Yacht design

cosc

.~160

PE~;Et\f~Cfl F'F~CkJECT

DEF't\F~H'1ENT OF CCI!"1PLITEF~ ~:;CIENCE UNIVEF~SITV OF CANTEPBUF~V.

Y HCHT IJESIGil.

Chapter

Page.

1. Jlf[f{DDLLCT I

QH

The Problem.

Revievv· of other vvork with hull shape development. Current work in Ol1al~lsis of ~1acht hulls.

Dbjectivet~.

Fair lines.

Initial aims and objectives. Clltmges in oi ms ond obj eel i ves.

Final

airnt~ and

objectives.

The

standard representation.

Dio~]onols.

Desi

~1n as on i ntui t.i ve process.

By

hand.

By

Computer.

4..

ltJ

P L E t···t E

rfr

t\

T

LW:il)

E C l_gj..Qf_i;~

1.

'7

J.

4.

5.

6.

7.

cl

10. 12. 12. 14. 15.

5. THE

_.LCU:lf?.1HIR

rtCJ12Il:

The need for a data model.

The requirements of the data model.

The basis for

u·,e

computer model. Description of Uw model used

~\imp 1 i fi cations. Restrictions.

Ho'·l·l the rnor:Jel satisfies the requirements.

::;peed.

T lle alternative. con~:i dered.

The independencE! of the Sp 1 i ne routines.

The USt3r interface consistenq1.

Vo/i mlov·ts.

I would like to thonk rnq Dod Vv'llo qeve rne the interest ~ ~

em!

the

bock~wound to be eble to do this project} eH·tcJ produced the designs use:~d in the testing process of the program at very short notice. Also I would like to tht:mk all those who kept me seme end fed while I worked through the

Jll'lHDDUC_TIDD

ThE1 problern being re!::earclled is that of hovv· cornputers can help in u·1e

dE1sign process thal is employed in designing a yacht hull. This is a

problern that has been reseerched before but with di fferenl results to

whet have bE,en achieved in this projE,ct. The main airns ~vere not to

provide fl true computer aided design program} but

a

useful set of tools

that can _. be used in the desiqn process. ~ .

The rnanual process for drewi ng up a set of curves to represent a hull is

a tedious process that often suffers frorn loss of accuracy on the dr-awing

boar·d. 1-\fter an initial st:1l of lines IHJS been drafted .. the process of

refinernent begins until the shape is acceptable to t11e designer. The final

stage of the design is to pEwfonn a sirnple analysis of the design .. usuallhl

in the fonn of a displacement apprm<irnation and a curve of area to

estimate the centre of di~•placernent from.

t\ny desi~1ner doing a thorou~11·1 job will rnake a detailed analysis of the

vveitlht that ~1oes into a boat to find thfl centre of mass of tlw boat. This is follovv·ecl by an accLwate as possible estimate of the centre of

clisplac,?.tnent of t11e boat and an effort to balance the centres of mass and

displacement. If this is not done the boat will not float on its dosigned

water line.

It is ver-~1 hard for the computer to help in the estimate of the rnass

tlwt goes into tht:1 boat without a great deal rnore infonnation than will be

·-considered ir1 Hli~; pr-oject. 'Where the cornputer can !Jelp is in the process of finclinq thE! disple1cernent e~ncl centre of clisplecernenl. This is not a tri viol process

to

perf

onn

by hand~ as we 11 as being very i naccurote in most ceses. Using o suite1ble nurnet .. icel rneUwd~ the cornputer can rnake a mcwe eccurote est i rnotE! of these porornef.ers.

REVIE\~1 _{OF UHlER \·'/llF~I<} 1_{1'1'ITIJ HULL SH;\F'E DEVELOPI·'1ENT.} ---.. --~---~--,---··--·---·---~··-·---·---·-·---·--

~---·---·-·---·---~---t\ nurn!Jer of programs are comrnerci fl 11 y ovfl i 1 eb le for hu 11 shape

development. The best-known of these is ~John Letcher's Fflirline 2 and George Ht~zen's Faslyocht. [ 1

1

t\ 11

o

t

tJ1ese

programs o

ll

ovv U1e

des i gnf3t" to deve 1 op

o

hu 11 shepe in the

cotnputer using relatively sirnple cornrnonds. " The sirnpler and less

e~wensive ones

ewe

not very well suitocl to rnore cornple~< sl1apes such as those you rnigl'lt wm1t to dr·e'N around thE! stem of

on

10~: ( lnternat.ionel Offslwre ~~oling ) boot or 1:1 12·-·l''let.rel while the more sopbisticated rmd

e)<pemd ve ones will hand! e just about any shape you rni ~lhl wont to

clravv

but often do so eJt. the e>(pense of requirin~l the us€H" to heJve doctoral€~ level rnetllernel i cs. " [ 1 J

Softwere is ovoilable in New Zeolond for hull design from ~1cDonnel Douglm::~ 1Nhich is advertised os ideel for· 3-Dimentdonol hull desi~w~~ os

well os colculoting the volumetric parameters and infornwtion used in the bui 1 cJi

ng

process.

t\nother effort in tbis field was the invellwble project of I. T. Foster who inplementE!d e C;~D ( Computer 1~icled Design ) s~1stem for hull design. [2] The nwin drawbecks to the previous project were twofold. First wos

..-,

tl"'ot it 'vVas Lretc1·1 oriente ted os opposed to interflctive. This was because. of lwrdwore I i rnitCJti ons rot her then on~~thi ng else. The second drowtreck wes Hlflt the representation of the boet relied unpon e ::;et of curves that were totellly dis-sirnileH· frorn the stenderd views of the boet theit e designer is f mrli l i or will!.

