The optimum diameter of marine propellers: a new design approach

THE OPTIMUM DIAMETER OF

MARINE PROPELLERS:

A NEW DESIGN APPROACH

B

PROFESSOR,L. C. BURRILL, M.Sc., PhD., Vice-President

A Paper read before the North East Coast Institution of

Engineers and Shipbuilders in Newcastle upon Tyne

on the 11th November, 1955, with the discussion and

correspondence upon it, and the Author's reply thereto

(Excerpt from the Institution Transactions, Vol. .72).

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THE OPTIMUM DIAMETER OF MARINE.

PROPELLERS: A NEW DESIGN APPROACH

By Professor L. C. BURRILL;M.Sc., Ph.D., Vice-President

11th November, 1955

SyNopsisIn the first pltzce, the Author discusses the problem of the optimum

diameter of marine propellers working in a uniform stream and finds that, the

results deduced by theory are in good agreement with those indicated by standard-series data The optimum diameter and optimum pitch distribution for propellers

working in a single-screw variable wake stream are then examined and it is found

that when account is taken of the difference in wake velocities associated with smaller diameters, which cut Off only a portion of the basic pattern, there is

advantage in reducing,the diameter materially as compared with the open-water optimum condition This is a most important conclusion in view of the recent

increase in propeller diameters for large tankers and other high-poweied

siñglë-screw vessels in that it indicates a means whereby the weight and moment of

inertia of such propellers may be reduced without sacrifice (and possibly with a

gain) in propulsive effideAcy.

Finally, a. design procedure is established which will allow the optimum diameter

for given conditions to be determined by calculation without reference to standard series data and useful diagrams are provided which will enable such investigations

to be pursued as a part of normal drawing office procedure without having recourse to long and elaborate calculations.

T the present time, the practical design of marine propellers is

based partly on theory, partly on experiment-tank tests with model

propellers, and

very largely on experience with full-size ships

The theoretical treatment of propeller problems has advanced

considerably during the past twenty-five years and, in the Author's

experience, it has been notable that the outcome of each new application

of theory has usually been to confirm the results previously obtained

from sound practical experience and experiment data, rather thati to

suggest some entirely new hne of action which would materially improve the propulsive efficiency Of ships.

On the other hand, the thôoretia1 approach to propeller problems his

greatly improved our control of design variations and has helped to

eliniinate the possibility of pitch errors arising from an incomplete

understanding of propeller action.

For example, the twin concepts of

no hft effective pitch and of the importance of centreline camber on the

lift for a given angle of incidence have made possible the ieady

compan-son of widely different designs, while the study of the pressure distribution

around different section shapes has done much to explain the observed

effects of erosion due to cavitation.

The ultimate aim Of the designer should, of course, be to contrOl all variations

58 THE OPTIMUM DIAMETER OF MARINE PROPELLERS: A NEW DESIGN APPROACH experimentation, whether it be on model scale or full size. This may be thought, for the present, to be an almost unattainable ideal, owing to the many variables involved and the fact that most theoretical work depends on simplifying

assump-tions which are necessary to bring the calculaassump-tions within workable limits, but

each step forward is considered to be of some practical value, even 11 its result is merely to give greater confidence in existing procedure or to provide greater flexibility of analysis.

Mainly as a result of the late. Admiral D. W. Taylor's excellent experimental

work with 16 in and 20 us standard series propellers, and his clear thinking

about the problems of data presentation, it has now been appreciated for a long

time that in open water (i.e. uniform stream condition) there is an optimum diameter for each set of working conditions, namely, speed of advatice Va, revolutions N and power F, but our decisions, in this respect have up to now

been governed entiiely by the results of standard series tests with model propellers.

It is known, for example, that the optimum diameter for gven speed, power and revolutions diminishes with increase in blade-area ratio, but the results derived from existing standard-series charts are not entirely consistent in this

respect. it is also known that, in general, an aerofoil propeller should have a

larger diameter than a rOund-back propeller of similar area. On the other hand, it is not knOwn whether the optimum diameter is influenced by the adoption of wide- or narrow-tipped bindes or by the use of a variable pitch from root to tip' of the blades, or whether in fact the'opthnuni diameter derived from open-water

test series data can be directly applied to the ship.

The principal reason for the lack of theoretical treatment of this problem is that while the vortex-theory, as it is usually applied, may give some guidance on the optimum distribution of loading when the diameter is fixed, it does not readily furnish a solution to the problem of the optimum diameter fO'r given

speed, power and revolutions.

In a recent paper' read before the Association Technique Maritime et

Aéro-nautique in May Of this yoar, this problem was approached in a slightly different

manner by means of the Vortex-Momentum-Blade-Element Theory, using the basic equations

K'Q'=

ITXO

(1 - a') (1 + tan2 c) CL

sin(± y)

2K'0

1

K'r

K'T

_{x tan (c5 ± y}

and v =

(tan

- tan ifr), tan [

+ y]

where a1

₌

1 + tan çS, tan (cb + v)

andCL==. sin cS. tan (çS

-the symbols being -the same as those used by -the Author iii -the paper

"Calcu-lation of Marine Propeller Performatice Characteristics "2 and it was found that

the optimum diameter obtained by theory was verb' closely in line with that deduced from standard-series tests in open water.

The ultimate object of this work. was to establish a design procedure which would enable the optimum diameter for given conditions to be determined by calculation without reference to standard-series data and to take into account.

such factors as the amount of blade area, the radial distribution of blade widths and thicknesses and, finally, the effect of a radially varying wake pattern such as obtains for example on a single-screw ship. Since that time the work has been extended and the Object of this paper is to give anaccount of the method, together

with some of the fu±ther results obtained, and finally to provide useful diagrams

for the designer which will enable such investigations to be pursued as a part.

of normal drawing office procedure without having recourse to long and.

elaborate calculations.

THE OPTIMUM DIAMETER OF MARiNE PROPELLERS: A NEW DESIGN APPROACH .59 Method of CalculatiOn

In the first place, the method of calculation -w based on the consideration

of the conditions obtaining at four characteristic radii, namely, 25, 50 75

and 875R.

This was done partly to limit the amount of calculation and partly

because it had been found that fOr the open water condition the total Kr and KQ for the blade down to 25R could be obtained by the simple process of adding the K'r and K'Q values for these radii and multiplying by one quarter

of the length of blade. This procedure had been tested on numerous occasions

and found to give very satisfactory results.

In the second place, In order to fix the blade widths and thicknesses at each radius, it was convement to chose a typical propeller as a basis design, and for this purpose the propeller KCB 4 for which full details. had previously been published in the paper "Propeller Cavitation: Some observations from 16 in. propeller tests in the new King's College Cavitation Tunnel "8was used. This

propeller, KCB 4, has a constant face-pitch and the blade sections are of N.A.C.A.

66 type (slightly modified at the tail to avoid the cusp-effect), the centreliñ cambers having been chosen to suit a J value of 80 and a face-pitch ratio of

unity. The blade-area ratio is and the blade thickness fraction 045. The next step was to choose a range of J values from which the values of i,fr at each

radius could be obtained (i.e. tan

.'

=

-), and a suitable range of values of

4, the hydrodynamic pitch angle.

The corresponding, values of CL could then be obtained from the equation

CL=-,sinc5,tan(c5*)

since o = is known, and Ke is the Goldstein factor corresponding to the

pitch angle of the helical vortex sheets in the ultimate wake, (see Fig. 3 of Ref. 2).

