Correlation of model and ship trials of a shallow draught rhine vessel

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CORRELATION OF MODEL AND

SHIP

TRIALS

OF

A SHALLOW

DRAUGHT RHINE VESSEL

B

Prof. Dr.-Ir. W. P. A. van LAMMEREN, Member

and Dr-Er. J. D. van MANEN

TECHNISCHE UNIVERSITEIT Laboratorium voor

Scheepshydrmech

Archief

Mekelweg 2, 2628 CD De?ft

Tel.: O15-786873.p _O15.73J3 APaper read before the North East Coast Institution of

Engineers and Shipbuilders in Newcastle upon Tyne on the 26th February, 1954, with the discussion and correspondence upon it, and the A uthors reply thereto. (Excerpt from the Institution Transactions, Vol. 70).

NEWCASTLE U'ON TYNE

!'UBLISHED BY THE NORTH EAST COAST INSTITUTR)N OF ENGINEERS AND SHIPBUILDERS, BOLBEC HALL

LONDON

E. & F. N SPON, LIMITED, 15, BEDFORD ST., STRAND, W.C.2

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THE INSTITUTION IS NOT RESPONSIBLE FOR THE STATEMENTS MADE, NOR FOR THE OPINIONS EXPRESSED

IN THIS PAPER, DISCUSSION AND AUTHORS' REPLY

PARTICULARS OF MEMBERSHIP of The Institution will be supplied on application Io The Secretary (for address sec cover)

MADE AND PRINTED IN GREAT BRITAIN

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CORRELATION OF MODEL AND SHIP TRIALS

OF A SHALLOW DRAUGHT RHINE VESSEL

By PROF. DR-IR. W. P. A. VAN LAMMEREN, Member

and

DR-IR. J. D. VAN MANEN

Communication from the Netherlands Ship Model Basin, Wageningen, Holland 26th February, 1954

SYNOPSIS.TeStS with a river vessel have shown that it is impossible to determine

the speed of the ship by direct measurements in a restricted depth of water on the

river. The ship is constantly in accelerated or decelerated motion, as a result of

the irregular flow-phenomena of the river. This circumstancé does not simplify

the determination of the allowances necessary to bring the service results into good

agreement with results of the model tests. In this paper a method is given to

determine these allowances, taking as starting point the results of the model test and the revolution-power relation measured on the ship.

In model tests the influence of the tank-width increases as the depth of water

decreases. The fact, however, that the resistance curves for one depth of water

Vs

and varying tank widths, when plotted against the Boussmnesq number

coincide, provides a simple yet valuable basis for the elimination of the wall-effect

in model tests.

Introduction

IN

order to judge accurately the resistance and propulsion qualities of a river vessel by means of a model test, it is necessary, first of all,

to make a study of the allowances required to bring trial-trip and

service results into agreement with the results of the model test.

The allowances on the model-test results of river vessels are of

another kind than those of sea-going vessels. On the one hand, there will be no resistance increase in the case of river vessels due to sea-way,

and on the other hand, owing to the flow phenomena of the river,

acceleration and deceleration forces will cause extra resistance. More-over, these non-stationary phenomena present an extradifficulty in the correlation of the model-test results and the results of the actual ship.

A satisfactory reproduction in a flow tank of the flow phenomena of a river

will in many cases be hampered by great difficulties. Beside this, the definition

and the determination of the velocity of the model in a flow tank form a problem in model investigations of river ships.

The Netherlands Ship Model Basin thought it advisable, therefore, when investigating the service and trial-trip allowances of river ships to start with model tests in undisturbed water. A diagram showing power and revolutions at various depths of water, plotted on a basis of model-velocity is indispensable for the determination and investigation of the above-mentioned allowances.

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280 CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL

1. Description of the Rhine Tanker "Arabia" (owners, Messrs. Plis, van

Ommeren, Rotterdam).

The single-screw Rhine tanker Arabia, of which two models were made according to the scale = 12 and x=20, has the following dimensions:

The screw is a four-bladed screw of the B-series with D= 1,800 mm. and a constant pitch of 1,250 mm. while the blade area ratio Fa/F=05387. The propulsion installation consists of a 6-cylinder, 4-stroke Werkspoor engine T.M.A.S., which is capable of developing 650 b.h.p. metric at 325 rev./min.

The body-plan and the stem contour are given in Fig. L The ship has a

tunnel plate and is equipped with two rudders (Fig. 2). In Fig. 3a the

arrange-ment of the Chernikeeff-log is given and in Fig. 3b a schematic sketch of the arrangement of the measuring apparatus.

The magnitudes measured during the trial-trip were:

(a) During the resistance tests;

L Velocity Vs in relation to the water with the Chernikeeff log. The towing force R, with an Amsier towing-force dynarnometer.

The relative wind velocity and wind direction with an anemometer and wind-indicator.

(b) During the propulsion tests.

The velocity Vs in relation to the water with the Chernikeeff logs. The torque Q with Maihak torsion-meter.

The number of revolutions n of the propeller-shaft with a revolution counter.

The depth of water D minus trim aft with an Atlas-Werke echo-sounder. The relative wind velocity and wind direction with anemometer and wind-indicator.

The trim with a flask water-level, an apparatus for trim-determination, based on the principle of communicating vessels. The draught was kept constant for all tests. For a tanker this was easy.

In a central measuring-room the velocities of the different Chernikeeff logs were recorded on a time basis on a recording table. The revolutions of the

propeller shaft were recorded. The receivers of the Maihak torsionmeter and

of the echo-sounder were also set up in this measuring-room.

Before the measurements on the Arabia were carried out the intermediary shaft was statically calibrated by the firm Werkspoor at Amsterdam. Fig. 4 shows the calibrating apparatus for the intermediary shaft. With this static calibration both a simple torsion test and a combined torsion pressure test

were carried out. The maximum torque with these calibrations amounted to

1,440 kgm; the maximum pressure 6,000 kg.

lt appeared then that no

hysteresis phenomena occurred and that the torsion measurements are not i nfluenced by a pressure force.

Length between perpendiculars... 76°50m.

Length on c.w.l. ... .. 77-73m.

Breadth ... ... ... 1000m.

Draught at even keel ... i 85m.

Displacement moulded ... 1,095 m.

Midship section coefficient ... 09914

Block coefficient (on perpendiculars) ... 07739

Prismatic coefficient (on perpendiculars) 0-7806

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COIl RELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RIIINE VESSEL 281

The modulus of elasticity in shear that can be calculated from the results of this calibrating with the Maihak torsionmeter amounts to:

G=8279

lO5kg/cm2

In Fig. 4 the arrangement of the thrust-meter is shown. This thrust-meter, which is constructed according to a principle of spring flanges and in which an inductive method of measuring was applied, did not come up to expectations, so that in this paper the results of this thrust-meter cannot be given.

The ms. Arabia was originally painted with two coats of red-lead, one coat

of black paint and one coat of black lacquer. Before the tests were commenced,

the shell of the Arabia was scraped and one coat of coal-tar was applied. The ship at the time of the experiments was three years old. With the help of a camera which was designed by the Geodesy Laboratory at the Technical University of Delft especially for this purpose, a number of photographs were taken of the uneven surface of the hull of the ship. This method is based on the principle of photographing the shadows of the ship's uneven surface cast by incident light falling on them slantwise. These shadows were stretched in one direction by the pantograph of a photogrammatic calculating-instrument (see Fig. 5) and measured.

2. Resistance Test with the Rhine Tanker "Arabia."

The resistance test with the actual ship was carried out along the New Water-way between Rotterdam and the Hook of Holland. The depth of the water along this waterway is fairly constant and amounts to 12m. while the width of the navigable water can be estimated at about 300m.

