[ img - tumi2.gif ]Hotel in Lima
[ img - inca-sol.png ]Quechua
#7 Fifth Edition:
[ img - raftlogo.gif ]
[ img - incaruna.gif ]

Inca's Balsa Log Raft

The Power of Hull-shape - and Sails

Directional stability of a craft depends of hull shape.

Rule for free floating bodies
Anything as can float free, we can move-on and navigate,
by hands and feet, poles, paddles or oars
- or too with a motor of some kind -

That statement is true; but if we want to use sail for more than downwind running, then we have to take care and develop the underwater hull of our vessel with a low forward resistance and a high lateral resistance

Sail Ship development

A sail powered ship need a clear axis to keep a steady course when sailing ahead with wind across. 'Clear axis' is the one with obvious smallest water resistance compared with any other saildirection.
A 'clear axis' not necessarily means a symmetric hull, because a heeling sail-ship always has an asymmetric underwater hull shape - more heeling = more asymmetry - and despite their mounted "sidecar", neither the Pacific sail-powered out-rigger canoe nor the 'flying proa' from Marianas Islands show any sail-problem - on the contrary. The hull of a proa is normaly asymmetric along the axis, and is peculiar by always having same side - the outrigger side - to windward, shunting to reverse direction when tacking.
The elegant shaped Venetian gondola too is designed with an asymmetric hull shape, but that is to compensate the one-sided propulsion from her only oar.

[ venice-gondola+canal.jpg ]
Venice gondola showing her asymmetrical hull

Not every shape of hull can be sailed by the wind
The underwater shape of a hull should hold one (and only one) such sail direction, which is identified by the lowest Hydraulic Resistance - and that direction should be identical with the pointing. To take in account both wind from starboard as well as from port, it should be a good choice to have the centerline as this prefered saildirection - and not any diagonal or other.
- in all other directions a craft powered by sail need to have an increased Water Resistance, specially perpendicular to the sail direction - to make the pointing stable and keep leeway of minor size.
Whatever you use for propulsion, the lesson learned by our hundreds of years development indicates that a pointed prow and a smooth behind make sailing easier and speedier, but the years too indicate, that a hull shape with a high length /beam ratio - or a hull with straight sides will improve the stability on the pointed course. Later on we learned to talk about streamlined shape.

When we in pre-historic time tried to mount a sail on our "floating vessel" to catch the wind, we first drifted downwind, but nevertheless we had got a propulsion, as in some situations was supplementary to our paddeling. But not each time we hoisted our sail, the wind blew to where we wanted to go with our vessel, and we had therefor to get something else, as could push along and keep a pointed course - even with wind across.
And that could our rowing boats, so we didn't meet difficulties in that. But to use a sail as only propulsion is rather more problematic, because we have forces from the wind crossing our sail-direction. But soon we learned to manage the sail sailing along in directions other than the wind blew.
But the old steer-oar remained many centuries on its place aft starboard side, where it was landed as paddle from our canoes and rowing boats.

The hidden keel-effect

Keel we call the central backbone of the hull - even if there are no outer fin to see.
In historic time very few sail ships have had a typical outer keel, because all ships were build on the shore - or in the larger cases, on a slipway. Nevertheless, the shape of a hull gave the needed sail-stability. Long and slim for speed - or more wide for better transport capacity - but all crafts were sailing well in the pointed sail-direction.
Streamlined the hulls were, and with only one clear axis - and not square nor circular, as these forms could have more than one sail axis.

For stabilizing purpose a raft should hold a pointed stem and a straight sideline
as work as a full-length keel.

The spell between Hull and Sail

[ img - OwnShip.fig-124.png ]

The old-fashioned way to use CE and CLR:
Estimation of heeling - or calculation of ballast boulders

Only few centuries ago we in shipbuilding went from extrapolation of experience to calculation of consequences.
The calculations of CE and CLR started in the waning era of sail-ships, mostly to calculate worst case of the heeling of tall ships and large yachts - setting the forces on those centers in balance with the weight of the vessel concentrated in the Gravitation center together with the buoyancy forces through the Metacenter.
That was the time when the ballast still was placed in the bottom of the ship as boulders.

