A method for the design of contra rotating propellers

The Technical University of Norway

A Method for the Design of Contra-rotating Propellers

by

Knut Minsaas

List of Symbols _Page 1

Abstract

Mutually induced Velocities ₅

Self-induced Velocities and Ilydrodynamical Forces 8

ProfileCaracteristics ₁₁

Design Example ₁₇

Appendix I ₁₉

(UTS) . (UTS) ₂ *

(Us)z

(Uas) i

(U)

2 * (U ) as i (Uas);

Self-induced tangential mean velocity in the slipstream (forward propeller)

Self-induced tangential velocity in the slip-stream (aft propeller)

self-induced tangential velocity calculated for a finite number of blades (forward pro-peller)

self-induced tangential velocity calculated for a finite number of blades (aft propeller) axial self-induced mean velocity in the slip-stream (forward propeller)

axial self-induced mean velocity in the slip-stream (aft propeller)

self-induced axial velocity in the slip-stream calculated for a finite number of blades.

(forward propeller)

self-induced axial velocity in the slip-stream calculated for a finite number of blades.

(aft propeller)

(Uai)i axial induced mean velocity at the forward propeller from the aft propeller

(Uaj)2 axial induced mean velocity at the aft

pro-peller from the forward propro-peller VA = (l-w)V5 speed of advance

V _{ship speed}

w(x)1 _{local wake fraction (forward propeller)} w(x)2 _{local wake fraction (aft propeller)}

V

resultant inflow velocity to each _{blade-section}

r(x) _{bound circulation of each}

section of one blade

G(x) _{nondimensional circulation}

per blade

G(x) F(x)

z number of blades D propeller diameter R propeller radius i chord length rh Huh radius p _{density of water}

cavitation number based on resultant velocity

V

hydrodynamic pitch-angle of the propeller sections (forward propeller)

i2 hydrodynamic pitch-angle of the propeller

sections (aft propeller)

hydrodynamic pitch-angle in the slip-stream (forward propeller)

i2 hydrodynamic pitch-angle in the slip-stream

(aft propeller)

T1 propeller thrust of the forward propeller

T2 propeller thrust of the aft propeller

Q1 _{propeller torque of the forward propeller}

Q2 _{propeller torque of the aft propeller}

CL lift coefficient of the blade sections CD dragcoefficient of the blade sections

C

= drag-lift-ratio

L

RPM _{revolutions per minute}

n _{revolutions per second}

CL ideal lift coefficient

Cc drag coefficient due to angle of attack

Cfs friction coefficient of the suction side Cfp _{friction ceofficient of the pressure side}

3m

resultant angle of attack

cxii ideal angle of attack for CL. = i

k t(x) correction in angle of attack due to thick-ness (lifting surface)

k _(x) correction in ideal angle of attack due to lifting surface effects

k c(X) correction in camber due to lifting surface effects

a ratio between total lift and lift by camber ratio between lift-slope for viscous and ideal flow

m ratio between angle of attack for 3 ande 2

cx

dimensional flow

m2 ratio between zero angle of attack for viscous and ideal flow

R Reynolds number

Tv shearing force

K equivalent sandroughness

fg geometrical camber of the propeller sections

x = = nondimensional propeller radius

(r)1, (r)2

corresponding ratio on the forward and the aft

propeller

Po static pressure at the actual propeller section

with the blade in the upper position

Abstract

This report is a description of a theory used for the design of contrarotating propellers at SMT, and a computer program developed for this theory. The theory is mainly based on principles given in (1) , (2) , (3) , (4) , (5) , (6) , (7) , (8) and (9).

The primary objective in contrarotating propeller-theory is the calculation of self- and mutually induced velocities over each of the propeller blades. In this work the self-induced velocities are calculated with induction factors as in conventional propeller design and as devoloped by Lerhs for moderately loaded propellers.

The mutually induced velocities are calculated directely as functions of the circulation and not by using distance factors calculated for propellers with optimum circulation like those given by Tachmindji or Lerbs, the latter derived on the basis of an uniformly loaded sink disk.

The work is a by-product of a study on the interaction between bodies of revolution and different propulsion systems. The study is financed by the Royal Norwegian Council for Scientific and

Industrial Research. Fragments of computer programs for the design of conventional propellers have been used. These programs are

developed for and financed by a group of Norwegian propeller manufacturers. (l

A','1 2rIR1Xtg where * {l - w(x) }V_{1 s} + (U

_asl

₎ + (U

_as2

) tg -* 2lln1xR1 -

TSl +

(UTS)2

For the aft propeller:

F2

z2 r dr

Ay 2

1. _{MutuallX induced Velocities.}

As a first approximation it is assumed that the pro-pellers have equal diameters and that vortices shed from the forward propeller at a given radius coincide with the vortices shed from the corresponding radius of the aft

propeller. It is also supposed that the induced velocities at each propeller disc are one half those induced infinitely far behind the propeller and that the tangential induced velocity is zero forward of the propeller, and _immediately behind the propeller rises to twice the velocity _{at the} propeller disk.

When calculating the mutually induced velocities _only the time averages are considered. _{The velocity components} which are time independent are calculated by _{assuming an} infinite number of blades or by "smearing" _{out the vortices} in such a way that the equivalent vortex _{system consists of} an infinite number of horse-shoe vortices built _{up of bound} vortices along different propeller radii and free _rectilinear vortices trailing from the end of the bound vortices _together with infinite tubes of ringvortices.

The horse-shoe vortices induces tangential _velocities, the ringvortices axial and radial velocities.

Assuming equal mean vorticity for the infinite _{and finite} bladed propellers the strength of the _{vortex cylinders}

(vortex rings) shed from the forward propeller _{at x are:}

ar1

z1 _dr

From z dr = {l

- w(c)V

_{+ (Uasi +}

(U);

i r (UTS) + UTS

2llnxR

it is evident that a variation in R of about 5% will have minor influence on Ay.

The induced velocities are expressed in the following way:

U)

+ 2lln2xR2

-IS

2

TSl

z1 (UTS)l -2r[xR1 z2

r2(x)

(UTS)2

-2rIxR2 X

asin

= E Ay1 X n x

(U)2

= E xn

., (UTS) 2

and (U)

1'

(Uas)

2 are self-induced time

averaged or mean velocities in the slip-stream.

(UTs), (U15),

_(Uas);

and _{@ias are self-induced velocities}

in the slip-stream calculated for _{a finite number of blades.} If the strength of the vortex-cylinders _{are known, it is} possible to

calculate (Uai)i and

_(Uai)2

The axial velocities through the propeller disc are: = {i

- w(x)1} + (U)1 +

_Uas)1 and V = V {l - W(X) } + (U ₊

_Uas)2

2

ai2

2 s

Applying the equation of continuity to each annular element, we obtain: and whe re q (x) = 211r V (r ) Ar i i nl q2(x) = 211r V2 (r ₎ Ar n2 n R1 _{- rhi} Ar = m V1(r ) Ar Ar n n V2 (ra) R1 _{- rhi} 1 + 2(n - 1) = rhl + m 2 n

(r)

=r

+EAr.

n 2 n2 n 1

It is assumed that the self-induced tangential velocity immediately behind the propeller disc is twice

the velocity at the disc.

A ring of fluid of radius (rn)1 immediately behind the propeller disc has a certain amount of circulation and

this circulation must remain constant as the ring of fluid passes downstream. Hence:

(r )

_nl

ti

(r (UTS)i

ni ₂

m R2 = _{rh2 +} Ar

n

2. Self induced Velocities and HXdrodnamical Forces.

Fig. i shows the velocity diagram giving the hydrody-namical pitch of the propeller sections. The velocities

at the forward propeller are:

i = speed of advance,

(Uai)i = axial induced velocity from the aft pro-peller. U * as U *

21

211n1xR1 A2 U * as 2 U *

= self-induced axial velocity,

= self-induced tangential velocity, = tangential velocity.

