I am interested in learning more about the Mini landyachts discussed in this forum.

I usually approach design problems by putting numbers onto a spreadsheet. Each line drawn requires answers to why and where things go. The decisions become mathematically linked together and what results is a parametric model that begins to look like something, in this case a sail. I started with the design presented by BenBoulder in the topic, 4.6 Mini Sail.

Here are the inputs and outputs for my first attempt. Any input(s) may be changed and the rest will automatically recalculate. The mast bend is a circular arc and there is no allowance for draft. I hope to get a little more information before finalizing these.

Please have a look, could be worthwhile.

General

Luff panel

LE Circular arc. This shape also defines the Mast curve.

Battens

5 Battens on sail extending from the Leech TE to the Luff pocket TE
4 Battens oriented horizontally and distributed evenly on the vertical span limited by the Head and Foot TE on the Leech.
Batten 5 is oriented below horizontal joining the Head TE to the Batten 4 LE.

Aft panels

Area behind Luff panel divided into three triangles and one trapezoid (upper).
The peaks of the three radial panels are located along the Z dimension of the Leech (quarters).
The peaks of the three radial panels are located along the X dimension at the same fraction of their local chord behind the Sail LE.

Luff panel overlap

When laid flat the Luff panel TE overlaps the Radial panel LE allowing for sail draft.
There is no overlap at the intersections with the Head and Foot.
Overlap determined as a percentage of the average sail chord between the Head and Foot TEs, applied to the local chords at the three radial panel peaks.

Input

Mast

Origin (X) 2500.0 mm
Origin (Z) 0.0 mm
Diameter 50.0 mm
Rake 10.0 deg

Luff pocket

Origin (Z) 500.0 mm
Luff pocket flattened 100.0 mm
Ratio of full to flattened 0.67
TE end to end (chord of arc) 4650.0 mm
TE peak at chord center 185.0 mm

Aft panels LE

Location on local sail chord line 0.30

Luff panel TE overlap

Overlap at average sail chord between the Head and Foot TEs 0.0 mm
Note: Sail is currently flat

Exterior Layout

Foot length 1445.0 mm
Foot angle -10.0 deg
Leech 3945.0 mm
Head 440.0 mm

Output

Layout

Sail area 4.595 m^2
Centroid (X) 1315.5 mm
Centroid (Z) 2416.0 mm
Aspect Ratio 4.25
Leech angle 96.9 deg
Head angle 31.2 deg
Luff panel LE angle (end to end) 109.0 deg

Radial panel 1 (bottom)

Length along Foot 1062.9 mm
Length along LE 1185.7 mm
Length along top 1277.0 mm

Radial panel 2

Length along Radial panel 1 1277.0 mm
Length along LE 1008.6 mm
Length along top 2041.9 mm

Radial panel 3

Length along Radial panel 2 2041.9 mm
Length along LE 1023.0 mm
Length along top 2951.1 mm

Trapezoid panel 1 (top)

Length along Radial panel 3 2951.1 mm
Length along LE 1264.2 mm
Head 440.0 mm
Length along Leech 3945.0 mm
Diagonal-Head TE to Radial 3 Peak 1235.0 mm

Luff panel

Length on Foot 382.1 mm
Length Foot LE to Head LE (straight) 4650.0 mm
Length on Head 57.8 mm
Length on TE (straight) 4461.0 mm

First change

I placed the sail model onto a 5.6 Mini that I am working on. In order to have the boom
clear my head, I raised the sail base to 600 mm and increased the boom angle to -15 degrees. It fits but...

- The mast length is approaching 520 cm. Availability of this mast length may become an issue.

- The sail centroid is 130 mm aft of the rear axle. The 5.6 Mini mast step is already 150 mm ahead of the
rear axle relative to the LLF Mini. If this is an issue for the handling I could investigate moving the mast
step again or changing the rake. A variable rake would help if several sail sizes were to be used.




