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#7 - Sixth Edition:
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Inca's Balsa Log Raft

Sails for balsa rafts

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True course and apparent wind are the conditions for adjustment of sail.

We have to regret, but we don't know much around what type of sails the original Inca Rafts used. But we know they were made by cotton cloth. The Spanish chroniclers laconic say us "the same type of sails as on our "navios". Navio means big ship.
And what means that? is the question now 500 years after.

We know two types of common sails from the Mediterranean Sea, as we can demonstrate with this picture:

[ img - ships-of-Columbus.jpg ]
the 3 ships of Columbus discovering their way to "India"

The lateen sail was used on the Caravels. The square sail was main sail on the Carracs - but with a Lateen sail as spanker. The carracs were the ocean going trade ships.
But which type the Spaniards had build on the Pacific side of Panama isthmus, we have no clear evidence.

Nevertheless, some hundreds of years later we got drawings and later on photos as showed the square sail, and never a latin sail - even if we can't refuse the choice of John Haslett using two lateen sails on his last replica rafts. In all cases the lateen sail is considered beating better to the wind - mainly because of the slanted rigid yard to cut up against the wind. Therefore beating against the wind wasn't Haslett's problem - that was the missing wind in the Calm Belt near Equator - and finally the shipworm Teredo Navalis.

We don't know much around the South American square sail, but both the drawings of F.E.Paris and the photos of Brüning show us a curved yard.
We have no experience with curved yards - but we can't see any bad in that construction.
The main task of a yard is to stretch out the square-sail, and that is only to cut the head-leech in shape, and then tie it to the yard. Too other rigs use a rather slim and flexible yard, as not break so easy. For example the lateen sail.    [ img - latin-yard-jovenvicenta.jpg ]

An other advantage could be the weight, as it seems possible to reduce to well under the half of a classic stif yard of pine. That lightweight construction could show up very rational, specially in the time before arrival of the Spaniards, when they didn't know the use of a block nor a sheave in top of the mast. With a lightweight yard, it could be much easier to hoist the sail.

One of the core points for wind sailing is to minimize side drift, what means a high lateral hydraulic resistence and that can be obtained either by employ a long slim hull or by giving your floating item an effective keel, that can keep a steady course - and don't forget, that a straight side trunk on a raft work as a keel.
Upon this floating hull we mount a rig with sail as can catch the wind from nearly any direction and transform wind-force to a force pushing the craft along in its sail-direction. Both Square rig and 'For and Aft' rig as the Lateen rig can that.
Until now raft expeditions have focused upon the sailing and less upon analyzing the function of a Guara-system, often relying on the theory, that if they plunge sufficient Guaras down between the trunks, then they will obtain sufficient keel to permit beating against the wind. That is now by the Kontiki2 expedition verified, not to be true - that is the hull as has to give that stability. Guaras are mainly for steering.
Two masts instead of one will add more steering options by balancing the wind press, but that is not decisive - if we have Guaras.

Reiteration of the common rule:
A CE will always blow to lee of its CLR
- and if the sail is adjusted for the now pointed course, you will sail -

With the knowledge, that we can create our hold in water, where we want it on the raft, the core point of the rule is now: "if the sail is adjusted - - - "

The task of any sail is to change the crude forces of wind into a forward directed force as provide propulsion in that forward direction, where we have lowest Hydraulic Resistance + plus a force across the hull as can be opposed by a high Lateral Water Resistance of keel and sideline.
The pointing of the raft is as explained a result of the Center of Wind forces in connection with the Guaras - but some leeway we will always have - except when sailing directly downwind.

By Beam reach the wind begin to be able to sweep along the cambered canvas and create what the airplane engineers call a lift across the sail, but together with a drag along the canvas, and the size and direction of those two forces are clearly dynamic and dependent of the wind speed.

The size of drag and lift is too dependent of camber, and where a "for and aft" sail can have a rather asymmetrical profile just as an airplane wing, a square sail hold a symmetrical profile, due to its need for changing of leech from "leading edge" to "trailing edge" and viceversa, when coming-about in a tack. This symmetry has as consequence, that the attack-point with sufficient accuracy can be calculated as the center of canvas just as the static Center of Wind.

