Subject: [harryproa] Schooner v. Unarig |

From: "Herb Desson" <squirebug@yahoo.com> |

Date: 11/28/2006, 5:08 AM |

To: harryproa@yahoogroups.com.au |

Reply-to: harryproa@yahoogroups.com.au |

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

and the square of the radius

( http://en.wikipedia

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)

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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