For this resistance test the screw was removed from the shaft and round the shaft was a dummy hub in order to bring about a favourable flow.

The Arabia was towed by the sea-going tug Zuidzee belonging to Messrs. L. Smit & Co's International Towing Service by means of a nylon cable 250-300m. in length. The towing-force was measured with the Amsler towing force dynamometer placed on the fore-deck of the Arabia. At this distance it was easily possible to keep the m.s. Arabia out of the propeller-water flowing from

the tug. In this way no disturbing influence from the tug was exerted on the

resistance measurements.

The Amsler towing-force dynamometer consists of three parts, namely a cylinder filled with oil, linked up between the rope and the rope winch or towing bitt; an automatic pump driven by an electro-motor, with an oil reservoir and switch for the two measuring-fields of 0-10 tons and 0-20 tons respectively; and the self-recording manometer for both measuring fields with the measuring tape. A generator driven by a petrol motor produces the 110 volt, direct current required for the pump.

The pump ensures that the piston of the cylinder remains approximately in the central position and that the oil leaking along the cylinder piston is pumped back into the reservoir. It switches itself automatically on and off by means of electric contacts fitted inside the cylinder. The oil pressure, a measure for the towing force thus developed, is recorded by the manometer which is equipped

for two measuring fields. The required measuring field of the manometer is

switched on by the switch in the pump box. It is not possible to take

measure-ments when the switch stands at the zero position as the oil supply to the

recording-apparatus is then cut off. In the cylinder, electric contacts are to be

found which set a buzzer going in the pump-box if the piston makes too large a deviation from the central position, for this might be dangerous. They thus limit the movement of the piston. This apparatus has only recently been brought into use. it is proving entirely satisfactory, however, and is accurate to within a very small percentage.

The arrangement of the apparatus for a resistance test is shown in Fig. 6. The velocity was measured with a Chernikeeff log calibrated on the measured mile, placed under the bottom of the ship at the place of the foremost cofferdam.

Table 1 gives the details of this resistance test. Fig. 7 gives the results of the

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TABLE 1.-Resistance Test with the Rhine-tanker

"Arabia" on the New Waterway

(depth of water = 12m.), 12th September 1952

The water-temperature rose between Rotterdam

and Hook of Holland from 15 8°C. to 165°C.

The specific gravity of the water

was at Rotterdam I 000 and at Hook

of Holland I -Oli Kg/j3. I-.)00 n o

r

- o z o'1 o o

i

'-I

r

o z

r

o o o 01V,

r

Run IVo. Time of Start Time of Finish Vin k,,:. ¡h Cher,:, R in kg. Sailing direction Wind Velocity _{in ,n. ¡sec.} Wind direction in 1 9-21 9-27 9,244 825 to Hook of Holland 2-3 90-120 SB 2 9-37 9-44 10,645 1,020 ,.

35-4

125-130 SB 3 0-00 10-07 12,197 1,350 ,, 3'7 105-110 SB 4 0-13 10-20 12,917 1,610 ,, 3_,3.9 90 SB 5 0-27 10-36 14,688 2,200 ,, 65-8 60 SB 6 0-46 10-53 13,896 1,900 ,, 6-8 60 SB 7 1-16 11-24 18,036 3,950 to Rotterdam

95

45 P 8 1-34 11-41 17,633 3,600 ,, 7 50-60 P 9 ₁₀ 11 12 1-45 1-57 2-08 2-52 Il-50 13-00 17,150 16,650 16,974 15,282 3,350 3,150 3,355 2,550 ,, ,, ,, to Hook of Holland 9 9-10 ₁₀ 5-6 45 p 40 p 30 p 45-60 SB 13 14 3-07

-13-14

-15,361

-2,675

-,,

-7-10

-30 SB 15 3-40 13-46 16,538 3,100 to Rotterdam 7 60 P 16 3-50 14-02 16,826 3,300 ,, 6 45 P 17 4-07 14-14 17,183 3,300 ,, 6 60 P

18'

-19 20 21 22 4-30 4-38 4-50 5-30 14-36 15-36 16,682 17,086 15,314 12,175 3,250 3,150 2,680 1,450 ,, ,, ,, to Hook of Holland 7-8 7-8

75

8'S 45 P 45 P 0 ₆₀ SB 23 24 25 26 5-40 5-53 6-04 6-30 13,414 14,317 14,911 14,814 1,770 2,100 2,300 2,400 ,, ,, ,, to Rotterdam

50 70 75

65-7 fjJ SB 45 SB 45 SB 45 p 27 28 6-43 7-10 17-17 15,602 14,494 2,740 2,180 ,, ,, 65-7 65 45 P 45 p 29 7-26 17-31 13,543 1,850 ,, 6 45 P 30 7-36 17-45 12,352 1,530 ,, 55-6 20 P 31 32 7-51 8-00 17-57 11,851 10,789 1,420 1,200 ,, ,, 6 6 45 p 20 P

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CORRELATION OF MODEL AND Sl-OP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL 283

3. Propulsion Tests with the Rhine Tanker "Arabia"

On the New Waterway, along the "measured mile ", propulsion tests were carried out in flowing water, and at the same time several Chernikeeff logs placed in front of the ship and the Chernikeeft log in the foremost cofferdam were calibrated at different speeds. Here the "mean of means " was con-stantly determined from four runs per number of revolutions. Moreover, propulsion tests were carried out with the Arabia on the North Sea Canal between Amsterdam and Imuideri, that is, in still water. The depth of water in this canal is 12m. and practically constant, while the width amounts to 150-160 m. During these measurements the speed was registered with the Cherni-keeff logs in front of the ship.

The results of the propulsion tests on the New Waterway and the North

Sea Canal are given in Fig. 8. Differences between the results of measurements

in the New Waterway and those in the North Sea Canal are due not only to the influence of the width of the water but also to weather conditions.

During the measuring-trip along the Rhine between Rotterdam and Basle both up and down stream, the torque, the number of revolutions and the water depth minus trim aft were measured at definite intervals of time. From velocity measurements carried out with the calibrated logs, it appears that the motion of vessels on the Rhine, with the restricted depth of water there is continually accelerated and decelerated as regards the water. In Fig. 9, the measured powers and number of revolutions are plotted as functions of the ship's velocities, measured with the Chernikeeff-logs, for different groups of water-depths minus the trim aft. This shows clearly that under the given circumstances it is impossible to measure directly the velocity of a ship on a river.

For similar reasons it turned out to be impossible to measure the trim ori board the ship: but it is possible to determine the relation between the power and number of revolutions for different groups of water depths minus the trim

aft. (See Figs. lOa to 10f inclusive). These results increase our confidence in

the accuracy of the measurements that have been carried out. In Fig. 10g the revolutions-power relation for the various water depths minus trim aft have

been assembled together.

4. Experiments with the Models of the Rhine Tanker "Arabia"

(a) Resistance Tests

For the model tests in shallow water the N.S.M.B. uses a false bottom in the model basin. This false bottom consists of 25 sections, 8 m. long. The construction by which two sections are connected is given in Fig. 11. One end of each section is suspended from the wall of the model basin, the other rests on the adjacent section. In this mutual pressure between upper and underside of the bottom is excluded by these connexions. The gap between the pontoons and the wall of the basin amounts to 4 cm.

The model on scale = 12 was constructed of paraffin wax, and provided with a trip-wire (0=1 Omm.) at I /20L of the f.p.p. to ensure a turbulent flow along the model. The model on scale =20, is a lacquered wooden model,

likewise provided with a trip-wire (0=1 0 mm.) on 1/20 L off.p.p.

