analysis of sailboat mast design

Sailboat Mast Design

LITERATURE REVIEW AND APPLICATION TO THE U20 CASE

BY : ALEXANDRE BERGERON ( 3784293 ) THESIS SUPERVISOR : DR. NATALIE BADDOUR

MCG 4100 THESIS DEPARTMENT OF MECHANICAL ENGINEERING

UNIVERSITY OF OTTAWA

APRIL 20TH, 2009

ABSTRACT

The following is meant to be a review of sailboat mast design methods and their practical application. In the first portion, the Euler‐Bernoulli beam theory, the P‐Δ method, Skene’s method and the Nordic Boat Standard are summarised and evaluated as design methods for masts. It was found that the Nordic Boat Standard represents the state of the art available in the public domain. In the second portion, the practical case of the Ultimate 20 racing yacht is reviewed. The Ultimate 20 has shown a tendency for the mast failing by buckling at a stress concentration on the bottom of the mast, and several solutions have been brought forward to solve this issue. In order to quantitatively establish which configuration is best, this boat’s mast was modelled according to Euler‐Bernoulli beam theory and practically tested using strain gauges. The results of both the mathematical model and the practical testing show consistent results and trends. It was found that the best single solution to reduce the chances of mast failure was the addition of baby stays.

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TABLE OF CONTENTS _Toc227999970

Abstract............................................................................................................................................ii

List of Figures ..................................................................................................................................vi

List of Tables ...................................................................................................................................ix

1.0 Introduction ......................................................................................................................... 1

1.1 Historical Context .................................................................................................................. 1

1.2 Problem Definition ................................................................................................................ 2

2.0 Literature Review................................................................................................................. 3

2.1 Euler‐Bernoulli Beam Theory ................................................................................................ 3

2.2 P‐Δ Method ........................................................................................................................... 5

2.3 Skene’s Method..................................................................................................................... 6

2.4 Design Standards................................................................................................................... 7

2.4.1 Nordic Boat Standard (NBS) ........................................................................................... 7

2.5 Design Method Overview.................................................................................................... 12

2.6 Literature Review Conclusions ............................................................................................ 13

3.0 The Ultimate 20 ................................................................................................................. 15

3.1 Background information ..................................................................................................... 15

3.2 Typical Failures And Hypothesis.......................................................................................... 17

3.3 U20 Proposed Solutions ...................................................................................................... 18

3.3.1 Backstay........................................................................................................................ 18

3.3.2 Baby stays ..................................................................................................................... 19

3.3.3 Combination ................................................................................................................. 20

3.4 U20 Modelling ..................................................................................................................... 21

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3.4.1 Model Assumptions...................................................................................................... 21

3.4.2 Model Geometry And Free Body Diagrams.................................................................. 21

3.4.3 Static Equilibrium Equations......................................................................................... 26

3.4.4 Modelling Results ......................................................................................................... 28

3.4.5 Modelling Conclusions.................................................................................................. 34

4.0 Testing on the Ultimate 20 ..................................................................................................... 36

4.1 Testing Plan ......................................................................................................................... 37

4.2 Physical Setup...................................................................................................................... 38

4.2.1 Dependant Or Measured Variables.............................................................................. 38

4.2.2 Loading or Controlled Variables ................................................................................... 41

4.3 Test Results .................................................................................................................... 43

4.3.1 Inconclusive Data .................................................................................................... 44

4.3.2 Standard Configuration........................................................................................... 45

4.3.3 Backstay .................................................................................................................. 48

4.3.4 Baby Stay................................................................................................................. 51

4.3.5 Backstay and Baby Stay Combination..................................................................... 53

4.4 Conclusions And Recommendations.............................................................................. 56

4.5 Future Testing ..................................................................................................................... 57

5.0 Conclusions ............................................................................................................................. 58

5.1 Design Methods and Realities............................................................................................. 58

5.2 Modelling and Testing: Suggested Improvements ............................................................. 59

5.3 Future Work ........................................................................................................................ 60

6.0 Bibliography ............................................................................................................................ 61

7.0 Appendices.............................................................................................................................. 62

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7.1 Righting Moment................................................................................................................. 62

7.2 Stress Concentrations ......................................................................................................... 64

7.3 Loos tension Gauge ............................................................................................................. 66

8.0 Private Communications from Mr. Sheppard......................................................................... 67

8.1 Testing PLan ........................................................................................................................ 67

8.2 May 14th 2008 Testing Report............................................................................................. 72

9.0 Sailboat Anatomy.................................................................................................................... 84

9.1 Glossary ............................................................................................................................... 85

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LIST OF FIGURES

Figure 2‐1: Column Support Factors (k factors) (2) ........................................................................ 4

Figure 2‐2: Euler's Buckling Formula (2) ......................................................................................... 4

Figure 2‐3: P‐Δ Effect (4) ................................................................................................................. 5

Figure 2‐4: Skene's Method (3)....................................................................................................... 6

Figure 2‐5: Rig Classification ( (3) figure 11.2 ) ............................................................................... 8

Figure 2‐6: Worst Case Transverse Loading ( (3) figure 11.3) ........................................................ 9

Figure 2‐7: Transverse Dimensioning ( (3) figure 11.9) ................................................................ 10

Figure 2‐8: Longitudinal Dimensioning ( (3) figure 11.10)............................................................ 11

Figure 3‐1: Ultimate 20 (4)............................................................................................................ 15

Figure 3‐2: Halyard Passage Stress Concentrations (5) ................................................................ 17

Figure 3‐3: U20 Backstay Arrangement (5)................................................................................... 18

Figure 3‐4: U20 Baby stay or High Wind Kit (5) ............................................................................ 19

Figure 3‐5: Baby Stay Chain Plate Mountings (5) ......................................................................... 20

Figure 3‐6: z‐x Plane Mast Model ................................................................................................. 22

Figure 3‐7: z‐y Plane Mast Model ................................................................................................. 23

Figure 3‐8: Boom Inwards at 0 Degrees and Outwards at 80 Degrees ........................................ 24

Figure 3‐9: z‐x Plane Bending Moment, Original Configuration................................................... 28

Figure 3‐10: z‐y Plane Bending Moment, Original Configuration................................................. 29

Figure 3‐11: z‐x Plane Bending Moment, Backstay Configuration ............................................... 30

Figure 3‐12: z‐y Plane Bending Moment, Backstay Configuration ............................................... 30

Figure 3‐13: z‐x Plane Bending Moment, Baby Stay Configuration.............................................. 31

Figure 3‐14: z‐y Plane Bending Moment, Baby Stay Configuration.............................................. 32

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Figure 3‐15: z‐x Plane Bending Moment, Combined Configuration............................................. 33

Figure 3‐16: z‐y Plane Bending Moment, Combined Configuration............................................. 33

Figure 3‐17: Comparison of Bending Moment to Boom Angle at the Critical Location (0.8255 m)....................................................................................................................................................... 34

Figure 4‐1: Data Acquisition Locations (5) .................................................................................... 37

Figure 4‐2: Example Mast Strain Gauge Arrangement (5)............................................................ 38

Figure 4‐3: Mast Strain Gauge Positions....................................................................................... 39

Figure 4‐4: Shroud Strain Gauges (5) ............................................................................................ 39

Figure 4‐5: Baby Stay Strain Gauges (5)........................................................................................ 40

Figure 4‐6: Shroud Tensioning Screw (5) ...................................................................................... 41

Figure 4‐7: Boom Vang Load Cell (5)............................................................................................. 41

Figure 4‐8: Spinnaker Loading Setup (5)....................................................................................... 42

Figure 4‐9: Non Zeroed Shroud Gauge Voltages for Combined Configuration, Boom Vang and Spinnaker Loaded.......................................................................................................................... 44

Figure 4‐10: Standard Configuration, Boom Vang Loaded ........................................................... 45

Figure 4‐11: Top Gauges, Standard Configuration, Boom Vang Loaded ...................................... 46

Figure 4‐12: Standard Configuration, Boom Vang and Spinnaker Loaded................................... 47

Figure 4‐13: Middle Gauges, Standard Configuration, Boom Vang and Spinnaker Loaded......... 47

Figure 4‐14: Backstay Configuration, Boom Vang Loaded ........................................................... 48

Figure 4‐15: Bottom Gauges, Backstay Configuration, Boom Vang Loaded ................................ 49

Figure 4‐16: Backstay Configuration, Boom Vang and Spinnaker Halyard Loaded...................... 50

Figure 4‐17: Baby Stay Configuration, Boom Vang Loaded.......................................................... 51

Figure 4‐18: Baby Stay Configuration, Boom Vang and Spinnaker Loaded.................................. 52

Figure 4‐19: Middle Gauges, Baby Stay Configuration, Boom Vang and Spinnaker Loaded........ 52

Figure 4‐20: Combined Configuration, Boom Vang Loaded ......................................................... 53

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Figure 4‐21: Combined Configuration, Boom Vang and Spinnaker Halyard Loaded ................... 54

Figure 4‐22: Top Gauges, Combined Configuration, Boom Vang and Spinnaker Halyard Loaded....................................................................................................................................................... 54

Figure 4‐23: Combined Configuration, Boom Vang and Spinnaker Halyard Loaded ................... 55

Figure 7‐1: Righting Moment (10) ................................................................................................ 62

Figure 7‐2: Stability Curve (3) ....................................................................................................... 63

Figure 7‐3: Stress Concentration Factors for a Rectangular Bar in Bending (11) ......................... 64

Figure 7‐4: Stress Concentration Factors for a Round Bar in Bending (11).................................. 64

Figure 7‐5: NBS Mast Hole Guidelines (6)..................................................................................... 65

Figure 7‐6: Loos Tension Gauge (5) .............................................................................................. 66

Figure 9‐1: Anatomy of a Sailboat (11) ......................................................................................... 84

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LIST OF TABLES

Table 2‐2: Design Method Overview ............................................................................................ 12

Table 3‐1: Ultimate 20 Specifications (4)...................................................................................... 16

Table 3‐2: Mast Model Measurements ........................................................................................ 24

Table 3‐3: Mast Model Angles ...................................................................................................... 25

Table 3‐4: Mast Model Input Values............................................................................................. 25

Table 4‐1: Test Scenarios .............................................................................................................. 38

Table 4‐2: Measured Variables ..................................................................................................... 40

Table 4‐3: Loading Variable Summary .......................................................................................... 42

Table 4‐4: Standard Configuration, Boom Vang Loaded .............................................................. 46

Table 4‐5: Standard Configuration, Boom Vang and Spinnaker Halyard Loaded......................... 48

Table 4‐6: Backstay Configuration, Boom Vang Loaded............................................................... 49

Table 4‐7: Backstay Configuration, Boom Vang and Spinnaker Halyard Loaded ......................... 50

Table 4‐8: Baby Stay Configuration, Boom Vang Loaded ............................................................. 51

Table 4‐9: Baby Stay Configuration, Boom Vang and Spinnaker Loaded ..................................... 53

Table 4‐10: Combined Configuration, Boom Vang Loaded .......................................................... 54

Table 4‐11: Combined Configuration, Boom Vang and Spinnaker Halyard Loaded..................... 55

Table 4‐12: Percent Improvement, Boom Vang Loaded .............................................................. 56

Table 4‐13: Percent Improvement, Boom Vang and Spinnaker Halyard Loaded......................... 56

1.0 INTRODUCTION

1.1 HISTORICAL CONTEXT

For several thousand years, sail powered craft were the primary means for trade, travel, warfare and exploration. Whether they are small river or lake boats used for fishing and local trade to the largest, steel clippers used for the tea trade in the latter part of the 19th century, all of these craft employ similar operating principles; aerodynamic lift, provided by sail made of fabric material. All of these vessels, regardless of their origin or sail configuration, require a structure to spread the sails themselves into their aerofoil shape. For the vast majority of cases, this is found to be in the shape of a single, or multiple masts, to which sails, spars and booms are attached.

With the advent of modern scientific and engineering processes, sailboat design and naval architecture in general remained a few steps behind. Indeed, with the advent of the steamship and further developments in propulsion, sails lost their role as prime mover for the world’s ocean shipping. This hindered development simply because the interest was nonexistent and the majority of the research and development was focused on commercial interests. Yachting, for a time, remained in the domain of wealthy or dedicated enthusiasts from various backgrounds. This remained true until the invention and widespread use of fibreglass as a hull construction material in the 1960s, when sailboats came within reach, pricewise, to the more average consumer.

