A procedure for sailing performance analysis based on full scale log entries and towing tank data

Deift University of Technology

Ship HydromeChaflics LaboratorY

Library

Mekelweg 2, 2628 CD

Deift

The Netherlands

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A PROCEDURE FOR SAILING PERFORMANCE ANALYSIS BASED ON FULL SCALE LOG

ENTRIES AND TOWING TANK DATA

Kerwin, B. W. Oppenheim

and J. H. Hays Revised Edition December, 1974

g

Report No. 74-17

A PROCEDURE FOR SkILING PERFORMANCE

ANALSÍS BASED OÑ TLL SCALE LOG

EÑTRIES A1D TbING TANK DATA by

J. E. Kerwiti, B. W. Oppenhéïm

änd J. H. Mäys Revised Edition. December., 1974

Note:. A limited number of drafts of this report dated July,

1974 contain significant errors in the tabulated sail

force coefficients. Those dtafts dated July, 1974

should be discarded.

This research was caried out undet the North Aéicàn

Yacht Racing Union Ocean Race Handicapping Project, M.I.T..

OS Project No. 81535. The generous ùpport o the individual

donors to this program is gratefully acknowledged.

i

E.

ï. 13-:ES

APR 2-1975

ABSTRACT.

A cOmputërbased procedute is develope4 for combining fu1lsca1e sailiflg log data with towing tank data to obtai±i sail force coefficients

for all poits of sailing. Cothbination 6f these sail force ôoeffic±ents

with tank data provides a means for simulation of the sailing

perfor-mance of yachts with simIlar rigs. Sàil force coefficients for the

yacht BAYBEA are derived by this method from the perfôrmane data tken

during the 1974 SORC. A performance polar diagr for true wind speeds

from 5-15 lots is developed The effects on boat speed due to changes

in sail àrea and t-ightiig mOment ate obtáid as a example of the

I

I k CONTENTS

Page

Nomenclature - -

- - _-

i

1.

Introduction

___

3

2.

Sail FOrce Coefficients Program

7

3.

Performance Prediction Program

18

4.

Remarks

-

33

5.

References

₃₅

Figures

1.

Coordinate System

r - 6

2

Side Force versus Leeway Angle

₉

3.

Driving Force Coefficient versus Heel Angle

12

4.

Side Force Coefficient versus Heel Angle

12

5.

Upright Coefficients of the Driving Force

16

I

6.

Upright Cöefficients of the Side FOrce

-

16

7.

Polar Plot of Boat Speed

27

Tables

1.

Range of IrlLlependent Parameters in Tank Testing

___ 3

2.

Output of the SAIL COEFFICIENT Program

- 1-3

3.

Sa1 Force Coefficients

17

4.

Predicted Performance for the SORC Data

--- 21

5.

Predicted Performance by Systematic Variations

of the True Wind

22

6.

Effect of Increased Sail Area on Predicted

Performance

-

28

7.

Effect of Increased Stability on Predicted

Performance

- _- 29

8.

Performance Program Flow Chart

- - -

30

Appendix

1.

Polynomial Coefficients

- - 37

f

NONCLATURE

Text FORTRAN

Symbol Symbol DefinitLon

name of boat

NCERT 10R cert-ificate nUmber

RHC bR, righting moment corrected (ft-lbs/deg)

h YCE heeling moment arm = 0.45 (1-1-DM)

DM measured draft

L height of foretriangle

J base of f oretriang].e

foot of mainsail

S SA normalized sail area =(I.J+E.P)

DPOL drag force polynonia]. coefficients

POLD name of, drag fore subroutine

SPOL side force coefficènts

POLS name of side force subroutine

KC total number of log entries

VB boat speed

VA apparent wind speed

WINA .jndjcated. apparent wind ange

iteration counter

BEEL heel

-ALEE leeway angle

smallest WINA tàken from the log datá

APPA actúal apparent wind angle

VT true wind speed

TWA trué wind angle

SIDEF side force (hull/sail)

in

velocity frame of

ref erencç

SO side force for arbitrary heel, speed and zero

leeway

S4 side förce fOr arbitrary heel, speed and

40 leeway

DRAG X drag force (=saii force)

in

velocity fraie

of reference VS VA

o,

A min VT FO F4 FR

NOMENClATURE (continued)

Text FORTRAN

Symbol Symbol Definition

TRI speed triangle subroutine

p density of air = 0.00237 lbs/ft3

v VMG speed made good to windward

CXO upright drag force coefficient in velocity frame

of reference

c CXO' ao uncorrected for heel

cYO upright side force coefficient in velocity frame

of reference

c CYO' CYO uncorrected for heel

cR,cH CX,CY faired upright drag, side fórce coefficents for

true wind angles between 20 and 180 degrees

acH

ACXO slope coeffïcient of CXC) dependence on heel

aCR

CY0 slope coefficient of CYO dependence on heel

2

Q-1. INTRODUCTION

A model of the yacht BAYBEA was tested at the MIT towing tank

facility in 1967 This mode]. was tested in calm water by systematically

varying the speed, heél, aúd leeway angles and measuring the resulting

side and dag forces. The ranges of these parameters are given in Table 1.

Full Scale Speed Heel Angle Leeway Angle 4 to 8 knots o to 3Ó degrees O to 6 degrees in steps of 2 degrees Table i

Thé forces resulting from these tests were ubjecte4 to a least

squares processing, deletion of dubious data and scaling. tO tu-l-1 size.

The product is two thirteen term polynomials, one eàch for side and

drag force, as a functIon of boat speed, leeway, and heel ang:e. These

polynomials are given in Appendix I.

With the hull force known, it is necessary to have performance

data to estiate the sail forces required to stablish an eqúilibrii.

between the aerodynamic and hydrodynamic forces.

In Janúary, 1974, a navigation/performance data form was prepared

for distribtitiôn tb all boats participat-ing in the 1974 SORC. The format

of these log sheets is given in Appendix 2.

The information requested included readings of onboard instruments, sea state, weather and current estimations, sail suit carrie4, as well

as time and position f ór each entry. Navigators were reeted tö make

frequent entrIes describing all stable sailing cpn4itipps encountered

so as to produce a large sample of data that could be procéssed with

importance vo aid in estimating the effect of sea state on performance

and to assist iti Synoptic correlations of racing conditons. To date,

MIT has received three completed race logs from the SORC fleet.

The SORC was chosen mainly because it coinçided conveniently with

our project progress and because of the high quality of competition.

It was intended originally to subject the entiré SORC data to a

statis-tical analysis in order to obtain --eflabe iMo at-ion concerning sail

forces and yacht per-forances. In der to do this, was necessary

to know not only the performance of each boat (speed and hee. for a given wind), but alsO the weather condition at a g;iven time and the relative position of each boat at the time the log entries were made. The log sheets were therefore prepared in such a way as to permit all

this inEo±matiQn to be written down. Since only three logs have been

receive4 by MIT after thê races, t was impossible to perform any

statis-tibal analysis, and it has been therefore decided tó evaluate only one boat, BAYBEA, using analytical and numerical techniques, rather than

státistical. Thus, only the information concerning the BAYBEA speed and

heel angle and the wind speed and angle were utilized in this procedure. The reason for choosing .BAYBEA is that her hull hydrodynamic forces described above had been known.

The procedure for obtaining f aired values of the sail force coef-ficiénts is described in the section entitled SAIL COEFFICIENTS PROGB»1. A second program, PERFORHANCE PRIcTION, accepts as input these sail

coefficients as well as a given true wind angle and spéêd, and calculates the requisite heel, leeway angle, atid boat speed necessary to establish

equilibrium. Both computer programs were written in FORTRAN V, using

bcth the lime Sharing Option and tha Bathh System of MIT's Information Processing Center.

Figure 1 explains thé coordinate system used throughout this report as well as the symbols which are explained in the nomenclature.

Note t-bat thé coordinate SyStem is aligned with the direction of

motion of the yacht. This- differs from the direçtion of the fore and

aft ëënterl-iúe of the hull by the amount of the leeway angle.

It is important for the reader to keep in mind that the quantitative results obtained from the study were obtained from a very limited set of

data. The results should therefôré be regarded as a demonstration of thè

method of ànalysïs, and as a réasonablè gross ëharcterzation Of sailing performance.

-I

6

Fig. i.

Coordinate System

q

2. SAIL FORCE COEFFICIENTS PROGRAM

This program computes upright, f aired values of the sail driving and side forces coefficients ät all points of sailing in the yacht

velocity frame of reference. The computation is. based on full size

logged entries, results of towing tank tests and the IOR III measuremens. The yachtts name and bR certificate ntbet äre read in as are its1 righting moment, estimated heeling moment arm, sail area and polynomiaiJ

coefficients of drag and side force as determined by previous towing

tank tests. The righting moment used is the bR corrected righting

moment (RMC); the heeling moment arm is estimated by the empIrical formula h = .45(I+DM); and sai]. area Ls defined for all log entries as a constant equai to thé area of the fore triangle plus mainsail area less roacb. The polynomial coefficients were taken from reference (1) which contains

the orIginal BAYBEA tank test data. The ethodology behind these

poly-1

nomials is fully described n [1]. The polynomial coefficients as well

as-theIORIII data for BAYBEA are given in the Appendix. Th.e following

are the values of the six IOR parameters used in the calculation:

Raw log entries of boat speed, vS , indicated apparent wind speed,

vA , indicated apparent wind angle, w , and heel O , are inputted to

the ca].culat-ion sequence..

