Loss of propulsion power caused by yawing with particular reference to automatic steering

ARCHIEF

B.S.R.A. Translation No: 2610.

Loss of Propulsion Power Caused by Yawing with Particular Reference to Automatic Steering.

By

K.Nomoto* and T.Notoyama

"I'

J.Soc.Nav. Arch. Japan, 120 (1966), p.71 (Dee)

Lab.

y.

Scheepsbouwkinicie

Technische Hogesch

DeIIL

*Shipbuilding Department, Pac , f Engineering,

University of Osaka.

**gjneerjng Research Depart iversity of Osaka.

1. General.

f

Moat modern ocean-going vessels are fitted with automatic steering devices in order to maintain correct course. The

principle of such devices is based upon any error in course being detected on the compass and the error being converted into an "error signal" which in turn actïvatea a relay circuit which applies an automatic course correction. _{Owing to this}

system of correction, a certain degree of delay in

manoeuvring is unavoidable. _{In addition to this, modern} automatic steering gear includes an adjustable interval

(either electrical or mechanical) during _the

_transmission

_from the compass of the course _{error signal, and when yawing of} minor amplitude occurs under the influence of successive waves, correction is liable to fail to correspond with _the

yaw. _{This is the so-called "weather adjustment" problem}

and, combined with the above-mentioned interval, tends to increase the delay in application of rudder adjustment after a course error occurs.

Theoretical considerations of automatic _{control indicate} that the delay in signal transmission is a factor which

hinders the reliability of auch systems and also resists the reduction of the natural oscillation of the entire lay-out. Calculations based on these theories show that in a fully-laden cargo vessel a relatively long yawing period of around loo seconds may result, which is shown by free o8cillation of the automatic steering system. _{These calculated values} have in fact been corroborated by readings from course recorder in actual vessels.

Nevertheless, and at least as far as normal

_ocean-going

service is concerned, yawing of such amplitude and period is no great problem from the point of view either of navigation or safety. _{What is more important and cannot, be disregarded,} however, is the fact that _{a significant loss of propulsion}

power may result from movements of this _{nature. As an example,} rough calculations carried out by _{LlrJlotoyoshi on certain.}

cargo vessels have shown that the average loss:.of propulsion power can reach a level of 10%.

In

the recently developed tankers of high tonnage and wide beam the deterioration in course stability has become a marked characteristic and one of the current problems as far as general merchant shipping is concerned is the establishment of criteria for minimum course stability. _{Loso of such}

stability aggravates this long-period yawing characteristic

of automatic steering and causes further loss _{in propulsion}

power. One of the fundamental points of consideration _in connection with this problem is the establishment of limits of natural course stability in order to keep the _{loss of} propulsion power due to yawing below a certain level. _This problem is inevitably linked with that of considerations _of ship handling in restricted channels and represents a major factor in establishing minimum manoeuvrability characteristics

for, super-tankers.

In

_{addition, this question must also take into account}

the design and control of automatic pilot equipment.

This paper therefore sets out to discuss _{the loss of} propulsion power brought about by yawing.

2. Dynamic Analysis.

Pig. l.

m i Co-ordinates and Notations

The co-ordinates and symbols to be applied in the

equation of motion (for nlanoeuvririg movement) _{are shown in}

Pig.l above. Pollowing the

conventional

_{sequences the} following may be set

(.,+N,)#+(us+ii,»iç= Y (1)

(where

_{m, m}

and are added mass and X, Y, N are wake forces operating on the hull)

The "surging" which accompanies nlanoeuvring is shown in the first of the above equations and in this case the

variation in V is extremely small relative to V itself. Again is a very minor angle and therefore this equation may be

adjusted as :

T(it)= (m.) +(m+i,)V3+R±R,

(2)

(where T : Propulsion power

t : Rate of loss of propulsion power. R :

Hun

resistance

Rr : Rudder resistance )

Equation (2) shows the propulsion power which should be maintained by the propeller during manoeuvring.

