I have the V46 on an 03 K1200RS and have not experienced the instability being reported. A top case will definitely change the airflow over the bike, so not sure other Givi models would be much different. Note: I only use the Givi when riding two up on longer trips, so maybe there are issues when riding solo.
I also have the V46 on my 2003 K1200GT. I use it when riding double with my wife and haven't noticed any instability up to about 85 MPH indicated, at which point I usually get the knees in the sides. I've used it with the Dunlop Sportmaxes as well as the Michelin Pilot Roads.
After some experimentation, I discovered that the instability on my GT w/ the V46 only was noticeable when riding solo. Two up, the problem seemed to all but go away.
I fabricated a bracket out of 1/8 aluminum plate to rigidly couple the Givi mounting plate to the stock GT grab bar (I double checked that the Givi plate mounting bolts were tight - they were). After putting on the homemade reinforcement to the Givi plate, the wobbles went away immediately, even w/ a heavy load in the V46. This result tends to confirm the following:
(1) The instabilities are definitely aerodynamic
(2) They are much worse when the top case is hanging out all alone in the turbulence (i.e. no passenger to be a wind break). The heavier the load and the more turbulent the air, the worse things get.
(3) The stock Givi mounting scheme can allow the case to resonate/vibrate in rough air at a frequency that couples directly into the bike. Stiffening up the mounting can address this problem.
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