Sea trial analysis of the vertical axis propellers

ARCHIEF

MITSUBISHI ZOSEN TECHNICAL BULLETIN

No.

b

Sea Trial Analysis of

the Vertical Axis Propellers

by

Kaname Taniguchi

A paper presented at the 4th Symposium on Naval

Hydrodynamics held in Washington, D. C.

I h

_r

e

u

_T. (

Tcchfthdle

Ich0.J

DeIft

December 1962

Mitsubishi Shipbuilding and Engineering Co., Ltd.

1. The Performance Characteristics

of Vertical Axis Propeller

The author obtained the theoretical formulas' of vertical axis propellers which enable to calculate the thrust, torque and efficiency under the adequate

as-sumptions.

In his second paper2 he got the correction factor

of the formulas by carrying out the model experiments. Further he has developed the designing method of this

propeller.3>' Several types of vertical axis propellers up to 1,000 ps have been designed by the author and

manufactured.

In the present paper the author reports the trial

analysis results of the seven ships which are installed

with these vertical axis propellers.

The method proposed by the author for calculating

the performance characteristics of vertical axis

pro-pellers is based on the following assumptions: The motion is quasi-steady.

Only the longitudinal component of induced velocities contributes to the thrust and torque of the propeller.

The longitudinal component of induced

velo-cities is thought to have uniform value over the transverse section of propeller stream.

(The correction factor e is introduced for the non-uniformity correction.)

Then choosing the blade motion of the orthodox

type which satisfies the relation

e cos O

tanç=

. (1)

1e sin O

between the blade angle , the eccentricity e and the

orbit angle O, and also choosing the semi-elliptic blade outline in order to obtain the constant induced velocity

over the spanwise length of blade, the following

for-mulas are derived.

8

UDC 629. 12. 037. 17. 001. 4

The Sea Trial Analysis of the Vertical Axis Propellers

Kaname Taniguchi*

Sea trial results of the seven ships equipped wit/i the vertical axis propellers which

were designed by the author are analyzed and compared with the calculation.

The fairly good agreement is obtained between the results of the bollard trials and

the calculations. The wake fractions obtained from the analysis of speed trials are

0.25-0.35, which are a little bit larger than the expected ones from the model tests.

Tice similarly analyzed resistance-thrust ratios are much smaller than expected and there

remains a room for further study.

(2)

V vnD/T=Ç4

Fig. i Plot for Evaluating K

LS

LS

- 0.02

* Assistant DirecSor of Research Lobo:aoy & Chief, Experimental Tank, Dr. Eng.

CT=27:2_L (A1A) ₍₃₎ K 4 rc;0 k 8 t2 I2+--(e_A,)2I3 } (4) A C e5=-2

5

where,

1Çir.'2 _{\/l+2,2_2A1 sin}

cos2 OdIi

f+e(e +A) sin O

i

ir!

(1A1 sin O) vu1+A1-2A0 sin o.dO 1r _-irr2

iÇir/2 _{(1+A1 sin 0)/l+Al2À5 sinO}

cos2 O.do

7: )xri2 (1+eA1(e+A1) sin O

C is obtained by solving equations (2) and (3) simul-taneously. e in equation (3) is the correction factor (project area reduction factor) foi' the assumption of

the uniform distribution of the longitudinal component w of the induced velocities. Its value can be estimated, provided the distribution of w is assumed adequately.

For instance, e becomes 1.33, if the distribution of w is assumed as a parabola of third power. Cxx and k

in equation (4) are the parameters to express the two

dimensional drag coefficient C. of the blade section as

follows.

Cx=Cxo+ ka2 (6)

The values of C0and k can be derived from the

experimental data on aerofoil sections. In the present

case the author obtained the values of e, cxx and k from the analysis of' the model experiments of the

vertical axis propeller, the diameter of which is 20&

mm, numbers of blades are 6, e=0.4 and s/D=0.6. In

Figs. i and 2 the analyzed results are shown.

