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- Summary
What we know
What we NOT know
Material & Tools
Fate of Log Rafts
Guara steering
Hull Shape
Sails on Rafts
Modern Gear
+ Addenda
[ img - inca-sol.png ]Quechua
[ img - tumi2.gif ]Hotel in Lima
Boats of Pharaoh
[ img - egypt-image.png ]Thousands of years ago
INCA Tupac Yupanki expedition
[ img - inga.png ]year 1465
[ img - DK-flag.png ]
[ img - incaruna.gif ]

Incas' Oceangoing Balsa Log Raft

The Power of Hull and Stem

The Hull: LOW forward hydraulic resistance combined with a HIGH lateral ditto

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 ditto

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. She is 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

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 for more speed, and with only one clear axis - and not square nor circular, as these forms could have more than one sail axis.

If a free floating body hold a LOW forward resistance together with a HIGH lateral ditto
- then we have the basis to power her by sail
the arrival of CLR and CE

The spell between Hull and Sail

[ img - OwnShip.fig-124.png ]
[ img - Walton+CLR.png ]
Boat - CLR
[ img - raft+CLR.png ]
Raft - CLR
The static Center for Lateral water-Resistance (the underwater hull) is defined for any vessel

The old-fashioned static 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 and model building 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's book: '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.

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 ]
wind and water up against weight and buoyancy
[ img - heeling-sail-boats.jpg ]
normaly heeled ship
[ img - Vasas_hull_profile.jpg ]
Vasa with bolders in bottom
[ img - Vasa_kantrar.jpg ]
Vasa capsize
And such simple calculation could probably have saved the famous oldtimer Vasa as in 1628 capsized just outside the shipyard.
HEELING:    the torque made by wind against lateral water-resistance - in balance with the torque of bouyancy against gravity
- but the only parameters as skipper can influence are sails and the weight of boulders in bottom (sailing in ballast)

That is so, if a ship is heeled because of wind, then a certain percent of winds force on sails alone will press downwards and augment the weight of ship - and with that increase the seize of submerged hull:   10° heeled - give +17% of winds force, 20° heeled give +32% of winds force - and 30° heeled give +44% of winds force to be added to the weight of the ship.

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.
From a static CLR to a dynamic CLR

The DYNAMIC influence of streeming water

[ img - static-CLR.png ]
The CLR - Center of Lateral Resistance [ img - CLR5-star-33.gif ] was in the beginning defined alone by the static situaton - without sailing.
The purpose was estimation of heeling - or calculation of the need for ballast boulders.

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. But too she wil gain leeway until the sidewarts force from same sail will match the growing lateral hydraulic resistance.

Technically the contribution from the dynamic forces, as created by the streaming water when sailing, is explained by the few sketches
- and that is the same whatever you have a pointed, a rounded or a square-off bow.

First figure:
the STATIC situation
[ img - CE+CLR-1.PNG
as CLR was defined more than 100 years ago
Second figure:
sailing ahead
[ img - CE+CLR-2.PNG
the pressure in bow-wave increase the LATERAL resistance in bow
Third figure:
the drift leeward
[ img - CE+CLR-3.PNG
of course the leeway too have a similar increase of forward resistance
Fourth figure:
resulting true course
[ img - CE+CLR-4.PNG
the result is that the CLR move ahead and a bit to leeward
First figure - The static CLR is more or less in the geometrical centre of the underwater hull

Sailing with a wind abeam, the wind as will try to blow ALL the craft sideways - but with the grip from bow-wave the wind will mostly be able move the aft-end.
Second figure - Sailing ahead:
The vessel will plunge her bow into the sea and due to the press of water in the bowwave the bow is seized and hindered in side-sliding - whereas the water is slipping the aft-end without hindrance of nothing there.
The result of this hold of water around the stem play together with the old static CLR and create a new = a dynamic CLR (Center of Lateral Resistance) more ahead. And with more sail-speed = even more ahead.
The new dynamic CLR = Center of Lateral Resistance is here indicated by a blue ring [ img - bluering-266.png ] and is the combination of old CLR [ img - CLR5-star-33.png ] + the water pressed around the bow.
The arrow [ img - bluearrow.png] indicate here a common hydraulic resistance with its attack point - and nothing around movement.

