Dumb question:  If I swing my UHF aerial around to point at the Sky Tower instead of Waiatarua, do I need to change the orientation of the aerial to match the polarisation?

According to Kordia, Sky Tower is vertically polarised and Waiatarua is horizontal: http://www.kordiasolutions.com/node/1176

I'm getting corruption on the TVNZ channels (29) with the bad weather at the moment, so I was going to give the Sky Tower (chanel 28) a try.  Our Prime/Trackside analogue reception is quite snowy, so I was actually surprised that we got ANY freeview reception, but it was fine until the rain set in :)

So yeah, do I just pull out the GPS and swing the UHF aerial around to point at the Sky Tower (which might juuust be visible from up on our roof), or do I also need to change the orientation (and probably the damn bracket because of that)?