There is alot more to penetration than the weight and diameter and speed of the arrow such as stiffness of the shaft, size of the head, number of blades, length of the arrow, number and length of fletching. All things above being equal a smaller diameter shaft will allways penetrate better than a larger diameter one due to less surface area and less friction. A stiffer arrow (carbons) will penetrate better than a weaker (aluminum) arrow due to the bending of the arrow when it makes contact with the target. A stiffer arrow transfers more energy into the target as opposed to the weaker one that will bend more when it hits a target. If you are shooting into the same target medium, whether an animal or target, the smaller, faster arrow will always out penetrate the heavier slower arrow provided they have the same KE. The fatter shaft (More surface area) will always generate more friction than the thinner arrow (Less surface area) no matter what you are shooting into. That is a fact and is indisputable.