The Pluto loudspeaker designed by S. Linkwitz is special in that the mid-woofer element is positioned horizontally in order to get omnidirectional radiation. We want to see how well the mid/woofer element radiates to the side, i.e. in the direction of listeners. 
The mid/woofer element is used up to the cross-over frequency of 1 kHz. Ultrasim was used to find the beam pattern of the mid-woofer element to see the effect of the horizontal placement.
The mid/woofer element is used up to the cross-over frequency of 1 kHz. Ultrasim was used to find the beam pattern of the mid-woofer element to see the effect of the horizontal placement.
The 5.25" element has an effective radiating area S_d = 91 cm^2, i.e. diameter 107.6 mm. It is modelled by placing 500 points over this surface. Ultrasim assumes a piston source, i.e. no cone breakup effects are taken into consideration, and only a single mode of vibration.
To the extent that this model is valid, one can see that the response only falls with about 1 dB at 1 kHz at 90 degrees angle, i.e. horizontal placement. At lower frequencies it is even less, e.g. at 500 Hz the response is only -0.26 dB down at 90 degrees.
Therefore such a loudspeaker element can very well be used lying on the side in contrast to the usual vertical positioning of a loudspeaker element.