Although the yawing which results from automatic steering is not entirely a simple periodic sine motion it may be termed as auch for these purposes. In calculating the free

oscillation of the automatic steering system a simple periodic yawing j8 obtained but in normal operating conditions the

irregular exterior influences which act in succession on the hull produce a pattern of continuous free oscillation where there is no appreciable decrease. The motion in such cases has a sharp spectrum and it is relatively simple to indicate, by employing "energy spectrum" methods, that this is, in

essence, a free oscillation with virtually negative attentuatio: Observations of course recorded on ships in service have in

fact frequently confirmed regular and long-period yawing of such a pattern.

In the light of such consideration, it would be

appropriate to represent the yawing motion as a simple periodic

sinemovement when considering the loss of propulsion power due to yawing under operational conditions. In this case the rudder itself also describ a aine movement of similar

period. _{When the energy spectrum of yawing is employed, the}

4/

calculation of tota]. propulsion power.

If regular yaling in a simple periodic form is assumed, thc angular velocity of yawing (

¶6),

_{drift angle}

C ) and

rudder angle ( _{) will all undergo a amical change with} the steering period and therefore

:-öksin(we+. ß=I3sin(wI+s). J=:inwe

(the symbol

i I indicates half-amplitude and Cf)

and (show

the phase difference between-.f. and _{.-f3 respectively).} Calculation of the second inertia term in equation (2) will be obtained as

:-(s+.) _{Pc= f(iii+n,)Pi *: (O$(-)}

$(2wt++))

(3)

AB _{is shown below, the variation in V is extremeiy small}

and therefore it will be suitable to take the average V value. The inertia resistance undergoes sinical variation at double the steering frequency.

Taking rudder resistance as the resistance component of direct rudder pressures, this will be shown as

:-RP=fA1V,I5!

(4)

and this also will form a variation, around a certain average value, of double the steering frequency.

(

AR : Rudder area

Vr : Plow velocity towards rudder

Direct pressure ratio.)

Under such conditions of yaw the hull resistance (R) is assumed as being virtually identical with conditions of direct forward movement, but in general this resistance forms a pattern of variation of a multiple of the yawing frequency. If the propulsion power during yawing is measured on a free-running model a complex fluctuation where the steering period ïs taken as the base oscillation is obtained on the lines of Pig.2, but the _{component of a multiple of rudder} frequency which would be expected from the observations above is not clearly evident.

Pig. 2. Measured Ship Motions and Propeller Thrust V tC.'b. M.

,L.

. t ' -1.33a4 7? : + rw /.322'¼.

j

-3

j/0

iii

20

25Jc.

This would appear to be illogical but Buch is not the case.

The thrust from the propeller is determined only by the flow velocity against the propeLler in relation to fixed revolutions and there is no reason for the flow velocity to vary with a multiple of the rudder frequency. In other words developed thrust is governed by revolutions and inflow velocity only and force of inertia and rudder resistance bear no direct relationships. This point will be discussed further in this

paper.

However there is no doubt that the developed thrust at any given moment is equal, as a whole, to the propulsion

required for motion, as indicated in equation (2). _Therefore any variations must be made good with the first inertia term,

(in + u) 1. Thus, in there are two components, namely, the multiple of rudder period, which is made _{up of inertia} resistance and rudder resistance and the complex variation

of propeller thrust which reflects wake variation while yawing, and these óscillation profiles are made up of many

separate factors. _{Where the mass of the vessel is very great,} the amplitude of V is extremely small arid when this is

integrated the resulting variation in velocity is almost negligible. _{Por instance, in a model ship of 700 kg, the} amplitude of thrust variation obtained by measurement is

and rudder resistance is about loo gr. This will relate to a value of V of 0.003 rn/s2 _{at the highest and in an actual}

vessel, calculation where even a long-period yaw of about 200 sec. is involved will show that the resultant fluctuation in thrust will not exceed 1%. Therefore when the averages

of (m + m) V, and Rr are considered, fluctuation of V may be ignored and the average velocity V only taken into account.

Thus, as regards the component of periodic fluctuation,

both (m + m)

_VP

and Rr will fluctuate as a multiple of the rudder period. On the other hand, the thrust operating on the propeller will undergo a different periodic fluctuation and the difference will be made good by (rn + m) V. With reference to the average values, so long as the vessel does not increase or decrease its speed the average value per cycle of V is O and therefore the average values of propeller thrust

and of (m +m)

_V139

+ IÇ + R must be in equilibrium. The hull resistance, R, does not undergo any appreciable

variation between yawing and normal condition and. therefore it

may be assumed that the average value of (m + m)

vp4

_{+ Rr}

corresponds to thrust increase due to yawing.

