Circle tests with a radio-controlled model of a cargo liner

MEDDELANDEN FRAN

STATE NS SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL_TANK)

Nr 53 GoTEBORG ₁₉₆₃

CIRCLE TESTS

WITH A RADIO-CONTROLLED

_MODEL

OF A CARGO LINER

WITH AN EXTENSION OF THE FIRST-ORDER

TRANSIENT ANALYSIS BY NILS H. NORRBIN ibliothee Ndeling Sche Technisc DOCUm DA M

SCANDINAVIAN UNIVERSITY BOOKS AKADEMIFoRLAGET.GUMPERTS.GoTEBORG Mekelweg 2, 2628 CD Delft Tel: 015, 786873_{- Fax: 015 781836} ATIE an de en Scheamadhunde e56,,ol, Del

SCANDINAVIAN UNIVERSITY BOOKS

Denmark: IKUNICSGAARD, Copenhagen Norway: r NIVERSITETSFORLAGET, Oslo, Bergen Sweden: AKADEMIFORLAGET-GTJMPERTS, Goteborg SVENSKA BOKFORLAGET/NOrStedtS -Bonniers,Stockholm

Wa.t,ss

PRINTED IN SWEDEN BY

instrumentation of the model was controlled by radio from a

shore-side station. Some aspects of wind disturbances are reviewed, and

the testing facilities and instrumentation are briefly described. The primary object of these tests was to investigate

the validity of the linear theory, with possible extensions; the influence of hull draught, trim and initial heel; the influence of bilge keels;

the merits of different types of rudder, i.e. the "Simplex", spade

and "Mariner" types;

the correlation of model tests with full-scale trials.

The results are presented in different graphs and tables of transient and final turning data, and some of the conclusions are summarized at the end of Section 9.

The tests have earlier been used for the prediction of full scale turning data, and a comparison of model and full-scale results and analysis was presented before the RINA in 1961. This comparison included part of the stopping tests also run with the model as well

as with the full-scale ship.

During the summer of 1961 a series of zig-zag tests was

success-fully concluded with the same model, and the results and analysis

will be given in a separate report.

Finally, the tests with the free-running model have recently been

1 Introduction

The tests described herein form part of a larger program for the investigation of manoeuvring qualities of ships, set up five years

ago at the Swedish State

Shipbuilding

Experi-mental Tank (SSPA) with the financial support of different

foundations for ship and model research.

Among the main objects of all model work are to be found the

verification of theories and the prediction of full scale behaviour,

especially the prediction of a better behaviour. It is then also

neces-sary to know the present standard of this behaviour.

When considering the manoeuvrability of a ship . as characterized

by its turning ability and its response to rudder motion, this

know-ledge may be acquired from circle tests and zig-zag manoeuvreswith the ship or its model. It may also be predicted bytheory using effec-tive hydrodynamic coefficients derived from earlier tests with similar forms or from a synthesis of (first order) "stability derivatives", and

higher derivatives, taken from graphs of systematic captive model

test data; the accumulation of these data has started at many model

test establishments in different places.

Model results must be applied with caution, and it is necessary

to acquire it full understanding of "scale effects", which are not always

of hydrodynamic nature. It is also necessary to establish the limits

of the linear theory, especially those of the first-order

approxima-tion first suggested in our field by KENSAKIT NOMOTO. It is anxious

to investigate the most important parameters of the hull geometry

in order to reduce the number of captive tests required. For instance,

to what extent will the ship performance be sensitive to the load

conditions, i.e. initial trim and heel? Have bilge keels to be fitted to all the models of a systematically varied series of forms ?

In view of such inquiries it was decided that an

experimental

investigation ;should start with free model tests to determine the

turn-ing ability, and related characteristics, of a modern form, for which

it would be possible to obtain the full scale results aswell. Of course,

there would then be an opportunity to look for the results to be

gained from tests with a modified rudder arrangement, which would be of more immediate interest to the owners.

screw ships.

The method developed for tracking the model by use of two base,

angle recorders has been described in some detail in a contribution to the 9 t h ITTC in Paris (1].1)

The first model to be fitted with radio controls for the manoeu-vring of all-electric propulsion and steering engines ran its "trials,'

late in 1958; it was built from paraffin wax, as had been the previous models used in the open lake tests. The steering engine incorporated a three-component balance for rudder forces and torque.

For the present investigation it was realized that the scale effects

due to rudder flow phenomena etc. could be kept within the desired

limits by use of a fairly large model only, and its size was to be

governed by handling and transport facilities.

An 18.5 ft model was built to represent a class of modern cargo liners,, which then for a few years had been subject to service

per-formance analysis by SSPA and the owners', the Br ostr om

Group of shipping companies.

The new model was made from reinforced plastic, and the pro-pulsion system was redesigned for Ward-Leonard speed control,,

supplied by a gasoline power unit.

The turning tests were successfully conducted through the summer

seasons of 1959 to 1961. In 1960 a programmed speed and rudder

control was added, by means of which it was possible to run stopping tests and combined manoeuvres. Part of these investigations together with full scale trials has been presented in reference [2]. The present, paper covers more fully the model results for different test conditions,

and it is tried to give a description of the measuring and recording

devices onboard the model. Some of the results will be further analyzed in a future report.

A control unit for zig-zag manoeuvres was designed and operated' in 1961, and the results and analysis will be given in a separate report. Recently this same model has been used in captive tests with force

measurements in oblique (yawed) towing in the main basin These

latter tests' have also been repeated with a somewhat smaller geosim, which was towed submerged in the form of a double model.

2. Symbols and Units

When applicable, the symbols and abbreviations here used have been chosen in

accordance with the nomenclature suggested by the IT TC Manoeuvrability Commit te e, and the general practise in related fields touched upon.

Some symbols used in defining the circle test manoeuvre are also shown in Fig. 1.

Dimensional numbers are given in metric units; wherever so is the case the units are clearly stated.

Symbol Definition Physical

Dimension Non-Dimensional Form as Used A Ar A;., A; AD B 111 C CO D E FL I., .1 K K; L L_PP t N i

Reference area for non-dimensional coefficients; A ---LppT

Tot. proj. area of rudder

Symbols defined in Table VII Maximum advance (Cf. also Fig. 1.)

Emperical constant defining

hydrody-namic roughness

Symbol defined in Table VII Capacitance in analogue circuit Ship or model centre of gravity (in

nauti-cal estimates taken at LWL position)

Diameter of propeller Voltage applied to RC-circuit

FRouDE number; FL=UlliTL Mass moment of inertia about the axis

of z

Propeller advance coefficient; J=

nD

Static loop gain of linear equation for turning, or "steering index"; cf. Table VII

-Average" value of K' from non-linear

manoeuvre

Length of reference (Here L=L) Length of ship or model btw perpon-diculars

Yawing moment about the axis of z

L2 L2 L L (CGS units) L Mi ,2L1,2T-1 (CGS units) ML2 T -I L L ML2T -2 1;r=in'kl_ K'=KLIU P N' =NI U2AL 2

R R, T T; 17,, T; U U0, I a, b, c 4 a1,. bi, c1, d1 11,0, k , kl., ks in I n r t ii t',.. u u(z) v v' yr x, :tic. z 1

Resistance of analogue circuit

Radius of steady turning circle Time lag of first order system

Time constants in second order system; cf. Table VII

Time constant defined in Table VII Velocity of origin of body axes relative to the fluid; speed of ship (Suggested to

be replaced by symbol V), Propeller speed of advance

Hydrodynamic force on body along the

axis of y

Constants of polynom fitting curve. vf

LppIRc(8); b= K'

D:o for curve of L/AD,(8).

Effective height of roughness. ' 1

H Characteristic height of roughness ele- li

ment

Non-dimensional longitudinal radius of gyration of body

Nikuradse equivalent sand. roughness Mass of body

Number of revs, of prop. in unit tithe

Angular velocity of yaw; r = 41 Time

Time of rudder travel

Virtual time lag in circle test with ini-tial disturbances

Speed of body along the axis of x

Wind velocity profile (Section 3 only)

Speed of body along the axis of y; drift veloc'ty

Friction velocity

Voltage over capacitance

Orthogonal coordinates of a righthanded

system of body axes, moving with the

body

Height above ground surface ,(Section 3 only) (CGS units) L T LT=!