At the aft propeller the velocities are:

= speed of advance,

= self-induced axial velocity,

= self-induced tangential velocity,

(Uai)2 = axial-induced velocity from the forward propeller,

(U)2

= tangential-induced velocity from the forward propeller,

2lln2xR2 = tangential velocity.

The hydrodynamic pitch-angle of the forward propeller is:

*

(l-w )V

+ (as)

+ (J ) xl s

22

ai2

tg2

= IT * TS 2lln2xR2 -

T2 +

(U.)2

The propellers are designed by using lifting line theory and induction factors. The self-induced velocities at x are

i * IJ i dG dx

aS(X)

_{= f} a dx x

-x

Xh and fig.(12) * UTS i dG dx

(x) =

_{dx x}

_-x

VS Xh whe re

= axial induction factor

i, = tangential induction factor.

The induction factors are calculated according to (6)

When calculating the induction factor

jl and

are used.

The thrust of the propellers is obtained from

T1 =

z1

f

p/2

V2

_CL 11(cos

ii

.

-. sin

il

xh

i

t t T2 = z2

f

p/2

V2

C i (cos . -c. sin .2)dr. L 2 i2 i2 i Xh

The torque is given by:

Rl

Q1 = R1z1

f x p/2

V 2 _CL 11(sin . +c.cos ii i rm1 1 V R 1 2 Q2 = R2z2 f x p/2

V

CL 12(sin . i2 i rm1 2

62)dr.

In these equations: 2r1 CL _li

-V

xl

CL

CD = drag coefficient of the blade section

CL = _{lift coefficient of the blade section}

The circulation of the two propellers is obtained from:

V -col Cos il 2 CL 12 = V co * TS + 1j ₎ 2fln2xR2 -

T2

_{ti 2} Cos i2

d/l

2 F(x) = px, - x where

X - X

1 _{- Xh} d,e,p = constants,

Xh = Hub diameter ratio,

or by

F(x) ₌ p {a sin(fl(x _{- xh)) + b sin(211(x_xh)},}

where p, a and b are constants.

It is further possible to use the distribution

n' F = k (a0 + a1x + a2x2 + a X j.

n

By these formulas most of the actual types of pitch distributions are covered.

effective angle of attack. The lift slope, ideal angle of attack and the angle of zero lift are corrected for lifting surface effects and viscous flow.

In addition the lift is corrected for profile thickness resulting in a change in angle of attack. To obtain the

eometrical pitch of the different propeller sections, the following angle must be added to

57,3 + 57'3(a-l)C . + ci

=C

3m Li m2x03 _Li 211 m1 211m1 57,3k . t(x) D where a ₊

k-

- o2 ci02 + a.2 57,3 ci02 211 - a. )C il Li CL _{total lift} CLi lift by camber

k = correction in angle of attack due to

thick-ness effect.

t/D = max. blade thickness fraction

in2 zero angle of attack (viscous flow) zero angle of attack (ideal flow)

in

-

zero angle of attack (3 dimensional flow) a

zero angle of attack (2 dimensional flow)

GLi = ideal lift coefficient

a. = _{ideal angle of attack for C = i}

il _Li

m1 = _{ratio between lift-slope for viscous and}

ideal flow

k = _{correction in ideal angle of attack due to} a

lifting surface effects. The following stadard values are used:

= 1.00

In = 1.00

= 1.05 NACA a = 0.8 (modified)

The camber of the different sectiones _{are obtained from:}

1 wh e r e

a _{kc CLi(x)}

a = _{0.06790 for NACA a = 0.8 mean lines}

a = _{0.06651 for NACA a = 0.8 (mod) mean lines} a = _{0.05515 for NACA a = 1.0 mean lines}

kc = _{correction in camber due to lifting surface}

effects

The corrections for lifting surface effects are calculated separately using lifting line and lifting surface theory as

developed for conventional propellers.

The drag coefficient of the different sections _{may either be} spesifid or calculated separately.

In the latter case:

C = C

+C

where

4

= l + 2 () + 6O(.) _} (CfS + Cf)

C = _{frictioncoefficient of the suction side,}

fs

Cf = frictioncoefficient of the pressure side, tu = maximum blade thickness fraction of the

section

i = chord length.

C

a

In the first equation:

R(S)

-= (a-l)CL sin {

where m, , k and a are defined in chapter 3.

= a function of the nose radius of the

section (0.25 - 0.75).

The friction of pressure and suction sides may either be spesified or calculated. In the latter case radial flow along the blades due to friction and centrifugal forces are assumed to cause an increase in drag compared to the drag in 2 dimensional flow.

According to Schiicting the tangential shearing force of a rotating disc showing lamininar flow is given by:

Tv(0) _0.616 p y

/R(e)

For a plank: 0.332 pv2

/R(e)

V

0r

57,3 _{k(a_l)}

Ci}

2Thm, B /R (0)

and

R

n

X

where 0(x) = (z = distance from the leading edge to the actual point)

If there is no pressure gradient in the flow direction the flow is supposed to start as a flow along a plank and then approach the flow on a rotating disc at 0 =

The shearing force anlong the propeller sections may then be obtained from: T (G) y 1 0.007572 p.V2 = /R (0) (0.616 + 2.35 (0.2 + 0) n giving:

T(0)

_0.616 pv2 - /R (0) n T (0) y 0.332 pV2 _{/R (0)} v'i for O = for O = 0.

If the Rn of the sections are defined as:

= i _+(fl

X

model tests in open water seems to indicate that the suiction side of the propeller remains laminar up to RflK2_3 l0

while the critical R for the pressure side is:

RflK 6-8

l0.

(7), (12).

For R higher than the critical number but lower than fln=3l07 the friction of the pressure and the suction sides are obtained

from: c 0.455 A(R ) nK f

(logR

- R n n

where R = critical Reynolds number.

nk

Rk

2 1U 3 s lO io6 3 io6

A 700 1050 1700 3300 8700

In turbulent flow and with rough surface:

0,572(1,085 log(R ₎ 0.45) n 1 if where Po - e

(log R)3

Cf > 0,455 (1ogR)2'58 and Rn > 3

10

If not: 0,455 Cf

= (logR)2'58

(fig. 2)

The equivalent sandroughness K is obtained from:

K K

T

where K is mechanical roughness and T is a function of the machining and finishing of the propeller surface. _{( 2-5).}

The cavitation safety is defined as: V 2

(r)

- 1 = S =

1-nl

G o p/ 2V2 o

and =

f(.)

= _{chordwise surface velocity.}

The chordwise distribution of velocity is obtained from:

V v 2

J=(L+

-±--V V V V co co whe re + _{= suction side,} - _{= pressure side,}

IVa = _{velocity due to angle of attack,} 1w = velocity due to camber,

y = velocity due to thickness.

= (CL - CLi) f X = CLI X = ( f3(1-) - 1) + 1 i 0,06

1 f2 (i.) and f3 () are specific functions

for the actual mean lines and thickness distributions in 2

dimensional flow. a V co V_co y V_co (X 1

4. Design Example.

When starting the design it is necessary to specify the type of circulation distribution on each propeller together with the diameter of the forward propeller.

Further blade number, blade area ratio, or cavitation safety, chord length, chord length distribution, mean line, thickness distribution, strength requirements, RPM, absorbed power or wanted thrust, wake distribution, ratio between lift by

camber and lift by angle of attack, propeller immersion. Hub diameter ratio, skew, section drag and blade finish are specified separately for each propeller. Finally the

axial distance between the propeller centerlines must be given.

The design starts with the calculation of two propellers with-out interference but giving desired thrust or torque. From

this calculation we get self-induced velocities and circulation as output which is used as input for calculation of the mutu-ally induced velocities and the radius of the aft propeller.

IThe

design is repeated with mutually induced velocities and the adjusted diameter of the aft propeller. As output self-induced I velocities and propeller circulation are obtained. Mutually

induced velocities are calculated anew and the process repeated until satisfactory convergence is obtained.

As a design example a pair of contrarotating propellers

with

blade outline and thickness distribution identical to those of the propellers in (3) have been calculated at SMT. Also the distance between the blade centerlines are identical to-gether with thrust RPM and speed of advance. Both designs have been made for uniform flow.