Cites from Thomas Walton: 'Know your own ship', 1899
In that time the CE = Center of Wind's Effort was calculated with "only such sail as could be carried safely in fresh breeze" and "those sails were supposed to be braced right fore and aft" (worst case).
Finding the CLR = Center of Lateral Resistance was a bit more tricky, but it was "approximately and sufficient correct for all practical purposes as the center of the immersed longitudinal section passing through the middle line of the ship" = the Center of Broadside Plane.

And such simple calculation could probably have saved the famous oldtimer Vasa as in 1628 capsized just outside the shipyard.
Under this conditions were calculated the heeling -
Or rather, they calculated the boulders needed in ballast to keep within certain heeling:
A fresh breeze attacking in the CE will turn the ship over the calculated CLR and the ship will heel down until the geometry of the heeled hull has moved the buoyancy center sufficient out from the central plane and together with the weight of vessel concentrated in the gravitation center have reestablished a balance.
When in balance, we have the searched heeling.

So it was then; but since naval architects and yacht designers still use the CE and CLR for general design purposes, because they are convenient and easy to calculate.

[ img - heel-balance.png ]
[ img - hms-victory.jpg ]
boulders in bottom
[ img - heeling-sail-boats.jpg ]
HEELING:    the torque made by wind against water-resistance - in balance with bouyancy against gravity
- but the only parameters as skipper can influence are sails and the weight of boulders in bottom (sailing in ballast)

Heeling and ballast isn't of much interest for balsa-rafts, but the core of the above mentioned theories around CE and CLR developed hundred years ago seems to be a useful tool to explain the Guara-steer system and the static turn in a more technical way - but too as a supplementary theory as is special useful for wide-beam vessels, as rafts and catamarans.

Historical note:
A consequence of those heeling calculations was the recognition, that with the ballast and cargo placed most down, the ship could carry more sail to drive her forward - and as soon the shipbuilding technology permitted the constructions, we saw deep aspect keels and fin keels with deep-down ballast replacing the boulders in hold.

Understand more spatial the old CE and CLR

[ img - ce&clr.gif ]

Just as the windsurf-board sketched, we today understand CE and CLR more spatial - as the conditions all around a sailing vessel.

CE we use as acronym for Center of Winds Effort - or simply the Wind-center - of the vessel, whatever static or dynamic wind-forces on hull, hut, rig and all sails in the position as the sails just now are adjusted.

CLR is now a metaphor for the Center of Water Resistance as is the attack point for jointed static and dynamic forces on the underwater hull - the point of pivot.
Of course we can split-up and distinguish the water resistance of Lateral resistance as control the leeway - and Forward resistance restricting the headway.

Note the simple fact, that the dynamic contribution of both water and wind will oscillate due to gust and waves, and that make exact calculations of CE and CLR impossible; and therefor we can't make any beforehand calculated tuning.
But there is no need to do that, because with these theories, then skipper know in what direction he has to move CE and CLR to obtain the wanted reaction from his vessel, and that he will do by adjustments on sail and Guaras.

The common rule for EVERY sail-vessel:
CE will blow to lee of CLR
- and if sails are adjusted for the now pointed course, you are sailing -

With other words:
"The Wind-center will blow to leeward of the Center of the Hydraulic Resistance" - (and that simply is so, because there is no other forces as influence on the situation)
What we do, is to "steer". We react on the 'now-situation', with what we know about the nature of CE and CLR, and we move either CE or CLR by changing one or both of the dynamic components - or one or both of the static components:

Dynamic components work by: water flow around rudder and the flow of wind around sails
Static components are guaras plus hoisting, lowering or reducing sails (moving CE)

what to influenceinfluencing force
Sails and Rigging
on each sail
- flow around sails
under-water hull
water press on HULL
- flow around RUDDER

The sailed course of a craft is a result of those two mentioned parameters: CE and CLR.
Correction of the pointing is due to manipulation of one or both of those two parameters:
1): The rudder controlled crafts we are adjusting course by manipulating the streeming of water - the dynamic component of the CLR
2): The Guara controlled rafts we too are adjusting the CLR, but by changing the shape of the under-water hull - the static part of CLR
3): The rudderless sailors are moving their Center of Wind by balancing the wind press on their sails, but too - when possible - moving the CLR by moving a ballast (crew) between for and aft or tilting a centerboard.

