It is getting windier
Aquabelle has a lot of sail, even with the self tacking jib and main only. The SA/D number calculated with the fore triangle is somewhere around 20 which can be considered “ultra light racer”, at least by old standards. The main sail has three reefing points with the third beeing at 40 luff length, I suspect to be compliant with offshore racig rules – I didn’t order the sail. The first reef we normally take at about 6-9 m/s depending on the mood, skill, and the available weight on the rail. Second reef is taken soon after. When the times comes to start furling away the self tacking jib it is only blowing something like 11 m/s. The self tacking jib looks horrible though and gets very full, hence barely loosing power. For you non-scandinavians 6-9 m/s is about 12-18 knots or upper 4 beufort, while 11 m/s is about 22 knots or just about force 6 beufort. These winds seems to be getting more and more prevalent here on the west coast of Sweden. Since we are protected by the archipelago it is not really a problem to sail in this weather, it is not the North sea. The first year with the boat, the first couple of days it was blowing somewhere like 15-18 m/s (force 7), but because of the protection of the islands almost no waves for long parts of our routes. So it is just a question of having an adequate amount of sail up.
When sailing of the wind it is simple enough to roll in the jib and the boat sails acceptably well. However, trying to work to windward back home after 2024 Tjörn runt in about 13 m/s in flat water made us go more sideways than forwards. We really would need something forward of the mast. Because I really like sails, engineering, and building things, I decided to order a new jib that is going to be hanked on to an inner forestay removeable forestay in dyneema. To roll in the jib and hank on the inner heavy weather jib should be almost equivalent to taking a reef in the main. This means that it is very flexible when it should be hoisted. For cruising days it is very likely that it will be set in harbour when the first reef is expected to be taken, instead of the first reef. Backstays will probably need to be used, so the usage mode will most likely go through some trial and error.
How big is too small?
Since making this big sail is beyond my skills, time, and tools, it had to be ordered and therefore almost correct from the beginning. Since there are some uncertainties, such as stay sag, and economic factors, I decided to order a dacron sail. A membrane sail would have to be made correctly from the beginning but a dacron sail can be altered quite liberarly without more problems than the cost of the work. In the distant future when It needs replaceing I hopefully know details more closely and can order a membrane sail for better performance.
Now to the big question: how big should the heavy weather jib be made? It is not a super simple question since the power of the sail also very much depends on the shape and fullness of the sail. In my initial calculations I therefore simplified the problem to areas of the sails only. From the last couple of seasons sailing primarily with main and saelf tacking jib I have a fairly good idea of what reef on the main is suitable to different wind strengths. I used this knowledge to getting some initial numbers. The very simplest formula that can be used to get some number of the force in a sail is to take the area of the sails and multiply with the wind speed squared. This should then be the same as another sail area and windspeed. In an equation for situation x and y (ignoring mainsail area):
A_x * W_x^2 = A_y * W_y^2
which will transform to
sqrt( A_x * W_x^2 / A_y) = W_y
for trials and further simplify with knowledge of when the mainsail needs to be reefed for the first time to
sqrt( 19/A_y * 8^2) = sqrt(1216) / sqrt(A_y) = 34.87/ sqrt(A_y) = W_y
I started to toss some numbers to this equation, but really I should have put this into a graph and then choosen the correct point. From this I could start discussions with a sail maker. From these discussion we agreed that a heavy weather jib of about 13 m2 would be appropriate. The reduction in area would be about the same area reduction as the first reef. To get some feel for this I did some more calculations but now also including the CE (Center of Effort) of the sails so that the heeling moment resulting from the sails could be taken into account. The calculations used in the below table are not much more advanced. The resulting moment is calculated according to the first equation, and then the appropriate max wind is guesstimated with the help of the second (which should remind you of the previous used as a starting point for the jib area).