With the results of these two models on different scales, efforts were made

to analyse the influenceof limited tank-width. In Fig. 12 the resultsofresistance

tests in different water depths are given, dimensionless, on the basis of Reynolds' number. From these data it is clear that the results for the smallest model for a considerable part of the tests are influenced by the occurrence of a laminar boundary layer, notwithstanding the introduction of a trip-wire.

In Fig. 13 the resistance-curves for the ship are given, as derived from the model tests. These resistance curves hold for the smooth ship, and were extrapolated according to Schoenherr from the results of the model on scale o=12. _{The width of the water corresponding to the width of the tank amounts} for the curves to 12 X tank-width = 126 m. Also, for the high velocities, the

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284 CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAIJGHT RHINE VESSEL

results of the model on scale a = 20 are drawn in this figure. Here the width of water corresponding to the width of the tank amounts to 20 X tank width = 210 m.

On the matter of the wall-effect of the tank on the results of model tests, several interesting data have been published. The most valuable study on

this subject is, apparently, the paper by Comstock and Hancock'. If, however,

in accordance with the conclusion of Comstock and Hancock, we introduce and LID as the most important parameters, it appears that the data derived from the tests of Comstock and Hancock for restricted water-depths

are insufficient. The depths selected by Comstock and Hancock are too

great to be of any use in the construction of directions for determining the influence of water depths such as actually occur when navigating rivers like the Rhine. In his most recent paper, Telfer' concludes from the work of Comstock and Hancock that there is rectilinear connexion between the specific resistance of a model in a restricted depth of water and with limited width on

(x)

the one hand, and the blockage coefficient m = on the other.

Br0k D

-In the contribution by Lap' to the discussion on Telfer's paper, the results of Comstock and Hancock have been plotted in the way mentioned above.

(See Fig. 14). In this figure the relation does not appear to be rectilinear.

Nevertheless, we will investigate the value of Telfer's method as an approxima-tion for the eliminaapproxima-tion of wall-effect in the model results. In Fig. 13 some points are given of the ship's resistance for infinite width, calculated from the results of both models of the Arabia according to Telfer's method.

From Helm's study3 concerning the influence of water depth and width on the resistance of the ship, it appears that if the ship's resistance per ton is

plotted against the Boussinesq number V,I /g& the results obtained with equal

depth but different width of water coincide fairly well up to the critical velocity. This means that for the resistance-curves at different depths, the ratio of the velocities at equal resistance must be equal to the ratio of the root from the

hydraulic radii Rh. If we check this for the results of the models on scale

a = 12, respectively a = 20, we then obtain the values given in Table 2. TABLE 2

I)

B, D

Bj+2D

'Numher refer to list of References at the end of the paper.

2) Rh=

B..D_(X)

B, -j- 2 D ± bm ± 2d D V,z=12 I)

-2)

-Va=20 V, V 12 0967 0967 0951 6 0980 0982 0960 5 0984 0986 0962 4 0984 0989 0963 3 0977 0991 0963

25

0975 0992 0962

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CORRELATION OF MODEL AND 5H11' TRIALS OF SHALLOW DRAUGHT RHINE VESSEL 285

It appears from the table that, at equal resistance values and down to a depth of 3 ru. the ratio of the velocities calculated from the results of the z = 12 and = 20 models agree pretty well with the ratio of the velocities which follow from using Helm's method (equal Boussinesq numbers), particularly if we choose the hydraulic radius

B, D

Rh

_{- B, + 2D}

If we calculate the resistance curves for infinite water width by this method, Telfer's method appears to agree to a considerable extent with Helm's method, except in the case of very limited depths.

The theoretical deduction of a connexion between Telfers' and Helm's methods meets with difficulties on account of the shape of the resistance curves. If we assume a simple relation, e.g. quadratic, between the resistance and the velocity, there appears to be no relation between the two methods. It is impossible to judge Helm's method in the same way as Telfer's, namely, by the data given by Comstock and Hancock, as these data are too incomplete. With the help of the Boussinesq number, however, it is possible to deduce the resistance curves for other widths of water from a given resistance curve, determined for a limited width of water or of the basin. If we calculate four or five resistance curves in this way, it is possible to plot out the resistance increase according to Helm as a function of the blockage-coefficient. This

has been done in Fig. 15. it shows that this resistance increase, plotted against

the blockage-coefficient, can indeed be called linear, which implies that the

methods of Telfer and of Helm practically agree. The advantage of the former

method is that possibly a test on one model at one tank width will suffice. If the data of two models at one tank width, or one model at two tank widths, are known, Telfer's method will give a better approximation than Helm's for very shallow water.

In conclusion, the resistance curves for the different restricted water depths have been constructed from the resistance curves for "infinite" depths according to Schlichting4 (see Fig. 16), which shows that the resistance values given by Schlichting, for a ship of the same shape as the Arabia, are too high. In Fig. 17 the resistance curves for D = 12 in. and B = 126 ru. respectively 300 ru. (average river width) and B = so, are calculated according to Schoenherr

and Helm from results of the model on scale = 12.

The resistance curve for 12 m. depth, calculated according to Schlichting from the resistance curve for D = so, appears again to give too high results. The point calculated according to Telfer's blockage method from the results of both models, agrees pretty well with the resistance curve, calculated for B = by Helm's method. From measurements of the roughness of the hull (Fig. 5) it appears that the unevenness amounts to about 02 to03 mm. (about 001 in.). This degree of roughness practically coincides with the Mare Island hot plastic pattern in which, for the high Reynolds numbers, Todd5 found a roughness allowance of 000062 on the Schoenherr frictional resistance coefficients.

The allowance found for wind resistance and steering resistance amounts then on an average to about 9 per cent., which may be considered as acceptable. The wind velocity and direction are given in Table I. In contra-distinction to the propulsion tests on the Rhine which have still to be treated (at depth of water less than 6 m.), no interference from non-stationary phenomena is met with a depth of 12 ru. and the ship's speed can be measured very well.

(b) Propulsion Tests with the Models

The propulsion tests with the models on scale = 12 and = 20 have been

carried out without frictional corrections Ra (self-propulsion point of model). The reason for this is, on the one hand, the uncertainty of the accuracy of the frictional correction (Ra) for model tests in restricted depth of water, and on the other, the fact of the trim being influenced by the propeller load. So long

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286 CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL as the propeller load of the actual ship is unknown, it is impossible to establish

the correct propeller load in the model. But, for the rest, there is no objection

to this method of carrying out tests. Whether, when scale tests are made, the extrapolation is taken from the s.p.p. of ship or from the s.p.p. of model, both methods must eventually lead to the same values for the ship. The results of the propulsion tests without Ra of the model according to scale

= 12 are

given in Fig. 18.

In Fig. 19 the results are given of the above-mentioned propulsion tests with the skin friction correction, as calculated according to Schoenherr. In these calculations the following scheme was followed: with the help of the resistance values for the smooth ship, extrapolated according to Schoenherr from the results of the model on scale z = 12, the thrust as a function of the ship's

speed is calculated with the thrust deduction fraction derived from the propulsion test of the model on scale z = 12. When the wake fraction is known (in this case the effective wake values are determined from the propulsion

tests and an open-water test for the model screw on scale = 12), the correct

number of revolutions can be determined by means of the well known trial and error method, from the A - K - relation. The corresponding torque constant KQ can also be read off from the open-water diagram, by which the power can be calculated as a function of the ship's speed for any depth.

