Sailing yacht calculation procedure

(1)

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Lab. y.

Tech

Det

SAThDG YACHT CALCUlATION PROCEDtJBE

by

Cyrus Haititin

February 19%

Technical Menioranduni No. 108

Davidson Laboratory Stevens Institute of Technology

(2)

!EBRUARY 19ES

STEVENS INSTITUTE OF TECHNOLOGY

EXPERIMENTAL TOWING TANK

HOBOKEN. NEW JERSEY

SAILING YACRI' CALCULATION PROCEDURE

compiled by

Cyrus Hamlin

( TECHMtCAL MEM(ANDUM 108

örmerly Note

2 of July 191..7)

(3)

TABLE OF COENTS

Page

NOTATI0IS tEED. IN SAILING YACHT TTING

i

DATA AND CALCIJLATION SHEETS

Set-Up Sheet

b

Upright Resistance Data Sheet, Plot and Calculation

s

Kinetic Stability 8

'Heeled Test Data Sheet, Plot and Calculation 9

Plot of Upright and Heeled' Resistance 12

Balance alculation and Diaara 13

Calculations and Plots foe' Wind and Boat Speed

Standard Speed and Stability, Plot and Calculations 18

INFORMATION FOR CLIEI'Tf 20

NÒT CPLAINING DETAILS 0F.SÂJIING IA.CHT CALCULATIO&

Sai]. Area and Cerrter of Effort 36

Calculations for G ' 37

Stability Calculations ' 38

Tow Point Shift ' ' Iii

Sliding Weight Shift ' 142

Rig Shift ' 142

Unbalance Arm Calculation 143

Calculations

for

Wind and Boat

Speed 14h

Method of Finding Characteristics at Standard _VT Method of Finding Characteristics at Standard Speed

and Stability 146

BIBLIOGRAPHY 1i7

ADDENDUM

6-Meter Boats 148

(4)

N0TATI05 USED IN SAILING-YACHT TTING (from Technical Memorandum No, 16)

A

: Displacement, in pounds, or tons of 22140 pounds,

(specify which)

R Resistance, in pounds, in water

Rt Total resistance

Rf frictional resistance

Rr Residu.al resistance

F Force, in pounds, in air

FH Heeling force, 'taken norma]. to plane of symmetry

FR Driving force, taken parallel to course

FT Resultant force

WA or A Wetted area, in square feet

SA Sail area, in square feet

MA Midsection area, below LVJL

3

HA Heeling arm. Vertical distance from center of

lateral resistance. to center of effort.

S _{Area of projected lateral piane, in square feet}

p (Rho). Mass density of water, Slugs (1.990 sea

1.937 fresh), Density: Sea 614 lb./'f t.,

Fresh 62.3 lb./ft.

Mass density 'of air, (.00238)

-' (Nu) Kinematic viscosity,

V Velocity, in knots

VA Apparent wind speed

VT True wind speed

*V(m

or s) Boat or model speed

Speed made good to windwerd

y

Velocity, in ft./sec.

V(.

_or

₈₎

Model or boat speed

*Nt

_{Small m or small}

s subscribed to terms indicates model

or' ship, respectively,

.TM-108

(5)

-1-*

KH K

Ct

Cf C

LL, 8 , L

B H

L

I)

9 (Theta)

°

_(alpha)

ocw P

(Beta)

A

(Lambda)

(p + x)

y

(Gamma)

(Delta)

Coefficient defined Force Coefficient defined

(SA)V2'

used

for airY

only

Reeling coefficient, taken normal to plane of

synmietry

Ih'iving coefficient, taken

parallel to

course

Resultant coefficient

Force

(SA)

or

A V2

Notez To convért K to C (for air)

F. AV F

KAY2 CA2

Ç AV2 2 2 K A . V2

px 2.85

_{2.38 i 2.85 i} 29t.5

Force

are stated

in that form.