Third figure - Drifting leeward:
The same hydraulic rules reign if the vessel drift sidewards; but due to the fact, that the most vessels hold a high lateral resistance, the leeward speed are much smaller, the pressure in the "bow-wave" therefore low and the CLR move only a bit against lee.

Fourth figure - Resulting situation:
And when the wind blow abeam, the result of those two movements - as are connected to the headway and the leeway respectively - place the dynamic CLR more ahead and a bit to lee.
The truth is, that we seldom calculate with any sidewarts "bowwave", because it is totally dominated by the changes in the shape of a heeled underwater-hull. - but it exist!

Generally we only say: "When sailing ahead, the CLR moves ahead" - without to say much more.

Strip of START-occurences
[ img - CE+CLR-0.png
the STATIC CLR is defined as the Center of Lateral Resistance
- no movement ahead -
[ img - CE+CLR-5a.png
when hoisting sail and sheeting out, the wind will blow its center CE to lee of the actual CLR
[ img - CE+CLR-5b.png
that means that the vessel before gaining speed will be prone for lee helm
[ img - CE+CLR-5c.png
more speed ahead bring more press in bowwave, and CLR move more ahead
[ img - CE+CLR-5d.png
full speed ahead place CLR most ahead
- now prone for weather helm

Sequence of events:   When hoisting the sail, we establish a CE = Center of Winds Effort, and this will play together with the actual CLR - first the static CLR and then the dynamic - and as the vessel gain speed the CLR move ahead.

The now modified common rule  
The actual CE will always blow leeward of the actual CLR and thus define the pointing of the vessel!

That rule is a rule for any sail-powered vessel, and that means that we can control our course by either move CE - or move CLR - or move both.

The most normal is to move the CLR by using either rudder or Guaras
what are we doing when we steer

The classic rudder and CLR

A rudder is a wonderfull steer system, as angeled out push on the streaming water and move the aft end sidewarts until you have your new course.

On the course a motordriven boat then have to set the rudder neutral - whereas a sail powered boat have to keep the rudder angeled to sail on with the new course.

The STATIC Center of Lateral Hydraulic Resistance = CLR

In the begining the calculation of CLR = the Lateral Hydraulic Resistance was used for evaluation of heeling and for estimating of the amount needed of boulders in balast - for a static situation only - but a static CLR center says something around pivot point for the chosen shape of hull - without sailing.
[ img - dynCLR1.PNG ]

Today we mostly use this 'static CLR' for considerations, when we lay 'Heaved-to' or we are drifting slowly sidewarts (without forward heading).

When sailing ahead, we have to add the forces as come from the streeming of water around the underwater hull.

[ img - dynCLR2.PNG ]
In same moment as the sail is hoisted and the boat begin moving ahead, then is formed a bow wave as by the pressure inside the wave seize the prow and hinder sidesliding of the same. And because the bow wave hindering sidesliding, it contributes to the Lateral Hydraulic Resistance, and is influencing of the place of its actual center. The CLR-static move ahead and form a CLR-dynamic. And further speed ahead, give harder grip from bowwave - and CLR-dyn move still further ahead.

[ img - dynCLR4.PNG ]
RUDDER steering 1
Sailing ahead with wind abeam make the boat try to give leeway, but as the bow is kept by the bow wave and hindered, then only the aft will flow with the wind, and introduce a tendency to turn up into the wind. That is called weather helm.