There currently 8)';i~;t

o

nurnber of peckages otternpting to colculote verious pererneters of ~tocht hulls. The most cornmon forrn of colculotion perforrned on hulls is thot of ciisplocernent end centre of displecement. This rc~pre::;ents the rnost boring oncl leborious task~ as 'Nell es onE! that cen not be done very eccurotel~l try lwnd. Without this effort either bq

·-cornputer or by hend .. e boot buil det- connot be sure t11et t1 new boat wi 11

float on its proposed water line. The theoreticel wt~ter linE! is the line eround the hull thtit the wetEw corne::: to wllen the boot is ot rest in the vvot.er encJ not l1ee lee!. Tl1e boot is heeled wben it is l eeni ng to one side of vert. i co 1.

The ne)<:t logicol step is l"rydrostetic celculotions. An exornple of this is stability. To do o proper job~ oil hydrostatic CC!lculetions should be mede for e voriety of floetations) ond should take into eccount the feet thot e botlt spends o lot of its tirne not floating level but heeled on en engle.

t~fter the h~ldrostetic celculotions con·res the structural tlnerlysis. It is important for tbe designer to know how t11e llUII wi 11 trend end wlwre· t11e stresses crnd stn:rins ore upon the hull. This field is quite odvernced es o nurnbEn- of pockc1ges 8)\ist~: to perform the structurell enelysis on

orbitroril!:l cornple)~ sl-,ape~;. The type of analysis used for this is finite elernent analysis.

The next useful step it; colcult~tion of the rating of various hull shapes.

The

formules

are

t;pecificolly set up to focilitote the writing of relatively t•treight forwarci progromrnes. The re~ling of e~ boot is used for hondicop purposes so boots of different sizes and ratings cem roce E!Venly

a~1 fJ ins t eoch otJ-1er.

The fined step is thot of perfornwnce predicition. This is the most cornplE!X port of yacht cletoi~Jtl At present lhe greotest use for perforrnonce pn:1diction is the cornporing of two clesigns. A lot of effort is being put into t11is field but to rnake ony kind of realistic prediction~ toclays

f3UF'ER

COI''lF'UTEF:~; need

lo

be

u

li 1 i sed to handle t11e comp 1

exitw

of the prob 1 ern.

1~l pr-esent the current ~::oft

wore

rnoke o number of sirnplifications that cut

bacll~l into the

occurocy

of the celculotions. The greatest use of the cutTent soft ware is

in

cornpfJri

ng

tl'leori t i

ca

1

desi ~1ns.

Hopefully .. the sustem developed in this project will be eble to be used on ettdlrer-il~J complex shopes end yet still retoin the sarne procet•s tht~t o designer hos olwa~1s Ut:E!cl .. without t~ny specific knowledge of mothemotics bein£1 necest•tiry. The only fornilicwity useful is thol of the "stonclord" l"laci ntosl1 interface~ ·vvlli ell lws been uti 1 i zed.

ThE! targeted use for the project is to provide a tool for people clesiging smtlll racing dinghiE!S who m-e currently using Uw troditionel drafting boards end not getlinu around to doing ony forrn of displacernent analysis

lwcouse it is too hord ond tirne consuming or becouse tht::~y do not hove the knowledge necesser~1 to rnoke the enBlysis. t1eny of these people heve either e)<:isting boots or occess to existing boets thet cen be physice:Jll~!

weighed to find the mess cmd the centre of mas~:. Having

e

boet thet does not float

on

its proposed Yv'etet- line is the dinghy designers greatest feult.

The concept of e feir set of lines is introduced here os it is referred to throughout the report. A line is seid to bt:1 foir when it is

e

srnooth curve ond r:ontoins no bumps or hollows. A curve is usuelly feir when there is no

chan~w of si~1n in t11e second derivotive of the curve. It is usually the det:i gners goe~l to produce

e

f oi

r

set of curves. EXC!trlp 1 es of fBi

r end

non felir curves ewe included leler in the report.

Tlw initial aims of u·,e project were to irnplernent B suiteJble dota rnodel to represent

a

boat on o cornputer end perform en anel!dSis of this model.

The onol~jsis \·Yfls to consist of hYo seperete pBrts. First WF.JS EJ

~Jt"Bphical EJIH:'Il~!sis of t11e

hun

in tbe form of o set of lines dreiwn

by

the computer. The set of line~; ore the stonderd vvoy o boet is reprE!sented on o cornputer. The lines ore u::;ed

by

the designer to obtBin an ideo of tile

~dH:Jpe of

u·,e

boot oncl to see if the boot is f ei r.

Tl-,e secoml 1_NDS for the computer to perform sorne simple colculetions

on

the

hull

to ol:ltoi n o nurn!Jer of

pc1rorneters.

The peJrerneters

ore

needed

I

to find

if

the

hull rneets the requirernents the designer has chosE!Il The

most

irnportent parorneter tllat

e cornputer could calculate is

the

displEJcernent of the boat.

,\fter the cornputer rnodel for the boat and part of the graphical output of the de:::;ign vvere irnplemented on the PI~ 1 1'1E in the fin:;t term, a problem arose when examining the plots produced as EJ results of testing the model

on a si rnp I e design. TheSE! prob I erns caused some change in objectives to be rnade.

Th£1 protJ I E!ln 1Nas to do with the choice of data points to reprE,sent tl"le

shape of the hull.

By

a bad choice of points the following frarne for a boat was obtained.

0 200 400 600

0. ---t-·f-·--t--+--1-+ -l

200- .

[image:11.595.177.436.368.564.2]

400-~---~~---·111··"-11! ... _

figure 1. An 'unfair' curve.

Exornple of a frame with badly chosen data points.

vv'hen atternpts were

rnade

to correct these curves

by

choosing

different data points it vv·as found to be impossible to choose the clata points correctly by changin£1 the numtJers that represented the points.

Tllen1 were man~t problems. First was the turn around

tirne

from

editing

the

data points in

a

file

to

receiving the plots that represented tile

curves. Tl'ds tirne vv·as nE!Elr an hour if thE! plots could be retrieved i rnrnecli ate l ~I after printing.

