Geometry 101
 

What is the largest triangle (area) that can be fitted into an area
bounded by the boom, mast (between gooseneck and backstay crane),
backstay crane and backstay?

This is basically the problem that is causing such a kafuffle in a few
other threads here.

Well actually it's not going to be a triangle because the boom does not
extend to the backstay. We can increase the area bit by bowing out the
leech of the sail to just reach the backstay at a point roughly
perpendicular from the position of the clew on the boom, this is roach.

For structural reasons the top of the headboard is not pointed but
rather chopped of parallel to the foot and this is partly why the
backstay is carried aft of the mast head by the crane, allowing the head
board to hoist a bit higher.

Now hear is the rub: If we lower the headboard by a foot and increase
the curvature of the roach to meet the headboard at the new lower
position we REDUCE the area of the main. The roach, expressed as a
percentage of the area of the main increases. This happens for two
reasons: 1) The leech is now at a position further forward of the old
on, so the distance from the point of maximum roach to the line
connecting the clew and head is a bit larger. 2) The area of the
triangle defined by luff, foot, and line connecting clew to head is now
smaller. Consequently the roach percentage rises.

BUT, the overall area of the sail is LESS!

Now why would you not want a sail that hoists to the black band?

Cheers
Marty

Geometry 101
 

"Martin Baxter" wrote in message
...

What is the largest triangle (area) that can be fitted
into an area
bounded by the boom, mast (between gooseneck and backstay
crane),
backstay crane and backstay?

This is basically the problem that is causing such a
kafuffle in a few
other threads here.

Well actually it's not going to be a triangle because the
boom does not
extend to the backstay. We can increase the area bit by
bowing out the
leech of the sail to just reach the backstay at a point
roughly
perpendicular from the position of the clew on the boom,
this is roach.

For structural reasons the top of the headboard is not
pointed but
rather chopped of parallel to the foot and this is partly
why the
backstay is carried aft of the mast head by the crane,
allowing the head
board to hoist a bit higher.

Now hear is the rub: If we lower the headboard by a foot
and increase
the curvature of the roach to meet the headboard at the
new lower
position we REDUCE the area of the main. The roach,
expressed as a
percentage of the area of the main increases. This happens
for two
reasons: 1) The leech is now at a position further forward
of the old
on, so the distance from the point of maximum roach to the
line
connecting the clew and head is a bit larger. 2) The area
of the
triangle defined by luff, foot, and line connecting clew
to head is now
smaller. Consequently the roach percentage rises.

BUT, the overall area of the sail is LESS!

Now why would you not want a sail that hoists to the black
band?


I don't know, but all the racing boats I've seen are.

Scotty

Geometry 101
 

Martin Baxter wrote:
What is the largest triangle (area) that can be fitted into an area
bounded by the boom, mast (between gooseneck and backstay crane),
backstay crane and backstay?


Clearly, the largest sail area can be achieved by completely
filling in that triangle... or by thinking "outside the box"
and ignoring the artificial limit imposed by the backstay.
Some boats have sails that overlap the backstay, other boats
don't have a backstay at all.



This is basically the problem that is causing such a kafuffle in a few
other threads here.


No kafuffle, just Bobsprit showing his ignorance.



Now hear is the rub: If we lower the headboard by a foot and increase
the curvature of the roach to meet the headboard at the new lower
position we REDUCE the area of the main. The roach, expressed as a
percentage of the area of the main increases. This happens for two
reasons: 1) The leech is now at a position further forward of the old
on, so the distance from the point of maximum roach to the line
connecting the clew and head is a bit larger. 2) The area of the
triangle defined by luff, foot, and line connecting clew to head is now
smaller. Consequently the roach percentage rises.


Yep. One of the consequences of being able to make sails
with higher roach than before is that more classes are
defining a mid-girth measurement for all sails.


BUT, the overall area of the sail is LESS!


Did you confirm this with a licensed rocket surgeon?


Now why would you not want a sail that hoists to the black band?


A DUCK!!

DSK

Geometry 101
 

BUT, the overall area of the sail is LESS!


Now why would you not want a sail that hoists to the black band?

The hoist of my sail is about 4.5 inches short according to the specs
from Beneteau USA and the original sail. The roach is 8.5%. The old
sail head went to a fairly sharp point and had little or no roach. The
new sail has a broader headboard and so that "point" is missing. The
loss of sail area at the top is not even a single square foot. Lying
both sails on top of eachother revealed the foot to about the same, but
the roach was far greater than the original 35s5 sail. There is no
doubt that the new kevlar sail is larger...none at all.
I think you're working out the geometry based on cutting at the foot,
which would result in a great loss of sail area. Visualize a triangle.
Cut a foot off the base is far more area than a foot off the tip.
Being a large mained fractional rig, this current sail was found to be
excellent both in this material and the less exotic version it was
coppied from...that sail being from North. After posting all of the
pics, talking with my loft and checking the main at Doyle there is no
doubt....except in the small mind of Sloco.
As far as the black band goes, my 35s5 has none. When we hoisted the
main we were positive it was hoisting further up that the original
main, which was odd.
Again, none of this matters in the least.