The next and most important step was to assume that in each case the sections,

while having the same thickness ratio tic as the basic design, would be given the

centreline camber appropriate to the minimum proffle drag for the CL value

under consideration. It is this assumption which makes possible the subsequent

calculatiOns and an examination of the results given in N.A.C.A.. Report 824

indicates that this procedüre.is fully justified and that. the CD value, then becomes a simple fUnction of the thickness-ratio. tic (see Fig. I).

Knowing the values of tr, çS, CL and C1, it is then a simple matter to determine K', KQ1, and the efficiency at each radius.

In order to establish the optimum relationship between ifr and the calculated

results were then presented in the form of diagrams (Figs 2 3 4 and 5) in

which efficiency curves are plotted for fixed values of 4' to a base of the functiOn

(K'/J4), which is directly related to B'ü.

It will be seen that these curves resemble the (p, 8) diagrams of Taylor (Figs. 211 to 214, "Speed and Power of Ships ", 1910) which -first revealed the existence of an optimum diameter for given p, (now written B&). The upper envelope of these curves gives the optimum value of q, as a function

of()

. In.reference I, other curves

giving .ir to a base of (KT/J) for constant Jhave been shown, bUt it is not

thought necessary to repeat these here. If then fixed values of J are, taken it is

possible to lift the optimum value of (K'rfJ) for each characteristic radius

and thus calculate K1T. Hence, by integration of the thrust grading curves, the

optimum value Of KT for each fixed value of J can be obtained.

It is then a

simple matter to tranSform these values into a curve of otimum 8 to a base

Büand this was done in Fig. 10 ofRef. 1. Table 1 shows a comparison of these - results with those given by the Troost B-Series diagrams for Bti values from 7

60 THE OPTIMUM DIAMETER OF MARINE PROPELLERS: A NEW DESION APPROACH TABLE 1Comparison of Calculated Values of Optimum & with Troost B Series

It'wiil be noted that theexperimental results do not show a consistent change in the optimum 'alue 0 8fOf change in blade-area ratio, whereas the theoretical

figures give a more or less constant reduction as between b.a.r. 50 to b.a.r. 70.

The propeller diameter varies' directly with 8. The calculated results fOr b.a.r. 70 have been' obtained in the same manner as those for b.a.r. 50 the Values of

o for each tadius being increased in the ratio 70/ 50.

Since that time, the range of these results for b.a.r. = 50 has been extended, and the new diagram Fig. 6 in this paper shows the caiculated optimum values

of & and' 'i plotted to a base of Bp4 from 6 to 25, together withthe corresponding

values lifted from the Troost standard series B.4 40,.B.4 55 and B.4 70 charts.

It will be seen that the calculated results are ëlosely in line with the experimental

values.

It may be observed that the B.440 design differs from the KCB.4

design and that the centrelilie cambers do not vary ih the manner prescribed above, but, despite this, the agreement is quite remarkable. However, it was

feI that compar son with these well-known and greatly used results would be the most satisfactory form of comparison for those designers who frequently

use the B.4 4O and B.4 .55 series as a standaid for preliminary design purposes,

although their final designs may not conform exactly to the Troost B-series.

Having thus described the basis of the calculations leading to Figs. 2 to 5 and

indicated the apparent reasonableness of the resulting curve of Optimum

diameters (i.e. 8 values) shown in Fig. 6 it is not proposed to discuss in great

detail the later portions of the paper (Ref. 1). It should perhaps be mentioned, however, that the radial distribution of the hydrodynamic pitch corresponding to the optimum diameter calculations (with drag) differed somewhat from the well-known Beta condition (without drag), the result obtained 'being shown in

Fig.7forj=

80.

In this diagram the function x tan çS represents the ratiohydrodynamic pitch,

and it will be seen that for the uniform stream condition the loading is slightly

increased at the tip and somewhat diminished a, the rqot, when drag i' taken into account. At the same time, the calculated difference in efficiency as between the

two conditions was very small being 712 for the optimum distnbution in open water (with drag) and' 708 for the Beta conditions (without drag). _{It is also}

notable that optimum curves of Kr1 (i.e. radial distribution of thrust) for J

70, 75 and 80 were found to be almost identical.

Optimum Distribution of Pitch in a Variable Wake Stream (W

_{= 32)}

Itt the final section of the paper1 the results given in Figs. 2 to 5 were used to

examine the problem of the optimum distribution Of hydrodynamic pitch corresponding to a radially variable wake stream 'and it was found that the

application of the principle of optimum local efficiency led to a radial distribution

Opt. 8 'from StaAdard Seriei Opt. 8 (calculated)

7 117B440

1l45

B455 118B470 BAR 50 ' 119 ,BAR.70, 115 8 125 122 127 127 123 9 133 130 134 135 131 10 140-5 ' 137 140 ' 142 138 124- , 158-5 154 155 159 155 15 _'174 170. 169, 175 ' 169 174- 188 ' 184

''183

189

-20 202 199 196 202

THE OPTIMUM DIAMETER OF MARINE PROPELLERS A NEW DESIGN APPROACH 61

of thrust in the behind condition which was almost identical with that for the basic uniformstream condition, the total efficiency for the propeller being 712

in each case. On the other hand, using the princirde of minimum energy loss

it was found that the loading was considerably increased in the inner parts where the wake is high and that this led to an increase in the overall efficiency, despite the decrease in the local efficiencies at these inner radii. This is in agreement with previous work.

the curves Of xii tan

_{corresponding to the three cOnditions considered,}

namely

:-are shown m Fig 8 and the corresponding thrust and torque grading curves

are shown in Fig. 9. For cOnditiOn No. 2 it was fOund that the curve of xii tanc5 gave a very large reductioi towards the root, the Cj values and hence the corres-ponding angles of mcidence being almost identical with those for condition No 1

while condition No. 3 indicated Only a moderate reduction towards the root. As a further check the conditions under which the basic screw KCB 4 (which has a uniform face pitch) would work in the same vanable wake stream was

examined and it was found that in this case the gain in efficiency in the variable wake was of the same order as for the screw designed in accOrdatice with

con-dition No. 3.

Further Examinationof the Variable-wake Condition (Wi' - 32 constant)

In the calculations described above the conditions examined in the radially variable wake stream were those corresponding to the optimum diameter in the equivalent open water stream (i.e. thrust-identity for similar / value).

It

was therefore decided to pursue the investigation further in an attempt to. find

out whether the optimum diameter would be the same in the variable stream as

for the uniform stream. To this end,. four new conditions were examined

namely

Diameter = D0 x

1 '10

Diameter = D0

X I 05

_{Mean wake fraction maintained}

Diameter =

)

x O95

constant at Wi' '32

Diameter = D0 x 090

where D0 is the optimum diameter fOr the open condition. As before, the

principle of total thrust identity as adoptedas the basis of comparison and the same radial wake distribution, which is reproduced in Fig. 10 was used This

radial wake distribution was deduced from van Lanimeren's data and was intended to represent a Taylor wake of 32. For the new calculatons it was assumed that this radial distribution corresponded to the optimum-diameter propeller D0 and the appropriate distributions for the other diameters were derived from the same diagram by lifting the values at. the correspondingly increased (or reduced) radii. - -.

In the first place, for conditions Nos. 4 to 7, the problem 'was approached

in the same manner as for the normal design procedure. That is to say, while the radial distribution was altered the mean wake value was maintained at 32

throughout.

From the previous calcUlations it had been foundthat this mean wake value

of '32 corresponded to the local wake at

645R, Which agreed with earlier e*periënce for single-screw wakes of this order, and for the practical purpose

of these new calculations it was assumed. that in each case the mean wake would

occur at this radius. In other words, the ,P, at 645R was adjusted to agree

I.

_{Unlfortn stream j = 80 (Opt. local effy.)}

P712 2.

