Comparison of propulsive performance between model and ship of a hydrofoil boat

THE NORWEGIAN SHIP MODEL EXPERIMENT TANK CABLE: SKIPSTANK PHONE: 28020 S Kl PS MOD E LLTA N KE N

YMPflfl Jì\1'!

ON I ES I ING

I ECHNIQUES

IN SHIP CAVITATION

RESEARCH

PREPRINT OF

Comparison of Propulsive Performance Between Model and Ship of a Hydrofoil boat.

by K. Taniquchi, K. Watanabe, and H. Tanibayashi, Nagasaki Technical Institute, Japan.

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K. Taniguchi, K. Watanabe, H. Tanibayashi,

Mitsubishi Heavy Industries, Ltd., Nagasaki, Japan.

1. Introduction.

In considering the propulsive performance of hydrofoil boats, it should be noted that there are many aspects which are different from those of ordinary displacement type ships. The performance of a hydrofoil boat cannot be discussed without re-ference to the dynamical balance of the boat, which has little influence on the propulsive performance of ordinary ships. The proportion of the resistance components - viscous resistance, induced drag of foils and air resistance - is different as well, and the effect of cavitation on propeller characteristics should

also be taken into account.

In the course of the development of a O knots hydrofoil

boat built in our shipyard, extensive investigations into the pro-pulsive performance were carried out to cover those aspects:

resistance tests on the individual underwater elements as well as on the boat-and-foil configuration as a whole, the wind tunnel tests, the behind tests and the propeller cavitation tests. New techniques were developed by which the resistance tests can be

carried out at the same dynamical condition as in the

self-propelled condition.

A rsum of those investigations is given in this paper, primarily concerning the estimation of the full-scale propulsive performance and the comparison of the estimated results with the

actual trial data.

2. Hydrofoil boat.

The hydrofoil boat, of which the performance study is to be described in this paper, is 21 m long and is about 33 tons in displacement at the designed load condition, carrying 80 passengers. The maximum speed is about 4Q knots at the maximum engine output

of 1500 Ps (BHF). The general arrangement of the boat is shown in

Fig. 1, and the principal particulars are given in Table 1. The

hull form, having a single hard chine, was designed based on our experience on the design of many high-speed torpedo boats, the

highest speed of which exceeds 140 knots. The foil system consists

of two main foils of surface piercing type on both sides and an

aft-foil fitted to the pod of the transmission gears. The

pro-peller is driven through the Z-type transmission gearing system.

2

5rERING GEAR SPACE

STRAIN (&E TYPE

TORSION-METER

Fig. 1. General Arrangement of the Hydrofoil Boat.

CRUÌSIN( CONDITION W.L

W.L FLOA NG c4DITION

3. Model tests.

3.1. Resistance tests.

The draught and the trim of a ship in self-propelled

condition are determined in such a way that the weight of the ship, the buoyancy (statical and dynamical), the resistance and the

thrust of the propeller can be balanced. In the resistance tests,

therefore, it is desireable that the towing force should be app-lied on the line of action of the propeller thrust in order to eliminate the error due to the difference of the draught and the

trim.

In the case of ordinary displacement type ships, certain allowance can be taken to this requirement; the variation of the towing point and the towing direction causes only a slight differ-ence of force and moment so that the resulting variation of the running condition of the ship scarcely affects the resistance. In

the case of hydrofoil boats and planing boats, however, the towing point and the towing direction have significant influence on the draught and the trim of the vessel, and the variation of resistance

cannot be neglected. For such vessels, therefore, the significance

of the towing method is much more accentuated.

Dimensions Length(overall) 21.00TS

Breadth(oaximum) 4.8Cm

i3readth(at water line) 4.14m

Breadth (maximum between hydrofoils) 11.4Cm

Depth(hull) 2.5Cm

Depth of hydrofoils(from bottom of keel) abt. 2.0Cm

Designed draught at full load

(to the bottom of hydrofoils at hull-borne cond.)

abt. 3.0Cm

(to the bottom of hydrofoils at foil-borne cond.)

abt. 1.00m

Gross-tonnage abt. 75 tons Displacement tonnage at full load abt. ₃₃ tons

ain Engine High-speed 2-cycle diesel engine x i unit

ìaximum output x revolution 1,500 PS z i,600 rpm Nornal output z revolution 1,350 PS z 1,500 rpia

Speed Maximum speed abt. 40 knots

The propeller of the hydrofoil boat, with which the present investigations are concerned, is driven through the Z-type trans-mission gearing system, and therefore the propeller is far below

the hull. In such a case it is impossible to tow the model at a

point on the propeller axis. If the towing force is applied on the

hull in the direction parallel to the propeller axis, the moment due to the distance between the towing rope (or rod) and the pro-peller axis causes the variation of the trim and accordingly the

variation of the lift of the foils. Such variation will lead to

a dynamical condition of the boat which is considerably different

from the self-propelled condition. The resistance tests should be

carried out, therefore, with a device by which the towing force yields the same effect on the boat as the thrust of propeller. In

Figs. 2 and 3 are presented schematically the methods we have

de-veloped, by which such requirement is satisfied.