However the above points bring about certain facts which should be borne in mind, namely :

Measured thrust and torque fluctuation reflect variation in wake distribution resulting from yawing and the fluctuations of both inertia resistance and rudder

-resistance when loss of propulsion power occurs are both unrelated factors. Por instance, if both rudder period and yaw period are extracted from the torque fluctuation measured on a ship in service, the result would not be linked with any increase in propulsion power based on yawing.. _{The same also} applies if the multiple of rudder period were taken. Loss of power must be considered in the form of an increase

necessary áfter comparing the average thrust relative to mean ship's velocity with normal forward motion.

Analogous conclusions may also be established for motions other than yawing. _{Por example rolling brings about}

a periodic inclined flow in the propeller area and in most vessels the amplitude is in the order of the angle of roll

and the period

IB

of course the same as the period of roll. When looting at the case of yawing in an actual ship, this periodic inclined flow is considered as resulting in a marked torque

fluctuation in

_{the rolling period but this has no}

direct link-up with increase in propulsion power resulting from rolling.

Basically, any increase in resistance to forward propulsion (the resistance originating in the movement of the ship) is related not to that movement but to its square.

Therefore it is not a period of the movement but is derived from the occurrence of a time fluctuation on a pattern of variation in the multiple of the period of a certain average

"plus" value of the motion. _{Loss of propulsion power of} course is included in this average value.

Average thrust and Loss of propulsion power when yawing; The average of thrust per yawing period may be obtained as follows from the above and from equations (3) and (4)

:-8C

-

en,)

iøi aic-

V,1_;g:

(R is the resistance along the ship's length

_and

_{not the drag} acting in opposition to the ship's axis of movement at any given moment). Drift angle

j9ia

_{small but even so there is} a considerable difference between drag and resistance _{and it} is not possible to equalise both. _{The factor which may be} balanced with thrust is the resistance. _{Drag shows a clear}

increase in

conjunction

with _{bùt, in relation to a low value} of

_(b

,

_{this resistance appears to be virtually the same as}

resistance to normal motion.

(5)

* _{See Bibliography 3) and 4) in this connection.}

In

making an analysis where a model is towed in a yawing condition this point must be taken into account.

In Bibliography 4) the X force measured during oblique motion is THRUST minus RESISTANCE, and therefore the oblique running resistance is obtained by measuring the oblique rumiir thrust of the Baine ship and deducting this.

These results show that when the phases of angular ve1ocjt

of yawing (cj) and drift angle (/3 ) _{are approximately the}

same, cos (

4q)

_{i and inertia resistance brings about an} increase in average thrust. _{Essentially this term is the} same as (m

+ m)

_{V and is the term expressing inertia and} therefore so long as the vessel's velocity neither increases nor decreases an average figure will show a tendency for this thrust to decrease, although this is not invariably the

case.

This term may be taken as the component of resistance of centrifugal force of the ship's rotating motion, but when

phases of cf' _{and (3 are similar the centrifugal force is normally} in a rearward direction whether rotation is to the left or the right. _{That is to say it is made up of factors of resistance} and therefore if its average value becomes a resistance of a certain magnitude an interpretation may be made.

Yawing under automatic steering conditions is fundamentall caused by free oscillation in the steering system itself and therefore it is a movement brought _{about directly as a result} of steering operations. _{The relationship between}

_theand/

phases caused by steering _{may be determined by simultaneous}

analysis of parts

_{(2) and (3)}

_{of the fundamental equation}

_of

motion above (See equation (1)),

_{In general, fluctuation}

in V and values of

i'

and

_f

_{are small and in normal instances}

both equations may be aligned

_{and if bothf and'are}

_eliminated

the following equations are obtained

:-T1T2J+(r1T)-=Ka+Kr3-

_i

¿J (6)

J

In this case K, T1, T2, T3 _{arid K and T3}

are assembled from factors of equations aligned with the basic equation (1), _and are functions of ship profile and rudder area. _{In relation} to periodic manoeuvring in period c _{the following equations are} found :-.