Variable wake Wr =

.2 (Opt. local effy.) 712 3.

Variable wake Wr = 32 (xii tan e = coast.) 756

62 ThE.OPTIMLJM DrAMETER.oFMARNEpRopELuRs: A NEW DESIGN APPROACH with the Jvalues given. in Table 2 and the values àt.other radii were adjusted to. give the desired. radial distribution. . Having thus: fixed the J' values it was. a

simple matter to cakuinte the corresponding values, of

The value of

(xir tan e = constant) was then varied until the correct K was obtained and the results. of these calculatiOns are..shown in Table2. It Will be seen that the calculated .j values forD/'D., =095 and 090 fell below that forDID., = 1 00, and this was also true for

DID., = 1-b, thus

confirthing the existence of an optimum condition in the region of

DID., = 1

00. The value obtairted for

DID., = 1 05 was in fact 004 greater than that obtained forDID., = 1

00 but

it is felt that this lies within the accuracy of the calculations. It was therefore concluded that for the chosen conditions the optimum diameter for the open

water case could be taken to represent that for the variable wake, providing that

the mean wake remained the same throughout.

In order to verify that this result was not influenced unduly b the condition

that the mean wake would occur at 645R the

DID., = 0

95 condition was examined more closely by putting this screw into a uniform stream and thus determining the thrust identity wake After some iteration it was found that when a true balance was obtamed the relationship between the efficiency for

D = 0

95D.,andD = 1 00 D.,was the same as before This procedure was

then repeated using the pnnciple of torque identity instead of that of thrust-identity and although the condition of balance was thereby changed slightly

the order of superiority was the same as befOre, the results being shown below. TABLE 2Results for Conditions 4, 5, 6 and 7, WT = const..

(Thrust identir9)

TABLE 3Results for conditions

4a, 5á, 6a

and 7a, Wr = const

(Torèjie identity) Condition DID0 .

K.

K ii

Q.Pc.

4 1-10 O-725 . 0-0992 00153 0749 0-848 5 1-05 0-762 0-1175 0-0187 0-760 0-861 6 0-95 0-843. 0-179 00321 0-749 0-848 7 . 0-90 0-889 0-221 0-0434 0-722 0-818

Basic condition DID0 = 1-00

3 1-00 0-80 0-1452. 0-0245 0-756 . 0-856 Condition DID0 1 K K Q..P.C. 4á 1-10 0-725 0-098 00152 0749 0848 5a 1-05 0-762 ' 0-121 00192 ' 0-760 0-861 6a

095

0-843 0-177 0'0316 0749 0-848 -7a

090

0-889 0-212 0-0415 . 0-725

082l

THE OPTIMUM DIAMETER OF MARINEPROPELLER5: A NEW DESIGN APPROACH 63 Effect of Adjusting W to suit the. Diameter of the Swept Disc After some further consideration, it was decided to approach the problem m a slightly different manner as follows Instead of assuming that the mean wake fraction would be the same for all the propellers of different sizes, it was

decided to assume that the wake pattern corresponding to Fig. 10 applied to the

basic condition D D0 and that if, for example, a smaller diameter were to be adopted this would only occupy a portion of this basic stream; so that the

mean wake would be increased. This is in fact what would happen on a given

ship if propellers of different sizes were to be fitted At first sight this would seem to be a more complicated procedure to apply than that previously adopted, but this is not so, as the need to determine the mean wake can be obviated entirely by comparing the results on a basis of a propulsive efficiency in terms of

instead of JlQ In other words, if the propellers are desigued to give the same total thrust then V5 will be the same and the order of superiority will be

represented by the change in torque necessary to provide this thrust. It may be

argued that this basis of comparison is incomplete, as it does not allow for a change in thrust deduction with change in diameter but m our present state of

knowledge it is difficult to see how one could proceed otherwise. In fact, the

q.p.c. is given by

fT.J'\

q.p.c. =

_2ir

₎

.

-(I - 1)

and in this investigation, in order to provide a reasonable basis of comparison, the value oft has been taken as 23 throughout. Finally, these calculationswere

made for a range of conditions from DID0 = I 05 down to DID0 = 085,

as shown below.

)

W allowed to vary with

diameter of swept disc.

The resUlts of these calculations are summarized n Table 4 and the derived

q.p.c. values are plotted iii Fig. 11. It will be seen that the-shape of these curves

now differs entirely from those obtained when the mean wake was maintained at- a constant value and although the curve of efficiency is relatively flat between say DID0

090 to 098 the optimum value now occurs at approximately

TABLE 4Results for Cozditions 8, 9, 10, II and 12

(Wr allowed to vary with diameter)

tan ç5

(tan e + tan

1r)

Condition DID0 Js Q.P.C. 8

l05

11204 01203 0Ol96l 0843 9

100

li765

0l452

0O244O 0860 10 0'95 l2383 01799 003l40 0870 11

090

l307l

02272 004l96 0867 12

085

l384l

02797 0O5546 0856

8. .D = D0 x 105

9. D =D0 x 100

10. D = D0 x O95

11.

D = D0 x O90

12. D = D0 x 085

9

m

oprIMuM DIAMETER OF MARINE'PROPELLERS: A NEW DESIGN APPROACH

D1DO = O94. this is mterpreted to mean that owing to the change in wake

associated with the' smaller propellers there is a.slight gain in propulsive efficiency by reducing the diameter to 094 of the open-water optimum value and, in' fact, the diafiieter could be teduced toO- 90 D0 without serious loss, providing always

that the centrelihe cambers can be chosen to ive the basic minimuni drag

condition,.

A close examination of this latter consideration revealed that' the CL values

corresponding to the inner radii for cOnditions 8 to 12 were relatively high and

further that the approximation tan ç5 = (tan e + tan *) which had been used in these calculatiOns was not sufficiently' accurate fOr these high values of ft

-

*. After some consideration, it was decided that for these large angular differences it was more correct to use the equatjq

= J(e° + b-°)

and the calculations were therefore repeated on this new' basis. These new conditions were numbered 8a to 1a, respectively, as shown below:

8a. D

= D0 x 1-05

9a. D = D0 X

1 00

W- varying with diameter

lOa. D = D0 x 0-95

_{as before, butç5 =}

_{(e + ir}

lid. D = D0 x 0:90

12a. D=D0 x 085

This had little effect on theç5 values for the outer radii, 'but resulted ma reduction'

of those for the 25R. There was also very little change in the optimum q.p.c. values as shown in Table'S and Fig. 11, but thecurious result now obtainedwas

that the diameter could be still further reduced, with advantage, although the critical CL values now become those in the outer parts.

-TABLE 5Results for Conditions 8a, 9a, 100, 1 Ia and l2a

(WTallowed to vary with Diameter)

c5=c+k)

For example, when the diameter is reduced to 0-85 D0 the lift coefficients for

x = 0:875 and x = 075 become 025 and 0-33 respectively, and the question

arises whether suitable sections can be designed,for the small thiëkness ratios tic

concerned, and still maintain the, minimum drag condition on which the

calculations are based. An examination of N.A.C.A. Report 824 and the

earlier N.A.C.A. Report No. 460 indicates that this is quite reasonable (e.g. the

minixrnm drag for N.A.C.A. 4406 occUrs at CL = O4O, which exceeds the above

values). ' '

In viów Of the recent increase in propeller diameters for large tankers and other

high-powered single-sërew vessels this result is a most valUable one in that it

indicates a means whereby the weight and moment of inertia of such' propellers

aindition DID0 ' Js .KT K , Q.P.C. 8a 1-05 ' 1-1204 , 0-1188 ' 0-01948 0837 - 9a 1-00 1-1765 Ol453 '0-02432 '0-862 lOa

095

1-2383 0-1777 ' 0-03110 0-867

ha

0-90 1-3071 0-2202 ' 0-04067 ' 0-867 '12a 0-85 1-3841 0-2741 0:05376 0865

THE OPTIMUM DIAMETEROF MARINE PROPELLERS A NEW DESIGN APPROACH .65

may be reduced without sacrifice it propulsive efficiency It also gives a lead as to the procedure to be adOpted when the diameter is restricted for reasons

of clearance, draft of water etc., a problem which has in the past presented very considerable difficulties.