In Fig. 17 are given at the same time the values calculated from those results of the model on scale z = 20, for which it could be said with certainty that no

more disturbing laminar-flow phenomena occurred. 1f we determine at equal

resistance the ratio of the velocities for the results of both models, i.e. where the water-breadths are 126 and 210 ra. respectively, this ratio agrees well with the ratio from the roots of the hydraulic radii. As regards the DHP curves, Helm's method (Boussiriesq number) is therefore very useful for eliminating

the wall-effect of the towing-tank. The alteration in the propulsion coefficient

resulting from the alteration of the load, when the water-width is varied, is so slight that it can easily be ignored in this method of approach.

In Fig. 20, the results of the open-water test with the model screw on scale = 12 are given both with and without the tunnel plate. Considerations concerning the wall-effect lead to the expectation that with an equal advance coefficient A, both the thrust constant Kr and the torque constant KQ decrease as a consequence of the presence of a tunnel-plate. The screw efficiency 'je,

decreases slightly.

In Fig. 21 both the thrust-deduction fraction and the effective wake values

are given, based on the depth-draught ratio. The wake values were determined

in different ways with the help of Fig. 19 at varying water depths and full load

of the ship's engine. In this figure the influence of the presence of the

tunnel-plate on the determination of the effective wake fraction is shown very clearly. Both wake fraction and thrust-deduction fraction appear to increase to a great extent in shallow water. That this increase is not brought about solely by alterations in the potential flow is clearly seen in this figure. For, if the increase were solely due to potential flow phenomena, the increase in the wake fraction would have to be equal to the increase in the thrust-deduction fraction. Whether, on the other hand, the increase in wake fraction and thrust-deduction fraction is due solely to frictional phenomena, it is difficult to conclude from Fig. 21.

5. Correlation of the Model Tests in Restricted Depth of Water and

the Propulsion Tests with the Actual Ship

In Fig. 22 the results are given of the propulsion tests on the North Sea Canal and the New Waterway compared with those of the model tests on

scale = 12. By means of Helm's method the curves are deduced for widthr of water of 160 m. and 300 ra.

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CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL 287

The allowance on the results for the smooth ship, calculated according to Shoenherr's frictional coefficients, amounts for the North Sea Canal to an average of 269 per cent. (before the wind), 409 per cent. (against the wind), and for the New Waterway to an average of 47 1 per cent.

The wind velocity for the tests on the North Sea Canal amounted to an average of 5 4 m. ¡sec. and for the tests of the New Waterway to an average of 7.0 m./sec.

Difficulties occur when determining these allowances for river navigation at different depths, for it turned out to be impossible to determine the velocity of the ship on the river by direct measurement. It also turned out to be impossible to determine the trim.

For the first attempt to solve this problem, use was made of the regression-equation.6 & These equations were set up for the different depths for the

model on scale = 12, and also for the actual ship in 12 m. depth of water. In

this way we hoped to be able to deduce the regression equations for the other depths for the actual ship. lt appears, however, that the wake fraction for restricted depth, both as regards the determination and the conduct, gives rise to such difficulties that the regression equation becomes too rough a method of approach to obtain useful results. For the same reasons no results are obtained from the method by which the torque constant is calculated from the known revs.-power relation of the screw of the actual ship ; and with the aid of the open-water diagram of the model screw on scale = 12, the speed of advance Ve, is determined and subsequently with the aid of the wake values of

the model on scale = 12 the ship's speed V3.

The scale-effect of the wake and the roughness of the ship also play an important part here. If we assume that in the open-water test with the model screw on scale = 12 there is an absence of scale-effect, it follows for the open-water screw diagram that the wake-figure for the rough ship during the test on the North Sea Canal amounts on an average to 026. The wake figure

for the model amounts for this depth of water to 022. From considerations of scale-effect it follows that in corresponding conditions the wake fraction of the smooth ship must be smaller than the wake fraction of the model. As a result of the greater roughness of the ship, the wake, however, increases. Quantitative considerations of the magnitude of the above mentioned decrease

and increase must, however, be taken as speculative (see Appendix). If, though,

we take the wake fraction of a ship to be 022, i.e. equal to that of the model, the KQ-curve in the open-water diagram would have to be shifted further than considerations of scale-effect would lead one to think possible.

In conclusion, we shall deal with the method which has made it possible to determine the allowances for the ship on the river. Use is here made of the fact that with a certain overloading of the screw of the ship or model, the number of revolutions of the screw diminishes at constant power.

By means of the propulsion tests without Ra of the model on scale = 12 and the propulsion test on the North Sea Canal (Fig. 18) a diagram can be constructed in which for different engine powers the decrease in revolutions of the screw is given as a function of the overload of the model screw (Fig. 23).

This overload i due to the difference in depth of water. From Fig. 10g, the

diagram showing the revolution-power relation for the actual ship at different water depths, it is possible to determine the decrease in the number of revolutions in relation to that at 12m, depth minus trim aft, at various values of the power and the water depths minus trim aft. In Fig. 23 the overload percentage corresponding to this decrease in the number of revolutions can now be read off. In this way we have determined the overload percentage for the different depths of water minus trim aft, and for different powers, with respect to the power

curve for 12 m. water depth, minus trim aft. As, however, for the 12 m. water

depth, minus trim aft, the revolutions- power relation on the basis of ship's speed Vs is known (North Sea Canal), the power curves with the corresponding

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288 CORRELATION OF MODEL AND SHIP TEJALS OF SHALLOW DRAUGHT RHINE VESSEL

revolutions can be constructed as functions of the ship's speed (Fig. 24) for

different depths of water. In Figs. 25, 26, 27, 28 and 29, the values, measured

for the actual ship and deduced in the manner given above, are plotted together

with the results obtained from the model tests. The curves for different widths

of water have been deduced again with the help of Boussinesq's number from the curve for B = 126 m. (model on scale = 12). The allowances are calculated, starting from curves for B = 300 m. this being about the average width of the Rhine.

When comparing the propulsion tests carried out with the model on scale = 12, and the propulsion tests with the rough ship on the Rhine, special attention must be paid to the fact that the depth of water minus trim aft was measured with the Atlas-Werke sounder at the position of the

echo-sounder. Since this trim could not be measured on the Rhine, the results of

the actual ship have been given for constant water depth minus trim at the position of the echo sounder. In reality, the measured power curves of the rough ship plotted as a function of ship's speed hold, therefore, for a variable depth of water, for the trim of the ship varies with the ship's velocity.

With the aid of the trim diagram (Fig. 30), determined from measurements on the model, the model test results plotted for constant depths can be adapted to results holding for constant depth minus trim.

If in Figs. 24 to 29 inclusive we calculate the allowance percentages necessary to bring the results of the model tests into agreement with the service results of the rough ship, we then obtain Table 3.

TABLE 3Allowance Percentages on Model Results Calculated with the Schoenherr Extrapolator

If we study the allowance percentages applying to Rhine navigation.

(D - ta = 6 to 25 m.) we see that, with the exception of D - t = 25 m.

the allowance percentages at full power increase as the depth of water decreases,

Also, the allowance percentages increase with increasing power. It should be

mentioned here that at high speeds the bow waves came up over the bow

anchors. At high speeds and small depths the stern anchor was dragged

through the water as a result of the considerable trim aft. It is practically impossible to reconstruct these conditions reliably on a model basis.

The allowance for Rhine navigation at full power amounts to 45 to 70 per cent. This allowance consists of the following components:

Roughness allowance: 15 to 20 per cent. (see Appendix II). Wind resistance: 8 to 10 per cent.