Drag and lift is a theme for much discussion, and I will therefor limit my part to say, that the leech of our square sail has to be able to split up the wind in two:
one part to go to back of sail and blow up the canvas profile - - - and another part to sweep along the front-side of the canvas where controlled by the coanda effect, it will keep along all the curved surface and create both a drag along the canvas and as named, a lift perpendicular to the sail.

The camber has neither to be too high nor too low, to keep the coanda adhesion. Beeing a square sail with the needed symmetry, it is neither possible to calculate anything from a foil-table for standard air-plane wings. So take it as it is, and counteract with the Guaras.

This make me memorize my first homemade sail (sewn by an unexperienced 15 year schoolboy on his mother's Singer machine). Result: a too abrupt leading edge and a too abrupt trailing edge to let the air flow, and this phenomeno had as consequence, that I only could sail with wind pressing on backside of canvas and in no way against the wind.

Vessels with more sails and/or masts simply have more options - they can move their Center of Wind from for to aft
[ img - CE_Dinghy-Sails.png ]
The rule is still:       Wherever the Center of Wind will be, it will be blown downwind of the Center of Water Resistance
- and thus moving around the "attack-point" of wind we have another way to controll the pointing of those crafts -

Such sail manoeuvres as pictured are not possible with vessels as have one mast and one sail only - and that whatever we are talking vikingship, Inca-raft, catboat, optimist with whatever type of lonely sail.

Rigging af earlier rafts - all in the wake of Kon-tiki
[ img - Kon-Tiki-1947-3sails.jpg ]
Kon-Tiki 1947
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Seven Little Sisters 1954
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Tahiti-Nui-2 1956
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Kantuta-2 1958
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Tangaroa 1965
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Manteña 1998

When Thor Heyerdahl in 1947 prepared his raft Kon-tiki he knew rather well the original South American balsa-hull shape, but around the sail he only knew that it should be a square sail. Fortunately square sail was and still is an integrated part of the Norwegian sail tradition, so he transfered a norse rigging and mounted it on his A-mast. Square sail with a little strange mounted topsail. Furthermore he of unknown reasons placed a minor square sail on a mizzen mast located well aft of the main mast - as a ketch - but that mizzen was only seen in the start from Callao - it disappeared on later photos, probably because a mizzen is dangerous for the stability when running downwind.

On a raft you can rig-up
whatever you want of sail

[ img - 7-sails.jpg ]
square sail - spritsail - gaff sail - stay sail -Bermuda sail - lateen sail - junk sail - - - the most of those sails have been used on raft replicas

Square sail is - square !
Lateen sail belong to the family of 'for and aft' sails. Lateen rig - Bermuda rig - spritsail and gaff-sail are all considered as 'for and aft' sail; and 'for & aft' sails are known to beat higher to the wind than a square sail. This probably is due to the fact that windward boltrope is laced to a yard or tied around a mast as can sustain a cut-up against the wind without flutter in sail. But nothing is gratis, and the price is, that operating behind a mast or yard induce some turbulence as render ineffective the first strip of the canvas.

[ img - for&aft-rigging.png ]
       the leading edge of 'for and aft' sails is tied and sustained by a mast or yard.
[ img - mast hoops-sailrings.jpg ] [ img - spanker-sail.jpg ] [ img - lateen-sail-fasteninge.png ]

A stay-sail too is a 'for and aft' sail. It is very effective and can work higher to the wind due to the fact, than a slim forstay is rigid but doesn't create the same wind-turbulence problem as a thicker wooden boom.
That indicate, that if we can create and maintain the the windward leech on square sail with a sharp cutting edge as doesn't crimple nor flutter, then we could have a perfect sail - but exactly that is still not seen.

Sailing a craft by sail means to MASTER the interaction
between the craft and the two elements of nature: WIND and WATER.