K(i+T)

#=Arg _{(1+iwTt)(t±iwT:)}

Ki(I±iwT)

.$=Arg

In normal vessels T1

_{T3> P2>}

_T3p

_{and T3}

therefore both and t» have sïmilar values although in fact the value of ia slightly higher. That is to say that when yawing OCCU8 duo to rudder changes the phases of ) and are

almast the same Therefore all component s in the average

thrust are required to be taken into account when yawing occurs This of course excludes

any

increase in propulsion power and

this value can,

in certain circumstances, be very h±gh.

On the other hand yawing brought about by certain wave conditions can produce a pattern, such as Mr.Kawata shows in his calculations, where and are in right-angle phase and therefore no increase in average thrust would occur in the s

circumstance a.

Thus the average thrust necessary for movement is given although yawing is taking place as a result of periodic rudder

changes. The term H in equation (5) shows almost

no

change from the direct motion resistance even when yawing occurs and therefore inertia and rudder resistances correspond with the

excessthrust. This agrees with the conclusions drawn by Mr.Motoyoahi in his approximated calculations. As was shown above, there is virtually no change in ship's velocity and. therefore the product of the excess thrust and velocity will, with no modification, give the excess thrust horsepower.

Conversely, the proportion of the forward thrust contained in the excess thrust will itself be the proportion of loss of propulsion power.

As equation

(5)

shows, the excess thrust due to yawing and therefore horsepower will increase by V3. Average velocity during yawing shows a slight drop but the increase in power is significantly greater than this.

3. Test of Fluctuation in Propeller Thrust under

Yawing Conditions.

Fig.2 has shown the results obtained from progressive measurement of thrust values under yawing conditions where an experimental free-running model was used. This

fluctuation is conspicuous when yawing is increasedànd shows

The fluctuation itself is of a confused pattern and in many cases the rudder period is greater.

On measuring ship's fluctuation with a flow meter (See Fig.2), the resulte show that, as might be expected from the

analysis &bove, this variation is extremely small and therefore the high fluctuation in thrust _{cannot be attributed to a}

"slip fluctuation" due to changes in ship's velocity. _Since it is permissible to assume constant propeller revolutions, _the remaining possible cause is that of drift resulting from

yawing. _{In the degree of yawing encountered here, the drift}

angle / is between 0.5e and 30

_{and the non-dimensional aular}

velocity r' is from 0.03 to 0.1. _{Therefore there will be a}

periodïc variation of/S with amplitude of

_±

10 to 6° at the propeller.

The available data on propeller performance under

conditions

of inclined flow show that _{it je probable that even} when a small inclined flow je present this will give a

considerable variation in the effective wake. _{With regard}

to the effect of yawing on the wake, it is insufficient merely to reduce the movement in terme _{of stern drift angle /3b. only}

and the drift ang1e3 at _{the centre of gravity as well as the}

curvature r' are two variables which should be included.

However, for simplicity in test procedures, it is assumed _that the fundamental element is that of _{and tests have been}

carried out with the model moving in. an oblique fashion, _at

an angle of(3, in order to obtain _{the effective wake coefficieri}

by measurement of thrust _{in such conditions of oblique movement.} The principal difference _{between model test and operational}

conditions is that owing to the rotary movement of yawing drift angle is smaller a _{it approaches the bow area in a} sea-going vessel while in the _{tests 1is a uniform value.}

ç li

/

Fig. 3. Effective Wake Fluctuations at Oblique Running.

-s -' -# -2 0 2 1

The test resuitS are shown in Yig.3 which indicates that even with an inclined flow of 20 or 30 a considerable variation

occurs in the effective wake. Using these results an

attempt is made to deal with the question of thrust fluctuation when yawing.

is obtained in the following way from readings of

and

From Fig.3 also c, in relation to various values of , may be obtained and plotting this against the time a

pattern of variation in G during yawing may be gained. On

the other hand a comparison may be made between this pattern and another series of & values obtained from measurement of thrust during yawing. 4 gives an example of such a comparison, which shows fairly close agreement in the two methods.