Resistance due to non-stationary flow phenomena and the anchors 22 to 40 per cent.

Dta

600 DHP service 500 DHP 400 DHP 300 DHP 200 DHP 12m. 161% 235 320 364 370 still water 6 460 449 408 383 360 5 511 453 389 402 316 4 639 475 361 277 258 flowing water 3 685 470 250

lll

7O

25

376 241 4-2

107 lll

(13)

CORRELATION OF MODEL AND SHIP TRJALS OF SHALLOW DRAUGHT RHINE SESSEL 289

The non-Stationary flow phenomena are evident both in the accelerations and decelerations of the ship with respect to the water in the sailing direction, and also in the variations in direction of flow with regard to the ship.

At

D - ta

= 25 m. a negative allowance percentage is found over a part

of the DHP curve. The reasons for this may be:

The correction of model test results for limited width of water can no longer be regarded as a good approximation at very small depths of water.3

The trim diagram used when calculating the

D -

= constant-curves applies to the condition of the load: model without Ra, therefore self-propulsion point of model. This load condition is not equivalent to the load condition of the rough ship on the Rhine, so that properly speaking the overload tests ought to be carried out with the model. In great depths of water the dependence of the trim on the propeller load will be small. However, in very small depths of water(D

= 25 m.) the

propeller load will certainly influence the trim.

The trim diagram applies to still water. It is difficult to say in how far

the trim of the rough ship, proceeding in the velocity profile of the river, which varies in the direction of the depth, deviates from the trim

in still water. It is certain that, if differences arise, these only occur in

very shallow water, i.e. therefore when the bottom of the vessel enters an area where flow velocities decrease strongly towards the bottom. The DHP curves for the smooth ship are calculated from the model results of the propulsion tests without Ra. In these calculations the

effective wake fraction w is used. In very shallow water the

determina-tion of the wake fracdetermina-tion cannot be carried out with high accuracy.

Telfer's method, it is true, will at

D - t

= 25 m. lead to better results,

but the elimination of the influence of the width on model results with the correction value found for high velocities, over the entire speed range remains a rough approximation.

For very small depths of water the relatively greater thickness of the boundary layer of the model may be the cause of the deviation of the model test results from the results of the actual ship.

6. Conclusions

From the above investigations and calculations the following conclusions can be drawn:

The speed of a ship, navigating a river, is not to be determined by direct measurement.

From Figs. lOalOe, it

is evident that the revolution-power relation up and downstream is the same for various depths of water. A fall

resistance is, therefore, not measured on the actual ship. It is remarkable

that even at very small depths no difference occurs in the revolutions-power relation for either up- or downstream navigation. This shows that

the differences in the influence of the velocity profile coefficient of the flow on the river, the influence of the ship's speed in relation to the bottom of the river, and the fall resistance of the ship up and down stream neutralize each other. The fall resistance for the Arabia amounts, at 1,016 tons of water displacement, to about 10 kg. for a fall of the river of 1 cm. ¡km. At those places where the propulsion tests have been performed the fall of the Rhine amounts to 8 to 24 cm. ¡km. From this it would follow that tests with river vessels could be adequately carried out in normal towing-tanks, so that the construction of special flow tanks for this purpose is not necessary. This far-reaching con-clusion, however, ought to be tested by other cases before being wholly accepted.

(14)

290 CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL (e) In these tests, the great influence of the tank-width on the results of

model tests in restricted depths of water has once more been brought

to light. lt was not possible to determine this width influence with the

data of Comstock and Hancock'. On the one hand, the hull forms investigated by Comstock and Hancock in this case differ too much, and on the other hand the shallowest water investigated by Comstock and Hancock is much deeper than is to be found in rivers such as the

Rhine. Both Helm's method (Boussinesq number) and that of Telfer

(blockage-coefficient) turn out, in this case, to be good methods of approach for eliminating the influence of the towing-tank width in model test results.

If the model data are available for two blockage-values, Telfer's method is to be preferred for a very shallow water depth. Nevertheless it must be taken into account that when applying both methods, for both very small and unlimited depths of water, there will be deviations, it could already be seen in Helm's experiments that the resistance curves for one depth of water and different widths, plotted against the Boussinesq number, no longer form one coinciding curve at very small water-depths. The experiments with the two models at small depths (25 and 3m.) confirm this.

From the above it follows that in experiments in restricted depths with models of river ships in a towing tank, a proper correction for

wall-effect is of far more importance than the reproduction of the velocity profile of the river and the velocity of the water relative to the

bottom. That the approximation methods dealt with here will not be

correct for unlimited depths, can be ascertained best of all by

Boussinesq's method.

According to Helm's method:

V.

VB, D1

VB2 ± 2 D,

V, -

- VB, . L

VB. ± 2 D,

If D, = D,, the formula becomes:

V,

Vl±2D/B,

V,

_{- Vi + 2D/B1}

For a depth ofwater in the tank of55m.and withawidth B1 = 105m. the ratio V,/V., for B. would be 071. Considering the agreement between Telfer's and Helm's methods, the application of both methods, when eliminating the wall-effect from the experiments on model families at unlimited depths of water, will involve too great corrections. The non-linear ratio between the resistance coefficient and the blockage-values in Fig. 14 is already an indication in this direction as far as Telfer's method is concerned.

(d) In Figs 25 to 29 inclusive the results of the measurements on the actual ship on the Rhine are compared with the model-test results.

For actual depths of water occurring in most of the rivers in Europe (4 to 6 m), the results of model-tests at restricted depths in the tank

appear to yield reliable results. The allowances found are high compared

with the allowances for sea-going ships, but they can be accounted for in connexion with the non-stationary phenomena.

At very slight depths (25 m.) negative allowances appear to be necessary over a part of the power curve to bring the model-test results into agreement with the results on the actual ship. This is chiefly due to the lack of a good correction method for the wall-effect.

(15)

7. Indications for Future Research

The results of the investigations into the allowances on model-test results of river ships showed the desirability of carrying out the following research in

the

future:-The performance of propulsion tests with the m.s. Arabia in still water at varying depths. In this way, the influence of non-stationary phenomena in the flow of the river on the ship's resistance can be investigated.

Comparative tests with a model in the tank and in a flow tank. These tests have already been carried out with the model at scale = 20. The laminar-flow phenomena of

this model in the tank and the

comparatively small dimensions of the flow-tank make the comparison difficult. These tests will have to be repeated on such a scale that the comparison cannot be hampered by subordinate phenomena.

Experiments in a limited depth of water in the basin at various widths of water in order to determine as accurately as possible the width-influence on results of ships sailing in restricted depth of water. This can be achieved by erecting artificial banks in the model basin.

Experiments with a model family in limited depths of water. In this way it may be possible to indicate a better method than the present one of extrapolating model-test results

by means of plate

frictional

coefficients.

Acknowledgments

At the conclusion of this paper, a word of thanks is due to all those who have lent their assistance during the carrying out of the experiments. The Authors wish in particular to thank:

Messrs. Phs. van Ommeren Ltd., shipowners, for placing the Rhine tanker Arabia at their disposal and for the extensive help given during the measurements on the large ship.

Messrs. Boele's Shipyards and Machine factory, Bolnes, for manu-facturing and setting up the apparatus for taking velocity measurements.

"Werkspoor" Ltd. for their co-operation in the static calibration of the propeller-shaft and in the measurements on board the Arabia.

Messrs. Smits International Towing Service Ltd., for towing the Arabia

during the resistance test. The Rijkswaterstaat (Department of Public

Works) for their co-operation in providing and working the echo-sounder apparatus.

