Darren austin

OPTIMIZATION ON A EXISTING 42FT CRUISING YACHT USING RIG & SAIL INCREASEING WITH THE AIM OF ACHIEVEING LARGER BOAT VELOCITIES AT LOWER WIND SPEEDS. D M Austin, Falmouth Marine School, University of Plymouth, UK SUMMARY The scope of the paper will consist of hull design theory and hull comparison techniques using basic parameters and appropriate formulae. Hydrostatic analysis and calculations will be conducted between two vessels using academically accepted theory and methods, structural conclusions and recommendations will be drawn from the information using mathematical theory and formulae. Underwater foil recommendations will be based on hydrostatic information and conclusions.

The paper will also cover material science with emphasis on marine composite structures and specific applications.

Design strategies and implications will conclude the paper using information provided by the separate areas of above study.

In depth hull and underwater foil structural calculations will be left as a further area of study and conducted at a later date.

NOMENCLATURE A AR AP B BG BM Bmax BR Bwl C CE CLR DWL E Fn FP FRP g G GM GRP GZ HA I IT Ix Iy J LCB LOA LWL m M RM RM1 RM30 RM90 SM SA SAF

area, general aspect ratio aft perpendicular beam of hull amidships, or centre of buoyancy distance between centre of gravity and buoyancy metacentric radius maximum beam of hull ballast ratio beam at waterline chord length centre of effort centre of later resistance design waterline modulus of elasticity, or base of mast froube number forward perpendicular fibre reinforced plastic acceleration of gravity centre of gravity metacentric height glass reinforced plastic righting arm heeling arm moment of inertia, or height of fore triangle transverse moment of inertia of water plane transverse moment of inertia of mast longitudinal moment of inertia of mast base of fore triangle longitudinal centre of buoyancy length over all length of waterline mass metacentric height righting moment righting moment at 1 degree righting moment 30 degrees righting moment at 90 degrees Simpson multiplier total sail area fore triangle sail area

SAM sail area, main Sw wetted surface area T draft of yacht VCG vertical centre of gravity Φ heeling moment Δ (kg) Displacement Kilograms Δ (m3) Displacement meters 3 1. INTRODUCTION The aim of the study is establish a need for the incensement of the rig and sails of a well established production cruising yacht with emphasis on generating larger boat velocities at lowers wind speeds.

The study will focus on two similar luxury blue water cruising yachts designed for serious offshore sailing and luxury cruising easily capable of withstanding medium to very strong winds. The main aim will be to justify if the study yacht can be adapted to have the ability to increase its rig and sails further without jeopardising the stability, performance and structural integrity without being forced to make any major hull, keel or superstructure changes.

The two chosen yachts for the study are both British built Rustlers, the 42 and the 44DS. [2] Rustler have been manufacturing since beginning of the 1980s and are extremely well established and respected for producing luxury, well performing cruising yachts whilst still offering a high level of customization and design flexibility to the client on every build. Rustler currently has dealerships worldwide for example USA, Italy, and Netherlands but this study has been fortunate enough to work with the UK based home branch situated in Falmouth, Cornwall where the yachts are designed and developed by a dedicated team of design staff and fitters/builders.[2] The focus of the study is directed at the modification of the traditional 42 model by taking initially easily proposed assumptions and applying detailed yacht design theory and appropriate mathematical formulae.

A measure of how she will behave will be created using collected data and variables, obtained from undertaken hydrostatic analysis.

Analysis and the collection of data provided were presented by the change in key component specifications developed from the idea of adopting the rig from her big sister the 44DS. Early assumptions were made so easily and justified based on how the design of the 44DS was derived and developed, the 44DS, despite being a very different and higher performance yacht than the 42, is essentially still the same boat as the when glancing at cross referenced dimensions, parameters and difference percentages.

Figure 1 presents the raw data and specifications for both yachts, note key and expected data was obtained courtesy of the builder’s full brochure specifications, all other dimensions needed to calculate meaningful hydrostatic analysis were measured physically from the specimen vessels at the builder’s premises.

