Comparing four methods of marine propeller design

\TEN

A tion of the agree that truthfully numerous

NAVAL architect approaches an examina-world of propeller design he is likely to

James Joyce's "world without end" is

"whirled without aimed." There are

paths which exist for the design of

ma-rine propellers, and one is confronted with

difficul-ties in comparing and evaluating these different

paths.

Four design methods have been applied by the

writer to the calculation of propellers for a variable wake single screw Tanker and a twin screw Liner.

The methods applied were those of Burrill,

Eck-hardt and Morgan, Wageningen (according to Van

Manen), and hill, as outlined in the referenced

publications. Each method, while based on the

vor-tex theory calculation of lift, thrust and torque,

differs in the initial assumption of the minimum

energy loss condition, and in the correction factors applied for determining the camber and mean line

pitch angle necessary to develop the required lift,

COMPARING FOUR

METHODS

OF MARIIVE PROPELLER DESIGN

THE AUTHOR

prepared this paper while a Society of Naval Architects and Marine

ngi-neering post-graduate student (1957-58) im naval architecture at King's

Col-lege, University of Durham, Newcastle Upon Tyne, England. He is employed

by the Electric Boat Division of General Dynamics Corporation, and is a

graduate of Webb Institute.

INTRODUCTION

thrust and torque. Burrill uses the Gutsche datá

for corrections, Eckhardt and Morgan use the

Lud-wig-Ginzel camber corrections and Lerbs lifting surface corrections, Van Manen uses the

Ludwig-Ginzel camber correction, and Hill uses empirically derived correction factors.

The object of this paper has been to compare the

four design methods considered, by applicatin to

the de.gn of propellers for two widely differing

ships. It is a hydrodynamic study, and all designs

have been based on thrust identity. No detailed

strength calculations have been made for the pro-pellers. Curves are presented sho;ing the angles of resultant velocity distribution, lift distribution,

camber ratio, incidence angle, pitch, ratio, and effective pitch ratio. In addition the approximate pressure distributions have been calculated at two of the outer blade sections for each propeller, and the results plotted. Typical pressure distribution

calculations are given in the Appendix.

NOMENCLATTTaE r. = axial inflow factor at propeller a' = rotational inflow factor at propeller B(mid) = moulded breadth

b = blade section length

(b' =aver age blade width from the tip to any sec-tion in Hill method.)

BAR, blade area ratio c = blade section length

C1, = block coefficient

C = midship section coefficient

C,., = vertical prismatic coefficient CT = thrust coefficient

CT. = thrust coefficient based on ship speed

CT1 = ideal thrust coefficient

C. = power coefficient - ideal powei coefficient

= lift coefficient

C NACA data design lift coefficient

C1 drag coefficient

D = maximum propellei diameter Dr = draft

EHP effective horsepowei

f maximum camber of mean line 2rr

(g gap ratio in Hill method (g=

J' = advance coefficient

= advance coefficient based on ship speed Goldstein function

thrust coefficient based on propeller

revo-lutions

= local thrust coefficient based on propellei

revolutions

KQ torque coefficient based on propeller

revolu-tions

K'Q = local torque coefficient based on propeller

revolutions

slope rorrection to lift angle, between theo-iy and experiment

K, correction to no-lift angle. between theory and experiment

blade section length

LBP = length between perpendiculars

LWL waterline length

n propeller revolutions per minute

'li = ideal propeller efficiency

Th hull efficiency

PfD - pitch ratio, where pitch is measured to the nose-tail line

p/q = pressure coefficient

q.p.c. = quasi-propulsive coefficient

R = maximum propeller radius r = radius at any blade section T = propeller thrust

THP = thrust horsepower t = thrust deduction fraction t' = local thrust deduction fraction V = ship speed in knots

speed of advance

= velocity distribution over an aerofoi.l

sec--

tion at zero angle of attack

1iV _{velocity distribution over an aerofoil}

see-V = tion corresponding to the design load dis-tribution of the mean line

Ua

= velocity distribution over an aei-ofoil cor-responding to the additional load distri-bution associated with ancle of attack.

W = resu,lant inflow velocity ahead of blade

section

W' resultant exit velocity behind blade section w = Taylor wake fraction (mean)

w' = local wake fraction

x = nondimensional radius (nR) y = maximum camber of mean line

. y = curvature correction to mean line

Z = number of blades p = mass density of fluid

À = advance coefficient based on speed of

ad-vance

X0 = advance coefficient based on ship speed

= advance angle

ß, 4, = hydrodynamic pitch angle

(4, pitch angle at any radius by the Hill

method.)

= ultimate wake pitch angle

x = change in angle during flow curvature past a blade section

tan y = drag-lift ratio = cavitation number

(o = Folidity in the Burrill method ((1=

= displacement

Zi'

An effort has been made to use the nomenclature

adopted by authors in the list of references. As a

result, in some cases different symbols are used for the same terms. Nomenclature not defined above is

defined in the text of the paper.

DESIGN PARTICULARS

Following are the particulars for each of the pro-peller designs undertaken.