- The scale is in inches for the moment

Hi Your mast will be long but doable with an extension top and or bottom on a 460 windsurf mast
Your sail has a quite high aspect ratio
The centre of effort on your sail will be forward of the centroid A rough rule of thumb is one third up from the foot and one quarter back from the mast Accurate calculations for centre of effort are complicated
The trend with minis is to move the mast more forward than previously thought to be the optimum
An oval shaped mast step allows mast rake and centre of effort to be adjustable and helps to get the balance right

Select to expand quote

Hiko said..
Hi Your mast will be long but doable with an extension top and or bottom on a 460 windsurf mast
Your sail has a quite high aspect ratio
The centre of effort on your sail will be forward of the centroid A rough rule of thumb is one third up from the foot and one quarter back from the mast Accurate calculations for centre of effort are complicated
The trend with minis is to move the mast more forward than previously thought to be the optimum
An oval shaped mast step allows mast rake and centre of effort to be adjustable and helps to get the balance right

Thanks for the tip. I added some lines to the spreadsheet and the location of the quarter chord on the mean aerodynamic centre is now part of the output.

Output

Layout

Sail area 4.512 m^2
Geometric Centroid (X) 1291.5 mm
Geometric Centroid (Z) 2584.4 mm

Aspect Ratio 4.32

Mean aerodynamic chord 1097.4 mm
MAC/4 (X) 1570.3 mm
MAC/4 (Z) 2590.5 mm

The aerodynamic centre (AC or MAC/4) is located at 9.26% of the wheelbase. I am still reading up on balance issues but for now I can locate the AC.

I think you are trying to make this just come down to numbers, keep in mind the mast does NOT have an even curve as it is a tapered tube and not of constant diameter , 2 piece masts do flex slightly differently than a one piece mast.
The Centre Of Effort is constantly changing (within a region of the sail) with wind direction, yacht speed, and sheeting tension.

Select to expand quote

Gizmo said..
I think you are trying to make this just come down to numbers, keep in mind the mast does NOT have an even curve as it is a tapered tube and not of constant diameter , 2 piece masts do flex slightly differently than a one piece mast.
The Centre Of Effort is constantly changing (within a region of the sail) with wind direction, yacht speed, and sheeting tension.

No doubt this is a numbers exercise, I had to start somewhere. The calculations will handle masts with variable curvature, I threw in a circular arc as an opener.

I can imagine acquiring a mast, loading it up in some fashion and making measurements to define the curve. Having that, what the Sail LE should look like is not clear. What has worked for those who have made a sail?

The COE was a byproduct of the rest of the sail design, got it for free. It will be useful in locating the mast on the frame or when comparing sails of different sizes. Fine tuning of its location is possible with mast rake. Chook2 has been experimenting with this.

Sail leading edge curve

I'm not sure how the sail leading edge is determined. I have read that there is a relationship between the
mast bend characteristics and the shape so here is what I found out about masts.

Mast Bend characteristics

Indexed mast check system (IMCS) measures mast deflection (cm) with 30 kg suspended from mid mast

IMCS Stiffness = Length^3 / (Mid Point Deflection x 216225)

Bend Curve % = (deflection at .75 / deflection at .50) - (deflection at .25 / deflection at .50)

The higher the number the more flexible the mast is in the upper half relative to the bottom.

One mast manufacturer claims that a 76 - 64 (12%) bend characteristic suits 80% of the sails on the market.

A survey of available masts from two other manufacturers shows that the Bottom ratio varies from 62.0 to
64.5%. On a 460 cm mast the difference amounts to 4.5 mm... not really noticeable on a mast that long.?

Deflections for a sample mast

Length 460 cm
IMCS 25
Bend curve 12 %
Bottom ratio 64 %
Top Ratio 76 %

@ .25 Length 11.5 cm
@ .50 Length 18.0 cm
@ .75 Length 13.7 cm

Graphs

The top graph shows the sample mast plotted with the leading edge curve from the sail presented by BenBoulder
in the topic, 4.6 Mini Sail. The curves don't match, perhaps the Sail LE needs to be cut flatter at the top to increase tension there.