Application of the Method to Design Problems

The general method of approach has been illustrated in the foregoing sections

but, in order to facihtate the application of these principles to other problems

(i.e. different wake patterns, different pitch ratios etc.) the results:given in Figs.

2 to 5 have been extended and presented in a more suitable form for design

purposes.

Figs. (12, 13 and .14), for example, provide a means whereby, K'r KQ' and ?Ir

may be obtained for x = 0 875 in terms of J' and tan çb and similar diagrams

are provided in Figs. 15 to 23 for x = 075, x = 05O andx =

025.

In dealiig with a wake-adapted screW, for example, the first step would be to

draw a curve of Va', or (1 WI), in terms of x r/R for the expected wake

variation., Assuming the propeller is to be designed for a given ship speed V1, a given delivered horse-power P and a given numberof revolutions N, and that

the wake fraction W is known the value of Va, the mean wake speed, can be

obtained and hence Bp From Fig. 6 the. cofresponding optimum

and efficiency ij,, for the uniform stream condition can be obtained for valuesof Bp up to 25, or since the calculated values appear to agree with standard series

data such curves may be used for values above 25.

Knowing 8, the value of

D0 may then be found (i.e. D0

₌

to see how thiS agrees with the

maxi-mum diameter which can be fitted. The next step is to decide on a suitable diametcr less than P° say D - O90 D0 so that J

-,

=

and the

Vat

..

values of Jva = at each radius, may be determined. This procedure will

give the value of tan Jr at each radius(i.e.tan

=

it is now necessary to chose a value of (xii tan e) as a starting point for the ca1culations In the absence of previous experience this may be best done by adding a suitable angle, say 6° tO 8° tO the value of

fr'for x = 065 and working out xii tan

on this

basis (i.e. xii tan = xli tan (i(r. + 8°.say).

Using this value of (x ir tan e) as a constant for each radius, work out tan 6

and hence e° for x = 025, 050, 075 and O875 and using the

expression

=

(i° + °) find the corresponding value of for these radii.

It is then an easy matter to lift the values of K1T from Figs, 12, 15, 18 and 21. By simply adding these four values of K1r and multiplying by 020the cOrres-ponding value of K is obtained. This may then be compared with the required value of K, and if it is too small (x ii tan e) must be increased and the procedure

repeated until the necessary balance is obtained. Starting as we have done

from N, P and Va it may be asked how the required.KT is to be obtained.

NP

..

. NI)

Now Bp

- where N is r.psn., P isd.h.p..and Va is in

knots and 8

₌

So that .Kà which is maybe represented by . .

NP

Va5

603x550

KQ=-V- X

_N5D5 X

_px2ir

(.) x 953 x 106 (where p salt water = 64/32 2)

K0ti2n'.8

Bp2

-and

Kr

_l0133

,

66 rna oi'lmiuMDIAMETEROF MARfl'E PROPELLERS -. A NEW DESIGN APPROACH

In this way, the requiredKTmay be determined from the basic Bp, 8 and

values, or, alternatively, the calculations may proceed on the basis of equal KQ (Le torque identity), if this is preferred.

As an example of the simplicity of these calculations-the process followed for

D

=

0-90D0 is given in Table 6 (i.e. condition ha).

TABLE6Example

of

Design Procedure using Figs. 12, 15, 17and20, etc.

.ls = 1-3071 Required KT =.0-221 For the case when the diameter is restricted to 0-9 Do.

The KT of 0-145 for the optimum diameter is increased to 0-221.

.Tàkingxtan e =0-4640.

=

(fr+ c).

x

J,

tan&- xtanc

tan e e ifr tanqS

K'

0-875 0-993 0-3612 05303 27-94 19-86 239O 0-4431 0309 0-75 0-915 0-3883 0-6187 31-75 2122 2649 0-4984 0-378 0-SO

0627 0-3992 "" 0-9280 42-86 21-76 32-31 0-63240-329

0-25 0-319 0-4062 '1' _{1-8560 .81-69 22-10 41-90 0-8972 0-097} 1-113 0-2 0-2226

..

K = 0-2226 x 1-Q12

=

0-2253 (Required value 0-221) A closefcomparison can be obtained by reducing the value of x tan c.

K1-

=

0-2176 x 1012

=

02202 -andKQ = 0-0410 x 0992 0-04067 qp.c.

_K

x J x

(1t)

0-2202 0-04067

-;

q.p.c. = 0-867.

The integration constants 1 -012 for K and 0-992 for K0, used in this example are those found necessary give aimost exact agreement between the

approxi-mate integration method and the results of a careful integration using a large number of ordinates for thrust and torque grading curves of the characteristic

shape corresponding to the behind condition Table 7 shows such a companson

for several cases and it will be seen that the use of these constants gives very

satisfactory results.

For practical purposes the integration constants may either be neglected during the iteration process or apphed to the required Kr and K0 values In any case, the degree of accuracy, in terms ofpower absorbed or thrust delivered is thought

to be equal to that of any other design procedure in commOn use today.

where (I - /)

= 0-77 say 1-3071 x 0-1225 KQ' Takex tan e

=

0-4608. 0 875 0 993 0 3612 0 5267 27 78 19 86 23 82 0 4415 0 302 0 066

075

0-915 0-3883 , 0-6145 31-57 21-22 26-40 0-4964 0-370 0-075 0-50 0627 0-3992

04u

0-9216 42-67 21-76 32-22 0-6302 0-319 0-053 0-25 0-319 0-4062 '1' _{1-8432 61-62 22-10 41-81 0-8944 0-097} 0-011 1-088 _0-205 0-2 0-2 0-2176 0-0410

THE OPTIMUM DIAMETER OF MARINE PROPELLERS: A NEW DESIGN APPROACH 67

1ABLE 7ompathon of Full and Approximate

Methodr of Integrating K'r

and K1Q Curves Full Integration 094044

_{- 003135}

= 30 5-4065

_{= 01802}

KT=

₃₀

Having determmed the final values of Kr, KQ and '' (or q.p.c.) for the case where D = 090 D0 in the manner described above it may be found that the

-efficiency is sufficiently greater than that on which the onginal estimates of speed and power were made to warrant a chaxge in the expected speed V3 (or a

reduc-tion in power for a given speed), in which case thecalculations may require to Ae repeated, but this is part of the. normal iterative procedure which will be

x K'0 S.M. f(K'0)

K'r

f(K'r)

1:0 -

-

-

-0975 00219 I 00219 0-0795 00795 0950 0O309 001545 01300 0-0650 0925 00367 1 00367 11655 01655 H 0900 00412 0-03095 01925 01443

085

00478 2 00956 02320 0-4640

080

00516 .1 0.05I6 025S5 0-2585

075

005325 2 01065 02749 05498

070

00534 1 00534 02840 02840

065

00526 2 01052 02890 O-5980

060

00507 1 00507 02895 02895

055

0-0480 2 00960 Q-2860 05720

050

004445 I 004445 02787 02787 045 0-0402 2. 00804 0-2650 05300

040

00353 1 00353 02460 02460 035 0-0294 2 0-0588 02180 04360

030

00229 1 0-0229 01760 01760 0-25 001542 2 003084 0-1201 02402

020

00075 000375 00590 0-0295 0-94044 54065

Approx. Integration. SummaryDID0 1-05 to 0-90

x

0-875

K'T 0'2145

K'Q

0-01542 DID0 FullIntegration

Approx. Integration 0-75 02749 004445 KT 01203 0-1203 0-50 0-25 027870-1201. 005325 004500 I 05