Mr. H. Nijding, member of the staff of the

Research Department of the N.S.M.B. To him a special word of thanks is due for performing an important number of measurements on the ship and models, and for working out and analysing a large portion of the results.

(16)

292 CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHThJE VESSEL

APPENDIX I

The tests with the model-family of the Simon Bolivars have led to the following conclusions as regards the scale-effect in the

wake:-The wake-fraction w decreases as Reynolds number increases. The wake-fraction w increases as a result of the roughness of the hull. For extrapolation of the wake-fractions of the models according to the wake-fraction for the technically smooth ship, the following train of thought may be important.

From the point of view of impulse, the frictional resistance of a body (ship) is

directly proportional to a quadratic function of the frictional wake-fraction. An element of frictional resistance of the body (ship) can be represented by:

dRj, = pV'(V5Ve)dF = p(l -. Wfr')(Wf,') V dF

in which Ve' = the ship's velocity minus the frictional wake-fraction at a point in a

plane behind the body (ship) at right angles to the direction of motion. The total frictional resistance will then become:

Rj, = pV . f(l - wpr') (wfr')dF = p V2 F(a Wfj' + b Wf,2)

in which the integral extends over the whole plane behind the ship at right angles to its direction of motion. From this equation it follows, however, that:

R1,

2

= = C1 Wfr + C1 Wfr

If we calculate the wake-fraction for the smooth ship by means of the data from the

Simon Bolivar model-family and from this equation, we then obtain the following

result:

In this calculation the potential wake-fraction is considered as being independent of Reynolds number and is accepted as 010.

From the data of the models on scale = 25 and 15, it follows that:

Hence ?fr = 00044 wfr + 005427 Wfr2

so that for the smooth ship at Re 73l . 10 and jr, = 1592 . l0- the frictional

wake-fraction becomes wf, = 0 135 and the total wake-fraction w = 0235.

If, owing to the roughness of the ship's hull the frictional resistance coefficient

increases, the increase in the frictional wake-fraction can likewise be calculated from the deduced relation between rjr and wfr.

Wake-fractions for the Actual S/zip "Simon Bolivar"

r Wf, W(0

-

0135 0235

00002 0146 0246

00004 0155 0255

00006 0I65 0265

is the roughness allowance on the frictional resistance coefficient of Schoenherr. Similar considerations can be applied to the Rhine ship Arabia. However, the lack of results from tests with a model family, an open-water test with the screw of actual dimensions, and the rather defective knowledge concerning the roughness influence on the ship's resistance make these considerations in this case speculative. It remains, however, a remarkable phenomenon in the case of the Arabia that even with increase

in the torque constant due to scale effect, which can be accepted as reasonable, the

wake fraction of the rough ship will remain larger than the wake fraction of the smooth

model. With a relatively equal translational velocity of model and ship, a smaller number of revolutions of the ship's screw in respect of the model screw would

correspond with this. This decrease in the number of revolutions has indeed been

observed during experiments with the Arabia.

Re 10_6 fT l0 w tot Wfr

25 641 3158 O304 Ø 204

(17)

CORRELATIONOFMODEL AND SHIP TRIALSOFSHALLOW DRAUGHT RHINE VESSEL 293

APPENDIX II

When calculating the roughness-allowances for restricted depths of water, we must bear in mind that the potential flow-velocities along the midship increase as the depth of water decreases. When carrying out the model-tests with the Arabia, velocity

measurements were taken at different places along the moving model on scale a = 12.

if, however, the resistance coefficients of the model are plotted as a function of

Reynolds number, the magnitude of these resistance coefficients for low model velocities (wave resistance = 0) and different water depths will likewise give an indication of the magnitude of the velocity increase along the midship as a consequence of the potential phenomena. The following relation will approximately have to

hold:-(V,01.') :

D=a

D=b

D a

Dh

In the following table, the comparison has been made between the measured and

thus calculated potential flow velocities along the midship.

measured. The measured values apply to measurements along the midship over 0 3L, at draught

and 065 to t OB from centre-line of ship. t Calculated.

In this table, therefore, when calculating the potential flow-velocities from the resistance coefficients, the measured velocity increase of 3 per cent, at D = was used.

From this table it appears that a practically constant difference exists between the calculated and the measured velocity increases.

If we multiply the constant roughness allowance ¿fr according to Schoenherr (for the Arabia jr = 000062) for all depths of water by the factor p V û in order to calculate the resistance increase due to roughness, then we make a fundamental

mistake.

The resistance increases resulting from roughness will increase when depths of water decrease by increasing potential flow-velocity. At the same time it becomes clear from

the increase in potential flow-velocity along the midship with decreasing depth of

water, that the extrapolator of the resistance coefficients of models equidistant from the frictional coefficients of plates for limited depth of water is fundamentally incorrect. From the increase in potential flow velocities for the model, the conclusion can be drawn that the resistance coefficients for limited depths of water must be smaller for

the smooth ship than follows from equidistant extrapolation. Since, for unlimited

water depth the potential velocity along the midship of a similar hull form to the

Arabia amounts to about 3-5 per cent., the extrapolation of model-test results to those of the smooth ship, equidistant from the plate friction coefficients, likewise for unlimited depth of water, is fundamentally incorrect. The method suggested by Lap and Troost9 for extrapolating model-test results points already to this phenomenon. If the correction for the potential flow were taken into account, the allowances found would still increase

and, indeed, most strongly in very shallow water. D 12 V,,01.. V5 3-64 3-64 x 1 035 103-5 103-5 VP0,. -V, 3,5%

-t0t i0tO 1-000 1-000 V, 3-5 3-5 6

-

4-03 1-106 108-8 8-8 5

70

4-18 1148 1108 10-8 4 9,5 4-41 1211 1138 13-8 3 13-0 466 1-280 1170 17-0 2-5 15-0 5-19

(18)

294 CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL SYMBOLS B in Width of water B1 m Width of tank bm m Width of model D in Diameter of screw D m Depth of water

DHP metric Horse power delivered to the screw

d m Draught of ship or model

G kg/cm modulus of elasticity in shear

K = p

D2

Thrust constant Q KQ

-

Torque constant p D n2 L m Length of ship

0

in = Blockage coefficient B1. D

-

(r)

n 1/min. or_l ¡sec. Number of revolutions of the screw

Q kgm. Torque of the screw

R kg. Ship's resistance Re Reynolds number Rh in Hydraulic radius T kg. Thrust of screw

TR

T m Thrust-deduction fraction m Trim aft

V, V, rn/sec.,km/h. Ship's speed

Ve rn/sec. Mean entrance velocity in the screw

V5 V

- w0

Mean wake fraction over the screw disc

Wfr Frictional wake fraction

Wpor Potential wake friction

w' Mean wake fraction on a cylindrical

section of the screw Model scale

(r)

m3 Midship section area

Total resistance coefficient

fr

Frictional resistance coefficient

¿ r Roughness allowance

T.v

= D.H.P. Efficiency of the screw

A Ve Advance coefficient

(19)

CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL 2.5

REFERENCES

I. COMSTOCK, J. P. and HANCOCK, C. H.," The Effect of Size of Towing-tank on

Model Resistance ", Soc. N.A. & Mar. E. Vol. 50, 1942.

TELFER, E. V." Ship-model Correlation and Tank Wall-effect ", N.E.C. Insin., Vol. 70(1953) p. 1.

HELM, K." Tiefen- und Breiteneinflüsse von Kanälen auf den

Schiffswider-stand," Hydromechanische Probleme des Schiffantriebs, Teil II, 1939.