In all 3 cases the rule is:
The CE will blow leeward of the CLR

On a rudder-steered vessel, the nature of the dynamic component cause, that you constantly need a helmsman with hand on tiller
On the Guaras controlled raft, the static component will stay stable as a weathercock as long as the wind blow stable from same direction

The family of rounded bodies

[ img - hullshape-01.png ]
round - and rounded stem and stern
[ img - hullshape-02.png ]
roundship and longship
longship drawn with double length and half width
Round Shape
On an extreme left of the scale we show circular shape as in no way are able to sail by the wind other than drifting. Coracles and Basket Boats are examples of round boats. Basket boats we find in Iraq, India, Tibet, Vietnam etc under names as 'Thung Chai', Kufa, Gufa or other - but too exist in Ireland and Wales, but in the English world she is known as Coracle - sometimes 'a Moses'.
Basket boats exist in all sizes - for personal use, for many people and for cargo. All are build light-weight as a basket woven of willow-withies or bamboo-split or whatever are at disposal, and covered by a hide or weaving as is sealed watertight by tar or varnish. A light weight construction with least wetted surface against largest carrying capacity - and too possible to ROLL on land [ img - RollingBasketBoat.jpg ] - as they always have done.[ img - GuffaOnWayTo Eufrat.jpg ]

Circular Baskets are lightweight boats

[ img - Kufa-Iraq.jpg ]
Kufas are basket boats from Iraq
[ img - Iraq-Kufa.jpg ]
Guffa used too for heavy load
[ img - man+coracle.jpg ]
Welshman carrying his coracle
[ img - coracle-Wales.jpg ]
Coracles we still find on the British Islands
[ img - Rundboote.jpg ]
the paddle normally is used to push - or to pull
[ img - basket-Tugs.jpg ]
in Vietnam we see a fin to stabilize direction of move
Circular boats we can push or pull by paddle or we can row, but any skew force on those circular crafts will turn them around more than move them along. And those whom have tried to navigate a circular boat, a life-raft, a life-buoy or an inner tube from a car will understand.
In Vietnam, as seen on the photo, they have removed that "rotation problem" by mounting a fin /rudder
For the experimenting people: how to build a coracle: [ img - coracle-fi.jpg ]
A little bit better is the cousin to Coracle - the short and nearly square type of rowing-boat  ( img: halfpea.jpg ]
[ img - humber_keel_draw.gif ]
flat-bottom, mast well ahead rounded bow and stern
[ img - humber_keel_photo.jpg ]
Square sailor - for narrow and shallow waters
[ img - Humber-keelmen.jpg ]
sailing beam reach
Second Shape could be a Humber Keel as was the daily "work horse" for cargo on Humber river, the inland canals and on the east coast of England. Shaped as a box with Square rigged mast placed in front of middel, slab sides and round for and aft - not fast, but stable and able to carry a heavy load and navigate in narrow waters.
The long slab side grant a very high LATERAL resistance and work just as a full-length keel - specially when loaded deep down.
The slab sided style came into ship development together with the use of iron sheets in hull-building.
[ img - ottar.jpg ]

[ img - norlandsboat.jpg ]

Third Shape - Roundships is a medieval expresion for cargo carrying ships - in contrast to longships = the speedy troop transporter
The pointed stem came early into our boat-technology by the simple feeling of easier paddling and higher speed of our dugouts and canoes; so when we mounted a mast with sail, the hull-shape was given, and we learned to appreciate the sharp bow.
Thousand years ago the shown type of cargo ship (knarr) verified their seaworthiness serving the trade route from North of Europa to Iceland, Greenland and to America.

The last Shape - Longships
The few words to say is, that with longer hull relative to beam (high length /beam ratio) we gained speed in relation to load capasity, and the Norlandsboat could be a lovely successor of this. This type was in common use until around 70 years ago.

