We see them arise in the fossil record some 203 million years ago and then go extinct 66 million years ago.
We had originally thought that this might not be the most aerodynamic design but it was clearly effective as they used the extra set to create a wee vortex that aided in their propulsion.
In terms of mechanical design, they have a little something in common with an unlikely favourite of mine — dragonflies.
We have recreated plesiosaur movements and discovered that they were able to optimize propulsion to make use of their own wake. As their front flippers paddled in big circular movements, the propelled water created little whirlpools under their bellies. The back flippers would then paddle between these whirlpools pushing the plesiosaur forward to maximal effect. This use of air currents is similar to how dragonflies move through the air.
They were very successful hunters, outcompeting ichthyosaurs who thrived in the Triassic but were replaced in the Jurassic and Cretaceous by these new aquatic beasties.
Our ancient seas teemed with these predatory marine reptiles with their long necks and barrel-shaped bodies. Plesiosaurs were smaller than their pliosaur cousins, weighing in at about 450 kg or 1,000 lbs and reaching about 4.5 metres or 15 feet in length. For a modern comparison, they were roughly twice as long as a standard horse or about as long as a good size hippo.