The side force, _H which is a horizontal veòtor perpendictilar to the

boat speed, is found frOm the transverse equilibrium condition shown in

Fig. 1.

FR h / cosO =. M O

Next, the leeway angle, À , corresponding to FR , is found from the

assumed linear reiat-ionship between the side force and the leeway angle

(Fig. 2). -. 57.13 i = .19.93 DM = 7.29 P = 53.18 E = 17.5 RMC 2129.5 (F11-F) X = 4 (F4-F0)

where F0 and F4 are the side forces at A = 0° and A 40 respectIvely,

found by calling twice the subroutine POLS, which computes side force from a given polynomial coefficients set, boat speed, heel angle, and lee-way angle.

Fig. 2 as adopted from Fig. 10 of [1] based on the BAYBEA tardc

tests. It indicates that, for example, at 100 heel and 6 knot speed,

the side force increases ¿lmost linearly as the leeway angle increases. For larger values of heel the relationship Is not quite linear, but because .f the scatter of data poíts. th±ough which the polynomials were originally fitted, and because the plynomial representation of the hüll

forces was unreliable for leeway angles greater than 60, it was decided

to linearize side force with respect to leeway angle. A = 6° was the

largest leeway angle at which t1e model has been tested All coefficients

in the sidè force polynomial that are nonlinear in A have been

there-fore set to zero*.

the wind angle,, w , indicated by the masthead indicator is not the

actual aparent wind angle , which is defined as the angle which the

vecor si of the boat and true wind velocities makes with the boat velocity.

Thre correct±ons are made to w in order to obtain The first

cor-recidn is due to sail interference. It assunes màst heád anemometer

place-ment and is abitraily defined by the transforniat-ion,

(180°-22°) (w-w_min. )

- 180-w

min

In effect it shifts the lowest indïcate wind angle wrnin (which happe.ed

to be 250) to 220, causes greatest corrections for close-hauled sa:iiing,

and decreases linearly to zero for rúnning. With this correction, the

spùd made good values are ore reasonable. Comparable corrections to

wind speed were not rnàde.

The next correction results from adding the leeway angle A to w' ,

and, is necessary in order to obta:i the apparent wind angle relative to

the boat velocity direction, rather than boat centerline. The last correct-ion

*Tbjs 'is a matter which has caused concern for at last the last decade

[2], and still appears unresolved Tank predicted side forces, coupled

with full scale static stability and obsèrved heel angles frequently

result in predicted leeway angles as high as 8 degrees There are many

who question whether such large angles are actually encountered, and

accurate full-scale measurèments sti 1 appear to be lacking.

F4

Q,

C.,

F

Fig. 2

Side Force versus Leeway Angle

2

4

5

X (deg)

e

.\O

1Ç?

I'

a)

0

_I I (I) _I I I I A t I I

applied resolves the indicated angle from heeled to upright values:

= tan1[tan(w+X).cos0]

The apparent wind angle can now be entered to the velocity triangle

computation, together with the logged boat speed, _vS , to yield thé

true wind speed,

_{VT ,}

and angle y

VT =

/V2

+ VA - 2VA V coSe

V 2

+v

2

V

2

0

_-1

S T.

A

y=180 -cos

E

]

VT

Thé drag force, FR , is computed by thé subroutine POLD which is

entéred with. the logged values of boat speed, heel angle and computed

leeway' angle. Both side and drag force are in terme of the tL.qeoCjyfl

frame of reference. That is, the longitudinal axis is in the direction

of movement of the boat, the vert-ical axis is normal to the sea level,

and the transverse axis s horizontal, perpendicular. to the two others.

These forces are nondimensionalized acëordïmg to:

CR(

-+PVA2 S

H0

+P''A S

c and are the sail force coefficients calculated for each logged

entr but uncorrected yet for heel. The sail area In this normalization

process has bêen kept constant for ali points of sailing. For a given

true wind strength (and representatIve sea state) the actual sail area

and disposition will vary greatly depending on the point of sailing. The

convention has been adopted that this variation be absorbed into the

coef-ficients themselves as the forces vary. That this is not altogether

arbi-trary can be seen if it is remembered that the nature of sail forces on

-a spinn-aker -are completely different from those on -a close-h-auled jib

regardless of the fact that their areas are different However, if we

maintain the poiñt of sailing but now vary the wind strength it is obvious

10

that sail suits and shapes will change.

It is reasonable to expect that the sail force coefficients

them-selves vary with heel. This dependence is in addition to the cosO

variation that the boat centered side force expetiences. At = 27°

there happened to be 9 separate log entries supplied. For these points

the coefficients c and c were calculated and plotted in Figs.. 3

and 4, together with the GThbBACK coefficients, taken from [5]. The

plotted points indicate a reduction in the magnitu4e of the coefficient

with heel. With the limited data available, a straight line least

squares fit was considered satisfactory as an interim measure. For both

c. and.

cp lines the slopes are gïven by CRÒ and RO . The points

on the Obtained lines corresponding to O = 00 are called the upright

sail force coefficients:

CRO / ao

CROCB,

(1-CH0 = C(l

CH

O)

Wé can note the similarity of the BAYBEA coefficients heel dependence to

the GCRACK coefficients. The latter are smaller than the BAYBEA

coef-fcients by approx:Lthately 22%. This can be explained by the. fact that

the sail camber designed in the

VT '

' 's'A

W ,

rat-jo is much 'bigger' on modern boats than' on the yachts

thirties. The computed value of , X , c , cH0

and FR , along with the corresponding logged values of

and O are presented in Table 2.

This page intentionally blank.

12

THE AVERAGES 0F

'

9 WINDWARD' VALUES OP CXO ¡INI) CYO ARE RESPECTIVELY:0.667

2.332

FOR WINDWARD POINTS

Cb'2.385 CD0.443 L/D=5.386, AT 20° CRO.400' C»2.392 THE SLOPES OF CR AND CH

AT TRIS ANGLE ARE RESPECTIVELY:

2.392 -.400 Table 2 C11, 2.33, c,,/20 .016 CR,, 'I VR VA WTNA APPA HEEL ALEE CXO CYO VT 1W4 SEflE F ORAG F

5.3

q

32.9 32. Ifl.O

3.4

0.7,1 3.('4

.3

64.1

123. 17.2:. 5.3

9.0

27.0

27.0

tO.O

3.4

O71

3.04

4o9 56ot 723. LiZ, 503

5.0

91.0

9O4

3l

i..n 1.79

2.64

7.3

136.9 220. 15fl. 3.fl 2.fl 150.0 149.6

0.2

0.2

3.33 1.05

4.8

167. 15. 46.

4.0

, 5 135,0 134,7 1.0

0.6

2.14

1,74

6.9

L590

73. 90.

6.5

14.0 28.0 27.6 20.0

4.4

0.69

2.96

8.8

47.7

1380. 136. 7.6 22.0 25.0 2.3.0 .30.0

4.5'

.,

0.74

2.17

15.3 34.1 1908, 116. 7..5. 17.0 21,0 ?5!4 20.()

3.0

0.79

2.01 10.1

42.9

1180. 572.

7.2

28.0' 26.0 24.5 30.0

5.3

0.71 2.62 13.8 37.0 1908. 567.

72

22.0. 20.0 .27.0 27.0 25.1 25.4 30.0 10.')

5,7

. 5.3

0.53

f1,71 2,17 2.62 16,0 13.8 36,1 38.1 1908, 19)8. 509. 567. 7.2 18.0 27.0

'5.7

25.0

4.1.

0.72

2.45

11.9 40.8 1664. 523. 6,3

5.8

16,0, 12.fl 77,0 27.1 27,:fl 26.4 20,0 Ifl.')' 4,.? 2. R

0,49

0.41

2.27

1.71 LÓ.8 42.4 47.2 1380. 721. 3:12.

'01.

6.7

13.0 27.0 26.1 15.0

1.0

0.71 2.37 7,.6 49.0 1064. 328,

7,8

12,0 50,() 48,1 ' 10.0 1.3 1.46 1.71

8.9

88.6 723. 632.

7.3

8.0 100.8 99.5

5.0

0.8

2.02 1.78 11.7 137.6 366. 420.

7.0

.

9.0

170.0 170.0

1.0

0.2

1.20

0,26

15,9 174,4 71. 336.

7.5

9.0

121.0 1.19.8 5..0

0.7

1.85 1.40 14.3' 146.9 366. 488. 8.3 10.0

95.0

97.4 14.0 1.5

3.42

3.67 13.8 134.0 997, 957, R 2 11 0 60,0' 54,9

25,0

2,9

3,64

6,55

9.2

101.8 1664. 987. 8.1 13.0 75.0' 70,5 21.0

2.5

2.12 3.67 12.8 107.0 1440. 877.. 7.2 13.0 25.0 23.6 15.Ó

2.5

0.94

2,3F

7.0

47,9

1064. 436.

6,1

8.0 60..0

58.7

1,0.0 2.0. . 1.56

3.84

7.3

110.4 123. 299.

6.7

9.0

40.0

30.7

l'I.')

2.2

1,27 3.40

5.6

86.1 793. 304.

7.1

13,0 27.0 25,7 15,0'

2,6'

088

2,37

7,3

5Q,7 1064. 410.

7.6

10.0 60.8 56.9 28.0 '2.9 2.45 '5.81) 8.6 1')4.3 '1380.. 611. 7.2 9,0

60.0

5.7..3 28.1)

3.3

2.35 7.16 7.9 1107.2 1380. 476,

6,8

15.0 28,0 .26,7 12,0

2.3

0.50

1.35

9.4

45.7

86?. 327. 7.1

17."