In a tanker selected for test

CL/B 6.0, CD 0.8 - M No 99)

the above method of obtaining thrust fluctuation was found

to be effective even with varying periods and rudder angles. On the other hand, taking another ship type, this time a cargo vessel (Li.No 152) with

L/B

7.0 and CB 0.7 the amplitude is fairly consistent with the earlier example but as far as phase and cycle pattern are concerned the above method did not give particularly close agreement. The reason for this

is assumed as being due to the ship being of wide beam causing a strong "viscous" wake which result in the effect of yawing to be represented, approximately, by .... Asopposed to this,

gr

W

j3i cLw/"

,N'

W' cf

kire

r.is. ("AL.

_i

p.

¿Ç dr'ed

1ram

f

'i

I '\

mtaurad T r

r

\\\\,

V

'I

/

Figs 4 Effective wake Fluctuation at Yawing

A1 M qq, J

8. 7: /2 'zc.

in a ship of normal lines the effect of potential wake, _and in particular of the circulation in that wake, is stronger

_vihi':

makes it impossible to simplify in terms of ÇD1only as r' also must be considered. _{This point has further been clarified b,:} measurement of thrust during

turning

_{and observation of thrust} and wake areas under varying conditions of _{and r'.}

The above tests show that the principal cause of torque fluctuation, and consequently variation in propeller thrust, i: the fluctuation in stern wake location as a result of yawing.

4. Test o _{Yawing and Thrust Increase - using} Free-Running Model.

Fixed amplitude and rudder period are applied to free-running models to result in yawing and the series _{of measuremei:} of ship's motion and propeller thrust give an empirical

relationship between yaw and thrust increase, _{This is}

useful in that it provides rational confirmation _{of the analys....}

above.

Table l Test Model Details.

M.?o. 113 132

Rg!urk SR 1-TÀNKER

_{i'!F.R SERiES-A)}

L,, I 4. 500 & 4.300 ¿IB 6.00 &33 7.00 Bid 2.76 73 j.50 C 0.80 0.31 i 0.70 131 _¡eo P,D 0.71 0.30 LIO 0.10 0.30 Z 3 4 1 .4a14 i .i i 0.6 1 71 3 £ 1.71 _{L1 2.42} V.,/L 017

Details of the three model types are given in Table i and these consist of a conventional tanker and cargo vessel, while the third type was specially constructed to give poor

course stability.

The main part of the test was conducted in the Osaka University test tank (80x7x3.6 metres) _{but one series of}

tests was made in the manoeuvring test _{area atthe University} in order to examine the effect of the _{ship's sides. In}

distinguish the "sidewall" effect with the degree of yawing obtained on the models because of the size of the tank in relation to the model dimensions.

The extent of yawing, _{representative of a long-period} yaw under automatic steering was selected as

_±

50

to 150 of

rudder amplitude with a period of 7 to 25 seconds (equivalent _to 50 to 200 seconds in an actual ship). _{Yawing angle was}

between 10 and 50 _{Models were under full load COnditjon}

and velocity was limited to a representative level.

The following is a summary of the test method employed. In order to bring about yawing of the model's wake parallel to the centre-line of the tank, a number of personnel will be required. _{At a position slightly off the centre-line}

acceleration is applied to the model by means of a pulley so that it moves parallel to that line (this parallel movement must be accurate). _{On reaching a specified velocity the}

acceleration of the p&lley is checked and the model allowed _to run free with the rudder operation applied simultaneously

in the cosine phase. _{The object is to achieve the appropriate} maximum rudder angle while the model is

_running

_{free and for} the model to be moving on a course parallel to the tank centre-line at that moment. _{It may be necessary for minor corrections} to be made, after a number of "dummy runs", to the _initial

"shift" interval, centre of rudder amplitude (i.e. effective "zero" rudder angle)and _{so on..}

Apart from the _{conventional manoeuvrability}

test

equipment, a free-running _{dynainometer is used.}

At the tank it is possible to make an electrical connection _{between the} model and the traction pulley by means of3lead _{hanging from} the end of a fishing rod, but the _{manipulation of the rod calls} for considerable practice. _{it should be particularly noted} that a flow meter should be installed at the bottom of the model in order to give accurate recordings of the _relative velocity of the water.