LT,

MLT-2 L L L M T-I T-1 T 'I' LT-,

LT-I-LT'

LT -I 1 yr 12Li: /2T-1 (CGS units), L L 7% = TUIL 174=17IiU2A P .ia' =-ml --,TAL =rLIU t'' =al IL 1 /c -=t1E1 I L = u -= Y z

-Advance AT) inautical

definition)

Reach _{thnum advance from C.G. tra e0or_y_plot}

Reference heading W=0

Subscripts r, and are applied to N and Y to define the 'first partial

deriva-tives of yawing moment and lateral force with respect to modes of motion so indicated. .(For non-dimensional forms, see also ref. [8]4

A ,(dot) over a symbol stands for a derivation with respect to time. A ' (prime) of a symbol' is used to indicate the non-dimensional form.

3. The Manoeuvring Lake

The manoeuvring tests were performed in the "harbour bay" of

an inland lake eight miles from the site of the model tank

establish-ment. The ground is private property, with two permanent jetties and storage facilities., The free access to this ground is gratefully

acknowledged.

Outside the shallow western beach, where in addition to the jetties

there is a pair of simple launching ways, the -depth of water varies

between 2 and 6 m.

On each one of the two permanent jetties, and exactly 90 m apart,

are placed the two theodolites or "base angle recorders", which are used for tracing the model path. The tracking and plotting equip-ment, and the accuracy of the method, has been described in ref.

V 13 I, a st -,c 77, 773 , 0 1 Volume. displacement of body (Suggested

to be replaced by tr)

Angle of drift or sideslip of body;. pi is initial angle at rudder execute

Rudder angle (deflection); 8, is neutral angle for straight course in ideal condi-tions, 8, constant angle applied in circle test

Thickness of laminar sublayer vow KkamAN universal constant

Constants of polynom fitting curve of L pi,' L3, L T-' , I I ij,'= tisLIV ;(i,=Lpplitc) ( I.?

c)

Change of heading angle

Rate of change of heading; liJ, is initial rate at rudder execute, constant rate

10

A: Observation platform with control console and base angle recorder

base angle recorder

Ci. Storage Power supply Model slipway

2 m depth curve

Distance in meters

Fig. 2. Map of "manoeuvring lake".

[1]. The target tables previously used for the photographic recording of heading are now dispensed of, however, as a gyro compassis now

carried in the model. (The tests were earlier run in a smaller lake,

where the tables could be arranged all round the shore.)

On the northern jetty is also the manoeuvring pulpit, from which

the model is operated. The model may be controlled far away from the "harbour-, but because of safety reasons it is usually not manoeu-vred out of the 400 m range, within which the signal lights may still be observed by binoculars.

/

/

\

_N

\

5 10 15 m/S

AREA zARB lotCRIc UA R E INDICATE 9 OBSERVATIONS

IN 10

(a)

ALL WINDS

ALL WINDS

0 5

FOR WIND QUADRANTS. SEE FIG. 2.

( b)

WINDS IN QUADRANT I ONLY

ID 15 N

JUNE -JULY

15

AUGUST - SEPTEMBER

5 m/S 20

Fig. 3. Histograms and cumulative frequency diagrams of wind velocities at

Tors-landa Airport.

The test water area therefore is just a little more than 300 m squared, although the total length of the lake is about two miles in the WSW

to ENE direction. Part of the lake and surroundings are shown in

the map in Fig. 2, from which will be seen, that the bay is well sheltered from moderate winds from SW, W or NW.

The histograms in Fig. 3 are prepared from data in ref. [3], giving the variation of wind velocities at Torslanda Airport thirteen miles NW of the test area, recorded at a height of 40 m above the field at 14 o'clock each day of a 10 year period. (Usually wind velocities are slightly lower early in the morning and in the afternoon.) Accord-ing to these data the months of April, May, August and September all offer more

opportunities to outdoor model testing than do June and July. April and May are

less attractive when considering working in the cold water, however.

I M/S MAY ₂₀₀ 0 10 20 BOO JUNE JULY ₂₀₀ 1 2 '600 AUGUST SEPTEMBER 200

12

The cumulative frequency diagrams to the right in Fig. 3 directly show, for each two months period, the number of days during which a certain wind velocity is likely not to be exceeded. If one accepts a nominal wind velocity of 3 m/s, when the wind vector is in the quadrant marked "I" see Fig. 2 but, due to less shielding from wind and sea disturbance, not more than say 2 m/s when in the three other quadrants, then, e.g., one should not expect to have more than 6 full days of testing during the

months of August and September. In practice this means that it may be necessary to split up a test program on several weeks, taking advantage of fine mornings and

afternoons.

The choice of the acceptable wind speed will be further illustrated by the discussion below.

The nominal wind speed so far mentioned refers to an altitude of 40 m above ground

level; according to the logarithmic law the wind speed will be just about 60 per cent of that value at a height of 0.6 m above lake surface, which was the height of a field

type "Ostman" anemometer carried onboard a small boat on the lake, and which

corresponds to the observers height 15 m above sea level on top of wheel house on

the full scale ship.

The ship as well as the model moves in the boundary layer near to the water surface.

The logarithmic law of the velocity distribution has proved to be valid for the natural

wind profile all way down to the displacement layer close to the surface, where laminar stresses dominate.

Outside the thin laminar sublayer with thickness 5, the velocity distribution in the

turbulent flow over rough surfaces may be written in alternative well-known forms, i.e.

u(z) 1

5,

= In -4-.13

v.

where v, is the so called friction velocity (which can be estimated from the initial

slope of the wind profile) and x=0.4 is the VON KiamiN universal constant, and

where k and B is a pair of empirical constants together defining the roughness: k is a characteristic height of the roughness elements and B is a constant depending on

le

the quotient (which is in fact a Reynolds number based on roughness size and friction velocity) and, less clearly, on the type of roughness as well. In the

"com-pletely rough" flow regime all roughness elements protrude through the laminar sublayer, and in this regime engineering type roughnesses are often described in

terms of the NIKURADSE equivalent sand roughness ks associated with a constant B value equal to 8.5. It is easily seen that there is an effective roughness height ho, smaller than the actual height k, which, if substituted for k in the formula, makes the constant term equal to zero in the rough regime,

u(z)

1 5

In

-vs ho

in the case of sand grains of maximum density obviously ho= but a higher 30

value must be expected for isolated roughness elements. In recent years several z

a

125 scale

164 scale wind tunnel tests.(Ref (GI) /

IA power law

0 0,5

SCALE OF RELATIVE WIND VELOCITIES

1,

MEAN HEIGHT OF TOPSIDES

20

Fig. 4. Comparison of wind velocity profiles as calculated for model and ship.

investigators have proved that the macroscopic flow of natural wind over different surfaces of sea and ground may be treated more or less as the completely rough flow in microscopic hydraulics. The reader is referred to articles by URSELL and EwsoN

in ref. [4] and by MONIN and OBUCHOW in ref. [5]. There is reason to believe that the

effective roughness of the sea is less dependent of actual sea state but chiefly

char-acterized by the small ripples; any definite conclusions are obscured by the additional

complexities introduced by water drift currents, relative velocity of wind and rough-ness elements, thermal conditions, etc. For the present we takeh0-=-0.001 m for the

sheltered lake, whereas for the open sea in a moderate state we take it to be 0.005 m, which is the value also reported for snow. The thickness SE will be ignored in practical estimates, as for instance the figure for snow is stated to be of the order of

0.03 m only.

In Fig. 4 are shown the calculated velocity profiles for model and ship, and the frame contour of the model. (Model freeboard was made to correspond to the mean height of the topsides of the full scale ship.) Also shown is the "1/64th scale" wind

profile as measured above the wind tunnel floor in ref. [6].

The "effective" wind speed may be calculated as the root mean square velocity over some suitable height of the superstructure; this height will here again be taken equal to the mean height of the topsides, and it is observed that it is just about half the height of the observer on top of wheel house. Due to the presence of deck erec-tions and masting the true effective height is likely to be somewhat higher.