28.0 26.8 .17.0

2.9

0.55

1.:62 11.1 43o5 1194. 424.

7.0

17.0 28.0 26.9 25.0

4.6

0,73

2,74

11.2 43,3 1664. 471',

L2

15.0 32.0 30..5 20.'!) .3.3'

0.eS

2.58

9.5

53.1 1380. 476.

54

4.0'

148.0 119.4

0.6

0.2

2.75

0.79

FiR' 162.9 44. 153.

5.1

5,0

150.0. 149.6 '

0,6

0,2

1.59 ' 0,51 9o7 165.0 44. ' 138. R.? 20o0 70.0 61.3' 30.')

3.0

1.86

262

17.6 87.1 1908.' 1485. 8.5 16.0 75.0 68.9 24.0

2.5

2.06

2.92

15.2 100.4 1610. 1211. R,')

90.

110,0 111.6

12,0

1.5

319

3.16

14;1 143.5 862. 748.

8.0

8.0 90.0 88.1

10.0

1.2

3.85

3.84

l'I.!.

134.1 723. 138.

9.3

14.0. 120.0 122.0 15.0 1.1 3,08 2.04 20.5 144.6 1064. 2088,

6,5

13.0 30.0

29.0

12.0

2.6

0.57

1.80 8.1) 52.3 862. 21.9.

6.3

15.,0 28.0 27.3 13.0

3.0

0.41 1.49

.8

44.4

930. 260.

7.8

8.0 120.0 119,3

3.0

0,4

2,86 1.03 13.6 149.2 220. 622.

5.3

6.0

180.0

1800

0.0

0.0

1.17

0.0

11.3 180.0' '

0.

148.

LEAST SQUARE SOLUTIONS FOR THE HEEL CORRECTIONS:

CR'

.668.,

aCR0/ae

The vàlues of c and cH0 are plotted next versus apparent wind

angle, $ . A modified least squares spline fit program called SIJPRDK

was used to fair these pints. SUPRDK differs frdm thé standard spline

fit in t-hät the resulting curve is required to pass through the end

points and may at these points have specified slopes, as in a

clamped-clamped bean. Further program flexibility is available through

place-ment of "ducks" which stat-ist-ically weight the data in the program for

éhosen abscissa values. Dücks weé placed at 520,

100°,

ànd 148° apparent

wind angles.

The logged wind angles have a rather random distribution along the

apparent wind angles axis. It was decided to fit the coefficients curves

in the range of angles

ß = 20°

to 180° , i.e., to cover the entire

range of points of sailing. The following procedure was applied in order

to find the values of CR and CH as well as theït slopes at = 20°

It is based on the assumption that the lift-drag ratio sts constant in a widé rangé of closé-hauled angles due to adjustments of the sheets for

a g:iven apparent wind direction,. Since 9 log entfies were available at

w 27° it wàs pôssible to calculate a relatively reliable value of

the lift-dtag ratio at this angle. For these 9 entries the following

average valües were found:

(27°) = .667

(27°) = 2.332

(27°) = 19.4

(27°) = 4.00

The apparent wind angle resulting from these averages is:

(27°) = tan'[tan(w27Ø) + 4.0°) cos 19.4°) = 26.6° where (180°-22°)(27°-25°) 22° - 4° (27°) - (l80°-25°) + - 2 14 1

w

The lift and drag sail force coefficients ere deteïmined by resolution

of boat side and drag forces with respect to apparelit wind angle.

CL

Cj0(7o)

COs(27O)_

CD = C110(270) sin(27C.)

+ CF(27Q)

COS8(270) = .443

LID 5.386

This lift/drag ratio is slightly more than the rule of thi.imb value (approx.=5)

claimed for modern ocean racers. The small data sample prevents placing

too muh significance on this value.

Rearranging the terms in the above equation and solving fOr _CR and

CH at = 20° gives:

CR (200)

= CL

sin20 - c, cos20 = .400

CH

C 2 0 ° ) CL cos20 + CD

siclO 2.392

The slopes at = 20° are:

3CR

(200) _{CL cos2O + CD sin20 = 2.392}

CH

- (20°,) = CL sin20 + CD cos20 = -.400

Thè above values f orm the boundary conditions for the spline fit.

15

8 7 6 5

4

3 2

Fig.5

Upright Coefficients of the Driving Force

I I I I I I I I I I

o

o o

Driving force coefficients

o o o o o o

o

-

.1

I I I I I I J

20 :30

40

50

60

70

80 90

lOO 110

20

30 40

150

60 170

80

Apparent Wind Angle /3

(degrees)

40

50

60

70

80

90

lOO 110 120

130 140

150 160 170 180

/3

Fig.6

Upright Coefficients of the Side Force

Table 3

8 CR CH CR CIL : CR CH CR CH ß CR CH

20.

0.40

2.39

52

1.90

4.21

84

2.67

3.62

116.

2.84

1.97

148.

2.37

0.89

21.

0.45

2.39

53

1.94

4.25

85

2.69

3.56

17.

2.84

1.94

149.

2.34

0.86

22.

0.50

2.39

54.

1.98

4.29

86.

2.70

3.50

118.

2.83.

1.90

150.

2.31

0.82

23.

0.56

241

55

2.01

4.32

87

2.71

3.44

119.

2.83

1.87

151.

2.28

0.78

24.

0.61

2.43

56

2.05

4.35

88

2.72

3.38

120.

2.82

1.83

I52

2.25

h74

25.

0.66

2.45

57

2.08

4.37

89

2.73

3.32

121.

2.82

1.80

153.

2.22

0.69

26.

0.71

2.49

58

2.11

4.39

90

2.74

3.26

122.

2.81

1.76

154.

2.19

0.65

27.

0.76

2.53

59

2.14

4.40

91

2.75

3.20

123..

2.81

1.73

155.

2.15

0.61

28.

0.81

2.57

60

2.17

4.41

92

2.76

3.14

124.

2.80

1.70

156.

2.12

0.57

29.

0.86

2.62

61

2.20

4.41

93

2.77

3.08

125.

2.79

1.67

157.

2.08

0.53

30.

0.91

2.68

62

2.23

4.41

94

2.78

3.02

126.

2.78

1.63

158.

2.04

0.49

31.

0.97

2.74

63

2.26

4.41

95

2.78

2.96

127.

2.77

1.60

L

159.

2.01

0.45

32.

1.02

2.80

64

2.29

4.40

96 2..79

2.90

128.

2.76

157

160.

1.97

0.41

33.

1.07

2.87

65

2.31

4.38

97

2.80

2.85

129.

2.75

1.54

161.

1.93

0.37

34.

1.11

2.94

66

2.34

4.37

98

2.80

2.79

130.

2.74

1.51

162.

1.89

0.34

35.

1.16

3.01

67

2.36

4.35

99

2.81

2.73

131.

2.72

1.47

163.

1.85

0.30

36.

1.21

3.09

68

2.39

4.33

100

2.82

2.68

132.

2.71

1.44

164.

1.81

0.27

37.

1.26

3.17

69

2.41

4.30

101

2.82

2.63

133.

2.70

1.41

165.

1.77

0.23

38.

1.31

3.24

70

2.43

4.27

102

2.83

2.58

134.

2.68

1.38

166..

1.73

0.20

39.

1.35

3.32

71

2.45

4.24

103

2.83

2.53

135:.

2.67

.1.35

167.

1,69

0.17

40.

1.40

3.40

72

2.47

4.20

104

2.83

2.48

136.

2.65

1.31

168.

1.65

0.14

41.

1.45

3.48

73

2.49

4.17

105

2.84

2.43

137.

2.63

1.28

169.

1.61

0.12

42,.

1.49

3.56.

74

25i

4.13

106

.2.84

2.38

138.

2.61

1.25

170.

1.5.7

0.09

43.

1.54

3.64

75

2.53

4.08

107

2.84

2.34

139.

2.59

1.22

171.

1.53

0.07

44.

1.58.

3.71

76

2.55

4.04

108

2.84

2.29

140.

2.57

1.18

I

172.

1.49

0.05

45.

1.62

3.79

77

2.57

3.9.9

109

2.85

2.25

141.

2.55

1.15173.

1.45

0.04

46

1 67

3 86

78

2 59

3 94

110

2 85

2 21

142

2 53

1 11

174

1 41

0 02

47.

1.71

3.93

79

2.60

3.89

ii]

2.85

2.J7

143,.

2.51

1.08

175.

1.37

0.01

48.

1.75

3.99

80,

2.62

3.84

112

2.85

2.13

144..

2.48

1..04

176.

1.33

0.00

4

179

4.05

81

2.63

3.79

113

2.85

2.09

145..

2.46

1.01

177..

1.29

0.00

50.

1.83

4.11

82

2.65

373

114

2.84

2.05

146.

2.43

0.97

1.78.

1.25

0.00

51.

1.87

4.16

83

2.66

3.68

115

2.84

2.01

147.

2.40

0.93

179..

1.21

0..Ö0 H .. ... .

180.

1.17

'0.00

3. PERFORNANCE PREDICTION PROGRAN

The previous program gives a continuous curve representing upright

sail force coefficients as a function of relative wind angle.* Given

a true wind angÍe. and speed, this progra uses an iterat-Ive method to

achieve hydrodynanu.c and aerodynamic equilibrium Side force is assumed

to be Linéar in leeway. The. region below the range of the original towing

tank polynomial (VB ( 4 knots) is approximated by a straight line ** For

VB > 8 knots, the. extrapolated valües as given by the polynomials were taken to be accurate.