The method shown in Fig. 2 is suitable for a small model,

the weight of which exceeds the design displacement. In this figure,

w is the weight to compensate the difference between the weight of

the model W and the design displacement L. The pulleys P1 and P2

are fixed on the towing carriage and P3 on the model. The towing

rope is connected to the weight w at one end and to the resistance

dynamometer at the other. Placing the pulley P3 in such a way as

AQ3 AH and towing the model in parallel with the propeller axis NM, we can give the model the same moment as the propeller thrust.

The limitations of this method are that the balance weight w should be larger than the towing force T and that a slight deviation of the cord AB from the vertical line leads to the error of thrust in proportion to the angle of deviation; the latter limitation can be relieved by using the additional pulleys as shown on the right part

OB

0P2

Fig. 2. Towing Device Yielding the Same Force and Moment as in Self-Propelled Condition (1).

The method of Fig. 3, on the other hand, is suitable for

a large model and are free from those limitations. In this method

the difference of the moment given by propeller and by the towing rope (difference of moment TH, h being the distance between the

propeller axis and the towing rope) is compensated by the shift

of the weight w with a spring having the spring constant w/h. It

should be noted that here again the towing rope should be so

ad-justed that it is in parallel with the propeller axis. RESES TANCE L'YNAMOPIETER 77 ThP, q.Tu5y So ThAT fl5' ¡S VERT/O?L

B

COWNECTEt TO

Fig. 3. Towing Device Yielding the Saine Force and Montent as in Self-Propelled Condition (2).

The next problem is the method of scaling up the model

test results to the full-scale condition. The full-scale

re-sistance can be estimated according to the same principle as in

the case of displacement type ships. The viscous resistance

re-lating to the wetted surface area and the form factor is

extra-polated with reference to a friction formula for a flat plate and the non-viscous resistance is obtained by scaling up directly the

residual resistance ( total resistance - viscous resistance) of

the model. It should be noted, however, that the proportion of the

viscous and non-viscous components of the resistance is consider-ably different from the proportion of displacement type ships.

Therefore careful investigations should be made on the scale effects in connection with proper evaluation of the viscous resistance.

In order to establish a reasonable method of correlating the model and ship resistance, the resistance tests were carried out on the two geometrically similar models, the scale of which

were 1/lo and 1/5. They were towed by the use of the techniques

described above: the smaller model by the method of Fig. 2 and the

larger model by the method of Fig. 3. A photograph of the 1/5

model is shown in Fig. Lf, and the model running at the take-off

condition and at the design speed is shown in Figs. 5 and B,

re-spectively. The comparison of the measured draught and trim between

the two models is shown in Fig. 7. The test results on the two models

agree in general, though a slight discrepancy of the aft draught can be seen which may be ascribed to the low Reynolds number of the

aft-foil of the smaller model.

RES!S TANCE DYNAMO fr1ETEf

w

o

Fig. . 1/5 Model.

Fig. 5. 1/5 Model at "Take-off".

Fig. 6. 1/5 Model at Design Speed.

0----

---s-- MODEL

Fig. 7. Comparison of Draught and Trim of Geosim Models.

The procedure of calculating the ship resistance is shown

in Fig. 8. The wetted surface area of the underwater part can be

obtained from the draught and trim measured at each speed. The

viscous resistance of the individual foils and struts were esti-mated by the use of the empirical formula on the struts with

circular arc section (1).

3.0-o 20 E J.o- 30 0 20 25 20 30 is 35 45

Non-viscous Resistance of Model

R rR -R

orn trn vm

Measured Total Resistance of Model Rt 8 Noi-viscous Resistance of Ship Rpm (scale)3(ns/nm) R

Total (Water) Resistance of Ship R rR fR WS S VS Tota.]. Resistance of Ship :R fR. ws air C ( y 2 ) pv (1+K)SCf y 2 Tpv S where vc 2.58 Cf O.L55!(1og-_) 1K 38 (tIc)2

t/c : Mean thickness-chord ratio of a foil or a strut

S : Wetted surface area

The validity of this method had been checked by the resistance

tests on the individual foils. The form factor of the pod was

assumed to be 0.05 based on the published data (2) of the bodies

of revolution.