SCHLICHTING, O." Schiffswiderstand auf Beschränkter Wassertiefe" Jahrbuch

der Schiffbaurechnischen Gesellschaft, 1934.

TODD, F. H." The Hydromechanics Research Programme of the Bureau of

Ships, U.S. Navy," Trans. ¡.N.A., Sept. 1953.

BONEBAKKER. J. W." The Application of Statistical Methods to the Analysis of Service Performance Data," N.E.C. Instn., Vol. 67 (1951), p. 277.

GERRITSMA, J." Theoretische beschouwingen bu het Analyseren van

Log-boekgegevens," Schip en Werf, 7 November, 1952, No. 23.

LAMMEREN, W. P. A. VAN" Analyse der Voortstuwingscomponenten in Verband met het Schaaleffect bu Scheepsmodelproeven," Thesis, Publication No. 32 of the N.S.M.B.

LAP, A. J. W. and TROOST, L." Frictional Drag of Ships' Forms," Bulletin,

Soc.N.A. & Mar.E., Vol. VIII, June 1953, No. 2.

(20)

(21)

g,.

6Y

"Correlation of Model and Ship Trials of(z Shallow Draught Rhine Vessel ".

Paper by Prof. DR-IR, W. P. A. VAN LAMMFREN, Member and DR-IR. J. D. VAN MANEN

Plate V

A

-'.4 7Y 8 91/2

Fig. 1Body-plan and Se,n-co,,tour of the ,n.s.

Arabia" io

__p.---D BO

1Y2 2 2Y2 1/a. 1 2. 2)

(22)

(23)

(24)

\anemomeer

eIephone

Fig. 3bSc/u'nie of !vfeasuii,iç Apparatus

on board the ,n.s. " Arabia

trim

(25)

(26)

CORRELATION OFMODEL AND SHIP TRIALS OFSHALLOW DRAUGHTRIflNE VESSEL 301

A.uionatic pump

1 Fig. 5Results of Measurements of Roighness of the Hull

Ro e

Ge ne ra or

Fig. 6-Arrangement of Towing-force Dynamometer y PHOTO 2 10mm 3/5L Pori 1/2 d. k E E

-w

PHOTO 3 10mm 1/2L PorH/2 d.

-__\

PHOTO 4 10mm 2/5L PorM/2 cl. PHOTO 5 10mm 1/5L Pori 1/2 cl. E PHOTO ¶ _4/5L _{Port 1/2 d.} _E E

Cylinder filled wh oil

(27)

0

1000

500

302 CORRELATiON OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL

5000 4500 4000 3500 3000 2500 2000 4500 4000 3500 3000 2500 2000 1500 1000 500 o 9 10 11 12 13 14 15 16 17 lB 19 V5 n km/h

(28)

CORRELATiON OF MODEL AND SHIP TRiALS OF SHALLOW DRAUGHT RHINE VESSEL 303

n/rn in.

North Sea Canal r against

1 before the the Rotterdam wind

/

wind Waerway New

/

10 11 12 13 14 15 16 17 18 1g 20 Vs in km/h

Fig. 8Results of Propulsion Tests with the m.s. "Arabia" on the New Waterway and on the North Sea Canal

35 30 25 2 15 D-D 600 500 400 300 200 100 o

(29)

E

304 CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL.,

n/mm.

-. -.

.?.

-. DHP

_...-.

'r.

..'

-.

':t..' . ...

:..

Da2.53.Om

60m 65m Th

-.lt

-

-Dta=3.O3.5m

D-t= 3.5-40m

4.0-45m

D-

4.5-50m

Dta5.0

p

D a60

10 20 30 4.0 5.0 V5 in rn/sec.

Fig. 9Results of Propulsion Tests with the m.s. "Arabia" on the Rhine 40 30 20 00 00 00 00 00 00

(30)

loo 150 200 250 300 350

n,rnIn

Fig. 10 (a)Revolutions-power Relation for a Depth of Water Varying between 50 m. and 60 m.

(31)

Q-X

5CC 500

4CC 400

100

o oc o

H

0 - F8 = 45 - S down up the m the river river o 50 loo 150 200 250 300 350 n/mm

Fif. 10 (b) Revolutions-power Relation for a Depth of Water Varying between 45 n. and 5 0 ni.

(32)

SO

5

40

20

10

CORRElATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL 307

)0 e S 4 Dta=4-4.5m down up the ic he ricer rIver o 0 50 100 150 200 250 300 350 n/mm.

Fig. 10(c)Reolu1ions-power Relation for a Depth of Water Varying between

40

n. and 45 m.

(33)

6 50 40 30 o-20 10

308 CORRELATION OF MODEL MD SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL

O I-51

.

41 21 1C

0ta354m

down be river up he river a 50 100 150 200 250 350 nf min

Fig. 10 (d)Revolutions-power Relation for a Depth of Water Varying between 3'5 in. and 40 m.

(34)

COREELAJ1ON OF MODEL AND SHiP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL 309 600 500 400 300 z 200 700 o . 4 L 2 down up the he river river o o 50 00 150 200 250 300 350 n/mm.

Fig. 10 (e)Revo!utions-power Relation for a Depth of Water varying between 3 Om. and 35 m.

(35)

6

4

E

o-310 CORRELATION OF MODEL A ND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL

51 41 31

I

31 ii D - =2.5-3 rn .down he river p he river o 50 100 150 200 250 303 350 fl/non

Fig. 10 (f)Revolutions-power Relation for a Depth of Water Varying between 25 in. and 30 m.

o

(36)

70 60 s 40 Q-20

CORRELATION OF MODEL AND SHTP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL 311

46

D-ta-25m D-t6-30m 0_r16 _40m

iI

_________________________________________ 0- = 50m

.50

0- L =12.0 m

40C

0 X

pp1t-

20( 100 o 100 125 150 175 200 225 2 275 300 325 350 fl/m n.

(37)

500 4000 3000 D, = 1000

312 CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL.

Adjuslable boticm

o

8 9 10 11 12

V5 in km/h

Fig. 11Construction of the False Bottom in the Towing-tank

13 14 15 16 17 18 19

Fig. 13Results of the Resistance Tests with a Model (model-scale = 12) Extrapolated for tile S,nooth Ship According to Schoenherr

20 5000 000 000 000 1000

AA

VA

VIIV

ii.

Depth of water in m

!II1ii

_{B =126m} B=210m

(38)

---Fig. I 2-Results

of

the Resistance Tests with Models as a Function

of

the Reynolds Nu,nber

0.0071 0.006 0.0O5 0.004

2

0.003 0.002 ¡ 0.007 0.006 0.005 0004

£

0.002 I ¡ 2.51

/

/3,!

//

/

¡

/

/ I /

/

1

J

12 Depth of water in m

Model results Model results Ship trial

(rough) =12

o(20

I

1 --

-'7-

_V,

7/

-p,

4 j

5/

/ 1/121

--2

//

-

.-1___.,,._______.

/

D12m

/'

/

0.003 oenherr 6.2 6.4 66 6.8 70 log Re 7.2 74 7.6 7.8 8.0 82 84 8.6 8.8 "Correlation of

Model and Ship Trials

of

a Shallow Draught Rhine Vessel ".

Paper by Prof. DR-IR, W, P.

A. VAN LAMMEREN, Member and DR-IR.

J. D. VAN MANEN

(39)

CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL ₃₁₃ 0.02 5 0020 + MODEL 6 d,4o338 .MOOEL9 d/00t67

---. MODEL13 d/00331

/

I

//

/

kn.

