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I found a site dedicated to this and was so enchanted by some of the pictures i could not resist re-blogging here in a brief impromtu post.

The original pictures are all from http://saveirodabahia.blogspot.com/

Bateira do Nordeste navegando rapido

This is the type called “Bateira” from the states of Ceará and Rio Grande do Norte.

Note that the planform on the mainsail is just about the theoretical optimum as described here.

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The following images are all of the Bahian saveiro Vendaval, which measures 14 metres LOA and built in 1947. The mainsail area is 98 M². There is no purchase on the sheet. Saveiros use a single balanced halyard. Obviously there is no auxiliary.

O Saveiro Vendaval

From afar. This is not a typical amount of crew. They are on an outing here.

Mestre Nute directing operations aboard his ship.

Mast step; no messing around, proper sturdy.

http://saveirodabahia.blogspot.com/

Following on from the last technical post on induced drag, this week i’ll give an overview of e, that quantity i left provisionally defined as 1 in the equation for induced drag;

.                                                $C_{D_i} = \dfrac{{C_L}^2}{\pi{e\Lambda}}$

$\Lambda$ is the aspect ratio.

Planform is the word that describes the shape of a foil when looking at it’s broad side, for instance profile view of a boat’s keel.

As you cannot have discontinuities in the fluid medium , the lift produced does not stop at the end of the wing abruptly, rather it tapers off gradually. It follows that if the planform is rectangular (leading and trailing edges parallel to each other) the pressure will be less at the tip than over the root of the foil. In other words the tip will be underloaded due to the fact that the lift must taper off but the chord retains it full width all the way to the end.

Lift distribution along span of foils with varying taper ratios.

Similarly, for each planform with its varying rate of taper, there will be a corresponding lift distribution curve. For a triangular wing, as expected, the lift distribution tapers down more quickly than the lift distribution for a rectangular wing. However, it does not taper down as quickly as the surface does, meaning the tips are relatively overloaded.

One way to even out the lift coefficient along the entire span is to twist the wing along its length so that each section of wing is at a different angle of attack. In the case of a rectangular wing, one would have to twist it such that the underloaded tips are twisted to greater angle of attack than the root, in such a way that each section of wing is loaded the same.

For triangular wings, the tips are relatively overloaded, so the wing would have to be twisted the other way, with the angle of attack reducing towards the ends.

The problem with this is that the amount of twist needed depends on the overall coefficient of lift, which varies. Thus there is no way to create a twist that will correctly compensate for the variations of loading at all global lift coefficients.

Furthermore, Max Munk  determined that for the least possible induced drag for a given span, the downwash angle has to be constant across the whole span, so that the air stream immediately behind the wing is deflected in a perfectly uniform way.

Without getting too far into it, for uniform planar flows, an elliptical lift distribution curve will result in a constant downwash angle across the whole span. Also it will give the best possible value of $e$

It turns out that there is a planform somewhere between a rectangle (big tips) and a triangle (vanishing tips) that has a lift curve that matches the area distribution curve, thus making each piece of the wing work at the same coefficient of lift, or loading if you will, and that, at all global coefficients of  lift. In this case the local and global lift coefficient would in fact be equal at every position along the span.

An untwisted elliptical planform will produce the required elliptical lift distribution.

Another factor of planform is sweep; the foil can be swept back, or forwards, rather than being at right angles to the flow. This will also affect the value of e. Note that what is important in determining the sweep back angle of a foil is neither the chord midline, nor the leading edge, nor the trailing edge. It is the quarter chord line, about which one can consider as being the aerodynamic “center of lift” of any foil. Explaining the rather complex effects of sweepback and sweepforward will have to wait for another post though.

For now suffice to say, that in general, any sweep is a deviation from the optimum.

An early example of all this being put into practice is the wing of the british Spitfire. Observe not only the eliptical planform but also the practically straight quarter chord line.

The famous elliptical wings of the spitfire

There is however another issue to take into consideration and one which may not evident at first. A pure elliptical wing, despite having the optimal area distribution, has a trailing edge that blends smoothly to the tip and on to the leading edge. Where one starts and the other ends is quite ambiguous, and this has the effect of pulling the tip vortex in towards the wing root. The tip vortex tends to follow the radius of the tip around towards the trailing edge until the angle becomes too great, forcing the vortex to break away. This makes the vortex separation unnescessarily messy and means the tip vortices are closer together than the actual extremity of the foil, thus reducing the effective span of the wing.

This would force a substitution of $\Lambda_e$ for $\Lambda$ with $\Lambda_e \leq \Lambda$

In order to get the tip vortex to peel away as far outboard as possible and neatly, requires a sharp corner between the tip and the trailing edge.  This then requires a little manipulation of the quarter chord line near the tip.

Elliptical area distribution with straight quarter chord line modified near tip so trailing edge is straight and tip has vortex shedding corner.