Square sail is the most classic of all sails

  [ img - trimmed-boats.gif ]
The best yield of trimmed sail crafts

Small details:
[ img - square.jpg ]
ropes in mono-masted square rigging
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*    *    *
cringle spliced on boltrope + reef-eye /grommet in double layer canvas
 img - cringle.jpg
Square sail is the best sail you can get for running downwind - so excellent that it has got a modern descendant without yard - the spinakker - for use exclusively on downwind sailing in connection with 'for and aft' riggings as the bermudan rig.
Since prehistoric time the square sail rigged vessels have developed, got more masts and higher masts, as each mast has got more sails with the result, that all square sail knowledge to-day is connected to vessels with more masts and more square sails. A reason too is, that in the same time the smaller boats have abandonned the square sail and changed to lug-sails and 'for and aft' to gain a better tack against wind.
But in north of Norway the square sail has continued until end of the sail ships era and propelled their 'Nordlandsboats' and cargo carrying 'Jekts'.
That have had as consequence, that when the finding of viking-ships wrecks with age of around thousand years, nobody knew how to rig and sail them. There the funny case came, because the sail and rigging-knowledge from the Norwegian boats of Nordland were transfered back to the many new vikingship-replicas as were build - inclusive their "beitaas" for fastening the tack. Nobody says that this was "state of art" in Viking-time, but that is our best bet - too for replicas of square sail rafts. The only difference we can register is that the Nordlandsboats can beat higher to the wind - probably due to their deeper keel - and not their pintle and gudgeon rudder as during the centuries has replaced the viking's steer oar.

Beating against the wind sailing mono-masted vessel with one square sail only:
the windcutting edge on the sail - the windward - is tightened up and tensioned most possible between tack and the yard controlled by downhaul on the lee brace and sustained with either a bowline or a sprit. The tension from bowline or sprit too will lower the camber and thus permit higher beat.

The experience from mono-masted square sailers is, that any square sailer should be able to beat 80 degrees to the wind.
With well trimmed sail the common is 70˚ - but the best I have heard is 58˚.

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a raft running fine with her baggy shaped sail - reefed

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sail with bow-line set, but the boltrope has shrinked and crimpled her cutting edge
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sail deformed by stay is difficulting lift from a sweeping wind ower upper part of the sail

A rather good description of square sail sailing:
[ img - SquareSail+Wind2.png ]
Brace the yard with sail, change tack and sheet when altering course on starboard tack:

1): Dead run: yard and sail are set across the vessel and both sheets and braces are used to control the sail.
2): Broad reach: Port yardarm is braced aft and the port clew is sheeted aft, starboard brace and sheet are loosened.
3): Beam reach: Port yardarm is braced further aft and port clew is sheeted in further, starboard clew is secured forward of the mast is become starboard tack.
4): Close hauled: The sail is set close to the centerline of the vessel as possible, port clew is sheeted in as far as possible and port yardarm is braced around as much as possible. Starboard tack is secured further forward and the starboard bowline may be tensioned to help maintain the tension in the luff of the sail.

Ref.note 4): Close-hauled:

square sail with bowline tight
- wind-cutting leech sharp
- rather flat camber
- no deformation of canvas leech

[ img - Havhingst3.jpg]

What a square sail can do

Mono-masted sailers with one sail only have not many options to make change in a spread of canvas, and are therefor limited in any balancing with their Center of Wind.
All what such a square sailer can do is to move her CE in a half-circle centered in the parrel around the mast - limited by the chocking of yard against stay. Of course skipper can change the radius a little by tie the tack to another cleat or sheet-in /sheet-out - but nothing else.

[ img - howToRaasejl.png ]
the half-circle as CE can move
Nevertheless such crafts can be good sailers, as steer with the dynamic and not the static part of the CLR: the streaming of water around the underwater hull - because they have their rudder - whether sidemounted steer-oar or rudder with gudgeon and pintle. Furthermore they are born rather balanced in relation to CE and CLR.

On an Inca-raft we have no rudder, but but we can by our Guaras work with the static part of the hydraulic forces and place CLR where we want all over the raft. That means, that on a raft we have to adjust everything related to course by our Guaras. We have no rudder and we don't need to rely on the limited options of our sail !

The eminent force of the square sailer with her lonely square sail is demonstrated here by this replica of an 1000 year old oceangoing longship - a swift beach-landing troop-transporter from the time of the Norman conquest of England 1066. The "Seastallion of Glendalough" is here showing her extreme fine sail-qualities going 58 degrees to the wind.

[ img - hovhingst2-kly.jpg ]    [ img - hovhingst1-kly.jpg ]    [ img - Havhingst4.jpg ]
- but behold: when sailing, the center of sail has moved ahead of the mast and out over the lee gunwale -
CE = center of the sail is marked with a [ img - CE4star-19.gif ]

Square sail tricks

On the same photos you too can study the fastening of a lonely square sail on this oceangoing vessel. Because of a relative slim hull, the tack often is fastened to the end of a "beitaas" as acording to norse tradition is a boom as permit to fasten the tack in a position outside the gunwale - what is needed by slim hulls. In English language you could call it a boomkin as more or less is to compaire with a spinnaker pole.
A cringle on the bolt rope of the wind-cutting leech is by a bowline tightened ahead to the stay or stem, to prevent fluttering - but too to stretch out and flatten the curvature - the camber - of sail when sailing close hauled.
The yard lean normaly against the same forestay and is confined to the mast by a parrel - and the position of the yard is only in some grade controlled by a lee brace - that is the tack and the sheet as keep the sail in position. The sheet is fastened with a rope astern - near helmsman.