In absence of an additional uniform ship speed component the ratio of "effective" wind speed to "observed" wind speed is 0.56 for the 1/25th scale model, whereas the

corresponding ratio for the full scale ship is 0.63. A light breeze of a nominal velocity of 2 m/s 40 m above model lake surface, or 1.2 m/s 0.6 m above it, thus gives an

effec-10 0,4

14

tive velocity of 0.67 m/s for the model. The corresponding velocity for the full scale ship is five times as high, i.e. 5.3 m/s as observed on top of wheel house. It is gene-rally accepted that this wind will be well tolerated on ship trials. The situation will

be more favourable for the model, too, as sheer and deck erections are omitted.

4. Model Tested

The ship model is an 1:25 scale representation of a modern Swedish 9000 tons d.w. cargo liner for the Far East service, having a 4-bladed right-turning screw, a Simplex type rudder, and bilge keels of normal

depth. The model was tested with alternative rudders and keels,

and the majority of tests was run without keels. Ship Model

Model No. 958 is built by Malmo Flygindustri AB in

Malmo, designed in a sandwich structure with paper honeycomb

core between Polyester resin laminates reinforced by fibre glass cloth. It was layed up by hand in a plastic mould, which had been formed

on an original aristo wax model made at the tank. Due to the small

tolerances the mould was stiffened up by a rigid tubular steel frame,

which enabled easy transportation and handling. The weight of the

model hull, with two WT bulkheads of a similar sandwich

construc-tion and fitted with a set of steel tube girders, is about 80 kp, i.e.

less than 10 per cent of its LWL displacement weight. The photograph of the empty model, reproduced in Fig. 5, may serve to demonstrate its lightness.

The model is built without sheer, with a freeboard corresponding to the mean height of ship topsides with bulwarks.

A drawing showing contour, waterlines and body plan is seen in Fig. 6. Configuration No. 958-A refers to the model as fitted with

the original stern and rudder skeg, whereas configuration No. 958-B

had part of the deadwood removed. (Fig. 7.) The main particulars of the ship and model are given in Table I.

Rudder Models

The model rudders R1, R, and R, as well as the original skeg

were made from teak to the drawing in Fig. 7. Model R2 is a 4 mm

Fig. 5. Sandwich model as lifted from plastic mould. (By courtesy of Malmo

Flygindustri AB.)

Simplex rudder, 111. All the rudders have stocks of stainless steel. which can easily be clamped to the steering engine mechanism. A

photograph of the four rudders is reproduced in Fig. 8.

By grinding the wetted teak by fine sandpaper the streamline

Table I

Spec. Ship Model

Length between perpendiculars, L_PP rn 135.6 5.424

Length in LWL m 139.0 5.580

Breadth, moulded B m 18.00 0.756

Mean height of topsides on LW L F m 7.5 0.30

Draught on LTVL, moulded T m 7.80 0.312

Lateral area (incl. rudder) AL m2 1036 1.658

Reference subm. area

LT

_PP m2 1058 1.692

Wetted surface (incl. rudder) S m2 3484 5.57

Displacement V rn3 13170 0.843

Block coefficient 8PP 0.60 0.66

i.

AA;

7

Vit. 6

2

Fig. 7. 'Model stern and, rudder arrangeinent.

rudder surfaces were given a finish, which is believed tb be

hydro-mechanically smooth.

The spade and "Mariner" type rudders are designed with total projected areas equal to that of the Simplex rudder. The particulars of the rudders are found in Table II.

Bilge Keel Models

Two pair of bilge keel models were made from 2 mm brass flat bars, with equal lengths but different depths. The keels were positioned in

the planes of bilge diagonals, symmetrically about the midship

section. For dimensions, see Table III.

LWL / I 1 112'4 C.__ 1 v 1

STILL _WATER LEVE BALLASTCOND

'I II R7 and I I, I l, / N S "R° and -R-4 11 I / I r" 1 I I _/ STERN "B". I 1 / 1 VI 7V V I 1 V ---; \ I

Table Spec: Ship Model Rudder Rudder (111) PI R2 R ,3 R ---7 - -Type

-Simplex Simplex Balance It Spade "Mariner"

Section- --=.-Aerofoil Aerofoil Plate Aerofoil Aerofoil Height at stock b in 5.600 0.2240 0.2240 0.2270 0.2300

Gap above rudder at stock

tj m 0.310 0,0120 0.0120 0.0085 0.0065 Mean chord (mean In 2.94 0,1174 0.1174 0.1195 0.1195

Chord at mean height of stock

c512 in 2.94 0.1174 0.1174 0.1185 0.1188

Thickness at mean height of stock

tht2 m 0587 0.0239 0.0040 0.0237 0.0238

Total proj. area

A r 2 17,1 0.0274 0.0274 0.0214 0.0274

Moveable proj. area

A rm 202 171 0.0274 0.0274 I 0.0274 0.0241 Gap ratio glb b2

-0.0554 1 0.0554 ,0,0554 0.0374 , 0.0283

I Aspect ratio (geometric),

A -1:84, 1 .84. 1:84 1,88 1931 A, Taper ratio °mink:vox

-1.000 1%000 1.000 0tt91 0:591 Thickness-chord ratio tIc

-0.200 0.200 0.034 0.200 0.200

Ratio of reference area to total proj. area

L TI Al,

-61.9 61.9 61.9 61.9 61.9

Ratio of moveable proj. area to total proj. area

A,,,,/A, .

,

Moveable area balance ratio

- --1.00 0.257-__

-1.00 0.257 = -1.00 0.257 1.00 0.257 0.88 0.151

II

-Fig. 8. Model rudders R1, R2, R3, and R4.

Table III

Dynamic Properties of the Model

The model was ballasted for dynamic similarity in all modes of motion. For the longitudinal mass moment of inertia of the loaded ship the radius of gyration was taken equal to 0.25 L within the

limits of estimate errors. The moment of inertia of the model in yaw

is very near to that in pitch and it may be justly defined from the

simultaneous similarity assured for the pitching and rolling motions.

The longitudinal positions of instruments and ballast weights were

therefore adjusted when the model was swung in air in the pitching

"cradle" used for models to be tested in waves, while the position

of the transverse metacentre and the period of roll were checked by inclining and rolling tests in still water.

Spec.

Ship Model

8, 8,

(Si)

Type of bilge keel Bulb plate Flat plate Flat plate

Length of bilge keel 30 m 1216 mm 1216 mm

20

As the influence of an initial heel was among the objects of these

turning investigations, it was decided to simulate a rather stiff ship

having a natural rolling period of 15 seconds in the load and 9 seconds

in the ballast condition, the latter figure also roughly realized for

the ship on trials.

Propeller Model

Propeller No. P829 was cast in white metal to the tank standard. The design is shown in Fig. 9, while further particulars are found

in Table IV. The full scale ship has a slightly modified propeller; cf. reference [2]. The open water characteristics of the model propeller are reproduced in Fig. 10.

Table IV

5. Model Test Equipment

The model was fitted with electrical systems for propulsion, steering

and data recording, all of which was controlled by radio from the operator's station on shore. A block diagram is shown in Fig. 11.

A photograph of the complete installation was reproduced in ref. [2].

Radio Control

The main control equipment essentially consists of a set with

manoeuvre box and UHF transmitter on shore, and of a receiver with manoeuvre and power relays in the model. In addition, there

Spec.

Ship "MANDALAY"

(F.)

Model

to ship scale Mod. P829 P Number of blades

Direct, of turning

Diameter, D Pitch (0.7.7?). P

Blade area ratio, AD/ AO

Pitch ratio. PID

4 Right 5.00 m 4.93 m 0.59 0.9 8 5 4 Right 5.10 m 5.30 m 0.55 1.04 4 Right 204 mm 212 mm 0.55 1.04

970

850

Fig. 9. Model screw P829.

