CHALMERS UNIVERSITY OF TECHNOLOGY DEPARTMENT OF NAVAL ARCHITECTURE
AND MARINE ENGINEERING
GOTHENBURG -
SWEDEN
THE EQUATIONS OF MOTION
FOR BOATS WITH SUBMERGED
NONCAVITATING HYDROFOILS
by
COSTA WAHL
DIVISION OF SHIPHYDROMECHANICS REPORT NO. 18
SPONSORED BY THE SWEDISH TECHNICAL RESEARCH
COUNCIL FILE NO. 353e AND ASEA
GOTHENBURG IN APRIL 1964
N- E.
S%.34M Av
== = =
a.t. C
JÇE 8F
A,-T1E *YDEoDU' DEP
O -EME BOA-T.
T4E BOA1
CØU%IN CAL
U.s.
kTcA-
ULP4
. . .hiZ. HPJIA
..
...
. . . L%. PITC.fr%.JA..
LL . . . . . IAb
OLLI.
1.z.
laNGQ. 0F A1k..E
cc ATT*..c1
o
ThE
A4b
-rUtbE.
O -r
M-flo
F TRE..t.Z.'.
øLL. . . . .70B2-64 S's 732 501 *4 2 t.z.4. O1L % 4C '?J %
. Ti4E
cA-r cW .A
Co4C %P2.'.
A.rcM o A
t Vr0 -rE.
C£LJE. OF TE
2.2. CHJIÇE. ÖF
r E
cr ATrfrCX.
or
fl4D*oDL.s
cjp. T.
,$FrAL
-rDp.-r4E Wt
2. Gb4Ai.,E
ri
%TU,
A.Jbe-r
&.DtE____
o
t4
OrrAL. Mb
P4 T...
?... f2!'3'_
i!'.
FLAP
A'JD 3.LF.EC1.%
Fe.I Ab4Fi.i
P...t
iB .
.
-F r4Q. AIL-E o
r-r
3.3. OL1tÑi.d;1.2. Prc.
t,
...
cv
3/ . C¼S 2ÇOl4
AND FLAP. -..
APPL,$b. ccLE-
I--1 -r0ASEA
) 'VLIFT
0,1
,FLAPr
aw,boroIL.
YYOÇ,C'OP,C
foi
oPE.LLÇ arc.
-.2. ELVTC bc
-..
4 i
'1 45
r
U.
OT&OoAT
Jrr*
_4
ø
OÇIVP4A4% W%t
F%JZre!bDM.
4EAVPiic
LLAt
JAThE. C-f cV T'M 1TUT%
C. VeJ
A'4
AY&L
rt
AbA
-rI
AJrl-\
WjS T0
IR,
To
.Cl4I,'r
A1 A& M
lJ '4 v H%tÌL
c
-r%E:c
1.TV.3-viArsC
Ar ,-v,:
DIV&O!'3 øç
s 50' 4 1
E.
To
E.. EOc.4 Ai
TWL<.
4
A'L
j TE D(rcp.
OF ÇI
O CT4.
c'T
& R.. VFb Ti 4
%-rI.(")
taio
(
p)
ca.cI.çi
U zI
64 s 501 4 X*
b II Ve2
.rO4'
uo
Çn
b 2OA T WA*(4
u u i. si-as k H ii
's-AwaI..t
Ç ATTr*tCK...O$ T.4t
4'?D1POL
n L
'r
L
-
LIFT CFFCtE
HL
tr
eOOL
Or
cr rsE
'3 Vtn-r
XLrb
aT j
Zz.4.C4
t.J4
E.pyouvZL.
urAcE..
.L) FI4CY oF
O-%L L'A'-E
¡NDME?
Pro
oAtD
FFIL
G1.1
tP4bL.
1ç
2.2.4. :(
1. THE.
ao-t
c-JATE
¿.1.
c
"r-K
OPJTHE..
OP1 T.
V1O1 oi.%
ç
SOAT.
t.t
-TArlA-.
'UL1W-j.
W1M
py
oASE.
CALI-i øJATLr.ALL T4E
4VD )EA CoP-'T
OF
.i.z.
viij
-i ic E T H--A'II4T
oAet.