Note:

Coefficients

defined

V l.689v 2.85 V2

- .00238 (l'or air)

!rM-l08

-2-Total coefficient

Frictional coefficient

of the form of Force

Residual coefficient

A

Load Water

Line of model or ship

Mad.mum beam at LWL

Maximum draft

Aerodynamic or hydrornamio lift

Aerodynamic

or hydrodynamic drag Heel angle

Angle of attack

Angle

of attack of mean sail

Angle

of attack of hull to watEr

Angle

of apparent wind to ship centerline

Angle

of leeway as weil

as

scale ratio

model of apparent wmnd to course

Angle

of true wind to fhip'

s heading

Angle

(6)

Áßpect ratio

-of Marconi

sailS Length of lut!

Length o! foot

of hulls

(2.x Draft)2

2 x Area of projected latera]. plane

E (Epsilon) Angle of ship' s head to resultant sail force

LATURE RaATING TO RUDDS ON SAILI YACHIS

l The rudder of á sailing, yacht ordinarily extends aft from the

rudder post, whereas the tiller ordinarily extends forward. The terms. defined below are for this usual arrangement o! rudder and

tiller, and they are used regardless of the actual7arrangement which may exist in particular cases.

Helm Angle means

the angle through which the. rudder post has been turned from its central position.

Weather (Leé) Héim An

le means

that thé forward end of the tiller pointa to weather (lee)0

Helm Torque refers to the torque on the rudder post to maintain

arr given helm angle..

Weather (Lee) Heim

Torque

means that thé

helmsman

has to exert a force on the tiller directed to weather

es.

Weather (Lee) He].m is used by' practica]. sailors without distthc

tion between angle and torque, This term is ambiguous and 'will

be avöided in our work ,

'TM-108

(7)

-3-Client

Ship

-J- Desiier

--

iength

ìo

(jj

Vo]um

Rati3s Areas

/oo:

Diaplacement

j-

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f Model SCa:1.e Alt. No. â lbS. â extra â test W.A., Sq.Ft. Test ti'

37.Q

3. 1 'G,L.Ò.G0 /.t,? S.A.,Sq0Ft.

9g:?

C.E. Hgt. C.E.Pos. A 2/AP. C.B.Area,Sq'.ft. B.C. B].00k. Coeff.

4&tU2P)31

H

'-o q..i.i

.ajL.LL.

C!E. Hgt. /L.L L.

Ejes ./.*.L0

Canter of Board Displacement, mo

Added weIght, such aa drew, Th. Totá], test weight, lb.

Wetted area, s.ft.

-Added wetted area for nidders, etc. sq. ft.

O'

Total test wetted area', sq. ft., withut, centerboaM

Center f gravity of ship, feet below LWL

Sail area, sq.

ft0

(e page 36)

Center of Effort height, feet above LWL (see page 36)

33'0Displademjt...]ngth ratio ,5t

Wetted areaL- 'Dispiaced voluin& ou.ft.

o

4-

3ijlaced volume?t.

5 S

iTBl: area ,. LWL of'. ship, ft..'

LW14' ft. 5

t9SC.E.

Rgt., Ít.,-4- LWL, ft.

.% C.E. Psition, ft

LWL, Area ft0 Ship tModel

fr.2. '':

Center of Effot position,, feét aft df Sta. b (see p.age 36)

37t I

3

7

Wetted area x

f

(fo! ship, sea water; for model, f'esh water)

i271ec1procal of

e above

.Wetted area ofcenterboard, s.

fta

A

. with centrboard.

Reoipr9ca]. of

.me

above

Ship Model Ship Model Ship Iodel Ship

L.01AO ,Ft. Length over aU, feet

L. B.P0Ft.

Length

between. per ndjclars, feet

:L.LL0,Ft. Load water line, feet, j

Basin, ft. Maximum beam a1 LWL, feet

Draft, Ft. .. ; Maximntnn draft, feet

â tons il 3S' Di8plaoement, .ong. tons sea Water

TM-108

ROJECT.NO. ;z.;-3

4=

(8)

- Model tested -__-

w

wModel tes1ed

--with 1/2" sand strip with 1" sand stri

at speeds 11 and above _{over complete speed range}

Q O . /Q_.3x 7.1I2/Iff,3

o.7/3,)

,'o.3155.