The distribution of circulation is slightly different as may be seen from fig. (3) . Nevertheless the pitch distribution

will be of the same type.

The DTMB propellers are designed for torque balance while the SMT propellers are calculated for thrust similarity. Never-theless the torque balance of the SMT propellers is acceptable.

and

i

The ratioes between the diameters of the aft and the forward propellers are: DTMB D2 = 0,9674, D2 SMT:

- =

0,9602. D

As a result of the calculations we obtain:

T1 KT = pn2D14 = 0,1294 K Ql Q1 _pn2D15 = 0,0281 T2 KT = 2 = 0,1298 pn D1 Q2 = 2 5 = 0,0277 pn

The mean values of thrust and torque have been compared to the open water results of the DTMB propellers (fig. 4). Fig. 4 was obtained by extrapolating the K _{and KT values}

V,,

for

A = 1,0267, (from fig. 27 in (3)). A comparision 1

of the two designs on the basis of the pitch at x = 0,7 (forward propeller) may be justified because the pitch dis-tributions of the two designs are almost similiar.

There seems to be acceptable agreement between the results of the model tests and the SMT calculation.

In the SMT design NACA 0,8 mean lines and NACA 16 thickness distributions are used. The lifting surface corrections are

from (10).

Futher in1 = 1,00, m2 = 1.00 and m2 = 1,05. The drag of the sections has been calculated for the actual R _{as described} in chapter 3.

The circulation of the propellers is obtained from:

2

F(x) = px1 /l - x

where p = 0,45 for both propellers.

In fig. (6) , (7) , (8) , (9) and in the out and input example

details from the calculation _{are given.}

Appendix I

A _{vortex ring at (x, r1) (fig. 10), will induce an axial} velocity in P1(r) and P2(r) given by the equation:

du ai 2(,-) - 1) e K(k) - (1 +

()2

_{+ (i_} )2 )E(k) } where: A dF 2]lr' 1

(fr)

2 (1,-+1) 2 +

ri-

+ 1)2 r'

K(k) and 11(k) are te complete elliptical integrals

11/2 dc K(k) = f A k2 2 o -

sina

11/2

.2

E(k) = f - k2 sin da o

Far given values of

x1

and F(x) the mutually induced velocity Uaj is calculated by integration from _{x = O to} x = , and then from r - rh to r = R.

Identical methods for integration in radial direction is used both for the lifting line calculation and for the estimation of the mutual velocities.

The accuracy has been tested by using the actual method

to calculate the downwash of a lifting line in 2 dimensional flow. The line has an elliptical distrihution of bound

circulation. See fig. 11 and 12.

As in the actual case the span has been divided into 400 equal parts. The table indicates that the accuracy of the method could be satisfactory.

Method 2

fic. 11.

Method 1

fig. 12

(used in the theory)

The theoretical value for w is 1.

0,05 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,75 0,80 0,85 0,90 w 0,858 0,925 0,958 0,968 0,972 0,973 0,972 0,968 0,964 0,958 0,947 0,925 x 0,05 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,75 0,80 0,85 0,90 w 1,0096 1,002 1,0006 1,0003 1,0002 1,0002 1,0002 1,0003 1,0004 1,0006 1,001 1,002

i 2 .) 4 ) ) ) ) REFERENCES

11.W. Lerhs. _{"Moderately Loaded Propellers with a Finite} Number of Blades and an Arbitrary Distribution of Circula-tion". Transactions of the Society of Naval Architects and Marine Engineers.

Vol 60, 1952.

I1.W. Lerbs. _{"Contra-rotating Optimum Propellers Operating} in a Radially non-uniform Wake", David Taylor Model _Basin Report 941, May 1955.

W.B. Morgan. 'The Design of Counter-rotating Propellers using Lerbs' Theory". Transactions of the Society of Naval Architects and '4arine Engineers.

Voi 68, 1960.

A.J. Tachmindji. _{"The Axial Velocity Field of an Optimum} Infinitely Biaded Propeller". _{David Taylor Model Basin} Report 1294, January 1959.

G. Dyne. "A Method for the Design of Ducted Propellers _in a Uniform Flow". Statens Skepps Provnings Anstalt.

Publication nr. 62, 1967.

W.B. Morgan and J.W. Wrench Jr. _{"Some Computational Aspects} of Propeller Design, Metods in Computional _Physics".

Academic Press 1965. New York and London.

K. Meyne. "Experimentelle und theoritische Betrachtungen zum Mass-stabseffekt bei Modellpropeiler Untersuchungen". Schifftechnik Bd. 15 - 1968, lIeft 77.

W.F. Durand. _{"Aerodynamic Theory". Volume IV Airplane} Propellers by H. Glauert.

9)

B.D. Cox.

"Vortex Ring Solutions of Axisyinetric Propeller

Flow Problems".

MIT Department of Naval Architecture and

Marine Engineering.

Report No

68 -

13.

10)

_{W.B. Morgan, V. Silovic, S.B. Denny.}

_{"Propeller Lifting}

-Surface Corrections".

Transactions of the Society of Naval

Architects and Marine Engineers, vol.

76, 1968.

li)

K. Minsaas, O. Rustan, J. Grönbeck.

"Konstruksjon og

Analyse av Propellere med BKP's regnemaskinprogrammer.

Nr. 1001 og 1002.

BKP.

Bedriftskoniitéen for Propellfremstilling, September

1970.

Rapport 1.

12)

B.S. Guibrandsen.

"Utvikling av metode for analyse av

propellforsøk ved lave Reynoldstall med full eher delvis

laminarstrØmming".

Hovedoppgave ved SMT,

1970.

ACKNOWLEDGEMENT.

The author wishes to express his thanks to sivi1ineniçr

Olav S. Slaattelid, who has been responsible for the computational and programming work.

2 'lin, FORWARD PROPELLER

*

UTS

_*

AFT PROPELLER

Urs

2 /1

FIG.

i

Equivalent sandroughness

Measured roughness

FIG

2

i.

IR

II

U.

11111

c

- 58

'V.

\1ii---

_iï

-

i -

I_i

ii

-

I!

-

zi--'32

-C,SF

i

11m

IRR

iíïiiliuuiiíi

_1111111

iO 2 3 6 70'

2 3

6V' 23

6 l0

23

6 V' 2 3 6 I,

k

L) 3 9 8 7 6

NOND/MENS/ONAL RADIUS X

0.20

-

. .

-/

_/

r,-\ SMI

/

/

_/

0.3 0. 0.5 0.6 0.7 BR

0.3

0.'

0.5 0 6

0 7

0.8

NONDIMENSIONAL RADIUS X

09

0.08

0.0'

o

o 1.0

-,-,

V

N

/

/

/

/NSMT

\

\

/

/

\

t _0.20 (D 0.16 0.12

COMPd4RISION BETWEEN _CALCULATED

VALUES AND MODEL TEST

_RESULTS

(MODEL _{RESULTS FROM}

_{3 j )}

0.40

030

0.20

SMI (CALCULATED)

DIMB (MODEL TEST)

SM T (CA LCULA TED) _{D 1MB (CALCULATED)}

DTMB (MODEL TEST)

EXTRAPOLATED FROM

_{DTMB VALUES}

USING TROOST B.4. 40 SER/ES

J4

1.0267 (SMI)

J4

1.0267 (D 1MB)

/D

(0.7)

ojo-o

0,7 0.6

0.5

_0.4

0.3

0.2

0.1 o T

*

(UAS

I,'

-I I'll

I -9 12 15 18

20

R0PEL tER BOSS

-n C)

06

0.5 0.4

0.3

(n 0.1 o

PROPELLER BOSS

PROPELLER

IP

*

(

/

((J

t$)

i

s).

*

/

_/

f

p.

--

-7 I _I

N

N

N

\

3 6 9 12 15 18

0.7

4PROPELLER BOSS

PROPELLER TIP

i-'o

('J

/

-04e)

(O

/ 12 15 18 9

(IV

NONDIMENSIONAL

RADIUS

X 1.5 1.4 1.3 1.2 1.1

FORWARD PR.