Single Screw Twin Screw

Tanker Liner LBP B (mid.) Dr. C. (LBP) C,', Head above C n V (service) Taylor w (mean) EHP (naked) EHP (service) T 550 TI-IP (scrvice) 1.688V (1w) T C p!2 I- (1.688 V) T KT

/ n \

pl .60 1 675' 98' 37.9, 57,570 tons .801 .990 .920 25' 105 rpni 16 knots .34 .19 9,822 (model data) 13,260 (esti-mated 333,000 lbs. 1.090 .190 740' 97, 32.0' 39.300 tons .574 .766 20 147 rpm 25.75 knots .09 .08 35,600 (model data) 43,700 (esti-mated) 601,000 1hs. (total) .543 (each) .182 (each)

DETERMINATION OF WAKE VARIATION

Given the Taylor wake fraction for the twin

screw Liner and single screw Tanker, it was

neces-sary to determine the radial distribution of wake. The Van Lammeren wake distribution was adopt-ed," adjusted and integrated to give the originally assumed wake according to the momentum mean

given by Yamagata,14

¡R

_{w' (1w') r dr}

where

_{.c (1w) rdr}

The wake variations are plotted in figures 1 and 2 for the Liner and the Tanker.

SELECTING THE OPTIMUM DIAMETER

An optimum diameter was selected for the Liner and Tanker, and the four design methods under ex-ainination used the same diameter for each

propel-ler. Eckhardt and Morgan recommend taking 97

percent of the open water optimum for twin screw

"IR Tanker Figure 1 tip "Io 'fc A 5.- 1O S "Liner" Figure 3

ships, and 95 percent of the open water optimum

for single screw ships, as given by the Troost series. This reduction compensates both for scale effect and

the open water testing of the model screws by

Troost. The diameter found by this "experience" reduction was used for the Tanker propeller.

Burrill has developed a method for

systematical-ly determining the optimum diameter for wake

adapted propellers. A wake variation is assumed

for the ship. By placing smaller diameter propellers

in this wake the mean effective wake acting over the disc increases, making possible higher

propul-sive coefficients at diameters below the Troost open water optimum. Thern calculations are made using a

series of K'TJ' and K'QJ' charts ° which, have

been developed for B.A.R..50 and minimum drag.

By calculating several diameters, the optimum

di-ameter may be selected from a curve of didi-ameter

vs. q.p.c.

KT

1t

.P.c.=__XJ.X

-i---where (1t) is assumed constant, reard1ess of the diameter of propeller. Recent self propulsion tesis

of a tanker model by the National Physical Labora-tory have shown higher q.p.c.'s at as low as 90 per-cent of open water optimum diameter, and have also

shown "t" to decrease with decreasing diameter.

Calculations were made to predict the Burrill

optimum diameters for the Liner and Tanker, and

the results arc plotted in figure 3.

A.S.N,E. Journ,,, A.00st 9Ó0 4ì7

1t

_{1.23 1.01}

1w

Propeller Diameter 23-2" 19-4" Number of Blades 5 4 101.27V .666 .918 nD 101.27V mD .212 .292 THP (service) =

EHP (service) 1 10,790 43,250 (total)

--%

q. pc. q .4 438 "IR

/

i

A.S.N.E. Journal. Auçust 19b0

o s_o li 7o -Figure 3

.,

"-IR

I

Burrill Method. _{se-tan=constant} (based on Theodorsen) (10)

Eckhardt & Morgan Method. tanß

(1_w'\l

xrtanr = constant tanß I S 4 «A*T I .«C4t I t «b S S

It is evident that the q.p.c. vs. diimcter curves

plotted show higher q.p.c.'s at somewhat lower than

the open water optimum diarne 1ers derived from

the Troost curves. The curves are relatively flat

over the range calculated, and ii.tdicate that the

diameter may be varied considerably with only a

small decrease in q.p.c. The Liner propeller diame-ter was chosen to be 19'-4" and the Tanker, 23'-2". It is noted that the Tanker propeller diameter cou!d

have been reduced, according to the Burrill

meth-od of selection.

Despite the many conditions aciped for

mini-mum energy loss, it has been shown on several

oc-casions that the resulting propeller efficiencies do

not vary greatly. and that no one nl the above con-ditions is preferred over another from an efficiency standpoint. To quote,2

From the point of view of overall emcicicy, and apw from any consideration of cavitation or flow brcakdow. there appears to be no material advantage to be gameti

from the adoption of a radial variation of pitch, both in a uniform and in a variable wake stream..

The condition of minimum energy loss adopted

predicates the thrust loading distribution for a

pro-peller. This

_{is evident when one compares the}

x.tanß and x.tanß1 curves for the Hill method.

which deliberately reduces the leading near the tip

and hub, with those for the other methods (figures

4 and 5). It will be seen that the same difference is reflected in the C1, curves (figures 6 and 7) and

I

(based on Lerbs) (11)

tanf377iI\1w )

WageningenMethod. tanß

fiw'

tane

_77 - constant

,7cOflstant

(based on Troost & _tanß

_1wi

Vari Manen) (4)

Hill Method. tanß tanß

- constant _?71 _Consthnt

(based on Betz) (12) _{tanß1 tanß}

CONDITIONS OF MINIMUM ENERGY LOSS

Variable Wake Uniform Wake

CONDITIONS OF MINIMUM ENERGY LOSS

The Betz condition for the optimum efficiency of lightly loaded propellers is initially used by Hill for

both the design of propellers in variable and uni-form wakes. The thrust distribution is then altered

by Hill in order to reduce tip loading, consequently

changing the values of tan ß as determined from

the Betz condition. The Wageningen and Eckhardt

and Morgan methods use the Betz condition for

propellers in a uniform wake; and the Burrill

meth-od where x.-.tanr=constant for the uniform wake is essentially the same as the Betz condition, since

in both conditions the vortex sheets in the ultimate

wake are assumed to move aft in rigid sheets of uniform pitch.