Latest in our sail development - after the sail-ship era - came ships with a dedicated high-aspect keel and later came the fin-keel - mostly under yacht-hulls. That technology wasn't possible in former times. Those fin-keels have given even better result by wind-sailing. Furthermore with ballast weight most down on such a deep keel, those crafts seem impossible to capsize.

The Floating Square Hulls >>> RAFTS

[ img - hullshape-11.png ]
[ img - hullshape-12.png ]
[ img - hullshape-13.png ]
Examples of square body-shapes lined up with increasing sail stability

Shape#1 and #2 - A square hull shape is not much better than a round basket-boat. It seems as a square craft /raft will be able to move equal easy in whatever direction - centerline as well as along one of her diagonals. But as named, she is a bit easier to row then a round.
Shape#3 and #4 - That bring us to the rectangular raft = a floating "box", as is missing a typical bow. That hull-shape is fine as pontoon or lighter - rowed, hauled or pushed. With sail it is more problematic. She can run fine ahead with wind directly from aft, but when wind is going abeam, the situation #3 without counteraction will change to #4, where she can stabilize her pointing along the diagonal.
To keep on sailing as #3 skipper need to do as the Incas: plunge more Guaras down in aft and make a 'balanced sidegliding'
An example of rectangular raft type#4 can be found at page #8.   RaftOnOcean.jpg
Shape#5 and #6 The testimonies from The Spaniards all tell us, that the oceangoing South American rafts without visible difficulty could beat against the wind. The common shape as reported was with a big trunk in the middle and some smaller along side - as the shape of a hand. That means that the South American rafts had a dedicated stem, and together with the straight sides as worked as full-length keel. On the other side, many drawings mad by tourists and explorers the next hundreds of years show sailing rafts with square prow.

In this view a shape as that of Tangaroa2-2006 (too shown in the collection below) seems rather ideal for raftsailing:   [ img - tangaroa-2006-1.jpg ]

Cite from their description:
"At the stern, the raft was 8 meter wide, and at the bow it was 6 meter wide.
The longest log in the middle measured 17 meter. Those on the side were 14 meter."

That means that with the V-shaped bow and a prominent stem, they had a stabilized raft cor center-sailing.
Furthermore, with 6 meters width at bow and 8 meters aft they got wedge-shaped sidelines, from which we can expect even more self-correcting action against yaw = rotation around a vertical axis.
Unfortunately no written report is published around that raft-sailing characteristics, more than that they landed on some island in middle of the Pacific Ocean.

The DYNAMIC influence of flowing water

The CLR - Center of Lateral Resistance [ img - CLR5-star-33.gif ] was in the beginning defined by the static situaton - without sailing.
When sheeting out the vessel begin to sail, and she will accelerate until the hydraulic resistance against this forward movment has grown to the same size as the forward force from sail.
The hydraulic resistance against sailing will approximately grow with the square of speed.

Technically the contribution from the dynamic forces created by the sailing is explained by the two sketches

[ img - bowwave3.png ][ img - bowwave4.png ]
Sailing ahead the stem is pushed into the sea and due to the press of water the bow is hindered in side-sliding
- whereas the water is slipping the aft-end without hindrance of nothing there.

Start sailing ahead
Next step will be adjustment of Guaras - more Guaras aft against aft-end sliding
That has as consequence, that sailing with a wind abeam - the wind as will try to move ALL the craft sideways, but will mostly be able move the aft-end.

The result of this force pressing on lee side of bow is playing together with the former static lateral resistance of hull and move the CLR ahead.
The new center indicated by a blue dot [ img - bluering-26.png ] is the combination of old CLR [ img - CLR5-star-33.gif ] + the water press on lee side of bow [ img - bluearrow.png] - That center of hydraulic resistance is moved ahead in direction of the attack-point of the bow-press.
But generally we only say: When sailing the CLR moves ahead - without to say much more.