The bottom graph shows the same sail plotted with a mast that has the curvatures flipped, a better fit.

Looking for some qualitative wisdom on how the mast and Sail LE curves should relate.

A little more on mast stiffness testing, reference included.

Mast stiffness (Ref. www.sailworks.com/pdfs/MCS_test.pdf)

Indexed mast check system IMCS measures mast deflection (cm) with 30 kg suspended from mid mast.
Mast is supported at points 5 cm from each end. Test length = Mast length - 10 cm.
Mast deflection has had unloaded deflection (sag) subtracted from total deflection.

IMCS Stiffness = Mast length^3 / (Mid Point Deflection x 460^2)

MCS Stiffness = Test length / Mid Point Deflection

Bend characteristics

Larger Bend Curve percentages indicate that the upper portion of the mast is more flexible than the bottom.
Deflections are measured at .25, .50 and .75 of the Test length.

Bend Curve % = (deflection at .75 / deflection at .50) - (deflection at .25 / deflection at .50)

One more graph

This time I plotted the Mast curve with the LE curve presented in the "How I re-cut sailboard sails to suit
landyachts" topic.

The mast calculation for Imcs I believe where they use the 30 kg weight at the centre and measure deflection
is a means of comparing one mast with another and enable a buyer of a sail to match sail to mast
It still doesn't give us the correct curve for the luff In my opinion as we don't know how much the mast bends
under actual sailing conditions This is where the skill and magic of the sailmaker comes in to play and how he curves the luff and draft of the sail to match the shape he wants.
The work you are doing here is great and maybe you can demystify some of this for us

How things bend

I wanted to see how a mast bent under different loading conditions. The IMCS test suspends the ends and hangs a weight in the middle. On a sail, the mast bend seems to be held against the leading edge of the luff pocket by tension from the head through the tack to the downhaul.

I imagine that things change somewhat when the main sheet puts tension on the sail through the boom and clew. I need to think about that one a bit more.

I don't have a mast at hand but thought I might simulate the problem with a strip of flexible plastic. I doubled the thickness over the bottom half of it's length to stiffen the bottom.

Both curves are very similar and no doubt that measurement error is an issue here.
If anything there is slightly greater curvature in the more flexible portion of the mast with the ends tied due to the direction of the load applied.



Test

Measured two ways to compare methods. Peaks at mid length matched.

Ends tied

MCS (l / mid deflection) 10.3
Bottom Ratio 0.62
Top Ratio 0.82
Bend curve 19.4

Suspended with weight in middle

MCS (l / mid deflection) 10.3
Bottom Ratio 0.63
Top Ratio 0.78
Bend curve 14.4

do not forget that booms that dont attach to the mast and booms that do bend the mast in very different ways. with no boom attachment and sheeting aft of midway on the boom the luff tension is reduced and the battens are in compression when unsheeted and go into tension to flatten the sail. very different from the boom on mast way of sheeting. im rather pleased that my By eye an a cane stick that feels right method is such a nice fit

Select to expand quote

landyacht said..
do not forget that booms that dont attach to the mast and booms that do bend the mast in very different ways. with no boom attachment and sheeting aft of midway on the boom the luff tension is reduced and the battens are in compression when unsheeted and go into tension to flatten the sail. very different from the boom on mast way of sheeting.

I have been considering the effect of the boom and sheeting loads on the sail. Saving that bit for future study, standby.

Thanks for joining the conversation, your work is largely what captured my interest in this.

Sail LE Shape

Here is my attempt to come up with a repeatable process for defining the Sail LE shape based on a given mast. The Sail LE curvature is based on increments to the mast curvature and are arbitrary. Examples that I have seen are bent further than the IMCS rating. It seems to make sense to increase the curvature at the quarter points; the top more than the bottom.

Mast length and rake angle.

Mast length = 4900 mm
Rake angle = 10 degrees

I drew the straight mast at its rake angle.

