To me a centered sound and a projecting sound go hand in hand. If you can play relaxed without tension in your breathing ,embouchure and body you can hear a core in the center of your notes,this core projects very well. This why when a player tries to over blow and blast,which too many do when in marching band,their sound spreads and doesn't carry.You can't hear that centered core in their sound. I played one band where the player next to me was playing so loud I couldn't hear myself. When I mentioned this to the leader he said he could only hear me out front. This other player was very loud but his sound was spreading with no projection.