Measured Draught and Trim of Model Wetted 3urface Area S

Viscous Resistance of Mode].

RrjV

Wind Resistance R_air

Fig. 8. Method of Calculating Total Resistance of Ship from

sistance, including the interference effect among the individual underwater elements as well, can be obtained by subtracting the viscous resistance from the total resistance of the model. Since the dynamical condition is simulated in the model tests, the non-viscous resistance of the model can be scaled up directly to the full-scale condition according to the law of dynamical similarity. The viscous resistance of the model was extrapolated in accordance

with eq. (1), where the frictional resistance coefficient Cf was

taken as 0.0035. The frictional resistance coefficient 0.0035 at

the ship's Reynolds numberX was taken referring to

Prandtl-Schlichting's calculation (3) for flat plates with sand roughness, assuming the sand roughness factor x!k 2 x l0. The roughness

factor corresponds to the sand roughness k 0.025 mm for the

fore-foil, the chord length of which is about 1 m. It is to be noted

that Cf of the model was calculated with respect to each model speed and the representative length of each underwater element, while Cf of ship was assumed constant since the Cf as affected by

the sand roughness is. almost constant for the range of ship's Reynolds number.

The total (water) resistance was divided by the

displace-ment (weight) and is plotted in Fig. 9. In this figure shows

the non-viscous resistance divided by the displacement. The

non-viscous resistance and accordingly the total resistance of ship estimated on the basis of the test results on the two geosim models show close agreement with each other over 30 knots. It

can be said therefore that the full-scale total resistance at foil-borne condition can be estimated satisfactorily by the present

method of calculation. The difference of E and E in lower speed

p s

range may be ascribed mainly to the difference of Reynolds number; as observed in the tests on the individual foils of the 1/10 model, the lift coefficient as well as the drag coefficient of the foils showed a considerable variation with Reynolds number of this order

(10 - 2x10 ). This suggests that the investigation in lower speed

range, especially around the take-off condition, should be carried

out on a large model to obtain the reliable test results.

X

Taking the chord length of the fore-foils as the representative length, the speed rane V 25 - 40 knots corresponds to

OEO 0:2 O. ¡O -hull 10 1/ _MODEL --(2) TOTAL (WATER)RESISTANIDISPLACF.MENT NON-VISCOUS PESISTANCEIDISPLAOEtEWT 004 0.02 (SUFFIX ßr MODEL, S. SflP) '5 25 45 Vs [Rn]

Fig. 9. Total (water) Resistance Estimated from Resistance Tests on Geosim Models.

3.2. Wind tunnel tests.

Air resistance of a hydrofoil boat, which aims at the reduction of the water resistance, has considerably large pro-portion of the total resistance compared to displacement type

ships. Proportion of the air resistance increases with speed,

since the water resistance increases only gradually with ship

speed as shown in Fig. 9. The estimation of air resistance on

the basis of published data, however, may lead us to erroneous results because of the irregularity of the superstructure, so that the wind tunnel tests of the above-water part of the boat

(including the hull and a part of the foils and the struts) was

carried out in our GØttingen type wind tunnel. A 1/25 wooden

model was fitted to the measuring section of the wind tunnel, to-gether with the wooden plate representing the water surface

(Fig. 10). The drag and the moment of the model was measured for

the speed range of 20 - 40 m/s (in tunnel), corresponding to the

Reynolds number (1 - 2) x 106. The test results showed that the measured drag and moment were scarcely affected by Reynolds number, and the drag coefficient was given approximately by

R.

o air 0.19 0.20

x 1 2 2/3

significant scale effects were not expected.

Fig. lO. 1/25 Model for Wind Tunnel Tests.

3.3. Cavitation tests.

(1) Cavitation tests on a series of propellers.

Around the designed speed of 40 knots the cavitation on the propeller blades cannot be avoided in general and the parti-culars of the propeller should be determined with reference to the

s 004 05 002 044 03 0. 0f

uf1

I-.

I...

IIE..

p----4

Fig. 11. Results of Propeller Cavitation Tests _{Fig. 12. Results of Propeller Cavitation}

(P/D r 1.2 and Ae/Ad = 1.1).

Tests (P/D 1.5 and Ae/Ad r 1.1).