Modern day yachts, in the vast majority, employ extruded aluminium alloy masts in their construction because it represents a good compromise for all of the above criterion as well as the ever so important issue of cost. Traditional designs, still in use today in many parts of the world, tend to use wooden masts and spars. Unfortunately, these traditional designs were never engineered into their shape, rather simply built using what was available and made strong enough to last for as long as possible.

As of the present day, sailboat design can be divided into two major categories; recreational or cruising boats and racing boats. Although many of the top level racing boats employ composite masts, several one‐design classes and Olympic level classes remain with aluminium alloy masts. Some so‐called “super‐yachts” employ steel masts, because of their large size. Thus, for the purpose of this study, only modern designs using more modern construction techniques will be analysed but only masts made from orthotropic materials will be considered.

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1.2 PROBLEM DEFINITION

Masts are defined as a vertical member designed to hold up sails, aerials, radar equipment or some other device that needs to be kept high up. In the particular case of sailing vessels, masts are subject to a rather unique and specific set of design requirements in order to accomplish their function. Sail masts are long, slender structures which must be able to carry the thrust loads imposed on them by the sails, which fluctuate constantly with the wind. Masts must also be capable of resisting the fatigue and creep caused by the environment in which they operate as well as impact loads generated by waves, operator error, collisions and the like. Unfortunately, several conflicting practical requirements impede the mast designer from simply creating a large, rigid structure akin to a radio tower or telegraph pole; the need for a low center of gravity and light weight as well as aerodynamic efficiency considerations. These aerodynamic drag effects are known as windage. Experience also shows us that a flexible mast is desirable in order to tune, or adjust the sail’s shape to improve its effectiveness. The mast designer must then consolidate all of these requirements into a cost‐effective package

The present research is an attempt to determine the state of the art in design and analysis methods for sailboat masts. As such, several methods will be discussed:

• Euler‐Bernoulli beam theory

• P‐Δ beam‐column design

• Skene’s method

• Nordic Boat Standard

The second part of this research is to try to apply these methods to a real world situation on the Ultimate 20 racing yacht, which have had some documented mast failures. In trying to determine whether or not the mast design is adequate, it will be compared with several possible solutions to solve the mast issues. The third and final part is a discussion on physical testing conducted on the Ultimate 20 and the effects of changes in rigging.

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2.0 LITERATURE REVIEW

The following represents what is “state of the art” in terms of mast design and analysis procedures.

2.1 EULER‐BERNOULLI BEAM THEORY

The following information is from (2).

Euler‐Bernoulli beam theory is the standard engineering approach to beam‐type of problems; it was developed in the mid 18th century by Leonhard Euler and Daniel Bernoulli. In essence, it is a combination of Hooke’s law of elasticity and calculus methods in order to calculate the deflection or maximal loads that can be applied to a beam.

The basis for this theory is an equation that relates beam deflection to applied load:

Where: x is the position along the beam

u is the deflection of the beam

w is the distributed load along the beam

E is the elastic modulus of the material

I is the moment of inertia of the cross‐section of the beam

Derivatives of the equation yield relationships between slope, bending moment and shear forces in the beam. These relationships also lead to the concept of stresses and strains in the beam.

As this type of beam theory is a well understood analysis tool, the only issue with applying it to sailboat masts lies in properly defining the loading conditions.

A useful development of this beam theory is its application to explain the buckling phenomenon of columns. This is a linearization of a non linear phenomenon (2), as columns can buckle in several different manners according to their end conditions; these end conditions being given in Figure 2‐1. Euler’s buckling formula can be used to determine the required cross‐section to withstand a given buckling load

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Figure 2‐1: Column Support Factors (k factors) (2)

Figure 2‐2: Euler's Buckling Formula (2)

As shown in Figure 2‐2, Euler’s formula is re‐arranged to determine the required stiffness EI, in order to withstand a known compressive load.

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2.2 P‐Δ METHOD

The following information is from chapter 8 of (4).

The P‐Δ method was originally developed as an extension of the Euler buckling method for applications in civil engineering. It is used to analyse and design beam‐columns, which are defined as “members in a structure that are subjected to both significant axial load and bending moments” (4). As beams are usually considered to be subjected to negligible compressive loads and columns are subjected to negligible bending loads, this method is an attempt at combining the two loading modes.

Figure 2‐3: P‐Δ Effect (4)

In Figure 2‐3, a beam‐column is loaded both in compression by Cf and laterally by a distributed load qf. At the ends, a moment Mf is also present. Similar to a beam, the applied loads of qf, Mf1 and Mf2 create first order moments in the member, illustrated here as Mo. These are calculated by solving for equilibrium in the undeformed beam‐column. These loads also cause deformation of the member by a quantity v, which is a function of position along the beam.

Because of the compressive load Cf and the deformation of the member caused by the lateral loads and moments, additional moments exist which cause additional deformation of the beam‐column. These additional moments are termed second order moments, because they would not be present in the beam‐column in its undeformed shape. They are illustrated here as Cfv. These second‐order moments add to the total deflection of the member, which leads to additional second order moments. Eventually, this effect stabilises when the final deformed shape is achieved.

The P‐Δ method should then be representative of the loading scenario on a mast where it is subject to compressive loading from the shrouds and lateral loads from the sail and swaying of the boat. At this time, no application of this method to a sailboat mast has been found.

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2.3 SKENE’S METHOD

The following information is from chapter 11 of (1)

Skene’s method is a combination of empirical factors, severely outdated since this method was originally published in 1904. There exist several variations, and it would appear that with each publication, certain factors are modified, added or removed. Several authors have also published re‐iterations of Skene’s method by performing such modifications. It remains in essence the same in all its forms.

Essentially, Skene employs the static measurement of the stability of the yacht and its buoyancy given in terms of a righting moment. This moment is further clarified in appendix 7.1 Righting Moment.

The mast is assumed to be a single component (no concept of panels). The method essentially determines the maximal amount of compression present on the mast, regardless of how the shrouds or rigging is set up.

Figure 2‐4: Skene's Method (3)

Here, in Figure 2‐4, we can clearly see empirical factors to compensate for the stays and greater heel angles. No information on exactly how these factors are determined could be found in the relevant literature.

With a maximal compression, an Euler buckling analysis is then performed on the mast in order to determine its required cross‐section. This follows the same procedure described in section 2.1.

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2.4 DESIGN STANDARDS

As yacht design evolves, new standards as well as updated historical ones are continuously developed. These standards include Lloyd’s register, American Boat Standard, ISO, Bureau Veritas, Det Norske Veritas, Germanischer Lloyd and Nordic Boat Standard. In terms of sailing vessel mast design, only the Nordic Boat Standard (NBS) provides a method specific to sailboat mast design.

It is interesting to note that even the famed Lloyds’s register founded in 1834, with much historical data from the wooden sailing ship era, does not provide a design standard for masts and spars.

2.4.1 NORDIC BOAT STANDARD (NBS) The following information is from Chapter 11 of (2).

An outline of the method is as follows:

• Determine the righting moment at 30 degrees

• Identify the rig type according to the charts and nomenclature

• Apply the equations to find the required moment of inertia Firstly, NBS begins by describing the type of craft to which it is applicable; small craft less than

15 metres, with a foresail area less than 1.6 times the mainsail area. Secondly, NBS states the nomenclature as to the type of rig, this being dependant on the number of spreaders (if any) and whether or not the shrouds are attached to the masthead (top of the mast) or not. This nomenclature is clarified in Figure 2‐5.

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Figure 2‐5: Rig Classification ( (3) figure 11.2 )

In order to dimension the mast, the loading is based on the righting moment at 30 degrees of heel for the hull in question, for further details, see appendix 7.1 Righting Moment. This is determined by relating the buoyancy of the hull to its inherent stability. This value, in terms of a moment can then be related to the sail loading. Since sail loads are by their nature, varying according to the conditions, this is a design assumption. For design purposes, two worst case scenarios are applied, one with only a full working headsail and the second with a reefed mainsail.

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Figure 2‐6: Worst Case Transverse Loading ( (3) figure 11.3)

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This loading is then applied to the respective panels of the mast for both cases in order to

determine their necessary moments of inertia in each of the transverse and longitudinal planes. The worst case transverse loading scenarios are shown in Figure 2‐6. From these moments of inertia, a suitable mast cross‐section can be chosen from what is commercially available or fabricated. This step for the transverse process is described in Figure 2‐7 and the longitudinal process in Figure 2‐8.

Figure 2‐7: Transverse Dimensioning ( (3) figure 11.9)

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Figure 2‐8: Longitudinal Dimensioning ( (3) figure 11.10)

This approach does not however, directly address the issues of buckling, nor the fact that the mast loading originates at the sails; it is however, the most thorough initial design method available.

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2.5 DESIGN METHOD OVERVIEW

To allow the designer to select a mast design method, it is necessary to compare them for all of their advantages and disadvantages. This is done in Table 2‐1.

Table 2‐1: Design Method Overview

Method Advantages Disadvantages

Euler-Bernoulli

• Common and well understood

• Proven to give accurate results

• Adaptable to any type of design

• Requires accurate loading inputs • Can be tedious to calculate all possible

loading scenarios

P-Δ • Masts apply well to Beam-Column theory

• Standards exist for many materials

• Never applied to sailboat masts • Requires known load inputs

Skene’s • Historically proven and in use for almost a century

• Quick and simple • Easily applied to an initial

design

• Entirely empirical • Not based on actual sail loads • Requires that the hull shape already be

reasonably determined in order to obtain the righting moment

Nordic Boat Standard

• Most modern • Considers the mast in

panels • Allows for tapered mast

designs • Easy to optimise the

solution

• Not based on sail loads • Requires that the hull shape already be

reasonably determined in order to obtain the righting moment

• Is only applicable to the standard type of Bermuda rigs

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2.6 LITERATURE REVIEW CONCLUSIONS

Although several methods are available to the yacht designer, all of these leave something to be desired. Primarily, all the methods described here lack a clearly defined link to sail loading, which is naturally what actually causes mast loads in the first place.

The more traditional engineering approaches to beam or column design such as the Euler‐Bernoulli and P‐Δ methods are sound in principle. They are well understood and, if the problem is defined correctly, yield fairly accurate results. Unfortunately, the issue with these is simple: How would a designer model the sail loads? These approaches are generic and not specialised; therefore they offer no solution to load modelling. It is up to the designer to resolve the loading.

Skene’s method is a method that shows its age quite clearly; while surely satisfactory at the time of its original publication in 1904, it does not offer sufficient justifications for a great many of its underlying assumptions. At issue here are two coefficients, the 1.85 for rigging and the 1.5 for heel angles. These are given without much justification and appear to be in place simply because they always have been and have always worked. In other “refined” versions of Skene’s method, the same problem exists; without knowing the proper origin or impact of these coefficients, this method leaves very little room for optimisation of the design.

The second point of contention with Skene’s method is its oversimplification of the problem of mast design. It does little to account for different configurations in rigging and shrouds or mast tapers. There is no care taken to account for the sideways forces imparted on the mast by sails or dynamic effects of waves and so on. Everything is neatly summed up as a maximal compressive force which simply leads to a buckling analysis. In this sense, Skene’s method is very limiting because the designer cannot optimise his or her mast design.

The Nordic Boat Standard is the most modern approach to mast design and the one which most resembles a modern design code used for engineering applications. It does appear to model the problem in a sufficient amount of detail to compare it with reality; concessions for rigging configurations, mast tapers, the panel concept and longitudinal and transverse loading scenarios. Unfortunately, the standard limits itself to Bermudan style sail plans, which although very common, are not universally adopted. The assumption which relates Skene’s method and the Nordic Boat Standard is the use of a 30 degree righting moment to define the loads imposed on the mast. No justification for this was found in any literature pertaining to Skene’s method, and references on the Nordic Boat Standard say this: “The starting point when dimensioning the rig is to calculate the righting moment. It is commonly agreed that a heel angle of 30o is a good design angle. This corresponds to a reasonably high wind strength with the sails still generating high loads and the boat making good speed through the water. Letting the boat heel over more....in reality means a slower boat owing to increased resistance, with a correspondingly smaller dynamic force.” (6).