10 KT 100K0

555

43 4695

Fig. 10. Model screw characteristics from open water test. FULL SCALE otmENsioNs IN MM 5300 5026 8 7 6 5 4 3 2 1 0 80 70 60 50

40

30

20

10

0 1 I I I 1 0 0,2 0,4 0,6 0,8 1,0 j. U a n D 500 6t5 0700

SHORE

ST,ATIO.N

-Helm angle Indicator

-4

Signal ₁

timer 18 V d c --HMV f Channe 1 Channel Manoeuvre box =LChanne 3 Channel 4

Helm angle rec elver

'Helm angle transmitter I Power cons. 4

Zig zag Program

Ahead st op Astern Drift angle vane MODEL am roller Fig,

la. 13lock diagram of Opntrol equipmehti

'mit S seteci

j=1 stop

stop

hioSterinitg

engine

jraaneinnialiBB

limit volt

Starboard pin contact Heading angle gyro

Port pin contact I Bal.0 nit Petrol D. C. Prop engine gen engine Speed 1

7E7,

III24V dc onverter Speed 2 eed 3

MI supply

Robot _camera oscillogr Tach.- gen._ gnallightS p.mactjust ITrTar ac

i _`3t

=1,

&-II - ' -0 Irfirfiai 73° elti-ii;v,=. JO. --- "11Z. 7/

Fig. 12. Photograph of selector relays onboard model.

is a transmitter onboard for teleinetring of rudder positions to the receiver and rudder angle indicator at the control pulpit.

The carrier wave frequency of the main transmitter may be

modu-lated by one or more of four tunes. In the receiver there are four relays, each one sensitive to one of the four tunes just mentioned.

The selector relays, again see photograph in Fig. 12 are made

sensitive to one' of this tunes, or two a combination of two of them; thus it is possible to transmit ten ,separate control orders. At present the following signals are used:

'Ahead choice" or "Stop" .(alternating) "Astern choice"

S. "Start" and increase of speed of propeller (in up to ten. steps)

"SB rudder" (progressive to end of signal, or to preset

pin-to-switch contact) "BB rudder" ,(do)

6, "Start" or "Stop" (alternating) of programmer, or of automatic

zig-zag test control

T.. "Start" or "Stop" (alternating) of oScillograph recorder

24

The FM rudder angle signal from the model (see above) is

demodu-lated and rudder position is displayed on the dial of an electronic frequency measuring instrument in front of the model operator; if he is busy with handling the controls a load speaker tune reminds

him of approximate rudder position. Besides, a green and a red light on top of the steering engine indicate helm out of zero.

Other coloured lights are used to indicate carrier wave failure,

backing of the propeller and the operation of the recorder. Model Propulsion Equipment

The model propulsion unit consists of a constant r.p.m. ILO LE 50 1.5 hp petrol engine and a Ward-Leonard type generator-motor

set with belt drive of the propeller shaft The speed control is achieved

by a stepwise change of field voltage, supplied from the 2 V cells

of a 24 V accumulator. An adjustable resistance is connected to one

of these cells. (When, alternatively, the programmer is used for

manoeuvring control the field voltage is changed by use of several

adjustable resistance potentiometers permitting a close simulation of

full scale engine manoeuvres.) When the model is not running the generator is switched over for charging the accumulators onboard.

Steering Engine

The steering engine is a 24 V DC shunt motor with worm gearing,

which gives to the rudder a uniform speed corresponding to a full

scale 70 degrees manoeuvre in 20 seconds; by lowering the field voltage

a slower rudder may be achieved. A three-component rudder force

balance is incorporated in the steering engine assembly, but was not used in the present investigations, however.

The design of the steering engine allows the use of a rudder deflec-tion of more than 45 degrees, but in order to prevent that the balance is jammed against the mechanical stops there is a pair of adjustable

micro switches, which stop the engine at a slightly smaller angle. An additional pair of switches may be used in combination with a pair of transposeable pin contacts in the steering engine quadrant,

by means of which the turning at a set of well defined rudder angles may be investigated. This method was the one originally adopted; in order that the manoeuvrability of the model should not be imperiled

these switches could in emergency then be by-passed by use of the radio signal now reserved for the mechanical programmer control.

instruments ashore most other data of interest are sensed and recorded

onboard on the paper film of the SFIM galvanometer oscillograph.

The evaluation of model heel angle from Robot camera photographs

released by radio at timer intervals has been described in ref. [1].

The oscillograph was used for a continuous record of the following items:

Ahead r.p.m. of propeller Astern r.p.m. of propeller Rudder angle

Drift (vane) angle Compass heading Rate of turning

Time in seconds (from built in clock-work) and timer interval signals are marked on the oscillograph record by means of special

relay event markers.

The r.p.m. of the propeller is proportional to the output of a perma-nent magnet DC generator.

The rudder angle is sensed by a potentiometer, which is geared to the stock of the rudder. The angular deflection of the rudder is

cali-brated by means of direct measurements of rudder trailing egde

position. The varying potentiometer signal voltage is also transformed into a varying frequency tune modulating the telemetring carrier wave. The drift angle (defined at the loaded model CG position) is measured

by an easily movable aluminium vane, mounted on a vertical shaft

through the bottom of the model and extending about 200 mm below

it. The signal transducer is a low friction ring potentiometer, the wiper of which covers the full circle for a ±18 degrees variation of the drift angle. The design of the vane instrument with damping fins is seen in Fig. 13; a second instrument has been built abroad.

Note that the drift angle may also be found from Robot picture

analysis (earlier method) as well as from plotting of CO trajectories

and compass heading. The vane method is the more accurate one.

Compass heading was sensed by a Sperry Mk IA gyro-magnetic

compass, to the repeater of which had been fitted a low friction

potentiometer; in the repeater is filtered out the small hunting motion

26

Potentiometer

Pick-up-_

Ball bearings

Camping tins

Drift angle instrument.

LW L.

6 seconds. In an other way the gyroscope has been said to average

the magnetic heading from a series of magnetic observations, which

are subject to acceleration errors. The deviation curve recorded for the bar magnet in the model has a total amplitude of about 4'; lead

weights only were used for adjustable ballast.

In some series of tests the rate of turning was measured by a Graseby rate gyro with potentiometer pick-ups available at the tank.

Summary of weights of outfit

The weights of test equipment carried in the model is given in

Table V. It was not considered necessary to keep down these figures. and relay boxes etc. have ample room for future expansions.

Table V

Weight of model hull with steel tube girders, empty

Weight of platforms, beds and supports Weight of UHF receiver

Weight of main control relays

Weight of speed control and dynamometer balance units Weight of programmer unit

Weight of petrol engine (incl. fuel) and d.c. generator

Weight of propeller d.c. motor with belt drive and shafting

Weight of power supply accumulators Weight of steering engine with rudder balance Weight of gyro-magnetic compass with repeater

Weight of drift angle vane indicator

Weight of camera record grid

Weight of rudder angle transmitter

Weight of miscell. instruments and cables Weight of instrument bridge voltage supplies Weight of oscillograph recorder

Weight of mast and signal lights Weight of model hull and outfit Total weight of model with ballast lead

80 kp 26 kp 14 kp 17 kp 12 kp 18 kp 19 kp 22 kp 87 kp 13 kp 14 kp 2 kp 2 kp 1 kp 5 kp 2 kp 2 kp 4 kp 340 kp 422-843 kp

28

6. Test Program and Procedure

The manoeuvring tests with models Nos 958-A and 958-B included

circle tests and the spirale manoeuvre, zig-zag tests, and stopping

and reversing tests without and with the aid of different rudder

manoeuvres. Part of the circle and stopping tests has been reported

in ref. [2], while most of the circle tests will be presented here. The models were tested in different configurations, i.e. with

differ-ent rudders and bilge keels, and at several loading conditions. The

parent configuration will be denoted APR1-000, i.e. model No. 958-A with propeller P-829 and rudder It, without bilge keels, on full draught with zero trim and zero initial heel. Other configurations are defined in Table VI. The full scale ship trial condition is seen to correspond

to APR1S1-530.

A total of about 120 circle tests was completed, most of them run at the same nominal speed on approach of 15 knots.

At the beginning of a series of tests the model was started at the trimming bridge and manoeuvred out on deep water, where it was stopped again for a final adjustment of receiver LF-volume, some 50 m from the operator. It was then brought onto a straight course

in the approach heading and at the engine voltage desired.

It was tried to steer the model along the straight course with a

minimum of rudder applications for at least one minute, corresponding

to five minutes for the full scale ship, i.e. to an approach run of a

little more than one mile. As has been described the rudder follow-up motion was displayed on a dial in front of the radio control operator,

an arrangement which proved to be of utmost value for a

good

steering in the absence of a positional helm control. If there had been

too severe a rudder operation prior to the approach, or if the model engine was then not working at the correct field voltage, the "one

mile" distance proved to be still too short.

