This is a copy of the stuff where http://www.aeolian-kites.com/kite.museum/science/stabilizing.principles.html used to point to

[Stabilizing Principles of Kite Flight]

     One of the inherent facts of single line kites is that they are very unstable.  Single line kites that are not stabilized will tend to dive, spin, loop, dart from side to side, and generally unable to stay buoyed for long, especially in strong winds.  Fortunately there are many methods to stabilize kites.  The following will discuss each of these more common methods in turn. Typical kite tails.

Tails & Drouges:
Flat kites and kites with high aspect ratios are the ones that tend to be the most unstable.  Tails are particularly effective in correcting the lateral stability of such kites.   A tail should be the first consideration in stabilizing a kite.  The tail only impedes the kites lift minimally while providing excellent stability against spins, dives as well as twist.  Because tails can be made from any light materials, adding colorful tails also enhance the aesthetics of many kites.

A tail functions because it produces drag directed in-line along with the tail.  This in effect lends to the stability of the kite by keeping the kite along a stabilized axis of flight.  This principle can be analogized to balancing a stick on your palm.  If you try to balance a short pencil it will surely fall, but if you try balancing something the length of a broomstick it is much easier.  This is so because it is easier  to rotate objects of shorter (less force required) length than objects of longer lengths (greater force required). In stronger winds, the forces on the kite is greater, therefore a tail of suitably longer length is demanded to stabilize the kite.

Rudders:
     Although rudders function differently from tails, they manage to achieve the same ends in stabilizing the kite.  A rudder is anything that is oriented perpendicular to the plane of the main sail of the kite. 

Vents:

Fins:

Bowing:

Kites in Train: