Airman by Eoin Colfer

From chapters.ca:
Conor Broekhart was born to fly. In fact, legend has it that he was born flying in a hot air balloon at the world's fair. In the 1890's Conor and his family live on the sovereign Saltee Islands, off the Irish coast. Conor spends his days studying the science of flight with his tutor and exploring the castle with the king's daughter, Princess Isabella. But the boy's idyllic life changes forever the day he discovers a conspiracy to overthrow the king. When Conor tries to expose the plot, he is branded a traitor and thrown into jail on the prison island of Little Saltee. There, he has to fight for his life as he and the other prisoners are forced to mine for diamonds in inhumane conditions. There is only one way to escape Little Saltee, and that is to fly. So he passes the solitary months by scratching drawings of flying machines into the prison walls. The months turn into years, but eventually the day comes when Conor must find the courage to trust his revolutionary designs and take to the skies.