The second ~vas the irnpossillility of manipulating the sl"lape of a t1oat as a set of nurntlers ond still rnaintaining somEl ideo of tile sl"lopE~ H1at was being procluced. 1\fter thE! data had been changed a srnall number of tirnes~

the twll was no longer the sarne st·,ape as t11e planned shape and if thE~

process had continued furt1·1er, a detailed analy~;is of sorne diffc~rent hull shape could have been performed.

The result of the testin~t W8~; u·,e idea thst

a

set of numbers is not

an

acceptable way to repn~srmt a boat when a human has to rnanupi late the shape of tb£J

boat. Thti

onl~J time that

a

set of numbers is

an

acceptable method, i~; for interfacin~J between various places like a plan and

a

pt1ysical set of frarnes, or for entry of an m<isting design.

·n1c1 fined

oirn of

Hle proJect i~; to pr-oduce a suitatde system for rnani pul ali ng tllCl shope of yacht t·1ull s H1at can be used as a basis for the

initial analysis. Using tt-Jis basis, a design could be entered into the systern, the ~;hsp8 rnsnipulated until it is as required, then analysed. t\fter

the sns lysis, U1e shape of tile hull can be changed for further ana 1 ysi s without leaving the cornputer.

Tl1is rneans the objecti'v'EJ is now to produce an interactive Computer AiciE:1d Design (CAD) sy~;tern tl'lat maintains eittler the original data rnodel ..

or- s cornpatab le data rnodel.

The CI\D systern needs to be able to enter an initial design, show the

design on the ~:crem·1 EJnd interactivly rnanipulate

u-1e

shape of the de£>ign

untll the designer is satisfied vvith it. The following is the sante frame as

in tl"le previous exrnple, e)<cept that it has been res!"Japed

using

such

a

systern.

0 200 400 600

0-- -t-+--t-1---1---+-

1-fi~1u1-e 2. I\ feir

frame.

The same frame 1Nith the date~ points moved sligllt.ly.

Tile universally accepted rnethocl of pictorially representing a yacht

hull i~; given by a set of lin8.2 .. " [2] Ttw lines are different views of the

same bull slwpe. For each vi e'vv, a nurnber of paralle I s I ices aro taken

througl1 the hull, and the view consists of the lines of intersection. Three

main views are usually used to represent the shape of the boat for visual

analy.sis. These ere the frames, the water lines and

u·1e

buttock lines.

Often a fourth set of lint1s called tliE:~ diagonals are also generated as an

appro~~irnation of a vievv of the boot when it is heeling. The di8£JOnals are at different angles to approximate different angles of heel. 1~n e>wrnple of

a set of lines cJravvn by hand is given in opendi >< A.

The lines are used to uniquely define the shapo of the hull in

3-Dimensions. From the lines the hull attributes can be calculated. The

final step in the design process is to toke rneasurernents off the lines to

serve as data for the builder of the hull. The measurernents taken off are

called offsets. It is the aim of the designer to produce the set of lines.

The final property the lines rnust have is they must be consistent. The

lines are consistent 'v'v'hen all pairs of lines in 2-Dimensiom: define the

sarne shape in 3-Dirninsions.

0 300 600 900 1200 1500 H 00.

---t--1--t--t-t-+--+--+

--•--t-

f+-

1·--·

-"'----~-0 600

--~----~

IJuttock lines

--

-

~---Frornes

·- UJoter

Lines

2100 2400 2700 3000

I I f - _I

I

I

/

_,_/

()

0--·-~~ ·

-figure 3. The cuts to genenJ te ltle different views.

Water lines

600

[image:15.597.24.553.97.534.2]

For the purpose of this pr·oject} the diagonals are not considered

i rnportant. The reason for t11i s is that the di egonals only give the designer

a vague i cJeo of the siH:tpe of the boat when it is 11E,el i ng. As a yacht actuall~l spends all of its tirne heeling vvhen it is seiling} it would be far

more useful to heel tilE! boat and redraw all three of the rnain vievvs again.

This would give an occurate picture of the shape of the boat lwll as it

passes through the water} as opposed to just an appro)dtnation.

Unfortunatel~l,. the heeling of the boat and the subsquent reclra'lving of the

lines .is outside the scope of this project.

Designing

a

boat is far rnore of on intuitive procE!~:s relying on the

skills of thE! designer then u scientific process following set forrnula. The

designer U8lwlly works within

a

frornework of requirements.

Given the same set. of requirements no f.\.vo designers will produce tt"Je

sotllE' desi9n. Both designs vvill be fair, both will meet the requirernents

end both will be very different. Cine of the two designs twill perform

better than the other but neiU'wr will be optirnol. Frorn onE! ~:et of

requirernents e cornputer will onl~t produce one desi~Jn₁ removing the

creative differences of the hurnen designers.

Initial Requirements eg Length,

Width ..

·--1·---rr: ·-·--·-- ---

c

-·--J-aw~~~ o~ i ne~ ~---····-·---·-·---

-_______ I ____

J

Analysis of Fairness Not Fair

Visual ~-ppraisal

---Not

u-,;;h~

~ir;d--Mol<e o change to one of the views, staying inside the initial requirements.

G

.

Calculate

~a~ameters ~·

Do!!<.£ not utidy

PK.am~t!l<r£.

g Centre of Displacement ·

-Draw a final Set of Unes

-Calculate a Set

of

Offsets

for Building Information

The most notable tiling about the design process by hand is tlwt it is

ver~1 slow. The tirne token to ckaw the example set of lines in eJpendix t\

was over four hours. The exornple hull ~diope is o very simplified cese tiS il hml no initio! requirernents oncl no porarneters to satisfy. The time

token 1_Nos in tl"le drowing end fairing process. _To ensure tllot the different

views were consistent .. onl~l care end excellent drafting ebilit.ief• wet·e needed. Ensuring consistency it: not o triol ond error process es is sornetirnes thought.

