I would never mount a beam for 11 meters Horizontal since it kills all of your local mobile & most base station signals because of the 20 plus db of attenuation it has from a vertical signal.You can work plenty of skip on a vertical beam & still hear the locals as well.Skip signals change polarity when bouncing around so I don't see the advantage of being Horizontal when the band is pretty much Dead most days for anything other than locals?
SIX-SHOOTER
The whole purpose of horizontal polarity is to accomplish:
1- Reduction of vertical signals that interfere with communication
2- Reduction of noise, most man made noise is vertically polarized
3- Increase the far field lobe of the transmitted signal
As far as number of elements & gain go after 4 elements the amount of gain
diminishes a lot .75 for the fifth- . .5 for the sixth- .25 for the seventh.
The spacing of the reflector and the driven element affect gain more than number of
elements, the length of the boom plays an important role in a yagi.
As far as band width the diameter of the elements determine that, thicker is better.
You guys that have been in the game a while remember the Wilson Long John?
It was the biggest bad ass 11 meter antenna you could have back in the 70's
The length of the boom is what gave it tremendous gain, not the number of elements.