At a signal the two observers at the base angle recorders now

unlocked the pens and started following the model by the binoculars. Half a minute before initiating the manoeuvre the operator switched

on the timer instrument; he then brought the rudder rightly

amid-ship for the last few seconds, without any further checking of a slight

unwanted turning. The rudder was started in the desired direction

and stopped as near to the proper helm angle as was possible. Because of the rapid operation of the model rudder it was usually not possible to repeat the exact magnitude of a rudder deflection; if this be desired

Table VI

--.

Configuration

Model data

Corresponding ship data

I

Ratios 7:, 0 ,-, Draught, moulded FL4.. ' 'zi

i

P ..-Draught, moulded -Ta -Tf T-= Ta+Tf Ta

-

Tf

-T' ._ +T

Taf

0

-1 1

,

a) u/ wj, co 0 0 o 'V, o § o 0 .9, ,_1 as .4,.., Z Ta-Tf

-2 2 ir eO c., ° "0 eO . P.4 P.:: 0-I 4., g . PEI. ins see mil in in 1113 -see

---in in in degr. 1 . _ 11

-=

-A P RI 000 0.843 1.8, 2:9 0.312 0.312 0.312 13170 9.0,14.5 7.80 7,80 7.80 0° 0.659 0 1 1 ' 003 0.843 1.8 0.312 0.312 0.312 13170 9.0 7.80 7.80 7.80 +4.7° 0.659 0 004 0.843 1;8 0.312 0.312 0.312 13170 9.0 7.80 7.80 1.80 -5.2° 0.650 0 010 0.843 1:8 0.336 0.286 0.311 13170 9.0 8.40 7.16 7.78 00 0.658 0.159 0.997 020 0.843 1.8 0.288 0.3:37 0./12/3170 90 7.20 8.42 7.81 90 0.660 -0.156 1.001 050 0.843 18 0.352 0.269 0.310 13170 9,0 8.80 6.72 7.76 0° 0.656 0.268 0.995 100 0.692 1,8 0.265 0.265 0.265 10820 9:0 6.63 6.63 6.63 0° 0,637 0 530 0.422 1 1.8 0.208 0.140 0.174 6600 9,0 5.20 3.50 4.35 00 0.590 0.391' 0.558 A A P P g, R1 s, S2 000 530 530 0.843 0.422 0.422 1,8 1 1,8 1 1.8 0.312 0.208 0.208 0.312 0.140 0.140 0.312 0.174 0.174 13170 9.0 6600, 9.0 6600 9.0 7.80 5.20 5.20 7.80 3.50 3.50 7.80 4.35 4.35 00 0° 00 0.659 0.590 0.500 0 0.391 0.391 A P R2 000 0.843 1 1,8 0.312 0.312 0.312 13170 9.0 7.80 7.80 7.80 00 0.659 0 B P R3 000 0.843 I 1.8 0.312 0.312 0.312 13170t 9,0 7.80 7.80 7,80 00 0.659 ,0 B P R4 000 0.843 1,8 0.312 0.312 0.312 13170 9,0 7.80 7.80 7.80 00 10.650 ,0 530 0.422 1,8 0.208 0.140 0.174 6600 9.0 5,20 3.50 4.35 0° 0690 0.391 0.558 , -s----a :

30

Fig. 14. Model turning in light breeze.

one may switch over to programmed control, however, or the alter-native method with contact pins may be used. (See above).

When the model had turned through a full circle and a further 60

to 120 degrees the test was interrupted and the model was brought up to a new approach in easy turnings, to regain speed and to let the observers have time enough for putting new papers in the base

angle recorders, a.s.o. Six or eight circle tests might be run without harbouring the model.

The photograph in Fig. 14 shows the wake of the model

approach-ing head on to a light breeze and turnapproach-ing hard to starboard.

In-cidentally, it may be shown that the characteristics of tactic tests, i.e. advance, transfer and tactical diameter, are less influenced by wind disturbances if approach takes place with the wind instead of against it, as is current practice in ship trials.

7. Reduction of Test Data

The primary information obtained from a circle test is normally presented in the form of model CG trajectories, with CO positions

Reference base line Heading_ angle

/

Time base scale Helm angle

Timer intervals Propeller rpm

(a). Configuration BR4P-000 Approach speed 14,8 knots at 101 rpm helm 290 to port

(Note here that initial helm is kept zero, causing an initial turning to port.)

(b) Configuration AR, R-000. Approach speed 11,5 knots at 80 r p rn helm 23° to port

(Note here that initial helm 15 manoeuvred to check initial turning.)

3-2'

20

Fig: 16. Speed-versus-r.p.m. curves.

recorder data of propeller r.p.m., rudder angle, drift angle at CG, and heading angle (alt. rate of turning), lifted from the continuous records at the 5 seconds interval marks and at intermediate points

of interest. The "gyro-magnetic" heading angle is corrected for devia-tion (but not for magnetic error) in the tables.

An example of film record is shown in Fig. 15, and a number of

circle test plots are reproduced in Fig. 20.

Next all data, including time interval stations, are plotted on base

of model distance sailed, this being measured from the CO plot by

use of a simple flexible millimeter paper rule. In the final graphs the abscissa has been graded in number of Model speed is obtained from the curve of abscissa distance values on base of time ordinates..

As mentioned in the last section the model did not always fully

reach its stationary speed on the approach. In these cases the nominal

speed as taken from several straight run tests at same loading has

been used for speed loss studies; when being in the final steady turn the model had no memory of the true speed on the approach, of course,

but only of engine setting. (Note, however, that the true values of

speed and r.p.m. must be considered in an analysis of the initial

manoeuvre.) The straight run speed-versus-r.p.m. curves are shown

in Fig. 16, 'supported by captive model test data; according to this

diagram the free-running model does not fully attain its "ideal"

speed, what is probably an effect of the additional resistance due to

115 120 Rpm. ---,... i v-...,v II .1, i 1 !

Modelstraight run mean curve,lballast cond.

model self propulsion, . speed trials.

straight run mean curve, on .LWL. model sell propulsion ..

in model and ship screws,

1Y. It I V Captive C7' Ship , Model fe Captive For differences .cf. Table I 5 90 95 10 01 h05 110 0 Lpp:s. .

< m x

.

cc r o a_ z 100_x o z z a o w CD lal Z a. o Le, 80 < -15 x C,_ o 14/ o 60 200° -10 3 -5 x4. /0

----_J__

_5,0

x-/0 ..,

1(7-

\

_{\TANGENT DIR.,4,13,} X PC

STEADY TURNING CONDITIONS

0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

DISTANCE ALONG PATH IN NUMBER OF SHIP LENGTHS SAILED

Fig. 17. Evaluation of "average" K', K;.,and drift angle g c from plot of records.

steering or drift. Also shown in this Fig. are measurements taken on

the MANDALAY at speed trials.

From the CO plots have also been obtained the path tangent

directions (referred to magnetic north), at the interval marks or at intermediate points on the path. A safe way of finding the curve of tangent directions on base of sailed distance is as follows: Assume

a small arc of the path to be a second order parabola, and draw two

chords parallell to each other and to the tangent wanted

the

straight line joining the midpoints of the chords is a diameter of the

parabola, and it meets the path in the tangent point proper. The

circle is a special case of this parabolic path.

Fig. 17 shows the curves of change of heading and change of path

tangent direction on base of number of model lengths sailed, and

curves of relative speed and r.p.m. as well, all for a typical manoeuvre.

2R, 2

The methods of finding the diameter ratio

PP

and the

Vc

mean angle of drift /3, in the steady state are obvious from the graph. 40

20

tan (8,-06)

-1 5 1

z

AD Rc (d ) I I I t; 2 RCV+v.K.E T = K V (a) ( b) 0 _6c 1 0 LPP 1 (e) (f) Rc

Fig. 18. Definition of steering indices obtained from turning tests.

stant, selectable voltage supply. Commercially available types of rate gyros are not suitable for recording during the transient phase of a

turning test.

The presentation of data in Fig. 17 suggests itself for defining a

value of steering index K' according to diagram (d) of Fig. 18. This

value of K' has sometimes been denoted K. Due to the effects of non-linearities the definition of initial K' >K; from diagram (e) of

Fig. 18 is the more adequate one for a linear analysis of manoeuvres

with small helm, whereas the IC may be thought of as an average

L pp

value of the slope of the

R, (Se) - curve during the transient

state of increasing R .

