Design of tug propellers. Part 2: Performance of three, four and five blade screws

A Station of the

Ministry of Technology

Lab. v. Scheepsbouwkunde

See note inside cover

Technische Hogeschool

SHIP REP..83

Delft

April 1966

NATIONAL PHYSICAL

LABORATORY

SHIP DIVISION

DESIGN OF TUG PROPELLERS

PART 2-PERFORMANCE OF THREE,

FOUR AND FIVE BLADE SCREWS

by

T. P. O'Brien

This report is a reprint of an article

Crown Copyright Reserved

Extracts from this report may be reproduced

provided the source is acknowledged.

Approved on behalf of Director, NPL by

Mr. A. Silverleaf, Superintendent of Ship Division

(I) Introduction

RESULTS of researchin particular, some recent work at the NFUhave shown that there are significant differences between the performance of three- four- and five-bladed screws. Consequently, to obtain equivalent performance, some of the geometric features of the screws need . to be modified.

The work described in the paper' comprised the results of calculations and experiments for two g"roups of model screws, one group of standard type, the other of non-standard type and both comprising screws having three, " four and five blades. It included comparisons of performance under non-cavitating and cavitating conditions based on calculations, open-water experiments and water-tunnel experiments. It gave correction factors for standard-type screws which enable three- and five-bladed units to be designed, and comparative performance estimates to be made, using data for four-bladed screws as the bases.

The first group of screws was selected from the NPL standard series" and comprised three sets of model screws, all having the same diameter (D = 0.7 ft.), the same blade area ratio (ch = 0.5) and the same blade thickness ratio (T = 0.045). The first set (Screws BN1 to 3) had a pitch ratio p, = 0.5: Screw BN1 had three blades and Screws BN2 and 3

Fig. 1

Part 2- Pertormance of Three, Four and Five Blade Screws

These three articles discuss differences between the performances of three-, four- and five-bladed screws under both non-cavitating and cavitating conditions. They summarise NPL model-experi-ment data; comprise correction factors and design data which enable three- and five-bladed screws

to be designed, and comparative performance

estimates to be made, using four-bladed standard series data as the bases; and give examples on designing additional three- and five-bladed screws

for a single-screw tug for which data for

four-bladed screws are available. Sections in the

articles are: Introduction; Performance

Com-parisons and Correction Factors,

Constant-Diameter Screws (both sections published in the November issue); Correction Factors,

Optimum-Diameter Screws in Free-Running and Towing

Conditions (published last month); Worked

°I Examples; Comparison of Results; and

Ref-erences (to be published in the next two issues)

by T. P. O'Brien, C.G.I.A., M.R.I.N.A., Ship Division, National Physical Laboratory.

had four and five blades respectively. The Second and third sets of screws were similar to the first, but had pitch ratios of

= 0.85 and 1.2 respectively.

Main geometric features of the screws are shown in Fig. 1. The open-water experiment results for Screws BN7 to 9 are shown in Fig. 2. Some of the water-tunnel experiment results for these screws are shown in Fig. 3, and photographs indicating the extent of cavitation are given in Figs. 4, Sand 6. The experiment results discussed above were for screws of constant blade thickness ratio. However, in designing screws the blade thickness ratio needs to be based on strength considerations; a method for doing this is described in an appendix to the paper' and some of the results obtained are given in Table 1. Correction factors based on the data given in the paper and comprising results obtained following the procedure given in the appendix are shown in Fig. 7.

(2) Comparisons and Correction Factors

Constant-Diameter Screws: Results of the comparisons

showed significant differences between the performance of screws having three, four and five blades under both non-cavitating and non-cavitating conditions. The open-water experi-ment results showed variations in thrust and torque coefficients requiring moderate pitch corrections to obtain equivalent

X = 0.9

/

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.

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. I I I 0.5 --9 1 I X = \ \ \ \ I I I / I 1 1 I-I \ \ \ /// \\ . BN. 1,4,7 N. 2,5,5.

