Help finding WE horn expansion equation

Remember that WE designed most of their horns before horns with a T value was invented (Salmon, 1942/1946).
Flare rate (and also T-value) will be different between the two planes because the aspect ratio differs from unity. Most likely WE used a changing aspect ratio in order to make the curving simpler/less compromised (horn relatively flat in the direction of the bend). Probably similar reason for the Sato horn.
 
This is true for Sato - mouth has two profiles only, sides are conical.
 

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