(Note that all K'-values are made up of

hydrodynamic coefficients for the hull and rudder: see next Section.)

Formally it will be possible to obtain the effective time lag T' from one single diagram of the type shown in Fig. 17, using the definition in Fig. 18 (d), but this is known not to work in practise,

where there are initial disturbances in g (and its derivatives) as well

as in According to the first-order-theory suggested by NOMOTO

[7], and in absence of outer disturbances, change of heading is given by the equation

= K'(8-8o)

where the angle 80 is the constant helm required on a straight course to prevent the stable ship from turning due to hydrodynamic

asym-metri. It is evident that this equation can not be used for finding T' in a case were there is an initial disturbance in /3, but only in In the next Section a method will be set forth, by which the

first-order-theory is extended to handle the more general case, within the

ordinary limits of the linear treatment. The results of that Section has been used to find T' from three or four of the circle tests

per-formed with the same model configuration.

Again, remembering the "extrapolated- character of the linea-rized theory, it must be pointed out that the proper value of T' may

be found from an analysis of -advance" measurements as in diagram

(f) of Fig. 18, where the tangent slope is defined by the method of least squares. In the limit, corresponding to small helm and small path curvatures, the "reach" is given by

-36

AD R,

_= T'

PP PP

Note that the "advance and "reach" in nautical usage are defined from point of helm execute and so include the distance t12, which

tends to zero with Se however. (See also Fig. 1.)

8. An Extension of the First-Order-Transient Analysis

The approach will be linear, which, above all, means that speed

reduction will be ignored. Heeling can more safely be left out of the treatment. Symbols have been given in Section 2.

From ref. [8], and taking advantage of the fact that the derivatives N'. and r are usually very small, there are then only the two equations

(m'

17 '03+ (

DIV + Y;(8-80) = 0t

N'fig(m7c1,N'dtil +NW 4-N;(3-8d = 0

I

By the Laplace transform technique the initial conditions are included through the general relation for the transform of a derivative of order

n see [9], e.g.

i[r(r)]

8"£[1(t' )] -8-1 /(0+ ) .

r-1(0+ )

Thus, after rearranging the terms,

(Ym')[/i]+ {(m' Y )s

Y;}i[g] = (979/ Y;,)fil roi[8 80] t

{(N'im' *82+ N',8}£[tk]+ N;£[g] =

8o]

The initial disturbances pi and now appear in the right members.

The characteristic equation has one root equal to zero; the two

1

other may be and

, . where 71; and 71, are positive

con-T T,

stants, as stable ships are considered at present. Solving for the

step response there is then

1 k01 = K'(8,--80) _{82{1-HT;+TD8+77.;82}} 1 ±Ic(A;ty;+B;Pi) _{8{1+ (T;+-T)s 7111,82} +} -FK' tV 1 1 (11',+T s +T'iT,s2

Y0+

+

(N m'.kt)ti N 1 T

+

Fig. 19. 'Change-of-heading transient with nitab disturbancies.

The first order approximation to this transient is seen to be

It 1

1-01= K'(8c-60)J 82(1±T's)+1c(A;CHLB;g1)

8{1±(7,;_FT),31--1

1 1d-(Tl-1-7'2)s

or, in the "time" domain,

CO= K'(8c-80),(eT'+T'e-tilr)+K'(+B;gi)(1e-rigyd-T,'))+

1 Ti+T;

This approximation is exact for large values of t' provided that

11'

T71-77;, and the first term in the right member is. the

expression given by Nomoto [7],. The symbols K' and T' were

intro-duced by him, and together with the three new .symbols 4, 4;

and B; they are given in Table VII.

The asymptote of the tit(r)-curve for large. t' meets the axis ti v= 0 in a point C (cf. Fig. ..19), defining the effective time lag from the relation

131.

T' = t,;+

_{isc_so}

+B'

1 sc_so

=

38

Table VII

Normally it is necessary to evaluate T', A; and B," by the method

of least squares, using the observations from several circle tests.

This procedure is also believed to cancel the effects of small but

un-known outer disturbances present during the tests. (Note that

and te, were assumed to be initial disturbances of the motion caused by bad steering or outer disturbances acting in course of the approach.)

It is sometimes convenient to introduce an approximate relation

between A; and B; , writing

B

m'

A;

m'Ic2N'

_L Y' 1c2 K' Y;NeYeN; Ye N e N; Ye 17; YiN; ( Yin')IST m' Y; N; N A m Y; Yij TT

;; =

(in'

l')(m'kLn

( Y; m')/V; IT iN; 1 (m' ki N;) Ye

(in' *N;

T;-1-- V; ( y;,m')/1r,j (m' Y".)N; Ti _{Y eN;} 13 T' = T; + T 2 T; A; (m' ki Ni; ) Ye Y eN; Y;ls1 e A; --- (m'

*(in'IciN;)

1 ' eN, Y :Or e B; (m' Y,' )N a Y eN; Y;IV h Y. = Y

It may be pointed out in this place, that, by simply dropping all

terms containing the factor in the original set of equations,

the equation for change of heading takes a form similar to that of

the first-order approximation, i.e.

T*'t./;'±ti/ = K'S

If time lags again are defined by the relations in the ultimate stage

of the step response, then

1

N;+

N; ("2/ ;)

T' = T* 1. (m' Y'd Yo

N;I Vo

1

_{N i; I V!,}

By use of numerical values available for typical forms it may be shown that T' is only about 2 per cent in excess of Tv . The factor

m' 172; is in itself not "small", and so this result which has pre-viously been given in ref. [10] may prove that the p'-coupling in

the motion is very weak.

9. Test Results and Conclusions

A number of circle test plots are reproduced in Fig. 20, grouped

to facilitate a direct comparison of helm angle and trim dependence.

The discussion of the results, however, will chiefly be based upon

the analysis of the continuous records of heading angles etc., as out-lined in the previous Sections, and on the curves of path curvatures and advance distances on base of helm angles presented in the

Appen-dix, Figs. A 1A 10.

Turning characteristics and steering indices of parent configuration AR,P-000

Table VIII summarizes the information on the geometry of the turning manoeuvres of the parent configuration, derived from

nu-merous individual tests or from the Figs. A 1 and 21. In all these

cases engine setting was such as to give an approach speed

40 a) 5B 17.3° e N 5B 28.2° (If 56 24.2,°/ START OF RUDDER

DRAUGI-IT IN METP2. HELM

AFT FORWID ANGLE

8.80 6.72 SB 18.6°

--o-- 7.80

7.80 SB 18.0°

7.20 8.42 SB 17.6°

Fig. 20. Examples of turning circle plots.

(a) Influence of varying helm - (b). Influence of change of trim.

ing to 15 knots for the 136 m ship. Other tests were performed at approach speeds of 12.5 and 17 knots, and the turning diameters

then recorded fell mainly within the scatter of data in Fig. A 1.

Although this result is consistent with most modern opinion it is

not promoted by the recent investigations by TAKARADA on minimum turning circles [11], nor by the theoretical analysis by PIING NIEN

Hu on the forces in linear theory with wavemaking, [12]. According to both these authors there would be a 10 per cent increase of turning diameters as the speed on approach is increased from 12.5 to 17 knots, i.e., when FL is increased from 0.175 to 0.24. Model engine charac-teristics may interfere with hydrodynamics in this respect, however.

(See also below.)

Turning ability and index K'

Stationary turning circles are seen to be smaller with increasing helm for angles all up to more than 35°. The diameter using 35° port rudder, corresponding to 4.3 times the length of the ship, may be compared with the figure 4.1 predicted from interpolation of

results of model tests by SHIBA [13], the latter also run without bilge keels. (For the effect of bilge keels, see below.)

