I have the same sucky antenna, at the same location my old rig with the Batwing got 12 "stations", while the Jensen on the new rig gets three, period.
I did some testing (I have an excellent background in antennas) and got similar results with a chunk of wire to the Jensen. The only thing it worked "better" then was no antenna at all.
Testing by other people have shown the Batwing with the Wing-Man addition works the best of any "RV" antenna.
When we need OTA TV we are usually parked for several days, so I picked up a Radio Shack "flying saucer" antenna, that I put up with two 5 ft sections of mast on the rear ladder of the rig.
At the same location as above, I get 25 "stations" with the Radio Shack antenna. But it is MUCH larger then any of the above antennas.
There are two rules with Antennas, higher is better then lower and bigger is better then smaller.
They used to make a motorized Wingman, but it appeared to me (last year) that either it was out of stock everywhere, so it may have been discontinued. The advantage it had, was you didn't need to be able to reach up and crank it.