In both the Burrill' and Eckhardt and

Mor-gan 511 methods, in deriving the optimum efficiency

condition for a variable wàke, the local thrust de-duction factor is assumed constant over the disc,

while in the Wageningen method it is assumed that

1t'

(1w's%

1t

\1w J

TA"4f.K t2 D (;) 2I Ttn

t.

I - T*n £ X Tu

t

L_r Cr. Figure 6. Tanker Figure 8. Tanker

- .-5'

Figure 7. Liner t-

t

'7

-j

4

.5 Pflc.,4 RATrO

Ac pnrcn RATIO Et'FECTI' PITCI.4

THRTJST, DRAG, AND EFFICIENCY

We have seen that the hydrodynamic pitch angle

(ß) is determined differently by each of the four

methods. All methods, however, employ,

i

4r.x.k

CL--=

_-

sinß tan (ß-f3)

to determine the circulation distribution. k" is the

Goldstein correction factor corresponding to ß,

ex-cept by Bun-ill, where k corresponds to the ulti-mate stream pitch angle (e).

In the Eckhardt and Morgan and the Hill

meth-ods, thrust and power are calculated from the ideal thrust and power distributions, assuming values of

CD.

(i t)

(i+ _LJ1)

Eckhardt and Morgan assume CD=.008 for all

sections, regardless of section thickness ratio or

in-cidence angle. Hill, on the other hand, takes C as derived from Gutsche experiments where CI) is de-pendent on thickness ratio and incidence angle. The

minimum value of C=.0075 occurs at zero mci-dence angle and about .05 thickness ratio. Bun-ill.

plots minimum CD values for aerof oil sections as a function of thickness ratio, and finds the minimum

dCT dCT

dxdx

dC1 dCv,

clx - dx

Cr.M*tDT **AA,&?. 5ut*rnj.. n.J&*t.J.4GS.._______J / s Figure 10. Tanker &CAMtCDT 4OCÚ.M -- bORtILL w**tN,MtN Figure 11. Liner

rtCCT,VE I1CN RATLD

'L

r j r i

A.S.N.E. Journa'. August 960 439

t I

j

j _{4 5} b

r j n

CAtSFP RATIO _{AT4t4Lt (DEG..)}

Figure 9. Liner

ultimately on the effective pitch curves (figures 10

& 11). In calculating x.tanß by the Wageningen

method 97 percent of the RPM is used (scale effect

correction), resulting in higher x tanß values than given by the other methods. Also, in calculating

x.tanß, the Kramer 71i is reduced to correct for the

difference between the pitch of the wake adapted

screw and the comparable B-series screw. Thus, the higher x.tanß values. These corrections applied by Wageningen in the first stages of a propeller design are essentially pitch corrections. (In making the

correction the thrust can no longer be determined

from the C, distribution calculated.) The other

methods make pitch corrections during the later

stages of design, in allotting camber and incidence

angle.

'4

CD=.0082. It would therefore seem that the Eck-hardt arid Morgan constant C0=.008 is rather low and would consequently predict higher propeller efficiencies than the Hill and Burrill methods for propellers with high section thickness ratio. (See the Tanker and Liner propeller efficiencies given in Table I.)

TABLE I

The Burri.11 method assumes minimum profile

drag and KT and KQ are based on curves for

B.A.R.=.50. For higher B.A.R.'s it is to be expected

that the drag would be underestimated and

conse-quently the resulting propeller efficiency would be

too high. In the Liner design considerably higher

B.A.R. ratios were adopted, the Eurrill K'T and K'Q charts therefore predicting high propeller

efficien-cies. The expressions for K'T and K' should

there-fore be calculated for B.A.R.'s considerably higher than .50, rather than using the K'T and K'Q charts.

The expressions for K'T and K'Q are:

K'« (1

a')2 (1+tan2)

sin (+r)

cos r

K'

_{x.tan (+r)}

2K'Q

(tnqtan).tan (4+r)

where a'= _{1+tan çf) t}

_(+r)

The Tanker propeller efficiency by. the Burrill

method is

in good agreement with Hill, where

B.A.R.=.584. For the Liner and Tanker propellers Eckhardt and Morgan predict higher efficiencies where C0=.008 appears low for the higher

thick-ness ratios adopted.

DIVIDING UP CAMBER AND INCIDENCE ANGLE

Burrili Method

If camber is allowed to entirely develop the

re-quired C1, at a given section, according to theory: i

«oTIi= .0 radians

where a,1.11= theoretical no lift angle of camber.

From experimental results, however, for a single

aerofoil,

«oACT=Kan.

where Ks,, is an experimental correction factor

ob-tained from wind tunnel results and is dependent on thickness ratio and the position of maximum

camber.

When an aerofoil is in cascade, as is the case of a propeller blade, there is an effective increase in the

resultant hydrodynamic inflow angle at each sec-tion due to a change in flow around each secsec-tion. This increase in angle may be represented by iag:

Ka0.

where Kac is based on Gutsche's experiments, and

is a function of the hydrodvnamic pitch angle and the cascade geometry. By Burrill's method is

added to the required incidence angle in order to

compensate for cascade effect, and allows the

cam-ber to develop its full experimental lift value, as shown below:

Zir A'. JI...