K0 001962

001961 08882 015812

Kr 01469

01452 0-2 0-2 100 KQ 0-02450 002440 017764 0031624 1-012 0-992 KT 0-1802 01799 0-95 ' 01799 003140 KQ 003135 003140 KT 02231 02272 0-90 KQ 004115 0-04196

68 TIlE OPTIMUM DIAMETER OF MARINE PROPELLEas A NEW DESIGN APPROACH familiar to all propeller designers. _{If, finally, it is decided to examine the effect}

of reducing the diameter still further to say D = 085 D0 the calculations will

proceed in the same manner as has been described above for D_{= 0 90 D0.}

- Blade Section Design

In the foregoing sections nothing has been said about section design other

than that the centreline camber has been assumed to correspond to the minimum

drag condition for each value of CL. The results of the calculations for each

value of DID, give the appropriate KT,.KQ and_{m,i (or q.p.c.) values and also the}

corresponding values of x tan çS the hycirodynanuc pitch ratio at each of the

chafácterjstjc radii. _{These results, are therefore quite general and any method} of section design may be employed, according to the preference of the designer

in order to give the necessary CL values. _{It is Vwell known that certain correction}

factors must be intrOduced to take account of the difference between the theor-etical lift coefficients at given angles of inculence and those_{obtained from wind} tunnel tests, and also for the effects of viscosity; flow curvature (e.g.

Ludwieg-Ginzel or Hill correctiOns) and, cascade effect (Gutsche or Shimoyama etc.), but so far as the Author is aware no method hasyet found general acceptance, and each designer may therefore choose to apply the_{system Of correction factors.}

which he has found to be most convenient.

In order to assist in this question of section design Figs 24 to 27 have however

been prepared giving the values of CL corresponding to different values of P and tan

_{for each of the characteristic radii 0875, 075, 0-50 and 025, and}

Table 8 shows the application of the correction factors used

by the Authors

tO the condition (1 2a) given in the- present paper.

TABLE 8Ca/cu/at ion of Face Pitches for Condition I 2a

Values of a,, (Theory) are for basic sections of KCB 4. Kag is from Fig. 15 Ref. 2. &sg = Kg x ao (theoy). (ao l- aNT) are for basic sections of KCB 4.

Opt. j/c

:

'

where Kc= = 0-079forN.A;C.A.66camber.

(y/c = centreline camber). Ka,, from Fig. 7 Ref. 2.

.f Opt camber

-

V__{-Act. carnber\}

- - - . x CEo (actual)

\

act.. camber I

V 0 = (çS + CE!).

-face-pitch angle

V V - .. . _. face-pitch

x ii tan 0 = face-pitch ratio

diameter

- _{The results ofVthis calculation, together-with thosefor Ccinditions 9a, lOa and 1 Ia are}

hown graphically in Fig. 28. V

V

V V

x Kao Opt. y/c Act y/c a,, ao 00 _{tan 0}

_{x tan}

0-875 0.905 O0231 Q-0143 1-18

073

2638 04960

l363

Q75 0903 00305 0-0195 161 0-91 29-SQ 0-5658 1333 0-50 0-903 00546 00248

207

-2-49 31.52 07678

l207

O25 0883 00969 0-0228 1-85 6-01 5348 1-3504 106 x J'w tan cS CL Ks ç50 Kgs 0-875 IO26 048l3 O25l 0-306 0-948 25-70 0942

257

075

093l

0-5378 0330 O446 0-947 2827 0-850 3.74. 05O 0-626 0-6745 0-588 0-731 0942 3400 0707 8.05

025

0323 0-9470

0995.

l23l

0-919 43-44 0553 -17-8g. 9-12 x CL Kgs see Fig. 16? -- for - Ref. - = Kgs X Ks ks see Fig. 6).. - 2 x - theory Kcg

&g

(o + CCNT) a! qS + al 0-875 130 0-015 0-02 1-18 141

27lI

075

1-78 0-056

010

l70

2l4

.30-41

050

2.29 0-185 0-42 2.46 6-01 4O0l 0-25

2l0

0-363

067

2.59

I605

59-49'

THE OPTIr1UM DIAMETER OF MARINE PROPELLERS: A NEW DESIGN APPROACH 69

Conclusions

The general conéhisions suggested by this investigatiOn are as follOws In the case of a propeller working in a tiniform stream- the values of the

optimum diameter deduced-by theory are m good agreement with those

indicated by standard-series data.

The optimum distribution of loading in a uniform stream when drag is tllkeh into account corresponds to a slight reduction in pitch towards

the root and a slight increase towards the tip as compared with the

Betz condition (xii tan çb = const.) without drag, but as might be

ex-pected from previous work the difference in efficiency- is, -for practical

pur,oses, negligible

The thrust-gradingcurves for optimum distributiOn of loading (with drag) m a uniform stream are almost identical for a wide range of pitch ratios

and there is very little variation in total K2- -for. optimum efficiency. This

- is generally in agreement with experimental results. For example, the

cuives given on p. 164 of "Principles of Naval Architecture ", Vol. 2 show -that the optimum line in terms of B0 -is mofe or less parallel to the

base.

-The application of the principle of optimum local efficiency to the case of a propeller working in a radially variable wake, such as that corresponding to a single-screw installation, leads to a large reduction in pitch towards

the root. The resulting thrust grading curve is very similar to that for

the corresponding open-water condition and the total efficiency is about

the same.

-The application of the principle of thi mum energy loss for the com-bined hull-propeller system (ie. xii tan = const.) leads -to only -a small

or moderate pitch reduction towards the root and despite the reduction

in local efficiency in this region the±e is a gain in overall efficiency arising

from the increased loading at the inner parts where the local wake is

high. This is thought-to be due to the more efficient use of the possibilities

of" wake gain" where the local velocities are relatively low.

- For the variable wake stream condition the open,water optimum diameter

remains unchanged providing the mean wake fraction is maintained at a

constant value. When, however, the general wake pattefn is assumed to remain the same and the mean wake is dependent on the diameter of the propeller disc (i.e. smaller diameters cut off-only a portion of basic pattern) the open-water optimum diameter is no longer applicablC and

there is advantage in adopting a smaller diameter, providing always that

the sections are suitably designed for the increased CL values. This is

- a most important conclusion in view of the recent increase in size Of

single-screw installations. Already, such propellers are frequently made

less in diameter than is indicated by standard-series data in oider to

reduce weight and moment of inertia, but the present investigation suggests

a means whereby this can be done without loss (and possibly a gain) in

overall propulsive efficiency. -

-The limit to which this reduction in diameter -can be carried out appears to be governed by (a) the intensity of the wake, (b) the limiting CL values

which can be accepted without danger of cavitation. It is clear from

the results obtained that either a large propeller, i.e. (D = D0), with

blade sections having low centreline cambers or a smaller propeller (say

D = 090 D0) with blade sections having high centreline camber (and

possibly a hollow driving face) can be adopted.

The amount of centreline camber is, in this investigation, adjusted to allow the sections at each radills to work at CLopt, or in other words at

70 THE OPTIMUM DIAME'rEROF MARINE PROPELLERS A NEW DESIGN APPROACH It must be remembered, however, that the cD mm condition corresponds to that for favourable distributiOn of pressure around the section.