With reference to the measurement of drift angle _{, the equipment in use at Osaka University}

is

as shown in Pig.5.

Satisfactory results have been obtained using the light acryllite impeller and jewelled _{bearings which} are features of this _{equipment., which has}

a resolving power

of lesa than /sec and an overall accuracy of lcm/sec,and if the pick-up projects from the bottom for a distance of more than half the draught this will give the accuracy required and will not represent a significant obstruction to forward movement. Any variation in velocity due to turning movements may be disregarded.

The average values of measured thrust in various periods are plotted against the corresponding average velocities.

e Velocity is obtained from the flow meter.

In this free yawing movement it is difficult to obtain total agreement between velocity under drive conditions and velocity during free-running and therefore there are frequent occasions when minor increase an decrease of average velocity

occurs. This average velocity V is measured by flow meter

(flow velocity differential) and the following corrections applied

:-Corrected Thrust -

-1t g

I IT Corrected Revolutions

-In these cases W : Weight of displaced water.

T : Observed thrust.

n : Revolutions.

Por the above purpose, the use of an accurate flow meter is essential.

In cases where there is a tendency for thrust

measurement to be erratic, such as occurs in ships with a wide beam, alternate periods of free-running yawing and straight movement are conducted and checks are carried out against the thrust in straight running which is taken as the datum value.

i

1 --

-SYN

r

Fig. . Speed and Drift Angle Pick-up.

Fig. 6. Thrust Increment in a Cargo-Ship Model (Yawing Conditions) s X o IC9. 4. 4. /1. I

j

i I.! ¿2 13 /4

T,: yawIng peiiod.

iT.: mensured thrtst Increment

: s&Lntztd :hruzt cremeo: by ¡r.ertiat mltance ¿1f z do. rudder rvstzItct

T5: measured thrust at straigh: r.nnig

An unexpected result of the tests

resistance due to yawing is small (again

conditional

upon

observat ion error)

rather than "drag" obtained elsewhere. yawing is high the tendency to exceed

but when considering

the finding wiLl. not

In this series of observed increase in the calculated value

is that ruader

/ (.

Fig.6 gives an example of the results obtained and shows that where either the yawing or the rudder angle are great,

increase in average thrust will also be large.

The tests enable the average values of inertia and rudder resistance to be obtained from equation (5) since the rudder angle and the other elements of ship motion and are recorded in succession. 't' may be deduced as a value of free-running forward motion and additional mass may also be obtained from the Motoyoshi chart. In Model M.No.152 rudder resistance is measured by observation and the remaining factors

obtained from the following Fujii equations, where ) is the rudder aspect

ratio:-N4 .4 V(l-w)'(1+3. E

Results of calculation etc. are shown in Table 2 and it may be seen from these that the increase in average

about by yawing may be rationalised.

Both 4Tm

4ATr) are equal, within the limits of observati

Table 2. Thrust Increase due to Yawinç.

thrust brought and

(4T

+

ori error.

this as resistance

contradict data already tests also, where

thrust shows a

of inertia and rudder

iT. i1 ¡T. iT-JT. jT..T. 113 gr S7gr 99er 16gr 8. ¿Y. 97 126 4.2 50 23 54 3.5 123 120 21 ¡41 LI 20 4 ₁₀ 0.8 203 63 ¡78 241 9.2 213 ro : 113 9.6 ro 75 19 46 63 3.3 V) Ì 12.6 0 27 136 213 10.3 155 4 136 190 8.8 13 20 i $3 Ti 4.5 20 S 13 I 13 1.2 T, 1I'O 11.6.. 15.9 1.3 13 1. 123m. 9.? 10.9 8.4 24.4

4.Sj

10.8 ¡31 I 13.6..' 15.6 6.0 Ill 1.210m.'. : :

I.

19 12.* I ii.!.. 15.9 7.2 . 132 1.310m.. 15.8 43 8.6 11.6 4.3 11.9

inertia combined. This is probably due to hull resistance. The direct increase in hull resistance following such an

extent of yawing is, at the most, only 10% of the total thrust increase and is regarded as less than 1% of the total of the thrust itself and it is therefore considered to be of minor significance.

Automatic Steering and Loss of Propulsion Power.