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A righting moment, in a nutshell is a static measurement made on a boat’s hull, giving a measure of its stability in still water. Although it can be made with calculation and verified with experimentation, the righting moment does not account for factors like movement, water resistance, hull planning, dynamic forces, wind gusts, waves or anything else likely to affect a mast. No justification was found for using the moment at 30 degrees of heeling angles other than the completely arbitrary justification given above. In practice, this could be any other angle the designer wishes to use. Most notably, the concept of a righting moment cannot be used to model the loads imparted to the mast via the use of a spinnaker type sail. The spinnaker is a large parachute‐like headsail that is used for sailing down wind. In particular, the masts of the boat of interest to this discussion, the Ultimate 20, have been known to fail under spinnaker loading.

In summary, it is clear that although much progress has been made in the last century in many aspects of sail boat design, there still exists a very large gap in the pool of public knowledge of mast design. Since the yachting industry is a very competitive one, ship designers tends to use their own, proprietary methods to ensure that their products offer safe and satisfactory performance. More to the point, no method exists to relate the aerodynamic loads of the sails, the dynamic effects of the boat motion and the many sail configurations possible. As a design problem, the tools exist to perform the design and analysis of a mast, but no method on how to accurately determine the loads on the mast is in the public domain.

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3.0 THE ULTIMATE 20

3.1 BACKGROUND INFORMATION

The Ultimate 20 (U20), as shown in Figure 3‐1, is a modern one‐design sailing yacht designed by Jim Antrim of Antrim Associates‐Naval Architects (3). A one‐design yacht is exactly as the name implies, all of the yachts produced adhere to strict rules regarding their construction, maintenance, sail manufacture and modifications. These rules are then regulated by a class association, run by the owners. The whole idea behind the concept of a one‐design is to promote fair and even racing between boat owners.

Figure 3‐1: Ultimate 20 (4)

The U20 is also designed to be a towable vessel, meaning that a basic requirement of the design was to ensure easy installation and removal of the mast and rigging for towing purposes. As such, the mast is deck‐stepped, and all hardware is easily removed. The towing requirement also means that the whole assembly should be light enough to be easily handled by one or two people. The typical dimensions of a standard U20 is given in Table 3‐1, as specified by the manufacturer.

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Table 3‐1: Ultimate 20 Specifications (4)

Specification

LOA (length overall) 20’ 10” LWL (length at water line) 18’ Beam (maximum width) 8’ 6” Draft (board up / down) 9” / 5’ Displacement 1260 lbs Ballast 450 lbs Jib Area 100 sq. ft. Mainsail Area 205 sq. ft. Spinnaker Area 454 sq. ft. Year Introduced 1994

This is therefore, a fairly affordable high performance craft, capable of speeds approaching 20 knots. It is also fairly light, which minimises rigging loads. Since its introduction in 1994, over 200 vessels have been sold and sailed. Local to the Ottawa region, 6 registered boats operate in the area, with several hailing from the Nepean Sailing Club.

Since 1994, Ultimate 20s have been successful both commercially and in their goal to be a fast towable sailboat; however, several mast failures have been reported in the last 15 years which bring up questions regarding the soundness of the mast’s design.

The mast’s collapse is not a pleasant experience; it results in immediate loss of control, major damage to the expensive sails and can result in serious injury to crew members. It is therefore in the class’s best interest to better understand the conditions which lead to the failures and how best to rectify the problem.

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3.2 TYPICAL FAILURES AND HYPOTHESIS

Generally most reported failures, for which some information was available, occurred during high wind conditions, somewhere upwards of 20 knots. These failures occurred under various boom angles; when reaching (with the wind perpendicular to the length of the boat) or when sailing downwind (with the wind parallel to the length of the boat, coming from the stern).

In all cases, masts broke at nearly the same point; where a hole is drilled into the side of the mast in order for a halyard to pass through to the top, see Figure 3‐2. This creates a stress concentration along the port side of the mast, near the foot or base of it. For an explanation of stress concentration factors and how they relate to masts, see appendix 7.2 Stress Concentrations.

Figure 3‐2: Halyard Passage Stress Concentrations (5)

This stress concentration is fairly high and localised; a single large hole for the halyards to pass through as well as four smaller holes housing rivets for the fixture. Most of the failures involved the failed mast toppling over to the starboard side, which would suggest that the stress concentration failed in compression.

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3.3 U20 PROPOSED SOLUTIONS

In order to attempt to rectify the mast collapse problem, several trial solutions have been proposed and field tested by some U20 owners. None of these solutions are homologated by the class, thus are illegal to use in races and regattas. It would be in the best interest of the class association to homologate the use of an acceptable solution in order to rectify the problem, yet no scientific testing has been undertaken to validate any of the proposed solutions.

3.3.1 BACKSTAY One of the peculiarities of the U20 design, which tends to conflict with traditional wisdom is not to include a backstay in the original rigging design. A backstay is simply a cable attached to or near the top of the mast and running as far back to the stern as possible. This arrangement can however cause some interference issues with the mainsail.

Figure 3‐3: U20 Backstay Arrangement (5)

In order to avoid the interference issue, a so‐called backstay crane, seen in Figure 3‐3, is attached to the top of the mast. This enables the cable to pass above the mainsail and clear it under any conditions or boom angle.

As previously mentioned, backstays are usually included in most modern yachts to counteract the strong pull forwards caused by the spinnaker sail which is usually attached in an opposite direction to the backstay.

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3.3.2 BABY STAYS Baby stays are in fact, a small set of stays or shrouds, designed to minimise deflection at their attachment point. In practice, they are different to mast shrouds in that their attachment to the deck does not extend all the way to the edges of the vessel. This arrangement in practice adds another panel to the mast.

Figure 3‐4: U20 Baby stay or High Wind Kit (5)

In the case of the U20, the idea behind the baby stay is to minimise the deflection of the mast near the halyard passage stress concentration. Its installation is by adding chain plate fixtures to the top of the deck and using the mainsail track to mount the stays to the mast. This is a solution offered by the manufacturer under the name “High Wind Kit”. A close up view of the baby stay arrangement can be seen in Figure 3‐4. This retrofit does require drilling and mounting fittings for the chain plates in the hull, these are visible in Figure 3‐5.

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Figure 3‐5: Baby Stay Chain Plate Mountings (5)

3.3.3 COMBINATION The final proposed solution is to employ both the baby stays and the backstay together in unison. This would seemingly make the mast much stiffer and, at first glance perform better. In practice however, this may simply force a mast failure to occur at another point instead of at the halyard passage.

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3.4 U20 MODELLING

In order to simulate the problem presented by the Ultimate 20, it was decided to model the mast as a simple three‐dimensional beam problem, following Euler‐Bernoulli beam theory principles. This will give results as to the maximum bending moments found at the critical location in the mast, namely where the stress concentration at the halyard passageway is located. Since the bending moments are directly related to the stresses in the mast by a proportion that is related to the geometry of the beam, this is sufficient to establish comparisons. Globally, this will also permit a quantitative comparison between the different solutions as well as with results found by the testing described in section 4.0.

3.4.1 MODEL ASSUMPTIONS

1. Mast is modelled as a constant cross‐section beam. 2. Consider shrouds as point loads. 3. Geometry measurements not readily available in reference literature shall be estimated. 4. Although mast is keel‐stepped through the hull of the U20, we will consider it to be flush with

the deck and this mounting as a pinned connection. 5. The shrouds are slack on the side opposite the boom as thus can be neglected. 6. Moment caused by backstay crane attachment is ignored: the backstay is modelled as attached

directly to the mast. 7. Compressive forces leading to additional stresses in bending (buckling) will not be directly

considered.

In order to maintain a consistency with the testing performed, the mast model shall be loaded in a similar fashion to the scenario described by the testing in section 4.2. Distributed sail loading will not be considered.

3.4.2 MODEL GEOMETRY AND FREE BODY DIAGRAMS The U20 mast is modelled in two planes, the z‐x plane and z‐y plane with the base of the mast as the origin. The z‐axis is defined as the vertical running along the mast, the y‐axis runs horizontally to the bow and the x‐axis from the origin to the starboard side. All of the rig loads, mast base reaction forces and boom forces are shown in Figure 3‐6 and Figure 3‐7.

21

Figure 3‐6: z‐x Plane Mast Model

22

Figure 3‐7: z‐y Plane Mast Model

23

A table of the relevant dimensions is provided in Table 3‐2, these were given in the literature in approximate inches. For modelling purposes, the conversion to SI units is given in parentheses. The bold values are estimates.

Table 3‐2: Mast Model Measurements

Location x-value inches (m) y-value inches (m) z-value inches (m) Shroud 47 (1.1938) 29.5 (0.7493) - Upper Shroud (US) - - 315 (8000) Top of Mast - - 360.5 (9.1574) Baby Stay 12 (0.3048) - 32.5 (0.8255) Spreaders 12 (0.3000) 18 (0.4575) 156 (3.9625) Forestay Chain Plate - 87.5 (2.2225) - Backstay Chain Plate - 160 (4.0640) -

In order to vary the model similarly to the testing procedure, the boom angle will vary within the model, from 0 to 80 degrees; this corresponds to the typical maximum and minimum angles permitted by the boat’s setup. In order to better visualise this angle, it is shown in Figure 3‐8.

Figure 3‐8: Boom Inwards at 0 Degrees and Outwards at 80 Degrees

Thus, with a boom length of 123 inches (3.1242 m), the x and y coordinates will vary in each plane according to the following trigonometric relations:

[ ][ ]sin(boom angle)

cos(boom angle)Boom Boom

Boom Boom

x Length

y Length

=

=

This will impact the angles of Fboom according to a similar relation. Other angles of interest for loads in both planes are given in Table 3‐3.

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Table 3‐3: Mast Model Angles

Location Θ (degrees) γ (degrees)

top 85.75 83.53 Upper Shroud (US) 77.29 85.79 Lower Shrouds (LS) 85.67 83.41 Baby Stay 69.74 - Forestay - 66.07 Spinnaker - 75

3.4.2.1 LOADS In order to obtain model results under similar loading conditions as those encountered during testing, the input loads are given the same values as the physical test values described in section 4.2.2.

Table 3‐4: Mast Model Input Values

Loading Value

Upper Shroud 500 lbs (2225 N) Lower Shroud 500 lbs (2225 N) Spinnaker Halyard 150 lbs (670 N) Boom Vang 400 N Boom Cable 280 N Boom Angle 0 to 80 degrees Gooseneck 400 N

The boom vang input is an average of the values encountered during the test. Also note that since the boom is connected to the mast by means of a pin joint known as a gooseneck, the force at this joint in each plane varies according to boom angle. This force, along with boom cable force causes the gooseneck to apply a force on the mast, the magnitude of which has been set at 400 N.

The boom cable force, using the law of levers has been approximated to 280 N, or roughly 70% of the physical input given in the test scenarios.

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3.4.3 STATIC EQUILIBRIUM EQUATIONS To solve the model for the reaction forces and to determine the bending moments, the following static equilibrium equations were derived.