T

AFT

_T

1

PR.

J

fl

ni

nc

no

VORTEX RING

PROPELLER DISK

Ix'

Ix,

X

(ELLIPTIC

CIRCULATION DISTRIBUTION)

yjdx

2 1 I I i

)

)

2 '

₇

_{'? 2 2}

I _I I X

'2

XI

X

i

dx

- 400

METHOD

i

X= i USED ¡W PROGRAM

dx=

METHOD 2

FIG.

li

r

r

i-

_\J

1

-(1

'e

ALTERNATIVE_METHODS FOR

_{INTGF?AT/QN_}

(LIFTING LINE AND MUTUALLY INDUCED VELOCITIES)

Xh

f(x)

X IT

q'

aG G3

G1 iG,

METHOD

i

4G, USED IN

PROGRAM

x= /

METHOD 2

FIG.

12

VA t4

AXIAL MUTUAL INDUCED VELOCITY

AXIAL DISTANCE BETWEEN

CENTERLINES

PROPEL LER. DiSK

b

d

I

r////

II

OF THE PROPELLERS

xR

R O X

_i

VORTEX TUBE

r

CIRCULATION r,, DISTRIBUTION

FIG. 13

z a

dr

2uTRX

tg.fl'

(4 ¿A3

(AL/as)

(4Uas)3 (AUas "q

( 4(Jcis )5

(AL/as)6

(4Uas),

(.U05 )

w;

h:

--'L-(j

u

u

(j

(j

(J

(j

(J

I

VORTEX TUBES

GIVING

NEGATIVE I VELOCITIES

VORTEX TUBES

GIVING

POSITIVE

VELOCI TIES

PROPELLER DISK

PROPELLER DISK

RESULTING

VELOCITY

O Xi1

_/

FIG. 1

NuMBEd F I4LADES DiAMETER PROPELLER: HUA DIAMETER DFSIRD IHRI.?ST SHIP SPFED PF4OPELLFR SPEED TAYLOR ?AKF PROPEILFR (IFPTH

BlADE AREA RATIO

ST RK .FKSP. 44 0.254 o .csi '4.6

S.l 3

B6 00

o. ico

C .250 0. '450 o 'sSO FL.'4Afi. 0,700 0.3C C.'40n En(F

_{1H. 0.000}

_{0.0CC o.00'ö} ,F0RF

0.020

0.023

C.02

AFTER O,fl20 0.0.23 C.cJ2A

r1.r)JST'4. 0.cOc

C.9r.cì

0.900

rHTCKNEcS AT

_{0,2CR 0,006 M}

rhTcKNEçs

r

fl.ò0F4 0.003

_tí M M KR K N O T 5 RpM M 2 0 _{KONTRAROTERENDE PROPELLSYSTEM}

THIS CMCULATTON IS BASED ON _{THE FOLLOAING SFT 0F TN PUT DATA}

CLASSTF!CATION PElUIPrMrNT DNV

MAxPc)FR

_IsO

_w

IAX.PPCP.sFEEr,: 5'4A.00 RPM

RAKE : 0.00 DEGP.

STRESS (ONST : EcO.o

INLFcT WAKE F0PDELIt.

J4

_{STANDARO 5TfKULASJONSFCPDFLINGFKSP}

21

INLFST SNTT1LV?GDFR

l31

_{VFR!1AS KR5V FOP FAST}

_POPELL

4t3 _{TYKKEI SESFORCELINO SE}

BFSKRIVFLÇE LS1 HTNS5 STIGN. KOFÈPEKÇJflN

6l

_{'4UHETS KORREKSJON ETTER MINSAAS}

71

STANDARD _{HYORODYÑAMTSW UTSKRTFT}

8I

THRUST 0IMENSJ0PEREN0F rCR RETTAI

.92

_{INDUKSJONS FAKTORER}

¿O0 lt:GFN

UTSKRIFT AV KAV,TPYKK-FOPDELING

j1l INNLES!NGAV

t

I20 STANDARD VERDIER _{SF FESVPIVFLSF. 560}

ELLOM PE5UIYATER FRA _{PROCE0I)PE SISKULASJON}

CTSz O2S99

O. 353

Oø 10630

O 2SOR

X

0,9Sg

0.9000

D e000

O

ir.00

O 6000

O 5000

0. '4000

O 3o00

o 2riOO SIR FX _{PET KB}

0.0715

O,338r

2i3387

_0.'422

0.0965

C.'4SSQ 22.45.29 _0.58CM

0.1231

0.5811

25.0043

_0,7476

0.1339

0.6318

_28.12'4'4

_0.8381

0.1344

0.63's0

32.0231

0,8862

0.1251 0.5962

3,9622

_0.9fl8j 0.109M 0.5189 '43,4598 _0.90Ml 0.0829 0.3897 52.1202 _0,8352 0.0000 0.0000 62,9731 _0.0000 i NRRs O i NPP _O PERM 15 STRE SS DESIRED POWER SPrc.RAv.PRopELL. ROt.JGHNESS : ROUj.NSS COREC.

1H! CK!ESS BLADET IP:

CAV.SAFETY AT 0.8R: 800.0

1.0

7,850

7,00

3 500

0.001

1.00

0.500

C.0O

0.000

0.000

0.029 0.032 o,o2% 0.032 0.900 0.900 KP/ M BHK KP/DM MY M z

o.7ro

0.800

O.9oci _O.9S0

0.000

0.000

_0.000

_0.000

0.03S

0.035 0.030

_0.023

0.035 o.035 0.030 0.023 0.900 .9C0

0.900

_0.900

DR/O V TO R o 0.2000 216368 O loco '4.6 1014 5000 N z NNY

FUL LSTEND!G GJENNONMREGNIN(' MFD TNDUKSJ('NSFKTQPFR FR GjENPnMFPT

MFLLOM RESUt lATER FRA PR0CEr)UE INDUKS

CT0 0.3115

PO

_-0.0010

R/R RETIU(S) RET!U(ç-1 I BETT S1R CL

'4 Q 1000 '4 0.3 186 n 0000 EKSP 0.14500 D o,25'40 H 0.2500 0.0280 GAPIA 1025.0000 0.2000 69"4812 ó9. I 91 63.9997 _{0.0000 0.0000} 0.2400 63.7795 63.6718 58.7203 0.0073 0.2230 0.2900

5.69i9

58.721 '4 _{5'4.0303 0.0099 0.2677} 0.3200 S'4.'43314 5415616 49.9983 0.0118 0.28314 0.3600 50.69114 50.8925 '46.144314 _{0.0133 o.28&3} 0.14000 '47.3659 '47.6193 43.2899 0.01'46 0.2795 O'4'4OO 414.3947 '414.6939 140.4821 _0.0166 p.2694 0.'4900 '41.7288 42.0403 37.9735 _o.oie14 0.25614

0S2OO

39.32714 39.6498 35.7238 _0.0170 0.21412 0.5600 37.1557 37,14797 33.6986 _{0.0175 0.22514} 0.éoOO 35.18141 35. 52cj 31.8686 0.0178 0,2101 0.6400 33o3876 33. 6930 30.2085 0.0179 0.19147 0.6800 3.714149 32.0327 28.6974 _{0.0179 0.2806}

0.7200

30.2383 30. 5143 27,3172

_0.176

0.1660 O.7A00 29.8528 29 .094Q 26.0528 _{0.0171 0.1527} 0.8000 27.5768 27 79Cc 2'4.8913 _0.0163 0.2416 O.8'4OQ 26o397Q _26.5830 23,8217 0.0152 0.1214

