Subject: [harryproa] Schooner v. Unarig From: "Herb Desson" Date: 11/28/2006, 5:08 AM

Hi All,

I have been reading Rob's comments that schooners are more hassle and
heavier than sloops, which seem entirely reasonable. But I wondered
how much? So after a bit of searching I found the following
surprising results, which also seem reasonable.

The angle of deflection of a circular thin wall beam is proportional
to the square of the length
( http://en.wikipedia.org/wiki/Deflection )
and the square of the radius
( http://en.wikipedia.org/wiki/List_of_moments_of_inertia ).

If we take a unarig and reduce it in area by 1/2, we will reduce the
length of the luff by 1/square root(2). But to obtain the same angle of
deflection for a given force, while maintaining the same wall
thickness and material, we must also reduce the radius of the mast by
1/square root(2). So with the schooner sail the weight of the luff
portion of the
mast is now 1 / (square root(2) * square root(2)) = 1/2. That seems
reasonable because there are now two masts instead of one.

However, each mast now has only 1/2 as much sail area, so the force on
each mast is 1/2 of what it would be for the single mast. The
surprising thing is that now each schooner mast is
1 / (square root(2) * square root(2) * square root(2)) = 1/(2 * square
root(2)).
So the total weight of both masts is
2/(2 * square root(2)) = 70.7%
of the single masted rig.

If we assume that the bury, boom and deck to boom distance also reduce
in proportion (which would certainly be true for boom and bury) then
the weight (and presumably material costs) of the total schooner rig
is 70.7% of the single masted rig.

Actually, it would be a bit less than that because the schooner is
shorter than the unarig, so the force on each mast of the schooner
would be less than 1/2 of the unarig. After some more searching I
found that the wind speed increases with the 7th root of height and
the force on the sail with the square of the wind speed. So the
weight of the schooner rig would now be (70.7%^(2/7))^.5 = 67.3%, but
that difference is so small it hardly seems worth bothering about.

So I am confused. Is a schooner rig really about 2/3 the weight and
cost of a unarig (ignoring sails), or have I misunderstood something?

Best regards
Herb

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