In simple terms fletchings stabilise and steer the arrow in a straight line. it does this via drag. The more feather you have the more stable the arrow will be but the more drag you have. In a hunting shot an arrow with a lot of fletching need to be aimed higher, will tend to drop further as it travels slower and is thus infleunced more by gravity due to the length of time it takes to get there. It will however straighten up quicker and will counter act the steering effect of a broadhead on the front of an arrow.
A small fletching will have less drag, so for long distance shooting at targets or for flight shooting it will go further.
Small 2 inch fletchings or smaller for distance, 4 to 5 inch for field archery , 5 to 6 inch plus fletchings for hunting.
A bow that is shot round the handle may need larger fletchings than a cetrne shot bow.
Mark in England