... at what point can you have infinitely large sails with no
mast at all?


Roger Long wrote:
Oh, so you want to follow that progression down to the end do you?
(I'm assuming this is a joke because, if you understand this as well
as you say you do, the answer is already obvious.)

All else being equal, the mast can get smaller as the rig gets larger.
At the same time though, the amount of wind that will heel the boat to
any specific angle is getting less since the righting moment is being
decreased by the weight of the added spars and rigging. The sails
could never be infinitely large because the added weight of cloth,
booms, and gaff will eventually bring the center of gravity high
enough that stability is zero. At that point, there will be no load
on the rig from wind and the mast could be infinitely small if there
were some other way to transfer the loads from the sails to the hull.


We'll make the spars out of carbon nanotubes inflated with
hydrogen so that they're lighter than air, and magnetize the
sails with an electrostatic charge to transfer the "sheet"
loads.

"Any sufficiently advanced technology is indistinguishable
from magic." -Arthur C. Clarke

Another possible solution is this
http://www.kiteship.com/
which looks like it would pose less need for righting moment
but even larger need for structural analysis. I'd like to
try one of these.

A point I was trying to make earlier is that while loads on
the rig (mast & standing rigging) are limited by the boat's
righting moment, the actual force on any given piece of
rigging can be far larger because of the geometry. For
example, the tension on the shrouds can be huge because they
are opposed by the opposite shroud and the compression of
the mast. Then you have the sheet loads, vang, halyard
tension, etc etc. The aggregate (or net) of these forces
will equal the righting moment plus the force required to
drive the boat thru the water at speed, but the boat's
structure has to be capable of holding up to the sum of
these forces.

This is probably not very clearly states so I will apologize
in advance and brace for argument

Fresh Breezes- Doug King