The dimensions in figure 1 clearly show the close relationship between the two vessels and begin to display some of the subtle changes that made it possible to produce the higher performing and more spacious 44DS from the traditional 42. [2]

[2] 2. RAW DATA 2.1 HULL SPECIFICATIONS The left hand side of figure 1 gives the basic dimensions normally always supplied by yacht manufactures.

Mentioned above was the subtle differences between the two yachts and is obvious when looking at the percentage margins between them with no more than 14 % and as little as 3% difference in all main yacht specifications.

The largest increases are in Δ (k) (3), (14%), and T (13%) which is understandable and then thirdly the SA (9%) which is very much a dimension of importance to the study. Note SA has been calculated with main and genoa set up and will be calculated the same way for max SA throughout the study.

The lowest % value was at Bwl which was one of the values recorded physically from the vessels as it is essential value for conducting hydrostatic calculations.

The percentage is small due to the hulls being identical in that area (apart from LWL), the increase is related to displacement, as displacement increases so does DWL and Bwl.[1] Other values physically recorded from the vessels were that of the freeboard and coach roof height, these differences become extremely important when Φ increases beyond 50 degrees. [1]

As the freeboard and coach roof begin to become immersed at larger angles of heel the wetted surface area of the vessel increases. The increase in wetted surface area is what will make calculating Φ at large angles tricky as it will increase as Φ does. The percentage differences in freeboard, but mainly coach roof height, display where significant changes have been made to the 44DS with its coach roof standing 40% higher which makes a huge difference (fig 5) at higher Φ.

2.2 (a) Non-Dimensional Ratios The information presented in the left of figure 1 are the non-dimensional ratios drawn from the hull specifications for the given vessels. They been derived using the following formulae, also a range of typical values are given for similar size cruising yachts,      

LOA÷LWL (1.22-1.24) LOA÷B (3.00-3.50) LWL÷3√Δ(3) (5.00-5.50) BR= B÷Δ(kg) (0.35-0.55) LWL÷T (5.00-5.70) SA÷(3√Δ(kg))^2 [1]

The values obtained will tell little more information on top of what has already been discussed in relation to each other of the vessels. However later in the study the ratios will help determine vessel parameters to give an

idea of typical speeds performance predictions. More will be explained about typical values when defining new vessel stats and characteristics later in study, SA/Δ (k) will be calculated and discussed later in study when predicting boat speeds.

2.3 RIG, SAILS & KEEL SPECIFICATIONS

height was acquired by company director when all other measurements were taken. The underwater foil measurements were taken manually so foil recommendation could be possibly undertook, but more important what factors of the yacht is its main contribution in stability to combating the extra sail area and heavier rig.

Figure 2 below presents all the rig information for the 42 and the 44DS. All but the E, J and I measurements were obtained from builder specification brochure, the main rig measurements were taken manually and mast

[1] Similar to that of values obtained in figure 1, with relatively low values for 11.5 m cruising yacht.

Sail combinations have been calculated to see percentage differences to identify max sail area combination, as mentioned mainsail genoa set up will be used throughout as max SA. The key information to draw from the table is the max SA obviously but more important will be mast and boom dimensions as they are essential later in study when rig weight calculations are conducted and examined.

The difference in mast heights is 9% and boom section double that at 18%. The wall thickness will matched to the mast section later in the study when a mast section and type of material will be recommended and calculated. All mast sections and boom sections are made from modern aluminium alloy.

Was interesting that design specifications supplied from builders for the 42 and 44DS mast sections didn’t match them of the ones measured on boat study specimens at yard.

The masts are all manufactured by Selden, one of the world leaders in mast technology and custom building, so therefore probably suggest there may be slight differences with many of the rigs fitted to Rustlers due to the level of customization and flexibility offered by both the rig manufacturers and yacht builders. However the 42 was close to that specified by builder as well as the boom section.

The not expected and interesting information was to notice that the 44DS had much sleeker modern section with a lot more length in the x axis and less in the y

axis than specified in builder’s specifications, which will act differently structurally and aerodynamically.

Despite the distinct change in the mast sections the main boom remains the same to the builder’s specifications but more importantly to the vessels.

They study will attempt to prove and justify the reason for these changes in x and y axis lengths from a structural angle, whilst also using the information to make new mast section judgements and structural considerations when adopting the change of mast material to something with different weight and structural properties to that of aluminium.