008 50 004 0,02 as 04 a e

12

propeller characteristics in cavitating condition. Another point of importance to be taken into account is that the propeller should produce the sufficient thrust to accomplish the take-off in lower

speed range. In view of those two aspects in the propeller design,

the hollow face blade section was considered to be most suitable and effective for the propeller of the present hydrofoil boat. In

order to obtain the design data of the propeller, cavitation tests were carried out on a series of three-bladed propellers for various

pitch ratios and expanded area ratios. The blade section of the

propellers was composed of MACA a i mean line and the elliptic

thickness distribution. Typical examples of the test results are

presented in Figs. il and 12.

The propeller was designed on the basis of the results of

those cavitation tests. The design calculation was performed with

respect to the various sets of propeller particulars, because the optimum propeller particulars should be determined in view of the take-off condition as well as the top speed running condition based

on the allowable rating of the main engine. The particulars of the

propeller thus determined are as follows:

D 0.760 m

P 0.912 m

PID 1.200

Ae/Ad 1.100

z

(2) Cavitation tests on aft-strut and aft-foil.

The cavitation number at the design speed of O knots is

0.52 at the draught of about 1 m. According to the preliminary

calculation of the cavitation inception, it was expected that the cavitation would occur on the aft-strut as well as on the propeller

blades. The observation of the cavitation was made, therefore, on

the configuration of aft-strut, pod and aft-foil, whose scale

corresponds to 1/5 model. The cavitation inception was observed

first at the fillet of the aft-foil, and then on the aft-strut. With the development of cavitation, vibration of the strut was

also remarked. Fig. 13 shows the cavitation pattern at the fillet

it was shown that the incipient cavitation number at the fillet of the aft-foil can be estimated by the sum of the velocity increase on the neighbouring members (aft-foil and aft-strut in

this case). Based on such a method of calculation the shape of

the fillet and the strut were improved to retard the cavitation inception as well as to avoid the vibration due to cavitation,

with satisfactory results.

Fig. 13. Cavitation on Aft-Strut.

3.. Behind tests.

Self-propulsion factors - thrust deduction fraction t,

wake fraction w and relative rotative efficiency er - were obtained by the behind tests instead of self-propulsion tests, since the simulation of the complicated transmission system on the model

scale requires a large amount of work and the difference of

pro-pulsion factors was considered negligible between the behind

con-dition and the self-propelled concon-dition. The aft-strut fitted

with the pod and the aft-foil was connected to the resistance

dynamometer. The thrust and torque of the propeller were measured

by the propeller open-dynarnometer. The test configuration is shown

in Fig. 1. The water speed was varied with constant revolution of

propeller to cover the range of slip ratio O - 85 %. The draught

of the strut and the immersion of the propeller were adjusted to

The test results were analyzed by the method of thrust

identity. The self-propulsion factors were almost constant with

respect to the variation of the water speed, and they were in

average t QQL w QQL er 1.00 PROPELLER OPEN DYNAMOMETER

k

Fig. 1t. Arrangement of Behind Test.

LI. Estimation of the propulsive performance.

Effective horsepower or the total resistance of the full-scale boat can be obtained as the sum of the water resistance and

the air resistance. The method of calculation of the water

re-sistance in higher speed range (in foil-borne condition) and the

results are shown 3.1. In this section the results of the 1/5

model was adopted to calculate the power and RPM curves, since

the results of the larger model was considered to be more reliable. On the other hand, in the lower speed range including the take-off condition, the method of scaling the model resistance has not

been established. Agreement of the model tests between the two

geosim models was not satisfactory, primarily because of the

difference of Reynolds number; in this speed range Reynolds number with respect to the foils of the 1/10 model is (2 - 3) x l0,

RES ¡STA N C E

and drag of a foil. Hence the water resistance in lower speed

range was estimated by scaling up directly the resistance of the

1/5 model. Although such a procedure leads to an overestimate

of resistance, the output of the engine required to accomplish

the take-off is certainly larger than that calculated on the basis

of the resistance in steady-state on account of the acceleration

of the, boat during such a transient condition. The estimation

based 'on Cm therefore, is supposed to provide a fairly good

approximation to the actual performance.

Contribution of air resistance to total resistance

in-creases with ship speed, since the water resistance in foil-borne condition increases gradually with ship speed and the rate of

in-crease is much smaller than that of displacement type ships. The

proportion of the resistance components is shown in Table 2.