1P4A HE.AP
MQTIOP.'o /Ç
zz.'t.
r)(E
DF
TTAC.
JILL
A C4E O
z
U
714E
ANAL. cF
c-
-1.Lrcr
IF 111E 50A7
EA !rC4
)ØtDTIOi'4E
44L. ol
A-r-rAc..'JILL
E-r A)1 L' Ñ TPIE
AÇ'-r
IL\-oL
P1At.L t T A o L .. i ' M O T O 4 T A L L. O A-r-rA JiLLA
-
r
(
ALLAÑAL
A4ts
JLÑ
osT
iEAVI?'J
eoL I)4
TE AIJA LL.
'cT
K W L.L.2-O.Jr
-o
u
u
L)(t-u't r)
-
-
4''- J'i')
(2/Ç
2.2. ¿4 A OÑo-r
- Z +'
4) - r)
iOr o
C ETiE
Ar'A
O.z.
o
AK1L. OP Ar-r.kC.. 0M vE..
'-b
r4.
J Db
ÑtP.
ON TI4M0cP.
0
T4
oL_,'r..*1i.
FiL
ST4.
&M4L...
0
AT-rp_c t-)1.2.Z. Yn
T4L 30A
MAKt-tLL..
EcoME
-tboA
)'
T41Eøî
o
o-S:
CT W
-3 /-ç
2Z. 1it. 4'4 W±L'
Tk.
44. oc
TbWc,
o$;
-
-Ö4 rWE
Aoe ir
cT4E
+ûtP.)
fl#.
-eu-r
f-(e
-L\
+ -e'-ApPoAcEt
A?'V.A"
b2E
t sLqJ&L_
-re, AS -c4
Tz A 1 'r4E..
UrOM
2. T«.0M .\
A N4,/
A:ì
AM.Lt
ToC1t.LI
OF 'T A X XtE
T!Ic'F
'\C%V.
Co
-'rr,
o+ x.
c - 1c T T4VLoy.r?
tP4 T'4bj
'
AeArY o4T
óv
r AT1c
orrrA.. VLc.rr'
r4E JiJ
A'
I
/PrVC
f&(E
AV TE
EAT$
E
(ut
- Ç)
s
+7
r
-T L e.p
LQh)
Coi x 7
;os[.ciQ
..1LLt (Ti4-Ç44sp,c-ro,
LEL
C-r
ep GD
['cobE +e'
4(u
ce_
ç
ZÑco
(u
.-
-e
+Tu.')
-_tJ
e
;o.
s>)-4
tw v
t
-+
*
=_k1k cc7
- - . E u-
t
f
$ 71i4
-'-
-p'
+7
si
.--c
r..
P c AT a )
\I £ S i1M( t.)t -r
(F%JJ. !tilt)
-
(0%t
-'rc't4tT
T'r'-4
o W U t K L. C O I-% P)..T JE. t.4J..Lo4L/
A FE'.'-,A'
)
4) /2) % A b
Ue
Oo
riJ L)ç'1p
-F
-t
Uca.
u
°
/4¶%[(()+
L]
Y1_)t
1'-I'4
Li
%Ip''
'i. 4ç.
tr))4.tw[(u)+
PlL)
'.Ej'l
Lh
]
r
i)
-Ç7pJ
Lp SU-c
-F1
NCf(.-.yL_
L(I
ti
u'op u',.,' uo
o
ir
e
ii. L14 4(c,
)
C. t-
a
iEiPI
IF'tr
--i-j
1(.
-c'k *
tP4Lç
) oo
o
3
w O
p[u_t*
'1cr]
-* 11/4']
i
ç-4o{c_t
j
o[(4_c)t,
']
ç!iP]
F]
uAf
'J -1 ACOtO41
i
s-wP o
Zy
i[1
'lì.L1[(--c+
+]
VOPDU- bMbI
CMMOrto
gP4r*E.
ALL')'.
CFc
rTm-
c%:
,(-
vI.J_ uU )>
TÑe. Lr?
AEC PLLtt
OÇ DT4V.s' A)'C
%J44
MA-44
WE.. QT-.
ZZLM
j
Vc
flU
T 'r2.'..