The J distance (forestay to mast) will also be an interesting value when hydrostatic calculations are conducted, as this will probably influence longitudinal stability or final max SA of the final yacht concept design due to limited J length.

2.3 (a) Keel dimensions The keel dimensions were very different to each other, there were subtle changes in AR with the 44DS understandably displaying slightly higher with its shorter chord and longer span. The key difference and an assumption at this stage of study was the high factor of influence the keel thickness will have. The main observations when taking physical measurements were the placement of all the keel ballast on the 44DS as it was displayed in the bottom of the quarter of the

thinner sleeker foil. This key point will be discussed after hydrostatic calculations made, to confirm the importance of the shift of VCG due to the shift in keel ballast.

3. METHOD

beginning and ending at AP of the LWL and FP of the LWL. The lengths of timber are used at AP and FP as the perpendicular datum (vital at 90 degrees) and are joined by string to create a baseline datum to measure horizontally out from Bwl to and creating the square triangle.

Before explaining the method fully, note that the Rustler range including the 42 and 44DS were designed

by Stephen Jones a naval architect based in Southampton. Problems occurred when obtaining hull lines plans seemed harder than initially planned. Hull lines plans of the vessels were needed or the half beam co-ordinates at the DWL so that (IT) could be calculated for each vessel.

The datum baseline is mirrored with vessel and are divided into equal stations in this case 10 (which is a traditional number).

Measurements are taken from Bwl horizontally to datum line and recorded all measurements are taken at all stations at the correct spacing trying to stay as accurate and level as possible.

Once all measurements are taken they are deducted from the AP and FP datum lines, which in this case is 2.40m.

The same process and datum measurements were used for both the 42 and 44DS in till all needed information and values of the water plane were gathered.

GZ curves were supplied by builder and could be reversed engineered using GZ=GMsinα, however the decision was made that was not enough information to conduct meaningful calculations and (IT) would have to be obtained for each vessel.

The half co-ordinates at Bwl would have to be taken physically from the yachts due to above mentioned issue regarding hull lines.

3.1 METHOD FOR LIFTING LINES Traditional methods were adopted when taking Bwl coordinates, plump lines alongside spirit levels were used so allow for slight discrepancy later when comparing to builders GZ curve once calculated.

3.1 (a) Apparatus     

2x (2.5m lengths of timber) String/plumb line Field tape Spirit level Calculator

The quick and easiest way to take then lines and still obtain good accurate values was create a square rectangle perpendicular to the CWL of the vessel

3.2 METHOD FOR HYDROSTATIC CALCULATIONS Once the co-ordinates are gathered for each vessels water plane area the calculation of the cubic half beams can be calculated to obtain the transverse second moment of area. The values for (IT) will then allow the beginning of calculations of the static stability up to 50 degrees for each vessel using transverse stability relations and funder mental stability formula.

GZ for each vessel is produced for angles of heel from 5 degrees to 50 to allow RM and then dynamic Φ to begin to then be calculated. The results will be briefly

cross referenced with GZ curve supplied by builder to measure discrepancy in (IT) measuring if any.

GZ for the 42 will then be calculated along with RM and Φ with addition of 44DS rig without any altercations made to rig to analyse how much the RM and Φ vary from that of the rig traditionally and originally fitted to vessel.

New GZ curve and final design conclusions will be drawn from 42+44DS rig values and the differences in RM and Φ.

The extra new RM will try to be created and increased by introducing new rig changes without compromising the size. Mast sections and materials will be analysed to find possible advantages to lowering VCG whilst still maintain strength to the safety factor already employed by vessels.

Design strategies within the hull will also be examined to help increase the opportunity of matching the new Φ by making subtle changes without any fixed or structural.

Structural, design and performance considerations will be examined with new rig installed.

RM and Φ changes firstly and there fore try to reduce the need for any major changes to the vessel apart from the new rig and sails itself.

The need for the extra SA to a lighter vessel will be examined and attempted to be justified using small craft non-dimensional ratios to give an idea of typical ranges compared to of them originally, to then see how much improvement has been undertook in the related parameters. Also the parameters will give a rough measure of performance against boats of the same size.