0.8DO

2Sa3075 25' '4652 22.8350 0.0138 0.1196

D?9D0

214.3011 214. '4312 21.9237 _{0.0117 0.1070}

0.9O0

23.38146 23. '4885 21.087e _{0,0086 0.1118} 1.0000 22.6346 22.6237 20.3120 0.0000 0.0000 ANTALL TTERÀSJONER IlL NAA 3R

INPUT IlL PROCEDURE INDUKS

L wx BI CDC O r. 03914 0.1000 0256 0.0169 O .0'42'4 O 1000 68 '4175 0.0156 2 0.01452 0.1000 514 1605 0.02145 3 0.01479 0.1000 ₂₅₇₀ 0.0136 '4 0.0505 C. 1000 '46 7033 0.0128 S 0.0530 0.1000 '43 _{'4960 0.0121} 6 0.0564 _{0.1000 '40.7077} 0.0115 7 fl.0578 0. 1000 38.2689 0.02 ID O. 06Ó3 0.1000 35.92 il 0.0105 0.0628 0.1000 33.9022 0.0101 0.0650 o 2000 32. 0'499 0.0097 11 0.0671 0.1000 3. .3956 0,00914 12 r.O686 0.1000 28 8660 0,0091 13 0.0701 0.1000 27. '4778 0.0088 l'4 0.0708 0.1000 26, ?059 o 0086 IS

0.0698

0.1000

0251

0.0085

16

(.0689

0.1000

73.9520 0,0083 17 0. 1Q00 22.91479 0.00814 ('.0585 0.1000 22.0127 0.0087 19 0.1000 2i.l '4614 0,0093 20 -0.0000 o 1000 2 .349 j 0.0101

!.r ¡JNLFÇT *AK'L FORDELIN,

1.'4 _{STANDARD S!RKUIASJONSFOPOFLING(EKÇP))}

21

INLFST SNITTtENGDER

3.1 _{YrRITAS KRAV FOR FAST PROPELL} *3 _{TYKKFtSF5FCRDELING SE BESKPIVELSE}

SI

MTPJSAAS STIN. KORREKSJnN

6.1 _{RUHfTS KORREKSjON ETTR MINSAAS}

7_j _{STANDARD + HYDRODYNAMYSK UT5KRIFT} p.1 _{IkRUST OTMENSJONERENDF FOR fETTAI}

5'2 _{TNDUKSJONS FAKTOREP}

10=0 TN(EN LJTSKRIFT Av KAV'TPVKK-FORDELING 111 INNLFÇ!Nc Av Ml

12.0 STANDARD VERDIER SE BESKRIVELSEN 560

LLOi RESLJLIATER FRA PROCEOIJRE _SIRKULASJON

FL.RAD. 0.207 O.3Cn o.4O c.500 0.600 0.700 0,800 _0.950

DC,E

rH.

0.000 _{0.000 0.000 0.0CC 0.000} 0.000 0.000 0.000 0.000 .FORF 0.019 0.022 0.026 0.028 0.031

_0.033

_{0.033 0.029 0.022} AFTER

0.019

0.022 o.c2s _{0.028 0.031}

_0.033

_{0.033 0.029} 0.022 r)ISTR. O.cOr 0.900 G.9C 0.9CC 0.9CC 0.900 0.900 0.900 0.900 H!CKNESS AT _{0.20E 0.006 M} hICKNEÇS AT C.6DF 0.003 t 3'462'4 .17518 .27565 X CTS 0.2770

SIR EXT _{3EI KR}

C .9600 o .077'4

0.3393

_{22.2137 O.'4233} 0.9000 o. 10'43 C.'1574 23.3662

_0.5693

0. 800 C. 1329 C.582'4 26.993'4 _0.7363 C 7n00 O. I'4'4'4 0.632'4 29.197'4 _0.8283 D. 600 0'! '432 0.6333 33.1582 _O.P781 O .5CC 0.1 3'47

0.6939

_{38.2368 0.900'4} O '4000 0.1 169 _{0.5139 '4'4.8171 0.8951} C 3100 0.0869 0.3793 63.5193 _0.9156 C 2r6S

₀₀₀₀₀

_{C.0o0 62.9731} 0.0000 2 NPRa O 2 NRP _o O _{KrNTRROTERENDE PROPELLSYÇIEM}

HIS CAl CULATION IS RASED CN _{THE FOLL0ING S[T rF} pj PUT DATA

'UMBER nr RLADES '4

TAMETEP PRCPETLLER: 0.2'e6 M _{PERM 1S.S'rRfSS}

800.0 KP/CM2

U8 DIAMETER C.0S1 M _{DESIRED POWER}

¡ 0,0 BHP(

ESIRFU THRUST '4.6 KP _{SPEC . GRA V PROPELL.}

7,850 Kp'0M3: IP SPFED

'! KNOTS _ROVGHNESS ¡ 7,00 MY

ROPELLER EED 5'46.i0 RPM _{R(ThHNESS COPEC.}

_{3 500}

AYLOR WAKE _{0.100 THICKNESS BLADETIP:}

0.001 M

PCPEI LER r)FPTH _{0.250 M}

CAV.SAFETY AT 0.8R: _{0.99 %} L.AOE AREA PATTO _0.'450

TRI( FK SP. O. L45 CLASSIFICATION pEÇUIRFP4FNT DNV MAX.POWER 1.0 BHK MAX.PRflp.SPEEr,: S'46.00 PPM RAKE _{0.00 DEGP.} STPESÇ CONST : 500.0

INPUT IlL PR0CQURE INDUES 0 0.0376 i 0.Q'40'4 2 0.O'431

o.csa

'4 ).0'482 S Q.OEQS 6 0.0635 7 _0.0561 8 0.0682 9 0.0602 10 * Q.0622 0. 064 '4 12 0.0659 J3 0.0613 l'4 0.067e 0.0668 16 0.0659 17 _0o0611 ¡8 _0.0552 19 0.0368 20 -0.0000 DR/f) V w To Ro O .2065 2.6368 0.1000 '4.6 i 04 5000 R/R C 2065

0.262

0.2859 0.3255 0.3652 C. '$fl49 0.4446 0. '1842 0.5239 0.5636 0.6033 0.6429 0.6826 0.7223 0.7620 0.8016 O 814 13 O 8810 0.9207 0.9603 1.0000 o 1000 o 1000 0.1000 0.1000 0.1000 O 1000 0.1000 0.1000 0.1000 o 1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0. ICOC 0.1000 0.1000 O 1000 0.1000 Al N z EE '4 NN'

BET ¡U S) BET TU (S-i

lo,569q 70.21436 64.9479 64.8362 59. 9077 55.7086 52e01 08 '48.7128 '$5. 7549 '43.0914 "0.6842 38,5008 36.5135 3+. 6987 33 0361 31.5087 30.1.021 28.8041 27 .604'4 26 '4946 25. '4689 24.5350 23. óó8 59.9601 56.8779 52.2657 49.0292 '+6 1136 '43 '4765 '41.0924 38 '1 2 36.9069 35.0777 33. 3946 31 8420 30. '4 066 29.0773 27.8451 26. 72S 25. 6 '4 '46 24 6p 1 23.7859 BI 63.0071 5 .8329 Sq,8931 Si 1195 '$7.6263 44.14817 '41.7191 39, 1930 36. 9382 34 8946 33. 0327 3i .3797 29 8459 2e. '4468 27. 1669 25.9591 24.8676 23. 8'438 22 o 8877 21.9992 21. 1784 '4

9i

1000 'i 0. 3 '403 o .oeoo F(JtLSTENDTç, GJENNONMRFGNIPJC, Mc0 T FJDUKSJC)NSFAKTORER FR GJErMFØRT

P4FLL0M RESULTATER FRA PROCEDURE INDUKS

CT0 0.3320 PR0 -0.001.3 REI! 64.5265 59,3866 54 '7914 50.8427 47. 3'49Q 44.2373 '41.4555 38.9607 36 7157 34.6885 32, 8516 31, 1819 29,6577 28,2634 2 6.. 98 39 25.8067 24,7213 23. 7186 22.7916 21 9'413 21, 1516 CDC .0172 0.0159 0.0 l'+7 0.0138 0.0130 0.0 123 0.0117 0.0111 0.0107 0.0103 0.0099 0.0096 0.0093 0,0090 0.0088 0.0087 0.0085 0.0086 0. 0090 0.0096 O 0105 EKSP D H KS GAMA SIR; 0.0000 O ç08 i

0.0110

0.0131 O O j '48

b.oi 61

0.0173

0.0182

0.0389

0.0197 0.0198 0.0198 0.0 15 0.0189 0.018 i 0.0169 0.0152 0.0129 o O '0000 0,4500 0.2460 0.2500

0.0311

1025.0000 CL 0.0000 0.2520 0. 30 35 0.3221 0.3244 0.3171 0. 3035 0.288" 0.2730 0.2572 0,2906 0.2227 0.2065 0.1901

0,1754

0.1628

0.