IMCS curvature profile.

Measured Length (ML = Mast length - 100 mm) = 4800 mm
IMCS stiffness (Mast length ^3 / (Mid Point Deflection x 4600^2) = 29
Mid Point deflection / Measured Length = 0.040
Bottom bend ratio (deflection at .25 ML / deflection at .50 ML) = 0.64
Top bend ratio (deflection at .75 ML / deflection at .50 ML) = 0.76

I drew the curved mast matching its LE angle with straight raked mast at base.

Curvature profile for the Sail LE based on increments to the Mast curvature profile

Delta Mid Point deflection (curve) / Length = 0.010
Delta Bottom bend (curve) ratio = 0.03
Delta Top bend (curve) ratio = 0.05

Desired exposed mast length = 500 mm
LE curve length (Mast length - exposed part) = 4400 mm
Measured Length (design: ML = LE curve length - 100 mm) = 4300.0 mm

Mid Point curve / Measured Length = 0.050
Measured Length / Mid Point curve = 20.0
Bottom curve ratio (curve at .25 ML / curve at .50 ML) = 0.67
Top curve ratio (curve at .75 ML / curve at .50 ML) = 0.81

I drew the Sail LE with its base LE angle matching the straight raked mast at the top of the exposed portion of the mast.

Thoughts on the Sail fabric

The sail fabric adjacent to and including the luff pocket is cut to match the desired LE shape.
The area is bounded by the luff panel leading edge and the fibers in the fabric connecting the head and the tack.
Under tension the fibers connecting the head and the tack form a chord line joining the LE curve ends.

The mast is fed into the luff pocket until it reaches the top.
A downhaul connects the sail tack at the bottom of the luff pocket to the base of the mast.
Downhaul tension draws the bottom of the luff pocket / tack towards the mast base forcing the mast into the luff pocket.
This causes the mast to bow outward toward the leading edge of the luff pocket.
As the mast is more flexible at the tip, it will meet the leading edge of the luff pocket before the base does.

Sufficient downhaul will cause the mast to be seated along the LE over its entire length.
Insufficient downhaul will cause looseness in the lower parts of the luff pocket.
Excess downhaul will not move the luff pocket along the mast any further, fabric tearing becomes an issue.

Any force that moves the luff pocket top towards it's bottom may require the downhaul to be adjusted.

If you want to get serious on the subject try this book / author ........Not cheap but full of info.
Your local library may have a copy or can get a copy.

www.amazon.com/Aero-Hydrodynamics-Sailing-Czeslaw-A-Marchaj/dp/1888671181

I have a few of Marchai's books but not the one you mentioned. He made quite a contribution in his time.

I am a little closer to the experimental stage of this endeavor. My goal is to mathematically define the shape of a vehicle based on the experiences from an active group of users. Having that, the design becomes a parametric model that can be readily customized to meet specific requirements.

I am getting closer with the sail model. One set of characteristics for four sizes, change one and all four update. Just need a little more feedback on the areas I have been presenting. What looks good or otherwise?

Sail LE Shape 2

Paul Day proposed a sail LE profile in the "How I recut sailboard sails to suit landyachts" topic. Here is how it looks compared to the model I proposed earlier.








I can recreate it in the model with the following parameters:

Delta Mid Point deflection (curve) / Length = 0.002
Delta Bottom bend (curve) ratio = 0.13
Delta Top bend (curve) ratio = -0.06

There seems to be a lot of curve required in the bottom end with a relaxation in the top.

Luff pocket sections

Was thinking a bit about the luff pocket. The mast tapers so why not the lull pocket too?

Shortening the chord increases the angle at the trailing edge of the pocket may have a negative impact aerodynamically. On the other hand a longer chord moves the batten end further away from the mast.

The spreadsheet does the hard work so I included the feature.