Financial conclusions will be drawn from mast sections and material differences in price from particular companies for the given and appropriate dimensions and rig m to find viable reason for the rig change.

4. CALCULATIONS AND ANAYLASIS 4.1 TRANSVERSE SECOND MOMENT OF AREA AND RELATED HYDROSTICS

Keel calculations may be explored along with recommendation, but the study will aim to resolve the

Figure 3 4.1 (a) Calculation of transverse second moment of area Figure 3 gives the values obtained for the Bwl/Dwl coordinates measured physically from the vessels.

Simpson rule is then used to calculate the m3 submersed area. The information is used then to calculate the transverse second moment of area of the water plane using the following fundamental formula 

IT =2÷3*A

Where;  A=2÷3*sum of products

4.2 STATIC STABILITY GZ can now be calculated and then there actual righting moment by multiplying by Δ (kg) as seen in the following fundamental formula; 

BM= IT ÷Δ(m3)

[1]

GM=BM-BG (where BG= T÷2) GZ= GM sineΦ

How ever the information up to 30 degrees was sufficient to compare study GZ curve to builder’s actual GZ curve.

[1] GZ curve 44DS Mearsured specifications

The GZ values were calculated for each vessel so that cross comparison could be done with actual GZ curves supplied by builder. The subsequent RM values were plotted the results are as followed;

(Note; Full T will be used opposed to Tc)

0.6 0.5

GZ (M)

The calculations for the 44DS GZ curve using calculated Bwl measurements taken the results are;

0.7

0.4 0.3 0.2 0.1 0

  

0

IT=29.98 m4 Δ(m3)=13.3m3 BG=T÷2= 1.05m

10

20

30

40

50

60

Angle of Heel (Degrees)

Figure 4

There fore; 

BM=29.98÷13.3=2.254m GM=2.254-1.05=1.204 1.204*sinα*cosα=GZ

There fore 

GZ@5degrees= 0.104 GZ@10degrees=0.205 GZ@15degrees=0.301 GZ@20degrees=0.386 GZ@25degrees=0.461 GZ@30degrees=0.521 GZ@35degrees=0.565 GZ@40degrees=0.592 GZ@45degrees=0.602 GZ@50degrees=0.592

The results began to decrease at 45 deg due to method only really valid up to around 30-35 degrees, reasons for this is freeboard and superstructure appendages begin to become immersed.

Without the freeboard and coach roof added max GZ occurs at 45 degrees and displays a poor range.

Figure 5 [2] As shown in figure 4, the curve begins to drop off at the values beyond 45 degrees the graph wasn’t plotted any further for that reason.

How ever when you look at figure 5 you can see that max GZ does not occur till 80 degrees, despite the beginning of a slight dip in the same place that the fig 4 collapse in curve begins.

The reason for this as spoken about a few times now is at 45 degrees freeboard becomes immersed and at 75 degrees coach roof becomes immersed, both adding to extra wetted surface area, creating higher GZ and a much wider range. In order to create a full GZ curve for the final design and comparison model, IT will have to be calculated differently for different angles of heel to get a more accurate comparison and meaningful conclusion. 

GZ= (5-45degrees) IT



GZ= (45-70 degrees) IT + freeboard height



GZ= (70-85 degrees) IT + coach roof height + freeboard height

Note that the extra measurements being added to the original IT will be done before Simpson calculations are conducted and are only added to 4 stations at amidships.

The GZ and RM calculations are as follows for the 42DS;   

IT=25.48m4 Δ(m3)=11.5m3 BG=T÷2= 0.91

The heeling moments are now calculated for the 42 at a range of wind speeds, so that a comparison can be made between the following heeling moments for its standard rig and the calculations of the 44DS rig applied to the 42 hull. Then finally the two sets of heeling moments will be used to measure the new righting moment required for the new bigger rig applied to the 42.

The formula and calculations are as follows; 42 standard rig HM= 

There fore;

HM=SA*WP*HA*Cosα^2

[1]

Where WP= 0.0196*V^2 

BM=25.48÷11.5=2.215m Where V=wind speed knots GM=2.215-0.91=1.305

1.305*sinα*cosα=GZ There fore;

HA is explained in following text, and note wind speeds will be calculated at matched value of heel for example 20 knots, 20 degrees of heel.