Table IX

Configuration AR1P-000

SB 35° SB 200 BB 20° BB 350

Steady turning diameter/Lpp 4.04 6.31 5.87 4.27

Advance/L, 3.75 4.75 4.31 4.08

Final speed/speed on approach 0.52 0.77 0.72 0.52

Final r.p.m.lr.p.m. on approach 0.93 0.95 0.94 0.93

L

Polynomial for PP Configuration Coefficient

Rc _a b---K' C" c d a-I-b8d-M/8 ARIP-000

0.006 1.126

0.546 AR1P-530 0.019 1.101 0.904 ad-b8+43 A11113-000

0.006 1.008

0.573 AR1P-530 0.020 0.928 1.136 a-P-6,6+00+a3 AR1P-000 0.005 1.293 1.355 0.878 AR1P-530 0.020 _0.984 0.313 0.739 a+bS±c52-1,/83 AR1P-000

0.026 1.016

0.110 0.608 AR1P-530 0.006 0.927 0.090 1.147 1 I

42 -0,6 -0,5 -0.4 -0,3 -0,2 -0,1 1,5 1,0 0,5 -0,5 P 0,1 0,2 0,3 0,4 0,5 0,6 Rc A R1 P-000 AR151P-000 -1,5

Fig. 21. Evaluation of initial T' from curves of advance versus turning rate.

The value of initial K', equal to -1.02 see also Table IX and Appen-dix is in good agreement with the prediction by use of stability de-rivatives from captive tests. Details will be given in a separate report. A curve of "average K' " or K; (see Fig. 18) on base of stationary turning rates is included in Fig. 32, to be discussed below.

Advance and turning lag T'

The curve of advance versus helm angle is rather flat at large

helms, and the benefit of using hard over in an emergency is essen-tially due to the greater loss of speed.

helm angles according to the method of Section 8 is T' = 1.35. (See

Table X.) The effect of bilge keels also displayed in Fig. 21 will be commented below, but a further discussion of these results will

be given in the report on the .zig-zag tests earlier referred to. Pivoting point position

Linear theory attaches a constant Value to the quotient

Lpp,

R, L

sin pc, as far as sin f3'c ..In general the results

Lpp Rc

of drift angle measurements may be approximated by a partial sum

'L 3 PP

of the series ,8.c. +7

-n

13 and using the series

Rc r

)

for sin 8 there is then

OP3 L

711+ 7h ) PP )

L 6 Rc

For the parent configuration was found 7), 0,61 and 713 = 0.58, OP

and the curve for shown as a full line in Fig. 22 clearly indicates

the sternward trend in the position of P at higher turning rates.

For "normal tight" manoeuvres P is closely aft of the stem, which is also in accordance with observations on ships of this type. The

effect of bilge keels is seen to be small in this case. Speed loss in turning, and screw loading

There is a marked rate of change of speed in the transient stage

of the tight turning manoeuvre, which may demonstrate the influence

of rudder induced drag, but the final speed in chiefly governed by

the fore-and-aft component of centripetal force, as has been shown

by DAVIDSON [14]. The large hull lift and induced drag due to drift

and turning, on the other side, resolve into- a "large" normal force

but only a relatively small component affecting forward speed which will not be strange to yachtsmen. One more factor determining final

speed, however, is the change of thrust due to the change of _screw

=

...,

44 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0,1 0,2 0,3 1 r _r ii ce 80 40 20 10 8 7 6 -0-- A R P-0 0 0 -d- AR1S1P-000 0,4 0,5 5 4 2R / L_{c pp} 3

Fig. 22. Pivoting point position in steady turning.

loading. This change of thrust depends on engine characteristics,

again, and thus is a source of "model effects".

In case of a constant torque, as for a diesel engine, a 20 per cent drop of model speed would be associated with a 5 or 6 per cent in-crease of thrust. In case of the present model shaft torque was not

constant but estimated to increase by 2.5 per cent as r.p.m. was going down by 1 per cent; accordingly, at a given loss of speed the model r.p.m. could not be expected to drop as much as did ship engine r.p.m. The speed reduction in steady turning was found to plot reasonable well on base of helm angles, and in Fig. 23 (a) and (b) the results are given for configurations AR1P-000 and AR1S1P-530. Full scale values are included, showing the trend of screw loading changes just men-tioned. (See also below.)

The curves choosen for approximating model spots are even

poly-nomials, but as far as curve fitting only is considered a knuckled straight line would be just as good. This reflects results similar to

0,6 Lpp Ftc 0,7

-0 400 300 200 10° 0° -10° -20° -30° -40° ( a ) 0 --4 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 -- 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 HELM DEFLECTION tSc-S. 0,6 0,4 0,2 0 -0,2 -0,4 -0,6 CONFIGURATION: AR, P- 000 HELM DEFLECTION bc-tS. 0 LEGEND: A R, S, P-530 0 SHIP MANDALAY co° 30° 20° 10° -10° -20° -300 -4cf b

Fig. 23. Relative loss of speed and r.p.m. in final turn.

0

0,9

0,6 0,4 0,2 0 -0,2 -0.4 -0,6

iz

-46

V

PORT HELM

/

/

-01 1 ../ - 0,1 ° L L PP. PP TI5 0,6 0,3 0,4 0,3 0,2 0,7 0,6 0,5 0,4 0,3 0,2 0,1 1 0,1 400 - 0,2 -0,3 - 0,4 -0.5 PP A STARBOARD HELMHELM

Fig. 24. Comparison of steady turning rates of models with streamline and plate rudders. (Curves for parent configuration, squares for plate rudder model.)

those reported from Mariner type ship trials by MORSE and PRICE [15], stating that "there is practically no speed loss in the 5 degrees

of rudder runs, and that the speed appears to fall off linearly with

rudder for rudder angles greater than 5 degrees".

Model turning, using streamline and plate rudders

Due to the increase of screw loading in turning the relative drop of

race velocity past the rudder is not much more than half of that of

model speed, and in a tight turn corresponding to the hard over

manoeuvre at 15 knots this race velocity is estimated to be of the

order of 1.3 m/s. Although the nominal REYNOLDS' number based on

chord of rudder is then 130 000 about, and, moreover, the level of turbulence in this flow is certainly high, there is still likely to be a scale effect in the maximum lift of the streamline rudder. (Cf.

dis-300 200 100

-10° -20° -30° -40°

1 , 1 ! i

In order to shed some light onto this phenomenon, a series of

turning circles was therefore run with a plate rudder (112), the maxi-mum local lift of which is known to be fairly insensitive to changes in REYNOLDS' number. In Fig. 24 the turning rates thus recorded are compared with mean curve Values for the parent configuration. There is an indication of a slight increase of initial K', but of no significant

change of minimum turning circles,; in relation to rudder

charac-teristics it would mean a somewhat higher slope of the curve of

plate rudder lift, compared to that of the thick profile, and that the

coefficient of maximum lift of the profile did not exceed 0.9.0, say. Influence of a static heel

The model was ballasted to simulate a rather stiff ship, and except

for the initial roll heeling angles were ignorable. The photographic records available have not been further analysed. The effect of heel

in turning was included, however, by running the model with a static

list. As can be seen from Fig. 25 it was then necessary to apply a small helm to make the model run straight, but final turning rates

were largely unaffected.

Influence of trim and load conditions,

A change of trim on full load is accompanied by a change of flow

conditions at stern, and so modifies the helm on straight

course;

when trimmed on the bow this angle is 30 or 40 to port as against

1.5° to starboard on LWL.

Again, when trimmed on the bow, the model becomes less stable

on course, and advance length Is increased, especially at moderate

helms. (See Fig. 26.) The minimum turning circle is not any smaller than that for the parent configuration, however, which might be due to an earlier stall of the rudder when more close to the water surface.

The trend to smaller starboard turns with trim on the bow, which was obvious from the lower plots in Fig. 20, is now seen to reflect

mainly the shift of helm on straight course.

At full load moderate trim on the stern gives the shortest advance and relatively small a turning radius, and it is also to prefer from the power point of view [21

p c 0,7 0,6 0,5 0/. 0,3 02 0,11 0,11 4 * 30° OORT HELM PORT 'HELM 06 0,5 AR LP- 00 4 (BB HEEL) 03 0,7 0,6 0,5 0;4 0,3 0,2 0,11 .0 I. r , 4, 0,1 400 300 '20° 10°' ---1.

6/

, STARBOARD HELM - t -1.0? -20* -30° -00 --0,3 -0,4 0,5 -,046 -0,7 -b -0,2 - 0,3 - 0/. -0,5 , ARe4Ci0 B HE EL A13,1 P-0.04 A-Ri P-OD3 STARBOARD HELM .200 _40° -400 1 1 - 1' -;2 -0;3

-4

-0;5 - 0,7 AR1 P-000

Fig.. 25. Turning characteristics as influenced by initial staticheel.