3- BLADES. 4 - BLADES. 5 - BLADES

110

.ftT 0-060 fR.Ge 0- 40 0-050 0-35 0.045 010 0-25 0035 0 20 0030 0.15 0.025 11/I111111111111111111111111111 1.20 B61_7. 3- BLADES. BN. B. 4-BLADES. BN.9. 0-055 0.05_0.015 111111111111111111111111111111111 0 40 0.50 0-60 0.70 0.80 010 1.0 1.10 All cases J = 0.9; a = 0.3 Above : Fig. 2 Right: Fig. 3

performance. Moreover, there were appreciable differences in screw efficiency. There were also significant differences in performance under cavitating conditions, as assessed by the water-tunnel experiment results and as shown by visual observations.

Consequently, large blade area corrections are needed to obtain equal margin against thrust breakdown. The correction chart shown in Fig. 7 comprises pitch correction factors and efficiency correction factors derived using the Troost B standard series data' and includes blade-area corrections and blade-thickness corrections based on the data given in the appendix to the paper', some of which are

0-10 0.40 0-30

summarised in Table 1. Two sets of correction factors are given, enabling the geometric features of either three- or five-bladed screws to be derived from data for four-bladed screws.

Power coefficient

In using this chart, the power coefficient B5is evaluated, and for this value of B, corresponding values of blade-area correction, blade-thickness correction and pitch correction are obtained and applied to the respective geometric

para-meters of the

basic four-bladed screw. Similarly, the Figs. 4, 5 and 6 (left to right).

J-07 0-20 040 060 060 1 1 111111111 1 1 1 ' J-0 5 J-04 0070 0065 .0.055 10045 .0040 70035 0-030 0.025 0020 0.015 0010 0-005 060 mil I p lp [limp _{_} 1 0-70 17 -0.60 / 0.70 050 0 40 0-60 0 30 7 0-20 0-50 637 --- 3- BLADES 4 BLADES 550. --- 5-BLADES 0.45 135 _ 0-40 41.

Screw BN7 Screw BN8 Screw BN9

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0 020 0.40 060 - 080

o

efficiency correction is obtained and applied to the available value of efficiency for the basic four-bladed screw.

The power coefficient is given by:

1 N

DHP

() 137,

VISVA

where N is the screw rate of rotation in revolutions per minute,

VA is the speed of advance of the screw in knots, is the relative flow factor defined by equation 9 of

Reference 2, and

s is the specific gravity of the fluid in which the screw operates (an average value for sea water is s = 1.026).

DHP is the delivered horsepower.

The data discussed above are not sufficient to cover the effects of varying diameter, in particular, change in optimum diameter due .to departure from four blades. For some screws improved performance can be obtained if the diameter can be modified to suit the optimum value for either three or five blades. This can be done by applying the procedure which will be described in Section 3 (to be published next month).

Table 1

Pitch ratio

Correction Factors to Blade Thickness Ratio and Blade Area Ratio for Departure from Four BladesScrews of

Constant Diameter

3 blades 5 blades

Right : Fig. 7

(3) Correction Factors Optimum-Diameter

Screws

Free-Running Conditions: Effects of change in optimurn diameter due to departure from four blades can be studied using the optimum-diameter and blade-area charts des-cribed in Section 3-12 of the books. Some of these charts for three-, four- and five-bladed screws are reproduced in Figs. 8, 9 and 10.

Each chart comprises two parts: a graph of speed coefficient 8, pitch ratio p and screw efficiency vlo on a base ofsquare root of power coefficient Al Br); and a chart of contours of

,

cavitation numbercrA8on coordinates of4B, and expanded

area ratio ch.

The speed and power coefficients are defined by ND

8 =

V, and

NiTHP

B, _{V_ .J}

where N is the screw rate of rotation in revolutions per

minute,

D is the Screw diameter in feet,

V, is the speed of advance of the screw in knots,

. 1.10 tt a8 0.85 1-0 10 0.95 09 1.10 1.05 10 0.95 0-9 1-05 10 0.95 105 . 0.95 090

THP is the thrust horsepower applied by the screw, and s is the specific gravity of the fluid in which the

screw operates (an average value for sea water is = 1.026).

If desired, the power coefficient B, can be derived from ' power coefficient B using the relation

= Bp,/ 710

where 7],, is the screw efficiency, and

B2,iS _{the power coefficient defined by equation 1.}

The cavitation number is defined by

2(p.8-e)

.7,03

pvA2

where (p.8-e) is the static pressure measured at the x = 0.8 radius fraction of the screw when at- minimum immersion

VAis the speed of advance of the screw in feet per second,

and

p is the mass density of the fluid in which the screw

operates (for fresh water p = 1.938, for sea water.

p=--- 1.988).