That we hinder with our rudder, as we always have done. We angel it out in such a way, that the streeming water press the aft up against the wind, and the boat away from the wind. Technically that means, that the rudder is adding a hydraulic force to the system (CLR-stat + CLR-dyn), and the result of those 3 forces together is, that the actual CLR as center for all the hydraulic forces - now move backwards.

If that counteraction with your rudder give the wanted course, then keep the rudder in position. If not, then correct the rudder angel.
[ img - dynCLR3.PNG ]
RUDDER steering 2
Your boat should be born with some trim of stability, as normally means, that with wind abeam you are sailing right ahead when your rudder (your Guara or your dipping paddle) is nearly in neutral position.

Setting tiller to opposed side than before will let your boat turn up against the wind.
What technically happen here is, that you add (or rather subtract) a force from the other side of the rudder - and that force together with the central + 'that from bow wave' act together and send the CLR-dyn further ahead, than any of the other examples. And your sail Center CE have to blow to lee of this newly created CLR - and the boat turn up against the wind.
Again:   If the counteraction with your rudder give the wanted course, then keep the rudder in position. If not, then correct the rudder angel.

[ img - dynCLR5.PNG ]
RUDDER steering shown with sail hoisted
That could be a Sprit sail, a Lug sail, a Square sail or whatever - and the 'one mast only' is rised where the sail type need.
What is important is, that the Center of Winds Force = CE is easily known on this sail (normally near center of canvas). That center will blow downwind of CLR = the Center of Lateral Resistance - and each time you move your tiller, then the rudder move the CLR - ahead or abaft - and the wind will then blow the CE downwind, according to which the boat will change pointing.

The rule for steering of ANY sail-powered vessel:
The wind will blow its CE down to lee of actual CLR.
If the sail is adjusted for that pointing, then you are sailing.

Note:   Any board /Guara set down + and any rudder /steer oar angled out - will brake the speed of headway.
      - and both board and rudder work together with the wind by moving ahead or abaft CLR = Center of Lateral Resistance.
Note the difference: A sail powered vessel often sail with rudder angeled, to keep a course - on motor powered vessels, the rudder nearly always is neutral.

This permanent angeling of rudder /steeroar was why Thor Heyerdahl had to struggle so much to keep his course.
A steer-oar is very hard to angle out and keep angled - harder than a rudder, because of the long oar-loom.

Resumen of the 4 different steer systems.

The sailed course is a result of those two centres: CE and CLR. They define the course, and a correction is due to manipulation of one or both of those two centres.
1): The rudder controlled crafts we are adjusting course by turn out the rudder, as push at the streaming water = a dynamic component of the CLR
2): A steer-oar as we either can dip deeper or twist (or both) - is a combination of a rudder and a aft-Guara
3): The Guara controlled rafts we change the course by changeing the shape of the under-water hull by setting down or lifting a board = a static part of CLR
4): 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. Ref: The 'Patin Catalan' = a class of dinghy, born without rudder

In all 4 cases the rule is:
The CE = the Winds Center will blow leeward of CLR = the Water-center
- and that is that, as define the pointing of your craft -
- and if your sail(s) are adjusted for the now pointed course, you will sail -

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

square off Kon-Tiki

Kon-Tiki raft sailing:   counteractions against weather helm

With more sails you can counteract (or trim) by move more ahead (or abaft) the CE = the common Center of Effort. That you can do by adjusting the sails (when more sails), setting a foresail, a jib or similar.
With only one square sail skipper can't do much with his CE - but he has the option to tilt (what is easier than move) the mast forward with parrel, yard and perhaps with tack and sheet too.
The alternative to move ahead the wind-center CE is to move backwards the water-centre CLR, what is the most normal to do; and that counteraction is the same, whatever you have of steer-system.
[ img - CE+CLR-7.PNG
Dipping Oar steering
[ img - CE+CLR-8.PNG
Guara steering
[ img - CE+CLR-9.PNG
Classic Rudder steering
Three steer systems are doing the same - and you can combine them as you may want
Start your sailing sailing ahead
- next step will be adjustment of Guaras: more Guaras aft against aft-end sliding

The relaxed explication: Balance the leeway of AFT-end against that of FORE-end.
The more technical /scientific explication: Move backwards CLR by one or more of these three ways:

1): Set down some paddel-oars down on lee side to hinder sidedrift - or
2): Plunge down some Guaras /Daggerboards into their AFT-slots to do the same.
3): Turn your rudder to push sidewards on the streaming water.

