I want to make it quite clear that all what is written below is not my brainchild. This topic has already been raised, discussed, and published in the early 80s. I remember some first class information in “Model Aviation” magazine by Mrs. Al Rabe, Ted Fancher, and others. Alas these articles are no longer available. Magazines have a habit of disappearing in paper waste baskets or getting buried deeply in collectors’ cellars. What a shame! Such valuable knowledge shouldn’t get lost. Putting it on the Internet should be a good place to make it available for everybody. That’s how this story began.
There are many forces which act on our airplane while flying; some can easily be seen and/or felt. Some of them appear a little mystic and have to be explained in detail in order to understand and to handle them. I’ll try to explain “Gyroscopic Precession” ( GP from now on ) with the help of several sketches (you know - a picture is worth a thousand words; I hope the sketches will save me several hundred). Let’s start with the basic principle. A gyroscope is anything that’s spinning around, preferably fast. So our spinning prop is a gyroscope, too. For ease of imagination let’s see the spinning prop as a solid disc, and to simplify things we let the disc spin to the right, when seen from behind (see sketch at right).                  
The gyroscope follows two basic physical laws. 1) as long as it spins (fast) it will try hard to keep its position; that means it will keep the direction of its axis and hold it steadily (that’s why bike riding is so easy). 2) as soon as a force (say F1) tries to change the attitude of the axis - and thus our prop disc - the gyroscope creates another force (F2). This force works in the same direction, however 90 degrees later on the spinning object ( in our case the prop disc). One example of this process is shown in sketch 1.
                               
        Let’s suppose we apply “UP” elevator for a loop or a square corner. The airplane moves it’s nose upward. The prop disc “feels” this as being “pulled” forward at the bottom! It (the gyroscope) creates another force which pulls forward, too. But since this new force acts 90 degrees later, it will act at the left side of the prop disc. So it will turn our airplane to the right because it works left of the center of gravity. Our airplane yaws to the right, out of the circle, thus increasing line tension for just as long as the airplane is turning upward. This is the reason we usually have better line tension on inside loops and corners.  
                                         
                   
                                   
                             
                                   
If all this sounds a little mystic I recommend to run a test. Take a strong power drill and hold it in your hand, not too tight. Switch it on and let it run. Now quickly move the drill and turn it upwards. Instantly you will see and feel that the drill moves not only upwards, but also to the right. Actually with a strong motor you will not be able to hold the drill steadily, means straight! You’ll be surprised how strong this force is.
                           
Of course the same thing will happen the other way round when we apply a force at the opposite side of the gyroscope (prop disc). Sketch 2 shows what happens when we apply “DOWN” elevator. The newly created Force 2 pulls the right side of the prop disc forward, thus turning our airplane to the left and into the circle. This is why we usually have less line tension in outside loops and squares. (sketch 2)      
I might add that not all airplanes suffer heavily from this behavior. Depending on the particular airplane there may be design features which minimize the effects of GP. I’m sure that the choice of prop ( weight and diameter) is partly responsible and should have an influence on the effect.
                  Now forces cannot be applied to the top or bottom of the prop disc only. We also have the right and left side of the disc. In most cases our airplanes fly counter clockwise. Which means that they are forced to fly in a left turn. This in turn means that we apply a force at the right side of the prop disc. Automatically a force is created 90 degrees later in the direction of rotation - and that’s at the bottom of the disc. This force tries to turn the nose of the airplane upwards - our airplane tries to climb (see sketch). Of course the opposite happens when we fly inverted - our airplane wants to dive. The effect may be very small and we have learned to compensate for this automatically. Nevertheless some pilots feel that they want to “trim” their designs right on the building board and add some engine downthrust and/or positive incidence to the stab. On existing airplanes a touch of “down elevator” might help. - - -
   
I’ve always been amazed seeing little kids playing with their “gyroscope toys”. Some heavy strokes with the top knob brings this funny UFO into high revolutions. I was fascinated to see that this object really could stand vertical instead of falling down. When rotational speed goes slow, it seems to fall - but not really: first it leans to one side, then to the side 90 degrees later, then again 90 degrees later etc. etc. The gyroscope begins to reel like a drunken UFO in a graceful dance until finally all energy is used up and the gyroscope lays down softly. GP in action - wonderful!
   
    Little did I know that I would have to deal with these forces later in my (modeling) life.