
Assume a dipole midrange planar line about 5.5" wide (and very long) and a planar tweeter dipole line about 2.6" wide and again very long. Further assume the crossover is a linear phase Neville Thiele 2nd order filter, with about 200db/octave slope. Assume the crossover occurs around 1200Hz.

If I butt these two drivers together to make a single "baffle" that is 8-8.5" wide, then the entire crossover will occur above the dipole peak of the midrange driver, which will occur around ~850Hz.

If I leave an open space between the mid and tweeter lines (say 1.5" of free air) then the half-wavelength freq will be ~1220Hz, which will also be about where the midrange has its dipole peak (half lambda at 5.5" wide is about 1200Hz).

So in this example it appears I'm trading off 1) crossover occurring above the midrange dipole peak but with no first-pass lobing problems between the mid and tweeter, vs 2) crossover ~at midrange dipole peak but closer to the 'problem zone' where the inter-driver separation distance is much greater than 0.5 lambda and headed toward 0.66 and beyond. (0.66 lambda in this example occurs at ~1625Hz).

See also John K's discussion at:
Dipoles and Open Baffles

Thoughts about which version would be less messy from a power response/lobing perspective?
 
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