Re: Why superships cost more per mass

agoodall@canada.com wrote:

> On Fri, 29 June 2001, David Griffin wrote:
>
> > The question isn't is a Battleship more complex
> > and harder to build than a Destroyer. The question
> > is is a 200 mass battleship more trouble/complex/
> > expensive to build than 4 50 mass destroyers all
> > put together.
>
> Yes. As Tom and I both pointed out, it's not linear. 4 mass 50
destroyers are 4 times as complex than 1 mass 50 destroyer. 1 mass 200
battleship is more than 4 times as complex as 1 mass 50 destroyer.
>
> > Are there really more points of
> > failure between say 1 big engine and 4 smaller
> > engines?
>
> Yes. For one thing, there's that whole question of inverse square and
inverse cube laws. Why can an ant carry many multiple times its own
weight in food when humans can't? A human being could never survive
being 50 feet tall because human bones just aren't strong enough (even
if they were proportionately bigger).
>
> In a sphere, the surface area goes up as a cube of the diameter. This
means that a sphere twice the diameter has 8 times the surface area, and
requires 8 times the material to cover that area.

Your bad, this implies that surface area is linearly proportional to
volume, which is FALSE.  The reason that the square-cube law prevents
fifty foot humans is that twice the height means eight times the mass,
but the cross-sectional area of the bones has only increased by a factor
of four, so the bones must handle twice the stress.  Doubling the radius
of a sphere increases its volume by a factor of eight (4PiR^3)/3, but
only increases its surface
area by a factor of four (4PiR^2), so a ship that has twice the linear
dimensions as another ship only needs half of the mass per unit volume
to skin the vessel.

Larger engines are easier to build to exacting tolerances than smaller
engines.  It is hard to build a four stroke engine for a model plane, as
the absolute manufacturing
precision is large compared to a 1.0 cubic inch engine (a monster in RC
flight), but marine diesels with displacements measured in cubic meters
can still have their parts manufactured to within 20 microns of the
spec, for a precision of one part in fifty thousand.

>
>
> > Ok, so I'm not a naval architect or a construction
> > engineer on ships. Is there anyone on the list who
> > DOES have actual direct experience -- i.e. who is
> > a real expert? If not, all we have is speculation.
>
> Well, we're speculating about starships, so it will always be just
speculation. However a number of us work in technology industries where
complexity does not scale linearly.
>
> I did some checking on the web. The only references I could find were
to CVN 71 "Abraham Lincoln" and DDG 82 "Lassen". Now, the Lincoln was
built in 1988, the Lassen in 1999. It took 40 million manhours to build
the Lincoln before it was christened, and 2 million manhours to build
the Lassen before she was christened. Their masses are about 104,000
tons and 8500 tons, respectively (though I also saw a reference to over
9000 tons for the Lassen).

The Lincoln has nuclear reactors and steam turbines, compared to the gas
turbines of the Lassen.  The Lincoln also has a number of finicky
systems that are not found on destroyers, particularily deck edge lifts,
ordnance handling equipment, catapults and arrestor cables.  A closer
comparison is the Enterprise and Long Beach.  Your straight comparison
also assumes that there were no productivity improvements between 1988
and 1999.

>
>
> This works out to 384.6 manhours per ton for the Lincoln, but only
234.3 manhours per ton for the Lassen. If complexity was linear with
mass, those two numbers should be about the same.
>
> In another set of web sites, I found that the Lincoln cost
approximately US$4.5 billion to build. DDG 100 will cost $338.2 million.
Note that this does not take into account inflation and the true value
of the dollar compared to the building times. DDG 51, the first in the
same class, was built in the early 90s for $143 million.
>
> In other words, the Lincoln is 12 times the mass of the Lassen. Yet,
the Lincoln took 20 times as long to build, and cost between 13.3 and
31.5 times the price (with the higher number being more accurate, as
it's in dollars of about the same inflationary value).
>
> So, while not exactly scientific, I think it shows that in today's
real world applications, a bigger ship costs more to build -- in time
and money -- per ton than smaller ships.

The problem is that the Lassen uses simpler propulsion and was the
thirty-second vessel of its class.  It also did not need to have its
construction time padded out to guarantee that there would still be a
shipyard that produced DDG's when the navy needed the next one.

Proper comparisons (if you could find them) would be between heavy
cruisers and destroyers in WWII, as they were built in similar
conditions and have systems of equal technologies (guns, radar, steam).