[ img - bowwave1.png ][ img - bowwave2.png ]
When sailing ahead, the FORE-guaras aren't needed - the squeeze of bow will do it - they are only needed for a static turn.
the pointing will be done by AFT-guaras alone, as demonstrated by Dirch

The skipper will experiment that starting sailing ahead, his vessel will luff up - or more correct: the aft-end is sliding leeways - and skipper will counteract as he allways have done:
By rudder-steering: turn the rudder dirigating the water stream against the unwanted movement of aft
- by Guara-steering plunge in more Guaras aft - or lift some Guaras up in fore-end to move the CLR backwards again.

Importance of a POINTED bow

[ img - bow-wave3.jpg ]
sharp stem cleaving the water in two streams - going left and right


every boy (or girl) who has flown a kite know that a V-shape stay more stable in the sky
[ img - kite-stability.png ] [ img - kite-inclinA.png ] [ img - kite-inclinB.png ] [ img - tradbox.gif ]
- the V-shape is self-stabilizing because when tilted, the enlarged wing /side will take more wind and correct the imbalance
- too valid for a box-kite -

- and from the kites in blowing wind it isn't difficult to see, what will happen with raft-bows of same V-shape in streaming water -
- even a minor change (here shown 10 degrees) in pointing raise immediately a course-correcting waterpress -
- and too we could ponder what influence the prow-angel has on the reaction-force against a minor yaw -
- and what furthermore a bulbous nose will apply to that -

Rafts with different bow-angel - all drawn 10 degrees inclined
[ img - 4-inclined-rafts1.png ]
[ img - 4-inclined-rafts2.png ]
[ img - 4-inclined-rafts3.png ]
[ img - 4-inclined-rafts4.png ]
A transom bow will not go back to central sailing,
the raft will find a balance when the two water-streams are equal
= diagonal sailing
Bow-angel as for example 120°, 90° or 60° will immediately create reaction against a yaw
Whereas the unilateral front-flow against a transom bow will promote a slant up to the balance at diagonal

Hull shape - a study of raft-prows

[ img - kontiki-old.jpg ]
Kontiki 1947
Thor Heyerdahl mounted a "snow plough" in the stem
[ img - KON-TIKI-replica.jpg ]
replica 2011 of Kontiki
(Tangaroa2 converted for Film)
[ img - p2-Las Balsas-1973-in Ecuador.jpg ]
Las Balsas 1973 in Ecuador
preparing for Australia
[ img - p3-illa-tiki+prow-draft.jpg ]
Illa Tiki 1995 - draft
[ img - p4-prow manteno 1997 .jpg ]
Manteña Huancavilca 1998
Tangaroa2 raft 2008 with her classic shaped prow
[ img - kontiki2-Callao.jpg ]
Kontiki2 2015 was born snub-nosed
- raft Rahiti Tane -
[ img - antiki-tourismoday+.jpg ]
An-Tiki 2011 - Could be a "4-bodied raft" - or a "double catamaran" ?
How to form the underwater body of a craft, we have discussed in hundreds of years and seen many solutions. The advantage of a balsa raft is its large load-carrying capacity - and the disadvantage is its slow headway. That has given basis for much new-thinking and many innovations. The Spaniards all described the balsa rafts having one big and long central trunk as a stem (just as a modern bulbous bow ?) And with minor and shorter trunks lashed alongside this. Always an odd number of trunks. As a hand !
The pointed stem seems a need for shape of flat-bottomed hulls, and that theme is the main objective for this site. With a raft as doesn't heel, certain symmetry seems important for tacking between port and starboard wind.

The photo of Kontiki is from the book: 'American Indians in the Pacific' by Heyerdahl. On his raft Thor Heyerdahl mounted a "snow plough" in the stem to pass better through the water - or perhaps to reduce the splash.
The Kontiki-raid showed us an awful seamanship - but was a wonderful adventure to tell about - and this gave impulse to many later adventurous raids.

The 3 balsas were build in Guayaquil in the classic Ecuadorian shape. Later on in 1973 they were sent over the Pacific Ocean, where they after a hard passing landed with the most of the rafts in Australia.