GZ@5degrees=0.113

There fore;

GZ@10degrees=0.223

 

HA=8.5m SA=103sqm

GZ@15degrees=0.326 HM@10knts=103*0.0196*10^2*cos10*8.5*cos10= GZ@20degrees=0.419 1664kg/m GZ@25degrees=0.499 GZ@30degrees=0.565

HM@15knts=103*0.0196*15^2*cos15*8.5*cos15=

GZ@35degrees=0.613

3602 kg/m

GZ@40degrees=0.642

HM@20knts=103*0.0196*20^2*cos20*8.5*coz20=

GZ@45degrees=0.652

6060 kg/m

GZ@50degrees=0.642

The Rig from the 44DS was then taken and adopted to the hull of the 42, new HA was calculated from the increased sail area, and the same Δ (kg) was used.

The original weight of the rig will be deducted from overall displacement when new carbon mast is calculated used to replace original.

The following calculations and RM will still give a good close set of values, so that the required RM can be calculated and attempted.

There fore; RM=GZ*Δ (kg)

(where Δ (kg) =11,791)

RM@5degrees=1332.3 kg/m RM@10degrees=2629.3 kg/m RM@15degrees=3843.8 kg/m RM@20degrees=4940 kg/m

The HM calculated for the addition of the 44DS rig is as follows;

RM@25degrees=5883 kg/m

There fore;

RM@30degrees=6662 kg/m

 

HA=9.25 SA=113.7sqm

There fore; HM@10knts=113.7*0.0196*10^2*cos10*9.25*cos10= 2053.2 kg/m

the rig of 44DS without changing dimensions to see if VCG could be lowered significantly enough to match new HM. The specifications, calculations and results are as followed;

HM@15knts=113.7*0.0196*15^2*cos15*9.25*cos15= 4444.3 kg/m HM@20knts=113.7*0.0196*20^2*cos20*9.25*cos20= 7477.6 kg/m The HM created by the 44DS rig applied to the 42 produces a significant increase on what was already generated by the old and traditional rig. At its largest wind speed of 20 knots the increase is almost 1500 kg/m. The main reason for the increase HM is the increase HA this is a measure of distance between the C.E of the sails and the CLR of the underwater body.

The incensement in SA and mast length pushed the CE of the sails up by 0.75m as well as aft longitudinally of the mast by 1m, because the underwater body CLR remains the same so the heeling increases. See appendices for HA calculations and CE diagrams.

      

Mast length=18.9m Mast section=CC263=266/136mm Boom section=175*90mm Boom sec weight=2.5kg/m Mast sec weight=4.8kg/m Iy=1844Gnmm2 Ix=638Gnmm2 [3]

Therefore the weight calculations for new rig are; Mast height*kg/m of the mast section= 18.9*4.8=90.97kg/m Boom length*kg/m of mast section= 6.1*2.5=15.25kg/m The total weight of the rig is there fore;

4. MAST MASS CALCULATIONS

(90.97+15.25)+20%

The mast dimensions of the 44DS supplied by Selden mast are as follows;

= 106.16+21.23=127.39kg/m

      

Mast length= 18.9m Mast sec= R232=230*130mm Boom sec=175*90 Boom section weight=4.66kg/m Mast sec weight= 8.16 kg/m Iy =1820 m4 Ix= 643m4 [3]

The mast and boom are calculated as 80% of the overall rig for simplicity and as general rule of thumb, the following calculations are as followed;

The difference in weight of masts is 92kg/m, which is huge saving of weight whilst still maintaining stiffness and strength in both mast section x and y axis. For the information displayed for both of the masts, its clear that carbon fibre mast can withstand greater moment of elasticity at same dimension whist reducing weight.

The 44DS rig is now deducted from the overall displacement of the vessel and the new weight applied, all dimensions of rig remain same so HM remains the same at 9.25m.

The Δ (kg)-44ds rig= 11791-219.19=11,571kg/m

Mast height*kg/m for mast section= The Δ (kg) +carbon mast=11,571+127.39=11698.39 18.9*8.16= 154.2kg/m Boom length*kg/m for boom section=

There for new displacement used to calculate new GZ and RM will be 11,698 kg.