3.4.3.1 Z‐X PLANE Force summation in the x‐direction:

cos cos cos cos 0us us Ls Ls x Babystay Babystay xGooseneck Boom BoomF F R F F Fθ θ θ− + + + − − + θ =

z

Sum of moments about the spreaders:

cos (z ) cos (z ) ( )

cos (z ) 0Boom Boom mast spreaders US Top US spreaders xGooseneck Spreaders Boom

x Spreaders BabysStay BabyStay Spreaders Boom

F z F z F z

R z F z

θ θ

θ

− − + − +

− − − =

−

Sum of moments about the top of mast:

mast mast mast

mast mast

cos (z ) cos (z ) (cos cos )(z )

cos (z ) (z ) 0US US US LS LS Spreaders US Top US Spreaders

BabyStay Boom BabyStay x mast xGooseneck Boom

F z F z F z

F z R z F z

θ θ θ θ

θ

− + − − + −

− + + − =

+

zθ

Sum of moments about the base of mast:

cos z (cos cos ) cos cos

cos 0BabyStay BabyStay Boom US Top US LS LS Spreaders US Top US

Boom Boom Mast xGooseneck Boom

F F F z F

F z F z

θ θ θ θ

θ

⎡ ⎤+ + − −⎣ ⎦+ − =

3.4.3.2 Z‐Y PLANE Force summation in the y‐direction:

ker kercos cos cos cos cos

cos 0Forestay Forestay US US LS LS y Boom Boom Spinna Spinna

Backstay Backstay yGooseneck

F F F R F F

F F

γ γ γ γ γ

γ

− − − − +

− + =

Sum of moments about the spreaders:

ker kercos cos cos cos ( )

( ) 0Boom Boom Spinna Spinna Forestay Forestay Backstay Backstay mast Spreaders

y Spreaders yGooseneck Spreaders boom

F F F F z z

R z F z z

γ γ γ γ⎡ ⎤− − + −⎣ ⎦+ + − =

Sum of moments about the top of mast

[ ]cos ( ) ( ) cos cos ( )

0US Top mast US yGooseneck mast Boom US US LS LS mast Spreaders

y mast

F z z F z z F F z z

R z

γ γ− + − + − −

− =

γ

Sum of moments about the base of mast:

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ker ker

(cos cos ) cos cos

cos cos cos cos

0

US top US LS LS Spreader US US US

Boom Boom Forestay Forestay Spinna Spinna Backstay Backstay mast

yGooseneck Boom

F F z F z

F F F F

F z

γ γ γ γ

γ γ γ γ

⎡ ⎤+ − +⎣ ⎦⎡ ⎤+ − − +⎣ ⎦

− =

z

These equations were inputted to a computer spreadsheet to facilitate the repetitive calculations and to allow for easy modification of the input variables.

As an output of these results, bending moments are suitable since they are proportional to stresses and, assuming linearly elastic material behaviour, proportional to strains. From basic relations, assuming a rectangular beam:

= and E

Where:σ:stressε:strainE: elastic modulusI: cross-sectional moment of inertiac: distance from the neutral axis

McI

σ σ ε=

We can obtain a proportional coefficient between bending moment and strain.

= McEI

ε

For the model at hand, this information is not known or measured with enough certainty. For instance, the type of aluminium alloy or moment of inertia of the mast is unknown. Instead of incorporating additional factors in the calculations, pure bending moments will be suitable to establish trends.

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3.4.4 MODELLING RESULTS The following section illustrates bending moment diagrams calculated with the model. These should reveal the impact of each solution on the tendency of the mast to deform.

3.4.4.1 ORIGINAL CONFIGURATION The original configuration model, which omits the baby stays and backstays, was analysed for 5 different boom angles; these are 0, 15, 45, 60 and 80 degrees. This is shown in Figure 3‐9 and Figure 3‐10 for both orthogonal planes of interest.

Figure 3‐9: z‐x Plane Bending Moment, Original Configuration

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Figure 3‐10: z‐y Plane Bending Moment, Original Configuration

In both planes, we can see the 4 critical locations. These are the boom (gooseneck) (0.8255 m), spreaders (3.9624 m), upper shroud (8 m) and the top of the mast (9.1567 m). Since the boom angle varies, we can see an increase of the bending stresses at this location in the z‐x plane with an increase in the boom angle. Inversely, this phenomenon is also present in the z‐y plane, where the bending stresses decrease as the boom angle increases.

Interestingly, the change is boom angle seems to make little difference to the bending moment in the upper portions of the mast in both the z‐x and z‐y planes. This is likely due to the fact that in this part of the mast, the major portion of the loading is from the pre‐tensioned shrouds, which are not varied, rather than the boom swinging.

The relatively lower magnitude bending stresses imply that the mast is not as well constrained as in other cases and thus more able to deform freely.

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3.4.4.2 BACKSTAY CONFIGURATION The backstay configuration model, which omits only the baby stays, was analysed for 5 different boom angles. This is shown Figure 3‐11 and Figure 3‐12 for both orthogonal planes.

Figure 3‐11: z‐x Plane Bending Moment, Backstay Configuration

The backstay solution shows absolutely no change to that of the original configuration in the z‐x plane. This can easily be explained by the fact that the backstay itself generates no force component in the z‐x plane.

Figure 3‐12: z‐y Plane Bending Moment, Backstay Configuration

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Where the backstay does show an impact is on the z‐y plane, the bending moment is actually reduced at the base of the mast. This means that a large portion of the forces that were applied to the base of the mast in the z‐y plane are now redistributed to the backstay.

Again for this scenario, in a manner similar to that of the original configuration, the boom angle has no impact of the magnitude of the bending moment in the upper portions of the mast, above the spreaders. The reason for this is the same; the boom load at the top is minimal compared to the shroud pre‐tensions.

3.4.4.3 BABY STAY CONFIGURATION The baby stay configuration model, which omits only the backstay, was analysed for 5 different boom angles. This is shown in Figure 3‐13 and Figure 3‐14 for both orthogonal planes.

Figure 3‐13: z‐x Plane Bending Moment, Baby Stay Configuration

In the z‐x plane, the impact of the baby stays is visible by the increased bending moments in the lower portions of the mast. Since the baby stay forces act at the stress concentration (0.8255 m), this is where the increase takes place. This force also affects the moments at the base of the mast, since the baby stay force is counterbalanced by the base. There is a large change at these two locations (0 m and 0.8255 m) when compared to the original configuration.

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Figure 3‐14: z‐y Plane Bending Moment, Baby Stay Configuration

The baby stay solution shows no change in the z‐y plane and is identical in this respect to the original configuration. This is logical, since the baby stays physically only act in the z‐x plane and add no additional force components to the model in the z‐y plane.

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3.4.4.4 COMBINED CONFIGURATION The combined configuration model was analysed for 5 different boom angles. This is shown in Figure 3‐15 and Figure 3‐16 for both orthogonal planes.

Figure 3‐15: z‐x Plane Bending Moment, Combined Configuration

Figure 3‐16: z‐y Plane Bending Moment, Combined Configuration

By the very nature of this solution, it combines the elements from both the baby stays and the backstay. Since the baby stay only contributes to the overall bending moment in the z‐x plane, the combined solution possesses the same bending moment curve in the z‐x plane. Similarly for the

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backstay, since it only contributes to the overall bending moment in the z‐y plane, the combined solution possesses the same bending moment curve in the z‐y plane.

3.4.5 MODELLING CONCLUSIONS

Figure 3‐17: Comparison of Bending Moment to Boom Angle at the Critical Location (0.8255 m)

Keeping in mind that the goal is to minimise the possibility of a buckling failure of the mast at the stress concentration present at the halyard passageway, each solution must be compared as to its ability to provide maximum support for the mast at this location. This comparison is shown in Figure 3‐17, where the bending moment at the stress concentration (0.8255 m) is plotted in both the z‐x and z‐y planes for each trial boom angle. What this essentially illustrates is that the only solution actually affecting the results at this location is the baby stay solution.

Since it has already been established that the backstay has no impact whatsoever in the z‐x plane, it is evident that there should only exist two variations of the z‐x curve in Figure 3‐17. These are

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the original/backstay z‐x curve, and the baby stay/combined z‐x curve. In contrast, no solution has an impact on the z‐y plane at the stress concentration; therefore all the z‐y curves are similar in each scenario.

This implies that if the goal is simply to better constrain the mast to prevent buckling at this critical location, the baby stay solution is the only one which can accomplish any improvement.

As whole, this simplified model does leave room for improvement. Several modifications or changes could be made that would improve the accuracy of the model:

1. True sail loads could be considered in the form as a distributed load along the length of the mast.

2. Compression along the mast could be considered and, with the appropriate data on elastic modulus and moment of inertia, buckling could be accounted for.

3. Another force could be added to simulate jib tension. 4. Additional degrees of freedom could be added for the different sail force magnitudes and

their various possible orientations. 5. Mast taper and rake could be considered.

These improvements would indeed lead to better understanding of the mast behaviour under certain loading conditions. As with all models, the issue remains what values to input to the model. In this case, this model was set up in parallel with the test conditions considered in section 4.0 Testing on the Ultimate 20. In order to simulate reality, several measurements remain unknown. These are:

1. Actual main sail force magnitude, distribution and orientation. 2. Compression caused on the mast by the sail. 3. Spinnaker tension and orientation on its halyard. 4. Jib tension on forestay.

As a design tool, this is model is limited to the designer’s ability to successfully predict the loading conditions imposed on the mast, which remains limited.

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4.0 TESTING ON THE ULTIMATE 20

In the summer of 2008, an Ultimate 20 owner and engineer, Mr. Van Sheppard, decided to perform some experimental tests on his boat in order to determine what solution is best in order to prevent future mast failures and to better understand the effects of the forces at play. These results would then be distributed to the class association in order to initiate the steps needed to modify the rules and achieve a solution to prevent future mast failures. The objectives are specified here by Mr. Sheppard, (note that HWK refers to the high wind kit or baby stays):

1. To understand the loads experienced by a U20 mast when the spinnaker halyard is highly loaded, the vang is also loaded and the boom is allowed to move out from the centerline of the boat.

2. To understand how the HWK helps to improve the loads experienced by a U20 mast when tested under the same conditions described in Item 1 above.

3. To understand how a backstay helps to improve the loads experienced by a U20 mast when tested under the same conditions described in Item 1 above.

4. To understand how a combination of the HWK and a Backstay helps to improve the loads experienced by a U20 mast when tested under the same conditions described in Item 1 above.

This testing should also allow for a decent idea of the deflection involved under controlled conditions and enable a valid comparison with any mast design model. At the very least, this would allow an objective and quantifiable comparison between all of the proposed solutions.

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4.1 TESTING PLAN

In order to accomplish the goals set forth, a series of strain gauges would be attached to the mast in what were thought to be critical locations. Several gauges should also be used on the fittings for the shrouds in order to determine the loads on the shrouds. Load cells should be used to measure the input loads at the boom vang and spinnaker halyard. This should give an accurate picture of the deflections involved. The desired arrangement is presented in Figure 4‐1.

Figure 4‐1: Data Acquisition Locations (5)

Note that this diagram includes the backstay and baby stays. The tests would be repeated without them, using them individually and in combination in order to establish a proper comparative basis.

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The test cases are as follows:

Table 0‐1: Test Scenarios

Test Number Support Configuration Boom Vang Loaded Spinnaker Halyard Loaded

0 Standard Configuration No No 1 Standard Configuration Yes No 2 Standard Configuration Yes Yes 3 Backstay Yes No 4 Backstay Yes Yes 5 Baby Stay Yes No 6 Baby Stay Yes Yes 7 Combined Yes No 8 Combined Yes Yes

Original documentation pertaining to testing setup is found in appendix 8.0 Private Communications from Mr. Sheppard.

4.2 PHYSICAL SETUP

4.2.1 DEPENDANT OR MEASURED VARIABLES A test setup using strain gauges was implemented by Mr. Sheppard and measurements

recorded. The strain gauges were mounted on the sides of the mast as near as possible to the centerline. This implies that values could be obtained to measure side to side deflections but nothing on the bow to stern plane.

Figure 4‐2: Example Mast Strain Gauge Arrangement (5)

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In Figure 4‐2, we can clearly see the mast track, which would be facing aft and the gauges positioned on the port (not visible) and starboard side of the mast. This arrangement was first positioned at the center point of the lower and upper panel indicated in Figure 4‐3 by the two green arrows.

Figure 4‐3: Mast Strain Gauge Positions

More gauges were then installed at the critical location where the stress concentration is located, this again in a similar fashion to those mentioned above.

To measure the shroud tensions, gauges were installed on the fittings near the chain plates; this was done for the upper and lower shrouds. These fittings are designed to allow the cables to move and pivot without wearing them, in a manner similar to a universal joint used on a shaft. The gauges needed to be mounted to the fittings because mounting them on the cables was not possible using this type of instrument.

Figure 4‐4: Shroud Strain Gauges (5)

In order to obtain data on the proposed solutions, a strain gauge was placed on the backstay block, in a similar fashion to those on the shroud fittings. This should measure the relative amount of load placed on the backstay. These shroud strain gauge placements are visible in Figure 4‐4 and indicated by the green arrows.

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Finally, another pair of strain gauges was installed on the baby stay fittings as in Figure 4‐5. These were aligned as best as possible with the cable orientation and glued to the baby stay fitting mounted to the mast track.

