Hornresp

Then why have the EXP, CON, & PAR segment options if 99% of BUILT models are for rectangular enclosures?

Con is used to model a conical flare horn segment. See Attachment 1 for examples of conical horns.

Exp is used to model an exponential flare horn segment. See Attachment 2 for examples of exponential horns.

Par (parabolic flare) is used to model a rectangular cross-sectional area horn segment having two parallel straight sides and two sloping straight sides.

Other available horn flares are:

Bes - Bessel
Hyp - Hyperbolic-exponential
Lec - Le Cléac'h
Obl - Oblate spheroidal
Rad - Radius
Sph - Spherical wave
Tra - Tractrix
 

Attachments

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Hornresp models the port tube as a cylinder, open at both ends. Each end can be flanged or unflanged.

Flanged end correction = 8 / (3 * Pi) * Rp
Unflanged end correction = 0.1952 * Pi * Rp

Where Rp = port tube radius

In the BP6S example used previously:

Ap1 = 800 cm^2
Ap2 = 200 cm^2

The Ap1/Lp1 port tube is shown highlighted in yellow in Attachment 1. One end is flanged and the other is unflanged. Because the radiation impedance is known at the flanged end, no correction is required at that point.

The correction at the internal unflanged end is:

0.1952 * Pi * (800 / Pi) ^ 0.5 = 9.79 cm

Total end correction for the Ap1/Lp1 port tube is 9.79 cm

The Ap2/Lp2 port tube is shown highlighted in yellow in Attachment 2. One end is flanged and the other is unflanged.

The correction at the flanged end is:

8 / (3 * Pi) * (200 / Pi) ^ 0.5 = 6.773 cm

The correction at the unflanged end is:

0.1952 * Pi * (200 / Pi) ^ 0.5 = 4.893 cm

Total end correction for the Ap2/Lp2 port tube is 6.773 + 4.893 = 11.67 cm

By double-clicking on the Lp2 slider label in the loudspeaker wizard the internal port tube Ap2/Lp2 can be changed from the default flanged/unflanged to unflanged/unflanged as shown in Attachment 3. The end corrections are adjusted accordingly.
Do we get a physical description of the flange? Width? Angle? Depth? I have read obout flanges and corrections for 40 years. Never seen numbers. I generally do a large round over or thumbnail profile. I guess a chamfer could also work.
 
Con is used to model a conical flare horn segment. See Attachment 1 for examples of conical horns.

Exp is used to model an exponential flare horn segment. See Attachment 2 for examples of exponential horns.

Par (parabolic flare) is used to model a rectangular cross-sectional area horn segment having two parallel straight sides and two sloping straight sides.

Other available horn flares are:

Bes - Bessel
Hyp - Hyperbolic-exponential
Lec - Le Cléac'h
Obl - Oblate spheroidal
Rad - Radius
Sph - Spherical wave
Tra - Tractrix
You didn't post a PAR enclosure because 99% of builds have 2 parallel straight sides. If anything, HR should default to PAR and the modeler would have to switch to the other horn profiles if they are going to build a non-PAR enclosure.