The flow chart of this program is presented on. the page 30. The Performance Prediction Program is initialized by reading in values that. pertain to the yacht itself: NA, ÇERT, RNC1 SA, YCE, SPOL,

DPOL., and CX and CY for APPA = 20 to 180°. The iteration dummy variab].es

VBASS and OLDALE are given initial values and the iteration counter, KÖNTRL,

-is zerOed. Particular values of true wind angle, TWA, and speed, VT, are

inputted Apparent wind speed, VA, and angle, APPA, are computed by calls

to subroutine TRI.

The first portion. of the program puts the yacht in heel equilibrium. The heel angle is incremented until the heeling moment is equal to the

righting moment If the heel angle exceeds thirty-nine degrees, the

program teinates éxecution, print.s a warning mess4ge and requests another. valüe fr true wind angle and speed..

The next part of the program puts hull drag and side forces into

equilibrium with sail forces by adjustments of speed

_and

leeway. Leeway,.

ALEE, is zeroed and the boat speed, VB, is adjusted from the initial value

VBASS = 2 knots until the hull drag equals the longitudinal sail force

*The syiñbols used in this section have intentionally been left in their original form as computer program variable names for ready identification with the flow chart enclosed.

**Ä straight line was used here, rather than a parabola as a temporary

expedient to avoid a large discontith.tity in slope at 4 knots. The present

tank test polynomial scheme is deficient in not forcing the proper behavior

at low speeds We are presently developing an improved fitting technique

which will Overcome this problem.

18

---J--At this point, ALEE = O and HEEL remainè às ca1cu1atd previously.

Next, ALEE is adjusted so that hull side force equals sail side force.

If ALEE is not within a specified convergence tolerance, VB and AL

iterations are repeated assuming nôw the latest value of BEEL and ALEE

by adjusent of VB. When ALEE finally converges, VB is tested for

convergence. If VB has not converged, thé vélocl.ty iteration is

con-tinued until equilibrium is attained. Presently, the convergence

toler-ances are: ALEE: .05°; VR: 0.05 knots;

HEEL: Ö.O].°.

If the number of iterations exceeds a specified value, an error

message is generated and another true wind is read in. Similarly,

exécution Is stopped if VB, HEEL or ALEE exceed specified upper limits,

which are presently: VB<l3 kts,

HEEL39°, ALEE0°.

The values of the hull forces are given as continúous fúnctions

of HEEL, ALEE and VB. Sail förce coefficients, CX and CY, are given

:j _{discrete steps for apparent wind angles between 20 and 190 degrees.}

Since the sail force

coefficient

curves were found à spine

through "experimental" points, it should be no surpr:íse to f mcl that when a true wind angle and speed, corresponding to logged data, are

inputted, the exact same boat speed, heel and leeway .re not necessarily

reacquired. Table 4 gives the predicted values of the Speed, heel,

leeway, speed made good, and forcés hích result from the true wind

speed and àng].é values corresponding to those in Table 2.

The differences in values are due to scatter in CXO and CYO. Compare

thé discrete CXO,CYO values with the CX,cY curves.

Similarly, the PERFORMANCE PROGRAM can be used tO calculate Speed

polar diagrams. Speed polars were computed for true wind speeds of 5,

7.5, 10,12.5, and 15 imots. The calculation of VMG waS done simu1taneoùSly.

By inspection, the best speed made good to windward for a given wind speed

can be deteinfd. The results are shown in Fig. 8 and in Table 5.

It should be remembered that all caicülations are pàrformed using

a "stretched" apparent wind. To unstretch this angle is siply a question

of transform ng the angle APPA back to WINA by the f ôrmula on pagel U

tu addition to the BAYBEA performance predictions, some interesting

increased by 10%, and the other with RNC (stability) increased by 10%. The output of these computations is in Tables 6 and 7, respectively.

As expected, the boat with the extra sail area sails significantly faster at low wind speeds, especially when beam reaching, and heels only slightly more, while the speeds ±ncreàse very little in strong winds. The second boat shows only a slight effect, in windward sailing, of the increased stability on the speed, in spïe of the decreased heel angle. These two calculations are examples of the application of the log data to

the handicapping problem. An analysis of these art-icu1ar changes in

relation to rating and time allowance systems -is not within the scope of this report.

20

tCAT IßMEz FavOlA CF9TIF.I(a1.Enj5u3228 RHC. '125.5 CE29.0 54=1035.0 TFE S1.GPI:5 0F T16

116ES CORRECTI6 FOR T14 IEEI. £P6I.E SQl

0.007.'2 FC)) CX A1D -0.02511 FCR Cv

'1

K1S)

TWß UIFG)

V.0 (XIS)

)-EL (DEC) 4LEE (91);)

VA orS) APPA .(DCGI

V 1X75) SF (11H 5.3 64.1 6.0 1Oo' .2.1 9.6

.9

2.61 743. 2L4. 56.5 .5.2 .4 1.3 11.9 21.4 2.96 (75. 160. 1.3 116.9 6.1 4.2 1.0 5.) 704 457 307. 221. 4.8 16:1.9 2.5 0.2 0.2 7.4 15'.3 -2.45 12. 21. 6.9 159.(. 3.9

).5

3.6 137.' -3.53 57.. 81. 8.8 40.6 6.7 19.4 4.1 16.1 ¿7.8 4.43 1422. b7. 15.4 36.2 7.1 3').9 '3.0 215 25.0 5.71 2441. 519. IC.8 43.3 6.8 22. 5.1 16.4 21.0 4.92 1787. 433. 13.9 39.4 7.0 7.13 llaR 26.4 5.43 2383. 543. 16.1 39.1 7.5 32.5 7.1 22.5 26.9 5.115 2183. 673. 14.0 4,3.6 7.2 29.t 70.0 21.1 5.44 2413. 586. 12.0 42.1 6.5 2',.Ç S.S 1.1.1 77.0 5.12

flll.

407.

1.8

43.3 6.8 2?.'. 5.3 16.4 26.9 4.52 17114. 4.9. 1.3 47.3 ¿'.1 14.4 3.9 12.2 26.1 4.111 1)99. 252. 7.6 45.3 6.4 15.4 3,11 11.7 27.0 4.1.5 (172. 299. 9.9 bO,.b 7.7 19.6 3.1 1.1.9 48.4 0.19 1530. 657. 11.? 131.6 1.1 7. 1." 1.9 96.7 -5.69 563. 5,79. 114.4 7.0 0.4 0..) n.s 170.0 -6.qO 31. 339. 14.3 146.5 7.8 6.4 0.11 I1i8.1 -6.55 475. 13.6 134.1 13.1 11.3 1.3 11.0 97.11 -5.14 q4.3_ 1C2.4 7.8 17.9 2.7 10.8 51.5 -1.67 1385. 683. 12.9 1Cl.'. 11.5 24.1 1.7

1'.l

69.4 -2.54 1942. 1236. 7.1

'..2

b.0 13.1 3.8 11.9 26.1 4.00 1133 241. 7.3 ¡10.5 7.1 11.1 2.0 8.2 56.2 -2.50 944. 399. 5.1 86.8 6.6 LO..6 2.? c.e ).3'7 794 293. 1.3 51.0 6.4 14.8 3.6 12.3 27.4 4.00 1L21. 2114. 11.7 104.6 1.6 15.9 2.! 11.0 57.2 -1.52 1215. 592. 11.0 IC1.:5 1.4 13.5 2.? 9..) 56.8 -2.12. 1)23. 491. 9.4 45.8 6.7

1.5.

4.5 14.0 27.0 4.64 1515. 371. '11.2 4'.c 6.9 ¿3.5 5.4 16e') 27.4 4.9.1 1q80. 469. '11.3 44.7 7.0 23.8 5.3 17.0 21.9 4.96 1q14. 492.. 9.6 53.3 7.2 21.0 4.1 15.0 31.1 4.24 1152. 51)1.. 9.6 162.9 4.6 0,5 0.4 4.6 146.2 -4.35 69. 114. 9.7 lsS.0 4.9 0.9 0.4 5.1 150.6 -4.75'

6'.

1:30. 17.1 138.2 HEEl. 3q.oú N1(:r. TO P) f P 15.3 10,3.') 8.11 31.0 4.1 16.2 111.4 -1.67 771,% 1786. 14.1 143.6 7'.') 1.4 0.') 9.0 111.2 -6.39 5411. 694. 11.1 V34. 1 1.7 11.5 1.2 .fl 90.2 -5.35 627. 576. 20.5 144.1 8.9 13.0 1.? 1'..? 113.6 -7.23 916. 1472. 8.0 52.5 .6.7 16.7 3.1 13.2 28.7 4.00 1783. 349. 5.5 .4.7

(.1

20.5 4.Rì

l.4

26.9 4.75 1612. 391. 1.3.6 149.2 7.6 '5.2 0.11 0.I 120a6 6.49 384. 510e 11.3 180.0 5.3 0.0 01.0 6,0 .1110.0 -5.30 0. 148.