0.06 0.05 0.04 F0.03 In 0.01 o

J.-

p)

.-.00ti ,2L0 026. (5) Mark 0 8 o e 0.615 Q5 0.35 0.2 o +8 _' A Mark e * o 0.6150.5 8 0.35 a 0.2 0.015 0.02 0.005 0.01 )eA

Fig. 2 Plot for Evaluating the Section

Drag Coefficient

1.5

The Sea Trial Analysis of the Vertical Axis Propellers

2

U U.! 0.2 03 04 05 06 07 08

C=Q/pnsD'

Fig. 3 Characteristic Curves of a Vertical Axis

Propeller (Calculated for Actual Ship)

Generally the minimum drag coefficient C6,0 of aerofoil

sections can be derived from the frictional resistance coefficient C1 of the flat plate of equivalent size by

correcting the thickness effect adequately. By author's experiments C may be expressed approximately by

the following equation.

Co=2C1(1+38(tJc)2} (7)

Since the Reynolds' no. based on the mean chord length of blades, i.e. defined as l(2rnD)/, is nearly

1.7 x 10 in the case of the author's model tests, the

frictional resistance coefficient of the corresponding fiat plate may be taken to C1=0.0066. Also the effective

mean chord-thickness ratio is 0.15. Therefore

C,0=2'<O.O066)l+38xO.l52) =0.0245

and this is in good agreement with the analyzed result

C0=O.025, as being shown in Fig. 2. From this analysis

it seems reasonable to correct C0 for the actual pro-peller according to its Reynolds' no. Since the

Rey-nolds' no. of the blades of the actual vertical axis

pro-pellers of 1OOE-4,000 ps is (3-5)x 106, C1 of the blades of

actual propellers may be taken to be a half of that of

the model in the mean value, i.e. C1=O.0033. Therefore C0=0.0l25 is estimated for the actual propeller.

The performance characteristics of actual propellers are calculated by equations (2), (3) & (4) with ir and k values given in Fig. i and 2 and also C0 value (0.0125) which is given above.

Fig. 3 shows as an example the calculated

charac-teristics for the actual propeller of z=6, =0.4 and

s/D=0.6.

2. Sea Trial

The principal dimensions of the vertical axis pro-pellers designed by the author and those of typical

seven ships on which these propellers are installed, are shown in Table I. These ships have twin vertical axis propellers at the stern and are harbour tugs except ship B which is a car-ferryboat.

The blades of these propellers are all made of Ni-Al-Bz alloy. The outline of the blade is of trapezoid, of which the tip root chord ratio is nearly 0.6 and the

tip corners are rounded.

The blade axis is chosen on 40í of the chord length

from the leading edge. The thickness form of blade section is symmetrical and its camber line is curved into a circle whose radius is l.4R, in order to get an

effectively symmetrical section for the mean trochoidal path of blade.

The relation between the blade angle çi and the orbit angle O is not the same as that of the orthodox

motion given in equation (1), but slightly deformed in

the actual case by the limitation from its mechanism.

The values of O at which the maximum and minimum

values of ó occur are shifted slightly torward 00 and

180° respectively from the orthodox çb-O distribution.

In all ships the propeller on the port side rotates

counter clockwise and that on the starboard side rotates

clockwise, when looking downward.

The bollard trials (except ship B) and the speed

trials were conducted with these seven ships and their

powers absorbed by each vertical axis propeller, pull

force, ship speed etc. were measured.

Ship models were made for most ships and the resistance tests were carried out under the same con-ditions as those of the corresponding ships in the sea

trials. The wake measurements at the propeller

posi-tion were also made using Pitot-tubes on the typical

model s.

The conditions of actual ships in sea trials and of models in tests are given in Table II.

The pull force in bollard trials was measured by the tension meter, mainly of strain gauge type. The length of the towing rope used in tests is nearly three

times the ship length.

Table I PRINCIPAL PARTICULARS OF SHIPS AND VERTICAL AXIS PROPELLERS S/D=0.6 t0/C0=0.2 t1/to=0.1

Z6

ir=Ø.4 Cx00k=1 *---Fg.1 a=5.34_-0125 2 -,.