And that is more or less the same conditions we have on an inca-raft.

South American versus Norse square sail rigging
[ img - square-mono-rigs.png ]
same brace, tack and sheet - but with a sprit (as at sprit-sail) into a cringle on bolt rope on leading leech - versus bowline to the bow

The small differences:
An inca-raft doesn't need any "beitaas" because there is enough width in the hull to fasten the tack on a cleat inboard. The incas seems not to use a bowline to the forestay - the more than one hundred year old glassplate photo shown first on this site indicate a sprit /spar /pole to sustain the windward leech in the same cringle on the boltrope and the sprit perhaps held in position by two toplines. That gives more spatial options for sail-adjustments, as the Norwegians wasn't able to do - and can too stretch out and flatten the camber.
One point more to the Incas    ;o)

A sail can work together with the wind in two ways:
- 1): catch the ram-presure of wind directly on the backside of a perpendicular sail, pushing the boat ahead.
- 2): lead a flow of wind along the curved frontside of the canvas as will add an aerodynamic lift to the force on the backside.

Four ways the Winds Work

[ img - coanda-fig1.png ]
1): Running for the wind - yield a clean push of wind.

The square sail (and the spinnaker) are very fine for roomy downwind sailing, making use of the ram-force of the wind - just as the Spanish galleons and caravels did passing over the Atlantic Ocean

By downwind sailing both the square sail and of course the spinnaker work best with a "baggy" shape, but inside the "bag" there are normally a "pillow" of stagnant air

[ img - coanda-fig2.png ]
2): pure reflection of wind flow

Taking the wind from more broad-side bring other options as reflection of the wind
A wind as reflect from the back side of the sail will give a push - just as a simple billard ball give a push against its cushion when reflected

Ref. Newton's third law about Action and Reaction

[ img - coanda-fig3.png ]
[ img - coanda-fig4.png ]
3): Creating conditions so a wind is sweeping over a cambered surface (sail, wall or hilltop), then is given options for the coanda effect.
The coanda phenomeno is that fact, that a laminar flow along a curved surface will keep sticked to the same curved surface. Such a deviation of a flow from a straight line take its force from the canvas all along the cambered surface, and the result is a perpendicular force to the sail.

If the flow is broken by turbulence it may leave the canvas, and the lift on sail is lost. Deformation of the curved surface such as a change too steep in camber - or a stay deforming the profile - will favour a turbulence.

- Try the coanda effect in your kitchen with a spoon
- not only the jet is bend, too the spoon is attracted

Ref. Coanda effect = the sticking flow Ref. Coanda effect says, that a flow of gas or liquid will follow a convex surface, when it enter as a tangent to this surface.

[ img - coanda-spoon2 ][ img - coanda-spoon1 ]

[ img - coanda-fig5.png ]
4): When an airflow is split up in such a way that the front flow is passing over a courved surface, before unite again with the other flow as pass behind as a chord - then the speedy flow on the convex front side will lower its internal pressure in relation to the other.
As result the pressure difference create a "lift" perpendicular on the sail - and that is just in same way as an airplane wing work

Ref. The aerodynamic lift - according to the teorem of Bernoulli

More around the aerodynamic lift

Bernoulli's theorem formulated several hundreds years ago states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure
- and that means that a wind sweeping over a curvy surface of a sail will create a low air-presure on its curved side as add a pull to boat -
[ img - umbrella-airflow.jpg ]
many people in rainy countries know that an umbrella, not inclined against the wind suddenly will lift up
That is the same lift we can have on sails
[ img - top-view.jpg ]
the same curved shape on a square sail should give a similar lift

To obtain the aerodynamic lift the windward edge of sail has to split up the flow of wind in two:
A): one part to sweep along the curved front of the canvas and give aerodynamic lift
B): other part to fill the sail and blow up the cambered profile
And beating close to the wind, where the angle between wind and sailed course is narrow, a flattened camber can go higher.