If desired, the cavitation number a,.8 can be derived from

-the basis form of cavitation number a, by applying -the relation 25sD] =

[

(P0-6A.8 _c74

0

the

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_ 3-BLADES _{_} .

-7... _

--

THICKNESS CORRECTION _

-

_ _ _ 5- BLADES

---

5-BLADES

-

---_

-_ AREA CORRECTION

-Z - =

--

-_

-_

-_

-_

3 - BLADES

-,

--_

-

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-....

--. -- .

.

-

PITCH CORRECTION _

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--5- BLADES

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EFFICIENCY CORRECTION - ...3- BLADES . _

-_

-

-_

-5- BLADES _

_

-iiiiltmliiiiIiiilliiiilitirliiiilimlilli-0.5 1.06 0.89 0.955 1.10 0.85 1.07 0.875 0.950 1.11 1.2 1.08 0.86 0.945 1.12 Blade Blade Blade Blade thickness area thickness area

ratio ratio ratio ratio Pe: 10

10 20 30 40 50 60 70 80 90 100

where -(po-e) is the Static pressure measured at the screw axis and the basic form of cavitation number is given by:

; 2(po-e)

(7) ' ere =

p vA2,

The procedure for designing screws using the optimum-diameter and blade-area charts is as follows:

First, the cavitation number aA is evaluated using equation 7 and the power coefficient BE is either directly determined using equation 3 or derived from B, using equation 4. Next, the speed coefficient 8 is read from the chart, and this enables the screw diameter to be evaluated using equation 2, and the

, cavitation number aA. 8 to be derived from aA using equation 6.

_Finally, the blade area ratio a, is obtained from the contour chart, sand corresponding values of pitch ratio p and screw "efficiency Tjo (by interpolation for change in expanded area

if necessary) are read froin the chart.

Effects -of diameter variation

If desired, the Optimum-diameter and blade-area charts s can be applied in deriving correction factors similar to those shown .in Fig. 7 (last month's issue), but also including effects of variation in diameter. A procedure for doing this is as follows:

First, values of speed coefficient 8,, blade area ratio aET, Pitch ratio p and screw efficiency 71,,T are obtained from the " optimum-diameter and blade-area chart for the _basic

four-- bladed .screw (Fig. 9). Next, corresponding values of these

.parameters for the non-basic screw are obtained (three blade, Fig. 8 or five blades, Fig. 10): This enables the following correction factors for departure from four blades' to be

."determined.

The screw diameter for the non-basic screw D is derived ';frorn that of the basic (four-bladed) screw Di by applying a

diameter ratio k, defined by

D 8

(8)

81

where 8, is -the speed coefficient for the basic four-bladed

screw (Fig. 9), and '

8 is the speed coefficient for the non-basic screw (Fig. 8 or 10).

The blade area ratio and screw efficiency are derived in a similar.way using ratios k3 and k, defined by

aE k2

aE,

(10) k3 =

-1101

whge (1E1 and 71,1 are the blade area ratio and efficiency

for the basic four-bladed screw (Fig. 9) and

are the blade area ratio and efficiency for the non-basic screw (Fig. 8 or 10).

(9)

a, and 710

In deriving the pitch corrections a procedure similar to those discussed above -is followed, but here an additional correction needs to be made. - The data on which the _-optimum-diameter and blade-area charts are based on those of the Troost B standard series.4 Both the three- and five-bladed screws of this series had uniform pitch p, but the four-bladed 'screws had non-uniform pitch (constant over outer region of _blades with reduced values near boss and

relation between maximum pitch PT and mean- pitch p given

-by PT _= 1.016 p). Consequently, the pitch cOrrection is defined by

(11) k, = 1.016-E

P1 PT

OPTIMUM ' DIAMETER AND BLADE -AREA CHART

TROOST 8 - 3 SERIES TWIN SCREWS

TuICKNESS RATIO 0-050

111111111101BRUMMUIrdell

MIL11111111111601121111MME

1111011111111111MMIGMENNEM

11911111111111111101101112111ER

1111111111111111111,1111111111111MMIM X; Fig. 8

where PT is the pitch ratio for the basic four-bladed screw

-Pi is the mean pitch ratio for the basic four-bladed screw (PT = PT/1.016), and

p is the mean pitch ratio for , the non basic screw (Fig. 8 or 10).

