The cunningham is set at the forward end of each sail and as you tighten it, it will pull the luff of the sail down.
Tightening the cunningham will primarily pull the sail cloth down, bringing forward the max draft of the sail. Also by doing so will open the top part of the leach.
What it is not is “a rope that makes the sail looks better by removing the creases !!!” As I’ve heard too many times. These creases are a good visual aid to tell you that your sail draft is aft. Thus helping in pointing.
I personally don’t use it until the wind is becoming too strong for the sail area I have. It helps in de-powering the sails by opening the leach as described earlier. It’ll allow the boat to stay flat in a gust as the top of the sail will twist. Put your thinking cap on and think of a wing of a plane. Also look at the windsurfing sails. They are particularly good for observing this. The cunningham works for the main as well as with the jib. It does the same action on both.
Your sail shape band are pretty good at showing the difference in the shape as you tighten the cunningham.
It is a very effective control when beating however you don’t want any as you head down the wind. So with no crew onboard you need your cunningham configuration to get tighter as you sheet in and looser as you sheet out. There are few ways to achieve this. I’ll go through soon.
The outhall control the depth of the foot of the mainsail. It affects the bottom 2/3 of the main. The more you pull it out, the more depth you remove from the sail.
The theory is to have a relatively flat in light and heavy conditions, and with more depth in medium and choppy conditions. Even though the set up is similar for light and heavy wind conditions the reason is quite opposite. In light air you want the airflow to go through the sails as fast as possible and also to avoid the airflow to stale due to its low pressure. In a full main, the airflow will take longer to exit at the back and this extra time to exit won’t be transferred into boat speed. Here again the comparison to the wing of a plane is relevant. A plane needs to travel at speed through the air in order for the wing to create the lift required to keep the plane in the air. As the speed reduces, so is the lift generated and at a critical speed the wing is no longer generating enough lift and the plane stales. Going back to our sails, a flat sail will help the airflow go through the sails quickly without breaking.
In medium condition, the airflow is strong enough and so you can make the sail fuller to maximise power and lift. Have you noticed that airplane wing have trims that extend and bend to create more lift at lower speed. Same reason. Also as the water gets choppy you need a fuller main to power through the waves.
To recap. You need a “flat” sail in light and heavy wind conditions and fuller in medium to maximise power and lift.