Figure 4‐5: Baby Stay Strain Gauges (5)

To summarise, the measured variables for all the tests are as follows:

Table 0‐2: Measured Variables

Measured Variable Testing Method

Top Mast Port Strain Gauge Top Mast Starboard Strain Gauge Middle Mast Port Strain Gauge Middle Mast Starboard Strain Gauge Bottom Mast Port Strain Gauge Bottom Mast Starboard Strain Gauge Upper Shroud Fitting Port Strain Gauge Upper Shroud Fitting Starboard Strain Gauge Lower Shroud Fitting Port Strain Gauge Lower Shroud Fitting Starboard Strain Gauge Backstay Fitting Strain Gauge Baby Stay Fitting Port Strain Gauge Baby Stay Fitting Starboard Strain Gauge

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4.2.2 LOADING OR CONTROLLED VARIABLES In order to simulate conditions of heavy air, where the sailor would likely increase the tension on

the mast shrouds in order to prevent over deflection of the mast, the tensions on the shrouds were increased to a fairly high level. The Ultimate 20 has recommended shroud tension settings of 600 lbs (2670 N) in the upper shroud and 500 lbs (2225 N) in the lower shrouds for heavy air (6). In practice, tensioning of the shrouds in done by means of a graduated tightening screw at the end of the shroud as shown in Figure 4‐6. These were set to what is considered a high level. Experimentally, this was measured with a Loos tension gauge, details of which are shown in appendix 7.3 Loos tension Gauge. For this test, the tension was set at about 500 lbs (2225 N). It is important to note that this was not changed during testing.

Figure 4‐6: Shroud Tensioning Screw (5)

As mentioned in the testing plan, the intended inputs are the spinnaker halyard and the boom vang. Since only one load‐cell sensor was available, it was decided to install it on the vang. This device measures the tension in the cable and this is regulated by a pulley system incorporated into the rigging used during sailing. This system’s function was not modified in any way from the original setup except for the addition of the load cell, which is visible in Figure 4‐7.

Figure 4‐7: Boom Vang Load Cell (5)

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To compensate for the lack of a second load cell, the Loos tension gauge was once again used to determine the tension on the spinnaker halyard. To provide the loading on the cable itself, an improvised setup using another boat trailer’s winching mechanism and an extended cable was devised. The other winching mechanism was positioned in line with the bow to stern axis on the U20, at a sufficient distance to simulate the ordinary angle of the spinnaker halyard. This is shown in Figure 4‐8 with the halyard highlighted in red for clarity. For testing purposes, the spinnaker tension was kept constant at approximately 150 lbs (670N).

Figure 4‐8: Spinnaker Loading Setup (5)

The final variable is the boom angle, since no way was provided to accurately measure it, the boom would be gradually swung from its center position up to its outermost position; resting against the upper shroud. This should represent the full motion of the boom during sailing.

Table 0‐3: Loading Variable Summary

Loading Variable Loading Method Value

Upper Shroud Tensioning screws 500 lbs (2225 N) Lower Shroud Tensioning screws 500 lbs (2225 N) Spinnaker Halyard Improvised winch and cable 150 lbs (670 N) Boom Vang Load Cell Standard pulley system Dependant on angle Boom Angle Manual rotation Centerline to upper shroud interference

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4.3 TEST RESULTS In all tests, the strain gauges output raw data as voltages. These voltages could not be converted to

strains without having more information as to the manufacturer and model. This would include the strain gauge conversion constant, as given in manufacturer literature. As the information on the gauges themselves is not known, only relative deformation can be measured in terms of the magnitude of the voltages in each test.

The test runs all follow a similar procedure. When the run begins, the boom is centered in the bow to stern plane. Then, it is gradually swung outwards as far as possible, the limiting factor being the location of the upper shroud. Subsequently, it is returned to its original position. In all cases, the slope of the curve is indicative of the speed at which the boom is swung.

The magnitude of the voltage is directly related to the strain in the mast at the gauge’s location. A positive voltage indicates a compressive strain whereas a negative voltage indicates a tensile strain.

For the purposes of interpreting this data, it has been referenced to a baseline run, in order to zero the data properly.

Initial analysis was also performed by Mr. Sheppard, focusing primarily on the spinnaker loaded tests, these results and his interpretation can be found in 8.2 May 14th 2008 Testing Report.

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4.3.1 INCONCLUSIVE DATA The data registered by the strain gauges installed on all the shroud and backstay fittings was

inconclusive. In practice, the data indicate so little change in voltages that no useful trend could be ascertained. This is due to the construction of the stainless steel fitting itself. As most marine fittings tend to be oversized to account for wear and corrosion present in the environment, the actual deflection of the fitting was minimal.

As an example of this, Figure 4‐9 shows the raw data for shroud strain gauges in the combined configuration. This data has not been zeroed with a fixed reference.

Figure 4‐9: Non Zeroed Shroud Gauge Voltages for Combined Configuration, Boom Vang and Spinnaker Loaded

As time passes, the boom is swung from the centerline out to side until it hits the upper shroud and then back to the centerline. It is clear that, for the duration of the test, there is only noise present at these sensors and no change is perceptible. Similar results occur at these sensors during all test runs.

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4.3.2 STANDARD CONFIGURATION These two tests are essential in determining a benchmark with which to compare all the other

scenarios. Factors of importance in this case are the magnitudes of the voltages, as they will quantify the effectiveness of all the other proposed solutions.

4.3.2.1 BOOM VANG LOADED The results of the test with the boom vang loaded are shown in Figure 4‐10.

Figure 4‐10: Standard Configuration, Boom Vang Loaded

By order of magnitude, the voltages are highest for the bottom gauges: this is expected as the strain should be increasing from top to bottom along the mast. The strains are also non symmetric, the compression (positive voltage) on the starboard side being roughly half of the magnitude of the tension (negative voltage).

Initially, from 0 to 20 seconds, there is a tensile strain present when the boom is along the centerline. The magnitude of the strain measured by the gauges is minimal at small boom angles, up to a critical point, shown at roughly 50 seconds. This is because the boom loading is gradually being transferred to the plane of the gauges.

The data also presents interference, or noisy behaviour; this is an indicator of the vibrations present in the mast.

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Figure 4‐11: Top Gauges, Standard Configuration, Boom Vang Loaded

The strain along the top gauges, seen in Figure 4‐11 remains nearly constant throughout the test. At approximately 75 seconds, when the boom is completely swung outwards, the strain is marginally reduced. This would suggest that, for the top panel, the stiffness is much higher in the port to starboard plane.

Both top gauges indicate the presence of a tensile loading; this is counterintuitive and this result is present for all tests. There are several possible explanations to this. The first possibility is that the mast is pre‐stressed in tension, but this is unlikely because all the shrouds affecting the top are causing a compression. The second possibility is that the baseline test run was not accurate, thus resulting in an incorrect zeroing value. The final possible explanation is that the gauges are not on the neutral fibre of the mast on the port to starboard plane. Since the mast is being deformed in the bow to stern plane then this could result in tension measured at the top gauges.

To summarise these test results, the values when the boom is at its most outward position are given in Table 0‐4:

Table 0‐4: Standard Configuration, Boom Vang Loaded

Gauge Direction Voltage Top Port Tension -0.101 Top Starboard Tension -0.165 Middle Port Tension -0.465 Middle Starboard Compression 0.124 Bottom Port Tension -0.437 Bottom Starboard Compression 0.208

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4.3.2.2 BOOM VANG AND SPINNAKER HALYARD LOADED The results of the test with the boom vang and spinnaker halyard loaded are shown in Figure

4‐12.

Figure 4‐12: Standard Configuration, Boom Vang and Spinnaker Loaded

These results show a similar behaviour to the previous test, in fact, one would expect that the effect of the spinnaker should not change the values registered by these gauges as it acts in a completely different plane to that of the gauges.

In practise however, the spinnaker has a large impact on the values of the top set of gauges, roughly doubling the voltage from the previous test. Also of great interest are the changes occurring to in the middle set of gauges, shown in Figure 4‐13.

Figure 4‐13: Middle Gauges, Standard Configuration, Boom Vang and Spinnaker Loaded

These curves show that the compression on the starboard gauge has halved and yet the tension on the port gauge is increased. A possible explanation for this is that the mast is significantly deflected forward by the tension on the spinnaker, and this also causes significant stretch in the shrouds. Once out of position, although the total loading on the mast has actually increased from the previous test without

47

the spinnaker halyard loaded the compression on the starboard face decreases. It is likely that the compression is just transferred to another face of the mast, in this case the forward facing one.

A summary of the test results at the most outward boom position is given in Table 0‐5:

Table 0‐5: Standard Configuration, Boom Vang and Spinnaker Halyard Loaded

Gauge Direction Voltage

Top Port Tension -0.204 Top Starboard Tension -0.292 Middle Port Tension -0.554 Middle Starboard Compression 0.051 Bottom Port Tension -0.523 Bottom Starboard Compression 0.143

4.3.3 BACKSTAY Since the backstay is primarily intended to counteract the effects of the spinnaker, it should not impact results too much for the boom vang only test. Inversely, since it acts directly in plane with the spinnaker halyard, one expects that it will tend to keep the mast straight and minimise deformation in the bow to stern plane, but increase compressive loads.


Figure 4‐14: Backstay Configuration, Boom Vang Loaded

In this scenario, the backstay has had a fairly significant impact on the distribution of stresses on the mast. For the top portion, in the port to starboard plane, the tension at these gauges is severely diminished, likely due to the increase overall compression at this point, when compared to the boom vang only test in the original configuration. This is further confirmed by the fact that for both the middle and bottom gauges, there is an increased compression on the starboard gauges and decreased tension on the port ones. The results for the bottom gauges are shown in greater detail in Figure 4‐15.

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Figure 4‐15: Bottom Gauges, Backstay Configuration, Boom Vang Loaded

Note that the spike present at 85 seconds is an anomaly, and not indicative of any special circumstances of effects. It is probably the result of the test operator knocking the boom.

The results of this test, when the boom is in the outward position are shown in Table 0‐6:

Table 0‐6: Backstay Configuration, Boom Vang Loaded


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4‐16.

Figure 4‐16: Backstay Configuration, Boom Vang and Spinnaker Halyard Loaded

For this test, in comparison with the original configuration, there is a general reduction in the tensile loading of the starboard side while showing an increase in the compressive loading of the port side. The top gauges show a significant decrease of loads as their voltages are roughly a quarter of their previous values.

The gauges showing compression; middle and bottom starboard side indicate that compression at these has approximately doubled while the tensile values of the middle and bottom port side have shown a marginal reduction of about 0.1 volts.

The results of this test are summarised in Table 0‐7.

Table 0‐7: Backstay Configuration, Boom Vang and Spinnaker Halyard Loaded



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4.3.4 BABY STAY The baby stays act at the location of the bottom gauges, essentially to reduce the sideways

deflection at this point. As such, we expect to see a reduction of the voltages for these gauges.


Figure 4‐17: Baby Stay Configuration, Boom Vang Loaded

The baby stay configuration does indeed show a marked improvement on the strains measured. A consistent reduction in the magnitude of both the compressive and tensile measurements for all gauges is present, this being greatest from the bottom gauges upwards. This configuration also outperforms the backstay configuration in the port to starboard plane.

Also note the presence of an apparent tension from 0 to 25 seconds in the middle port side gauge and this is apparent in other tests involving the baby stays. The fact that compression is minimal suggests that the mast is bent by the pre‐tensioning of the stays.

A summary of the loads when the boom is in the outwards position is given in Table 0‐8:

Table 0‐8: Baby Stay Configuration, Boom Vang Loaded



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4‐18.

Figure 4‐18: Baby Stay Configuration, Boom Vang and Spinnaker Loaded

Once again, the baby stay configuration causes a large reduction in the strains. For the top gauges, the strains are almost negligible, and show a clear improvement from the original and backstay configurations.

Figure 4‐19: Middle Gauges, Baby Stay Configuration, Boom Vang and Spinnaker Loaded

It is interesting to note that the results for the middle gauges, in Figure 4‐19, from 0 to 20 seconds when the boom is along the centerline of the boat indicate a tension present on the starboard side, similar to other tests involving the baby stays.

The test results of this test, when the boom is at the outward position are summarised in Table 0‐9.

