A:Boy, thats a tough one. You probably have, what, a Forest River Wildcat? Or something like thata 24-foot RV trailer, more or less.
Anyway, the short answer is: Anything is possible. Whats likely or do-able, thats another matter. The back bumper on the RV may not have the heft to take a bike rack and a 35-pound bike, which together could put a lot of leverage on the bumper. But the thing has a chassis. So one thought is to visit a welding shop that specializes in adding trailer hitches and the like, and see what they could do to bolt/weld some steel to the chassis. That could lead to an extension for a Class 2 hitch, and at that point you can add most any bike rack you wish.
The problem with that, however, is that you then have the ends of the tandem sticking out into traffic on each side of the RV. So you might consider a second option. I assume you have this RV attached to a Ford F150, Chevy Silverado, or similar (Gear Guy is conversant in all matters pickup and uses a 1993 Ford F250 to haul gravel. Do not ask about gas mileage). Then you could get a roof-mount rack. Dont blanch at the prospect of military-pressing your tandem up onto the roof. The Yakima SideWinder ($375) is a tandem rack that swings out and pivots so that even one person can easily load a tandem. Youd also need a set of Q Towers ($145) and crossbars ($60).
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