Well, we don't know how many Newtons of force she can exert, that 30,000 HP could in theory be a very large number of newtons over a very small distance.
Yamato's mass is 72,000 tons full load, that's 700 million Newtons of force of gravity.
Houshou's output is about 22.5 million watts (Joules per second) If houshou exerts 700 million Newtons of force but only gives 22.5 million watts of power, then that's over a distance of about 0.032 meters per second.
In theory, Houshou can lift Yamato to orbit, very, very slowly. As long as the constant thrust is equal to gravity and there is an initial upward velocity, anything can reach orbit. If the constant thrust is greater in magnitude than gravity, well...
It's not about power, but displacement. Assuming that both are floating (no jack-up leg or beached), you can't lift more than your (ballasted) displacement... Hell, even half your displacement is already stretching the limit...
Well, it would depend on what other objects there were around to obstruct the view, and what stage of completion Yamato was in. Even if you were trying to block sight of a destroyer with Yamato, if people could just walk around and see the destroyer from the other side of Yamato, it's totally pointless. Presumably, Yamato would have had to have been obscured from view on all but one side from some of the construction facilities, so you'd only have to block one angle of view by placing Houshou there.
Beyond that, the height factor still wouldn't necessarily have been an issue if you just moved Houshou closer to any viewer (and there were no tall buildings they were civilians were allowed to climb that would allow them to see over Houshou) based upon the same principle as how a solar eclipse works - if Houshou is 2-3 times closer to you than Yamato is, and you're at near-sea-level, then Houshou will appear 2-3 times taller relative to Yamato to you.
Welllll, it sorta worked. See, the idea wasn't to hide Yamato in the "no one can see this" sense; it was to hide bits of her--behind dockyard structures, behind Houshou, and so on--so that an observer couldn't easily get a sense of how big she really was. Obscure the scale of the project rather than the project itself. That part worked reasonably well; Allied intelligence knew the Japanese were developing powerful battleships, but had such a poor grasp of just how big they truly were that initial sighting reports of the Yamato-class ships during the war were't considered credible. What are those guys drinkin' out there? Nobody builds battleships that big!
Welllll, it sorta worked. See, the idea wasn't to hide Yamato in the "no one can see this" sense; it was to hide bits of her--behind dockyard structures, behind Houshou, and so on--so that an observer couldn't easily get a sense of how big she really was. Obscure the scale of the project rather than the project itself. That part worked reasonably well; Allied intelligence knew the Japanese were developing powerful battleships, but had such a poor grasp of just how big they truly were that initial sighting reports of the Yamato-class ships during the war were't considered credible. What are those guys drinkin' out there? Nobody builds battleships that big!
But the Iowa class was bigger than Yamato-lengthwise, of course.
But the Iowa class was bigger than Yamato-lengthwise, of course.
Iowa wasn't launched until late August of 1942, and I daresay not everyone serving in the Pacific was intimately familiar with the project at the time. The preceding South Dakota and North Carolina classes, which were in service when the war began and so more likely to form a casual basis for comparison, were significantly smaller.
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