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Table 0‐9: Baby Stay Configuration, Boom Vang and Spinnaker Loaded



4.3.5 BACKSTAY AND BABY STAY COMBINATION During these test runs it is expected to see the effect of the backstay and baby stays functioning

in concert to give the best results


Figure 4‐20: Combined Configuration, Boom Vang Loaded

This test presents the most consistent reduction of compressive strains under the boom only loading case. As such, this is the most effective combination to minimise sideways movement of the mast.

This scenario also yields the largest magnitude voltages for the top pair of gauges. This is attributed to the presence of a backstay pre‐tension and no spinnaker halyard load.

The results of this test, when the boom is in the most outward position are summarised in Table 0‐10.

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Table 0‐10: Combined Configuration, Boom Vang Loaded




4‐21.

Figure 4‐21: Combined Configuration, Boom Vang and Spinnaker Halyard Loaded

Figure 4‐22: Top Gauges, Combined Configuration, Boom Vang and Spinnaker Halyard Loaded

Almost no deflection is measured on the port to starboard plane in Figure 4‐22 for the top pair of gauges, regardless of boom angle, which should vary between 20 and 60 seconds.

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Figure 4‐23: Combined Configuration, Boom Vang and Spinnaker Halyard Loaded

The effect of the baby stays while the boom is at the centerline is to keep the mast at zero deflection. The results seen in Figure 4‐23 showing the readings for the bottom gauges is what is expected of properly pre‐tensioned baby stays. The reason why this test showed no initial error in the pre‐tensioning of the baby stays is unclear.

The results for this test, when the boom is in the outward position are summarised in Table 0‐11:

Table 0‐11: Combined Configuration, Boom Vang and Spinnaker Halyard Loaded


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4.4 CONCLUSIONS AND RECOMMENDATIONS

To summarise the results, they are displayed in Table 0‐12 and Table 0‐13 as average percent improvements as compared to the baseline tests. A negative value indicates that the solution worsened the strains at a particular gauge.

Table 0‐12: Percent Improvement, Boom Vang Loaded

Percent Voltage Reduction (%) Gauge

Backstay reduction Baby Stay Combined Top Port Tension 90 64 -20 Top Starboard Tension 55 82 42 Middle Port Tension 18 45 41 Middle Starboard Compression -72 12 276 Bottom Port Tension 20 50 60 Bottom Starboard Compression -38 25 148

Table 0‐13: Percent Improvement, Boom Vang and Spinnaker Halyard Loaded

Percent Voltage Reduction (%) Gauge

Backstay reduction Baby Stay Combined Top Port Tension 76 81 20 300 Top Starboard Tension 54 98 14 500 Middle Port Tension 24 51 160 Middle Starboard Compression -255 -145 -64 Bottom Port Tension 17 56 174 Bottom Starboard Compression -71 -34 -23

Bearing in mind that the main goal is to reduce the compression at the bottom port side gauge where the stress concentration is present on the mast, the best apparent solution is the combination of the baby stays and backstay.

Physically, the baby stay was the best single modification to increase the stiffness of the mast in the port to starboard plane. This is no surprise since the backstay and spinnaker do not act in this plane. Their effect is however obvious, they increase overall compression on the mast and, combined with the sail adding to the total deformation favour buckling. These small stays address the problem directly by limiting the deflections at or near the problem area.

The backstay does also serve to increase mast stiffness and resistance to buckling, but in another plane to the baby stays. In actuality, the backstay increases compressive deflection at the critical area and does not represent a good solution to the buckling issue at the stress concentration.

Globally however, when taking into account the enormous variability of loading conditions on an actual mast caused by waves, boat motion, wind gusts and the environment, it is best for the mast to be as well supported as possible. This would indicate that it is preferable for the U20 Class Association to homologate both the baby stays (High Wind Kit) and permit the use of a backstay.

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Finally, If this the baby stay is not a practical solution or consensus cannot be reached within the class association, perhaps it should consider a change in the rules concerning overall spinnaker dimensions. A reduction of the spinnaker size would reduce the loads on the mast and may solve the problem.

4.5 FUTURE TESTING

Future testing should, if at all possible, include more sensors to gather more data. In the ideal case, load sensors for every cable in the mast system. This would include:

• Upper shrouds on the port and starboard side

• Lower shrouds on the port and starboard side

• Forestay

• Boom vang

• Spinnaker halyard

This would allow every more precise control on the inputted load cases and give a more complete picture of the compression on the mast. These variables are responsible for nearly all of downwards load on the mast, except for the downwards component of the sail forces and weights.

The winching system used to load the spinnaker halyard is probably ideal, considering the difficulty of implementing this otherwise, but future testing should account for changes in the angle of the spinnaker halyard and the fact that this force may or may not always be directly in line with the bow of the boat. An easy way to do this would be to vary the distance between the top of the mast and the winch, and then to simply calculate the angle via Pythagoras’s theorem.

Strain gauge placement on the mast should be done in both the bow to stern and port and starboard planes. This means that gauges should be placed on all four “corners” of the mast, in order to measure the complete deformed shape under loading.

It would be also advisable to have some sort of boom angle sensor, or at least a precise way of measuring it. The test should then be repeated under different angles, in order to obtain a larger sample size. This rotation should also be done on both sides of the boat. Having data from the other side of the boat would allow to average out the effect of not having the boat on a level surface or at least to show whether or not the system responds in a symmetric fashion.

Finally, testing done so far neglects the influence of the sail itself, which would indeed have an impact on the deformed shape of the mast. Field testing or aerodynamic calculations could provide a baseline for testing the distributed sideways load imposed on the mast itself. These forces could then be transferred from a distributed load to a point load on each panel. This point load could then be applied to the mast in a manner similar to that of the spinnaker halyard loading technique.

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5.0 CONCLUSIONS

5.1 DESIGN METHODS AND REALITIES

Several methods in the public domain are available to assist the yacht designer in his or her task of designing their vessel’s mast. One of these is a generic beam analysis method based on Euler‐Bernoulli beam theory. This method is well known and understood to engineers and proven very accurate.

The other tool, although simply an addition to Euler‐Bernoulli beam theory, is the P‐Δ method. The P‐Δ method is more representative of the loading imposed on a mast but remains limited by the assumption that maximal deflection in the beam‐column occurs at or near the middle. This is not necessarily true if one considers the mast as a whole, and still not necessarily true if one considers the mast in several panels. As such, this limits the designer in optimising the solution.

The biggest setback to the implementation of these tools to mast design is that Euler‐Bernoulli beam theory and the P‐Δ method do not offer any way of estimating the loads on the mast.

Methods specific to sail boats; the Nordic Boat Standard or Skene’s method, do remedy the problem of determining the loads on the mast through the use of the hull’s righting moment. This technique is apparently satisfactory, but very little evidence actually justifies this.

Skene’s method is very primitive and does not allow for optimisation. It is probably most useful as a first pass design method, in order to get ballpark dimensions but not suitable for a comprehensive design.

The Nordic Boat Standard is the more thorough and comprehensive design method: it does account for various rig geometries, materials and configurations, worst case loading cases are considered. Again, the basic assumption at issue is that of the righting moment as a basic assumption.

In summary, there are several tools which can lead to a solid and optimised design. The reality of mast design is determining the loads imposed by the sails. Aerodynamic effects can change the distribution and magnitude of the force applied on the mast by the mainsail. The same can be said of the spinnaker or jib. No information on what combination of conditions creates the highest loads on the mast, which is necessary knowledge for design.

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5.2 MODELLING AND TESTING: SUGGESTED IMPROVEMENTS

With regards to the modelling of the Ultimate 20 mast, several improvements have already been suggested that could improve the accuracy of the results. These range from more degrees of freedom to calculating the strains along the actual mast, rather than limiting the model to bending moments.

The modelling on the Ultimate 20 was carried out after the testing. Typically, modelling should be done prior to testing, in order to aid in determining the necessary data acquisition points and what relevant information is needed to establish valid and useful results. In this case, more physical testing on the U20 should be done, with

For a more meaningful modelling approach, the entire process could be rethought in terms of mast design. If more details were available in terms of the actual design process, they could be used as a starting point for modelling. If for example, the design was determined using the Nordic Boat Standard as the primary design method, the mast could be modelled using the worst case loading conditions from that method. Once the results of this model are known, then a testing plan could be formulated to simulate the same loading conditions on the actual mast and the results directly compared with those obtained from the model.

In the case of the present study, only general tendencies as to the mast’s behaviour in theory and practice could be ascertained. With directly comparable results from design, modelling and testing, specific conclusions on the validity of the method used for design could be achieved. This could go a long way in validating the mast design in a scientific manner.

The typical design validation of a sail boat and its components is by initial sea trials. These usually involve actually sailing the new boat in increasing wind conditions. If everything checks out, then the boat’s design is deemed fit. The same goes for the mast and rig, if nothing appears unusual, cracked, loose or broken, then the mast design is satisfactory. Although this is a very practical, quick and relatively easy method of design validation, it is hardly scientific.

This on the fly design validation has several important drawbacks:

• No information is available as to whether or not the mast has actually been subjected to its maximal design loads.

• The rig may be overdesigned, but there is no way of knowing this.

• The rig may be under designed, but since there is no way of knowing this, it may fail under certain conditions considered to be normal use.

This last point is certainly true of the Ultimate 20. Unfortunately for owners, the problem only becomes apparent once a large number of customers are already in possession of their boats. This could be avoided with the more scientific approach of modelling and strain gauge testing.

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5.3 FUTURE WORK

The field of sailboat dynamics in general is wide open: little publicly available literature exists on how a sailboat behaves in its environment. This includes comprehensive aerodynamic studies on sails and their interaction with the mast and hull. All of the design methods are based on static measurements because there is insufficient research on dynamic loading of masts. This can include study of the effect of waves on mast loads or how heeling impacts sail forces. In terms of mast design, the process itself does require serious research on sail loads in order for any kind of breakthrough to be made. As there are several large yacht design and construction firms, as well as cutting edge research teams involved in yacht racing, the research is definitely happening. The issue here is that none of it is in the public domain, remains proprietary information or the closely guarded secret of a racing outfit. It is well known that much of the high‐end boat design is done with the help of computer resources such as velocity prediction programs (VPP) and finite element analysis software. These tools require a knowledgeable and well funded team effort, which may not be the reality for every yacht design outfit. Most common yacht designs on the market today have been designed by a single person, in the words of Steve Killing, “Most yacht designers work alone” (9). This means that this one person must become an expert in a large number of fields ranging from aerodynamics, hydrodynamics, composites, programming, interior design and so on. Because of this, most yacht designers tend to be very conservative in their design, sticking to what works or has been proven. Customers are also, generally speaking, sticking to proven designs, since they invest large sums of their personal fortune on their vessel. This attitude for conservatism because of lack of understanding tends to restrain yacht design from evolving and improving. For the specific case of the Ultimate 20, it is clear that the baby stays, or ”High Wind Kit” should be offered as a class legal retrofit to all owners, at least in the form of a stop gap measure. The manufacturer should also further investigate these mast failures. A documentation process needs to be undertaken for each and every known mast failure. Data ranging from wind conditions, boat heading, sail configuration and samples of failed masts could be collected and used to confirm this study’s findings and the basic assumption that all failures occurred at the halyard passage near the base of the mast.

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6.0 BIBLIOGRAPHY

1. Gere, J. M. Engineering Mechanics of Solids. 1st Edition. s.l. : Prentice‐Hall Inc, 1998.

2. Janssen, R. Best Mast: a new way to design a rig. HISWA Symposium. [Online] 2008. Best Mast: a new way to design a rig.

3. Kulak, G. L. & Grondin, G. Y. Limit States Design in Structural Steel. 7th Edition. s.l. : Canadian Institute of Steel Construction, 2002.

4. Skene, N. L. Elements of Yacht Design. 6th Edition. s.l. : Sheridan House, 2001.

5. Larsson, L. & Eliasson, R. Principles of Yacht Design. 3rd Edition. s.l. : McGraw‐Hill, 2007.

6. USYachts. U20 Brochure. http://www.usyachts.com/. [Online] 2009. http://www.sailsports.com/pdfs/u20‐02‐12‐09.pdf.

7. Sheppard, Mr. Van. Private Communication. Ottawa : s.n., 2008.

8. Sails, Ullman. U20 Tuning Guide. U20 Class Association. [Online] [Cited: 03 24, 2009.] http://www.u20class.org/U20racing/tuningGuide.html.