Tip

Mast diameter = 30.0 mm
Luff pocket chord with mast inside = 80.0 mm
Luff pocket chord / mast diameter = 2.7
Trailing edge angle = 26.7 degrees
Allowance for sewn TE each side = 20.0 mm
Material width required = 220.6 mm
Luff pocket chord flattened not including flange for sewing = 90.3 mm

Base

Mast diameter = 50.0 mm
Luff pocket chord with mast inside = 100.0 mm
Luff pocket chord / mast diameter = 2.0
Trailing edge angle = 38.9 degrees
Allowance for sewn TE each side = 20.0 mm
Material width required = 277.0 mm
Luff pocket chord flattened not including flange for sewing = 118.5 mm

A little history on the subject of the Luff curve

Gizmo Posted 11/4/2009 in Sail-making/Recutting-sailboard-sails

...I will tell you how I did the luff curve on the "Sandpiper" yacht that I designed the sail for, many years
ago. The rig was set up on the yacht (no sails on) and a rope was tied to the top of the mast to the boom and
sheeted in to about the fully sheeted in position. A string line was then used between the top of the mast to
the gooseneck point taking measurements at equal intervals along the string line.

Landyacht Posted 13/4/2009 in Sail-making/Recutting-sailboard-sails

...the luf bend on the "recutting essay " came after trying flatter and rounder types of sails on a varety of
masts. I settled on a particularly nice sail that was made for landsailors back in 1991 by Ken O'brian of KA
sails Adelaide. I had had his sail slightly recut by Deiter Drabic of Drastic Designs in Esperence. that sail
and the other 10 we had made keep turning up after 18 years and they still work really well on a large variety
of masts, stiff and soft. Incidently,the original luff curve on Club88 sails was set by the sailmaker using
his "favourite wooden batten" on the loft floor as a template Basically its a good compromise bend considered
from 30 sails over 30 years.

nebbian Posted 3/5/2012 Sail-making/How-tight-should-it-be

...What you need to do is change the curve of the luff to match the curve of your mast. Normally this means
you measure the curve of your mast under load, then draw a slightly different curve for your sail -- it should
extend slightly forward of the mast near the base, then go slightly behind the mast near the top. At the very
bottom and very top it should be exactly at your mast curve though. The difference here is like a slight S
shape. This is called "Luff shaping" and is one way to get belly into the bottom of the sail. It is heavily
dependant on mast curve (which is definitely NOT constant between masts). Another way is called "Seam
shaping" which is where you cut each panel with a bit of a curve in it where you put the battens in. This is
much less dependant on the mast's bend curve, so is much more mast-tolerant. This would be my preferred
approach to getting a nice stable sail. Regardless of which way you choose, the top leech of the sail should
have some looseness to it, this means that it will flap around a bit and will work to make your sail a whole
lot more stable in gusts. When a gust hits, this will exhaust, and pull some shape out of the bottom of the
sail as well, meaning you don't tip over. When you hit a lull, the top of the sail swings back upwind a bit,
making the whole sail more efficient at low wind speeds. Which is exactly what you want!

Gizmo Posted 11/4/2009 in Sail-making/Recutting-sailboard-sails...

Here is a link to "How to make a sailboard sail" worth having a look at.

http://www.sailrepair.co.uk/makingsail.htm

This link explains what the fuss is all about but is no longer available online. I grabbed a copy from the
Wayback Machine and can post it here if there are no copyright issues. Please let me know.

The article also has a companion piece about adjusting the luff curve to suit different masts. It is also on
the Wayback Machine but it was saved without pictures. Does anybody have an intact copy?

www.sailrepair.co.uk/sailors.htm

There is a lot of good information on sail design on the Ezzy page as well.

www.ezzy.com/rig-support/ezzy-basic-sail-design-theory/

Where I am now

Luff shaping allows for control of twist and draft. If downhaul is increased to the point where the mast bends
to meet the Luff pocket LE, the sail will be flat, save for whatever seam shaping was added.

My models to this point did not account for this would have resulted in a slab-sided sail. I was struggling to
account for how Landyacht shaped his sail but I think I understand it better now. I will put some numbers to
it on my next post.