- M = A_m * CE_m + A_j * CE_j
- W_y = sqrt(M_x/M_y) * W_x
| Main Sail reef | Area (m2) | Lateral CE (m) | Jib Sail | Area (m2) | Lateral CE (m) | Total Area (m2) | Combined Moment (m3) | sqrt(M_x/M_y) | Approx Max Wind (m/s) |
|---|---|---|---|---|---|---|---|---|---|
| Full | 27.6 | 6.56 | ST | 19 | 5 | 46.6 | 275 | 0 | 8 |
| 1 Reef | 22.08 | 6.12 | ST | 41.08 | 230 | 1.0935 | 10-11 | ||
| 2 Reef | 17.2 | 5.7 | ST | 36.2 | 193 | 1.194 | 11-12 | ||
| Full | HW | 13 | ~4.6 | 40.6 | 240 | 1.07 | 10? | ||
| 1 Reef | HW | 36.08 | 195 | 1.188 | 11? | ||||
| 2 Reef | HW | 30.2 | 158 | 1.319 | 13? | ||||
| 3 Reef | 9.94 | 4.18 | HW | 22.9 | 101 | 1.65 | 15-17? | ||
| 2 Reef | HW 1 Reef | 9 | ~3.93 | 36.6 | 133 | 1.675 | 17? |
I also did some calculations for having a reef in the HW jib but since the HW jib area is already in the unknown territory, spending money on this seemed not worth it when discussing with the sailmaker. After the investigation with the table and different settings, and how I know the boat and sailing I do is, I figured the normal way of operations would be something like:
- 8-9 m/s first reef is taken in the main.
- 10 m/s heavy weather jib is set. Backstays needs to be used, tightened and slacked in each tack.
- 12 m/s second reef in main is taken. If wind is expected to pick up third reef is rigged. Backstays can now be permanently set.
- 14 m/s third reef is taken in the main or heavy weather jib is changed to storm jib.
- 16 m/s running with third reef and storm jib.
Sail details
For some time I was thinking about having reef in the heavy weather jib, but the sailmaker managed to talk me out of it. I decided to keep the clew of the reef for use either to get the foot of the sail off the deck in case that is wanted for sight or water evasion, or to use to get a better sheeting angle for off the wind. Since the sail will also live a life where the clews might be very lively, and the sail having some overlapp of the mast, I also opted to having soft clews to spare the mast and people being hit be metal.
Since this is a sail that is supposed to be hoisted on a dyneema stay the sailmaker recommended soft hanks which I went with. The soft hank will supposedly spread out the load a little bit on the stay and not chafe as much. They will also not corrode which might be a problem on a sail that spends most of its life under the forepeak stowed away. Since the stay will also be removeable and stowed by the mast, this opens up the possibility to sit on the coachroof and attach the sail to the stay. We will see how that turns out in practice once a cascading purchase system is attached to the bottom of the stay. Regardless it seemed to me a good idea to buy a so called race bag for the sail so that most of the attaching sheets, hanking on the sail etc can be made with the sail still in the bag.
Because I think it is a bit cool but also a little bit for visibility I specified to have the top of the sail in high-vis in some whay. I will just have to wait and see how that turns out I guess.
A dive into unknown forces
One of the major problems in this project is the attachment point for the inner forestay in the deck. For safety it can be argued that the scantlings of everything should be made to be able to function as a replacement for the normal forstay in case that becomes necessary. This simplifies the problem slightly so now the question is: What is the forestay dimensioned for? In essence all the rig scantlings always comes from the righting moment of a yacht, so this could be one way but since I don’t have any measurment of this it is still unknown but can be approximatly calculated from principle information about a yacht. The current stay and shrouds dimensions are known but it is uncertain how much overbuilt these are and what safety factor or method that was used by the designer. In conclusion there exists three avenues of approach to the problem of determining the righting moment which will probably need to be used together to form a good estimation.
A first estimation of the righting moment can be obtained for example through the Selden online calculator. For Aquabelle with 5 crew members on the rail, this comes out at 16.4 kNm for the boat with 4.6 kNm added by the crew, so somewhere around 21 kNm.
For calculations originating from the shrouds and stays I went and looked in Principles of Yacht design by Larsson, Eliasson, Orych which uses the Nordic Boat standard as a baseline for calculations. This book is the main source for the following calculations. Aquabelle’s rig is a fractional rig with one set of spreaders, with a mast that goes all the way to the keel.