[ img - sletsejlsprofil.jpg ] [ img - airfoil.png ]
an airfoil and a 'for and aft sail' can be asymmetrical due to same wind direction - a square sail has to be symmetrical

The camber of canvas is normally flattened along the yard and reduce therefor the dynamic lift. This fact can be mended or at least lessened by making the ropebands in head of sail longer near the mast and decrease grade them outwards
- an alternative is to cut head leech in shape

Note the decreasing ropebands on picture  >>>

[ img - ropeband1.jpg]
[ img - beiteaas.jpg ]
Beiteaas = boom to attach the tack of sail outside of a slim hull
- as a boomkin or spinnaker pole -

Everybody can run a boat for the wind - and to sail with wind abeam is neither difficult
"The art of sailing is to beat close hauled to the wind"

That is what will classify to excellence the skill of skipper and his sailing craft

The limiting geometry of square sails
- and its consequences

The wind shall fill the sail - and the sail shall push (or pull) the vessel forward.
For beating, a sail need a tight and rigid fore leech as neither flap nor flutter to cut-up against wind. That we have when leech is sustained by a mast or a yard as at the 'fore and aft' or lateen rigs.

A square sail don't have this facility, it has only a leech probably reinforced by a bolt rope. The square sail trick is to stretch this foreleech most possible - on one-masted square-rigging by tying the foreleech with a bowline to the forestay or the bow and at same time haul down in aft brace.
The classic more-masted square-sailers had to fasten where they could. But even so, the general was, that a square-rigged vessel on her best could go 7 point (70-80 degree) to the wind. In hundreds of years the western tall ships with square-sails had to wait for favourable winds before sailing off - or follow the trade winds on their way around the world.
A square sail is more fitted for running than lateen sails, specially those of more rounded shape like a spinakker. Of that reason many oldtimer Atlantic sailers of caravel type (lateen rigged) often got changed their rigging on the islands west of Africa, for then the next month or two to follow the trade wind across the Atlantic ocean to the Caribean sea equipped with square sails.

[ img - tradewind+atlantic gyre.jpg ]
The Atlantic Gyre = Equatorial tradewind out + westerly wind home

The "easy" running for the wind
- was not always without surprise -

[ img - palmsail.jpg ]
the most primitive of sails, a palm leaf - placed well ahead

[ img - running-latin-rigged-1873.jpg ]
running downwind with lateen rigged boat
the yard laid horizontal to keep the CE in center of boat
-note the men at yard reefing

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A classic Carrac from 1486 is a real downwind sailer with baloon shaped sails

[ img - studding-sails.jpg.jpg ]
a windjammer - with studding sails on fore mast
[ img - egypt-sailboat.jpg ]
Egyptian painting around 6000 years ago
sailing up the Nile by a Northern wind - and drifting down the Nile by the current flow

[ img - greek_trireme.jpg ]
Mediterranean trireme with raked foresail and double steer-oar

[ img - Nordland.jpg ]
Nordic square sailer
- CLR cause load well aft

[ img - goose_winged.jpg ]
fore and aft rigged sailing goosewing to keep the CE in central plane of boat

[ img - kontiki+wave.jpg ]
balsa raft running downwind
Sailing with the wind is easy. Just aim the boat ahead and the wind will blow you along, whatever you use as sail. And that way many post-Heyerdahl rafts have passed the Atlantic and the Pacific oceans following the trade winds.

Downwind sailing was the purpose, when the first sail in pre-historic time entered in the boats - to easy the rowing, as a first step. And boats depicted from ancient time was sailing downwind.
Sailing downwind we can only make use of the ram-force of wind and the speed of a boat running downwind will never get higher than the windspeed itself. But the general rule around the need to place the CE downwind of CLR are still valid.

Precautionary rule for running downwind:
Too by running for the wind the rule still is:
A CE will always blow downwind of CLR
Place Center of Wind well ahead and Center of Water Resistance well abaft

The Mediterranean galleys could be driven both by sail and oars, but in situations of broad reach they probably lowered their sails to avoid a difficult heeling and moved ahead alone by their effective slave-powered oars.
Even if they could employ both oars and sail they probably were very fine high speed runners for sail alone. To stabilize the running their two steer oars worked as a pair of aft mounted Guaras moving the CLR of the underwater body aft against stern, but they could move the CE further ahead by hoisting a foresail on a raked mast.