Sail LE Shape 3

Here is a model based on what I found out about Luff shaping.

Mast length and rake angle.

Mast length = 4900 mm
Rake angle = 10 degrees

I drew the straight mast at its rake angle.

IMCS curvature profile.

Measured Length (ML = Mast length - 100 mm) = 4800 mm
IMCS stiffness (Mast length ^3 / (Mid Point Deflection x 4600^2) = 29
Mid Point deflection / Measured Length = 0.040
Bottom bend ratio (deflection at .25 ML / deflection at .50 ML) = 0.64
Top bend ratio (deflection at .75 ML / deflection at .50 ML) = 0.76

I drew the curved mast matching its LE angle with straight raked mast at base.

Curvature profile for Paul Day's sail.

This is the Luff curve Paul Day proposed in the "How I recut sailboard sails to suit landyachts" topic.

I drew the Luff curve with the Head matching that of the curved mast and the foot resting on the mast's LE.
It is hard to see at the scale drawn but the Luff curve leads the curved mast in the lower part of the sail.





To get a clearer picture I plotted the distance between the Sail LE and the curved mast. The S characteristic of the
Luff shaping is clearly evident.

Positive increments allow for increased fullness on the lower portion of the sail.

Negative increments cause looseness in the Leech allowing twist.





Curvature profile for a generic sail with the desired Luff curve shaping.

I drew a curve from the Mast head crossing the mast curve and joining the Mast curve some distance above the Mast Step.

Vertical location of Sail foot on mast 400 mm
Location of crossover in percent of distance between Head and Foot 75%
Initial angle relative to Mast curve at Foot 3 deg.

The method works well and in the case of the parameters above, it matches Paul Day's Sail curve.
It can be seen in the second plot where it nicely overlaps Paul's curve. You couldn't see the difference in the first plot if it were there.

You are making me think about all this in ways I never have before !

Select to expand quote

Hiko said..
You are making me think about all this in ways I never have before !

That is the point of the exercise, its all part of the fun!

no idea waht you are doing ! I do recall a sailmaker measuring one of my sails and asking why the top of the luff was curving the wrong way I said that was how you stopped the head from collapsing. he didnt get it. . gotta love a big slab of concrete to draw sails on

Select to expand quote

landyacht said..
no idea waht you are doing ! I do recall a sailmaker measuring one of my sails and asking why the top of the luff was curving the wrong way I said that was how you stopped the head from collapsing. he didnt get it. . gotta love a big slab of concrete to draw sails on

It does seem a little tricky. I was trying to reverse engineer your sail and didn't have the background to understand why the LE was curved differently from the mast. I think that I have a better idea now though.

The answer came from one of Gizmo's older posts (2009) referencing a link to "How to make a sailboard sail" www.sailrepair.co.uk/makingsail The article is gone from the net but I got a look at an archive copy and John from Sailrepair has given me permission to re-post or quote from it.

On the subject of Luff shaping...

Clipped from web.archive.org/web/20120421140714/http://www.sailrepair.co.uk/makingsail.htm

It is how the curve at the front of the sail relates to your mast when it is bent with down / out haul that will determine the whole nature of the sail.

In the diagram below we have 2 masts; Mast A with a even bend curve and Mast B with a flexy tip. THE LUFF CURVE ON THE SAIL DOES NOT MATCH THE CURVE OF THE MAST. If anything the luff curve is almost a upside down curve the mast takes. The curve in the top third of the sail should be very slight and yet down near the boom the luff curve may be greater than the bend in the mast and that's what produces the rotation or battens sitting to the side of the mast.

The greater the difference at the head of the sail between the bend of the mast and the sails straighter luff curve the greater the pre twist will be in the leech (the more floppy the head will be).

Sail designers tend to sit in specific camps on what the perfect luff curve should be like, in one camp you have Ezzy and North wave sails with very little rotation and then there is Neil Pryde ,Tushingham, Naish etc. with their well rotated sails.