/

i;',

///

Ships A B C D E F G Type G.T. Tug 20(00 Car Ferry 260 Tug 150 Tug . Tug 220 Tug 183 Tug 240 LWL l3.0" 41.0 28.5

0

31.0 27.5 32.1 Bmld 4.2' 8.8 7.6 8.4 8.2 8.5 d 1.0" 2.1 2.3 e 2.6 2.8 2.8

j

29.8e 468.4 281.6 372 315 399 Cwr. 0.533 0.635 0.548 0.535 0.485 0.513 Main Engine 2x130P6 2x320 2x550 2x750 2x900 2x990 No. of Prop. 2 2 2 . 2 2 2 Z 4 5 6

0

6 6 6 D 1.000m 1.600 2.000 2.200 2.400 2.500 S/D 0.6000 0.6250 0.6000 _e 0.5909 0.6042 0.6000 e 0.3820 0.4029 0.4011 0.3993 0.4178 0.4202 p Designed PS/prop. 120P 320 550 750 850 990 Designed RPM 192 130.9 105 95.5 87.5 84 3 2. ç) 0.

The power absorbed by vertical axis propellers was

measured by the torsion meter of the inductance type on the pinion shaft near the propeller. The measured power, named SHP in the present paper, includes not only the power absorbed by propeller blades, named

DHP in this paper, the calculations of which were

treated in Section 1, but also the windage loss of the propeller disk and the mechanical loss of the inner

mechanisms of propeller. The difference between SHP and DHP is named idle power.

The measuring methods of speed, revolutions of

propeller, etc. are quite same as in the case of the speed trials of ordinary ships.

The eccentricity of actual vertical propeller was obtained from the following procedure. At first the

eccentric movement of its needle pointer on the top of the propeller is measured in each run.

Then the maximum and minimum values of ç5 are

obtained from this measured movement by the use of

the drawings of the vertical axis propeller.

The eccentricity e is taken to be equal to the e value of the orthodox movement corresponding to those maximum and minimum values of .

3. Analysis of Bollard Trials

Figs. 4 and 5 show the results of the measurements

of pull force (P) and SHP at the bollard trials in

non-dimensional forms, i.e. P/pn2sD3 and CQS=75/2'r.SHP/

onsD< respectively, and they are plotted on the base

of e which is obtained as described above.

In Fig. 4 there are shown not only the values of P/pn2sDa derived from the trial results but also the curves of CT obtained from the author's model tests

and from the calculation as described in Section 1

Note: Shiplines were modified after model tests.

MITSUBISHI ZOSEN TECHNICAL BULLETIN No. 6 DECEMBER 1962

Fig. 3. From this figure it can be seen that CT-curve

obtained from the model tests is in fairly good

coinci-dence with those obtained from the calculation and that these curves are in reasonable relations with the values of P/pn2sD3 derived from trials, since a small

thrust deduction may exist among them.

The measured results of ship G (plotted by+mark)

show consistently lower values. This may partly de-pend on the fact that a strong wind (8 m/s) which was

3

Table II PARTICULARS OF SEA TRIALS AND MODEL TESTS

05 .6

Fig. 4 Plot of P/pn2sDa & CT (Bollard Trial)

7 A

j

I

/1

Marl< o A 7 o + Ship A C D E F G

.-/'6/'

o'

-=o D;Ç / a

o

-i. e Ships A B C D E F G SEA TRIALS

Trial Bollard Speed Speed Bollard Speed Bollard Speed Bollard Speed Bollard Speed Bollard Speed

15. Dec. 1. Jan. 28. Oct. 1. Sept. 2. Sept. 19. Sept. 20. Sept. 10.Nov. _{11. Nov. 8 Feb '626 Feb '621. Dec.} 20.Dec.

a e _'59 '60 '61 '60 '60 '60 '60 '61 '61 _-1 j '61

Weather Rainy CloudyCloudy Fine Fine Rain Fine Fine Fine Cloudy Fine Fine Fine

Wind NNWWNW

w

NNW E l'° NW6" w

-

W 8"

Sea Cond. Smooth Smooth Smooth Smooth Smooth Smooth Smooth Smooth Smooth Smooth Smooth Slight Slight

Water Temp. 18°C 13.5 23 27 27 29 29 22 22

_Nt

8 12 12

Draft (mean) l.02'° 1.030 1.78 2.250 2.262 2.275 2.24 2.47 2.485 measured. 2.814 2.85 2.87

Trim Dispt., 4 0.l45' 32.0' °.lS0A 33.29 °.62A 322.7 °.'°5F 269.1

°"°F

271.2 °.11F 272.0 0.04.4 268.6 0.10.4 349 °.03A 352 same ₀₅₁₁ 323.1 0.27 403 o.z., 408 MODEL TESTS

