So conventionally kites are measured in square meters, with the projected area being the area directly providing lift.
The flatter the arc, the higher the projected area, and the more power per square meter when the kite is stationary.
Thinking about this made me wonder about the nature of ultra narrow arc kites. A super narrow arc kite would hypothetically create substantially less power at rest, but be capable of increased turning speed.
Increased turning speed on its own does not necessarily mean increased power though as the power isn't created by the turn but rather the speed generated by the line tension and flying deep through the wind window.
But stationary pull is typically what makes us overpowered.. meaning it should be possible to use a substantially larger narrow arc kite than a flatter arc kite.
The downsides would be increased weight and additional drag, but the larger wing tips should counteract the slower turning speed of a larger kite.
With the dubious nature of increased power attained from faster turning speed, I'm not sure what this results in.