The relation between cL opt and centreline carnber.for different values.

of tic is shown in Figs 8 and 9 of Ref 2 for sections of normal aerofoil type and further information relating to sections having the N A C A 65, 66 and a type centreline cambers is given in NA.C.A. Report 824 8. In this investigation the minimum energy loss condition adopted for the

variable wake patterns, i.e. x ir tan

= const. is that proposed by the

Author in Ref 1 and the reasons for the adoption of this condition are

repeated in Appendix 1 of this paper. The results obtained by calculation

generally confirm the correcttiess of this condiiton, but a comparison of

the figures obtainedfor conditions $ to 12 and those for 8a to 12a suggests

that this is not a very critiá1 Optimum condition. In view of the high

CL values Obtained for the inner sections it appears that there would be

some advantage from the point of view of section design in slightly

reducing the values in this region, without materially influencing the

overall efficiency The effect of such modifications may be examined by

applying Figs. 12 to 23, which cover a reasonably wide range of fr and

ç6 values..

APPENDIX I

I; The condition of minimum energy loss for a moderately loaded ideal screw may be obtained as follows, if V is constant over the disc.

dT

_{=2irp2a1Lr(la')Qr =pr(l a')Qr}

but

a'=

_4lTrQr

r:

_pflr.dr.

dl'.,

r

_4irrCr

ri

if now we add a small elóment of circulation 81' at the propeller disc, wó obtain

dT.,+(dT.,) 'r+"11

1'

par.di

-

'

t. 4iWQr 4lTrflr

2r

hence

i(dl,)

-

_{r (i}

4nr fl r 4nr fir Inasimilarmanner

_{V(l + a)r}

dr dQ.,

_r+ar

which gives dQ, + (dQ.,)

_{- (1' ± Afl (1 + a ± Aa)}

pVr.dz. Ar

ar+ar

wbere

a+ ila

1' +

_{or a + 'a}

hence dQ0 ± (dQ) 1'

+

T) (1 + +

pVrd.r

if

and 4Q0)

=A1'l±+f- a

pVr.dr so that lj"1 (dT.,) .Q.A (4Q.,) Now for minimum energy loss

V.t (dl'.,)

a

(dQ)

- constant = K

1. -

2a' -

rT . a'

- l+2a+;a

THE OPTIMUM DIAMETER OF MARINE PROPELLERS: A NEW DESIGN APPROACH 71

and when A F - o we have as the condition for mihimum energy loss tan e,,

11 - 2a'\

taik0

-

constant

which corresponds to the well known Betz condition.

2. If now we consider a propeller working in a variable wake stream, the condition for thihinium energy loss becothes

Va'.A(dT0)

flf'\

(l.A(dQ0) X

i,i - w')

= constant = K2 where 1' = local thrust deductiOn at radiusr

w' = local wake fraction at radius r Va' = local stream velocity at radius r

As before 8 (d7,) _{AT 11 - 2a'}

_a'

pflr.dr

-and

So that the condition for minimum energy loss (ship + propeller) becomes

1(2

_{= (}

ii') (

t',) = constant

V(l+2a)

I flt'

but taneb

_Qr(l-2f)

tafli/tb

K2lw'

tafleb

I flf'

or

_{= K2 'l - w'}

The constant K2 is indeterminate and may otily be found by trial and error, but a first approximation to its value may be determined as follows, If we imagine the mean value of w' as integrated by the propeller tobe w and the mean value of t' = then for the radius at which w' = w we have, for an equivalent propeller working in

a uniform stream Va = Vs (1 w).

and Va.A(dT0)

/1 - t\

fI - 2a'\

(1 -

_{- K}

(1A (dQ0) U - 4

±

) \f)

Furthermore, if and e are the initial and final flow angles and e for the radius at which Va = Va'

K

=.taii*o(It

_{tane,, \lw}

and we can assume, as a fl±st approximation, that K2 = K3

i.e. tan b / tan e,

I - w\ flt'\

tan e0 (1 w

tan1rb

ktan*ol

U w')

tatiqi0

l w'

Finally, if:' t we have

taflcb

/t\ (lw,

tan !kb tan L'01

kl - w'

which will enable the values of eb, and hence çb, to be obtained for each radius when

and ( =

w,) are known. Incidentally, this leads to the result that xir tan e is a constant; so that the vortex.sheets in the ultimate wake proceed aft as rigid helical

sheets of uniform pitch, as m the case of the Beta condition for a propeller working

in a uniform stream. This is in accord with Theodorsen's statement that "when the

propeller is operating in the wake of a body one has the unique case that there are no

induced losses chargeable to the propeller until or if the velocity. (i.e. induced axial

inflow iii the ultimate wake) exceeds the deficiency existing in the wake ", and means that the mass coefficients which he has proposed may be correctly applied to a propeller working in a variable stream.

72 THE OPTIMUM DIAMETER OF MARINE PROPELLERS: A NEW DESIGN APPROACH

3. The values of XII tan ç5 obtained in the above manner are not constant (as shown

in Fig. 8); they are however not greatly different from those obtained by use of the

Lerbs condition

tan ç6

L

A/lW

tan '/'b '7o V

and it can be shown that the Lerbs condition corresponds to the approximation

l-2a'

(la'\2

l+2a = J+a)

which agrees with his equation

Gi i (dSi) V

I - 8 (r) - K2

(dTi)

1 i/r(r)

and the other approximations which he makes in the H.S.V.A. Note: Bemerkungen

zur theorie und zum Entwurf von Nachstromschrauben.

APPENDIX II

The symbols used in this paper are as follows

:-/= V/nD;

_{KT= pn2D4'} KQ

tan fr = V/cr;

tan q5 = ;

tan e

-where V = axial stream velocity Clr = rotational velocity.

ii = number of revolutions D = diameter.

p = mass density

T = thrust

Q torque

a = axial inflow factor at propeller. a' = rotational inflow factor at propeller.

Q pn2D5

V(I + 2a)

Qr(t - 2a')

The equations used in the calculations are given

below:-(0.CL)

4K6.sinç5.tan(9Sfr)

(1)

to which a small correction

((r.CL) = CT.CL X

[tan(_qr)

(1 _K)]

has been applied, to allow for slipstream contraction, but which could be neglected

without significant alteration to the final results.

The values of K'Q and K'T have then been derived by applying the modified

blade-element theory equations (i.e. including drag)

K'Q d(KQ) (I - a1)(l ± tan2 g5) CL (?5 v) ₍₂₎ K'

T

d(K)

2.K'Q 3 dx xtan(qS+y)

()

'Jr X (4)

ri

CDI B.C.

where x =

I ;

tany =

I ;

=

iR

/CL 2irr

CL = lift coefficient; CD = drag coefficient;

B = number of blades;

C = chord of section at radius r

al (tan

- tan

fr)tan [ + y] 1 + tan gS. tan (ç5 + y)

Ke and Kç are the Goldstein factors corresponding to the flow angles e (in the ultimate wake) and ç (at the propeller), respectively. The actual values used were lifted from

D0 = optimum diameter in open water = 8 value corresponding to D0 factual diameter

DID0 =ratio(

_'

'-'0 V'0

xir tan 1r = J',,, =

=

local advance ratio

hYdrodynannc _{hydrodynamic pitch rato}

face pitch

x7T tan 8 =

. ''

face - pitch ratio diameter

ultimate wake pitch

Xl, thfl£

diameter' - ultimate wake pitch ratio.

REFERENCES

VoL 70 (1953-54), p. 121.