I

2 J

The process usee! to orive at

o

finell cle~:ign i~: an iteretive process of

essentioll~l clrm·ving the vie1_N$ emd evulating tlwrn. Vv'hen changes orE! rnt~de

to the vie'NS, the~1 are usuoll~l mode in sucl1 o fashion thot the design stays \Yithin the initinl I"EHJUirernE!nts. It is not difficult to keep o hull tit fJ fixed lt~ngtll when ci10n£1ing tile shnpe of i l.

Or1e of the prol:tlerr1s with the droflinu process it: o loss of detf.li 1 f.lnd the ecclweqJ being limited bkl t11e drofting skills of the designer. This cen leod to the fintll shape of the hull otter building, not being vVhtlt thE:~

(Jesigner vvtmted. If U1is heppens, it is every difficult process to change the shope of the hull to wiH'It tlw designer thought the design represented.

The second port of the evoluelion involving the colculotion of the simpler pore11r1eters like clisplocernent is often neglected os it is beyond the de:::i ~1ner skills.

T lie place that tilE! skilled desi ~1ner is neecled is in the vi sut~ 1 apprai so 1 of the desi~Jtl As no dit·ect coclulations exists to get the best possible desi ~1n, it is up to t11e desi uners intuition to rnoke design the best possi b 1 o hull shepe for the requirernents.

The cornputer should never cl1tmge the siH:'lpe of the boet

by

itself. All clwnges should be mode onl~l b~l the control of the designer. This is beceuse there are too rnen~1 veriatdes for the cornputer to deal with in boet design. Some work is now being clone on cornputet~ generated designs, on

super- computers, but os ~tel is not ver~1 successful.

To

be useful in

U1e

design process, the cornputer needs to

be

oble to do the following thin~r:::

1.

Input

on

i ni li

o

1 hull

slwpe.

2. t-Joc.li

fy

the hull shope.

5. Drovv the different views of the hull.

4.

C:elculote

tlie

required

porometers

of

the

hull.

If the~ computer con do o 11 of the above, it would si rnp 1 i

fy

ond speed the design process up. The rest of tl1e report is cleo 1 i ng with how the computer con be us eel to aci-d eve the above.

Ch.optl.'r 4.

I

UlP._LI;_lllEltiHJ

IOJl_DJ~C1S

I

DUS

Tile most fundornE!I"Itol requirement is that the computer preserve the some process of designing tile hull. The use of the computer is in sirnlifhling and speeding up the different step~; in the process. The computer should also be copoble of gr·et~ter· occuroq1 w·llicll \·\"ill t.llso help to improve the desi{ln process.

The ideas for the btlsis of the CAD system come from o ~·1e1cintosh

opplicolion, 1''1e,cDrow. The ideo frorn 1''1ocDra'tv wos to be oble to selE!Ct o curvE!, end retJn:~pe the curve. V/llen o curve is selected in t'1acDrow, the points defining the curve are hi[lhlighted. The cur·ve is resheped by

dro~Will£1 one of the points defining the curve with the rnouse, ond rednnvin£1 the new curve IJS the rnouse rnovecl.

From the abovo comE! Uw ide a of se 1 ecti ng a frarne end n:.~shapi ng the frorne interoctivly with U113 nwus€1.

Tile

otiH:n· required feolun~ wos

to

be eble to hove multiple vic~ws of the

hull shape. The eli ff erent views from eli ff erent eli rt1ct ions ore requi reel to enotd e the (iesi gner to vi suo

1

i ze the shape of t11e hull in 3-Di mensi ons. I deal

y

each view would remain consistent \·Vi th eoch other~ a I 1 updating when a change was rnelle tu any of then1.

Tlws tile feotures required for the planned CAD systern are a mouse, and some

woy

to irnple.rnent rnultiple groplliced views.

Frorn tl-18 r8quirt!d features carne to pl1ysical requirements, one a mouse, tile other is some forrn of graphics device. As it is not necessary

to !JSV8 all vi8YVs pre~a:mt at once, or indeed to t"lavB more than one vif~W at a time, a sin~J]e graphics window could be used on the screon.

The initial !-lope was to use

o

t'1acintosh as an intelligent graphics terrninal ami continue working on the PR 11"1E. 1\ prograrn called the Griffin Terrninal e)<ists that runs

on

t1"1e t·'tacintosh tbat emulates a graphics tN·minal, but it clicl not 11a'v'e 'fJ cornpetable baud rate to the network that

the F'RH'1E is connected to. The rnain problern vvith using a t"tacintosh as an intelliqent terrninal WElt: the speml that data could be sent to Uw terrninal.

To

draw 8 curve a~:

a

~:et of points

on

the screen at rnm~irnun resolution

would takE!

( 512 pixoles ·)\· 2 x,y

*

16 hH illto?gen: )

I

4cWO baud :: 3.4 sec.

This tirne is slow for an interactive systern, and fn~quentlu 1r1UC:h more elate tbsn one curve is sent to the screen.

The final (Jecit;ion wo~: to irnplernent the Ct\D systern on tbe t'lacintosh

itself

wt·lich could

support

rnultiple windows for the multiple views, and

hac! t11e e)<:cf~llent graphic routine~; of Quick Draw available, as well as an

i

ntegn.1

1 llwuse.

Cine of the protderns 'vVitb the t·'tacintosh is that compiled applications

for the t·'Jecintosl·l can not tJE, writen on tile t·'tocinto::JL Tl·1e two cornputers

available to 'v'vTit£1 t11e progrsm on wen1 th~1 departmental VA>( or the Lisa.

The Lisa vvas chosm1 a::: it supported an Object orientated Pa:::cal ttased I snuuage, ami a pack 8gB ca II ed t·'tacApp that i ::: used to :::i rnpl

ify

window and

rnenu maintenance.

For the Clilllput er to IJo atd

e

to perf onn ony useful function in the clesi gn

or

analysis process it must l1ave some internal representation of the

t1ull

shape. The prirnorll function of tlw computer then is to maintain J analyse

and rnanupilate this rnodel.

1-\s the proces~: of ~1ocllt de~:ign is

a

geornetric protdernJ no ~:itr1ple

cornputer data structurc,s: exist that n:dlect the structure of the problem. HenCE! sorne specific dt:Jta structure rnust be used to represent the shape of

tlw hu I l.