And after that the wind will do the rest as ever: blow CE leeward of the actual CLR - to point your boat /raft.

Note: Guaras in bow are only needed for a static turn
When sailing ahead, you can lift upwards your FORE-guaras (but not take away) - because the squeeze from bow-wave will take over
- all steering will have to be done in AFT-end by regulating of leeway - as explained above - or as demonstrated.
Shape your raft-bow as you want

Advantage of a cutwater = a POINTED bow

[ img - bow-wave3.jpg ]
sharp stem cleaving the water in two streams
- going to both starboard and port
[ img - bow-wave-pushed-barge.jpg ]
bow wave of pushed square-off barge

A pointed bow give a high lateral resistance of the bow

- a rounded less

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 furthermore we could think over what 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.
Whatever you have of angel on your bow, it will split up the instreaming water in two and thus create a reaction against a yaw
Whereas a bow-wave as is unilateral deflected by a transom bow will promote a crab-sailing along the diagonal
Hull shape - a study of raft-prows

Raft Prow Review

[ 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 with figurehead
stemhead:   [ img - stemhead.jpg ]
[ 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. That has given basis for much new-thinking and many innovations. The advantage of a balsa raft is its large load-carrying capacity - and the disadvantage is its slow headway. 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 is not a need for the bow of such a flat-bottomed hull, because the steering is done by Guaras, as statically change the underwater hull if needed. A raft doesn't heel, and loss because of capsizing is never heard.

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 hear about - and this gave impulse to many later adventurous raids.

The three 'Las 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 North-East-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'

[ img - Antiki4hull.png ]       [ img - antiki-raft+hut.jpg ]
structure of An-tiki
Square-off bow or pointed bow - the rules are the same

Attention on Square-off rafts


A square-off bow play a special play as not exist by the pointed bow
Running downwind, a square-off raft within few degrees can flip-over and change to sail on the other bow

Running for the wind- and broad reach

[ img - 5raft+inclinA.png]
[ img - 5raft+inclinB.png]
> > >
[ img - 5raft+inclinC.png]
[ img - 5raft+inclinD.png]
< < <
[ img - 5raft+inclinE.png]

raft.C):  a square-off raft will probably be able to keep a straight ahead course sailing downwind - but if any wry wind it get unstable.

raft.B and raft.D):   Unstable positions.
With minor unbalance, the lee corner take over the governance and divide the incomming water two unequal streams - the raft then will tumble over, due to the press from the one-sided deviation of the water and end as indicated at raft.A or raft.E - and each time the bow-wave change side, the raft will tumble over to the other side.

raft.A and raft.E):   When the two streams reach same size, a flat-bottom raft will find her balance and sail stable on along a diagonal - just as the boy's kites.

The counteraction for this slalom-course is the same for every vessel as is running for the wind: Set the CE = Wind Center ahead - and keep the CLR = the Hydraulic Center well back
For a Guara-raft that means: with the AFT-Guaras plunged down - and the rest up.
Just for every running vessel, the rule is:

a CE will blow leeward of a CLR

With wind abeam, a square-off raft need more Guaras down aft than a raft with a pointed bow - just to counteract the press from the one-sided bow wave.