CAP.i6.E
OTWE A
F0M TP
Ç,TttT Ab
0
-flIC
oI-rb..L
OVtOP
b-i
u -r X -A'JbJAJEs
IN A
ATo Tb1
xAg»
r1lE. AT 't,i4t
AI4&A Toe.FTS.
TMtCoI4p'T
Aoc
ATC.
o
-1tUTS A
r%DbEI.
AI4 T4ALc
L'
WI1..L.
ACT To
OL
y)
ÇA
44 u
u
j
_i!!±
--o-!±_
3.
o4
D.obtS
'b
1I
Lcr
e. Ab&OIZ.
L=
CIA+
CAL..o
'f-r«T TT
'4f-;
(-z+.
-u'*'-+)
TRE.(u.
-
-u*'
+A'b cJ
rt
A Ñt
f-O
1f-D -O )
Tw
u
.(u_)(-r
':
C-iw.Li
occE..
rr-r
-t
Jç
:
E +.=
_LL.Zf
z4/c
i(- 'ç)
(-Pt _-'
-.
-'r.4.
lto-
u-r'
OLLIN
ATiT I
S-=
;(+c"-i'%
(çz
4-:)+
k4('b-I
T4ut
THoeir Fo
A JT?.t,.44;
kcu
('ç- 'rb)[k
t+u"- -
-'(t1
AcroM -rPrn
U)
YA',t,4t,
,IortE.l4T.
T4 I4OHE.N1
Vø4 A..
T.UT ii
CL . uz
;;
'
aI pw-
Gt'+ Ç
çL'SI
L-i +t)
;è(+
4P4DT
L)g
19 pI'
i2i ç
2ZA.44
E.3LE
E QP
Fo-ai
- r'
F R(A)--
r)
\.D4I1ThI
P4 T4,. coiJ
4- Coi'+' -w*S.-C$U
.4-4.'3
(IP1
f iM' ,t9- -t. c-r Co.L-) +
t;
K Çsr
+ ?.
CaC-ZZ.LC4
MA
Z4-t
4JcF
r'oJ
£
- 9)
44 uP1-L
L1I
9
)
-+4.1.
f.AU.$A,
z
4,2d.
'±L
Tir4E.LA_ -IFT ÇDC
A,tt
UbDt
oI1E
L*A&+U')+
EtÑ,
-AÑO -rtu
STVt(ÁL
4 S e TWANAze.
c*WT.'cG
CA4E.L
#iC-.t.
trcI_
(
u-e7k)+
u
£1
LiZ
À)P _L4
WÑp+tJlp
c1...r
4.b. TGRt4 MOP4P4T%
tAUL,b
WOLll AMØ S
4+i?
iL
E +u'i)z
+ +u7(
. I
t+
(,.i
.t LJ
%: r e_ 4 -t A'4DrQE
)lar4
srAMs A1
FL..)
*-c-r
h
F T4 AV1 SiqEL
. YAaJLN .. c. -'
z:r
b'
A F1 45
rA-rgy
VAJM CL.-t
T.
? DCL..-
Ç -9-J L = Ç L-J
o&. -Ac.1 oP T4'E m-r. I W. C E.TE
øçi.
ç -tc1
*
OP DVI)T ACTO
FF CT
I-.I.
YbcPc. Focc
oi_ Pop
-rILE
crAT%N4
OAr CA bc
Ti4-r ODE..R.
A-r ry
i3poT
E.LEc.-rt.
IN --i4 -
c'i4
CpLL.O
Eç¿4-rA1c
o-t
LLE.%
b.O,Art.V4.1
54A?-ç
:NT,k.
-THE. -
E4AR
FotTAPC
RoTc
RSf
rrc
-t-$-
:cç- *
£ b1L..'1 1HE AY OSCc?' I
CLIt'L
TEARE. PtALL 1-'
AEO
roTI
o4
OF T
CU IP.4FQCES
4oJLD
IN THE W& e.
/4EÑ
r-
AÑ-ErIC
Tí
4'bc, FotL
A4U-4TO
k",'t.
A.T T4E.PEDS
I%N6
Ño1'
ThE pQçt-.E
cFIAbE.. V? c..L
-ro