)30 20° L_{P P} AD 0,5, 0,4 AS 0,2 0,4 0,2

/

- -0,5 (a ) -01 L %-AR,P-003 -40° I I -0,1 -0,2 - 0,2 - 0,3 - 0,4 0° --0,6

30° 2e jPORT HELM 400 '30° '20° 10° PORT HELM 100 0,3 0.,7 ;OA 0.5 0,4 0,3 42 0,1 1 4 4 71 0,1 0,7 0,6 0,5 0,4 0,3 0,2 OA - 4-- -4 - 1 CO -0;2 - 0,3 - 0,4 -0,6 a') 42. 0,2. - 0,3. -.0;4 b AREP-000 ARIP-050 STARBOARD -10° -200 - 40? -0,1 I; - 11 0;11 -0,3 -0,4 -0,5 -'0,6 -0,7 AR P-050 ARfP-020 STARBOARD HELM, - /CP - 20? -30° - 40° 11_ if

_V

4 -0,4 -0,2 -0,3 -0,4 -0,5 -46 -0,7

Fig. MI Turning characteristics as influenced by trimonfull load.

1 PP 01§ AD AR P-010 4 0,2 ( HELM

50

The complex dependence of turning radii and advance distances

on trim and displacement is condensed in the two diagrams of Fig.

27, giving starboard and port minimum values, all referred to the mean values for the hard-over-to-starboard (-35°)- manoeuvre for the parent -configuration. The curves are polynomials accepting a

linear dependence on relative change of displacement and a

linear-plus-square dependence on relative trim, defined by the method of

least squares applied to the total material. It must be pointed out that there may well be some preliminary spots fitting badly to the

scheme, which is directed towards tendencies. Also, even some of

these tendencies are not representative for models with bilge keels.

(See below, and Figs. 28 and 32.)

The differences shown up in displacement dependence for port and starboard turning again is due to stern flow conditions and effective helm. At moderate to large trim on the stern the emergency manoeuvre

is to be made using starboard rudder, if outer conditions so permit.

Effect of bilge keels

In Figs. 28 (a) and (b) the turning characteristics of model with

bilge keels are compared with the results from tests without keels,

on LW L and in ballast conditions. It is to notice, that the effects of the keels are quite different in the two cases, what is also clear from

the force measurements in captive towing, which will be reported

separately.

On full load the model with keels has a slightly smaller initial IC and a much larger turning radius at large helms than has the parent model, which may also be seen from the curves of Kis-values on base of steady turning rates in Fig. 32 (b)i; it proves that non-linear- forces are more dominant when bilge keels are fitted.

In view of the relative small decrease of K' the much larger de-.

'crease of initial T', in Fig. 21, is somewhat surprising. A more moderate

increase of the dynamic stability is suggested

by the analysis of

single turns (see Table X), and also supported by the zig-zag tests.

In the ballast condition the effect -of the keels again is more

pro-nounced at large helms, but now such as to flatten outthe -curve of

K. The presence of the keels on the heavily trimmed model mainly

increase her static instability moment, and at a certain turning rate and sideslip angle a- smaller helm is then required to balance the

-2,0 IR, Rco V -1,8 -\5.- 0,4/ /0,6/

/W/

/ / 1,0/

-1,4

z

Z

-1,2 -1,6 -0,8 -0,6 -0,2 1,0 04

FULL CURVES STARBOARD HELM DOTTED CURVES PORT HELM

Ta-Tf

RELATIVE TRIM ON STERN,

--i-_-I I I I I . -0,2 -0,1 0 0,1 0,2 0,3 0,4 ( a )

Fig. 27. Turning radius (a) and advance (b) as functions of displacement ratio and relative trim. (Model without bilge keels.)

--2,0 AD A Do _1,8 -1,6 V -1,4 V. 1 --.. -1,2 .---__. 2 V \----__ ---...---____

--- ...--- ____--V.

-_ --1,0

---0,8 --0,6

FULL CURVES STARBOARD HELM DOTTED CURVES PORT HELM

-0,4 -0,2

-RELATIVE TRIM ON STERN,

i . -0,2 -0,1 0 0,1 0,2 (b) 0,8 1,0

'1 C?' d...,_,;... .---' ,...". 0,70,6 0,5 0,4 op 0,2 WO° 300 200 'L PP 1 PP 316 Rc AD, a -0,2 -0,4 -0,5 - 0,6 A RI P-000 AR1S1 P-000 PP, Rc L pp AD STARBOARD HELM

AR P-53O ARA SiP-530 liAR/S2P-5.30

Fig. 28. Turning characteristics for model on full load and in ballast as affected by

bilge keels. 0,2 0,2 0,1, ./. ...,

..---/

'STAR BOARD' HELM

__II '4'CP 30° 20° 30°' PORT HELM ."/ ..."

r

11-II t rl _I -0,1 -13,1 :0;2 -0,3 -0,4 - 0,5 -0,,6, -0,7

-0.5 0,4 -0.3 -1 -30° -0.7 0,6 0,,3 0.1 -0,3

produce a tighter turn. (This reasoning is not upset by the fact that the relation between turning rate and sideslip may also be slightly

modified by the bilge keels; from Fig. 22 it was seen that this

modi-fication was ignorable in turns on full load, but unfortunately no measurements of drift angles are available for the model without

keels in ballast.)

The bilge keels may also be said to fix the locus of the midship

cross-flow separation in similar positions for ship and model, regard-less of actual depth of the keels. (Cf. Fig. 28 (b).) This effect will be most pronounced when turning with large helm angles, as the viscous cross-flow over the hull then plays an important role.

Comparison of ship and model turning characteristics

The full scale "Decca- manoeuvring trials with the MANDALAY have been reported in ref. [2]. The four turning circles were performed

in the ballast condition at an approach speed of about 16.5 knots,

i.e. somewhat higher than for the model. The relative drop of speed

and r.p.m. in steady turning are shown in Fig. 23 (b), and the

poly-nomial approximations to turning rates and advance lengths are seen from Fig. A 10.

Ship results are compared with model (AR1S1P-530) mean curves in Figs. 29 and 32 (c). Initial K' is probably about 15 per cent higher for the ship, which difference may be due to the wake scale effect [2], and to a possible scale effect in rudder lift curve slope indicated by the plate rudder test series, Fig. 24. As the model was run without a fric-tional allowance the scale effect in rudder flow velocities due to higher wake fraction was partly compensated by the higher screw loading.

There is a small shift in the rudder angle for zero turning rate,

Configuration Initial 200 helm (average) Initial Moderate helm analysis AR1P-000 AR1S1P-000 AR1P-530 AR1S1P-530

1.02

0.95 0.93 0.99

0.94

0.83

0.79

0.88

1.70 0.55 1.35 1.27 1.18

54 L PP. PP 0,6 !sic AO 0.5 04 0,3 0,2 .7 0,7 0,6 0,5 0,4 0,3 0,2 0,1

7'

...7 0,1

LP _{AR1SIP-530 A MANDALAY TRIAL}

L_pp

AD

Fig. 29. Comparison of turning characteristics of model and ship(MANDALAY).

80; according to the polynomial approximations in the Appendix 5,

is about

0.8°

for the ship and

+0.4° for the model, but these

figures obviously are well within the error of estimates, and the lack of records of small helm turns is regrettable. The ship as well as the

model has a greater ability for turning in starboard circles, and the

agreement in the mean is quite satisfactory.

In Fig. 32 (c) C-values are defined from the mean of port and

starboard turns, showing model result to be about 10 per cent on the

low side at moderate helm. At the hard-over helm angle, which for this particular ship was 30° to either side, the model mean value

is now about 8 per cent higher than ship mean value. This change

of trend is a "model effect" in engine characteristics, and is mainly

due to the more rapidly increasing model race velocities.

Advance values are largely similar for ship and model, as is in fact also evident from the analysis of the zig-zag tests performed.

r 1 I L __J PORT HELM .7 -10° -2Cr - 30° - 40° ..,-' 0,2 - 0,3 --0,4 -05 --0,6 ---.../ ,n, ..7 40° 30° -,0,1 R HELM I - 0,3 - 0,4 -0.5 -10,6- - 0,7 2d' no°