For the rnodel to bo itnplernented on the t"lacintosh for interoctive graphics~ it rnust bE! cornpoct os: tile t·'locintosh I"Jf1S very lirnited disc and rru::~rnory shape~ and rnust be capable of bei

ny

quickly evaluated and updated.

The ~:irnplBst rnoclel vvoulcl tw EJ s:et of points in three dirn£msiom: but to

have any kind of accuracy tl"'e arnount of data would be prohibitive. Thus

somE! morE! complel<: model to represent the hull sl"1ape on the computer is

required.

The follovving is a list of the requirrnE,nts that have been found as necossary for u·1e rnodel.

1. ThE' modE!! rnust be space efficient. The reasons for this are Uwt the model rnust be implemented on sorne srna

11

cornputer and rnust be rnanupi

1

a

ted in real t i rne.

2. The rnodel must be able to be evaluated quickl~l·

this is for two reasons. Firstly the calculation of the curves is ·to be interactive and hence the points

on

the curve rnust be atrle to btl found

quickl~l· ~:;econdly.. an~! form of pararneter

calculation on the hull is going to involve

a

large nurnbor of Bvaluations of different points on the lwll.

3. The rnodel rnust be able to bE1 evaluated at any

cliscrBet point on the surfece of the hull. This is again for parmneter calculation such as cl i sp

1

aCE! rnen t.

,4. The modtd must be capable of representing any hull shope. It would l~1e rnuch better to have

a

model that could ropresent all hull shapes rather than

s

t;rnall subset of tbe possi b 1 e siHlpes.

:;. The modnl rnust be easily rnodified. This is so thE.~

interactive pert of tht1 progrern con ch8nQE:1 the shape of the boat and not hove to wait

a

prohil)itive len£}tl"l of tirne before being atde to

examine tho result of the chan~1es.

A clesiu1wr should be able to rnanipulate the shapE.~

of the boat ond bave psrorneters calculated for the boot vvithout knowing how tho boat is represE,nted in tlw cotnput er.

7. It rnusl be feosibli;l to rJut

a

user intEwface upon the model. The in te1'·r ace need not supp 1

y

the

same

rE,presentotion as the~ intBtTJCil representation. Tl"le

rnoi

n requi rernent of the representoti on to the end user is

u-,at

it conve~1s

ell

the inforrnation

that

the traditional views of the hull convey. The simplest way to

clo tllis

would to have llle traditional view os

the

repre~;entation

to u-,e

user.

8. The modo! rrnwt be suitablo as a llasis for furu-,er

ono1~1sis like structurcJ! analysis using finite e 1 ernent ana 1 ysi·s.

NOTE ll is

not

thought thot the rnodel should autornatical 1~1 enforce

and produce fair lines for tho hull shope. Given the full set of views of the boat) it is not a hard process for the dE1signer to fair the lines as requirBd. Often in modern boots there

are

bumps and flats on the hull for

rating

purposes that are not considert~d fair, but are considered an overall advantogE' V'l't-Jen the rating is taken into account.

other reasons for not hovi

ng

the cornputer model produce fair I i nes is the inherent problem of cl8fining exactly what is o fair set of lines. In some coses different dc1signers do not consiciE'r the sarne set of lines as fair) so it falls on the desi~1ners opinion as to what is fair and what is not.

Finally) it rnust bE' kept in mind tt·1al the desi£1t18rs final airn is usually to ~~roduce a fair shape that satisfies U1e initial requirmEJnts. Hence it must not onl!d be possible to ~~~-oducE' fair lines) but also eas~1.

In reality man~t thousands of points would tte needed to accuretly dE,fine the shape of

a

IJoat

11u11,

or some cornplex whole surface equotions vvilh mon~1 coefficients couhJ be used. The oclual rnodel used takes the real building process into account and uses VBry few points to dEifine the shape of the boots hull.

\v'hen a boat is built, onlq a small number of points or offsets are used _{. ~} to define the frames. Tl1ese points ore srnooU1ec.J by bending flexible battons or splines around the points to give the final shape of the frarnE!.

A srnall nurnber of these frarnes are t11en usec.J to define the 3 dirnensional shapE1 of the boat. To decrease ti1E~ nunber of frarnet: necessary at the front

of the boat to clefine the profile cw stern .. a separately shopecJ keel is often

includE~d. CIVE!r the fronws planks of woocl ore bent, again gi'v'ing the shape of spline curvE~s. Thi~; process is even used when building rnodern boats out of fibreglass and other plastics, as the 1-,ulls are still originally built

over

wooden moulds.

So the repE:nesentolions I have used ref1E,cts the actual process of

The basic building block of the computer rnodel is a frarne of the boat. Each frarne is defined b~l a mnrtl,er of points, all in one plane .. and an offset forrn thE! front ( bow ) of the boat. Together ~,ovitll two end conditions, these points on

Hw

fn.:~ntH uniquel~l define a set of cubic spline curves that are used to interpolate IJelween the points when evaluating points on the fran·te. 1\ sE1l of thesE' frornes ( including their offsets from the bow) have the propori l~l of uniquely defining tll8 shape of the boat.

The cubic spline curvet; are chosen for the interpolatinq function as

. I

-they appro>~irnate tlw tJE,ndin~l of Et physical spline curve. The main

difference between tlw physical and the nwthernatical splines is that tl-te rnatherneticol spline::; ore infinitly thin and thus have different bE!11din~1

properties to the ph~l~;j cal sp 1 i nE~s the do:::i gner uses.

To provide increaSE!d cl€.~tail to the outline of the hull witbout having to mid

a

larg~::~ nurnber of frames onl~l hflving significant datapoints at their extretnes, a keEtl 1 i ne and a deck line are is also inc 1 uded in the basic 11ull shspc1 definition.

