Here are some of the comments I have personally recieved or seen floating about for circoflex kites. Prehaps you like to help add a few more!
If you look at the mini-circoflex kite photo to the left, you will see that the kite actually leans back slightly. Often this is so slight it is not noticable, especially on the full sized normal versions. Because of the lean, lift is attained.
To keep the kite in this position, a small amout of `ballast' weight is added just inside the trailing edge of the lower side (black section of the kite in the photo). Without this ballast the kite will fly upside down (which you can only do of a bridge) , as there is more weight above the bridle point than below.
As in basically all kites, the bridle is also off center, just as it would be in a typical box kite, though this is often invisible from the ground.
To make sure it keeps its circular shape a spar is inside the leading edge. And to stop the fabric from `rippling' like a flag in the wind, a line in the trailing edge (leech line) makes the rear edge a centimeter or so smaller in diameter. As such the wind is restricted slightly, and a slightly higher air pressure is on the inside the ring than outside, puffing out the fabric.