I was planning on putting together a Who Would Win post positing the Ottoman armies against Westeros and general A Song of Ice and Fire shenanigans but my google-fu failed to turn up good info on the Ottoman logistics. The best (but still questionable) info I got was that the army probably had 69 bombards organized into some 15 batteries with bombards such as the Orbis gun that wrecked the walls with ease and a handy chart on wikipedia with a breakdown of the entire Ottoman military, but no clue on the exact force composition at Constantinople. What sort of logistical footprint did this army have and how did the Ottoman's support it? How powerful was their fleet?
As much as I dislike Who Would Win questions, I can’t pass on GoT! If you've read the books, did you know Tyrion's use of a chain to block the harbour of King's Landing parallels the Byzantine blocking of the Golden Horn in 1453?
I digress. Turkish authorities set the total of the Ottoman forces at the Siege of Constantinople at not more than 80,000 (Nicol, 1993) George Sphrantzes, envoy of the Byzantine Emperor, estimated a total Ottoman force size of 200,000 (ibid) The truth probably lies somewhere between these two estimates. In terms of likely force composition, I am sure you will receive a more accurate answer from some of the experts here.
The Ottoman Navy in 1453 was estimated to consist of 350-400 ships of various sizes (Ágoston, 2009) However, the majority are likely to have been small trading vessels in the order of 50-100 tons. The tactic of traversing vessels across land to negate naval blockades, utilised in this siege and at least two others, gives credence to this.
It is important to note that it is only in the post-Byzantine period that the Ottomans invested significant effort into strengthening their naval capabilities. They didn’t represent a significant challenge to Venetian naval supremacy until the 16th century.
Hope that helps somewhat.
Sources
Donald M. Nicol, "Last Centuries of Byzantium", Cambridge University Press, 1993
Gábor Ágoston, "Encyclopedia of the Ottoman Empire" Infobase Publishing, 2006
If you want to learn more about the order of battle for both sides of the Siege of Constantinople, one source you could check out is "The Siege of Constantinople: The End of the Middle Ages, 1453 AD" by Ralph Vickers in Strategy & Tactics #66 published in 1978. Information from this fairly long and fairly well sourced (but using older sources) allowed Richard Berg to design the war game "The Siege of Constantinople 1453" Vickers and Berg agree with the newer sources cited by /u/Cadwaladr and place the Ottoman army around 80,000 troops. They still outnumbered the Byzantines by a four to one margin at the start of the siege. The Ottomans could replace much of their losses and they prevented the Greeks from getting any reinforcements. By the time of the final assault, the Turks outnumbered the Byzantines by a five to one margin.
http://boardgamegeek.com/boardgame/3936/the-siege-of-Xonstantinople I only offer this source, because when it comes to Order of Battle type information, Strategy & Tactics is a reliable source of information.