Table 4

0F' (I.8(

PO47 NAPE) 9IIYREA

C(1TIÇIC81UÇ))2'#

PC. Zl29.5

YCE.2q.O

SA.1035.0

TI-F SLCPES UF TI-F

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X A'1C -3.j2517 FCR (y

97 11(15)

Twa 1,3Fr,)

VR IKTSI

I-EEL infO) hl;F!. iO6)

VA (iTS1 APPA IDEO) - VUG (KIS)

SF (1.8) ßF

(liii

5.0

b.c

APPAPÇMT WINt ANGLE

)9.O DFO. 71-4F SAILS 111FF 31 J APPARENT WI6t ¡661 E 19.0 CFI.. TI-SII ILS 1.11FF 5.8 32.0

£DPARET WINC i.r.LF

19.9 I!F..

TIlE SAILS LUFF

5.0

33.0

APPARENT WINC ?P*C.l.E

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TI". SAII.S

11.3Cc

5.0

34..)

APPARI:NJ Wilsi A6Ç,LF . 11.9 CEO.

TI'E SAfl.Ç 111FF

S.0

35.0

APPAREN1 wiNt ANGLE

7-).i) GPO. TIII SAILS LUFF S.0 36.6 3.5 6.') 4.7 °.1 21,2 2.86 S('P. 5.i) 37. 3.6 1.fl 4.1 A.2 21.6 2.09 515. 63. 5.0 38.0 3.7 7.0 4.7 0.2 21.9 2.92 171.. 8i3. S.0 39.3 3.8 7.1 4.6 77.3 2.54 527. 92. 5.0 40.6 3.5 7.2 4.6 D,3 22.7 2.94 534. 97. 5.0 41.0 3 ç 7 3

4'

8.4 23.0 ..')fl 540, 101. 5.3 42.3 4.0 7.4 4.5 0.4 23.3 3.60 540. 106. S.0 43.0 4.1 ì.4 41 0.5 21.7 3.07 555.

ii').

5.( 44.0 4.2 7.6 4.7 8. 2..O 3.C3 563. 114. 5.0 45.0 4a3 7.7 4.1 P.6 24.3 3.C5 570. 119. S.0 46.0 4.4 7.0 4.1 3.7 24.6 3.05 578. 123. 5.0 41.0 4.5 1.') 3.9 1.7 24.6 3.06 106. 127. S.0 48.4) 4.6 3.6 0.9 25.1 3.06 593. 132. 5.0 49.0 4.1 8.1 3.1 0.8 75.4 3.06 601. 136. 5. 56..' 4.8 3.2 3.6 .R 25.1 3.06 6C0. 140. 5.0 51.0 4.0 8.3

3.'

8.') 25.9 3.05 615. 144. 5.0 52.0 4.S 8.4 3.4 Ile') 26.2 3.03 672. 148. 5.0 3.0 5.3 8.5 3. .0 26.5 3.01 628. 152. 5.0 4.0 .1 8.5 3.? 9.0 76.7 2.09 634. 356. S.0 55.L 5.2 9.6 3.1 9.0 27.0 29b 640. 160. 5.6 56.0 5.2 8.7 3.1 9..) 27.3 2.93 646. 164. S.0 57.6 5.3 8.8 3.6 ..1 77.6 2.89 651. 168. S.0 58.1) 5.4 8.8 3.0 9.1 27.9 2.85 oSI. 111. S.0 55.6 5.4 C.c 2.9 1.1 79. L 2.00 66)). 115. 5.0 60.0 5.5 43.') 7P 9.1 28.4 2.75 664. 179. S.0 70.0 5.0 9.2 2.5 9.0 1.5 2.C3 683. 207. S.0 8C.0 6.2 9.0 2.2 8.6 35.0 1.07 610, 226. 5.0 33 6.2 8.5 2.0 R,)) 38.8 -0.00 631. 230. S.0 100.0 b.1 7.6 1.0 1.2 ',o0 -1.07 5ò6. 220. 5.0 F1C.0 5.9 A 4 1.7 6.3 '.13.1 -2.03 411. 197. 5.3 120oj 5.5 4.1 1.5 5.3 '5.2 2.16 360. 165. S.0 )3C.0 4.8 3.1

I.'

4.2 7.1 -3.1) 229. 128. S.0 140.0 4.1 1.6 0.9 3.2 115,7 -3.12 111. 94. 5.0 153.0 3.4 0.1 1.1 2.7 110.8 -2.93 53. 63. S.0 16C.0 2.8 0.4 0.3 2.5 137.6 -2.65 28. 39. 5.0 11').O 2.6 0.1 0.1 2.5 119.9 -2.51 9. 29. S.C. 180.0 7.5 0.0

fl0

2.5 130.0 -2.47 0. 26.

Table 5

i

4 C4T AF.E! PAY8EA CFQTIFICATEZLSO3778 k'C. 2129.5 VCE.2O SA1O35.o.

ThE S1PES OP THE

1.I6ES CüPRECTUC.

Tb-C b-H. AÑI.LF ME. -u.r.n'2 F0. CX 4P() -0.0251 T FOR CV

vi IKiSI

TWA (DF.GI

VO (K1S.P

HEEl.

IflEr.j ALEE ID-CI

VA (IbiS) APPA IflFG)

Vb-O (KIS) SF (LP) ÒF II.R) 7.5 30.u3 APPARNT Ab.(,LE

N.f. nc.

T'lE SAILS LUFF

7.5

31.0

'APPAREÑT '.16E ,6IWE

u.o ElM.

THE 5411.5 LUFF

7.5

32.';

P3QINT wI6C 1'%ILE

19.9 1C.

1H' SAILS LIiEF

7.5

33.0

APPARENT WINE AN&;LE

on n 1H

MIL' 1.5 34.0 APPARÑT '.RC 8601.E 'j.o cEe,. 1,41 SAILS iUc 7.5 35.0 4o4 -12.5 6,'. 11.4 22.1 3.64 94). 154. 7.5 36.0 4.6 12.7 6.1 11.6. 22.4 3.74 96U. 163. 7.5 31.0 4.8 13.0 i.R 11.1 22.7 3.82 919.

IlL.

1.5' 38.0 5.3 13.2 5.5 II'.8 . 73.fj 3.91 995. 1RO. 7.5 39.0 5.1 13.4 S. U. 3.3 3.90 1016. 189. 7.5 43. 5.3 13.7 5.0 ¡2.0 73.6 4.05 1)35. 197. 7.5 41.0 5.4 13.S 4. 12.1 73.9 4.1) 1151. 24)4,. 7.5 42.0 5.6

14.1-4..

12.2 24.2 4. 14 1067,. 215. 7.5 43.0 5.7 14.3 4.4 12.3 '4,6 4.17 1082. 724. 1.5 44.0 5.0 14.4 4.3

¡'.4

24.9 4.1.8 irlOs. 233. 7.5 45..) 5.9 14.6 4.? 12.4 25.3 4.19' 11Cl. 243. 7.5 46.0 6.0 14.7 4.1 12.5 75.6 4.19 1115.

22.

7.5 47.0 6.1 14.0 3. S 1.7.9 76.0 4.18 1129. 261. 7.5 48.) ('.2 1S.0 3.0 12.5 76.. 4.15 1139. 270. 7.5 ..5.0 6.3 15.1 3.P 12.6 26.8 ''P.1.3 1149. 279. 1.5 50.0 t..4 15.2 3.7 12.6 27.2 4.09 liSio 2890 7.5 91.0 6.4 15.3 3.6 12.6 21.6 4.C5 1164. 290e 7.5 52.,) 6.5 15.4 3.6 ¡2.6 28.0 4.00 1111. 307. 7.5 53.0 6.6 15.5 3.5 12.6 28.4 3.95 1178. 315. 1.5 54.0 6.6 15.5 3.5 12.1. 26.0 3.85 lLES. 324. 7.5 . 55.i ('.1 1,5.6

3'.

17.6 29.3 3.82

iti.

3ra. 7.5 S6oC 6.7 15.7 3.4 12.6 29.7 3.75 1197,. 341. 1.5' 57.3 6.8 15.7 3.3 ¡2.5 .30.1 3.60 12C2. 34.9. 7.5 58.0 6.8 15.8 .3.3 12.5 .10.6 3.60 1207. 157. 7.5 59o0 6.8 15.9' 1.1 17.5

lI.)

3.52 '1212.. 365. 7.5 6i3.1 6.9 15.9 3.2 17.4 11.5 3.4.3 1216. 373. 7.5 70..) '7.1. 16.3 3.0 12.1) 36.0 2.44 1244. 435.. 7.5 59.0 1.3 16.1 2.6 1t,3 40.7 1.24. 1235. 412. 7.5 9u.0 7.3 15.4 2.(' 1.0.5 '45.7 -0.00 F175. 401. 1.5 ICC.0 7..! 14.0 2.4 c.s c..9 -1.21 1:5R. 46'.. 11,0.0 7.2 11.9. 2.11 8.4 56.6 -2.4:7 814.. 422. 1.5 120.0 1.0 9.2 1.6 7.3 2 7 51 ('79. 361. 1.5 O.0 6.7 (1.! . 1.

t.(i

1.1.9 -4.31' 461. '287. 7.5 ' 140.0 6.2 3.6 0. . .8 85.0, -4. 7.2 262.. 21ò. 7.5 150.0 .5.1 '1.6

).t

4.'

113.0 -4.45 129. 140. 7.5 IÒC.0 4.0 0.9 0.5 4. 139.6 -3.79 63. 92. 7.5 . lilaO 3.6 ' h1 0.2 4.1' IM.1 3.54 21. 72. 7.5 .18C.0 3.5 ' 0!C 0.0 4.0 180.0 -3.4.7 0. 67.

Table 5.