A procedure for deriving blade thickness correction factors, based on the Taylor strength criterion discussed in Section 6

of the series of articles2, is as follows:

-An approximate equation for the compressive stress sc at the blade sectional element at the x 0.2 radius fraction is given by

(12) s2 DHP

-IND3

.

where s2 is a coeffitient; the value of which is obtained from Fig. 5 of the series of artibles2..

DHP is the delivered horsePcwer,

-B is the number of blades

N is the rite of rotation in revolutions per Minute, D i0he screw diameter in feet,

is the chord-diameter ratio at the x = 0.2 radius fraction, and

T - is the blade thickness diameter ratio " (equivalent

value at screw axis).

For two screws of the same basic blade-outline shape the

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EIM11110111111111111116Mill

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1111E1111111111111111111Milii

- 49-06 05 0.4 - 0.5 04 0-3 0 4 40e, 4CO, 330 360 340 320 00 300 . mo Z60 040 a:0 140, 100 CO -040 045 050 - 055-0-600 043

R-0-1 g.0 6 o s Fig. 9 C.2

product B can be expressed in the form.

Bc.2 = KaE where K is a constant,

and equation 12 can be re-stated in the form

SC

-=-KND3 aE s, DHP

Applying the condition of constant stress to two screws of different diameter and different blade area ratio, absorbing the same delivered horsepower at the same rate of rotation, the blade-thickness correction is given by

T Di aEi s2

k. =

=

_{D aE} S21 which reduces to

k, =

=

(I)-k2

where k, and k2 are the ratios defined by equations 8 and 9, and

kE is the ratio of the strength coefficient for the non-basic screw s2 to that for the basic screw S21.

(4)

Correction Factors Optimum-Diameter

SCrews

Towing Conditions: In designing a series of screws of different diameter to operate under towing conditions the

t1.Ci coefficients could be evaluated directly using the basic 1.1.-a equations as given in Section 4 of the series of articles2.

-l0 (2.4 0.6 0-6 0.5 0-4

OPTIMUM DIAMETER AND BLADE AREA CHART

TROOST. 8-4 SERIES TWIN SCREWS

THICKNESS RAT* 0.04S

However, a simplified procedure using values of the coefficient for the basic screw, and applying correction factors for departure from the basic diameter, is as follows:

In their basic form the p.-a coefficients are defined by

(16)

=

pD3 (0-)

where VA is the speed of advance of the screw in feet per second,

is the.rate of rotation of the screw in revolutions per second,

D is the screw diameter in feet,

Q is the torque absorbed by the screw in lb./feet, T, is the thrust applied by the screw in tons,

p is the mass density of the fluid in which the

screw operates (p = 1.938 for fresh water, p = 1.988 for sea water),

Tp is the thrust pull ratio defined by equation 20

of Reference 2, and

Pu is the towrope pull in tons.

For two screws of different diameters absorbing the same torque and operating at the same speed of advance and the same rate of rotation, the relation between their 12-a

coefficients would be given by

9S iD V/2

k8 =

=

(D yl'

k1312

121 Di

where the coefficients 0, and are those of the basic screw, the coefficients # and are those of the non-basic

screw, and

k, is the diameter ratio defined by equation 8, and the ratio of their thrusts would be given by

ko Tu D, a

T0,

D al

Moreover, if the pull thrust ratio or, is assumed constant, the ratio of their pulls would also be given by this expression, i.e.,

,

P,

Di a

1 a

Kg =

=

,

rII1

" al

Ki ai

where a, is the chart value of the thrust torque ratio for the basic screw, and

a is the chart value of the thrust torque ratio for the non-basic screw.

