;
Root Entry
\pCalc Ba==@ 8@"1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1
Arial1
Arial1Arial1Arial1ArialGeneral 0.0000000 0.000.0000
0.000000 + ) , * ( (
(
@
`<FormulaExcelEQrrTbZ 3 @@
]OfThese formulas were provided by Konstantin I. Matveev. Website http://www.cco.caltech.edu/~matveev/]The implementaion in Excel is by Harry Larsen. Website http://www.cco.caltech.edu/~matveev/0The conditions when these expressions are valid:NearPLANE (low deadrise), SEPARATE (or installed at bow; but not at stern since flow can be affected by bow foil), SHALLOWLY submerged (depth is less than span), NONCAVITATING, STEADIALY moving foil in CALM seas.gHydrofoil is the profilled supporting surface on which lifting force appears at the movement of a ship.Lifting force is found by the expression (1), where 'rho'  liquid density, V  velocity, C  lifting force coefficient, S  hydrofoil area.z = ( rho / 2 )* V^2 * Ct * S:Lifting force coefficient is determined by expression (2).hCt = Ki * ( dCt/da ) * ( a + a0  da0 ) / ( 1 + ( dCt/da ) * ( Ki /( pi * L )) * ( 1+T ) * E *( h / L )) $&For practical calculation in viscous liquid the derivative of lifting force coefficient on the attack angle and the angle of zero lifting force are taken like in expression (3), f  profile curvature. Reduced functions with upper line are given relativelyd Ct / da = 5.5
a0 = 1.74 * fThe influence of free surface is taken into account by the function (4), c  the biggest thickness of the foil, h  depth of of foil immerssing.&Ki = 1 (.5 + Cb * exp( 2 * h^.6))fThe changing of zero lifting force of the profile due to free surface is calculated by expression (5).da0 = Cb / 2 * ( 1 / Ki  1)The influence of foil shape on the angle of flow direction and induction resistance is approximated by expression (6). 'lambda'  aspect ratio, approximately equals to the span divided by the chord.T = .9 * L^.5  .04Function 'dzetta' considers the influence of foil depth and reduced width on the direction of flow. This function may be calculated by expression (7) at condition (8).)E * ( h / L ) = .85 + .16 /(( h / L )^.5).02 < (h / L) < 1Expression (2) may be applied for plane foils. For foils having significant angle to the vertical, special diagram is used for calculation of additional decrement.Lifting force on foils with stabilisators crossing the water surface is calculated by taking horizontal projection instead of the foil square and the depth is exchanged by the average value.Lifting force of Vshaped foil is calculated by modified formulas for lifting force coefficient derivative and for changing of the angle of zero lifting force.XThe implementaion in Excel is by Harry Larsen. Website http://home1.gte.net/hlarsen0/ &Approximate formula for hydrofoil liftrNearPLANE (low deadrise), SEPARATE (or installed at bow; but not at stern since flow can be affected by bow foil)1, SHALLOWLY submerged (depth is less than span), cNONCAVITATING, STEADIALY moving foil in CALM water with SMALL (less than 10 degrees) attack angle.$Instructions: Yellow cells are inputSymbolsMetricEnglish Equiv.
Pi (constant)Foil Area (Sq m)S (Sq Feet)Speed in m/secV(Knots)Density of water (kg/m^3)rho"Thickness of foil divided by chordCbFoil depth divided by chordhAspect ratio ( Foil span/chord)LAngle of attack (Radians)a (degrees)Profile curvituref1This value representative of a flat bottomed foilnewtonspoundsz = ( rho / 2 )* V^2 * Ct * S
Liftz_Ct = (Ki * ( dCt/da ) * ( a + a0  da0 ))/ ( 1 + ( dCt/da ) * ( Ki /( pi * L )) * ( 1+T ) * E )
!%
'5
6Lift coefficientCt
dCt /da = 5.5
dCt/daa0=1.74 * f
Angle of attack(zero lift)a0
#Ki = 1 (.5 + Cb)* exp( 2 * h^.6)
Kifor h=0, exp=1, h large, exp=0da0 = Cb / 2 * ( 1 / Ki  1)
da0T = .09 * L^.5  .04TE = .85 + .16 /(( h / L )^.5)E(h / L)Notes:f is the distance between the highest point of mean line and the line connecting leading and trailing edges divided by a chord so for segment profile f is a half of relative thickness, for symmetric profiles f = 0.
Oycc
dMbP?_%*+&?'?('}'}?)'}'}?"d,,`?`?U}}d}} }@@@
w@
@@@;@@@ @
@;@g@
;@X@;@@@:@@@@@@
~
~
~
~
~
~
~
~
~
"
PH0(
>@WWdgg
dMbP?_%*+&?'?('}'}?)'}'}?"d,,`?`?U}}}@}}}} }
f}} }@8
@@@
@
@
@
@
@ ;@
@@ @
@@%@@@@@@@@;@@@@@ $@@
!W! @
"
#
$C?%
r.U@D
Q%@
$
%
&~
>% qw)=@D.!u?
'
(
)~
*
+~
C
,
~
S
.
/~
0
1(\µ?% /L{@DD
2
3
4?!
!5
6
7~
"8
#9
:6$@ DDDD
%$ywO@D??
~
";
<
=i%V 5?SD$DDD!D'DD$n! @DD*D
~
">
?@ @!@#g@$@%@&@'@)@*,@,@,@/,@0,@1@2@3!@4@5@6@7@~
!
!"@
!A
!"B%!ʡE?ףp=
?D
##~
$
$"C
$DB$%&ڳ&#?,?DD333333?A
%E%
&&~
'
'"F
'G.'&@0??DD$
))~
*
*#H
*I9*%Ɓ?#
ףp=
?D?{Gz?
,,~

#J
K;%ã?%333333?{Gz?D/?~
/"
/#
/L!/?DD0"
1M
22
33
44
5N5PH 0(
>@Kgg
FMicrosoft Excel 97TabelleBiff8Oh+'0HPp
Hydrofoil Lifting ForceLarsen5@^jG@@oSӿ@`Wc՜.+,D՜.+,\Root EntryF@Workbook.CompObjIOle
SummaryInformation(DocumentSummaryInformation8t