[ img - pitchpole.jpg ]
a more common pitchpoling caused by foolishness
- they not even have dropped their spinnaker

By downwind the risk for capsize is minor, due to minimal broadside wind forces and because we have a rather big longitudinal stability. Therefor normal running for a reasonable wind we se crafts make use of this and set all what they have of sails - but fore sails.

Nevertheless. Even rare, that happen we will hear about capsizing, forward roll or pitch-pole.

[ img - tambs1.jpg ]

Erling Tambs explaining his somersault 80 years ago, caused by a treacherous wave under gale conditions:
lifted up by a high and abrupt wave and then plunging bowsprit and bow into next wave

Neither pitchpole nor capsize is never heard for balsa rafts

downwind, a sail shall DRAW - and not push the boat
The real difficulty for downwind sailing is when the Center of Wind is too near or aft of the CLR. That is physically dangerous position, where a gust easily can overturn a boat, because the passing water yield a force on the craft, as can move the static CLR too far ahead. That is well enough as long as the sailing is right downwind - at least until the water stream against the bow as change or change side - perhaps because of a wave - vessel add a force as move ahead the static CLR. That is well as long as the sailing is dead downwind - at least until the streaming water against the bow change and switch over - perhaps because a wave - and hit the one bow only. That situation is not more dangerous than a quick helmsman could oppose, but doing that, the inerty of the ship probably will swing her over to sail on the other bow - and he again has to counteract. In that way his course will slalom ahead - first on one bow, and then the other - and each time with all risk for capsizing.

Coping stability-troubles downwind:
Move the Center of Wind even more ahead, to cope with the forward moving CLR
- or throw out a drogue astern to haul the CLR abaft

Move ahead a Center of Wind CE in general could be done by setting studding sails on a foremast only, hoist a spinakker or lower the sail on the mizzen - or perhaps move backward CLR flinging out from stern any type of drouge.
An alternative, as I personally have experienced on a catamaran as grew unstable and started slalom ahead, is to lower her aft centerboards, as brought the CLR abaft - and that too could be the solution for a stable running with a balsa raft: to plunge down more Guaras in the stern, moving backwards the CLR = the hold in water.

Some useful comments

The wind hit your vessel in CE = Center of Effort = center of sails.

The sails, if adjusted for sailing, will transform the force of wind to a forward force and a lateral force.

Both forward and lateral forces will accelerate the craft until the speed in the two directions have created a resistance of same size as the forces.
And because a underwater-hull normaly has a low forward resistance we will sail speedily forward - but even with a high lateral resistance it can't escape a slow sidewart movement = leeway.

Both hydraulic resistances are attacking in the same Hydraulic Center of the underwater hull - in the CLR.

Reiteration of the common rule:
A CE will always blow to lee of the CLR

That is a "useful" rule, but we don't know where CLR is placed exactly.
Nevertheless it is useful and easy to manage, because with that rule we know, how our vessel react on changes.
- and the rule gives us enough to control our sail-powered vessel.
[ img - stretch1.png ]
running directly downwind, the common rule is 100% correct
- too it is for drifting sideways without forward movement

we could explain, that the hull is "stretched out" between CE and CLR in the wind direction

[ img - stretch2.png ]
The pragmatic explication for wind abeam:

The bow-wave move the hydraulic center ahead, and the task is to move CLR backwards by plungeing in some AFT-guaras, so the CLR wil find its place upwind of our sail-center CE.
As long as the dynamic forces move forward both wind- and hydraulic centre, things seems fine, and the common rule work as it should: The CE blow to lee of CLR,
- and the pointing of the raft is given as "stretched out" between the two centres.

[ img - stretch3.png ]

Final Conclusion:

If a raft can't beat to wind it is NOT a Guara-problem
- the problem is either the sail or missing seamanship - knowledge.

The Evidence:

A raft is as a flat-bottomed sail-craft, just as every one of the sail-ships with lee-boards depicted earlier at page #5.
The vessels shown are all flat-bottomed sail crafts without keel, but nevertheless they without greater problems are able to beat against wind and keep a stable course - but of course, a lee-board of some type will make her beat even higher to the wind - or as in the Humber Keel-case give a turn-point for a slab-sided and stable craft.

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Lima - Yule 2017