From cascade experimental data, the required

to-tal no lift angle may be represented by:

i

i

a2,5( =

K, . . C.

where K, is a slope correction to the CL curve in

going from a theoretical aerofoil to an actual single aerofoil, and is a function of thickness ratio. Km is the Gutsche slope correction to the C1. curve when going from an actual single aerofoil to cascade, and

is a function of the hydrodynamic pitch angle and

the cascade geometry.

It follows, therefore, according to Burrill that the

total angle of incidence (ai) is: al «COR. ±-«m«,,lCT

In converting the camber no lift angle into the appropriate camber, Burrill uses:

J.

(Y'

c K, K5,, e

where

is based on the NACA. aerotoi

re-suits T _{(i.e. for a.S mean line T11.0679 C1).}

In using the a=.8 mean line NACA data it must be remembered that C1,, T is based on an angle of in-cidence as well as camber, and therefore the theo-retical camber no lift angle must be reduced

ac-cordingly.

Eck hardt and Morgan Method

For viscous flow the a.8 mean tine is

recoIn-mended where the camber ratio is equal to .0679 C1,. This camber ratio must be multiplied by two curvature corrections (k1, k) which are functions of the expanded area ratio, and are based on

Eck-hardt and Morgan's evaluation of all numerical

re-Propeller Efficiencies for: Tanker Liner

Burrill Method .545 .705

Eckhardt and Morgan Method .575 .682

Hill Method .550 .640

suits available inì propeller literature. Ludwig and

Ginzel's work on the curvature of flow at the half-way point of each section forms the basis for

Eck-hardt and Morgan's camber curvature corrections.

Further, Lerbs' work on the change of curvature of

flow over the chord length is used to make up for the deficiency in pitch which results in applying

only the Ludwig-Ginzel corrections. The addition-al corrections needed to make up for this pitch de-ficiency are put into angle of incidence. These

cor-rections are necessitated by three factors: blade friction, ideal angle of attack of the mean line, and correction from lifting surface effect. The first two

corrections are combined into one angle of attack ,

which for the a=.8 mean line is: a1.15 C7,

degrees. Correction for lifting surface effect arising from the free and bound vortices is based on a sim-plification of Lerbs' rigorous method of calculation.8

This lifting surface correction is made to the face pitch ratio, such that the final pitch ratio:

\ P/D

P!D=x tan (ß1+a,) (1-f

_PfD

P/D thri (ßj+a2).7 where 1+

PfD tan ¡3.7

and =angle of attack from lifting surface effect.5 PID _{is at the .7 radius.}

Wa.genin.gen Metlwd

Van Manen adopts the Karman-Trefftz profiles, which are built up of two circular arcs, and reads directly from cavitation charts for these profiles

(theoretically calculated at shockfree entrance) the

effective camber ratio required for a given

thick-ness ratio and lift coefficient. The effective camber

ratio found is then corrected for curvature of flow

using the Ludwig and Ginzei curvature corrections

(k); and, further, a friction correction is made

where 35 percent of the frictional decrease in circu-lation is put into angle of incidence and 5 percent into a camber ratio correction. The friction correc-tion factor p. is taken as a constant value of .75.

(1/L

_{\ ( i}

f.rr.

f 1.3+.7i'. I. 1 f..,.

--geom.=

-1 2 k

HILL Method b'.C1

Hill uses an empirical expression 15R(1x)

as the corrective addition to the theoretical lift co-efficient due to the flow around the propeller blade lip from the high pressure area on the blade face to

the low pressure area on the back. The lift

coeffi-cient, as corrected for tip flow, is obtained then by

using the blade section camber theoretically

re-P/D

quired to develop the given lift

coefficient. Hill adopts a1 camber, because at the time of his paper it was thought that this gave a nearly uniform pres-.

sure distribution (for shockless entry), and hence

was best from a cavitation standpoint. Theoretically

for a=i camber a lift coefficient of 1.0 requires a

camber ratio

of .05515. Experiments, howevei-, showed that only 74 percent of the theoretical lift

is actually obtained, whereas for circular arc cani-ber 80 percent of the theoretical lift is obtained. For'

a=1 camber the remaining 26 percent of CL is put in angle of incidence. With an angle of incidence

CL is increased at the rate of .1097 per degree.

In addition a curvature correction based on ex-periment is found, which is a function of the

num-ber of blades and and contrary

(gsin- -) cos

to earlier experience, according to the Hill method decreases with an increasing number of blades. This

additional CL required due to the curvature

cor-rection is developed by putting half in camber and

half in angle of incidence. The camber ratio

re-quired for the curvature correction is .10 times the curvature correction expressed in terms of

addi-tional CL. Hence circular arc camber is added to the a=1 camber initially calculated. There is some

cori-fusion on this point in the Hill paper. The design example worked by Hill is done in the manner

de-scribed above, and according to test results is found

in excellent agreement with the actual propeller

model performance. On the other hand, in the

"Comparison of Experiment and Theory" given

earlier in the paper, Hill states:

several propellers were designed using a=1 camber

for the theoretical lift and the tip correction and circular arc for the curvature correction. The experimental thrust

and power coefficients for the wide-bladod propellers D and E were considerably below the calcuiatLd values, but thc reverse was true for the narrow bladed propellers F and G.

