We know at what angle we need to tip a quinquereme like the one Polybius described in order to potentially sink it. About 9.24 degrees. At that angle the tip of the prow will be nearly seven meters above the water and the stern would be below it. The lighter model would need to be lifted 33.55 degrees out of the water, bringing the prow to about 23.5 meters above the water.

    Since we know how high the ship needs to be lifted and we know roughly how much it weighs we can approximate the work that our claw would need to do.


    To put that in perspective it is about the same amount of work needed to lift a 1600 kilogram car 1511 meters upward. Doing a similar calculation using our lighter boat and lifting it to an angle of 33 degrees gives us 46,127,625.53 Joules, about twice as much work.

    The legend says that Archimedes lifting devices were each operated by one man. This may be exaggeration or simply an oversight. Besides, how could the Romans know how many people operated them if the operators were behind the wall? But is it impossible? We know that simple machines and pulley systems allow us to do work on objects that would otherwise be much too heavy for us to move at all.

    In order for a person to lift this boat he would need to exert enough force to move a 50 kilogram weight a distance of  almost 500,000 meters. If the crane had a crank one meter in diameter that required that much effort to turn all the way around it would take roughly 160,000 turns to lift all the way up.

    Of course there is a more reasonable alternative. Archimedes machines could have been operated by means of raised weights. This way all the operator would need to do is push the weights off of a high surface and watch the crane reel in the helpless Romans. In fact, a 2 cubic meter container filled with water, (about 20000 N,) if dropped could lift our quinquereme in just over 1000 meters.

    So, what if Archimedes rigged up a 633 cubic meter container, filled it with water and then dropped it? This weight could do the work in under 4 meters. Where would he get such a large container though? Easy, you see 633 cubic meters is exactly one half the volume of displacement of our quinquereme. In other words, what if he used a boat?

    In fact, it is more than plausible that he used another boat. Since he knew exactly what type of boats the Romans had because they copied the design directly from the Carthaginians, he was in a major port, and since he knew the Roman quinqueremes were about three meters above the water line, knowing what he did about the displacement of water, all he would need to do is fill another quinquereme with water up to three and a half meters high. He even could have raised the water from the harbor using another one of his inventions, the screw pump.