(continued)

Table 5

(continued')

r

t'.04T RAME: 88Y8EA CERIIF,TC*TcsuSo32'n 8MO. 2129.5 YCF29.0 SA.1035.O 11.1 SLCPES oF 7I-'

'Ll'P.IS Ç.PRRECT,I'PG FJP' EEC hEEL 4P461( 4FF -9.0'122 FCR C4 t.Nf -0.02517

CR C.Y VT ('iS) VWA(uEç,I Vn IKISI iio,. (oE(I 81FF loFt;) VA IRTS) APPA 10FF.) VMG (XIS) SF (181) IC.0 30.0 APPARENT ,(I'C 8.F.L( . 20.) 0F1. THE. $811.5 I IIF 1'C.0 31.0 APPEflT I6r GIF 19.') CF3. .THF SAIiÇ LUFF 1'C. 32.0

APPARENT (.16E 1601E

70.1, rF(;. TH 58115 lUFF 0F (IR) IC.0 320 4.1 17.1 -¡4.? 22.6 3.94 1446. 225. IC.C. 34.0. S.0 19.1 1.9 14.4 22.8 4.19 14)3, 236. 35.0. 4.3 .1'R..S 1.2 14.? ZLO 4.34 1438. 749. l0.0 36.0 5.5 '131.9 6.7 ¡4.8 23.3 4.41 141)8., 262. 1(3.0 3.7.0 5.1.. 19.2 6.3 15.0 23.1 4.58 1496. 216. lu.0 .3.0 5.9 19.5 b. 14.1 24.1 4.66 1519. 291. ¡C.0 3'.O. 6.1 19.? 5.E 1.5.? 24.4 4.72 154'). 3(1.7.. 4(.0 6.2 1q. 4.5 15.3 74.9 4.16 1560. 322.. (C.0

'iI.0

6.3 ¿0.2 5.3 1 4.4 24.3 4.79 1478'. 338. 1'0.0 M2..0 6.5 ¿0.3 5.2 15.4 25.1 4.40 1'94. 354. 10.0 43.0 6.b 2'.5 4.0 15.5 76.2 4.19 ItC9. 370. i0.0 44.0 6.8 20.1 4.9 ' 15.5 26.7 4.18 1624. 386. 45.0

61

20.8 -,.8 15.4 27.11 4.16 11)37. 403. 13.0 46.0 (.8 71.0 4.7 ¡5.5 27.6 4.73 1641. 419., 10.0 47.0 6.9 21.1 4.6 15.5

7.1

4.69 1664. 435. 10.0 49.0 6.9 21.3 4.6 '15.4 28.6 4.65

I11.

451. 10.0

'..0

7.0 21.14 4.8 15.5 2°.) 4.63 11,89. 466. 10.0 50.0 51.0 7.1 7.1 21.5 2L.1 4.5 '..k 14.5 5.5 29.6 3C..1 4.54 4.49 17Cl. 1113. 482. 497rn IC.0 '2.0 1.2 7.1.8 4.4 5.4 33.6 4.41 1,125. 512. 10.0 5i.0 7.2 21.9 4.3 5. 31.1 4.35 1736. . 521. 1u.0 54.0 7.3 27.1 4.3 5.4 31.6 4.27 1149. 541. 10.0 55.0 1.3 27.12 4.3' 5.'. 32..1 4.19 1759. 55,5a 56..) 7.3 22.3 . 4.2

'.4

3717 4.1.1 177c. 569. 1C.0 57.0 1.4 22.4 4.2 5.3 33.2 4-02 1781. 583. 10.0 5P.0 7.4 22.5 4.2 59 33.7 3.93 1191. 546.. '10.0 59.0 7.4 27.6 4.2 .? 34.2 3.84 1901. 699. 1'C.0 6C.0 1.5 22.1 4.1 5.? 34.8 3.14 1411. 621. 7.7 23.5 4.0 4.1. 40.2 2.64 1e313. 126. 10.0 4û.0 1.31 ' 23.6 .3.8 3.7 45.31 1.36 1881. 791.. 93.0 1.9 22.6 3.5 2.31 51.6 -0.00 1193. 813. 10.0 lOO..) 7.9 20.3 3.0 1.1) 51.8 -1.38 1592. 1Q4 10.0 11C.0 7.9 ¡7.1 7.4 . (.4 . 64.5 -2.7i

thu.

134. IC..0 120.0 7.8 13.2 1.9

.1

72.2 -3.89 9"O. 638.

b.0

13I.0 7.5 °.0 1.3 .7.7 81.7 -4.85 67G. SI?.

b.0

140.0 7.2 5.4 3.1 6.4 94.4 -5.49 395. 383.

lu.)

15).0 6.5 2.3! 0.6 5.4 113.1 -5.66 7Cl. 252. 10.0 16).0 5.5 1.5 (1.5 5.2 138.6 -5.18 1C1. 160. IC.0 I7C.0 4.8 0.5 0.2 5.3 160.9 -4.16 37. 126. 10.0 180.0 4.6 0.0 0.0 5.4 190.0 -4.64 0. 1131.

pc,

IPEz Eá.YQEA CETtFICA1.Eflj32p c. 22c.S YCE,q.o SA1O35.O

TF!E SLPES UF tHE

LiNES fflRRECTjpfl FrR T}F ,F:1 Hr,i E 4PF -0.00722 Cx r -O.025L7 F(1R C-Y T li(1S1 TW (CECi Vt' IKTSI IIFFL (i'rçp 3LEE nír!I VA (kTÇ) APRA (Dr, 'G tKTS) sr (,;P,) UF tLBI 12.5 3fl.0 PPARE4T wti'r 20.0 fli-1. TI4E SATLS u'Fr 31.0 LEE. 1.5 PCT C(NvFf.1'4G I2o5 32.0 AUEC. 15.3 ÑÇT '0VEGJÑG 33.0

3tFF. L'I.) PIC! C.,I'vrqr;i,jr,

- ¡'2.5 B'.. 5.8 2'.. 0 .c L 7.6 73.4 4.79 tl?8. 312. l'2o5 35.J 6.0, 2'..4 7.9 iJ.R '.R 4.94 1065. 352. 12 5 36.0 6 2 74 1 7 4 17 9 74 2 5 04 1094 175 t2.5 .3?.0 6.4 ,2'..S 7.. 1 LR:.fl 74.7 5.11 202C. 19'. I'2.5 38.0 6.5 Z92 6.8 19.1 25.1 5.16 ?4S. 422. 12.5 39.0 6.7 2c. 6.6 19.2 75.6 5.19 20e,.?. 446. 'I2.5 h.P 25.6 6.4 1fl. 26.7 5.2) 2389. 4.1.1. 12.5 1.0 o.9 6.? 19.3 76.? 5.20 1ua. 405, 12.5 42,1 7.0 26.0 c..L lA.) 77.2 5.19 2)29. 520. 12.5 '.3,0 1.1 26.7 6.' ¡8.3 77.1 3.17 7149. 545. 12.5 44.0 7.2 2b.4 5.9 ¡8.1 '8.3 q.1'. 2169. 569. L2. 45.0 7.? .76,6 5ø ' 28.9 5.11 2.199. 594e 12.5 4'6.0 1.3 25.8 57 '1.,3 94 .5v«, 7.71)1. 618. 12.5 47.0 1.4 2loC 5.1 . '19.3 2J.Q 5.01 2227. 642. 12.5 48.0 1.4 ??,2 5.6 tO.) ¡0.5 4,% 7246. 665. 12.' 40.0 7.5 27.4 '1.6 ,1.3

II.

L 4.90 7766. ' 689. 12.5 5.O 7.5 27.6 SoS ' 19.3 11.6 4.93 2285. 712. 12.5 51.0 7.6 21.9 5.'S I'9a2 32.2 4.76 7395 134. 12.5 52.0 7.6 29.0 S. .I.2 32.8, 4.69 ?324. J56. 12es 53.0 7.7 29.1 5.5 19.? 33.1 4.61 7344. 178.. 12.5 54.G 7.1 7'Ij I

".4

1R.i1 13.9 4.52 ?3V»3. 900. 12.5 55.0 1.? 78.5 5.4 ¡'9.1 14.5 4.43 3P2. 821'. 12.5 56.,C 7.8 20.1 5.'.. L9.i' 35.I 4.". 2'4rL. 841. 12.9 57.3 1.8 2.3,9 5.4 'iR.a 4.25 22.0. 861. 12.5 58.0 7.8 ?'P.O 5.4 'l?.0 16.2 4.15 .438. 381. 12.5 59.0 7.5 2e.? 9.4 '17.0 36..) 4.05 2445, 00. 12.5 6U.0 7.9 7').) 5.4 'h.P 31.4 3.95 2473. 919. 12.5 7C.0 .8.1 lieS 5.4. .11.1 43.5 7.78 'o-14. 10:79. 12.5 80.0 8.3 -30.6 5..? 16.1 .9,1 -1.41 7615. 1182. 12.5 90o0 ,8.3 29.7 '4.6 15.0 56,3 -C.0) ?49. 12.5' LOC.0 .8.4 26,' 3.1 11.8 63.') -1.46 7154.. 1214. 12.5 11') 0 8.4 27.1 7'.8 1'?. 5 10.6 -2.97 115'.. 1136. 12.5 12C.'C 0.3 '17.? 2.1 11.0 '79.2 -4.16 1314. 1000. l2.:5 130.0 'P.:I. '11.9' 1.5 - '1 5.22 '821. 12.5 140.0 7.8 '7.4 1.-') P.? 1)2.6 5.90 545. 615. 12.5 150.1) 7.3 . 4.3 0.1 7.2 119.1, -6,79 313. 409. 12.5 160.0 6.6 .2.3 9.5 6.1 IC.4 6.L9 1.71. 259. ,1Z.5 17C.,0 o.o fl,P 0.2 6.6 ¡60.9 -5.9,5 5,1.. 196. .12.5 183.0 5.9 ' 0..O 0.0 6.6 190.0 -5.86 0. IAl'.