Vs ship speed; 'vs vs

nD

V0 mean wake speed I Ur 'Va Va

nD

V10 local wake speed;

.1',,, or J0=

1. BURRILL, L. C. Considerations sur le Diamëtre Optimum des Hélices. A.T.M.A., 1955.

2. BuRnu.L, L. C. Calculation' of Marine Propeller Performance Characteristics. N.E.C. Inst., VoL 60 (1943-44), p 269.

3. Buluuu., L. C.' and E?.mnsoN, A. Propeller Cavitation: Some Observations from 16-in, Propeller Tests in the New King's College Cavitation TunneL N.E.C. Inst.,

TIlE OPTIMUM DIAMETER OF MARINE PROPELLERS A NEW DESIGN APPROACH 73

Fig. 3 of the Author's paper "Cainulation of Marine Propeller Performance

74 THE OPTIMUM DIAMETER OF MARINE PROPELLERS: A NEW DESIGN APPROACH

-a

02 -04 06 08' -10- --12 --I4 16

/c

Fig. 1Variation of CD miñimüm ds a Fimction of tic

0 Fig. 2 -10 (K Fig. 4 -s IS Fig. 5 % /0 Q -

Fig.3

X 'R. p.870 a' 0.

Figs. 2, 3, 4, 5Local Efficiency . as - a Function of

(z

10 IS II -- - 'P 0.75

- __

0 0 4 4 II I-S 4 1* II I 014 012 6:0 U .00S c04 CO2 'U 11 .7 .1

THE OPTIMUM DIAMETER OF MARINE PROPELLERS: A NEWDESIGN APPROACH 75

p

Fig. 6=--calculated Values of Optimum & and Efficiency

-

--.

__

..._.__ll

7 1 5 160

--.i

0 44Q +

4E

Ss2IE A B47O Sa21

AU

20 8 +'

/

10 - 12 6 16

.--.

20 22 24 26 28 30

76 THE OPTTh4UM DIAMETER OF MARINE PROPELLERS.: A NEW DESIGN APPROACH IC 9 a 7 6 S 4 2 0 I0 8 7 X=R 6 5 4 3 6 0 OPT%MaI UFICIL,dCYLOCAL

I)

CONDIT

30

9- i-O

it

K'1

-.

C1TrANØ

Fig 7Comparison of Betzcondition with that for Optimum

Local Efficiency (With Drag) J - 0 80 (Uniform Stream)

/

a is

2 3 4 5 6 .7 6 .9 C

ri

%1rm & z1rm

THE OPTIMUM DIAMETER OF MARINE -PROPELLERS A NEW DESIGN APPROACH 77

Fig. 9Comparison of Thrust and Torque Grading curves, for conditions (1), (2) and (3)

-

_________

______lii.

I,,, 4 3

/

2/

-

/

I,,

I

-

--78 THE OPTIMUM D1AMFER OF MARINE PROPELLERS A NEW DESIGN APPROACH 9 8 -7 6 5

4

3 a 0 -2 .3

.4

J

J.o .I C. .5 .?

7

4 5 'G

(1ui)

Fig. 10Radial Variation of (1 - w') for Taylor Wake 032

:0 ).qo (r ,.80 ,70 V e 0' qS -105 -1.10 oqo

_.080

Ii t4 VARIP1G WITH Cia) DIAMETER

----.

(.. -CONS1ANT :1k), 3Z V. -:

-(8wINo)

H V COTW,TION5 V -4yo7.CoN5TNT T32 (4o. 070

COHDIT1ONS 4om7..CoNTaNT LKaM. V

-CONO) 015 8TOI WV.A_ B' .. V-W V -V V V V -V V I CONDI o1 V 8ro-I2 V [TANV T0WE /z(TA1e-I-L.-VA TANfr)1 -. V V V V' o85 o qo

oqs

-100 I05' -SCALE OF

I-

_z

'U ID

z

80 THE OPTIMUM DIAMETER OF MARINE PROPELLERS A NEW DESIGN APPROACH

Jl

f.

J

Fir. 24Curves

of CL for x = Q875

'.9

z

C' in

z

74 Vi

WA VA

V7AWA

WA

VAVAVAA'

DEEd/A

39 A 4 4

___aA.Roio.oO5

(uiTERUS OF &

-Plate II

J

J!

Fig. J(5

"The Optimum, Diameter of Marine Propellers; A New Design .Approach".

Paper by ProfessoI

L. C. BURRILL, M;Sc., PliD., Vice- resident

z

III 2 I-2 Li) 2

Fig. i6

Figs. 15, 16, 17K'r, K'Q and , curves for x = 075

50 48

46

.44

z

42

2

40

88 36 32 0 Fig. 17

IA VA VA VA

VA

3#MMMI

74VAi7AV

VAAVA::

-:

1

;

:-r

VA

VA VA

1áfM4 fl/i/A

IVADMAVA

7A VA WA'

AO5Ox=7S

' A4D)

filiAl A/I50

17/A

WIAWI1IIW.

VillA

IIJ

ii

Ii1iiUIILWi/A:

A

WIIiiW/A

V111114//A

_______

-H

BARO5o

x=o75.

CURVE'S OF

(IN TERMS OF TAW0ENT/

V/

' OPTIMUM ENCY LIKE

0

0

I-

wo

I!,

z

0

05

06

0.7

JI

06

0. I. I.

z

nl

z

-I

:11rAAr4:

UIffiAAVM4

A7ilAFI1

42d4iAifJfM

CURVES OF

;VA'W1AWAIi:

$PAVAVAM/A_

JW7ilMA

IA.R. O50.

x 0175.

CURVES OF KIT. TANGENTa (u4 TERMS OF .3 a

jiiwi#ivi

U 'O 044 044 042 040 0 5

.1111 VA 11111

111/i VII WA

111111

JIIIIuMWA

Jill I

8 0

o.4

LA.R.050.

x =0875.

riiiviir

-.

(IN TIRM$ OF 3' TAHGENTØ)032 OPTIMUM FFICIE$CY LIKE -IS A FUNCTION OF

"The Qptimum Diameter

of

Marine Propellers; A New Design Approach ".

Paper by Professor L. C. 'BURRILL, M.SC., Ph.D.,

Vice-President Plate I .5 8

la

Fig. 13 Figs.

12, 13, 14.K'T, K'0

and 'Jr

curves for x = O87S

.5 7 8

Ii

Jl

P7g. 12

05

06

07

08

,jiO9

t0

I.'

ia

Fig. 14 I-z 2 w IJ 2 2

13

I2

₀₇

₀₆

_{0-5 0-4}

04

.

.05

.4 0-5

ag

O6

07

Fig. 21

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"The Optimum Diameter

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Marine Propellers; A New Design Approach".

Paper by Professor L. BURRILL,M.SC., Ph.D., Vice-President

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"The Opzimim Diameter ofAfarine Propellers: A New Design Approach ". Paper by IFofessor i... C. BLJRRILL, M.SC., Ph.D. Member

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THE OPTIMtJM DIAMETER or MARINE ?RoI'ELLER A NEW DESIGN APPROACH 1

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82 THE OPTIMUM DIAMETER OP MARINE PROPELLERS: A NEW DESIGN APPROACH cA1E CF

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DISCUSSION ON "TEE OPTIMUM DIAMETER OF

MARINE PROPELLERS:

..

A NEW DESIGN APPROACH

" *

THE PRESIDENT (Mr. P. L. Jones): On hearing this paper I must say it is a

matter of mystery to me how Professor

Burrill can possibly find the time to carry

out so much research and detailed

investi-gation on top of all his academic and

administrative work at the University.

Somewhere in the paper he says that a propeller of 22 ft. diameter could be

re-placed by one of 19 ft. 6 in. diameter designed

according to the theory described in the

paper, and that the efficiency would be

increased thereby.

