175 comments on Rail Efficiencies
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175 comments on Rail Efficiencies
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I think the water case is more complicated. Fluid dissipation pretty much scales as the cube, but ships also have to contend with wave drag, whereby the ship creates a surface wave, that radiates energy away. The power in this wave, may vary with velocity, as the shape/wavelength of the wave interacts with the waterline of the ship. Those bulbous underwater blobs on the bows of ships can decrease wave drag, by displacing the bow wave ahead of the main body of the ship. I suspect all things being equal, that wave drag does increase pretty rapidly (I don't know if your sixth power is right). Nevertheless, the discussions of fuel saving for cargo ships that I've seen, seem to assume the cube law.
There's a thing called "Hull Speed" with displacement hulls. As the boat goes faster the surface wave emanates from farther back on the boat. When you've reached the speed where the wave is emanating from the back of the boat, you are at "Hull Speed" and it take substansive amount of power to go faster (then you would be planing). The "Hull Speed" for a displacement hull is a function of its length (1.34 * sqrt(waterline length)).