No, he meant years to work it out as in it would take years to work it out without Scotty giving it to him in advance.
Scotty made it clear he needed something strong and only a certain thickness and that in the year they were in there was nothing that was strong enough without it being too thick.
Remember when Scotty and McCoy told that plexiglass guy what they needed the guy said they couldn't make plexiglass that strong so small which is precisely why Scotty gave him the information for transparent aluminium...
That's what I believed until a few hours ago. Then I reviewed the actual lines from
the script and realized there are some unverified assumptions in that interpretation.
SCOTTY
Doctor Nichols, I might have
something to offer you.
NICHOLS
... Yes?
SCOTTY
I notice you're still working with
polymers.
NICHOLS
(mystified)
Sill? What else would I be working
with?
SCOTTY
Ah, what else indeed? Let me put it
another way: how thick would a piece
of your plexiglass need to be at 60
feet by 10 feet to withstand the
pressure of 18,000 cubic feet of
water?
NICHOLS
That's easy: 6 inches. We carry
stuff that big in stock.
SCOTTY
Yes, I noticed. Now suppose -- just
suppose -- I could show you a way to
manufacture a wall that would do the
same job but was only an inch thick.
would that be worth something to
you, eh?
...
An awesome series of figures and graphics are
appearing. PULL BACK to reveal Scotty, now master of
the keyboard, while Nichols watches in awe, next to
Bones. with a flourish, Scotty hits a last command,
and a wondrous three dimensional graphic appears.
NICHOLS
(wide-eyed)
Transparent aluminum?
SCOTTY
That's the ticket, laddie.
NICHOLS
... But it would take years just to
figure out the dynamics of this
matrix...!
BONES
You'll be rich beyond the dreams of
avarice.
SCOTTY
So, is it worth something? Or
should I just punch "clear"...
Nobody ever actually says that they need something stronger than Plexiglas, not in the script, anyway. And the discussion of the relative strengths of Plexiglas and transparent aluminum takes place within the context of Scotty offering something to Nichols. So this morning, I would've agreed with your interpretation, but now that I've heard another interpretation and considered the details of the scene, I think I was wrong.
I mean, think about it. Even if the formula Scotty gave Nichols was all that he needed to know, there's no way that equipment designed for making Plexiglas, which is a synthetic polymer made of carbon, oxygen, and hydrogen and formed into sheets either by casting liquid methyl methacrylate or extruding and homogenizing solid pellets of same, could be adapted to make transparent alumina armor, which is a ceramic made of aluminum, oxygen, and nitrogen and is produced by various arcane, specialized techniques. Plexicorp would've needed to manufacture whole new equipment to make the formula into reality. There would've needed to be extensive tests and calibrations of that equipment to make sure it was capable of doing the job. They would've had to train technicians to work the equipment. They would've had to run through multiple test batches to fine-tune the equipment and their skills until they got it right. Even given all the information they needed, it would've taken weeks at least to produce usable results. But Kirk's crew was in the 20th century for only a few days.
So I was wrong. I made an assumption that, I'm sure you'll agree, is reasonable enough to draw from a cursory recollection of the scene, but that doesn't hold up to further analysis. The whale tank was made of Plexiglas, and Scotty paid for it with the formula for transparent alumina/um.
A ten foot tank would only have a water pressure of some 19 psi....
You're forgetting the weight of two whopping great big hump back whales in a small confined space.
Whales are pretty much neutrally buoyant, otherwise they'd sink. That means their density is approximately equal to the density of the water they displace.
