When cutting self nocks in arrow shafts NOT made from shoots, wherein you have grain such as the growthrings, you will have to make allowances. For best strength of the nocks, you cut them across the grain so that they resist further splitting as the string drives deeper into the nock upon release. That means that the grain of the wood is now perpendicular to the bow. The arrow is less flexible on this axis than it would be rotated 90 degrees so that the grain would be parallel to the axis of the limbs. Clear as mud?
If you have an arrow shaft at hand, try this. Test bend it across the grain and with the grain several times, noting the difference. When commercial shaft producers (like the pros at Surewood Shafts, shameless promotion of some great guys) are organizing a pile of shafts they are sorting them into piles according to stiffness/spine. The shafts are universally tested flexing the stiffest side, which is along the same axis as the grain.
I have improvised lighter spine arrows by re-nocking stiff arrows to allow for hav ing the grain parallel to the limbs of the bow to SOME success. I was up against the wall and had to get some arrows put together to go with a kid's bow. I could have tried sanding the middle part of the arrows to take away material and lighten the spine, but time was of the essence. It worked....after a fashion. Fortunately, he lost all three arrows by week #2 with the bow, giving me time to get some lighter spined arrow shafts in the mail and fletched up.