Increase in mean thrust in yawing conditions is made up principally of the mean values of inertia resistance

(m + m)Vj!(j and rudder resistance, and, given the motion of the ship and the rudder angle, this increase may be

calculated. The motion is obtained from the rudder angle

and manoeuvring period and therefore, in effect, thrust increase is gained from rudder angle and yawing period.

If the results obtained and covered in the preceding

sections are "scaled up" to correspond with a 125m cargo vessel and a 250m tanker the horsepower loss may be deduced in the form of a percentage of the power when moving straight ahead

in calm water, such as je shown in Figs.7 and

8.

Compared with a model the "viscous" resistance of a ship is extremely small

and therefore the percentage lose of power due to yawing is greater in an actual vessel.

Pig. 7. Power Loss caused by Yawing in a Cargo-Vessel (Automatic Steering)

I

-70,. A FULL- L04.'ED

I

:2. !fLL!Z I ,c.

4

/

's: i 2.7 _&'.13)/ J

!jg. 8. Power Loss caused by Yawing in a Tanker (Automatic Steering)

so

A FLL-LOÂCû TA.*IKER!

The increase in power loss accompanying the periodic increase (i.e. a decrease in c ) is due to the fact that yawing will increase in direct proportion to the period relating to a fixed rudder angle. This tendency is

particularly marked in tankers where

hunting

characteristics are poor (i.e. course stability is inferior). On the other hand similar periods and inertia resistance are proportional to and therefore the total loss of power will also be

proportional to(1

It has already been concluded that long-period yawing when wider automatic steering is due to free oscillation in

the steering system. Included in this is the significant factor of delay in the "weather adjustment" which hinders the damping effect throughout the system and because of this the ship starts a

continuous

free yawing motion. This motion is one of long-period yawing in a curved

configuration

and

both its period and its amplitude may be determined by analysis of the automatic stecring system. If this analysis and the results of this paper are combined, it will be possible to estimate the power loss arising from automatic steering.

If calculation is made in respect of the cargo vessel

and tanker in question and the results expressed diagrarrnatical. the result will be the broken line curves in Pigs. 7 & 8, where

--:3.

amplitude of the weather adjustment delay into a rotating head angle while C1 is a proportional constant of the course error and rudder angle.

Based on the above, when fully loaded ships are running With the weather adjustment conveying some degree of effect

(i.e. the normal

conditions

of ocean service), yawing is

+ 2° to 30, rudder angle 2° to 6°, period 100 to 200 seconds

nd loss of pówer between $ and 5. However the diagrams show that in certain circumstances losses in excess of l0

can occur. This loss cannot in any case, be ignored and there are examples where Pacific crossings have been made with a

power loss of up to 18%.

Figs.7 & 8 Bhow that the autopilot is a significant

factor in bringing about loss of power. It may be seen that a large rudder ratio ("normal rudder angle adjustment") is highly undesireable. Thus when wave formation developes and where the weather adjustment is necessarily high (i.e.

4.is

large), the rudder angle ratio C1 must be kept to a minimum. However, in such sea conditions as these, external forces are usually strong and therefore it is unlikely that

the rudder angle ratio willbe reduced to any extent. It

is therefore hoped that, as a fundamental development, some study of the establishment of a type of weather adjustment system will be put in hand which will avoid the present

characteristic of reducing the damping effect of the system. In recent times, some effective results have been

obtained in controlling the yaw amplitude by means of angular velocity control (differential control) and calculation has Bhown that a reduction in amplitude of as much as 3Oj-' is

obtainable by such methods. This is considered to be a major

contribution.

Limiting the rudder angle does not influence the amplitude of yawing to any great extent but it does reduce

rudder resistance.

Thus it may be accepted that a significant feature in

the _{autopilot is the resulting loss of propulsion power}

"1e

_{Under automatic steering and a maximum loss of about}

may be expected in certain circumstances. This

:;teniatjc must be borne in mind on designing, adjusting

OPerating such equipment.

k

I

Lose of Power recorded on Course Recorder.