The 4 brave old men on the An-tiki-raft crossed the Atlantic in the wake of Columbus. They reduced the forward water-resistance by employing only 4 plastic tubes as floaters for buoyancy, so we feel doubt about it was a four 'bodied raft' - or a 'double catamaran'

structure of An-tiki
[ img - Antiki4hull.png ]

Bottom profile of Hull:

The underneath of an Inca-raft is not known from any chroniclers. The only indication we have from ancient time is, that the central trunk is bigger than those along side. Probably larger in both length and diameter. Shaped as a hand.
But with hundred of years of raft development in South America this raft design must have been optimized, and the hull shape therefor useful for balsa rafts: A pointed stem and a long straight sideline - and a steering controlled by Guaras /daggerboards.
If that is the general style of rafts known since Inca time, it probably has a reason, and my guess is, that this central trunk outside being a stem, has a function as low aspect long-keel - to stabilize the course under sail. The Guaras itself are to consider as adjustable fins to balance the broadside-drift, as all sail-ships with more masts can do, with wind abeam. That means to keep a pointed course by balance the side-sliding between for- and aft-end.
In connection with this it could be interesting to find out, if this long central trunk as the Incas used - had a function as the modern bulbous bow -
       1): reducing hydraulic resistance -
       2): change a bow wave before the bow -
       3): or it by its larger dimension (diameter) had a function in wind abeam as a stabilizing long-keel -

[ img - Kontiki2-bottom.JPG]
the smooth bottom of Kontiki2 2015
[ img - KontikiRaft-Callao-1947.jpg ]
Thor Heyderdahl building raft 1947

Theoretically we get a different result
by different building-methods:

A): Building on a slipway, laying up the trunks on an even plane as a steel frame, give a smooth underside, but the price could be the cuts in trunks to fit a junction with next layer of crossbeams -
B): Building floating in water as Heyerdahl did or laying the trunks on a flexible support - can give a smoother topside together with the opportunity to get a profiled underneath as for example a fat keel trunk - and too a chance to make the junctions with the overlaying crossbeams with minimum cuts and wounds in the surface.
Cuts in the buoyancy-trunks open up wounds for easy penetration of water and quicker water-logging - and perhaps an easy access for Teredo Navalis, the ship-worm.
C): Building in water, each trunk will find its floating balance in dependence of its curvature, before tied together with the neighbour - but the value of that isn't clear.
[ img - raft-princip-123.gif ]
The central bole is a matter as not has called for much attention.
Small changes could give more keel-effect - as indicated here -
if the straight sidetrunk doesn't give enough keel

[ img - shipshape+.png ]

Sails for rafts

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

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 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 sideline too has a keel-effect.
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 our craft -

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 ]
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.

Square sail is the most classic of all sails

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The best yield of trimmed sail crafts

Small details:
[ img - square.jpg ]
ropes in mono-masted square rigging
[ img - ottar-sail.jpg ]
*    *    *
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 than one mast and one square sail. 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˚.

[ img - kontiki2-running.jpg ]
a raft running fine with her baggy shaped sail - reefed

[ img - shrinken-boltrope.jpg ]
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 fom a sweeping wind ower upper part of the sail

A rather good description of square sail sailing:
[ img - SquareSail+Wind2.png ]
The changing of yard and sail, tack, sheets and braces 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 portclew 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.

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 the Guaras and not 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 en un position outside the hull. 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 she has enough width in her hull to fasten the tack at 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.

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.

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

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a windjammer - with studding sails on fore mast
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Egyptian painting around 6000 years ago
sailing up the Nile by a Northern wind - and drifting down the Nile by the current flow

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Mediterranean trireme with raked foresail and double steer-oar

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

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fore and aft rigged sailing goosewing to keep the CE in central plane of boat

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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 an unstable balance as easily can overturn a boat in a gust. The water streaming against the 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 the Center of Wind could be done by setting studding sails on 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 her 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 = her hold in water.

Final comments

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

The sail, 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 hull 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 small 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.

Then - if the hull shape is directional stable - we can sail-on with the small adjustments from Guaeras or rudder to compensate gust and waves.

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

That is a "fine" rule, but we don't know where CLR is placed exactly.
Nevertheless it is useful and easy to manage, because 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 hull, the sail or missing seamanship.

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 #6.
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