ThH end condition used for the splines is initially set as the second derivativE' being zero. This rneans tho splines ore initiall~~ natural splines. Tht::t ph~lsical Bffect of using natural splines is to ha'v'e no t1endin£~ rnoment on thE! splitHJ outside its 8)<lreme points . To give greater control

over-the onds of Uw curves .. four diffE,rent end conditions have been

implemented. The~1 are as follows.

This allows u-,e rate of chan~1e of the slopE' at the En·, cl t o t113 spec i f i E! cl. I f liH3 curve a t t h

e en

iJ i s

a

tight curve, the abso I

ut e

va 1 ue of tbe second deri'v'otive 'Nould be lor11e. Natural ~:~dines .. ie those defined tq~ bending a spline tbrough

o

set of

cl a t a p o i n t s o ncl le tt i n g t he end of t11e s p l i n e fl o a t free to f i ncl its own position, are appro>\i rna ted by settinq the second derivative to zero.

'>-2. ~;etting the first dorivative of the curve to a specific vo llw. If the s I ope of the curve is known

ot t11c-:! end point, then the spline can be set to have tbot slope ot its end point.

~~. Forcinfl the curve to be straight between the first or lost two data points. This is often 'v'v'f.lnteiJ wtwn dealing with the bow of

a

tloat

or

with the top

of

tlw sides of o rnodern liull sl1ape .. vv·here it is known to t:n:r strai ghl.

4. No condition, where the "not-a-knot" condition is used. this condition is included for completeness and is docurnented in the spllne calculation routine.

The curTEmt interface does not provide any facility for changing

u-,e

in i ti td end conditions.

The otlwr

views of Ul£! boat are generated frorn the intersection of the

plane that the viBW lies in with either the deck line or the keel line .. and

thE:! inten::ection of the said plane with the frames.

~~ nurnl,er of sirnplifications have beEm rnade about the design that make

the rnodel easier to irnplernent. ThEr simplifications can be rernoved by

rnaking Uw progrrn that irnplements the rnodel rnore cornplicated. The sirnplifications are as follo"vvs:

t.\11 rnE,i.lsurernents are taklm from

a

base line.

The stern( tbe back of tll8 boat ) rnust be a frarne of the boat.

The stern (tho front part of tbe keel line) rnust not be vertical.

TumblG hornE' can not be reprE,sEtnted. Turnble horne is where the sidEt of

)

,/

--·---·----~-·--··'_/

fuqure 5. Tum!Jl,::'! home ancl the "meot axe test"

the boat curves bock on itself. Tumble horne cannot be represented as

the~ interpolation curves for tile frames are functions and tumble horne bas

t'vvo cJifferent values for the function et one offset. The meal axe test is

t11ed. the curve must lleve only one point of intersE,clion with any vertical

line.

This is not thou[~ht of as a sEn-ious rostriction as modern boats no longer utilize turnble lwrne es maximum vviclth on the deck is now thought lo bE! an cn:Nanta~Je.

Chines cannot lte represE'!t"rted. No corners or discontinuity of

any

curVE! or its first and second Llerit i ve can be inc 1 uded in the design.

fi

gun:J

6. A frame with a chine.

The mociEd nw~1 possi IJ 1

y

be extended to inc 1 ude chines by having hvo data points on a frame at the sarne place, allowing a disconlinuty in the first derivate at the double point.

TIH:J model does not deal with any f orrn of appendages 1 ike kee Is or rudders. These are special cases and derserve special attention. Specialized softvvare has been written dealing with rudclers ancl keels, aclaptecl frorn 'vvork vvith aerofoils.

The rnoclel can be slw'vvn to satisify each of the rBquirernents either partly or full~l·

1. The rnodel is VE,ry spacf~ efficient. For tbe design given in opf!lldix 2, the text definotion is 12 I<Elytes. Each frorne of the boat uses let~s tllan I I<Bytes to store the points and spline coefficients. 2. The evaluation of the cubic spline function

involves onl~J four multiplications and di~·isions.

3. The

rnocle

I can

easily

bE! eva I uated at

any

point on a

frame. If the point of evaluation is not on a frt~rne,

o ternporau frarne can be generBtecl at that point. The points on the frarne con L1e generated from the intersection of the frorne with thE! buttock ancl water linc:,s. Thit; lllfjY semr1 a consibm-able

overhe8cl.. but for colculation such as di spl ocernent .. oncE' the fnll'ne has been generated,

rnan~1 other points of evaluation will fall on the frarnE!. This is because the points of evaluation on Ul8 surface of the hull will be in discreet lines.

11, ThE! rnodel is not capablfJ of represonting all hull shapes. t\s sta tEtd above.. the rnodel can not r€1present eithc:n- turnble horne or chines. Appetrl forrn these two special cases, tbe rnoclel is capable of rE,present i ng surf aces tiH.lt are conti ni ous in

zero~'' to the second derivative, ond are

sorne forrn

of B function~ iE' the surface pat;Se~; the meat axe test.

5. The model is be eosilU rnoclifiobd.al:de. It is easy to change the value of one of the doto points and

then calculate the ClWVE!S that define the boat a~ltli n.

6 . ."/

·rr,e

rnodel is dernonstroted to be transparent and suitablE! to put o user interfaCE! on in the implementation of the CAD system.

0. The model is a s~uitable twsis for finite elernent anal~lsis. F'oinf.t: on Uw surface can emdl~l t1e gE,nBratecl from the splines fJ1at are suitable few input to a finite element package.

In the progrorn, the speed of calcu1oting the spline~: is negligible cornparerJ to the tirne token to evaluate the splines. The splines can be evaluated fast etwu~lh fot .. a point on a curve to be dragged using the rnouse ond thE! curve ro-Ewoluoted oncl drawn on the screen. \vhen a nurnber of curVf:lt: need rE,dravv·i n~L 1 ike 'vVIIE!n an olternati ve vi ow is updated.. thEl majority of the~ lime Sf.IE!nt is in the eva 1uoti on of the curve~:. 'll1e current rE,prestit'l ta ti on of the sp 1 i nes uses a genera 1 i sBd form that is equally as

fe~:t colculetin~l the

rlh

clerivetive a~: the value at eny given point. To

speEJd up the evaluation of the splines .. a different n.ipresentation could be used that i~: quickE'r in calculeting tbe value at any given point .. but slower in ca 1 cul oti ng the derivatives.

