"He's got a grey beard, a little bit of a ponytail, so he's a little bit groovy. He has a little hat and a bow tie.
"And he has this magic compass so when he rubs that you can go anywhere."
The book's fictional family take off on a whirlwind magical mystery tour. They ride horses with a cowboy in the desert, face an army of crabs on a tropical beach and dodge an avalanche while having a picnic up a mountain.
"Grandude isn't supposed to be me," McCartney is keen to clarify. "Because he's magic and I'm not."