RB
35s5
NY

Geometry 101
 

Martin Baxter wrote:

What is the largest triangle (area) that can be fitted into an area
bounded by the boom, mast (between gooseneck and backstay crane),
backstay crane and backstay?

This is basically the problem that is causing such a kafuffle in a few
other threads here.

Well actually it's not going to be a triangle....

Actualy, yes it is. The largest triangle is obviously going to be a
triangle. Read your question again.

Now, I don't know why you are concerned with triangles, because sails
aren't triangles.

//Walt

Geometry 101
 

DSK wrote:

Martin Baxter wrote:
What is the largest triangle (area) that can be fitted into an area
bounded by the boom, mast (between gooseneck and backstay crane),
backstay crane and backstay?


Clearly, the largest sail area can be achieved by completely
filling in that triangle... or by thinking "outside the box"
and ignoring the artificial limit imposed by the backstay.
Some boats have sails that overlap the backstay, other boats
don't have a backstay at all.

Sorry, I should have specified that going outside the defined area was
not permited for this excercise.



Yep. One of the consequences of being able to make sails
with higher roach than before is that more classes are
defining a mid-girth measurement for all sails.

BUT, the overall area of the sail is LESS!


Did you confirm this with a licensed rocket surgeon?

Indeed, Dr. Who no less, he offered to put a new black band on Bob's
boat with his sonic screwdriver!


Now why would you not want a sail that hoists to the black band?


A DUCK!!

DSK

Geometry 101
 

"Capt. Rob" wrote:

BUT, the overall area of the sail is LESS!

Now why would you not want a sail that hoists to the black band?

The hoist of my sail is about 4.5 inches short according to the specs
from Beneteau USA and the original sail. The roach is 8.5%. The old
sail head went to a fairly sharp point and had little or no roach. The
new sail has a broader headboard and so that "point" is missing. The
loss of sail area at the top is not even a single square foot. Lying
both sails on top of eachother revealed the foot to about the same, but
the roach was far greater than the original 35s5 sail. There is no
doubt that the new kevlar sail is larger...none at all.
I think you're working out the geometry based on cutting at the foot,
which would result in a great loss of sail area. Visualize a triangle.
Cut a foot off the base is far more area than a foot off the tip.
Being a large mained fractional rig, this current sail was found to be
excellent both in this material and the less exotic version it was
coppied from...that sail being from North. After posting all of the
pics, talking with my loft and checking the main at Doyle there is no
doubt....except in the small mind of Sloco.
As far as the black band goes, my 35s5 has none. When we hoisted the
main we were positive it was hoisting further up that the original
main, which was odd.
Again, none of this matters in the least.

Holy Backpedal! Now it hoists higher on your boat, so you must have a
shorter than standard mast, or the Bennies in all those photos you
posted have higher than starndard masts.

Cheers
Marty

Geometry 101
 

Walt wrote:

Martin Baxter wrote:

What is the largest triangle (area) that can be fitted into an area
bounded by the boom, mast (between gooseneck and backstay crane),
backstay crane and backstay?

This is basically the problem that is causing such a kafuffle in a few
other threads here.

Well actually it's not going to be a triangle....

Actualy, yes it is. The largest triangle is obviously going to be a
triangle. Read your question again.

My question defines an area bounded by for sides, a quadrangle, I
suppose I should said "plane geometric shape" rather than "triangle",
sorry for the confusion.


Now, I don't know why you are concerned with triangles, because sails
aren't triangles.

Ummm, that's why I said "Well actually it's not going to be a
triangle...."

//Walt

Geometry 101
 

Holy Backpedal! Now it hoists higher on your boat, so you must have a
shorter than standard mast, or the Bennies in all those photos you
posted have higher than starndard masts.


My story has remained the same, and every photo of a 35s5 I can find
supports what I've said. The hoist on EVERY 35s5 looks a bit short to
me, including the one I just got. But it does appear higher than my old
sail. My old hoist looks about the same as this...

http://home.att.net/~captnerdo/images/Footloos.gif

But the new sail is more like this....

http://www.lakeontario300.org/images...windriven1.jpg

Then this Frers 51 seems to have a hoist a good 6 inches short...

http://www.lakeontario300.org/images...s/toscana1.jpg

and does this Express 30 main look short? Because it is!

http://www.lakeontario300.org/images...nts/tigger.jpg

But check the hoist on this C&C 99! I think it's almost above the mast!

http://www.lakeontario300.org/images...nchurchill.jpg

Does it really matter, Martin? Do you think my Kevlar main is going to
slow us down?


