How did the ottoman turks defeat the byzantine empire? what was the basis of their military strength?

The ottoman army was large in numbers, fast and effective. Now if you take in consideration the the origin of turks is not the middle east but central asia, and the fact that the ottomans were excellent businessman, they had access to black powder. They were the one of the first to bring it to Europe.

They had this strategy of digging tunnels right under the walls and blowing them up with black powder explosions or setting a fire underneath.