- . . The results obtained with propellers D and E indicate

that the combination of two different types of camber is

not satisfactory since it cannot be presumed that each type

of camber will oerform the function for w rich it is intended.

- . - In order to substantiate further the indications that the

combination of circular arc and a1 cr1i>cr behaves as

though all the camber were a circular arc, propeiicr i was made. Propeller I was identical with propeiiti D n all i-e-spccts including the camber ratio of each section. except

that all the camber was circular arc. The experimentally

determined thrust and torque coellicients of propellers D and I were identical.

Despite the fact that, according to Hill above experimental data, all the camber acted as if it were circular arc camber, the camber was calculated for the three designs included in this paper, as hull does in his worked example. Later, in ev;iluating camber

in terms of no lift angle, the cambi-r is considered to be all circular arc camber.

COMMENTING ON CAMBER AND INCIDENCE ANGLE

Camber Ratio

Regardless of the various data and different mean

lines adopted by the four methods in determining

the appropriate corrections to camber ând incidence

angle, it is interesting to note that ali but the

Bur-ri11 method require approximately the same camber

ratios at the .7 radius for the Liner and Tanker

designs (see figures 8 and 9). The Burrill method gave lower camber ratios at the .7 radius. Those required for the Burrill designs were based _{on the} theoretical realtionship between camber and lift

coefficient given in Reference (7) for an a=.8 mean

line:

y_ .0679

-CL

c _IÇ.Ka,,

where K, and Ka, are experimental correction fac-tors for slope and camber no lift angle.1 Burrill, however, in the Discussion Section of Reference

(1) has pointed out that the theoretical relationship should be taken as .10 (not as .079 as given in

Ref-erence (7) for NACA 6G mean line) when using NACA four-digit type centerline cambers. It is to

be supposed that similar increase should be made for the a=.8 mean line. Because no data was

avail-able, however, the calculations made for the two Bun-ill Designs adopted .0679.

Eckhardt and Morgan reduce camber to zero at

the tip, and Hill's camber approaches zero. Hill also reduces camber near the hub, whereas Bun-ill calls

for continually increasing cambers at the inner

radii. The Wageningen method increases camber at both the inner and outer radii. This increase in

cam-ber by the Wageningen method at the outer radii shows bad cavitation characteristics

(to be

dis-cussed later).

ANGLE OF INCIDENCE AND PITCH RATIO

The curves of incidence angle (figures 8 and 9) allowed by the Wageningen method show much lower values than obtained by the other methods.

Actually, the Wageningen incidence angles would be higher than indicated, if measured from thesame

norm as used by the other methods. The curves of incidence angles plotted were measured from the

calculated hydrodynamic pitch angle, which it will

be remembered was increased in the first stage of the Wageningen design by reducing the Kramer

. This is evident in the pitch ratio curves for the three designs (figures 10 and 11) where the

Wagen-ingen pitch is in better agreement with those cal-culated by other methods. While the agreement is

better, it will be remembered that the Wageningen incidence angles are purposely kept low, with hope of attaining shockless entry.

The Liner and Tanker designs show good agree-ment on incidence angle between the Bun-ill,

Eck-hardt and Morgan, and Hill methods

_{at the .7}

ra-dius. Attention is called to the comparatively _very

high values of incidence angles determined _{by the}

Bun-ill method at the inner radii for the Tanker

and Liner. (This is also reflected in the pitch _ratio curves.) The Gutsche cascade correction factors

(Keg and Kgs) determined from limited wind

tun-nel experiments require high incidence angles aT

the inner radii where the data show that cascade

effect plays a major role. Recent work in propeller

design has taken a skeptical view towards the va-lidity of these Gutsche cascade corrections.

EFFECTIVE PITCH RATIO

Effective pitch ratio may be interpreted

as a

measure of the intended thrust loading distribution on a propeller.

effective pitch ratio=x-r.tan (ß+a1±a,) where a1incidence angle measured to thenose tail line and a0=eamber no lift angle. The Eckhardt _and

Morgan and Bun-ill methods both employ expres-sions for determining a,. The (A) effecti'ce pitch ratio curves (figures 10 and 11) for the Eckhardt

and Morgan and Burrill methods are based on these

expressions.t The (B) curves and the Wageningen

and the Hill effective pitch ratios have all been

cal-culated on another basis, where camber is

evalu-ated by means of one expression, regardless of the

type of mean line. It is assumed that the lift

con-tribution of camber, CLI 10 -t, and that it may be

converted into camber no lift angle by means of the theoretical relation

a,,.

CLI or a=91.2 -i-. The

mean effective pitch ratios haie been calculated

(Table II), where:

Mean Effective Pitch Ratio

r j Eff PfD

TABLE II

If the .7 radius is considered the basis _for coni-parison, all four methods show fair _{agreement on} the effective pitch ratios needed for the Liner and Tanker (see figures 10 and 11). The _{mean effective} pitch ratios calculated by the Hill and Eckhardt and

Morgan methods show excellent_{agreement for each} design, whereas the Burrill and Wageningen

effec-tive pitch ratios for the Tanker

_{are considerable}

higher. The Burrill mean effective pitch ratio for * By _{the Eckhardt and Morgan}

method a

.139 CL3 for NACA a=.8 _{mean line and by the}

Bur-nil method tKao.

