Tony D was asking about the limits to propeller size in power absorption and whether the Nimitz class could have their power increased if the props were enlarged. Also whether there was a law of diminishing returns working here.
Enlarging props has been the traditional way of absorbing more power; the benefit is then that the speed of rotation can be slowed and that allows the prop to work with greater efficiency. By the way, a prop rotating infinitely slowly will have an efficiency approaching 100 percent!
The problems in a prop design are in three areas, the tips, the leading edge of the blade and the low pressure areas of the blade.
The problem with the tips is that their speed through the water increases in proportion to the square of the length of the blade for a given RPM. This means that there comes a point where the loss of efficiency from excessive blade speed exceeds the gain due to size. Also, the blade tips cavitate and that is a world of hurt. This can be offset by sculpting the blade tip so that its entry to the water is softened.
The leading edge of the blade has a similar problem. As the blade increases in length, the problems caused by the blade edge moving through water are increased and cavitation starts on the upper part of that edge. This is offset by curving the blade edge so it slices through water rather than battering it.
Finally the low pressure areas can cause sheet cavitation. Once this happens, if the area of the cavitation sheet exceeds a proportion of that of the blade, the blade is effectively rotating in a vacuum. This imposes immense stress and can cause the blade to blow up (I have a small scar on one temple caused by a chunk of bronze from just that happening). If the blade doesn't go the gears and turbines might.
So its more a question of physical limits rather than declining returns. Computer design has helped a lot (it makes modern quiet submarine props possible) and advanced material sciences have done a lot as well. Props today are very different animals from 40 years ago.
My guess is that the new generation props being designed for CVN-78
will have power absorbance some 10 - 20 percent greater than those in use
today. This puts the total maximum up to (say) 320,000 to 350,000 shp -
that could be provided by a new electric drive train. This is badly needed
- the decreasing speed of the carriers is causing a lot of concern.