Let’s start with calculating with the shrouds as starting point. They are 7 mm wire with a breaking load of about 37-43 kN depending on source. Shroud loading is also depending on the angle to the mast, I have through shroud and spreader lengths estimated this angle somewhere around 9.7 degrees. Since a yacht’s righting moment is dependent on the displacement of the yacht, for the shrouds the righting moment is calculated from the empty boat’s righting moment at 30 degrees of heel multiplied with correction factor for a fully laden boat and then crew weight righting moment added according to Fig 11.1:
RM = RM_30 * d/G + RM_crew
Now, equations in Fig 11.6 and Fig 11.4/11.3, while only considering the top shroud we get:
P_d2 [kN] = 3 * D2 [kN] = 3 * F2 [kN] / sin(B2) = 3 * T1 [kN] / sin(9.7°) = 3 * RM [kNm] /(I + freeboard [m]) / sin(9.7°) = 3/13 / sin(9.7°) * RM
RM = 40 kN * 13m/3 * sin(9.7°) = 29.2
This is a bit more than 21 kNm reported by the Selden calculator. With a lot of provisions, spare parts, 150 liters of water, 40 liters of diesel, say 600 kg. Then we add about 400 kg of crew weigth on the rail (400*9.82*1.5) we get
RM_30 = (RM – 5.9) * 31/41 = 23.3 * 31/41 = 17.61
Which is quite close to the boat’s righting moment from the Selden calculator. Moving on to the forestay calculations. The forestay is 6 mm wire with a breaking strength of about 31 kN. The formula for the fore most sail-carrying sail is according to Fig 11.8:
P_fo = 15 * RM/(I + Fs) = 15 * RM / 13.5 -> RM = 31 kN *13.5 m /15 = 27.9
This is more in line with Selden’s calculator. So to sum it up: from these calculations it seems clear that the designed righting moment of an empty boat is about 17 kNm while a fully laden and raced boat has about 28 kNm righting moment. Since the numbers seems to agree we can use the same numbers for the inner forestay. Since the attachment point of the stay will be slightly lower on the mast some numbers needs to be modified. The required breaking strength of the forestay and its fittings then needs to be:
P_fo_i = 15 * 28 [kNm] / (I + Fs – Ii [m]) = 15*28/12.9 = 32.56 kN
The shortcut would of course be to say: the existing forestay is 6mm with a breaking strength of 31 kN, let’s make the new one to the same specs. But math is fun and now I am certain of the load. If the stay if not designed to be holding up the mast the factor of 15 can be changed to 13 and the required breaking strength becomes 28.2, barely any change.
Picking out the parts
The forestay in essence is made out of three parts: top and halyard attachment; middle; botton attachment and chain plate. The main idea for the top is to use a barber hauler on the spinnaker halyard to pull it down for using for the Hw jib, while the stay itself would be attached to the mast in some fashion. After discussion with some riggers it seemed like the classic o-fitting from selden would be the suiteable option. For the barber hauler I am at the time of writing not entirely sure how I want to have that done, but I think I will move the existing unused halyard lead down and then make a small line for the small diameter dyneema line used as a barber hauler to pass through.
The middle part is both simple and tricky. To minimise stay sag while sailing the stay needs to not stretch. Really only two options exists: D12 SK99 Max from Marlow and Dynice Dux from Hampidjan which is a SK75 heat stretched line. Since this is more like an aft stay than a shroud, being tighted and then removed, then reset, construction creep is not as important as stretch the 24 hours or so the stay is used at a time. There are already miles written on the internet so I will not do that again. In the end I ordered 7mm Dynice Dux, a bit over size to get stretch down even more and the jib is going to have soft hanks, but still cheeper than D12 SK99 Max 6mm where I live. The spliced breaking load of about 67 kN will hopefully compensate a bit for the rather sharp turn the shroud will have to make at the top at the mast. To alleviate some of this problem I might also splice in a sailmakers thimble to get a smoother turn. The stay stretches about 0.2543 % per 10 kN of force. A stay length of 12 meters loaded to 30 kN would then get 12*0.002543*3 = 92 mm longer. Some of this will need to be handled by pretightening and some with the backstays, but some will be converted to stay sag. Some comparison: the shrouds get pretightened to 20% break load which will stretch them 4mm over 2 meters. Over 12 meters this will become 24 mm. When reaching breaking the shroud will have reached 120 mm elongation. The same math applies to forestay. The conclusion is that stretch is a problem but should be smaller than the already existing forestay.
To tighten the stay the plan is to have a 1:8 or 1:12 cascading purchase system with low-friction rings that will then attach to the bottom of the anchor box in the chainplate there. One of the things left to deside is if the cascade is going to be permanently attached to the stay of the chainplate. To get it set up when it is going to be used I have managed to get some second hand Tylaska T12 Trigger Snap schackles from an old Volvo Ocean race boat. They have a working load of about 27 kN and a breaking load of about 54 kN. So they should be good enough for the normal use case and for some time in the extreme.