How much should the luff curve away from the straight head to tack line? 25 cm may be a reasonable staring point on a 430 luff, more for bigger sails , less for smaller.

Today I measured the deflections on a mast I have here
A common type that is available on the second hand market and typical of what a home brew mini builder would use
It is a Kilwell 35%carbon SDM 2 piece constant curve mast with a MCS rating of 25 and is 4600 long

I suspended 30 KG in the centre stretched a nylon line along the top and took deflection measurements every 300 mm from the top to the bottom
which left 100 mm at the bottom where the zero point was
Starting at the top the deflection measurements were:-

0,48,90,128,160,184,200,208,200,188,170,142,112,80,46,10,0

Using the mast IMCS formula I have here IMCS= Mast length in CM cubed/ Midpoint deflection in CMx216225 using a 30KG weight
I get an ICMS figure of 22.5

Using the same method on another mast I have A french aluminium Serfiac of 4600 length I got :-

0,56,105,146,180,205,215,215,210,195,175,150,120,85,48,10,0

Applying the same ICMS formula on this mast I get an IMCS of 21.2 It is a little softer, more so at the top I think

I dont know if any of this helps put some figures on a suitable curve

Hiko's masts

Hiko measured two masts at increments along a line 4600 mm tying the ends. I assume that the masts are somewhat longer to account for the curve length and that the 4600 is the measuring length to define the bend characteristics. The Serfiac is not as stiff overall and particularly at the top.

Kilwell 35%

Measured Length (ML) = 4600 mm
MCS (ML / deflection at .50 ML) = 22.7
Bottom bend ratio (deflection at .25 ML / deflection at .50 ML) = 0.634
Top bend ratio (deflection at .75 ML / deflection at .50 ML) = 0.767

Serfiac

Measured Length (ML) = 4600 mm
MCS (ML / deflection at .50 ML) = 21.6
Bottom bend ratio (deflection at .25 ML / deflection at .50 ML) = 0.631
Top bend ratio (deflection at .75 ML / deflection at .50 ML) = 0.818

Luff curve

To illustrate the Luff Shaping model and how different masts will change the sail shape, I created a Luff curve for the Killwell mast. The curvature profile plot shows the Kilwell as well as the Surfiac masts. Both will have fullness on the bottom part but the fit of the sail with the Serfiac mast will be very loose at the tip.

Example:

Location of Sail Head is common with that of the Mast.
The lower portion of the mast is exposed. The Sail foot is located on the Mast LE = 400 mm
LE curve crosses Mast a percentage of the distance between Head and Foot = 65 %
Initial LE slope at foot relative to Mast = 5 deg









Measuring the mast before designing the sail is the way to go. Selecting the Luff curve parameters to produce the right combination of draft down low and TE looseness above is going to take experience.

Just a quick question, have you been doing your calculations with the sail / rig as a 2D shape or as a 3D shape also allowing for sideways flex of the mast.
And have you considered the results if an Asymmetrical mast was used?

The masts measured above were both 4600 long but did have a 1000mm stiffener inserted in the base with 250 mm sticking out the bottom to go into the mast step
The zero measurement points were at each end of the 4600 mast however where they were supported also for the bend test

Select to expand quote

Gizmo said..
Just a quick question, have you been doing your calculations with the sail / rig as a 2D shape or as a 3D shape also allowing for sideways flex of the mast.
And have you considered the results if an Asymmetrical mast was used?

I started modeling only the 2D planform. The discussions about Luff shaping are leading me to think about airfoil shaped cross sections and spanwise twist. Accounting for spanwise bending at the same time is getting a little hairy.

The same combination of side load and height of COE will lift the windward wheel. If the mast were to be stiffened side to side, that may happen at a lower speed and gust loads may become an issue. You could try adding stays to the rig and see what happens.

I am happy with what I have been able to put together on the sail layout. The spreadsheet will now easily produce the lines of a sail based on a small set of inputs. Time to build one and test out how it all comes together.