RB
35s5
NY

Geometry 101
 

Martin Baxter wrote:
Walt wrote:
Martin Baxter wrote:

What is the largest triangle (area) that can be fitted into an area
bounded by the boom, mast (between gooseneck and backstay crane),
backstay crane and backstay?

Well actually it's not going to be a triangle....

Actualy, yes it is. The largest triangle is obviously going to be a
triangle. Read your question again.


My question defines an area bounded by for sides, a quadrangle, I
suppose I should said "plane geometric shape" rather than "triangle",
sorry for the confusion.

OK. If you mean "polygon" please say "polygon".


Now, I don't know why you are concerned with triangles, because sails
aren't triangles.

Ummm, that's why I said "Well actually it's not going to be a
triangle...."

Fair enough. But I don't know why you are concerned with polygons, or
quadrangles, because sails aren't polygons or quadrangles.

(Or quadralaterals either, if you object to an obsolete definition of
quadrangle. http://en.wikipedia.org/wiki/Quadrangle )

Geometry 101
 

My question defines an area bounded by for sides, a quadrangle, I
suppose I should said "plane geometric shape" rather than "triangle",
sorry for the confusion.


Walt wrote:
OK. If you mean "polygon" please say "polygon".


Isn't a triangle a polygon?

Anyway, what is the point in using plane geometry to analyse
sails? They are not flat.

One way to maximize sail area would be to make the sails
more spherical, with boundaries defined by the limits of the
above-mentioned polygon.

DSK

Geometry 101
 

DSK wrote:

My question defines an area bounded by for sides, a quadrangle, I
suppose I should said "plane geometric shape" rather than "triangle",
sorry for the confusion.

Walt wrote:

OK. If you mean "polygon" please say "polygon".

Isn't a triangle a polygon?

Yes it is.

Anyway, what is the point in using plane geometry to analyse sails? They
are not flat.

Bingo. We've got a winner. Sails aren't triangles. Or Quadralaterals.
Or any other object from plane geometry.

One way to maximize sail area would be to make the sails more spherical,
with boundaries defined by the limits of the above-mentioned polygon.

Cool. Then you could make them out of leather from your spherical cow.

//Walt

Geometry 101
 

DSK wrote:

Now why would you not want a sail that hoists to the black band?


A DUCK!!

So this is the black band you've been talking about.

http://www.thom.org/gallery/animals/duck/

Geometry 101
 

"Martin Baxter" wrote in message
...


Did you confirm this with a licensed rocket surgeon?

Indeed, Dr. Who no less, he offered to put a new black
band on Bob's
boat with his sonic screwdriver!


Ha ha, before last Friday, I wouldn't have known what you
were talking about.

SBV

Geometry 101
 

Walt wrote:

DSK wrote:

My question defines an area bounded by for sides, a quadrangle, I
suppose I should said "plane geometric shape" rather than "triangle",
sorry for the confusion.

Walt wrote:

OK. If you mean "polygon" please say "polygon".

Isn't a triangle a polygon?

Yes it is.

Anyway, what is the point in using plane geometry to analyse sails? They
are not flat.

Bingo. We've got a winner. Sails aren't triangles. Or Quadralaterals.
Or any other object from plane geometry.


Jumpin' Jiminy, let's see if get a bit more sophomoric! It was merely an
approximation meant to illustrate the thought that if you start with
sail that fits the mast/boat combination correctly, and comes close to
but does not touch the backstay when tacking/jybing, a sail with a
shorter luff that fits the rest of the criteria will have LESS area.

Cheers
Marty

Geometry 101
 

Martin Baxter wrote:
Jumpin' Jiminy, let's see if get a bit more sophomoric!

OK, you go first


.... It was merely an
approximation meant to illustrate the thought that if you start with
sail that fits the mast/boat combination correctly, and comes close to
but does not touch the backstay when tacking/jybing, a sail with a
shorter luff that fits the rest of the criteria will have LESS area.


Less is more.

Ignorance is strength.

DSK

Geometry 101
 

Scotty wrote:
Ha ha, before last Friday, I wouldn't have known what you
were talking about.


What happened last Friday?

DSK

Geometry 101
 

"DSK" wrote in message
. ..
Scotty wrote:
Ha ha, before last Friday, I wouldn't have known what
you
were talking about.


What happened last Friday?


I'm sworn to secrecy.

SBV