Mean Effeetive Pitch Ratios for: _{Tanker Liner}

Bun-ill Method (B) .885 1.211

Eckhardt and Morgan Method (B) .825 1.205

Wageningen Method _{.848 1253}

Hill Method _{.828 1.210}

the Liner is in good agreement with that calculated by the Eckhard and Morgan and Hill methods.

When comparing propellers designed by these

several methods it is doubtful whether mean effec-tive pitch ratio is a justifiable basis for comparison.

While the overall agreement may be good on this

basis, the actual lift contribution of camber and in-cidence angle at particular radii may not be as was

intended by the several methods. Effective pitch ratio, or mean effective pitch ratio as a basis for

comparison, would truly be justifiable only for a

se-ries of propellers where the correction factors of

one method had been used in apportioning camber and incidence angle to develop the required thrusts.

CAVITATION

The Eckhardt and Morgan and the Wageningen

methods of propeller design emplpy incipient

cavi-tation charts in selecting the minimum length of blade sections at outer radii for supposed

cavita-tion-free operation.

Eckhardt and Morgan use

NACA section data and Wageningen uses

Karman-Trefftz profile data. The blade widths required by the latter to develop the same lift (see figures 1 &

2) are greater at the outer radii than those required from the NACA section incipient cavitation charts. For the twin screw Liner the blade widths given by

the Karman-Trefftz profile data at the outer radii

were exceedingly high; cOnsequently, reduced

widths were arbitrarily adopted. (i.e. at the .70

ra-dius only 91 percent of the chart width was

adopt-ed.) In both methods 80 percent of the cavitation number (if) based on resultant stream velocity is used for entering the charts. The blade outline

se-lected from the NACA data according to Eckhardt

and Morgan has also been assumed for the Burrill

and the Hill designs of the single screw Tanker and the twin screw Liner.

The following table gives the expanded blade

area ratios which resulted from using the incipient

cavitation charts for the Liner and Tanker

propel-1ers, and the expanded areas recommended by the Burrill cavitation chart.'7 The Burrill chart is based

on actual ship data, and for the Liner and Tanker the expanded blade area ratio given by the chart

is that appropriate to the normal merchant ship line.

Expanded Blade Area Ratio

NACA 66 nose Karrnan-Trefftz arid parabolic profile,

circu-tail with lar arc mean Burrill

a .8 mean line, line and shock- cavitation less entry. data.

Liner (4 blades)

....

.780 .843 (adopted) .738

Tanker (5 blades) .. .584 .642 .575

It is noted from the above that the Burrill ship

data allows lower blade area ratios; that the

in-cipient cavitation charts for Karman-Trefftz profiles

and circular arc mean line require higher blade

area ratios than the NACA section charts require.

Unfortunately, the use of cavitation charts in

se-lecting blade widths does not take account of the

effect of changes in incidence angle on the pressure

distribution. It is desirable, therefore, after having

selected the blade width, face pitch, and camber of the propeller sections, to check the pressure distri-butions at the outer sections. Since each method of design under investigation divides lift between

cam-ber and angle on incidence in different ways,it was

decided to analyze the resulting pressure distribu-tions by an independent line of reasoning. The final geometric carnbers derived by each of the methods were converted to effective cambers and cavitation

was evaluated in terms of the t1eoretical pressure distributions given for NACA sections and mean lines. The remaining lift, not developed by camber, was assumed to be developed by angle of incidence. In developing the corrections to geometric

cam-ber in order to evaluate the theoretically effective

camber the following method is used:

Theoretical effective camber= (geometric

cani-ber) . K K0,= --where K50 is the correction to

the camber no lift angle in going from the experi-mental value of no lift angle to the theorctically required no lift angle for a given C1. value. K is a

slope correction to the line relating C1. and lift

angle to the theoretically require lift angle for a

given C,,. K and K50 are derived from extensive single aerofoil experimentation and are plotted by

Bun-ill in terms of thickness ratio.06

Takeias the curvature orrecüon

to camber in going from the single aerofoil to an actual propeller section working in cascade. In evaluating it is assumed that the induced axial velocities occur

before and after the propeller disc, and not in way of the disc, and that the entire rotational velocity

is induced between 10 perccnt ahead of a blade sec-tion leading edge and 10 percent behind the secsec-tion

trailing edge,'9 and that the curved flow follows a

circular arc which passes through these two points.

The angle x in the diagrams below therefore

represents the total change in angle during flow

Q 2TTnn. VTfl

r

Velocity iaram -0-o '1ow curvature 443

curvature. From the following diagram Io ,/ ,',..s it is evident that, 1 5 ¿ y :1. 5

s1n7-

=--. -i-b. X y

i

=- X

e 9.6 1+a

where X=tan'(thnß.

_1-2a' tan'(tan/3. (1+a))

and a'=

(tan/?-tanf3)tan(/31+r)

1+tanß tan(ß1+r)

tan ß

a= -(1 a') -1

_tana

444 A.S.N.E Jouriral, Au'ust I96

Table III

The curvature correction to camber is in effect a macroscopic correction. It is a corret'tion Ofli to the maximum camber ratio of a section and is mere-ly a device for allowing one to predict the total

con-tribution of camber to lift. In general, the pressure reduction on the forward portion of the back of a propeller blade would be greater, and on the after portion less, than is predicted by this method of calculation. In addition,

if there is considerable

contraction of the slipstream behind the propeller. the angle will be overestimated by this method. Thus, the value of effective camber would be un-derestimated, resulting in a higher contribution o incidence angle to the lift developed. in any case

the prediction of face cavitation at the leading edge would be a conservative one, while a thus

calculat-ed absence of back cavitation would he subject to

review.