0.11 7, 7 1L00.3 . 7 O Date

Temp. of taxk water yn. checked_____

,, checked________

rn

r

Tow Bar cheCked

UPRIT RESISTA10E DATA 8IEET

UPRIGHT TESTS

40DELN0.

_{_-_I}

.---These columns -+ are computed the

.sar as for 1/2" sand strip. 2-a Date Temp. 7,Dp.I, Dyn. checked checked Tow Bar checked

Lbs.

sand 1/2"

X 1z;"

_{Sand 1" z}

Speed .Rcg. hesist. i C Rdg. [ResistJ c

No0 B-2-a 1/1000 ,A _B-2-a 1/1000

Spring used in dynaxnozter

DUT.

Avg. A.P. - .7a27

//1l

'p2.

(451

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(j

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O C)

These two co]umns are plotted as

on page 6 and the line faired through them gives the values

of C for plain hull.

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(9)

-5-. UPRIG RESISTANCE PLOT

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UPRIGff RESISTANCE COMPt?TÄTION

-lO8

Model No.2.3J

3-f

-.7-/0

WA6

37S.o

sq.. ft.

-5,5oo

ib.

Re6 LWL8 X X V11

x,,.7

3. 4

3./u-

x ':L.:

.(sea water) at S9°F. (Std. temp.) , ;c,"'3

LWL1x

:

x.7O*

Re m

m (1c'e)

. -

x.7

-v-

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1ö0F

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f

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*

: In calculating Reynolds nuer for the sai]4ng yacht L1L is multiplied by .70

r ,

because of the cut-away profile and f inenea of th hull form.

$t'w

ers,wE- V,qL-, L.s$t.P

(11)

Note: For an explanation of the method used on this form,

Form 10 refér to Appendix

_B.TM.2S

(pagé. 38).

NODJ NO.

L.3-f

KINEUC STABILITh 1ate

C.E. fabove f.b, aZ.i

.(2) (1)

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2f.ffc

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(7)

(6) x scale

Ina.0/'t.)

-in..j.5?,

.(8) (3) (7) j'.

-in.5.o

(9) 0 b].aw top of

deck

-inh.

3. Su;.

b= (8) - (9)

-in./,13.

.(11)

11s.Zbt.5. ,(12)

Amxb/a=

(11)x(1O)/(5)

/31

i i Model set up b i.

0=

ni

:*Ïors=10

** Standard

Sliding Wgt, Rig No.

&, noiina1

..

lb0

A, acruai

ci

lb0

t(Dist.; + 10) - 1

ni

(actual)

+

lb).

+10)

1 (c.G. oÇVe..st Nei

5eI0,$37)

TM-1o8

-8-O 10 15° 20° 50 300 (13) 2.00 x coe2 ê 1.985 " 1.9b0 1.866 1.766 1.6h3 .5oO (lii) 2.00

z

Cd

/a -

(13)/(5) o7go r _i

H

i (15) sin e cos 0 1/2 sn 2 0 .0869 .1710 .2500 .3211

.(i6)

when S = 0, (F11coa

₉₎

12) z (1,

.(17),

10*

(])

:(18)

whenX= 10kFHCOS)mm

(16) + (:

(19);

(FHcoa 9) Í*óm dati ohart

7H cos19)

- (&

b/a(1/2 sin

(S) - Slidirg

weiit shift

.383O 0J330 Li) - rc

e ,

iR-ieq

ii_Fcv.ce

f

fRZ&-LE1

te

9

: -Sept. 28,

₁₉₃₇

Alt.

Jan.