Table 5

(continued)

4

BEAT #AMEt eAynEA

CF3TIFIC8TFI,,So372n

P"C. 2179.5

YCE.2Q.f,

StLt)5.0

THE SICPFS ('F 1HE

I.1N15 CORQFCTI6G Fr)

T.MC

hEEl

ANI.F APE -0.00722 FOR CX AHI' -(.02517 FGP CY

T 3I(t5 - TWA (OVO) VR (K.1S) l-191 (0Er.) 81FF IflEGI yf (KTSI APPA IOFG) VIO (KTS) 513 (LP) OF (LB) 15.J 27.c 4PPAUCPT )l314r ?6fl1.° 'O.) fh. 114F S8II.S IUFV 1SaO 24.0 APPA8HT W3.Iffl ANC,IE 23I r,C,. THE 9*33.5 LUFF ALEE. 14.3 4TT CJNVFDÇ.jÇ 15.') 3).0 ALEE. 11.5 NC1 CC'Iv(i'GIÑG 15.0

fl.0

I(ONTRL 5ISrLUl.icpj F:'T CONVEaC.fNr, i5.0 32.0 6.3 29.1 ".4 20.8. 22.6 5.37 2449. 356. 29.4 B. ?ç.

2'.?

5.46 747%. 3139. 15.0 34.0 6.7 29.6 3.5 70. 23.7 5.53 2504. 423. 15.4' 35.0 6.13

,2.P

A.? '26.') 24.3 5.57 2526. 45R 15.0 36.0 6.13 3:1.1

'.'

73."

'4.8

5.61 25413. 493. 3'T.0 7.Ç 3')..3 7.7 21.1 24.4 5.63 7573e 528. 15.) 38.0 7.2 3).5 7.5 21.1 26.0 ,.h3 2596. 563. 15.0

3.0

7.2 30.7 7.4 21.1 26.5 5.63 2621 599. L-5.0 4'.O 7.3 31.0 7.7 21.2 27.1 5.62 2646. 634. 15.0 4t.tì 1.4 33.2 1.1 21.7 77.7 5.60 267!. 6613. 1'5.0 42.0

75

134

7.t 23.7 'P.3 5.57, !6'R. '7"4. 15."

43.'

7.6 31.6 ".0 71..' 28.13 4.5..

27?.

749. 35.0 4.o 7.6

3Ls

6. 21.2 79.5 5.5 2152. 773. 45.0

17

37.1 6.tl 71.2 3E.) 5.45 277°. 807. 15.) 46.0

l.a

32.4 6.13 21.) 30.7 5.40 28C11. 341. 15.0 41.0 1.8 32.6 6.13 21.1

'1.3

5.34 21336. 4375. 15.0 49.0 7.5 32.. 6.7

'3.1

31.9 5.27 2865. 907. 15.0 49.0 lo') 33.1 f..? 71.1 32.5 5.21 21395. 940. 15.0 S0.0 P.O 33.3 6.7

2).)

13.1 5.1.3 2924. ')72. 15.l R4 35.6 ,.R 213.5 393 439 323?. 1261. 15.0 70.0 13.1 37. I (,.

19.'

45.6 7.9'. 3413. 14eS.. 15.0 130.0 (l.A 37. 1 6.7 113.6 47,4 1.52 3419. 1646. 8.13

363

'.° 17.4 -0.03 3)1.1. 1779. 15.0 100.0 13.8 31.13 4.6

1..'

671.3 -1.53 2743. 1724. 15.0 110.0 0.13 26.9 3.3 14.6 75.3

-'.02

2214. 162.7 15.0 120.0 n.a 21.3 2.1 13.1 34.5 -4.313 1644. 1446. 15.0 133.0 43.6 14.9 1.8. 11.5 "5.3 -5.51 1133. 111313. 35.0 141.0 8.3 9.7 1.1 13.2 1013.6 6.37 722. 900. 15.0 150.0 1.43 6..J C.fl 13.1 124.8 -6.74 442. 611.. 15.0 j6').fl 712 3.4 . 0.5 3.6 143.? -6.81 247. 401. 15.0 11)..' 6.9 1.1 3.? 13.1 161.13 -6.76 81. 307.. 15.0 18t,'C 6.1 0.0 0.1' 13.3 1130.,) -6.13 0. 2131.

Table 5

(continued)

Best Speed Made Good

VT

TWA VMG VB

50°

3O

140°

VB [ktsj

50

470

3.06 4.5

75

450 419 5.9

10.0

42°

4.80 6.5

12.5

4QO 520 E.8

15.0

37°

5.6.3 7.0

&JAT NAME: 8AyRA CERTIÇIC4TEI'1S012;O RNC. 2)29.3 YC829.V) S4113R.5 THr S1(PFS F THF LIN'S CORRECTING

OR THF HFEL AN'LE ARE -0.30727 ÇOR CX ANtI -9.0251.1 TOR Cv

VT IKTS) TUS InEGI

VR IKI

HEEl. InFO) AI I0E.I 5.0 c. o c .,o 5.3 5.,) 5.0 7.5 1.6 7.5 7.5 7,, 5 7.5 43.0 70.0

q 3.

_{12').,O 150.0 183.1)} 4.0 6.) 6.4 5. n 3.5 2.5 5.4 7.2 7.4 1.2 5.4 3.6 Il. O _{IC.' 9.4 5.6 0.8 0.0}

_4.9

11.6 to.' I .8 0.0 5.0 7.6 2.1 1.6. 0.6 0.0. 6.4 1.2 2 R I.1 0.6 0.0 15.0 40.') '7.5 17.9 7.6 15.0 70.') HEFL. 39.00 NrF') TO DrEr 15.0 90.0 8.9 37.4 6.6 15.0 170.0 8.9 72.9 2.5 15.0 150.0 1.9 6.5 3.5 16.0 180.0 6.8 0.0 0.0

Vñ IRTS) 8PPA 10Er.)

vRr. ISITS') 5F (LB) OF (18)

q'.

o.

a

5.4 2.6 2.6 _{12.1 12.1} 11.6

7.'

'.9

3.9 22.4 11.0

'q"

_{53.3 (08.3 1RO .3} 23.5 15.5 45.3 62.4 _1:ob 7 1'RO.) 3.03 '.09 -0.00 -, pq -1.03 -2 52 4.10 2.41 -0.00 -355 4.A5 -3.55 5')). 758. 700. 410. 59. 0. i L32. 1359. 1286. 751. 134. 'O. iO.) 40.0 6.3 21.4 4.0 15.3 '4.9 4.79 1690. ' '4'.. 10.0 11.0 1.8 25.7' 4.3 14.6 4u1.0 2.61. 2044. 189. 10.3 03.0 5.0 24.3 1.8

l.A

61.4 -0.03 1954. 881. 10.0 120.0 7.9 14.4, 7.0 9.1 71.6 -3.94 1091.. 60e. 10.0 150.3 6.7 3.1 0.6 5.4 111.6 -S..?8 228. 275. t'.) 10.0 18).') 4.8 C.O 0.0 5.2 180.0 -4.7.7 0. 1?). Co 12.5 40.3 6.9 21.3 6.') 15.3 26.0 5.26 7251. 500. 12.5 71.0 5.2 32.4 6.9 17.1 417 2,81 7870. l'hO. 12.5 90.0 8.4 11.2 5.0 16.1 56.0 -0.00 2615. 1340. 12.5 120.0 9.4 1P.? 2.2 11.0 78.1 -4.11 1441. 1194. 12.5 15('.O 7.4 4.7 C.? 7.1 115.5 -6,39 343. 446. 12.5 180.0 6.0 0.0 0.0 6.5 tRO.ú -5.99 0..

lii.

Table 6 Effect of 10% Increase in Sail Area 23.3 26.5 5.16 7864. 1.70. 11.5 ' 59.7 -0.00 3455., 1882. 13.1 84.0 -4.43 1807. 1681.

1)

114.2 -6.84 447. IAl. 5.2 183.0 -6.93 0. 101.