The pressure distributions around two of the

outer radii sections were calculated by the above

method for all of the Liner and Tanker designs, and the plotted pressure distribution curves (figures 12

and 13) checked for total CL. Integration of the

curves showed the total CL'S to be from 2 percent

lower to 5 percent higher than the required C,

values. This error was not considered excessive. and Table III is based on the corrected pressure

distributions. Typical pressure distribution

calcula-tions are given in the appendix. Liner Burrill Design

max-

_q (T C, (integrated) . p ¡(T

Corrected

-Cr. (required) q x=.875 .124 .157 .99 .80

x.75

.160 .214 .98 .77 Eckhardt and Morgan Design

x.90

.130 .149 1.04 .83

x.70

212 .243 1.05 .83 Wagehingen Design x=.90 .177 .154 1.05 1.10 x=.70 .203 .251 1.04 .78 Hill Design

x.90

.096 .149 1.00 .64

x.70

.195 .243 1.04 .77 Tanker Bun-ill Design x=.875 .184 .240 1.02 .76 x=.75 .243 .338 1.02 .71 Eckhardt and Morgan Design

x.90

.184 .214 .98 .88 x=.70 .306 .383 1.05 .76 Wageningen Design x=.90 .206 .230 1.05 .86 x=.70 295 .410 1.05 .68 Hill Design x=.90 .151 .214 1.01 .69

x.70

.300 .383 1.05 .74

In entering the NACA incipient cavitation charts.

Eckhardt and Morgan recommend using .8o and

the calculations made on the resulting sections in-dicate a pressure reduction of from .76.r to .88(7.

Using the same blade outline and same type of sec-tion for the Burrill method shows a pressure reduc-tion of .7L7 to .80(T and for the Hill design, which uses a different NACA section and mean line, there

is a pressure reduction of .64-r to .77g. The lower

value, .64g occurs at the .9 radius, where the thrust

loading has been reduced in the Hill method. The

Eckhardt and Morgan, Bun-ill, and Hill designs for

the Liner and Tanker therefore appear cavitation

free (not in way of the leading edge), by a

sub-stantial safety margin. It is supposed that the blade

widths for all the designs could be reduced at the outer radii if a reduction in this margin were ac-cepted. Certainly the Hill designs could have the widths reduced near the .9 radius where the thrust

loading has been reduced.

Figure 12

The Wageningen Liner design, wi h the increasl in camber ratio which the method prescribes at the

outer radii (see figures 8 and 9), is in danger of

cavitation. The calculated pressure reduction at the

.90 radius exceeds the available g by lO percent,

The other radii calculated for the Liner and Tanker show pressure reductions of from .68g to .86g.

In several cases there is a marked reduction in pressure near the back of the leading edge, due to the fact that NACA data was used, whereas in an actual shaping of the nose, with a generous nose radius, the pressure reduction would be reduced.

Also, any thin trailing edge sections would be modi-fied. It is probably safe in assuming from the

pres-sure distribution diagrams calculated that there is no danger of back cavitation at the leading edge.

The Wageningen designs, however, at the .90 radius indicate face cavitation at the leading edge, which

is no doubt caused by the adoption of very little

incidence angle (see figures 8 and 9L

A.S.N.E. ,JeurnI. August ,o 445

'4 o .4.1,

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SOME CONCLUDING REMARKS

The four design methods have been applied in

their entirety, beginning with the condition

of minimum energy loss and ending with the selec-tion of appropriate pitch ratio and camber ratio.

Because no attempt has been made to establish

agreement between the corresponding steps of each

method, there are few joints at which a

quantita-tive comparison may justifiably be made. The value of this paper has been to show the relative effect of the several different paths followed by each method

considered. These effects have been graphically shown and discussed in some detail in the text of this paper. A further study could be made, where

for each propeller a common optimum load distri-bution is calculated and starting with this as a base,

the mean line pitch and camber ratio _{are selected,}

using the different data of the several methods. This study would make possible a quantitative

compari-Figure 13

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_{u.ju.r4g.iaut}

UILJ--=-J.

___ __

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_u.u..0

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son between the mean line pitches and the camber ratios given by each method. It would then remain

for the propeller designer to determine, with the aid of this information and experimental data for

the designed propellers, which method is desirable for a given design.

ACKNOWLEDGMENTS

The author gratefully thanks his tutor and

teacher, Professor L. C. Burrill of King's _College, The University of Durham, for the _{guidance and}

instruction given him when making the calculations

required for this paper. He especially _thanks Pro-fessor Burrill for the idea of the method used in

making the flow curvature correction in the

cavita-tion calculacavita-tions. The author also thanks Miss

Sa-rah Luchars for her great help

_{in preparing the} manuscript for this paper.

"The Optimum Diameter of Marine Propellers; A New Design Method." L. C. BurrilL NECI, Nov. 1955, Vol. 72. "Fundamentals of Ship Resistance and Propulsion," Part B, J. D. Van Manen, International Shipbuilding Progress. June and July 1957, Vol. 4.

'The Design of Wake-Adapted Screws and their Be-havior Behind the Ship," J. D. Van Manen and W. P. A. Van Larnnieren, Institution of Engineers and Ship-builders in Scotland, 1955.