1479

0.1383

0.1251

0.1329

0.0000

I r, CGt G2 cG2 3 0059 I

.(b8

2 _fl07 5092 97 3 ₀₁₀₉ .3737 .0121 3OP 44 _{Cl 2 2970 O1'4C} 5 .. O I '4o 2427 .OISS 2798 o _.0151 1991

Oi

67 2295 7 0160 .1610 'U i77 1856 8 _{.0167 1759 .0185}

1

'451 9 _{.0173 .0920 .0192} .1060 10 .0177 0581 .0196

.670

11 .0179 0233 .0198 .0269 12 .0179 - .0135 f198 -.0155 13 .0177 -'05344

0j97

- .0615 14 f1744

0i

92 .1129 IS fll67 -. 1'495

Cj

86 -.1 72 1.6 .01 SP

.219 0175

- ₂₁₄₄₂ 17 014t .2920 fl161 -.3365 18 .01 2' - . ¿4fl57 _01'42 - * '4677 19 .0103 .6005 'nl 1'4 - _.6922 20 0062 -1.1713 DOoR -1 ]Sc 1 IBTI 1.8873 1.5231 1.3246 I 1885 1 .0833 .9975 '9252 P629 P083 7598 .7162 6767 64405 .6071 .5759 .5467 .5 190 .44665 ' _'4f! TB!2 1 .97g3 1,5838 1 3681 1.2217 i 1096 1.0188 .9427 8776 .8208 .7707 .7258 .6853 648'4 .61444 .5830 .5536 .5259 .44993 14737 '4479 UAII 0589 0593 0596 .0597 .0598 0596 0593 oSp7 0578 0667 0553 .0536 .0517 .04496 .0472 .044446 .0420 0392 036'4 .0336 uA!2 .0276 '0422 '0967 .1377 .1698 1957 .2166 .2333 .24462 .2555 .2613 2634 .2616 .2554 .24442 .2267 2011 .1637 .1075 '0302 UT!2 .2297 3188 3490 .3576 3561

390

'3387 3263 .3126 2978 .282 1 .2656 '2482 2299 2103

1892

1669 '139M 107'4 0616

I

tIS1A

L1TSIA UASI 'JTSl UAS2A UTS2A UA52 UTS2

1

?36

2

260

44678

.3S9

-'023

23

2'463 .5171 -.Ol4j

.271

3

2i6

.3225 S

3i3

6

.37g

'17

Ñ0l4

.3899 .0837

31

.14458 .3459 .1911 352' .2266 .3494 .2758 .3081 .3406 .3711 '4R144 .44579 .4436 '4313 .1631 .2108 .2'4844

319

.3710 .3779 ,3147 7 _'14O7 8 _'44237 9 _'4'43i 10 14602 .3787 '3675 .1562 .34448

3i

.2779

'2o2

31&O

'3103 30'4-1 .3992

2So

.4695 .4196 '4079 .3961 .3842 .2787 .3033 .3229 '3381 .3661 35'4s 3'410 .3261 1)

'752

12

481

13

'4l

1 '5083 1

'14C

.3333 .3217

1102

.2988 '2876 .7767 *32044

29'4

.3268 .2739 .3793 .2577

3279

247

322l .2228 '4884 .5051

.j99

'5327 .5439 .3722 .3601 '34482 .3363 .3246

39l

.3560 .3688

.3572

310

.3103 .2937

2763

.258 1 .2389 16 '52214 17 '5277 18

32i

i .5374 '2661 '2560 '21464 .2381 .3116

2037

.2955 .1832 .2727 '1607 '2412 .ils '5535 .5619 .5692 .5756 .3133 .3023

2917

2818

.3395 .3219

271

.2626 '2185 .1965 .1723

1448

20 .5437 .2304

l7O

'10441 '1310 .0598 3 NRR

583j

.5912 .2733 .26514 O .2145 1'425 .1116 .0641

NRS 0,4500 0.2S40 0.2500 0.0311 1025.0000 FLit LSTNDt1 _'Fb

T NDUKSJONSF AKIORER FR GJENNnrØpT

MELLOM PESLJLTATER FRA PROCEOUPE _rro1Ks CT0 0.3115 PR0 0.000i

P,TIU(S) RETIU'Ç-i I

BET! 5îR

'4

1

CL

ANTALL ITERaSJONFR TIL NAA '4p. INPUT IlL PROCEDURE INDUKS

L _{Sj CDC} O 0.0394 0.1000 64.c139 0.0169 1 0,04214 0.1000 59.3581 _0.0156 2 0.0452 _{0.1000 4.7239 0.014S} 3 _{0.0'479 0.1000 50.70ü9 0.0136} '4 _{0.0505 0.1000 '47.1547 0.0128} 5 _{0.0530 0.1030 '43.9510 0.0121} 6 _{0.0554 0.1000 41.1676 0.0115} 7 _{0.0578 0.1000 3P.6226 0.0110} 8 0.0603 0.1000 36.3500 0.0105 9 0.062$ 0.1000 34,2987 0.0101 10 0.0650 0.1000

3.175

0.0097 11 0.0671 0.1000 30.7416 0.0094 0.0646 _{0.1000 29.1891 0.0091} 0.0701 0.1000 27.7749 0.0088 0.0708

0.13o

6.'4766 0.0086 0.0698 0.1000 25.2718 0.0085 16 0.0649 0.1000 24.1714 0.0383 17 0.0641 0.j000 23.1500 0.0084 0.1000 22.2076 0.0087 19 0.0395 0.1000 21.1442 0.0093 po n.0000 o.l000

2.598

0.0101 0.2000 69.9520

69.7c

64.5377 0.0000 0.0000 0.2400 64,3229 64.233P

_S.3300

_{0.0073 0.2197} o 2q00 59.2838 59.1829 54.6787 0.Q099 0.26142 0 3700 55.0507 54.938p _{50.6655 0.0119 O 2802} Do 36 00 51.3194 51.1986 47.1153 _{0.0134 0,2825} 0.9000 '47o9936 '47.8664

_43.9561

0.ÛI6

_0.2770 0 '400 '45.0135 '44.8824 _{'1.1347 0.0156 C 2674} 0. Gt00

₄₃₃₂₂

_{'42.1995 38.6062 0.0164} 0.2548 0G 5200 39.9104 39.7787 _{36,3321 0.0171 0. 2399} 005600 37.71143 37.5p44 34.2789 _{D.Q176 0.22144} 0.6000 35.7154 35.5897 32.4183 _0.0178 0.2093 0.6400

33$f94

33.7683 30.7260 _{0.0180 0. 19'sL} O, 600 32.2158 _{32.1007 29.1814 0.1801} C 7200 30.6774

_30.56l

_27.7670

_O.i7ó

_0.1657

0 7O0

29.2596

_291S87

_{26.4683 0.0171 0.1525} 0.8000 27.9506 _{27.8c73 25.2728} 0.0164 0.1915 0.8400 26.7401 26,6547 24.1701 0.0153 0.1283 0.8800 2S.6j99 _{25.S'422 23.1512 0.0138 0.1 196} 0.9200 24.5891 2'4.SI3R 22.2092

_o.i17

_{O 1070} 0 9.oQ 23.6396 23.5762 21,3442 _{0.0086 0.1118} 1,0030 22.7e32 22.7063 20.S'414 _{0.0000 0.0000} i rpp i D./0 0.2000 Al 4 _FKÇP V _{2.6368 N 9.1000} 0 w _{0.1000 z} Tn '4,6 _{FE4 0.3403} lfl'4.S000 NNY 0.0000 c,AMA

NRa DR / D V w TO Ro

0.2083

7.6368

0.1000

'4.6

i o ,snoo

FULLSTEND T G GJENNÜNMRGN ¡ NG MFD

TUSJONSrKTORER ER GJENNoNFRT

MFLLOM RESIJI.TATER FRA PROCEoUPE INDUKS CT0 0.3380 PkO 0.0(;25

R/R 8E1 TU(S) RET IU(S-I FETI STRi' CL

AI N z EE4 NNY 4 9 1000 '4

ri .3403

0.0000

EKÇP 0.4500 D 0.2438 H 0.2500 KS o.0311 GANtA 1025.0000 O 2083 0.2479 0. 275 66 807S 60. 1666

555O80

66.3410 59 ₉₃₂₁

55. '

60.8fl147 S'4,9324 50.8211 0.0000 0,0083 0.0113 0.0000 0.2899 0.3388 0.3711 S2 1608 52 T 7O 47.7394 0.0135 0.3500 0.3667 49 3498 449e '4434 _'45.1137

_0.012

_0.31452 O '4063 '46. 856 0)48 '42.7825 0.0166 0.3322

0.