9. Killing, S. & Hunter, D. Yacht Design Explained. 1st Edition. s.l. : W. W. Norton & Company, 1998.

10. Shigley, J. E., Budynas, R. G. & Nisbett, J. K. Shigley's Mechanical Engineering Design. 8th Edition. s.l. : McGraw‐Hill, 2008.

11. Parts of a Sailboat. White Mountain Sailing . [Online] [Cited: April 15, 2009.] http://whitemountainsailing.com/parts.aspx.

12. Perry, R.H. Yacht Design According to Perry. 1st Edition. s.l. : McGraw‐Hill, 1998.

13. Claughton, Wellicom & Shenoi. Sailing Yacht Design, Practice. 1st Edition. s.l. : Addison Wesley Longman Limited, 1998.

14. Claughton, Wellicome & Shenoi. Sailing Yacht Design, Theory. 1st Edition. s.l. : Addison Wesley Longman Limited, 1998.

15. Avallone, E. A. & Baumeister, T. Mark's Standard Handbook for Mechanical Engineers. 10th Edition. s.l. : McGraw‐Hill, 1996.

16. U20 class association website. [Online] www.u20class.org.

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7.0 APPENDICES

7.1 RIGHTING MOMENT

A hull’s righting moment is often called upon as the starting point for mast design methods. It is, in essence, a measure of the buoyant stability of the vessel. Since the weight always acts as a downward force situated at the center of gravity, the buoyancy of the vessel is the force keeps the vessel afloat. The buoyancy force however acts at the center of buoyancy, which is at the center of the volume of water displaced by the hull. This implies that under most circumstances, the centre of buoyancy is not at the same location as the center of gravity. When a force, such as a loaded sail, tends to tilt or heel the boat to one side, a force couple between the weight and the buoyancy, known as the righting moment, exists to counteract heeling. This is detailed in Figure 7‐1

Figure 7‐1: Righting Moment (10)

It is important to note that this moment is typically calculated, and environmental effects and boat motion are completely ignored. This means that the righting moment is a measure typically used to compare relative hull stability from one design to another.

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Figure 7‐2: Stability Curve (3)

For the typical hull, the stability curve resembles the one shown in Figure 7‐2 where GZ is the righting moment, plotted against heeling angle Φ. This moment is increasing up until the point where the hull would capsize. In terms of design, the righting moment is needed at an angle of 30 degrees, but usually, hull designers only calculate the righting moment at 1 degree (3). In this case, the value of the righting moment at 1 degree is multiplied by a factor of 30, which means that the first portion of the stability curve is considered to be linear; this is illustrated on Figure 7‐2. For the purposes of mast design, this implies that the righting moment is grossly overestimated, which renders mast design even harder to optimise.

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7.2 STRESS CONCENTRATIONS

In practical terms, in order for the sail boat to function, holes in the mast for mounting fixtures and running cables are inevitable. These holes lead to stress concentrations at their locations, essentially multiplying the value of the stresses on and around their periphery. Stress concentrations in general are undesirable and the designer should always try to minimise their occurrence and impact. Several factors affect their impact; these include size of the hole and width of the beam. For example, Figure 7‐3 shows a rectangular bar in bending and Figure 7‐4 shows a round bar in bending. These figures are for solid beams and represent holes drilled right through them, not necessarily representative of sail boat masts, but give a clue as to the impact of such holes.

Figure 7‐3: Stress Concentration Factors for a Rectangular Bar in Bending (11)

Figure 7‐4: Stress Concentration Factors for a Round Bar in Bending (11)

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In terms of sailboats, holes are usually only drilled on one side or face of a hollow mast. This is then measured in terms of reduction in moment of inertia at a particular location. The Nordic Boat standard addresses this issue with the following guidelines in Figure 7‐5:

Figure 7‐5: NBS Mast Hole Guidelines (6)

Where it is permissible to drill holes in the mast at given locations near the ends of a mast panel. The amount of allowable reduction of moment of inertia is given as a percentage to allow the designer the greatest amount of freedom as to the placement and combination of holes desired.

For masts, typically, failure occurs in the form of buckling, a case demonstrated by the Ultimate 20. Holes on the side caused the mast to buckle at that point. This is known colloquially as the “dimpled soda can effect” where a person standing on an empty aluminium soda canister can be supported, but should there be the slightest stress concentration induced on the skin of the canister, it will buckle at this location. In the specific case of the U20, the stress concentration is not only a single hole, but rather an entire fitting; this is shown in Figure 3‐2. This fitting is riveted in four places and has a large hole in the middle for the halyard to pass through. The fitting itself, being made of stainless steel, changes the localised stiffness of the mast. This effect can also lead to higher stress concentrations.

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7.3 LOOS TENSION GAUGE

The Loos & Co tension gauge for cable is a device that allows approximate measurement of cable tension without the use of a load cell. It operates using a calibrated spring gauge used to measure how much force is needed to apply a sideways deflection to the cable. This in turn yields a relation on sideways deflection to cable tension. A close up view of the Loos tension gauge is shown in Figure 7‐6.

Figure 7‐6: Loos Tension Gauge (5)

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8.0 PRIVATE COMMUNICATIONS FROM MR. SHEPPARD

8.1 TESTING PLAN

1. To understand the loads experienced by a U20 mast when the spinnaker halyard is highly loaded, the vang is also loaded and the boom is allowed to move out from the centerline of the boat.

2. To understand how the HWK helps to improve the loads experienced by a U20 mast when tested under the same conditions described in Item 1 above.

3. To understand how a Backstay helps to improve the loads experienced by a U20 mast when tested under the same conditions described in Item 1 above.

4. To understand how a combination of the HWK and a Backstay helps to improve the loads experienced by a U20 mast when tested under the same conditions described in Item 1 above.

Test Equipment:

1. One U20 sailboat, sitting on a trailer and tied down as if ready to travel 2. One additional U20 trailer positioned in front of the U20 so that the winch on the trailer can be

used to generate a high load on the spinnaker halyard 3. One HWK including any modifications required to the U20 4. One Backstay arrangement including any modifications required to the U20 5. TBD number of TBD model strain gauges 6. 1 data acquisition system TBD number of channels (minimum of 6 channels) 7. 3 strain bars (0.25” diameter aluminum bars) 8. 2 load cells (250 kg capacity) 9. 1 video camera with 4 tapes.

Test setup:

1. Start with mast lying on ground or tables so that there are no bending moments or compressive loads in it.

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2. Attach strain gauges 1 to 6 in pairs on each side of the mast. Ensure that they are attached on the neutral axis for fore aft bending (approximately half way along the mast when looking from front to back). See figure 1.

3. Attach strain gauges 7‐12 in pairs on each shroud. Ensure that they are attached to the shroud in a way that ensures they will see the entire load in the shroud. If it is desired to determine the loads in the shroud based on the strain measurement, then the strain gauge must be mounted on the shroud in a location where the cross section dimensions can be accurately measured.

4. Attach a strain gauge to each strain bar. 5. Attach as per manufacturers recommendations. 6. For the gauges on the upper part of the mast, run the wires down to the bottom of the mast and

secure them to the sides of the mast so they do not get damaged when the mast is being raised. 7. Attach a length of red or blue rope (1/8” to 3/16” diameter) at the hounds of the mast so that it

runs down in the sail track when the mast is stepped. The rope should be long enough to reach the gooseneck and be tied in place. This rope will be used to measure sideways deflection of the mast during testing.

8. Install the mast in the boat. Ensure that the mast is straight and vertical in the boat. In other words tune the mast correctly.

9. Tune the mast for sailing in high winds. Minimum of 500 lbs tension on the outers and 250 lbs tension on the inners.

10. Attach the boom to the mast. Do not install the boom kicker if one is present. Do not run the mainsheet. The boom should be free to swing on the gooseneck.

11. Connect the main halyard and the outhaul to the ends of a strain bar. Tie off the main halyard at the base of the mast and then cleat the outhaul such that the boom is parallel to the waterline.

12. Connect the vang to a load cell and then connect the load cell to the boom using the bale that the vang normally connects to.

Test Procedure:

1. Pull on the vang to create a load in the load cell of 150 Kgs. Cleat the vang so that this load is sustained. Keep the boom centered while doing this.

2. Arrange the video camera so that it sits on the centerline of the boat and is fully zoomed in and focused on the sail track of the mast. Elevate the camera so that strain gauges 3 and 4 are in the center of the vertical field of view.

3. Starting on centerline and moving out in 5° increments, swing the boom out to the starboard side until the boom reaches the upper shroud. At each point, record the value on each strain gauge as well as the value of the load on the load cell.

4. Return the boom to centerline and then connect the spinnaker halyard to an extension rope that is low stretch and long enough to reach almost to the winch on the second trailer. Now connect the extension rope to one end of a load cell and the winch on the second trailer to the other end of the load cell.

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5. Ensure the trailer is braced so that it won’t move when the winch is used to impart a load to the spinnaker halyard.

6. Using the winch, load up the spinnaker halyard until the load cell indicates a load of 150 Kgs. 7. Arrange the video camera so that it sits on the centerline of the boat and is fully zoomed in and

focused on the sail track of the mast. Elevate the camera so that strain gauges 3 and 4 are in the center of the vertical field of view.

8. Starting on centerline and moving out in 5° increments, swing the boom out to the starboard side until the boom reaches the upper shroud. At each point, record the value on each strain gauge as well as the value of the load on the load cells.

9. Return the boom to centerline and attach the HWK wires. Tension them according to recommendations. If no recommendations are published, then tension to approximately 250 lbs.

10. Repeat steps 1‐8 for this configuration. 11. Return the boom to centerline and remove the HWK wires. 12. Connect the backstay line to a strain bar and connect the strain bar to a tensioning apparatus.

Pull the tensioning apparatus until the backstay is taut. 13. Repeat steps 1‐8 for this configuration. 14. Return the boom to centerline and connect the HWK wires. Tension them to the same value

used in step 9. 15. Repeat steps 1‐8 for this configuration. 16. Testing is done!

Analysis Plan:

The first test run will provide baseline data.

• From the mast strain gauge measurements the localized loads on the mast will be inferred.

• From the shroud strain gauge measurements the increased loads caused by the spinnaker halyard loading up will be seen.

• From the load cell on the vang it will be possible to see if the loads from the vang change as the boom is rotated away from centerline.

• From the video recorded it will be possible to understand the amount of sideways deflection that the mast experiences as the boom is rotated away from the centerline.

The run with the HWK wires installed will be analyzed to get the following information.

• From the mast strain gauges it will be possible to see if the bending loads have been reduced and by how much

• From the bottom pair of strain gauges on the mast it will be possible to see if how much additional compression load is imparted to the bottom of the mast column by the HWK wires.

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• From the shroud strain gauge measurements it will be possible to see how the HWK wire loads up as the boom is rotated away from the centerline.

• From the shroud strain gauge measurements it will be possible to see if the HWK results in higher or lower loads on the shrouds.

• From the load cell on the vang it will be possible to see if the loads on the mast from the vang are different as the boom is rotated away from the centerline.

• From the video recorded it will be possible to see how much the sideways bending of the mast is reduced by the HWK wires.

The run with the Backstay installed will be analyzed to get the following information.

• From the mast strain gauges it will be possible to see how much the compressive loads in the mast have been reduced

• From the shroud strain gauges it will be possible to see how much the loads in the shrouds are reduced when the spinnaker halyard is loaded up.

• From the video recorded it will be possible to see if the sideways deflection of the mast has been reduced and if so, by how much it has been reduced.

• From the strain bar installed in the backstay it will be possible to see the relationship between loading in the spinnaker halyard and load in the backstay.

The run with both the HWK and the backstay installed will be analyzed to get the following information.

• From the mast strain gauges it will be possible to see how the overall loads in the mast have been reduced and also how the bending loads have been reduced.

• From the video it will be possible to see how the sideways deflection has been reduced.

Predictions for the testing:

Existing U20 configuration run:

• Expect high compressive loads in the mast as the spinnaker halyard is loaded up.