_{2. 1938}

(12)

Form 7

Model No.

Z3-e'

(See No.

_Q

13.IJ1) and Tole Cord Tension_______ - Date Sp.-O Note: odel Model

O?.O°

. Sliding weight /.00 g.g3

o.3-i.3.

_zs4

?.i 35l.': /3

Ii4.

o33

i

7,'

/0.3 .3$

/.&t.o

g.gj

_.44.O? _O3S

2.39 3s'7,i

o.37

?.3

/3.

L-1

¿:Ia)Q

:b

0

.-,-4 a, 4 04

o

w ,l cd

c c4

LongI-Longl

Leew rdgJ Resist

/7H

C6-;-a-) ,Ç000

k

a,

o

a) w

k

t,

43

ii

4)

,,00

:0 I

O

;43

43 CI,

k

43

-a)

43 w -rl

-'

a,

-I

'do

.

0

O.a)

da)r4

l:.i

0,-4

.rl g

o

Ot,43

-f40

.CQa,

43.f4 cd .,4 r44-) O)Cd Q, O-P Added .Weight Q

40

04.4 C, cd o 43 o r144

430 _o

a, 43 .r4 O 43 0_cdc)

u

It is usually

sufficient to obtain

_{9Etest points at each heel angle.}

This is done b3r testing 3 different values of speed with 3 different

values of F,,. cos 9 per speed0 These 9 points are then plotted as illustrated on page 10.

On this form the test engineer record3 heeled test results.

Stup

eight Checked _{Leeway Zero Checked}

_I"

i

E. Jig Rollers

Checked

V'

Dynamometers Checked V

}T1.D

TEST DATA SHEET TM-l08

--9-(see p.li2),

Boat

3t.U0

OHE. Rig3hift

i

LWL

3.

Model Wt _{?. 4. Z5}

Ri. g Position #

_o

E ck.

RudderCe.4pLBoard

Water Level

1im

'CLR

Tota].

-Aft. Lat. F

0°033° _7/.7

i3O00o.3S

Is 0. 33o I /,Oo

o.3(S

il

(13)

(14)

'HCO39j Sp.No.

i

E w o w o) Q w

I. Sp.No.

-9 Leeway, inches

,

degrees Result. FH cos Q

Pist, aft Sta, O

ÇLR, LWL rl . V w w 4.3

rlQ

_k

wo

E

cdrl

e7 2j3

.5.3Jt

,391L /3,3v

3j,,DO 3Jf°

3S'7/ LJ)

!Paken fvom Plot 14, page 10, at resultant

FHcosQ

Line above x 2(1" in 28.6S sbtenda 2° arc

Taken from Plot 1, p.10 at intersections

Taken from Plot 3, p.lO, at resultant _FHC0SQ Line above 4 LWLm in

inches x loo

Form 8 TM-108

-;i-]--,?;

_1?

,3(o.oaf7a.?.V.

WS.7

azo

3'7$

eèled Comriutations

Model Test No. 2

a 3-!

and-(4)

_-

LC.

R Ct ÌACF

c

(AV2)I R

(15)

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i uiL ta.. i

ir

111 1 1

Ir p

i

EjIJ

i.J'i.0

hiI' E 9i1 I 1ji 5:1111 1qI1II 1111 II i 1 i

ii

Li h i HF I I 1 I ::WhlI u! Sp 11 5

195i'E j I

I !'11b II

9!!

HYnE iii n n y

r-01 r-J

(16)

.(14) Ra/FN C:05 Q

.C.E.Hgt.. (ft)s

C.E.Hgt. (in)m

(7)xsin9

C.E.Aft.Sta.O(ft)s

C. E.a.ft.Sta.O(in)zn

(6) C.E.aft.T.P. (in)m

(8) Unbal.Arflis(in)m

_{W3.Sca1ed off dia'am, page}

₁₁₄

Unbal, Arms (f t) s

W .

