Nice looking design. The profile just looks so much like the Calypso.
Being a 4-person shuttle, I don't know how much inertial dampening it even really would have.
[Hocus TrekTech]
It wouldn't be about the number of people aboard but how many gees it could pull while sublight and whether it's warp-capable. It's pretty much a given that all
Star Trek vessels that are warp-capable have inertial dampeners to keep the crew from being straight-up killed while using the warp drive. I see a couple of warp nacelles there, and if it can get into orbit in a matter of seconds from class M planets, then it has to have inertial dampeners for that reason too.
But since they'd pretty much have to be there anyway, I was just pointing out that having them on either while the craft is on rough waters or while it's (aggressively) maneuvering on the surface would solve a lot of problems, including allowing the crew to move around inside without having to worry about, frankly, getting injured. But that's no reason not to think about how to move around, avoid falling, etc. when they're not on.
[/Hocus TrekTech]
Actually, I'm not sure that going to warp produces that many gees, if any at all. Otherwise, that'd mean that the Phoenix must've had them, otherwise Cochrane and whoever else was flying with him in any timeline would've been turned to mush as soon as the Phoenix went to warp.
This means that either the inertial dampener was likely invented before WW-III, or going to warp produces negligible to no gees.
I think it is the impulse drives that causes the dangerous accelerations to the point that g-forces become deadly.
And if it is capable as maneuvering as well as a race boat, it'd need more than hand holds for the safety of the crew. Either inertial dampeners, or safety harnesses to keep the crew strapped in.
Well, one could always reason that the inertial dampers are only used when at warp or impulse speeds, and not while moving at the relatively slow speeds used while in 'aquatic' mode

.
I actually kind of like the idea of it being able to travel at supersonic speeds, even underwater.
Why?
Well, this comes from reports of UFOs/USOs being able to travel at high speed, even at supersonic speeds, even submerged, in real life.
I'm thinking that maybe at this point, Federation technology is advanced enough that this sort of feat is trivial, especially for a specialized flying submersible. I'm guess it would use some sort of specialized forcefield that would minimize the displacement of water, and so prevent underwater shockwaves.
Actually, this is probably how all ships prevent themselves from creating a sonic boom at supersonic speeds, because lets face it, their air frames are clearly not made to prevent or reduce sonic booms.