If anyone would like to have a go, here is the sample input. Let me know what you would change.

Typical Input

Mast

Total length = 4600.0 mm
Tip diameter = 30.0 mm
Base diameter = 50.0 mm

Center deflection / IMCS measured length = 0.040
IMCS Bottom bend ratio = 0.64
IMCS Top bend ratio = 0.76

Mast pivot X = 2400.0 mm
Mast pivot Z = 280 mm
Mast base above pivot = 50 mm
Rake = 5.0 deg

Sail LE

The Sail foot is located on the Mast LE at Z = 700.0 mm
LE curve crosses Mast; % distance between Head and Foot = 75 %
Initial LE slope at foot relative to Mast = 3.00 deg

Luff pocket tip chord / mast diameter = 2.67
Luff pocket base chord / mast diameter = 2.00

Sail TE

Leech roach / leech length (+, 0 or -) = 0.015
Bottom bend ratio = 75 %
Top bend ratio = 75 %

Aft panels LE

Location on local sail chord line = 0.30

Luff panel TE overlap

Overlap at average sail chord between the Head and Foot TEs = 25.0 mm

Exterior layout parameters

Foot length / Sail length on LE curve = 0.320
Foot angle WRT ground (independent of rake) = -15 deg

Head / Sail length on LE curve = 0.070
Head angle WRT ground (independent of rake) = 25 deg




Output

Layout

Sail area = 3.99 m^2
Geometric Centroid (X) = 1537.6 mm
Geometric Centroid (Z) = 2480.2 mm

Aspect Ratio = 4.24

Mean aerodynamic chord = 1070.4 mm
MAC / 4 (X) = 1810.3 mm
MAC / 4 (Z) = 2487.6 mm

Head length = 297.8 mm
Head angle = 25.0 deg
Leech (end to end length) = 3606.4 mm
Leech angle (end to end) = 268.9 deg
Foot length = 1361.5 mm
Foot Angle = -15.0 deg
Luff pocket length (end to end) = 4198.7 mm
Luff pocket TE angle (end to end) = 103.4 deg

Luff pocket

Tip chord = 80.0 mm
Base chord = 100.0 mm

Radial panel 1 (bottom)

Length along Foot = 1034.0 mm
Length along LE = 1175.2 mm
Length along top = 1258.9 mm

Radial panel 2

Length along Radial panel 1 = 1258.9 mm
Length along LE = 912.0 mm
Length along top = 1948.8 mm

Radial panel 3

Length along Radial panel 2 = 1948.8 mm
Length along LE = 918.7 mm
Length along top = 2762.2 mm

Trapezoid panel 1 (top)

Length along Radial panel 3 = 2762.2 mm
Length along LE = 1051.1 mm
Head = 297.8 mm
Length along Leech = 3606.4 mm
Head TE to Radial panel 3 Peak = 1027.0 mm

Luff panel

Length on Foot = 327.6 mm
Length Foot LE to Head LE (straight) = 4198.7 mm
Length on Head = 14.5 mm
Length on TE (straight) = 4049.1 mm

Sail family

The frame that I am working on is designed with a movable stem. It is designed to accommodate four rake
positions by relocating one bolt. The mast fits over the stem.

This drawing shows a family of four sails with the bottom of the mast at a common location. The rake of the
sail changes for each size to keep the relative location of the aerodynamic center in the same place. The
inputs for each is the same with only the mast length and rake angle changing.




The second largest sail is the layout from the previous post.

Sail 520

Mast Length = 5200 mm
Area = 5.20 m^2
Rake = 3.30 deg.

Sail 460

Mast Length = 4600 mm
Area = 3.99 m^2
Rake = 5.00 deg.

Sail 400

Mast Length = 4000 mm
Area = 2.92 m^2
Rake = 7.21 deg.

Sail 340

Mast Length = 3400 mm
Area = 2.02 m^2
Rake = 10.0 deg.