Why do we say 'grandmother' but then 'great uncle'? Why not grand uncle? Where's the logic?

The grand denotes a direct blood relation via offspring. For lack of a better description its means mother's mother, the mother of your mother or father. Since your uncles, aunts etc. are indirect blood relations the word great is used to show at which stage they branch off from your own place on the family tree. The same goes for great-grandmothers, it shows at which level within your family tree they are compared to you, but keeps the emphasis that they are a direct blood relative.