Roman Troopships

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What I got:

Die Zusammensetzung der Besatzung

Die Besatzung einer Triere besteht aus athenischen Bürgern, aus Metöken und aus angeworbenen Fremden11. Der Anteil dieser drei Gruppen an der Besatzung bestimmt sich nun wie folgt:
1) IG 112 1951 (a. 413?), Aristoph. Ach. 162f. (a. 425) und Thuk. 6,31,3 (a, 415) sichern, daß z. Zt. des peloponnesischen Krieges die 6 Mann der Schiffsführung. die 10 Epibaten, die 4 Bogenschützen und aus den Reihen der 170 Ruderer die 62 Thraniten athenische Bürger waren, also von den rund 200 Mann Besatzung rund 80 Mann.

Source: Ruschenbusch, Eberhard (1979), "Zur Besatzung athenischer Trieren", Historia 28: 106–110 (110)

-> The crew of an Athenian Trireme in the Peloponnesian War consisted of 170 rowers and 30 'marines'.

With the amount of deck space legislated by Marseilles for each pilgrim or crusader, ships of the size of the average three-decked ship could carry around 500–550 passengers. One thirteenth century Genoese ship, the Oliva, is known to have had a capacity of 1,100 passengers. Such ships were intercepted and captured by Saladin’s squadrons in the 1170s and 1180s and were referred to in Arabic sources as bu>ash. According to Arabic sources, one ba>sha wrecked off Damietta in 1181/1182 was carrying 2,500 passengers, of whom 1,690 were taken alive. The figures are probably exaggerated, but perhaps not by a great deal if the ship was indeed very large. They could also carry up to 100 horses, normally on the lowest deck, as revealed by a Marseillese contract of 1268 with Louis IX, which specified a fare of 25 shillings for passengers if horses were not stabled there.

Source: John Pryor: "Ships" in: The Crusades. An Encyclopedia, 2006

The contract between Venice and the Crusaders of the 4th crusade is also instructive:

The contract called for the transport of 4,500 knights and horses, 9,000 squires, and 20,000 foot soldiers. In addition, Enrico Dandolo, the doge of Venice, offered to supply 50 galleys crewed and armed at Venice’s expense. Horses and squires were to be carried on horse transports (Lat. uisserii, Fr. uissiers), and lords and their men on sailing ships. Transports were to be available for up to a year from departure on 29 June 1202. Venetian commerce was suspended while the fleet was being made ready. Some 7,500 men would have sailed in the battle fleet. For 4,500 knights and 20,000 foot soldiers, perhaps around 40 first-rate sailing ships would have been needed; proportionately more smaller ones would be required if larger ships were unavailable. Around 4,500 sailors would have been needed for a fleet with a capacity of 24,500 passengers. Venetian uissiers of 1202–1204 probably required around 130 men each, or 19,500 men in total. In the end not all the ships and men were needed, but the Venetians did not know that. The fleet that assembled had 50 war galleys and around 150 uissiers, with total crews of around 27,000 men, plus an unknown number of sailing ships with crews of around 4,500, a massive commitment.

Source: The Crusades. An Encyclopedia, 2006, p. 872