'4'458 44.6176 1414 _8Q63 '40.6719 0.0177 0.31145 0. 485'4 42.5660 '42 7O9 38.7389 _0,0187 0.2964 0.6250 '40.61486 '4C 8786 36,95'44 0.01914

0.2791

D 56'46 38.8723 39. TOPI 35.2967

_O.0t9

0.2619 0 60142 37 2091 37. '442l 33,7485 0.0203 0.24144 o. 6 '133 ₃₅ 6 36. P692 32,2962 0.0204 0.2259 0,6833 34.1647 34,3755 30.9237 0.0203 0.2094 0.7729 32. 789

32,9509

29,62214

0.0200

0.1928

O. 7i625 31 .4156

31.5853

28,3794

O.O114 Q,1780 0.8021 30' 1232 30.2679 27.1826 0.0186 0.16514 0e8'4 17 28.8678 28 9357

26.0175

_{0.0173 0,1.505}

0.8913

27 6296 _27.7 2'4.8631 0.0156

0.1410

o 9208

26 3658

26, '42P

23.6746

0.0133

0.1278

0,9404

25.0842

25 1209

22.'4490 0.0097 0.1358 1

0000

23 7662 23.7765 21.1766 0.0000

0,0000

'4 NR ₂

ANTALL TTER5j0N T IL NAA 5

INPUI IlL PROCEDURE. !NDUKS

L wx R! CDC O n 03 7 6 0.1000 60.5674 0.0171 O4n4 0.1000 55.2682 0.0158 2 O 0432 0.1000 _50.R3CS O.Ci'47 3 0.0457 _0.1000 47.6293 L.0138 '4

ri.

049.2 0.1000 0.0130 5 0.0509 0.1000 0.0123 6 _0.0536

C boo

0.0117 7 _{0.0561 O . 1 000 38.4860 0.0111} g 0.0583 0.1000 36.7005 0.0)07 9 0.0603 0.1000 35.03g7 0.0103 10 0.0673 0.1000 33.'181 0.0099 il 0.0644

0.1000

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1pPuT TTL PROCEDURE TNDUKS

L wx 0

n.

0394

01000

O 0'124 0. iCCO 2 0.0452 0.1000 3 C' 0479

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¿4 _{n 0505} o i ono S n 0530 0.1000 6 o 05sM

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n. 089

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1 7 0.0641 0.1000 18 n 0585 0.1000 i9 0.0395 0.1000 20 e 0000 0.1030 0 2000 69. 9599

0.200

3326 0. 2R00 59 2948 0.3200 SS 0622 o 51.3313 0. C100 0055 0. '41400 .0253 0. '$800 o 3 4 38

'ADIUS

CAy. SAFFTY

SIGMA LIFT _LEWCTH THICK-NESS

IlL CAPI8ER PITCJ4 LENGTH LENGTH FORE AFTER 0,200 9R.4 _24.960 0.000 0.039 0.0060 0.1523 0.0000 o.34i

0.020

0.020

o 300 97.63 18.74'4 0.274 o.O'7 0.0052 0.1110 0.0011 0.322

_0.023

_0.023

O. '400 97.33 13.891 0.277 0.053 0.004'4 0.0830 0.0011 0.314 0.026

0.026

0. 50 97.15 10.415 o.247 0.059 o.o37 0.0623 0.0011

0.311

0.029 0.029 o 600 _7'O 7.972 0.209 0.065 0.0030 0.0462 0.0011 0.309

_0.032

_0.032

O 70o 97.11 6.238 o.171 0.069 0.0024 C.03'43 0.0010 0.307

0.035

0.035

o 800 7.l7 '4.985 O.1'4i 0.070 0.0018 0.0259 0.0009 o'3o5 0.035

0.035

o.

9Go 97.24 4.058 3.111 0.060 o.0n13 0.0213 0.0008

_o'3o3

0.030

0.030

o. 95 96.71 3.685 0.122 0.046 0.0010 0.0225 0.0007 O.30'4

0.023

0.023

FSULTTJÇ, THRUST ¿4.7 WFIGHT BLAOrS 0.4

OWER CÖNVFRTED 0'? GD2 BLADES TN AIR 0.0

rF C IEÑCY _{0.777 G02 TOTAL IN AIR 0.0}

LADE APEA 0.02 G02 TOTAL IN WATER 0.0

LADE AREA PATIO

A V N(Jt1FER o,454, 6,298 BP-NUMBER DELTA-NUMBER 11.71 98.6

FAN FFF.PITCH 0.323 ACT. BUPRIL 0.087

FAN N0.P1TCH

01306

RFLATTV RADIUS _{0.20 0.60}

STRFSSES DUE TO THRuST AND TORQUE FOPCES '49,4 _30.3

STRESSES DUE TO CENTRIFUGAL FORCES 4.6 _liS

TOTAL STRESSES 5'4,O _31,8

CALCULATED THICKNESS 0.0016 0.0006

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2.2

3.6

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5.6

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3.2

2.3

3.7

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38.7

34,9

30.1

25.8

21.5

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0.0

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2.5

4.2

5.3

5.8

6.0

5.9

5,4

'4.7

3.5

2.5

1.8

39.4

35.5

33.5

27.6

73.6

9.7

5.8

11.8

7.9

3.9

2.0

3.0

0.0

N R 0.2084 Al '4 EKÇP 0.4500 V 2.6368 9.1000 Li o,2'437 0.1000 Z 4 0.2500 '4.6 EE4 n.j'03 KS 0.0311 lfl'4.B000 NNY n.n000 (AMA 1fl25.0000 FIJI LSIFNDTG p-!NDUKSJONSFAKTORFP ER GJENNn1FORT

EL0

ESUITATER FRA PRCÇEDIiPE INDUKS CTC 0.3382 Pf0. -C.0C2'. R/R RETIU(5) PETILIS-1 F E' I STRv CL 0.2084 66.8111 66.3151 60.7998 0. floOD o 0000 0. 2u8fl 0. 2P.76 60.1724 SS.Si7

S9.i2i

S5.'4104 54.9323 50.8291 0.0083 0.0113 0. 2932 013392 0.3772 52.1718 S2.1.77 47. 74449 _{0.0135 o 3So3} 0. 3 , 6 7 '9'3ó24 49.4344 '15.1209 0.01 2 0.3455 O '4063 '46.8793 '47.007

42 709

0.0166 O 3326 o '1459 '44.6321

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'40.6e 12 0.0178 0.3148 0. '4BS '42.6709 't2.767 38. 7'4g7 0.0187 0.2967 0. 5 25 1 40.6638 40.8754 36 9645 0.0194 O 279M 38.8877