It would be of considerable assistance if rough

calculation of power loss could be made from simple yawing records when

analysing

motion of ships in service. The

paper feed of a normal course recorder is 0.6 mlrv'min and yawing in the period of encounter is not detectable. If

however regular yawing of periods between 50 and 200 seconds is recorded this may be regarded as representing a long period yawing motion giving rise to losses in power. If half-amplitude

i8(1°

the period T (sec), ship's length L (m) arid displacement weight W(ton, the average value of inertia resistance will be found as follows

:-1=O33WL(ç5'/T1) kg (7)

This equation adopts the following values

:-(m+m)/m =

1.8

cos ('-je )

= 0.75

1IfI1ì

= 0.4

which are close approximations to the yawing

conditions

of merchant vessel8.

Rudder resistance is obtained from the Fuji equations thus

:-L0.013 Vr'(1w)(ì+3.63t6) (8)

where Vk : Ship's velocity (knots)

s = i - 0.514 Vkt (1 - w)/ np : Slip ratio

?:

Rudder aspect ratio

: Half rudder amplitude (deg)

Where there is no record of rudder angle, the amplitude may be deduced from the yawing amplitude by checking the appropriate extent of rudder angle adjustment (rudder angle ratio) and the extent of weather adjustment.

Conclusions.

1. Long-period yawing which is frequently encountered when under automatic steering is brought about by free oscillation from three areas, namely the ship itself, the steering

not significant but the loss of propulsion power can range from 2 or 3 to 2O4 of the calm water normal power.

The loss of power is brought about mainly by inertia resistance (in + m)

V(1j3

_{, and rudder resistance, both of} which are set up when yawing motion developes.

If amplitude, period and rudder angle is obtained from a course recorder, power loss may be calculated using equations

(7) and (8) above.

Direct oscillating yaw, caused by wave action does not develope any significant inertia resista&ce. Therefore so long as unnecessary steering movements relative to wave

motion are not made, this type of yawing will not bring about any notable degree of power loss. _{(If steering movemenis are} made, power loss will occur in proportion to rudder resistance

only.)

It appears that hull resistance due to yawing and the resulting oblique motion is small, _{If the latter movements} are great, however, there is some minor tendency for this resistance to increase, but in the normal pattern of yawing this increase will only amount to a maximum of 1% of total

running resistance. _{This however is not the normally accepted} type of resistance but rather one which shows "drag" tendencies.

The thrust and periodic torque fluctuations operating on the propeller are related to variations in wake locations at the stern when yawing _{occurs. It should therefore be}

noted that this pattern of fluctuation has no direct relationshi with that of fluctuations in rudder resistance or inertia

resistance both of which exert a considerable influence on average thrust increase

When an autopilot is used, _{the rudder angle ratio shoul1}

be kept to a minimum (ratio _{of rudder angle to course error).} In particular, where both weather adjustment margin and rudder angle ratio are high, there is a strong probabilïty that an appreciable loss of power will result.

Acknowledgement.

The experiments in connection with this paper were conducted at the graduate research institute of the Osaka

University Shipbuilding Department during 1965 and 1966. The

authors would wish to record their appreciation for the valuable assistance received during this period from Messrs.Onishi,

Sakurai, Murakami, Okada, Onoki, and Takai of that organisation.

Bibliography.

Nomoto "Stability in Automatic Steering". J.Soc.Nav. Arch. Japan Vol.104, 1959.

Motoyoshi

'Automatic Steering and Yawing in Storm

ConditionB". J.Soc.Nav.Arch. Japan Vol.94,1954

Kaininaka

Pukase etc.

"Turning of High Speed Ships". J.Soc.Nav.Arch. Japan Vol.111, 1962

M. Chialett

J.Strom-Tejeen "Plan Motion Tests for a Mariner Class Vessel". Rep.No.Hy-6 Hydro-og Aerodyamisk Lab.,

Denmark, 1965

5) Nomoto "Manoeuvrability of Ships". Shipbuilding

Symposium, 1964 H.Eda, C.L.Orane Yarnagata Pujii, 'Tauda

."Steering Characteristics of Ships in Calm ?Iater and 7aves". S.N.A.M.E.,1965

"Ship Propulsion". p.159

"Rudder Characteristics of Free-Running Models". (No.2) J.Soc.Nav.Arch. Japan Vol lii, 1961.