"The Design o Ship Screws of Optimum Diameter for

an Unequal Velocity Field," J. D. Van Manen and L. Troost. SNAME, 1952.

"A Propeller Design Method," M. K. Eckhardt and W. B. Morgan, SNAME, 1955.

"The Design of Propellers," J. G. Hill, SNAME, 1949.

"NACA Report No. 824, Summary of Airfoil Data,"

Abbott, Doenhoff, and Stivers, 1945.

"Propeller Pitch Correction Arising from Lifting

Sur-face Effect," H. W. Lerbs, DTMB Report942, 1955.

"The Effect of Radial Pitch Variation on the

Perform-ance of a Marine Propeller," L C. Burrill and C. S.

Yang, INA. 1954. A. Section Particulars; tic = .057 tanß = .200 CL = .2430 CD = .0086 CD= tan r = .0354 CL r = 2.03° = 17.80° r+ß1 = 19.830 tan (r+/31) = .361 tan ¡3 = .321

"Theory of Propellers," Theodorsen, McGraw Hill, 1948.

"Moderately Loaded Propellers with a Finite Number of Blades and an Arbitrary Distribution of Circulation,"

H. W. Lerbs, SNAME, 1952.

"Schraubenpropeller mit Geringsten Energieverlust," A.

Botz, Nachrichten von der Gesellschaft des

Wissen-schaften zu Gdttingen, 1919.

"Resistance, Propulsion and Steeaing of Ships," Van

Lammeren, Troost and Koning, 1948.

"Measurement of Wake," F. Horn, Symposium on Pro-pellers, NEd, 1938.

"Some Effects of Blade Thickness Variation on Model-Screw Performance," T. P. O'Brien, NEd, 1956. "Calculation of Marine Propeller Performance

Char-acteristics," L. C. Burrill, NECI, March 1944, Vol. 60.

"Developments in Propeller Design and Manufacture

for Merchant Ships," L. C. BurriU, 1MB, 1943.

"Effect of Cavitation on the Performance of a Series of 16 in. Model Propellers," R. W. L. Gawn arid L. C. Bur-x-iii, rNA, 1957.

"La Courbure Induite des Ailes Minces," R. Guil.lotor, Association Technique Maritime et Aéronautique, 1955.

APPENDIX

Typical Pressure Distribution Calculation

SINGLE SCREW TANKER, .7 radius; Eckhardt and Morgan Design

(tan /3-tan /3) tan (r+/3)_0392

a'_{= 1+tan /3v tan (r+ß1)}

tan /3

a =_tan/3 .(1-a')-1=1.543

1+a \

= fl1(tan/3

_1-2a')

tari-' [tan /3.(1+a)]=.0241 rads.

c 9.6 Geometric camber,

.1

= .0270 C K, = .946 (Ref. 16) K00 = .890 (Ref. 16) = .0227 = .0025 C y Effective camber, - = .0202 c

A.S.N.E. journal, Auut l96 447

B. Pressure Distribution (Ref. 7): Section: NACA 66-006, a=.8 mean line

CLI=1.00, (y/e) =0679, (tIc) =06, ,=1.54°

x

(4

()

(-.)

For Section under consideration:

t/c

r

(1)=[()

-]

_(tic),

_+1=L()

_1]

(.950)-t-1 zv ¿v ylc

(2)=(V)

.

(YIC)(V)

.(.298) Va

V\

[ =

()

.

rv

.V LV

(4)-1-I

---q

LVVV

x .025 .05 .10 .30 (1)-i- 1.033 1.040 1.050 1.064 (2) .083 .083 .083 .083 -.053 -.038 -.026 - .013 Back:

rv

v +

_--

+ --

1.063 1.085 1.107 1.134 Face: rv _- v .v«1

-v-- -y-j

1.003 .995 .993 .994 (4) Back -.130 -.177 -.255 -.286 q (4) Face - -.0006 .010 .014 .012 q a=cavitation number .383

(See Figure 12 for plot of pressure distribution.)

Time and material studies of four ships from I 20 to 3500 tons in an

East German shipyard showed that 22-40 welder hour, 60 to 77 pounds

of electrodes and 880-1300 cubic feet of gases were requked per ton of ship weight. Conversion from manual to submerged-arc welding

re-suited ¡n better utilization of yard area.

Experiments with a corona-discharge torch consisting of a tungsten

electrode surrounded by nitrogen, 002, argon or hydrogen and powered

by a ¡-kw triode at 27 kc showed that the flame was too unstable for

practical use. However, tungsten and molybdenum wires, steel sheet

0.032-inches thick, refractories and quartz could be melted or welded.

-from WELDING JOURNAL

May 1960

44S A.S.N.E. Journal, August 960

y/e . (-.055)

(y/c)] -

()

.50 .70 .80 .90 .95 1.069 1.054 1.019 .975 .946 .083 .083 .083 .041 .020 - .009 -.006 -.004 -.003 - .002 1.143 1.131 1.098 1.013 .934 .995 .977 .940 .937 .928 -.303 -.279 -.203 -.026 -.071 .010 .045 .116 .122 .139 .025 .05 .10 .30 .50 .70 .80 .90 .95 1.035 1.042 1.052 1.067 1.073 1.057 1.020 .974 .943 .278 .278 .278 .278 .278 .278 .278 .139 .069 .967 .695 .474 .245 .161 .102 .075 .047 .030