In order to ensure

that the designed power is absorbed at the same number of revolutions per minute the

smaller propeller would, of course, have

to have a correspondingly increased effective pitch resulting in a greatly increased pitch

ratio; I would like to ask whether the

resulting increase in efficiency claimed by

the Author is not due to some extent to

this fact, quite apart from other alterations in detailed design;

It would be interesting to know whether Professor Burrill has sufficient faith in his new theory to feel that a shipbüilder could

guarantee that the speed obtained, not

onl, on trial, but under service conditions,

would be as good with the 19 ft. 6 in.

propeller as with that of 22 ft; diameter. Personally I will admit that I have a very

strong preference for the bigger propeller.

I agree that this may be difficult to justify

but it is a fact that the view which is

generally held in the shipbuilding profession is that, other things being equal, the bigger

the propeller diameter the better. The

Author was, in his early days, engaged in

the practice of shipbuilding, and I shall be glad to have his views on this pOint.

Dr W. MUCKLE, Member of Council:

I have lead this paper with considerable

interest and it is pleasing to see that in

these days when everything is becoming

bigger and better than ever, Professor

Burrill is recommending smaller and better propellers. The way in which the Author

has approached this problem appears to be

a \'ery sound one indeed. Clearly

every-thing depends upon the accuracy of the

basic theory and he has therCfore checked

his theory against reliable experimental * Paper . by Professor L. C. Bürrill, Ph.D.,.

Vice-President. . See p. 57 ante.

data. It comes as something of a surprise to me to find that that theory is now suffici-ently far advanced -to permit of its replacing

experimental results for the purpose of

designing -a propeller It is evident, how-ever, from the results in the paper that this is so and one reason why such goOd results are achieved is probably- because the

comparison is made for optimum conditions.

As this is the normal design condition it

seems to be perfectly satisfactory.

The striking result of the- paper is that

when the propeller is designed for variable wake -conditions the diameter of thC

propeller can be less than for the ordinary open-water condition without loss in

efficiency or with even a- slight gain in efficiency as indicated in Fig. 11. A point

here is that as account is taken of the

different wake distribution as the diameter is diminished the-average wake is increased.

It would be interesting therefore to know how much Of the improved performance could be accounted for by the increased

hull efficiency brought -about by the higher

wake and how much can be attributed to

the impEoved efficiency of the propeller

It would seem that the reduction -in

propeller diameter of the -order of 5 per

cent would reduce the blade- area by

something like 10 per cent as compared with propellers designed on the ordinary

principle. It would be of interest to know,

therefore, whether the Author considers

that this might in the case of heavily

loaded propellers lead to cavitationproblems. A further point in connexion with wake

distribution is that the wakes assumed in

the paper are presumably for single-screw ships. In twin-screw ships reduction in

the optimum diameter might not be pOssible

because of the low intensity of wake in any case; although by so -doing it might

be possible to set the shaft centre lines

nearer the h011 and so obtain a slightly

higher wake.

The method advocated by the Author leads to the determination of the hydro-dynamic pitch of the propeller. The-designer still has to clothe a real propeller round -this hydrodynamic pitch distribution. This means that the final result may differ -to -a considerable extent depending upon the data used by the designer for such

D2 THE OPTIMUM DIAMETER OF MARINE PROPELLERS: A NEW DESIGN APPROACH

of these quantities would appear to be still a little uncertain as to their exact magnitude

it may turn out that the best propeller is

not obtained finally. Only the application

of this method in practice can possibly

decide such matters.. The design procedure

outlined in the paper should be of great assistance in explaining the method pro-posed by the Author.

It would be of interest to know what

influence the variation in propeller wake round the revolution would have on the

results. If the propeller is designed for

the mean wake at any particular radius, at

some parts of the revolution it will be in more intense vake and at others it will be iii less intense wake so that the angles of

incidence of the blade sections will fluctuate. This of course always happens but it would be of interest tO. know whether the effect

would be more critical with the method of design proposed by the Author.

Turning nOw to the question of roOt.

sections, I think that it is indicated in the paper that these sections might be hollow

faced. This is rather a startling conclusion

since the practice in the past appears to

have, been to introduce face camber on

these sections, with a view to reducing

cavitation. Might it not be expected,

therefore, that some cavitation danger

will exist with this new method of design

of these sectidns?

The final matter which I have to misc

concerns the question of force distribution on the blade. The curves in Fig. 9 indicate

that with the new method of design the inner sections are more heavily loaded

than with propellers of conventional design.

The effect o this is that for given thrust

and torque the centroids of the forces will

be nearer the root with the net result that the bending moments on the root sections will be reduded. This should permit a

reduction in scantlings of the blades which

should lead to reduction in weight in

addition to that due to reduction in diameter. Also it would seem that with thinner blades a slight improvement in efficiency might be expected.

In conclusion it may be said that the

Author appeais to have opened up a new

field in propeller design and that the paper is an exceedingly valuable one on .a

fascin-ating and intriguing problem.

Mr. N. CARTER, Member of Council:

Despite the fact that the design of

propellers has now developed into a science

understood only by the expert mathe-matician, Professor Burrill has tonight given .us a paper both instructive and

interesting.

It would appear that by hollowing the driving face of the propeller, additional

thrust is developed, and the Author suggests reducing the diameter to restore the balance.

The concave face probably moves the

centre of pressure aft on the blade, thus

virtually increasing the pitch, and it seems

probable that by making the curve of a parabolic form, even further advantage

might be gained.

Mr. J. W. ENGLISH, Student:

Professor Burrill has shown us this

evening that the loss in overall efficiency

due to reducing the optimum chart diameter

by as much as 15 per cent and possibly

more is negligible, provided that sections

can be designed to operate at their minimum drag coefficients. For restricted diameters this involves using sections with high

camber ratios, and possibly hollow faces,

as the use of increased incidence and hence pitch, which is the. method usually adopted by propeller designers, carries with it rather

large increases in drag.

In the past,

I believe, experiments with propellers using highly cambered sections in an attempt, to

obtain .shockless entry conditions have

been disappointing in both performance

and cavitation characteristics. This is thought to be due to our rather limited

knowledge of the curvature problem, and,

since the Author adheres to the simple

two-dimensional cascade corrections,, I wonder whether reliable sections can be designed on this basis. I would like, to

hear the Author's views on this matter

as I think discrepancies might be felt for large reductions from the optimum

open-water diameter.

I have found that the Author's new wake

design condition gives reasonable results when compared' with existing propellers, the comparison being made on the basis of effective pitch; the pitch curves were

quite fair, except possibly at the root when the camber is low, but this is probably due

to the Goldstein factors in this region

increasing above unity, as these factors are' uncorrected for the existence of a boss. Mr. F. I. LEATHARD, Associate Meniber:

-Having been privileged to carry out.some of the work entailed in this very interesting paper by Professor Burrill, I should like to

add to the discussion.

By taking the original section camber

lines for the model screw KCB 4 and modi-fying these to the required values of

centre-line camber (y/c) given in Fig. 28, for

screws of O85, 090, 095 and, I -00D/Do,

the new camber lines can be drawn. The fairings or streamlined bodies of KCB 4 sections can then be superimposed on the

new camber lines to give the final section' profiles. From the drawing

of these

sections, it will be seen that for the screws

ofD/Do= O85 and 090, the face of each

section considered will be hollow. At the

sectionr/R = 025 of the085D/Doscrew, the maximum face' ordinate is 0124 in. in a chord of 387 in, The sectiOns for

3:87'

0-124'

--0.875 075 '0.25

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