The alternative consisered that was capable of rnataining the same basis for the rnoc1e1 was spline surreces. [ 5 ] The points ogainst spline surf aces ore : t1'1ey are rnore cornp lex to i rnp 1 ement, tht:~~l requirE' points on o recten~]ular ~rric.l, are much slowE'r to calculate and evoluate. The main point for the sp I i ne surJ aces is that they can t1e eva l uatled anywl1ere on the surf ace with the sarne arnount of work.

Becsuso of the rnodula structure of the pro~wern, the cubic spline interpolation could be changed to another from of interpolation, ie least squares or splines under tension, without having to change the parts of the

progr8rn

that use tbe splines. The basis for the code for the spline

routines cornes forrn

I

4]. The code in

I

4 ) had to be exetecled for sorne of the end condi lions and translatecl into psscol.

.J]iEJi1liJl

H

n

JJl

It_R F

H

C~

There ere CE.~rtein features found in almost eVE!ry t'·Jacintosh application. Typically, tho user con ~:croll oncl resize windo'v'v'S, perform docurnent operelions like open, seve end print, ond issUE! editing comnwncJs like cut, pe1st .. and undo. In addition, W£~11-written programs will report errors emd recover fl-om thern. [ B J

Decf.lllSE! rnuch of stondertl t·'tecintosh user interfece is irnplernernted

by

t·'tacApp, it is easier to conform with the standard than violate it. This

does not meen that t'lec;\pp does oll the work in the progrorn, as it only provides

a

fretnt!\'Vork to write a t·'tocintosll application within. ThE! main job of l"loct\pp is the calling of t11e procedures to do the work of the prow

om

in thE! correct on.ler.

The ~:tenderd t·'tocintosh interface hos b£len adhered to as much as

possible. The Undo cornrnond is

on

importont cornrnemd

in

the interface. v'/llen o cornrnond has been performed oncl the result is not os rEJquired .. the cornrnand ct::ltl frequentl ~~ be undone. Undo is supported os often os possi b 1 e.

Th£1 docurnent seved on disc for this opplicotion is the text definition of

t11e points that define t11e yC~cl1t hull.

'-ThE! date on tilE! f:creen if: presented in windows. Tl1ere may tre more

tiltH., one window on tlw screen at a time, but only one windovv \·Vill tre the

currently SE!lectell \·vimlow. Tl·te current!~! f:elected V·iindow lws 11orizontal

lii'IE!S in its title trtw ancl will be the top of an~1 overlapping winclci\·Vs. The

\Vindci'WS

may

be

rnovBu atrout

tlw screen and resized to suit

u-,e Lwer.

The picture f:een tt1roug11 tile windo1_N

rnay

be larger t~ttm tl"te window

itsEdf ancl Uw window

moy

l:re movod over tl'lE! pictUrE! to

:3ee

different

parts of tlw picture.

l.r~~£~UI_ClE

.. CW·1tt8HD_S. ..

t'lost cornrnands ore CJenon'lted t11rouql1 selectinq rnenu itE!ms . .,_ f ... ...

rut

t

npq

Pa~1o

100 t h:nr

200

uram

E>~mnple of selectin~l Undo menu command.

Some of tile menu command can also tJe generated

by

key strokes. An example of this is t11e Undo command above ma~1tre given by typing tile

Llutterfly ke~1 and Z. The ke~~ strokes for commands are shown in the

menus.

Tl'le other form of

cornrnond E~ntry is clicl<ing tlie mou~;e t1utton ot

different plBces on

u·1E'

screen. Ttw most cornrnon of t11is thiPE' of cornrnaml

is ciHJnging thE! current vvlndovv Ll~l clickin~l t11e rnouse button in some

\·Vinclow ot1'1er t11en tlw

currently

active windOVY'.

'-IJiE__CIUJ1EJlT ElliSElLD HJlf

Tll1~_ilQJlBD ~

The feol.lwet: irnplernented in the program end the ease of use of the user inter-fece ore best dernonstroled

by

thE! use of the program itself.

CCl[l

CL

U_SlQUS.

Tile data moc.1el is c.Jernonstratotl]e fea:::ltrle as slw~;vn be the resulting

prognHn.

Tile speE'd of some of tile opperati

on is

not e>::cellent

but

compaired to tlw proces::: perforrned b~l t·,and, 1t is rnony onJers of

magnitude foster. Tile onl~l part of tile model tested is it's suitatdlity for

tilE!

calculatlon

of

ttw

required porarneters.

Tt1e rnain

proLJlem wiu-, tile implernentotlon of ttw model and

the inter-race was

u-,e

difficulty

of

building a program

to

run

on

t11e l'·lacintosh.

Tlie

J()W

of conservation of complexity stales

tllat

1f life

gets

easer

for

tlifJ user, it rnust get more complicated for t11e programmer. [ 8 J This is

found

to

lie

tnw wlwn tryin~l to worl< on t11e 1·1acintosh.

Tl1e task

of

rnataining multiple windo\·Ys, organizing menues and

all

the

ou-,er u-,ings involved

in o

nactntosli application is not

trival.

r1ost of

t11e

t i rne ~:pent in

H1e

1 otter 110 1f of

tt1e year

lias

been

spent working on tl"le

irnplernentt~tlon of

u·1e

l"lacintosl·l interface.

Tlie project as it

novv·

stends, is a suitatlle interface to implement

U'1e

origenallu

proposed

rnaU'lemetical analysis

upon. Tlw

author

hopes

to

continue and implement parts of the mwl y:::i s as u·1e tool

tlw

program

represents

is

still required.

HPPEI1DIX

1.