In designing towing-duty screws, the diameter ratio lc, is evaluated and corresponding values of lc, and k8 are derived: this enables values of torque coefficients 95 and p. to be derived from those of the basic' four-bladed screws .(01 and p.,). Next, a set of values of pitch ratio p and thrust-torque ratio a is o,btained from the appropriate p.-a charts for three-, four- and five-bladed screws, and pitch correction k4 and pull ratio k8 are evaluated: this enables the pitch. ratio and pull for the three- and five-bladed screws to be derived from those of the basic four-bladed screw. Finally, the blade-thickness ratios are estimated following the same procedure as for the free-running screws. 111110111111111111111111111111111111111111111C

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T2e/ Q Q (18) a 357 D Tu 357 D Pu Q 0- 1-5

04 0.9 g as E. 0.7 05 0.4

OPTIMUM DIAMETER AND BLADE AREA CHART TROOST B- 5 SERIES TWIN SCREWS

. 79ICKNIESS 9470 r. 0.090, 11111111111111111111.111111111111

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jr. so 065 Fig. 10 (5) Worked Examples

It is required to prepare design calculations and to make performance estimates for four additional screws for a single-screw tug.

The design calculations and performance estimates for the basic screws are given in Section 8 of a previous article of

mine in SHIP & BOAT BUILDER INTERNATIONAL.' The first pair of additional screws (Screws 3 and 4) are to have three and five blades respectively and are to be designed for free-running conditions. The second pair (Screws 5 and 6) are to be similar to the first, but are to be designed for towing

Table 4. Particulars of Screws 1 to 6

conditions. Towing performance estimates are to be made

for Screws 3 and 4, and free-running propulsion estimates are to be made for Screws 5 and 6.

The design calculations for Screws 3 and 4 are to be made using the optimum-diameter and blade-area charts and applying the correction factors derived in Section 3 (last month's article). The design calculations for Screws 5 and 6 are to be made using the Troost B series charts and applying the correction factors derived in Section 4 (last month's article). The towing performance estimates for Screws 3 and 4 are to be made using the 14a charts, and the free-running propulsion estimates for Screws 5 and 6 are to be made using the Troost B series )32,-8 charts, following the same procedure for the basic screws (Screws 1 and 2) as described in the earlier article.'

Screws 3 and 4Calculations and Towing Estimates

In making the design calculations given in Table 2, values of power coefficient B, and cavitation number crA., are

derived from the corresponding values of power coefficient litz, and cavitation number a, for the basic screw obtained from Table 2 of the earlier article.' This enables values of speed coefficient 8, blade area ratio ch, pitch ratio p and screw

efficiency710 for a set of three-, four- and five-bladed screws to be read from the optimum-diameter and blade-area charts (Figs. 8, 9 and 10, last month's article): for each value of pitch ratio, corresponding values of strength coefficient S, are obtained from the Taylor strength-chart (Fig. 52).

Next, two sets of correction factors for departure from four blades (k k,, k,, k, and k,) are derived. Finally, each correction factor is applied to the respective parameter of the basic four-bladed screw (Screw 1) to give corresponding values of diameter, blade area ratio, pitch ratio, blade-thickness ratio and screw efficiency for the three-bladed screw (Screw 3) and the five-bladed screw (Screw 4).

The towing performance estimates were made using the charts and following the procedure for Screw 1 as given in Table 4 of the earlier article.'

The geometric features of Screws 3 and 4 are summarised in Table 4 of the present article, together with those of Screws 1, 2, 5 and 6. The screw performance data and comparisons are given in Table 5.

Deliv. Rate of Dia. No. of Blade Pitch Thk.

Screw Design H.P. Rotation (ft.) Blades Area Ratio Ratio

- No. Condition Ratio Remarks

DHP RPM D B as PT 7 1 Free-running .. 1,100 200 9.00 4 0.50 0.853 0.047 1Basic 2 Towing .. .. 1,100 200 9.00 4 0.60 0.580 0.052 f Screws 3 Free-running .. 1,100 200 9.45 3 0.44 0.798 0.054 4 9 9 .. 1,100 200 8.70 5 0.59 1.012 0.043 5 Towing .. .. 1,100 200 9.45 3 0.53 0.560 0.049 6 9, .. .. 1,100 200 8.70 5 0.71 0.620 0.048 440 480 400 590 560 540 520 800 to, sea 260 g 290 2201 .200 180 160 140 120 100 0 8 0 7 '2 06 g05 0,50 ass 060

Table 2 Scrcs i and '4-Design Calculations-Free-running:Conditions

, .

BASIC SCREW-SCREW I (Reference 2, Table 2)

, ..

