The economic consequence of ship service speed reduction

ARCHEF

o. Introduction

Today ships are designed for good performance with respect to resistance and propulsion. lt is also possible to calculate the trial speed with great accuracy.

The effect of the efforts to attain the best possible initial speed in relation to installed horse power and

main dimensions, is greatly reduced when tise ship is in

service. Reduction of the service speed begins shortly

after a ship has entered service.- The speed reduction can be considerable, and means a corresponding reduction in the ship's efficiency as an instrument of transportation.

The speed reduction comes from reduction

in the

efficiency of the underwater hull, the propeller and the machinery. The major part of the speed reduction is due

to increasing frictional resistance caused by increased

roughness and fouling of the underwatei 1juli. Damages to the propeller and propellei roughness may, in special cases, also be of importance. Machinery efficiency shows only small reductions, although increased hull frictional

resistance and tile corresponding speed reduction and wake increase may necessitate a reduction in horse power to avoid a too high mean indicated pressure in

diesel engines, or a too great torque in steam plant gears. To compensate for the speed loss in service, including

speed loss caused by weather and other factors, the

installed horse power in some ships lias a so-called sea

margin. The sea margin is insufficient to maintain the initial speed, and can therefore only partly counteract

the economic loss brought about by service speed

reduction. However, regarding tankers, it is common practise to use the available horsepower one hundred per cent right from the beginning of the ship's service time. Any increase in resistance will, for these ships, mean a reduction in service speed. Speed reductions as great as 2

knots in 16 months can be observed. A corresponding

increase in shaft horse power to maintain initial service speed would have to be over 50 per cent.

Reconditioning of the underwater hull surface, and if

necessary the propeller, can

be done by docking.

Selection of the best docking interial is therefore of great importance.

Norwegian Maritime Resecrch

No. ¡/1974

18

The Economic Consequence of Ship Service Speed

kidho Hojch1

by

Deift

BjØrn O. Si//crud, (siv. ing.) Division of Ship Design,

/t

C'

Norwegian Institute of Technology

J

¿ ,L (L

Abstract vC

¿t-CP_

The objective of this report is to clarify some &f the economic consequences

of ship service speed reduction. The methods and principles presented are generally valid, but in this report Large tankers are considered.

A reduction in

the ship service speed is

to a great extent caused by

roughening and fouling of the underwater hull. A simple (manual) method to

find this speed reduction and a method to evaluate the minimum docking interval with respect to treatment of the undcwater hull are presented. An

extension of the off-hire concept is given. Results are presented in a way that make them almost independent of ship size and freight rate.

1.1. Reduction in earning potential due to speed reduction

A mathematical model is used

to calculate the

economic influence of speed variation. The annual

ransportation capacity of a ship on a certain route may

be expressed by:

Cdw

A (1)

where: C

= (ton/year)

annual transportation capacity

dw (ton)

the ship's cargo carrying capacity A = (voyage/year)

the average number of voyages per

year

The thip's annual earning potential, I, viu1be:

I = R dw

A

where: I = (kr/year)

the ship's annual earning potential R

= (kr/ton)

average net freight rate

It should be noted that the annual earning potential is

not always equal to the actual annual freight revenue. This depends on the extent to which the shipowner is

paid exactly in proportion to the annual transportation capacity, which again depends on charter terms and the accuracy in the determination of A.

When the ship's speed, V = Vo. Le. remains constant;

we have for the average number of voyages per year:

AAo

-

365OH

(2)

L

+TH

where: OH = (day/year)

annual off hire, normally about

15 days/year D (n.miles)

round sailing distance TH = (day)

total time in port for each voyage In general, A is a function of speed (see Figure 1):

/

A=

365OH

24.V+ TH

8y logarithmic differentiation of eg. (2a) we get:

D

dA _dV

24V

j

_V

TR If V = Vo, we get:

dAdV

TSo

Ao Vo TSo+TH

where:

ISo = (day)

time at sea per round trip when

V Vo

dV

= (kn)

may be considered as the mean value of the speed reduction, Vo - V, with respect to time. It will in the following be denoted

by iV:

f(VoV)dtjfìV(t)dt

L0 _O or discrete: 1

tV

LViLti

T

_i1

where

the time T is

divided intà smaller parts tt1 with corresponding mean speed reduc-tion V1.