.35 I 3, o7

Line above .-- model scàle

Unbal..Arms (

L.W.LO)

17.2.9 W,Sc?Line

_{above ---LWL, ft., xlOO}

*

Mote:

_{Numbers on left side of page refer to}

_{steps on page}

114.

'53Taken

from plot

14,

page 10

/.31

j.

37 Towpoint offsei, taken from tble on

_{p. li].}

/, t'

I. I (

_Di1'ferexice

/3,3?

Taken from Plot 3, page 10

/ Q. ?' Line above minus 2." (the twpoint distance

from Sta,. 0)

Resultant water for ce Ön hull'

/, o7 .3

J, J? 7 Line above x

14 _FHcosQ

scaled to lj,"

for ease in plotting

.

. ---' Center Of effort above LWL

- r Line abóve x mOdel Sca.e

Horizontal effect of C.E. due to heel

Horizontal distance af of Sta, O

'Line above x model so4e

J. ?(,

-

Line above - minus

2.S"

F'm 6

Note:

For explanation of method see page 143

.TM-108

For explanation òf towpoint offset, see page 1].

₁₃

-.Model Test No. ¿3-1

Balance Calculations.

ßp. No

- Q

aeeway(in)

(J.)'

*TP

_(in)

2) Leeway - T.?.

.CLR Dit.

t,

_T.?.

from Sta noti

(17)

H-PAODL ÑO. 23-1

Note: F explanation of method uued

see page 143.

_{Numbers in circles refer to line}

numbers on page 13, Balance

calculationaD

ê

$Ño.= L

9 _{#L.D CE}

P0.siTiQIJ

SCP.LE:

SLOPE oP

_{1E VEC.T0S}

o#J MODEL

DsSTPJc E

ET%&EEpJ

FOF

itID i

i DVJAMOMTES.

T4

PswEÑSIot.J

s T4E JÑ PPUJt

pR4

(18)

VT Vmg Vmg/

vs

vi ri

9 Áo

s=

II.3A/(L/l0O)

S.A.=9T'TL

_/.f

C.E.Hgt.

Calculation for Wind and Boat Speed

S2.17 J i 11mg X 5.3.f,'

5.o

C.L.R.(

LWL)

3Oo3'9C

Unbal.

Arms (ft.)

Unbal.

Arms (

Rèsuits at

7l

_).3o

t.°5 5j7:

5-7/

C

_»75

53'

(2.7o

5°

//4

-':

3j.

1!-j

Wo

J

C.E.Pos. j;_o'

Heel angle Standard Values of VT Standard values

From page 17 at standard VT Li ne above

from page 17 at standard VT Line above

From page 17 at standard _VT

33°ip

LA.

Vo..

_{1.O G3j.?'cJ,,}

Vol.

039j

Speed Nô. / Cl

Vs

¿)+

e1ocity:of ship, knots

R5 Ship Resistance, lb.

_from

page :11

(FHcOS9) Resultant from Piot 1, page 10

(FHcosQ)s Line above x displacemeit ratio

(FHcos9/ )s Line above diplacement in tons

(Rs/FHcose ) s

.;.993

Resultant water torce on hull

X

9c5

From Girnack sail coefficients

X SA x 1O Line above x Sail area in s. ft.

V2A

:3gj

R3 -- line above

VA

/7.(i

./7

j line

above

VA/Vs

Z?

Line above

.4-

V, ship

Speed

( + From Gimcrack sai]. coefficients

/.5c /.?7

From contours of: solutiöns of

triangles. See note SLa (see p. Iü& also

Vmg/V5

Form 3

Note: For explanation, see page bL Th-108

15

-Model Test No. 273-I

J.

From above (X V) From page 11

ñom page U

From page 13 From page 13

(19)

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(21)

Sp0 No.

Leeway

inches

X, deees

Result

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Pages 21

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_{are the forms on}

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Original in test f ôlder

m-108

20

(24)

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