39.lSP

35 3070 0.0199 0.2622 0.6092 37.22'45 37.44j3 33.7599 O 0203 0.2447 0.6438 35.6596 3S.8P' 32.3056 0.0209 o 2262 0. 63'4 _39.1800 34,3754 30.9342 0.0203 o 2097 0.7729 32.77'41 32.9516 6329 0.0200 0.1930 O 7625 31.4308 31.5868 28,3899 0.Oi9S 0.1782 0.8021 30.1384 30.2702 27. 1932 0.0186 0.1656 0.8417 28.8830 2P.9P9 26.0282 0.0174 0.1507 C.88 13 27.6448 27.7241 2'4 .8739

0.Cl7

0.1912 0.9208 26.3814 26.'43'44 23.6858 0.0133 0.1279

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25.lOOt 25.1771 22. '4605 0.0098 0.1360 23.7615 23.78'41 21 1876 O 0000 0.0000 '4 NRP '4

ANTALL ITERASUONER IlL NAA B

INPUT TTL PROCEDURE INDUKS

L PT CDC o r.0376 6 r 46 9 C.O1 71 C.0'40'4 0.1000 Ss. 1964 C 0 1 58 2 r,0'432 0.1000 5r .7815 0.0147 3 0.0457 _0.1000 '47 .6049 0.0138 4 0.0482 C.1000 44 .'480 0.0130 5 0.0509 0.1000 ¿47 _0.0123 6 0.0536 0.1000 '40.4671 0.0117 7 .056I 0.1000 51 6P 0.0111 r',0583 _{0.1000 36.7371} 0.0107 9 fl.O60 0.1000 3ç 0.0103 10 r.0623 0.1000 33 .c2'c 0.0099 11 C.0e4'4 0.1000 32 0.0096 12 0.0659 0.1000 .7093 0.0093 0.0674 0.1000 29.4204 0.0090 0.0678 0'lCOO 2P. ¶832 Cl 0088 15 0.0669 0.1000 26 .977 0 0087 16 0.0659 (.1000 2c 0.0085 17 0.0610 C'.ÌCOO 24 .727 O 0086 0.0561 OSICCO 2.1. '43 0. 0090 j9 _{r.C368 0.1000} 22.2722 0.0096 20 fl.0000

C.13Q

2i .r35 0.0106

CAy. SAFFTY

SlC,MA LIFT LENGTH THICK-NESS

T/L çAP1ER PITCH LENGTH FORE

LENGTH AFTER 33.47e 0.02e Q.33R O.007 0.152g 0.0001 0.287 0.019 0,019 97.P8 23.B O3'4S

c.o4

o.00sn

0.1137 0.0013 o'278 0.022 0.022 97.30 jS.7p0

_0'32

0.So

r.oD'3 0.oR'4 0.0012 0.292 0.025 0.025 p7.13 11.291

O'.9r

o.ûs7 r.0036 0.0623 0.0012 0.303 0.028 0.028 9é,.9 R.'4, 6.6C' o.2'4 0.?O?

0.02

C.0'6 0.0029 fls0323 O.o',8 fl.03L16 0.001? 0.UO 0.311 0.316 0.031 0.033 0.031 0.033 5.266 0.166 0.067 0.0017 0.02h1 0.0010 0.317 0.033 0.033 97.11 .337 0.132 0.057 0.0012 U.L216 0.0009 0.312 0.029 0.029

9.51

3.9é4 0'1' C.0'43 D'COlO 0.0232 0.00o O.3o7 0.022 0.022

Rf SUL TI iG THRUST ¿4,7 WEIÇ,HT BLAOrS 0.4

ThWFR CONVFRIF ri C 2 (D2 BLADEÇ IN TR 0.0

E: F F I C I E C Y _0.75R GD2 TOTAL IN AIR 0.0

ADE APEA 0.02 (D2 ICTAL TN YJATFR 0.0

t ADE AREA QT In . 454 F. P - NU ?I B F P 11,71

i. V s NUMF R 6.736 DEL T A - N J P Fi R 94.6

1FAN FFF.PITCH o ACT. BURRI) 0.083

IrAN NOM,PTTCH 0.

RELATIV RAOTUS 0.20 _0.60

STRESSES OUE TO THR,5T ANr TORQUE FORcES

5.9

33.2 STRESSES DUE TO CENTRIFUGAL FORCES '4,1

1.4

TnTAL STRFSSFS

61,0

34.6

CALCULATEO TkIÇKHrS 0.0016 0.0006

THICKNESS PFOUIRFLn RY VERITAS 0.0057 0.0027

FL-Ar)1uS o.2C n. 30n o 'O o n 0n 0.600 o 7 On 0.800

O. 00

o o

*. H

R/R 0. 20 0.300 O 400 O' 600 O .7Qfl o . n -0' 90n O (J s 2O o r _o

I

n son

o.

e n IO 7 00 in . n i .0 90 r O 95n r'

0' 300

n '40e'

n Son

O 60fl n. 70n 0' 8 n n 0. 9Qfl

o 95n

YDROD

CF n Dl 7 1 '4 n'al44Q 0.01243 0.01096

n O05

.O9 i

I

.flfJtS72 o 0o878 i 0094S CL! 1.01 95o 0.34496 33'43o n

28983

n 2 4 I S

0.2021

. I 6Ò 12 0.13217 n i 77M l'E 3 1 I i 07 2770 27 ?30fl Sr i I '4f.. 9 1 i I A 1 Fi ' Q i'47'4.61U t in. 16ï i I77.53 1120.431

Kl

j

A AN A t. F A 1 1 I'IALFA

YNAMI

CX

0.00000

o .0oO0 O o 0000 i o .00coo O 00000 Û 0O00i o .00000 0.00000 0. 0000n CL o 01956 o 3'496 0' 33'43/ O 28983 0.24615 o 20213 0.16612 0.13217 0 ¡'4774 8F I bO.4733 5776 '9i 26 37.8910 33, 6h4 30. 1543 27.0415 24.1 156 22. S96 D, 1S30

0.03405

1.0699

1.0000

1.0000

i .000r)

I .0;On

Fp KKT KALFA KC M! 0.67622 0.33n5 1.62869 _{1.52420 I .00C 00} .DM j7 _{0.2653? i'40377 1.24607} I .Doc 00 16 _0.20587 1.28187 _{1.10416 I .00C 00} 0.03782 _0.15871 i'28896 1.13117 i 00C 00 o C '414 ¿4 0.12pQ7 _{1.31201 1.18267 1 .00C 00} o r' 4 E 42 0.086.74 _1'34902 1.26767 _{i .DOC 00} 0.05249 0.06196 1.46031 1.38643 i '00c 00 o I, ¿'4 1 0.04720 1.61285 _{1.70011 I .Doc 00} n 063°

0n43;9

1.70459 1.93004 i .00C 00

ALFA T _ALFAO

sIIGvN

_{ST!GVEF SIRK}

0. 4P23

0.lSln

_60'9556

61.1066 0.00 00 n. 8567 2.6624 50.4343 53.0967 0.08 69 Q. 6767 2.58Q5 '43.5893 _{46.1699 D.h 69} 0. SLs3é 2.2369 38.3846 _'40.6215 0.13 '4.7 0. '4390 1.89943 3'4.1236 36.0234 0.14 32 0.3506 1.5600 30.SC'49 32.0649 0.14 44 0.3009 1,2821 27.3425 28.6245 0.13 29 0. 2ts 12 _1.0201 24.3768 25.3969 0.10 143 0.3059 1.14fl3 22.9019 24.0422 0.07 74 C r A T CALFA 4 *1S CD _{Cr5 CFI RN}

0.00000

0.01714 0,00736 0,00546 8 806 .09 0. 00000 0.014 0.00691

0.0073

i 171 +05 o cocoa 0.01743 0.00650

0.0o11

1.553 +05 O C0000 0.01096 .0O614 0.00360 2.023 +05 0.00000 _0.00995 0.00587 0.00323 2 509,+05 0' 00000 0.00918 0.00564 0.00299 3.032 p.05 O .00000 0.fl072 0.00551 0,00277 3.407,+05 0'CCOOO 0.00878

Q5S7

0.00284

3. 2o 05

000000

0.0a9'45 0.00584 0.00319 2.569 i 05