'o ROAT P4AM SAYSFA CEPT'JF!C'ATEjUSO!,pq RMC 2342.4 YCF.29.ß 541035.0 THE SIOPFS 1( THF

LIPIFS C0c1ECT1Nr. FOR THE I.Ft ANr,tE 48F -3.00722 mu

cx AÑO -3.02517 FOR C

VT ('(IS)

TWA' (DF')

VI (KTS)

HFFL '(OF() ALEP (01G,)

VA (KYS) APSA (OEÇI

VMC. (K'TSÎ SF ILS) UF (LB) 5.0 40.0 3.9 6.6 4.6 8.4 22.6 2.97 539. 9B 5.0 70.3 6.0 8.4 7.5 .0 31.5 2.04 6119. 21'). 5.0 qo.o 6.2 7.8 2.1 5.0 31.7 -0.00 636. 231. 5.0 120.0 5.5 4.5 L.5 S.) 66.1 -2.76 362.. 165. 5.0 150.0 .3.4 0.7 0.5

17

-2.93 53. 63. 5.0 IPo.O 7.5 0.0 0.0 2.5 180.3 ?.47' 0. 26. 7.5 40.0 5.3 12.7

50

1?. 1 23.5 4.08 1053. 200. 1.') 70.0 7.2 15.1 3.0 12.0 36.0 2.45 1261. 440. 7.5 90.0 7.3 14.2 2.7 lJ.6 45.6 -0.00 1187. 485. 7.5 120.0 7.0 R4 1.6 .7.1 63.2 -3.52 603. '16?. 153.0 5.1 1.5 0.6 4.") 109.9 -4.45 120. 140. 7.5 180.0 3.5 0.0 0.0 4.0 190.0 -3.47 0. 67. 10.0 40.0 6.3 18.7 5.5 15.3 24.5 4.50 1594. 329. 10.0 70.0 7.1 22.0 4.0 14.6 4u.L .2.64 1914. 735. 10.0 90.3 7.9 21.0 3.5 I7..P 51.6 -0.00 L011. 520. 10.3 120.0 7.8 12.1 I.q Q.:l 72.2 3.49 995. 640. 10.0 150.0 6.5 2.6 0.6 5.4 113.1. -6.66 .207. 252. 10.) 150.0 4.1 0.') 0.0 5.4 130.0 -4.64 .0. .118. 4.0.0 6.8 24.1 6.4 1'9.,3 26.1

5."

.2.131. -453 12.5 70.0 8.1 25.9 5.1 17.1 43.4 2.7,8. 2651. 1Ò9t. 90.0 5.4. 7..4 4.5

l50

56.2 -0.00 .2498. 1239. '12.5. 120.0 11.1' 16.9 7.1 11.0 79'.) -4.1'. 132Q 1004. 12.5 143.0 7.3 7.9. 0.1

72

119.1 -6.29 115. 409.. l2.

j5Ø

. 5.9 'C.') 0.0 1.1, 150.J -5.86 0. 181. 15.0 4('.0 7.3 29.3 7.2 71.? 27.t 5.13 2711. 652. 15.0 70.') ' Ao;6 15.2 6.11 19.7

4.1

2.95 '3476. :1506. '15.0 93.0 5.8 31.3 5. 1.7.4 59.7 -0.00 1224 1748.

¡5.)

120.0 0.9 . 1:0.6 2.4 1:3.1' 54.4 -43fl I618e .1452. 15.0 150.0 ' 7.8 5.5 0.9 . 9.1 124.7 -6.74 46. . 612. 15.0 1RC.0 .6.7 0.0 0.0 9.3 180.0 -6.7.3 0. 781'.

Table 7

Table 8 PERYORHAICE PREDICTION FLOW CHART (Batch version) Start Read NAME,NCERT,R,SA,YCE yes no (Read SPOL,DPOL,cX,CY Read VT,TWA,LSKIP I VBASS no

Call TRI in:VB,VT

out: VA,APPA,VMG

yes

yes

Find HEEL from: RMC*BEEL

Ç(CYÀPPA)**p*SÂ*VA2*YCE cos(HEEL)(1+ÄCYO HEEL))

-ÇP4)

JALEE =

30

Write message

Cali TRI in:VB,VT

out: VA,APPA, VMG

X=ÇX(APP4) '

pSAVA2

_(l+A?JT)

Call POLD in:DPOL,REEL,ALEE,VB

out :DRAGF

VB=VB±4VB

Call TRI in:VB,VT,TWA

out: VA,APPA, VMG

no

>

APPA < 20 Write massage

OLDALEE=ALEE SV ALEE = .4,

Y=CY(APPA)pSAVA2' (1+CYQ1tEEL)

CY(APPA)

Call POLS in:SPOL,HEEL,VB,ÀLEE=O

out:SIDEF0

Call POLS in:SPOL,HEEL,VB,ALEE=4

out: SLDEF

ÀLEE= (Y-SThEF0 4

(sIDEF -S IDEF0)

Write inessagef

yes

es

KONTRL>KONTRL TOLERANCE Write message

OLDALEE-ALEE > ALEE TOLERANCE

no

V-VBASS<VB TOLERANCE>

no

Call TRI in: VB, TWA ,VT j

a.

out: VL,APPA,VMG_I

'f,

/Write

VB ,HEEL ,ALEE ,VA,APPA, VNG, SIDEF ,DRAGF 'J 32 T LEE > ]O >_yes > Write message J

V

KONTRL=KONTBL+l

The hull force polynomials were derived from calm water tests. Deviations from calm water were not considered in this report, even thotigh some degree of sea state obviously eiisted for all SORC data.

Sai]. shape, size, configuration and st-retch vary with wind strength. No dependence upon different wind speed regimés was introduced primarily

because of the modest data sample size. Prestimably with more data,

5ad.

force coefficients could be given explicit wind strength dependence.

Knowing this dependence, a "rigidt' upright sail force coefficient

_cou.4

be determined.

The present technique for considering the effect of heel on sail

force coefficients is empirical at best. It does show remarkable

sim-ilarity to GCRACK (higher values, but approximately the same slope). In future work an improed formulation for the heel dependence básed o

aerodynamic theory

will

be applied.

It is assumed that vesséls "using" these sail foce coefficients

will fly the "same" sail sûit for different relative wind angles

_as

does

BAYBEA in the average case.. The nondimensionalization with respect tO

a fixed sail area demañds this.. Just as the sail area woùld change with

different relative winds, so do the nature of the sail and hydrodynic forces, not to mention the shifting locatiOns of the sail center of

effort and hull center of lateral resistance.

The apparent wind transformation (w to ß) along with the ii dal con ditions determined for cH,cR curves were applied to assure a reasonable

value of the maximum vMG direction. This wa based on the fact that the

lift-drag ratio stays constant for a wide range of the wind angles at a

close-hauled

sailing.

6. Since the SÓRC data did not include any entry for wind speeds

greater than 20 knots, and only a few of the entries were given for the true c±nd speeds greater than 15 knots, a prediction extrapolation of

the performance f ot such wind speeds would be unreliable. Therefore,

the highest true wind speed at which the prediction has been flade was 15 knots.

5. REFERENCES

1 Hérreshoff, R.C., Paris, J.E., "Yacht Ùuii MOd.J. TESTS Y-107, Y-108",

ET port 67-12, 1967.

2 Herreshoff, H C , "Hydrodynamics and Aerodynamics of the Sailing

Yacht", Annual Meeting of SNA, 1964.

Marchaj, C.A., "Sailing Theory and Practice", Dodd & Mead, Ñew Yôrk, 1964.

Spearman, J.W., "A Comparis.on of Yacht Handicap Systems Using

Computerized Performance Prediction", S M Thesis, Dept of Ocean

Engineering,

ÑIT,

1973.

DavIdson, KS.N., "Some perthiental Studies of the Sailing Yacht"

APP END IX

APPENDIX 1

HULL FORCE POLYNOMIALS

DRAG FORCE

H = heal [deg], Y leeway

[deg],

V = speed [kts.]

[lbs] = P1 V2 P1 = -0.9560564E1-O].

+

P2 V3 P2 = 0.9622283E+Ol + P3 V P3 = -O.1853135E+Oi

+

+ y5 Pk = 0.7676196E-01 + P5 V6 Ps 0.5632639E-02

+

2 P6 = -0.5049596E-01

+

P7 = -0.1956465E-02 + p8 y Pa = 0.2401010E-01 + P H2 y3 p9 _{= 0.3997911E-03}

+P10 H2

y2 V2 Pio= -0.1245445E-03 + P11 H2 y2 Pii= 0.4295422E-05

+ P12 H2

Y2 V3 P12= 0.1961029E-04

+ P3

H2 V Y Pi= -0.8250439E-06 [lbs] = P H s _{P1 = -0.3074569E+OÓ} + P2 Y V2 P2 = 0.8485899E+O1

+P3.Y3.v2

P3= 0.0

+

Pk H2 Y V2 Pi _{= -0.5789433E-0?} + P5 H3 _V2 P5 = 0.0 P6 H V3 P6 0.5806643E-01 + P7 Y V3 P7 = -0.3140967E+O0 + P9 Y3 V3 P8

bO

+ P9 H2 Y V3 P = 0.1124692E-02 P10 H3 y3 . V3 P10= 0.0

+ P.

Y V Pii= 0.3475068E-01

+ P12 Y3

V4

_{Pi= 0.0}

+ P13 H2

Y V" P13= -0.8015778E-04 SIDE FORCE

YACHT DATE VE.NT

ON- BOARD INSTRUMHNT READU4GS

TIME

POSTON

COMPASS LAT LONG COURSE MR MIN DUD MIN DUS MIN DUG 5 p E E D KNOTS RHLATIVE WEEL WIND G SPESO DIR. TACk E 2 -, In 2 h-

H-WEATHER

fF. FULL I - SIN6tE REEF

2. 000SLE REEF N. NONE

10.v

_{1 :}

OASIoMALLy FREUUNTL.Y

TRUE

CURRENTUR

WIND

N LSNSTH HES.IT SPERO DIR. SPUED oin. G

I

L1 STORM TRYSAIL o Z J . O

z

J 4 I-O -w z III Z U) WAVE Z

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

DEPARTMENT OF OCEAN ENGINEERING

CAMBRIDOC. MASS. OZI3

NAYRU OCEAN EACE )IANDICAJ'PJNC PROJECT 1974 SORC SAILING PRYOPNANCE DATA

January 28, 1974

LOG SHEET

APPENDIX

2