6.1*4.66=28.462 kg/m The total weight of the rig is there for =

The new GZ calculated from the reduced displacement and larger rig is;

(154.2+28.462)+20% = 182.66+36.53=219.19 kg/m The calculation of a carbon fibre mast section from the same company as Selden mast was chosen to replace

  

IT=25.48m4 Δ(m3)=11.4m3 BG=T÷2= 0.91

GZ@5degrees=1333.5kg/m

GZ@10degrees=2632.05kg/m GZ@15degrees=3860.34kg/m

6. CONCLUSION & FURTHER AREAS OF STUDY

GZ@20degrees=4959.95kg/m GZ@25degrees=5907.49kg/m GZ@30degrees=6831.63kg/m The results differs slightly at small angles of heel but because of the linear increase with angle of degrees, and at its max increase at 30 degrees there was 820kg/m increase in RM compared to that of the original 42 Δ(kg).

5. DISCUSSION OF RESULTS The results obtained for the new HM where quite large requiring a significant new RM. Despite almost 45% weight saving in the rig in the form a carbon fibre mast the overall RM only increased minimally at small angles of heel, with its max plotted at max heel and wind speed an extra 820kg/m was generated.

This shows clearly that extra RM needs to be generated at larger angles of heel and wind speed. Either weight is needed added lower down to lower G or additional weight added in the hull or super structure which will create a higher wetted surface area. Suggestions are that further reduction in weight of 150 kg above waterline mass may bring the RM up to the required amount at 20 degrees, 20 knots which is around 600kg/m.

Or additional the same amount of weight could in the opposite case be added lower down keel ballast to create a greater righting lever.

All weight savings that can be done have been made in rigging structures, which only leaves shifts in weight in mass and keel.

The calculations show on top of the new RM required not being sufficient enough to match new loads from rig, that also the longitudinal stability may be compromised by the addition of a larger rig and sail plan.

The CE calculations to determine HA showed that as well as increase in effort horizontally in sail plan that which lead to large increase in heeling lever at therefore HM there was a shift aft longitudinally.

The shift aft was by about 0.8m about the same as the shift up, this shift aft will lead to increase weather helm putting more stress on either the rudder or helmsman.

Incensement in the genoa would have been suggested to shift CE back forward of the mast back on top of the CLR of the underwater body. Obviously that is not possible as new HM already exceeds new RM.

The above study concludes that extra work needs to be done generate a larger RM to equal HM at larger wind speeds and angles of heel.

Conclusions drawn are that the 44DS vessel compensates for the new rig with its extra weight and ballast added in the hull to bring VCG down.

The main area of weight added above water line in the hull is the addition of the raised coach roof which was to give it the extra headroom, obviously the extra weight still in coach roof still wasn’t enough originally so changes in keel dimensions and locations of ballast were made.

Conclusions to creating further RM for the new rig of the 42 would be to make changes in keel and rudder dimensions and weights.

General assumptions made are that if changes are made in the keel adding ballast lower down with also a small increase in aspect ratio will create more RM to operate at larger wind speeds and angles of heel.

Where the 44DS lowers VCG and centre of gravity of the hull is in the form of the raised coach roof, the hope is that the carbon fibre mast has made a similar impact concluding that a change of underwater foil would create adequate stability and good speeds at lower winds for the 42 without increasing ballast to much, just moving it down.

The problem was that the Rustler 42 and 44DS are big heavy displacement boats designed for comfortable cruising not ocean racing and by the addition of carbon fibre mast doesn’t make the impact fully, for example if you put a carbon fibre mast on a lighter shallower boat you would see a huge shift down in VCG. Despite the small overall weight reduction of the vessel from the new mast and rig, this coupled with 44DS would create the desired outcome of the study.

7. BIBLIOGRAPHY [1] LARSSON, L. and ELIASSON, R. Principles of Yacht Design. McGraw-Hill, 2001 [3]Selden masts, 2010, Home page available@ (http://www.seldenmast.com/firstpage.cfm) accessed 3/05/011 [2] Rustler Yachts, Home page available @ (http://www.rustleryachts.com/) accessed 3/05/011