• Expect high loads in the outer shrouds as the spinnaker halyard is loaded up.

• Expect large sideways deflection of the mast as the boom is rotated away from centerline. This is expected in both the spinnaker halyard loaded case and the spinnaker halyard not loaded case.

• Expect vang loads to be reduced as the boom rotates away from centerline.

• Expect this test with the spinnaker halyard loaded up to provide the worst case compressive loads in the mast. This measurement should be seen in the middle strain gauge on the starboard side of the mast, assuming the boom is rotated out to starboard.

HWK installed:

• Expect high compressive loads in the mast as the spinnaker halyard is loaded up.

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• Expect high loads in the outer shrouds as the spinnaker halyard is loaded up.

• Expect smaller sideways deflection of the mast as the boom rotates away from centerline.

• Expect the compressive loads in the bottom of the mast to be highest in this test case. Backstay installed:

• Expect the loads in the mast with the spinnaker halyard loaded up to be smaller than in the previous two tests.

• Expect the sideways deflection of the mast to be similar to deflection observed during the first test.

• Expect to see the same relative difference in compression loads on different sides of the mast as in the first test run, but expect the loads to be much smaller overall

• Expect the loads in the outer shrouds to be smaller than in previous test cases. HWK and Backstay installed:

• Expect this test case to provide the lowest overall loads in the mast since sideways bending is limited by the HWK and spinnaker halyard loads are mostly taken up by the backstay.

• Expect that for this test case, the sideways bending of the mast will be the smallest observed.

• Expect that for this test case, the loads in the shrouds will be the smallest observed.

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8.2 MAY 14TH 2008 TESTING REPORT

Test Results Summary:

The table below captures the most relevant data from the tests.

Middle Port Gauge

Middle Stbd Gauge

Lower Port Gauge

Lower Stbd Gauge

Range: Original 0.350 0.260 0.500 0.314

Range: Backstay 0.262 0.278 0.401 0.302

% Reduction: Backstay 25 ‐7 20 4

Range: HWK 0.177 0.182 0.272 0.225

% Reduction: HWK 49 30 46 28

Range: HWK & Backstay 0.149 0.163 0.226 0.193

% Reduction: HWK & Backstay

57 37 55 39

Original: Initial test run with original mast configuration and loaded spinnaker halyard.

Backstay: Slight reduction in the port side loads. No real change in the starboard side loads. For this test setup the starboard side loads are compression loads and are the most important ones to reduce.

HWK: Significant reduction in loads on both the compression and tension sides of the mast. Also, on the video of the test, there is a significant reduction of the visible bending in the mast with the HWK installed.

HWK & Backstay: Best case situation. It seems that with the HWK reducing the amount of bending that the mast can do, the backstay now helps by further reducing the loads on the compression side of the mast.

Testing shows that the HWK is the best single addition that can be made to the U20 rig to reduce the magnitude of the side loads experienced by the mast. An average reduction in the compression loads of 29% was observed when compared to test runs with the original mast supports. The tests also showed that this reduction was increased to an average of 38% when the HWK was used in conjunction with a backstay. This is an increase of 31% compared to the HWK by itself.

So, the backstay alone is not very useful. The HWK alone is quite useful. The HWK in conjunction with the backstay will provide the best support for the U20 mast and reduces compression loading in the conducted test by approximately 40%.

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The reduction in the noise on the recorded data from the different test runs is, in my opinion, indicative of how much better supported the mast is with the backstay and the HWK installed.

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Recommendations:

1. Modify the U20 class rules to permit the use of a backstay and to clearly state that the HWK is permitted. This provides the best solution it terms of preventing further mast failures caused by deflection of the mast out of column sideways.

2. If only one solution is adopted then the High Wind Kit is the most effective single change in reducing sideways deflection of the mast.

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Test Results.

The analysis to date has focused on the test runs where the spinnaker halyard was loaded at 150 lbs before the boom was rotated out the shroud. These test runs are named run2, bstay2, hwk2 and backhwk2. Default Mast Configuration (Run2) Data Analysis: For run2, the data from the 4 bottom gauges on the mast is show in the graph below.

The data was referenced to the zero reading for each of the strain gauges. A quick look at the chart shows that the two gauges on the starboard side (the ones in compression) show values that are approximately the same in magnitude, with the strain in the lower part of the mast (red line) being slightly larger than the strain measured at the midpoint between the mast base and the shroud. Given that the mast is more constrained at the base, this is expected. The two gauges on the port side of the mast show higher values. In the case of the lower port gauge (blue line) this was expected since it is located right next to the main halyard exit and some stress concentration would be expected there. In the case of the middle port gauge the

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larger voltage change wasn’t expected. The reason for this larger value isn’t understood at this time. Note that there is noise in the data for all 4 strain gauges. The slopes at 41 seconds and 151 seconds indicate where the boom was moved out to the shroud and then returned to the centreline. They show that the boom was moved out to the shroud slowly and returned to centreline quickly. That was not intentional. The table below summarizes the change in strain seen by each gauge for this test run.

Middle Port Gauge

Middle Stbd Gauge

Lower Port Gauge

Lower Stbd Gauge

Max ‐0.210 0.095 ‐0.019 0.185

Min ‐0.560 ‐0.165 ‐0.519 ‐0.129

Range 0.350 0.260 0.500 0.314

This data represents the baseline that the different support methods will be measured against. Backstay Test Run Data Analysis For bstay2, the data from the 4 bottom gauges on the mast is show in the graph below.

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The data was again referenced to the zero reading for each of the strain gauges. A quick look at the chart shows that the two gauges on the starboard side (the ones in compression) show values that are approximately the same in magnitude, as in the initial test case. The two gauges on the port side of the mast show values that have been reduced compared to the initial test case. Note that there is much less noise in the data for all 4 strain gauges. The slopes that indicate where the boom was moved out to the shroud and then returned to the centreline are more even in this test run. The test conductor’s performance is improving. The table below summarizes the change in strain seen by each gauge for this test run.

Middle Port Gauge

Middle Stbd Gauge

Lower Port Gauge

Lower Stbd Gauge

Max ‐0.154 0.203 ‐0.019 0.264

Min ‐0.416 ‐0.075 ‐0.420 ‐0.038

Range 0.262 0.278 0.401 0.302

% Improvement 25 ‐7 20 4

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The % Improvement line shows how the ranges for the backstay test run compare to the baseline runs. The loads on the port side of the mast have been reduced, but there is little or no change on the starboard side. Note that for this test the starboard side is the side in compression. High Wind Kit Test Run Data Analysis For HWK2, the data from the 4 bottom gauges on the mast is show in the graph on the following page. The data was again referenced to the zero reading for each of the strain gauges. For this test run, the values measured on all the strain gauges have been reduced from those seen in the baseline run. Note that again there is much less noise in the data for all 4 strain gauges. It is clear that the HWK has a significant impact on the loads in the sides of the mast. The table below summarizes the change in strain seen by each gauge for this test run.

Middle Port Gauge

Middle Stbd Gauge

Lower Port Gauge

Lower Stbd Gauge

Max ‐0.089 0.155 0.054 0.221

Min ‐0.266 ‐0.027 ‐0.218 ‐0.004

Range 0.177 0.182 0.272 0.225

% Improvement 49 30 46 28

As with the backstay, the largest reduction in strain is on the port side, but here the strains on the starboard side are also reduced significantly. On the side of the mast in compression we see a drop in the measured strain of about 30%.

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High Wind Kit & Backstay Test Run Data Analysis For backhwk2, the data from the 4 bottom gauges on the mast is show in the graph on the following page. The data was again referenced to the zero reading for each of the strain gauges. For this test run, the values measured on all the strain gauges have been reduced significantly from those seen in the baseline run. This configuration generated the best results in that the strains in the sidewalls of the mast are the lowest of all the test runs. Note that again there is much less noise in the data for all 4 strain gauges. This data is actually the least noisy of all the test runs. This may be because the mast is supported the best and has the least amount of freedom to move.

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This test shows that the backstay in conjunction with the HWK gives about a 10% improvement over the HWK by itself. This 10% improvement is seen on all 4 strain gauges. The table below summarizes the change in strain seen by each gauge for this test run.

Middle Port Gauge

Middle Stbd Gauge

Lower Port Gauge

Lower Stbd Gauge

Max ‐0.056 0.163 0.049 0.207

Min ‐0.205 0.000 ‐0.177 0.014

Range 0.149 0.163 0.226 0.193

% Improvement 57 37 55 39

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Conclusions: 1. The single most effective change in terms of reducing strains in the sidewall of the U20 mast

under side loading is the High Wind Kit. 2. The lowest mast sidewall loads are seen when the High Wind Kit and the Backstay are used

in conjunction with each other. 3. The loads experienced are smoother in nature with the Backstay or the HWK installed, and

are smoothest when both are used together. Recommendations: 1. Modify the U20 class rules to permit the use of a backstay and to clearly state that the HWK

is permitted. This provides the best solution it terms of preventing further mast failures caused by deflection of the mast out of column sideways.

2. If only one solution is adopted then the High Wind Kit is the most effective single change in reducing sideways deflection of the mast.

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During the testing there were some changes from the original test plan.

1. The mast has some sort of protective material wrapped around it below the gooseneck, so the lower set of strain gauges could not be mounted where show on the original diagram. Instead, they were mounted at point where the main halyard exits the mast. The starboard one was mounted halfway between the front and the back, while the port gauge was mounted alongside the aft edge of the stainless plate that covers the hole in the mast that the halyard exits through.

2. A second load cell was not available for testing. Instead a 5/32” diameter wire was included in the rig for pulling on the spinnaker halyard. Then a loos gauge was hooked on the wire and it was used to ensure that the loads being applied were the same for each test case. This was documented on video that will be uploaded to Youtube.

3. Testing with the spinnaker halyard loaded was conducted with the halyard loaded at 150 lbs. That was as far as the mast owner (me) was comfortable loading things up with no additional support.

4. The data acquisition system used for the testing allowed data from each strain gauge and from the load cell on the vang to be gathered and logged at a 1 Hz rate for each test run. This eliminated the need to manually record any of the data and sped up testing. It also meant that there was no need to stop at 10° increments and record the data. The procedure was modified so that when data recording was turned on, the boom was slowly rotated out until it touched the shroud on the starboard side of the boat. It was held there for approximately 30 seconds and then it was moved back to centre line, also at a slow rate.

5. The boom was never quite on the centreline of the boat for any of the test runs. This is because with the keel fully raised, it interferes with the boom vang and prevents the boom from moving all the way to the centreline.

6. Sideways deflection of the mast was supposed to be measured using a dial gauge, but one was not available. Sideways deflection was recorded on video during each test run. The video has been reviewed and it clearly shows the amount of sideways bending that the mast experiences. The video from each test run will also be uploaded to Youtube.

Some things that didn’t work so well; (aka lessons learned)

1. All the strain gauges were mounted on the sides of the mast, as close as possible to the midpoint between the front and back of the mast. This was to ensure that the side bending loads were accurately measured and it worked well. Unfortunately it also meant that there were no sensors on the front and back of the mast, so overall compression of the mast was not measured. This had been one of the goals of the testing and it was not achieved.

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2. All the strain gauges mounted on the shrouds and the one on the backstay were mounted on stainless steel. The loads experienced were very small on all the stainless parts, so the gauges didn’t capture good data.

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9.0 SAILBOAT ANATOMY

To facilitate the reader that may be unfamiliar with sailboat layout, parts and nautical terminology, the diagram in Figure 9‐1 illustrates the principal relevant components.

Figure 9‐1: Anatomy of a Sailboat (11)

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9.1 GLOSSARY

• Block: nautical term for pulley

• Chain plate: through hull mounting for a shroud

• Halyard: cable or rope with a function relating to hoisting or pulling upwards or on a sail

• Heavy air: high winds

• Heeling: lateral leaning or the hull, or rotation about the bow to stern axis

• Light air: low winds

• Reef: Attachment point designed to reduce the overall area of the sail. Used during heavy air situations lower the sail.

• Shroud: Cables designed to stiffen the mast

• Spreaders: Devices which spread the shrouds. Usually straight bars.

analysis of sailboat mast design

Documents

practical case of theultimate

skenes method

theirpractical application

eulerbernoulli beam

nordic boat standard

public domain