In the above image i have manipulated the quarter chord line in such a way that the trailing edge straightens out at 0.8 of the span, this is close to being an optimum planform for planar (non twisted) foils. It loses a tiny bit of $e$  but maintains $\Lambda_e = \Lambda$, ie , as high as possible.

The 1988 US catamaran Stars and Stripes with a vortex shedding tip planform designed by Burt Rutan.
Image from François Chevalier

Notice too that in all this, that the triangular planform is about the worst possible area distribution. There exist empirical tables for the value of $e$ and the further one deviates from an elliptical area distribution the lower $e$ becomes, increasing induced drag. Yet it has been generally considered over the last fifty years or so that the bermudian (triangular) is naturally the best shape for going to windward etc. Marchaj did a number of wind tunnel tests on this and confirmed that the triangular planform is actually quite poor. This belief mainly stems from whatever is the current trend in raceboats, setting general ‘idealizations’ about what makes a boat ‘fast’, when in fact raceboats have to optimize to arbitrary rules just as much as actually go fast. This conflict inevitably produces design distortions that are completely innapropriate for sailboats that do not have to conform to any race rule.

To be fair, sailboat rig span loading is actually considerably more complex than that due to the fact that a sailboat rig is not span (height) constrained but rather heeling moment constrained, which imposes optimization along somewhat different lines than as described above. But we’ll come back to the finer points of optimum rig lift distribution in due course.

The foot of the jib is in close contact with foredeck, effectively eliminating one of the airfoil tips.

The value for b or span is taken as the distance separating the separation points of the tip vortices. But what if the lower tip is closed off completely as pictured on the jib of the boat above? This would effectively eliminate the lower tip vortex. How to measure b? In that case, mirror theory states that one can model the three dimensional flow as being one half of the aerodynamic geometry and its mirror image as reflected through the fluid boundary, which in this case is the surface of the water. So b becomes from the upper tip vortex down to its mirror image (underwater).

In simple terms this means that closing off the gap doubles the effective span and thus also doubles the effective aspect ratio, halving induced drag.

This is a vast increase in aspect ratio and one that comes at no cost in heeling moment, so eliminating this gap is the single most effective way of improving a sailboat’s rig performance. This applies to not just jibs, but every sail. Of course, there are plenty of other reasons that may make it impractical to close off the gap completely, but if performance is high on the list of priorities, every effort should me made to reduce the gap as much as possible, for even if the gap is not reduced to the point of having a significant effect on induced drag, it still increases aspect ratio and sail effectiveness at no cost.

Apologies for the late post. I normally attempt to publish on thursdays, but was counting on posting another video montage. However, i’m having technical issues with the video renderer, obliging me to write after all at the last moment.

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The next few months at Guayama i spent changing the rig and making the boat livable.

A lot of the nativos don’t have floorboards; you just walk on the ballast itself, but the Oasis had floorboards fitted some years after being launched to make tacking faster. This is because when you tack the rail meat all leap down into the hole along with their sandbags and then climb out on the new windward side, but it is a long way up. You have to first heave the sandbag onto the deck and then climb out yourself, and this is easier if the hole is not so deep.

So i removed the floorboards and cut them such that they would fit just over the top of the ballast, for more living space, lowering it by 30 cM. Forward and aft there were no floorboards so i made them. The aft floorboards would become our bunk.

The blue floorboards are the original floorboards, recut to fit lower down and further forward. The paint on the hull shows where the floorboards used to be.

The Oasis is the only Puertorican Nativo which has the mast going through the deck , in front of the opening in the deck. All the others have the partners inside the hole, usually with a strap going across the aft side of the mast. This makes stepping the mast a lot easier, but would have forced me to rebuild the deck aft of the mast before being able to build up a cabin. The reason for this is that it is not good engineering to have the mast go through the cabin top, as it is much weaker than going through the deck which is an uninterrupted span across the boat.

As it was all i had to do was build up the cabin sides around the existing deck aperture and screw and glue to the existing coamings.

Cabin sides fixed to coamings

After this i was keen to not have beams eating into the little height i had so i made the rooftop out of three layers of 6 mM plywood glued and screwed together over three forms which i subsequently removed. These defined a variable crown rooftop increasing towards the stern significantly.

Moulds for cabin roof.

Using this constuction method enabled me to build a rooftop with no beams at all and quite strong enough. Some may wonder why i didn’t just make the cabintop higher; the reason is because raising the boom makes you lose the most valuable part of the sail, the part that is low down, contributing lift with very little heeling moment. As is, i only raised the boom 25 cM at the gooseneck, although much more at the after end so the boom would not hit the water so easily.

