The Antenna
The antenna I have used with great success is referred to as a 'ground plane' antenna.  Its characteristic signal pattern is defined in part by the proximity of a ground plane.  The ground plane of this antenna is made up of four elements bent down approximately 45 degrees.  They are electrically connected to the shield of the coax cable.  The signal wire is connected to the center conductor of the coax cable.  The implementation on this page was designed for use on the XCAM2 video transmitter.
Antenna considerations and options
I am by no means an antenna designer, and my current antenna selection has been a matter of trial and error.  The research I've done on the ground plane antenna seems to indicate that the main radiating pattern is a donut around the signal wire, but the donut is stretched upwards at about a 15 degree angle.  If you imagine this antenna hanging from an airplane with the signal wire pointed down, you can see that the bulk of the radiated power is directed toward the ground instead of into space.   That's the theory anyway.  I seem to get good coverage even when I'm flying upside down, which seems to contradict this theory.

I continue to explore different antenna design and will publish the results of my research.  The remainder of this page will describe the construction of the ground plane antenna as I have implemented it.
Construction Details
 The first step is to assemble all the materials necessary to build the antenna.  The base of the antenna is made from a small square of pcb board cut out of the original patch antenna that came on the XCam2 transmitter.  I carefully removed the plastic cover from the patch antenna.  This was a bit tricky as the case appeared to glued or welded shut, so I ended up using a pair of side cutters (wire cutters) to nip off the outer edge all around the case, thereby allowing me to separate the two halves and expose the patch antenna. I then used a soldering iron to detach the patch antenna from the thin coax cable. (picture shows the patch antenna still attached)
In this picture you can see how I've started to cut out a small square of pcb board from the patch antenna.  Using a Dremel tool with the ceramic cutting disk, I cut 3 of the four sides of the antenna base.  Before cutting the fourth side I drilled a small hole in the center large enough for the coax shield of the antenna to fit through, but small enough so that the PCB board rested on the outer insulation of the coax cable.
Here I've started assembling the new antenna.  The coax cable coming out of the transmitter was left "as-is" after removing the patch antenna.  The small bit of pcb board has been threaded over the center signal wire AND the coax shield.  The coax shield was then soldered to the pcb board.  Note that the signal wire is isolated from the shield and pcb board.  4 pieces of 14 gauge solid copper wire were then soldered to the pcb board in a star pattern.  The initial length of the wires was 4cm to allow for trimming later.  Click the image at right for a close up of the pcb board and solder connection.
A 4cm length of the same wire was then soldered to the signal wire, perpendicular to the 4 other wires. Click the image at right for a close up of the antenna base.
This is the final antenna shape.  The four outer wires are bent down at a 45 degree angle from their former position, and cut to exactly 3cm in length, measured from the bend.  The signal wire is also cut to 3cm, measured from where the signal wire exits the coax shield. 

As a final step (not shown), a small dollop of Goop was added to the base of the signal wire to stabilize it.  This antenna gives an approximate 15 degree up-slope to it's coverage area, so it will give good coverage when mounted pointing down on the airplane. Click the image at right for a close up of the antenna base.
That completes the construction of the ground plane antenna!   

 
To see my latest experiments in antenna design, click the picture at left