I was not a windshield guy. Never had one on my Sportster. I got the '11 RKC in mid-December. It has the stock windshield. I have put 2000+ miles on it over the winter in all kinds of conditions--warm, cold, windy, gusty, crosswinds, high speeds (up to 95), low speeds, highways, sweepers and twisties. I have experienced no wobble at all. I think if wobble was windshield related, I would have experienced it. I think your cause is elsewhere.
If you only experienced the wobble on a straight road with the shield on,you may not need a stabilizer.
I thought the stabilizers were for eliminating the wobble in big sweepers?
No! But that is where wobbles most often happen. The better stabilizers support the rear rubber mounts, behind the trans casing, hidden behind the passenger footboard mounts. They actually improve the ride quality at all speeds, from trickling along in traffic, riding those slow twisty back lanes, or blasting along freeways at speed!
If you want a stabilizer for a great price I just installed the one by Throttle-Up Industries on my bike this weekend. It's $129 for forum members. Works great and it's a good quality piece, too.
Ok now Im really confused. So many different answers. I guess I will take it my local bike shop and have them ride it and see what they can find.
Nothing to be confused about, if you took the winshield off and the wobble went away, then the windshield is influencing a wobble in the steering, not the chassis. The best you can do is verify/tighten the steering head bearings and reinstall the windshield to see if it helped. Verify no broken fairing mount brackets, they will allow the whole fairing to flex under the wind pressure and influence your steering. If the neck bearings are right, tires/wheels are right, brackets are right and you sill have a problem, either get a shorter windshield that doesn't catch as much air or learn to live with it as a handling charateristic of your bike, just part of knowing your own machine.
Maybe slow your speed down to 75 or 80. Just a thought.
I actually rode at 70 to 75mph yesterday and Im sure that helped make the ride better. I'm just going to continue getting more seat time, and who knows I may not even notice this after some miles logged.