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If you're going to bother with a jpole, just do a straight 1/4 wave antenna. The ground under a whip is key. You may well find that a 1/4 wave whip
with a good ground plane works perfectly well - most commercial antennas on metal GA planes are 1/4 wave antennas. They're bent back, but work acceptably with tranceivers in common use. No, it won't be perfect, but it should be acceptable.
The attached photo shows a VNA VSWR plot for a quarter-wave whip at 2 meters on the roof of my metal truck. I'd have no hesitation using something with a plot like this in the aviation COM band on a plane. Of course, you have a rag/fabric plane, so the ground plane will be different, and therefore the radiation characteristics will be different.
I will certainly defer to Jim and his tests (especially the absorption and blocking tests - radiation efficiency is the other part of this) - all I'm trying to point out is that a single element whip can work and have the bandwidth from an impedance match standpoint under the right circumstances. YMMV, of course, and the only way to learn is to do it. If you can borrow a VNA or antenna analyzer from a ham, it'll help. And well worth buying an inexpensive one if you're going to do much antenna work. Decent field strength measurement equipment is more expensive (even though I have a spectrum analyzer, I don't have a calibrated antenna).