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Seventh Edition of this page #6
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Inca's Balsa Log Raft

The Power of Hull-shape


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, 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, 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 spell between Hull and Sail

[ img - OwnShip.fig-124.png ]

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 -
And such simple calculation could probably have saved the famous oldtimer Vasa as in 1628 capsized just outside the shipyard.
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 ]
normaly heeled ship
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)

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 when we are sailing: work by the water flow around rudder and the flow of wind around sails
Static components are always present, but we can change them: guaras or dipping steer-oar(moving CLR) + plus hoisting, lowering or reducing sails (moving CE)

what to influencenature of influencing force
 STATICDYNAMIC
Center of wind CE
= Sails and Rigging
PUSH
on each sail
LIFT & DRAW
- from flow around sails
Hold in water CLR
= under water hull
HOLD in water
by GUARAS end KEEL
WATER PRESS on bow
+ flow around RUDDER

The sailed course of a craft is a result of those two mentioned parameters: CE and CLR. They define the pointed course.
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, pushing at the streeming water - the 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 too are adjusting the CLR, but by changing the shape of the under-water hull - the 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.

In all 4 cases the rule is:
The CE will blow leeward of the CLR
- and that is that, as define the pointing of your craft

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 outer shape of a hull

The round bodied family

Every sail-powered vessel hold a LOW FORWARD hydraulic resistance - and a HIGH LATERAL ditto.

[ 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 hull shape
The circular hull shape exist in many countries all over the world ,as basket boats, known as Kufa, Guffa, Coracle or 'Moses'. That is light weight constructions as normaly are paddled or rowed, because they can't be powered by sail other than for down-wind sailing - due to the fact, that theż don't hold the needed "LOW FORWARD hydraulic resistance - and a HIGH LATERAL ditto".
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
The SQUARE SAIL of Humber Keel have sailed on the rivers of Yorkshire in England since the vikings came to Jorvik 1200 years ago
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 'balance the sidegliding' of BOW and STERN - or give her a permanent aft-fin.
An example of rectangular raft type#4 can be found at page #8.   RaftOnOcean.jpg
Shape#5 and #6 - pointed and stepped bow 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 Tangaroa2 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 for 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.

Square-off bow or pointed bow - the rules are the same
A square-off bow has some special difficulties more than the pointed bow

Running for the wind- and broad reach

[ img - 5raft+inclinA.png]
raft.A
stable
[ img - 5raft+inclinB.png]
raft.B
tumbling
> > >
[ img - 5raft+inclinC.png]
raft.C
stable
[ img - 5raft+inclinD.png]
raft.D
tumbling
< < <
[ img - 5raft+inclinE.png]
raft.E
stable

raft.C):  a square-off raft will probably be able to keep a straight ahead course sailing downwind - but if any wind across 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 in two streams - the raft then will tumble over, due to the torque 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 ballance sailing along a diagonal - just as the boy's kites. [ Hyper Link ]

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: [ Hyper Link ]

a CE will blow leeward of a CLR

Running downwind, a square-off raft within few degrees can flip-over and change direction

With wind abeam

[ img - sail+hull-A.png ] [ img - sail+hull-B.png ] [ img - sail+hull-C.png ] [ img - sail+hull-D.png ]

fig.1):   static adjusted Guaras for pointing East - without sailing and therefor without any dynamic moving of Hydraulic Center CLR

fig.2):   sailing-on, the Hydraulic Center move ahead pressed by the unilateral deviation of bow-wave and the raft will turn to diagonal sailing
You can sail on this diagonal course, but you have to adjust your sail and rigging for diagonal- and not centerline

fig.3):   A Guara-raft can point in every direction you would like, and the wry pointing can be compensated to centerline-sailing by move backward the CLR = plunging more Guaras down aft

fig.4):   an alternative could be to move CE forward to match the position of CLR - by mounting a foresail or a jib in the stay

As always the rule is:

a CE will blow leeward of a CLR

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

In all cases the sail has to be adjusted for the real way through the sea, and 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 conditions for sail adjustments
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 equiped with foresail, bowsprit and jibs - and too have rather much skeg and keel aft - as the famous Bluenose from Newfoundland - the "Queen of the North Atlantic".   [ img - bluenose.jpg]     [ img - canadian10.png ]