Scale 1/6.5 1/10 1/lo

/

1/10

iio

LWL 13.02 40.41 28.486 Same as C 27.409 32.072 Bind, skin 4.212'° 8.816 7.616 8.216 8.516 Di'aft (mean) 1.0585' 1.770 2.241 2.849 2.849 Trim O 0.410/ o

/

_O.5llA 0.299f, Dispt 31.238' 355.0 270.0

/

323.1 410.0 Skin Area 60.28m2 384.0 247.9

/

263.1 314.8 Ch,. 0.5165 0.5463 0.5398 0.4900 0.5126 CPWL 0.6145 0.5965 0.6004 / 0.5641 0.5876 o 01 02 03

The Sea Trial Analysis of the Vertical Axi, Propellers 1.1 1.0 0.9 0.8 0.7 Q-0, 0.6 (N

--

_Lr) 0.5 II 0.4 ç) 0.3 4 0.2 0.1 O 1 0.2 0 3 0.4 0.5 0.6 0 7 e

Fig. 5 Plot of CQ7 & CQ (Bollard Trial)

accompanied with waves blew from the bow during

the bollard to'ials.

Although the measured points of P/pn2sD° are

con-siderably scattered, their tendency against e seems to agree better with C7-curve obtained from the model tests than those obtained from the calculation, if Fig.

4 is examined carefully. However, the amount of this difference is so small that CT-value derived from calcu-lation may be used in order to calculate the thrust deduction factor. Thus calculating the thrust deduction

factors on all measured 33 points, we get the mean

value of 0.056. This is a reasonable value when com-pared with the bollard trial results of ordinary tug boats equipped with screw propellers.

In Fig. 5 there are shown not only the values of CQ7 derived from the measurements at sea trials, but

also the curves of C0 obtained from the calculation for actual propellers as described in rSection i and obtained from the author's model tests. In this case C0 of the

model tests have been also corrected to the actual

propeller, using the difference of the calculated CQ

values for model and for ship.

The measured values of CQ7 at e=0 are also shown

in this figure. The curves of C0 obtained from the calculation and from the model tests coincide nearly with each other. Since the calculated values of Cr

have been shown to be reasonable as described above, the calculated values of C0 may be thought to be also

correct.

Therefore the difference of C07 and C0 may be con-sidered to give the idle torque constant C07 of the

propeller. Fig. 6 shows C thus obtained on the base

of Coo. Though C-values scatter considerably, they

o. 20 A Mark o A V o o Ship A C D E F G A o

I..

/O

+

.

, + 4.

,'

w"O

CY / /'CQ (expt.)at A=0 O.=o.4o

p,

V Mark Ship

.

o 500 1000 15 o Total SHP

Fig. 7 Plot of Pull Force versus Total SHP

increase proportionally to CO3 and the relation

CQ7=

may be chosen as mean value.

It means that on the vertical axis propellers about

113 of the input power is consumed inside the propeller mechanism as a loss and only about 2/3 is delivered to

the propeller blades. At no load condition, i.e. e=0, the mean value of C07 is equal to 0.06 and this is

ap-proximately 9% of CQ8 at the designed condition, but

with the increase of propeller load CQ7 increases

re-markably.

The C0.7-values of ship C are comparatively lower than others.

This may be chiefly due to the fact that the oil

pump of this propeller by which the blades are

con-trolled is driven by the separate motor outside the propeller, while in all other cases blades are controlled

by the gear pump which is installed inside the

pro-peller.

The idle power loss is

so large that it

is very essential to endeavour to reduce it for the further

im-provement of vertical axis propeller.

Fig. 7 shows the direct comparison between the

pull force (P) and the input power of the propeller (SHP) at the bollard trials. From this figure it may

he seen that the pull force per 100 Ps 5 in the order

of 1-1.3 tons. This pull force ratio is somewhat smaller

compared with the case of tug boats equipped with

controllable pitch propellers and it depends on the larger idle power loss inside the vertical axis propellers.