,

BASIC DESIGN COEFFICIENTS

." 11; ...:- 22 ...-, 8 =182 ro, = 0.618 ep = 1.02 12, =0629 (p.-e) - 2577 9.75 Bu = Bp V:11; -,-- 1715 (equation 4) V, = 9.0 feet [1

-

25sD 1 =8.9 (equation 6) (p. =- e) CORRECTION FACTORS "' -N , No of Chart 8 422 p -iio if' k2 .k3 ,k4 S2 k5 01 (1,) (1) (I) . (2) ' (3) " (4) . (5) 6) ,(7) , ' '' (8)' ,'..,Blades

' 4 'Fig : 9 180 " .0.40 0.830 . 0.630 1.000 -lxicio 1:000 1c.006 1240 IAN) : :f:do 3 - 1-ig. 8 189 0.35 0.765. 0.645 1.050 ' 0.875 1.025- 0.935 1350 1090t. ::-.-1c04

5 Fig. 10_, 174 047 0.860 0.605 0.967 1 1.175 - - 0.960,1 1.053 1200 i 0.968 "...-.0.96

...

(1) Values from charts (Figs. 8 to 10) 1.016 p

(5) (equation 11) lc,

2, Fig. 5) (2) (equation 8) k,

=

-i (6) Value from chart (Ref. -'

.(3) (equation '9) ..kr= -61 . ., . . . a2, (7) (equation 15) k3 :-1 __ (4) (equation 10) k3 = -7/01 (8) (equation 15)ko =, k %

--( J )-

1 k2 : . -SCREW. PARTICULARS_ ' -Dia. -.. 'Screw No of D aE _{' 74° ! 'IP} No ' Blades ''. (ft.) _.. Remarks, . (9) : -(10) (11) -_ '(12): , 7: (13) - (14) " 1 4 9.0 6.50 0.853 0.047 , _0.618 0629 _{- Basic S.,crey-".:} . 3 '945 " - - 0.44. 1 0798" 0049. ,: 0.634 _1 0.645, .; 5 8.70 _{P. 9 .} ...r 1012 . 0045 0.594 :1 0.605 , .-_-,,,

(9) (equaiiOn, 8) ' kID, - (12) (equation 15) t = k811,

(10) (equation 9),, dr.:-_:ki'gri:'. -- (13) (equation 19) "lb . - = - k1-r,161

-( I 1 ) -(cyciaiicin 11) P = ' kiPi- _{(14).(Ref.".2 eqUation'.12) T,7):=} 7) 7,0

.-:

' -' '

Operating.eonditiOns%.

. Free running - ,Towing (at V, , 0) , Screw No No of Blades- - Design Condition Propulsive '

Efficiency': ' , Speed ". Pull Vs ,.PIJ , . . knots . .tchas 1 4 1 Free -running ' 0.629. 1/50 '11'.47,-:,1,=-:--7 4 . .,1- '' Towing ,-: ..; .. ..

-

10.60 -3 3 ": Free running 0645 1150 11.65:-4 ::::: 6 . . ' .., 5 , 3 . Towing . .. .. . . 0.605

--

1250 10.60 10.65 ' -10.90", .: 14.75 -- - p.90-_ -,kt

3 3 Per Cern increase in. efficiency .

--.-,

and pull -, . . .. 2.-5

-' . - (Basic. ScieW-Screv, 1) .. ..

.

-4.0

.

-,i11

3 -" ' Per ce-' n't increase in pull and es ' - ;

speed - .. .. !

., .-.5r ''' .(Basic 'Screw-Screw 2) :. '

Screws Sand 6-Calculations and Eke-Running Estimates -In making the design calculations given in Table 3; values

of the torque :Coefficient [/.. are derived - from the value of the torque Coefficient '4, for the basic Screw , obtained from Table .3 of the earlier article.? This -enables values of pitch

'ratio . p and thrust torqueratio a :t6, be read from the

appropriate [./.-a charts given :in the.Troost papeil-: for each value of --pitch ratio; corresponding -values of strength 'coefficient S2 are obtained from the Taylor strength chart

(Fig. 52).-;

Next two 'Sets of correction factor's for departure from four blades (k4 k,, k6 k8 and k9) . are deriVed. .,Finally, each correction_factOr_is applied to the respective parameter of the basic: four-bladed screw (Screw 2) to give corresponding values_ of diameter,. blade' area ratio pitch tatio, blade-- thickness ratio and Pull korthethree:.bladed screw (Screw 5)

and the five bladed sere*" (Screw 6).