As soon as the cabin was made the boat became an oven, so i quickly made two hatches to re establish the proper ventilation. I also painted over the grey deck paint which would get so hot as to be painful on the feet, with pure white. For boats in the tropics, there is really only one acceptable color; white. I know the glare is something awful, but it is unavoidable, as that is exactly the desired effect; reflect the incident sunlight back away, to keep the boat tolerably cool. The equation is very simple; the less glare, the more heat, and vice-versa and there is really no way around it. Just good sunglasses.

My wife giving a hand painting the new hatch.

For unstepping the mast i used the mast of a sailboat that was sunk on the other side of the bay, heeled over at a sharp angle. I climbed up this mast, which was quite terrifying i must admit, and set up my block and tackle. Then by anchoring the Oasis with four anchors under the top of this makeshift crane i could pull my mast straight up and out of its hole. Unfortunately, the mast was stuck fast so hard that no amount of force would budge it. So i cut the mast near the heel and dealt with the heel later.

Of course all the hardware, being stainless steel in aluminium was welded tight. Very few screws came out intact, instead i broke them off, and some had to just be ground down. After leaving the mast as a bare pole, i cut 2.5 M off each end, leaving me the fattest part of the mast at the height of the partners. Oddly enough the fattest part had been a couple meters above deck.

For the ends i laminated up wooden plugs, carefully sculpted for a perfect fit. At the heel, a tenon sticks out that fits into a slot on the mast step. The top of this is sloped and liberally sealed with epoxy. A small hole allows any water to drain out of the mast. At the top the plug projects beyond the aluminium so i could shape the step that take the peak halyard and a sheave for the topsail halyard. Both of these were then glued and screwed in place.

Building up the plug for the mast end.

Roughly shaped and fitted ready to be glued in place.

The first step will take the peak halyard. The sheave slot will be for the topsail halyard. The topmost step is for the spinnaker halyard.

Shaped and sealed.

Blends right in with the aluminium!

In all i removed almost 60 kg of weight from the top of the rig. Selling the aluminium and stainless paid for the few bits of new hardware i needed, namely the new norseman compression cones. The gaff added less than 12 kg to the top of the rig. So i think that demonstrates the fallacy of gaff rigs being top heavy! And it is not true to say that that is due to actually having cut down on sail area, because with the topsail, the boat has almost the same sail area as originally and the topsail yard will only add another 10 kg or so, and that is weight that  is there only when needed, and that in light wind.
I think this last point is extremely important to understand; marconi rigs reef only the fabric. All the spars are fixed. On a gaff rig the topsail yard is taken down when not in use, and the gaff itself gets succesively lower with each reef leaving a bare minimum of weight and windage up when the going gets tough.

Sewing up the mast boot with some black denim.

Just needs a coat of paint – make that 7 – and no more water come in.

The finished boot

Another change was i eliminated the two internal halyards, routing everything outside of the mast and taking care to seal the mast up entirely. Although this adds a bit of windage it is not much in terms of total percentage and it makes for one less thing that can go wrong. Also it makes the boat almost uncapsizable; i did some righting moment estimates and with that kind of buoyant volume as soon as they go underwater the boat’s righting moment almost doubles, which is a great safety advantage, especially if you think about how unlikely it would be for a capsized boat to right itself with a hollow mast that is all flooded full of water..

Then i recut the sails using a favorite time saver; contact cement. To save effort i recycled all the corner pieces by cutting them out whole and transposing them to their new positions.

Raising the sail folded along the cut lines and viewing from afar allowed to double check that the measurements i had determined on the drawing board would indeed be correct.

A covered basketball court made an ideal place to work on the sails. All edges and corners were preserved and re-attached in their new positions saving an immense amount of work and money.

The boom also got cut by 2.5 M down from the original 11.3 m to 8.8 M. I also modified the gooseneck to allow the boom to be raised to an angle of around 60 degrees so that it could be used as a crane. This rounded out the boat well for earning money later as a “floating workshop” complete with generator, a large collection of woodworking tools and two cranes (the gaff and the boom) to move heavy objects or step-unstep masts. Not having a cockpit means that the entire stern of the boat is flat and uncluttered for working easily.

Oasis with mast down.
on one side a boat i was doing work on, on the other a boat i was lookin after and where we also temporarily lived.

Inside i made a galley that uses the entire beam of the boat under the companionway hatch (to vent out the heat and also so i would get standing headroom when cooking) with gymbaled stove and an adjustable angle cutting board. On a cruising boat the galley is the most important area to get right. Cooking at sea is always challenging so every effort should be made to ensure that the galley makes those daily hours as easy as possible.

Forward of this and up to the mast is the cargo area on either side all the way up to the deckhead, leaving a passage in the middle. This gives a good distribution of weight out of the ends of the boat.

The advantage with this sort of boat is that the modifications can be made rough and ready and it doesn’t clash with what is already there. if this were a fancy yacht with delicate wood trim etc, to keep the modifications on the level would require considerably more time and effort.

Christina makes us supper in the neighbour’s boat.