,. ') . \ '· \ __

,

',; \ '. ~ ,,,

' _{.\ I•}

.,,,_ < L 'I

~

,

I I .f

l \

_

_.]

·--·

---

·---~-~~--]'-..

-...

,

... ····-.... ... ~ ... ~~t·' .-~ >A/. t ' ,.-... ~~·· J"H ,d~<F ~~· ~ 11! •••••• .J'.,#' ~ ~·-·t"1"1~' ... -. ·4·-- ~.. ----,_.... 1 ,,..r• ... ,.,r· ;r,....,# " --(.) / .,...,.,

..

~ ' . -''"/ .... --·-· ---r' ·---~·;·""' ... ---~·-·

.ll

'r .

...

·-···

··-.

·[·

--

-~----·---· ..b...

---·----· ....

-~-!

-~-..

·---··

--·

··---.-,.._,

..-... ')

'--,J ()"\ (I

I

··-~{

..

--·

··-/-

---.,..

-

----,_,

__

,__ . ,, . ·----~ ·----~~--.... - ---~--... ____ .. _.__ ... __. •.. _~ \ • " I

\ ..

sr~

:::::~t··

=~--=-,,,

'

'/ ··-1 • '• ., t\....1

·-I:\

_....

--~

:::::~:_·~--·-..

··-...

_...lt.;:; _____ "'"

-~'-___

~ \~~...._

....

-·--.L----·~~-··-·-...-.

.l..t\

...

I ' -' I.J

\,,__

, r·-.__

~~.. ----·· ---~--... ""---·-· -- -~---q·\ ., ~ .... ..., ~~ ... ..., l' ,.~ ... , .... , __ ,~ • ..._ '} ;' '''-..••. .,_ "'·.ot.~ ...

-...

-~----·-!"

...

-~¥·•·!·""'·:-;-.:·--~ ... ~~;~---... ·-... -.J --- ·-·-- ---·---·--·"···"'"""' ... 00

rl;

r

J I . 'I

.

\ •)

PJ 1) '

·-

.. _L 'I I

C'1

"' ; ... '".

l

)

1:

.•

li)

... _l i .. \

I'

r·-\'1 I ti ~' l -~:

(,\ j'

J

II

I

HPPEHIJIX 2.

Daa·s boat

frame

1

offset

160

0

400

50

320

100

170

130

0

frame 2

offset

500

0

430

100

400

200

350

300

160

330

0

frame 3

offset

1000

0

460

200

430

300

350

400

340

450

290

500

140

520

0

frame 4

offset

1500

0

460

100

450

200

440

300

420

400

400

450

350

500

340

600

0

frame

5

offse

2000

1J11l

O•i<jCtvlGi \

~~C\(t;

0

440

100

430

200

420

300

410

400

390

500

360

600

320

650

0

frame 6

offset

2500

0

400

100

390

200

360

300

370

400

360

500

350

600

260

650

0

frame 7

offset

3000

0

350

100

340

2.00

330

300

320

400

310

500

2BO

600

190

·-····--..

~-· ... --... ·--··

, .. , ....

frame 2

FnHIH~ j

Frame

~)

Franw 6

11·<~m (~

n

F

rn rn

(? (}

_,... .... .r'"" ·

-..

,.,~--' .... ,, ... ,, .... .

, , •• t

, .. , .. ··''

(' -I

_)cc,,

e

4

·I

I

.r ...

~~t1''

0) .

~~N,llll(

sele<.

(e.J

W irnJ tH.U :'It r·c~ ~ cq:J(II\~j

-. ..: :;;~: --=-:#====-~~~~~::::::=.:::---=:= ' , ... , ..

t

f

!

f.

!

{ (

L

r

,-;

//

f:' f! I:

I r

i [

I . I :

/ j

.·

.

I.

file

600- .

~100--1

200--1500 ..

L.he.

()

0 " ·

-

1--,~

Dad's lwat

frmnt~ 1

offset

0

51

101

130

frerne 2

orr set

0

10 1

203

297

333

frorne 3

offset

0

203

297

399

449

500

522

frarne 4

orr set

0

I 0

1

203

297

399

449

500

601

frame 5

offset

160

399

319

167

0

500

42B

399

346

159

0

1000

457

426

377

341

290

1313

0

1500

457

449

442

420

399

377

341

0

2000

-lhe_

re},necd

J~~

0

442

101

42B

203

420

297

413

399

391

500

377

601

319

652

0

frame

6

offset

2500

0

399

101

591

203

377

297

370

399

362

500

345

601

263

652

0

frame 7

offset

3000

0

348

101

341

203

333

297

319

399

312

500

253

601

lOB

623

0

keel 1

offset

0

0

0

159

399

500

426

1000

457

1500

457

2000

442

3000

34f:l

tleck 1

offset

0

0

0

159

130

500

333

1000

522

1500

601

2000

652

2500

652

[ I

J !"lull,

Gewy.

Taking e b~1te eJt design. In /v'tm··ZeoitHlo' Fatlit.itJg, ~.lul ~~ 1985.

!

2 J Foster, I. T. Computer- Aicled 'r'ocht Design. C05t46~? tf'eseotY::IJ

projec~. 1../,tJ.ive.r~~itp of C6tJierbtlt~~i October 1979.

! 3

J De Boor, Cerl. A preticell guide to splines. 1978.

[ ·4 J Conet, ~;,D. & De Boor, C. Elementr~r nurnericol emolysis. t 972.

[ 5 J ~;pf'tth, H. ~;rd i ne

e

1 gori tllrns for curves f.lnd surf oces. 197 4.

I

6 J Tesler, Lorry. t\n lntrocluction to l"'lacAppr''1 0. I l/(.'1'ti"Jpp

{.rht:tltJ:retJit'd .iOJl fa/o'er F E)bruary 22, 198~-:i

[ 7 J Tesler, LarT~J. OttJect Pascal Peport. ./:i'o"CApp dact/lJ?etJI"'il/atl

la.ldt.?t~ Februor~l 14, 19t15

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