The free,rtinnini'propulsian estimates were made using the )32;4 charts and following; the procedure for Screw 2 as givenin Table 5,:of the earlier article 2

The geometric features Of Screw's 5 and' 6 are summarised in Table 4 Of the present article, together ,Witti those of

Screws r to 4.

The -screw performance data and com-parisons are given in Table 5.

_ .

(6): Comparison of Results_

' The screw performance data for Screws 1 to 6 are given

in-Table:5, where performance comparisons are also _made using data for the four-bladed screws as the base's: These

L

Table :3. _Screws _ 5 and,6-Design-CalenlationS--:-Towing Conditions'

Reprinted from Ship and Boat Builder International

-BASIC SCREW-SCREW 2 (Reference 2:Table 3) . .

. ,

.

BASIC DESIGN COEFFICIENTS

Pi --- 6.77 cri = 1 . 66 D, = 9.0 feet l'u/ = 14.60 tons

. - CORRECTION FACTORS , No of Chart k, k2 1(2 IL P

ak4

k9 . k3 k 6 Blades (1) (2) .(2) (3) (4) (5) (5) (6) (7) (8) (9) (10) B-4--40 1.0 1.0 - 1.0 6.71 0.600 1.76 1.0 110 , 1700- 1.0 1.0 B.-3-35 1.05 0.875 1.13 7.59 0.56 1.86 _I0.946 1.01 1800 . 1.06 104 5 _ B75-45 0.967 1.175 0.92 .. 6.17 0.630 1.62 1.066 0.951 1630 . 0.96 , 0.95. .

-..(1) p-a charts (Reference 4) . 1.016p

(2) Values from Table 2 (6) (equation 11) k, = pT (9) (equation 15) k2 =

-(3)(equation 20) k8_=,k1 °l. 1 a

'

. (4) (equation 20) p. = Icspi ,(5) Values from p-a chart,

(7) (equa.tion 21) k, = -_{k, al (10) (equation,15) k, =( -}1

_.-''

(8) Value from chart (Ref Z Fig. 5) ki' - k2 . ,

SCREW PARTICULARS Dia.

Screw No. of D aE P Pu

-'NO. Blades (ft.) tons \ _Remarks .

(II) (12) - (13) (14) . (15) , .. . 2 4 9.60 0.60 0.580 , -0.052 ; ' 14.60- ' Basic Screw 5 3 I 945 - 0.53 0.560 0.0,54 ' 14.75. 6 ' 5 ..8.70, ' 0.71 0.620 0.049 ' "" 13.90.., .

(11) (equation 8) D = kiDt. (14) (equation 1.5) 7 = ice+,

(12) (equation 9) aE = k2aE1

(13) (equation 11)p = ko, (15) (equation 21) Pu = k9 P1 .,

.. ,. .

-comparisons show that 'reducing'ihe-rnimber of blades from four to three results in improved perforinance;,bitt increasing the number,orbiadef from hint' to five generally results in adverse perforinance, -as summarised below.

For the three bladed screw (Screw' 3) designed for free-- running conditions' the increase ' in efficiency would be .-21 per cent and at towing conditions the increase in pull .

would be 11_ per cent For the three-bladed Screw (Screw 5) designed for towing conditions the increase in pull Would be 1 per cent but at free running conditions there Would be no

-Change in performance. .

-For the five bladed screw (Screw 4). designed for free running ,conditions the reduction in efficiency would be 4 per cent, and at towing conditions " the reduction in pull would be 5 per cent.. 4FOr the five-bladed screw (Screw 6) designed for towing conditions the reduction in pull would be 5 per cent but at free-running conditions there would. be-an increase in speed Of1 per cent.

REFERENCES

1. 0. Brien, T. P., Some Effects Of Variation in Number of Bthdes on Model Screw PerforMancif. Trans.: N.E.C: Inst. Engis._

Shipb.,-1965.; 81'.

2.' O'Brien, T: P. Design of Tug Propellers: - SHIP. & BOAT

BUILDER' ji4TEiNATIOIIAL,1965 18

3. 013ried, T. P: The Design of Marine .Screw Propelleri. Hutchinion.-Scientific--and Technical Press; 1962. ,.

4.' Trbost,: L.: Open Water Test Series with Modern Propeller