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It has been said the most fuel efficient way to fly is by flying in thinner air. On the other hand the largest plane in the world was the Russian "Caspian Sea Monster" Ekranoplan, which is said to be the most efficient plane for its weight. enter image description here

Which method of flying is the most efficient and by how much when it come to time and fuel?

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There really isn’t any strict single rule on whether an aircraft should fly high or use ground effect to increase endurance. It all depends on the design requirements and the purpose of the aircraft.

For cargo type aircrafts, it would make sense to use ground effect and fly over the sea, since speed is not really a major concern.

For reconnaissance aircraft, using ground effect is obviously impossible. For that they have to fly high and the optimum altitude would depend on aircraft parameters, and be a strong function of weight and possible induced drag.

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