/

,/

/

-f

/ /z

Vr2.Okn., ,,/P

-,,

-"

,__-

- V= 1.0 k n, __-o 0,05 _0.10

Fig. I 4influence of the Tank-width on the Model Resistance R

.ç V2

(40)

500C 5000 4000 3000 2000 -x o C 1000 B in m

A4

p_.

Depth or waler 4m 8 9 10 11 12 13 14 15 16 17 18 0 005 010 V5 In km/h m

Fig. I 5Co,nparison between the Methods of Helni (Boussinesq number)

and of Telfer (blockage coefficient)

(41)

500

400

3000

o Y

/

Lí

/7

Depth of wier in m 2.5 4

/

4 i 5 6

//

Model Schlichhng resu Its 8125m 8= 8 9 10 11 12 13 14 15 16 17 18 1g 20 V5 n km/h

Fig. 16Resistance Curves for Different Depths of Water According to Schlichting 2000 C 100 5000 4000 3000 2000 1000 o

(42)

316 CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL 4000 3000 2000 1000 O

/

/1

//,,

//'.'

/ /,//

_/

/

/ ///

/

.7

/ /

/

/ //,,

.

/

.

./

/

////

//>/

/ /

/

_Z

V/I-

I -, 7,

y,' '

'

z-'Z

7,' . 0=12m ship triai B=300m - rough ship 8= 300m -I ---smooth ship 8= 126m

Model reutts -- Smooth ship B=300m (Helm)

smooth ship 8= (Helm)

- - -Schlichtirig B =

L. Teller ₈₌

g 10 11 12 13 14 15 16 ₁₇ ₁₈ _1g ₂₀

V in km/h

Fig. I 7Comparison of the Results Measured on the Vessel with the Resistance Calculated from Model-tests

400 .300 200 C 1000 o

(43)

CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL 317 JO O

VL

Depth of water in n 2.5 5

1î11ii

A

rnu

-3'

UWfA

21 9 10 11 12 13 14 15 16 17 18 19 Vs in km/h

Fig. 1 8Results of the Propulsion Tests of the Model ( = 12) without Skin

Friction correction 35 30 25 20 15 C E S-D )0 o

(44)

n km/h

Fig. 19Results of the Propulsion Tests of the Model with Skin Friction

Reduction

Fie. 20Results of the Test with the Open-ivater Mqdel Screw ( = 12) 300

j!,

200

'1ai

p,,1a

H P - -17 200 23 1* lt n 1g 1g 19 07 07

-3

04111r

____

0.3

::

-,

IRa

04 05

(45)

CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHiNE VESSEL 319

Fig. 21 Wake-fraction Values and Thrust Deduction-fraction Values as a Function of the depth of Waler

a 07 0.5 04 03 02 0.1 \

\

w according la K1 -identily wilhoul tunnel plat.

lo K -dentlty with tunnel piale to 65 -identIty wirhoul lunnel piale

07 06 0,5 04 03 w accorOng w according

0.6---\

.

\

-',\

'

\

"

,'.

-...-_J

01 1.0 20 ac 40 5.0 6.0 7,0 °ld

(46)

Fig. 22Comparison oft/ic Propulsion Tests of the Actual Ship on the North Sea Canal and the New Waterway with the Results of the Model Tests 35. 300 250 20. 15. E 600 500 400 300 200 100 o

/

North North w RatIar. Sea Canai Sea Canai against before Wterwy the the wind wind

R

/

D HP -.._Dt812m 8=160m Model results _0ta12m _B=300m

10 11 12 13 14 15 16 17 18 19 20

(47)

Inn IAn IOn

overIoadrn p

Fig. 23-Reduction in tue Number of Revolutions as a Function of overload 5 C C 4

II1111fjr

i

i OHP 2'

1oo4V

AÀ

5c4

130041UP

VMA

B 6 B

6AI

____7

iiiiì

5 4 3 2 L 0 20 40 60 80 100 120 40 160 180 200 223 240 260 280

(48)

Fig. 24Revolution-power-ship's Velocity Diagram for Different Depths of Waler Deduced from Measurements on the Actual Ship

600 500 400 300 200 ioo 0. 400 350 50

':<

O-/ O-/

7/ /

1/7

/

///

0

/

V

DHP

:;::.-\

:Ship trial

results D ta_12m. B=300m D =12m. B=126m D-ta=12m, B=126m-D-tarl2m B=160m Dta12m B=300m I I

-Model 10 11 12 13, 14 15 V5 n km/h 16 17 18 19 20 21 22

(49)

z

Fig. 25Comparison of the Measuring Results on the m.s. "Arabia" on the

Rhine with the Results of the Model-tests *

Q-I 400 350 300 250

j

- fl/rn in. -=

-illa

500 400

7"/

J---

PII

Ship trials

results 100 0

-D ta6m; 8=30Cm

D =6m; B= 126m D _{1a 6m B= 126m} D-ta=6m: B=300m I

.

-I Model J 10 11 12 13 14 15 16 17 18 19 20 21 22 V5 in km/h

(50)

324 COPJLATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VESSEL

10 11 12 13

Vs in km/h

Fig. 26Comparison of the Measuring Results on the m.s. "Arabia' on the Rhine with the Results of the Model-tests

I

-/,/

V

400 35° 300 250 200 150

_______

TVnn.

/

-J---

4(7/

f/I

DHP

J.,

1/ Ship hials Modet resu(s

-D-a=5m;B=300m

D =5m;B=126m

-. - D-

= Sm B = 126m

Da5m.B300m

o-X 70 60' 50 40 30 20 10 22 21 20 17 18 19 15 16 14

(51)

CORRELATION OF MODEL AND SHIP TRIALS OF SHALLOW DRAUGHT RHINE VFSSEL 325

Fig. 27Comparison of the Measuring Results on the In.S. "Arabia" on the Rhine with the Results of the Model-tests

700 600

i

400 350 300 250 200 150

i

II

_/

300 200 100 o Ship triais results D ta-4m; D =4 D- ta4

Dta4m;

m; B = m; 8= B=300m 6=30Cm 126m 126m

:

-Model 10 11 12 13 14 15 16 17 18 19 20 21 22 V ¡n km/h

(52)

Fig. 28Comparison of the Measuring Results on the n?.s. "Arabia" on the Rhine with the Results of the Model-tests

o-7 '0 350 300 250 i

/1

fl/mn>

'/'

z

j

100 U

_150

Ship trials ta-3m; 8:30Cm

D 3m B 126m B=l26m B=300m J

t0ta3m;

results 1__Dta3m; _D -Model 10 11 12 13 14 15 16 17 18 19 20 21 22 Vs in km/h

(53)

700 500 500

3)

200 loo o 10 11 12 13 Vs n km/h AA 14

15 16 17 18 19 20 21

Fig. 29Comparison of the Measuring Results on the m.s. Arabia" on the Rhine with the Results of the Model-tests

22 00 350 300 250 50 C E

11'

I 1 i/

/7,

'-7

IDHP ,J.-" Ship rI&s resutft t D =2.5m; D- a2.5m:

D-25m:

-2.5rn; B=300rn B126m 8=30Cm 126m_

-D

.

-ModeL

(54)

328 CORRELATION OF MODEl. AND SI-II? TRIALS OF SHALLOW DRAUGHT RHINE VESSEL

Fig. 30Trim Diagram

9 10 11 12 13 14 15 16 17 18 19 20 21 22 550 450

II_i

SIlL

1111400

200 50 O

iii

350 30'

2'

liii

U

Depth of water in m 2.

sass:

___SWAS

d1iiii

4S4PP

_

9 10 11 12 13 14 15 16 17 18 19 20 21 22 V5 n km/h