Mo6 Shp 0. o0. .=0+ 0. ----h -03 04 05 06 07 08 C,.= 75/2)SHP/P,'D

4. Analysis of Speed Trials

Though the idle torque constant CQ shown in Fig. 6 is obtained from the analysis of bollard trials, it

may be applicable also tothe case of speed trials. Ce

can be obtained by subtracting C from the measured

value of Cet. From this C0-value and the e-value

measured, the effective wake fraction w of the actual ship and the thrust (T) of the propeller are calculated

by the torque identity method using the propeller characteristic curves. Thus the resistance-thrust ratio

r is obtained from the propeller thrust (T;) and the

resistance (Rs), which is deduced from the mcdel tests. The speed trial results of seven ships listed in

Table II have been analyzed by this method. Where the mean value of Cei as shown in Fig. 6, i.e. CQ=

l/3.G0, was used for the correction of idle power, instead of taking individual C, of each ship. The

propeller characteristics are calculated for e-value of each propeller by the method described in Section 1. In the resistance calculation of the actual ship from

the model test, the I.T.T.C.-l957 model ship correlation line is used with the roughness allowance of JC=0.3 X Fig. 8 shows the values of ws, r, and the propeller efficiency e5 obtained from these analyses on the base of Froude No. It can be seen that the plot of w shows the same trend and is distributed in the range of 0.25-0.35. The values of e5 are nearly 0.6 except the

lower speed zone irrespective of ships.

The values of w are somewhat larger than expected. The wake measurements at the propeller position have been made on the ship model and their volume means

were 0.15-0.20. Therefore it was expected that the

wake of the actual ships might be still less than these

values.

The values of r are considerably different among

the ships as shown in Fig. 8 and all ships have the similar trend to increase their values as the speed

increases, r may be expressed as - t)

according to its definition, where e means the relative

rotative efficiency defined on the torque base and t

2

O/L

Fig. 8 Plot of w, r & ep (Speed Trial)

MITSUBISHI ZOSEN TECHNICAL BULLETIN No. 6 DECEMBER i 962

means the thrust deduction factor.

In the case of ordinary tug boats equipped with

screw propellers, t is almost in the same order as w,

and e is nearly 1. in the present case, if these

iela-tions hold, r must be nearly in the same order as (l-w. But r reaches nearly the same order as )lw) only in its maximum value. In the lower speed zone

r remains considerably smaller than 1-W9).

The reason why r remains in these smaller values must be whether the prediction of the resistance of

hulls is too small or the prediction of the propeller thrust is tco large, or the both. As for the resistance of hulls, the predicted value of the resistance is in the

tendency of being under-estimated, since the roughness

allowance of JCj-=r0.3 10 used in the calculation

might be a little bit smaller for the small ship of this kind and increment of resistance caused by wind and

wares should be also considered. Since the thrust is

predicted from the measured torque, the over-estimation

of the thrust means the over-estimation Ce and the fact that the values of u' are larger than expected as

described above seems to support the opinion that the

over-estimation of C exists. Though the over-estinia-tion of thrust and w9 can occur also from the

incor-rectness of the propeller characteristic curves, it might

be hard to consider that the over-estimation comes solely from it. Because the prediction of thrust is

fairly good coincidence with the measured pull forces

in bollard trials, i. e. in the case of ¿=0, as shown

already in Fig. 4.

The author thinks that it comes from the following

causes. Firstly, these ships could not be free from

the zig-zag runs during the speed trials, because the captain had not been experienced sufficiently to

ma-neuvre his ship equipped with the vertical axis

propel-lers. Secondly, the propellers were used partly as a

rudder during the runs in order to keep the course

from the yawing caused by wind and waves. These actions may consume the considerably large power

comparing with the power needed in absolute straight

course, especially in low speed. Thus the larger CQ values might be measured in the trials and the thrust

corresponding to these C might become too large when

compared directly with the resistance in the straight

running.

Besides these, it may be also considered that the thrust deduction of vertical axis propeller becomes

considerably larger comparing with the case of screw propeller, as the propeller stream flows in close contact with the bottom of hull.

But it may be hard to discuss these problems

further unless the self-propulsion tests are carried out. It is highly desirable to carry out such further re-searches in order to make clear these points.

5. Conclusion

The author has made the theoretical and

experi-mental studies on the vertical axis propellers and developed a design method in his previous papers.

The several vertical axis propellers ranging 100-1,000 ps have been designed by this method and manufactured.

