inverted subs

Air displacement equals air movement (obviously). The only air being displaced, and therefore moving, is inside or near the port opening. The rest of the box exhibits merely compressing and decompressing of the air, very little movement.
Rounding corners reduces resistance/turbulance. This effect only occurs when there is actual air movement. Therefore rounding corners should only make any noticeable improvement when placed in the corners that are in a port, or very near its opening. Otherwise 'rounding' a corner does little to nothing beyond decreasing internal volume.
In theory that works but I have known a good few that have gained by just rounding the inside of the box(and this was on the meter not to ear)

Not saying point proven. just saying what I have seen first hand

 
The port works as a delay line. At the tuning freq, the pressure wave from the inside of the box through the port is exactly 180 deg out of phase with the motion of the driver. Since the port pressure is generated from the back of the sub, the net effect is that the port output is in phase with the front wave of the driver right at tuning. As you move away from tuning, the phase coupling becomes less exact.

As far as cone control goes, the air in the port has inertia. As is it moves out from the port, it reduces the pressure in the box at the same time, the driver is trying to move outward as well further reducing the internal pressure of the box. As the air starts returning into the box from the low pressure, the driver is trying to move in, boosting the internal pressure. The result is that the mass of the air in the port is added to the Mms of the sub at tuning. Makes for much less cone movement but effectively double the cone area and thus more efficient at tuning.

 
In theory that works but I have known a good few that have gained by just rounding the inside of the box(and this was on the meter not to ear)Not saying point proven. just saying what I have seen first hand
Then 1) rounding the corners of their boxes improved air flow, as I suggested above, or 2) reducing internal volume improved their scores. No voodoo here.
 
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