If the cacade is going to be attached to the stay or the chainplate permanently depends a bit on the design of the chainplate and I will have to consult with my crew what they think but I am heavily leaning towards it being attached to the chainplate and then connect the stay with the tylaska snap schackle. This will make adjustments to the length of the different parts of the cascade easier and manouvering the stay on deck easier.
The problematic bottom part
Well, the chainplate in the achor box is a tricky engineering problem. There are the classic engineering problem – weight, cost, performance all need to be balanced. It needs to perform sufficiently, be relatively easy to build, not cost to much, and be as light as possible under these constraints. We have the required load bearing from the previous calculations – 32 kN, not the challange is to distribute this force into the hull at appropriate places. Really, there are only two options available, either the deck/hull joint or the stem. Since the forepeak berth(s) are small enough already without having to combat an internal stay as well and I would like to minimise the amount of sanding inside the boat, this goes out. Then the only option is somehow transfer the loads out out to the side to the deck/hull joint. Two options then: attachment at the deck level. Since I would like the cascade to be as much below deck as possible to allow for easier sail hoisting, as much as possible needs to be in the anchor box and therefore much of the stay’s forces needs to go to the bottom of the anchor box somehow. Some can be distributed under the deck but the important thing for both solutions is that if something breaks it should be the newly added stuff and not the anchor box, and certainly not the hull.
I first naive approach: a simple carbon fibre cross beam accross the whole width of the anchor box’s bottom with supports upp to the join at deck level. Many programs online exists to calculate coss section stiffness and beam deflection so I will not go into much of the details but only the results. 700mm carbon fibre square hollow section 30*40 mm outer measurement with 4 mm thickness (about 13 layers 300 g/m2 UD) (89700 mm4), under a mid point load of 32 kN would give a deflection at center point of 14 mm. For the breaking load case then, the beam will introduce further elongation to the stay. It will change from 92mm to 106 mm and an increase of 15%. The effective stretch will increase from 0.002543 to 0.002930 or about 0.29 % for the stay.
The maximum bending moment of the beam will be about 5.5 kNm. Approximating that it is only the top part that will take up this force and that it will pivot around the bottom, the tension in the top can now be calculated. The top bar is 4 * 30 mm2 and the force is 5.5 kNm/(0.040-0.004 m) = 153 kN. 153 kN over 120mm2 becomes 153/120 = 1.275 kN/mm2 = 1.275 GPa. Carbon fibre has tensile strength of about 4 GPa, but adding resin content of about 25-30%, this will go down to about 2.5 GPa. Then the safety-factor is only about 2.
What about dividing the same amount of carbon fibre into two beams and putting half the force from the stay on each? This would result in a deflection of about 12.2 mm, which is an improvement, but not by much. Some other solution with shorter beams needs to be designed. If the beam would be only 400 meters long, the idea with a single beam would only deflect 5mm, a definite improvement.
Another idea would be to strengthen the aft small bulkhead of the anchor box significantly and have the standing ends of the cascades attach at deck level with forces carried by the bulkhead. Then build an L-bracket out onto the botton part of the anchor box to where the final working end of the cascade could attach. This might make it possible to have most of the force carried by the bulkhead, but the adjustments still happening as low as possible. On to drawings!
Chainplate design
It took a couple of weeks, designing in my sleep, on paper, and in the computer, but finally I had something I believed in. The basic principle is to build a chainplate that attaches to the whole anchor box bulkhead. To not flex to much only some reinforcement is needed on the bulkhead, it is stiff enough, the main problem will be to distribute the force downwards in the bulkhead. This is where the carbon fibre comes into play with its low stretch. The standing ends will all attach just below deck level in a stainless bar that is then held down by carbon fibre bands which in turn goes down and forms the chain plate.
The working end of the 1:12 cascade will go down to the bottom and then be routed to a Servocleat 33 with a SWL of about 2 kN. The idea is that if anything breaks, it should be the cleat and not something more serious than that. 2 kN with a 1:12 purchase will still be in the neighbourhood of 24 kN excluding friction losses. Once again excluding friction losses, if one were to pull with 40 kg of force that would translate to about 4.7 kN which is a little more than 14% of breaking strength of 6mm wire. It seems like it is finally a viable solution.
Of course this can probably be altered a little bit to get some more room in the anchor box by replaceing the bottom with some smaller better suited stainless bracket, but that might also require some good backing plate to distibute the 4 kN that spot will experience. That will also inhibit moving one or two of the standing ends down. It will however, mean that the final angle and placement can be indentified until after launching the boat, which is nice.