In this paper, the results of sea trials of typical seven

ships equipped with these propellers are analyzed and compared with the results of calculations and of model

experiments.

_...._ u.

Ship .

..._.

0.7 0.6 0.5 0.4 0. 0 .4 0. 0. 0.

The Sea Trial Analysis of the Vertical Axis Propellers

R efe re n ces

Taniguchi, K., "An Approximate Solution of the Voith-Schneider Propeller ", JL of Zosen Kyokai

(Trans. Soc. of Naval Arch. of Japan) Vol. 74

(1944) pp 153-161.

Taniguchi, K., "Hydrodynamical Investigations

of the Blade Wheel Propeller ", JL of Zosen Kyokai,

Vol. 88 (1950) pp 63-74.

Taniguchi, K., "Studies on a Trochoidal Propel-ler", Doctor of Engineering Thesis, Tokyo

Univer-sity (1960).

Haberman, W.L. and Harley E.E., "Performance of Vertical Axis )Cycloidal) Propellers calculated

by Taniguchi's Method ", DTMB Report 1564 (1961,

Nov.)

Taniguchi, K. and Watanabe, K., "A New Electric

Torsion Meter for High Speed Naval Craft ", JL

of Zosen Kiokai, Vol. 108 (1960) pp 105-113

Nomenclature

D : Diameter of propeller )2R)

s Length of blade (Span of blade)

c : Chord length of blade (Z effective mean of c)

t : Thickness of blade section and Thrust deduction

factor

e _Eccentricity

z : Number of blades

V : Ship speed in knot

r' : Speed of advance of propeller

w : _{Longitudinal component of induced velocities}

r1 : v+w

n : R.P.S. of propeller

T Propeller thrust

Q : Propeller torque delivered to blades

SHP: Power measured at pinion shaft DHP: Power delivered to propeller blades

a Solidity

çl ]3lacle angle

O : Orbit angle

a Angle of incidence

a : Derivative of the lift curve of blade section r Project area reduction factor

c : Lift coefficient of blade section

cx : _{Drag coefficient of blade section (c0+ka2)}

c1 Frictional resistance coefficient of flat plate C. : T/pn2sD3 Thrust constant

Q/pn2sD4 Torque constant

(75/2r).SHP/pn3sD4

CQS : CO3-05, Idle torque constant

Propeller efficiency

Relative rotative efficiency r : Resistance-thrust ratio

2 Advance ratio, v/mD

v,JmnD

w Wake fraction (Taylor's)

Reprinting or reproducrion without written permission prohibited

The following results are obtained.

The pull force measured in bollard trials are

in good coincidence with the values estimated

from the propeller characteristics which are

obtained from the calculations and the model tests. (Fig. 4)

The pull force per loo shaft horse power is

1-1.3 tons, (Fig. 7)

The value of the mechanical loss of propellers,

i.e. the _{idle power is estimated from the}

analysis of bollard trials. (Fig. 5 and 6) The

mean value of it is about 1/3 of SHP and it

is mostly necessary to reduce the idle power

in order to improve the performance of the

vertical axis propellers.

The effective wake fraction is obtained from

the analysis of the speed trials. It may be

taken as 0.25-0.35 for the kinds of ships treated

in this analysis (Fig. 8. These values are a

little bit larger than the values predicted from the wake measurements on models. The resistance-thrust ratios obtained from the

analysis of the speed trials remain in con-siderably smaller values than expected from

the predictions of the relative rotative

efficien-cy and thrust deduction factor. The tendenefficien-cy that the resistance-thrust ratio remains in lower value becomes more remarkable in the

lower speed zone.

The reason why it remains in such lower value is not so completely clear at present. It needs further study for this point and also for the larger value of wake fraction by car-rying out the self-propulsion tests. But it may be thought that the main reason of it

lies _{in the zig-zag runs during the speed}

trials.

Applying the analyzed results shown in this

paper, it is possible to predict the performance in running and bollard pull conditions of ships which are epuipped with the vertical axis

propellers, with the sufficient accuracy in

practical use.

Acknowledgement

The author wishes to thank the members of

Mitsu-bishi Experimental Tank (Nagasaki) for their close cooperations given to him, the members of shipyards for their constant supports and the head office of the