Table 2 Proportion of Resistance Components ( 1/5 Model

V (Km) 20 25 30 35 40 0.0523 0.0614 0.0716 0.0830 0.0277 0.0184 0.0181 0.0195 E. 0.0967 0.0800 0.0798 0.0897 0.1025 0.654 0.769 0.798 0.810 0.346 0.231 0.202 0.190 0.0967 0.0421 0.0514 0.0620 0.0741 0.0277 0.0184 0.0181 0.0195 0.0015 0.0023 0.0034 0.0046 0.0060 0.0982 0.0721 0.0732 0.0847 0.0996 0.584 0.702 0.732 0.744 0.384 0.252 0.214 0.196 0.032 0.046 0.054 0.060 E: Resistance / Displacement

E4: Viscous Resistance/ Displacement Non-viscous Resistance / Displacement Air Resistance / Displacement

Thus estimated power

and RPM curves are presented

in Fig. 16.

16

The power and RPM calculation from EHP was performed

according to our standard JTTC procedure (k). To obtain the

operating condition of the propeller, the propeller characteristics presented in terms of KT, KQ versus J curves as shown in Figs.

11 and 12 were converted into 11K /J, e versus J curves with

T p

cavitation number cv as parameter, as shown in Fig. 15, where

the propeller immersion for the calculation of the cavitation number was obtained from the results of the resistance tests. The

characteristics of the model propeller were used without correction for scale effects, because a reliable method of correction has not been established to take into account the allowance for the

full-scale condition.

The self-propulsion factors were assumed to be

con-stant with respect to the ship speed and the results of the

behind tests at 30 knots were

applied uniformly over the speed range to be calculated, although there might be slight variation of self-propulsion factors with

ship speed in connection with the variation of the aft-draught

and the trim. The scale effects

of the self-propulsion factors

were neglected because t and w were very small and the inter-action between the propeller and the pod was considered

mostly free from viscous effect. The transmission efficiency was

taken as 95 %, based on the estimation of the loss in the

transmission system including

the bevel gears.

lOo oO 0.6 H-. 04 02 of Actual Propeller. Fig. 15. Propeller Characteristics

-D 0760 P 01 ' 2 0-3 07 01 o io .2 0'l 0.G

SOD LO°Q

ft 20

500 FST!MATED FROM MOOSL

--O-- TRLEIL Dm14 (SHP)

30

V IknJ

40

sig. 15. Comparison of Estimated Propulsive Performance and Trial Results.

Comparison between the estimated propulsive performance

and the trial data.

On the trial run of the full-scale boat, measurements

were made of the shaft-horsepower by the strain gauge type

torsion-meter at the intermediate shaft (the location is indicated in Fig. 1) as well as the ground speed and the revolution of the

shaft. The results are compared with the performance estimated

from the model tests. As shown in Fig. 16, the agreement between

the measured data and those predicted from the model test results

is fairly good.

Conclusion.

Investigations were made into the method of estimating the propulsive performance of a hydrofoil boat from the test results

on its model as well as the techniques for model testing. The

results of the investigations can be summarized as follows.

18

New techniques for resistance tests were developed in which the model can be given the force and moment equivalent to

those given by the thrust of the propeller. By the use of

such techniques, therefore, the model can be towed at the same draught and trim as in the self-propelled condition.

The resistance tests on the two geosim models were carried out

using the techniques mentioned above. From the tests on the

geosim models a reasonable method was obtained to correlate the resistance of the model with the resistance of the

full-scale hydrofoil boat.

The overall propulsive performance of a full-scale boat was calculated from the estimated resistance, together with the results of the wind tunnel tests, the behind tests and the

propeller cavitation tests. The estimated propulsive

per-formance was compared with the results of trial run with good

agreement.

In conclusion we can say that the propulsive performance of hydrofoil boats, on which dynamical lift has significant in-fluence, can be estimated according to the same principle as for ordinary displacement type ships, if proper considerations are

taken for the method of model testing and the analysis.

7. Acknowledgements.

These investigations were carried out with the cooperation of all the members of the Mitsubishi Experimental Tank. The

authors wish to express their gratitude especially to Mr. K. Tamura and Mr. N. Chiba for their cooperation in the propeller design, the performance calculation of the actual hydrofoil boat and the

model testing.

References.

K. Taniguchi and N. Chiba, "Resistance Tests on Struts having

a Section Composed of Two-Circular Arcs", Report No. 1LI.38;

Laboratory, Mitsubishi Shipbuilding and Engineering Cb. Ltd.,

Feb. 1962.

(14) K. Taniguchi, "Model-Ship Correlation Method in the Mitsubishi Experimental TanktT, Mitsubishi Technical Bulletin, MTB 01012R,

Dec. , 1963 and Journal of the Society of Naval Architects of