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 permanent fin, a retractable keel, a centerboard or mount any row of boards, daggerboard, leeboard or Guara along the sides of your hull - or perhaps an outrigger.
As in any case, if you want to sail, that is the result you get, as count - not what you could, should nor would have done.
Comment around CLR of motor boats
We don't talk much about CLR in relation to motor boats, but of course the underwater hull of a motor powered vessel have a center of hydraulic resistance - and of course a motor have to thrust directly against this CLR to sail linear ahead.
If you want to change or correct this course you have two ways:
1): Move direction of trust as you do with an outboard motor   - or -   2): move your CLR with rudder, steer oar or what you have of steer system.
From a static CLR to a dynamic CLR

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. [ img - CE+CLR-1.PNG ]

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)

A complicating counterpart:
Too the lee-way movement create a similar, but minor bowwave a "lee-wave".
Technically the contribution from the dynamic forces created by the sailing is explained by the few sketches
- and that is the same whatever you have a pointed, a rounded or a square off bow.
[ img - CE+CLR-2.PNG
sailing ahead
+
[ img - CE+CLR-3.PNG
drifting leeward
=
[ img - CE+CLR-4.PNG
resulting situation
Fig.1 - Sailing ahead:
When the vessel move ahead she will plunge her bow into the sea and due to the press of water 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 created by the press of hull against water play together with the old static CLR and create a new = a dynamic Center of Lateral Hydraulic Resistance more ahead - and more sailspeed = even more ahead.
The new dynamic CLR = Center of Hydraulic Resistance is indicated by a blue dot [ img - bluering-26.png ] and is the combination of old CLR [ img - CLR5-star-33.gif ] + the water pressed on the bow.
The blue arrow [ img - bluearrow.png] indicate a common hydraulic resistance with its attack point.

Fig.2 - Drifting leeward:
The same rules reign if the vessel drift sidewards; but due to the fact that the most vessels hold a high sidewarts resistance the leeward speed are much smaller and the CLR move less against lee. The truth is that we seldom calculate with any sidewarts "bowwave" - but it exist!

Fig.3 - 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.
But generally we only say: "When sailing, the CLR moves ahead" - without to say much more.

The CE will always blow leeward of CLR and thus define the pointing of the vessel!

The bow-wave has as consequence, that sailing with a wind abeam, the wind as will try to move ALL the craft sideways
- but it will mostly be able move the aft-end.
[ img - CE+CLR-5.PNG
[ img - CE+CLR-6.PNG
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 as the vessel gain speed and CLR move ahead.
The first figure try to demonstrate an unstable start situation
- but the next figure show what happen when the boat is gaining speed: the CLR will move ahead of the CE and, if no counteraction is taken, the boat will turn up against the wind = weather helm (or more correct: the CE will blow to lee of CLR). And that is the situation for the most boats as I have met.

Counteractions against weather helm:

Start sailing ahead
Next step will be adjustment of Guaras - more Guaras aft against aft-end sliding
[ img - CE+CLR-7.PNG
Classic Rudder steering
[ img - CE+CLR-8.PNG
Dipping Oar steering
[ img - CE+CLR-9.PNG
Guara /Daggerboard steering
With more sails you can counteract by move more ahead 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 you can't do much with your CE - but perhaps tilt the mast forward.

The alternative to move ahead the CE is to move backwards the CLR, what is the most normal to do; and the counteraction is the same, whatever you have of steering.

The relaxed explication: Balance the leeway of AFT-end with that of FORE-end!
The more technical /scientific explication: Move backwards CLR by one or more of the three ways:
1): Turning your rudder to push sidewards on the streeming water,
2): Dipping some steer-padles down on lee side to hinder sidedrift, - or
3): Plunge down some Guaras /Daggerboards into their AFT-slots to do the same.

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 (not take away) your FORE-guaras - the squeeze from bow-wave will take over
- all steering will be done in AFT-end by regulating of leeway - as explained above - or as demonstrated here by Dirch -
Shape your raft-bow as you want

Advantage of a POINTED bow

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

 

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 ponder 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
= diagonal sailing
Whatever you have of angel on your bow, it will split up the incomming water in two streems 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

[ 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
tangaroa-stem.jpg
Tangaroa2 raft 2008 with her classic shaped prow with figurehead
[ 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 is not a need for the bow of flat-bottomed hulls, 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 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 ]
structure of An-tiki


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 side-trunk doesn't give enough keel
The existence of an outer keel is no condition for exercise of sail powered sailing

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.

Technical comment:
Rudder-steering and Guara-steering both do the same: they move the CLR = Center of hydraulic Resistance.
Rudder-steering work with the dynamic streeming of water
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, by using either your rudder, steer-oar, Guara or whatever you have. [ img - mail-kly-runasimi.gif ]

Lima - September 2018