With wind abeam

[ img - sail+hull-A.png ]
sailing diagonal
[ img - sail+hull-B.png ]
sailing straight
[ img - sail+hull-C.png ]
alternative ahead
[ img - sail+hull-D.png ]

fig.1) - Heaved-to:   the wind press is directly up against the HIGH lateral resistance = that means nearly a STOP of the vessel even with sail hoisted. And without streaming water, there is no displacement of the Hydraulic Center CLR

fig.2) - Diagonal sailing:   sailing-on, the Hydraulic Center is moved ahead; and pressed by the unilateral deviation of bow-wave the raft will tumble over to diagonal sailing
You can sail on this diagonal course, but you have to adjust your sail and rigging for diagonal - and not centerline. But a diagonal sailing will NOT yield the LOWEST hydraulig resistance.

fig.3 - Sailing straight on:   A Guara-raft can point in every direction you would like!
Therefore the wry pointing can be compensated to centerline-sailing by move backward the CLR by plunging more Guaras down aft - until CLR match CE. Don't forget that Guaras plunged down brake the headway

fig.4): Alternative ahead:   An alternative could be to move CE forward to match the position of CLR - by mounting a foresail or a jib in the stay. That too give indeed more forward force from sails.
This combination of the four presented is expected to give the raft her fastest headway.

As always - the rule is:
a CE will blow leeward of a CLR

- and if your sail is adjusted for that pointing, you will sail -

A more pragmatic explication:

Sailing ahead the stem is rammed into the sea and of this reason hindered in side-sliding - whereas the water is slipping the aft-end without hindrance of nothing there.
And that is why Dirch only is handling his 'dipping paddle' from the aft-end of his vessel:

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.

Result: With water press on stem, the CLR = Center of Water Resistance has moved forward, giving the ship weather helm, and we have to correct with our Guaras.
But either that is a greater problem. As explained earlier: On a raft with Guaras, we can controll sidesliding individually of for and aft, and we can move around our Hydraulic Centre as we will by plunging in or lifting up Guaras - and in that way correct any pointing.

In all cases the sail has to be adjusted for the real way through the sea + how the wind hit the raft - and if the sail is adjusted carefully for this - we will sail. If not, we will have a problem!

TRUE course and APPARENT wind are the parameters for adjustments of sails
'TRUE course' is the direction of your wake
'APPERENT wind' is the direction of your flag or vind-vane

And this moving ahead of CLR is perhaps the reason, why newer speedy sails-ships seems to carry rather much sails in front of the hull + eventually equipped with foresail, bowsprit and jibs - and too have rather much skeg and keel aft - as the famous 'Bluenose' from Newfoundland - called the "Queen of the North Atlantic".  

[ img - bluenose.jpg]       [ img - canadian10.png ]
The core of sail boat steering

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 a metaphor for the 'Center of Lateral Resistance' and is now 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.

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 - alternatively one or both of the static components.
Too the classic rudder work with the CLR.
when things go wrong
And if you by an incident or foolishness have build your craft, and the lateral resistance as should be high seems insufficient for your purpose, then you may try to increase this by mounting a skeg, a permanent fin, a retractable keel, a centerboard, a daggerboard, a leeboard or you could mount a row of boards as Guaras along the sides of your craft - or perhaps you could mount an outrigger.

If you want to sail, it is as in any other case of life:
What count is the result you get - and not what you could, you should nor you would have done.

But don't destroy your Guara-steering
The existence of an outer keel is no condition for exercise of sail powered sailing

Final Conclusion:

If a Guara-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
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.

Technical comment:

Rudder-steering and Guara-steering both do the same: they move the CLR = Center of hydraulic Resistance.
Rudder-steering work dynamically pushing on the streaming water - as push back and deflect on the rudder.
Guara-steering change the static CLR-position of underwater hull

And if you don't like to work with CE and CLR, then you could say:
Sailing ahead with wind abeam, the bow is hindred in leeway by the press in the bow wave - and that is the leeway of aft-end you contrawork and bring in balance with that of for-end, by using either your rudder, steer-oar, Guara or 'dip a paddle' - or whatever you have.

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Lima - December 2019 - Eleventh Edition of this page #6