V(kn)

f (month)

The corresponding relative difference in the annual .earning potential may then be approximated by:

¿M AV TSo Io Vo TSo + TR Equation (5) may be rearranged:

AIVIo

1

iSo

Vo TSo+TH

1 TSo

=V[(RdwAo)v

_TSo+TH'

AV K

where: AI

= (kr/year)

reduction in annual earning potential

K = (RdwAo) Vo iSo + TH - I TSo (6) TSo (6a) = (RT/Cdw 12) Vo TSo + TU

where: _RI/C [kr/(ton month)]

net time charter freight rate Vo here equal to the contract speed Lt may be seen from eq. (Sa) that the reductïon in the

earning potential is proportional to the

mean speed reduction. The constant, K, eq. 6, is proportional to the

sea time/roundtrip time ratio. For VLCCs this ratio is

almost equal to unity.

The exact expression corresponding to eq. (5), may be found by intergratingeq. (la):

T

I=RdwfA(t)dt

_To

(lb)

where: A(t) = (voyage/year (1/year))

the number of voyages pe year, as

a function of time, i.e. the number

of voyages obtained at the speed V(t). The integration is performed in appendix U, with speed as a Iineay decreasing function of time. _Appendix H also contains a numerical example that shows that eq. (5) under nonna! conditiois gives a reduction in annual earning potential which is about 1% too small in relation to the exact expression. Eq. (5) ¡s therefore considered to be a sufficiently good approximation.

F/g. _{1. Ship speed and number cf voyages per}

year as a function of time.

19

A (t)

t (month)

Norwe'ian Maritime Research No. 1/1974 (2a) (3) (3a) (4) (4a) (5) (Sa)

1.2. Speed reduction in terms of off hire time A common measure of a ship's running and operating economy is here daily freight revenue:

C0H365 = lo/365 I

where: Io = (kr/year)

annual freight revenue based on net

freight rate; i.e. harbour dues and

fuel costs subtracted C0H365 = (kr/day)

cost of off hire

= daily freight revenue based on net freight rate

As a ship earns money only during the time she is

actually in service, the above expression does not give

the full loss of a day out of service or "off hire". A

better expression is:

Io COH =

365 -OH

substituting

.Ao(TSo + 1H) 365 - OH (eq. 2a)

we get

COH lo

(TSo + TH)Ao (7a)

The annual loss of earning potential due to the speed reduction, ¿W, has an equivalent annual number of days

off

hire: DOH

COH (8)

Combining this expressior with eq. (5) and eq. (7a) gives

DOãV₌

(TSo Ao)

(9)

): Equivalent annual number of days off hire is

independent of ship size (dw) and freight rate.

The equations in this chapter have been made to

calculate the economic influence of service speed reduc-tion. The equations are, however, valid for other kinds

of speed variation, i.e. speed variations caused by

weather, improved navigational systems, etc.

2. Ship service speed reduction

Observations of ship service speed show great

vari-ation with

a general

falling trend with time. The

different causes for this speed variation can possibly be

listed as follows:

Weather (wind and waves) Deadweight

Trim Horsepower

Fouling and roughening of the underNater hull

Norwegian Mari ri mt' Rescarch NO. 1/19 74

20

Water temperature

Ocean currents and tide water Reduced depth under the hull Mixture of fresh water and salt water

IO. Log riot correctly adjusted and/or influenced

by boundary layer

Il. Damaged or rough propeller 12. Machinery efficiency variations

The majority of these

factors have a negative

influence on the service speed and therefore also on the ship's economy. Which of the factors can we influence, and how can we improve the economy?

For a given ship we can, among other things, use

weather routing. This will also generally make it possible

to utilize the engine power to a higher degree (less

slowdown due to weather). Good officers, effective hull stress surveillance systems and good navigational

equip-ment wiU have the same effect. However all the

improvements possible seem to be small in relation to the effect of fouling and roughening of the underwater hull. Corrosion, deterioration of the paint etc., give the hull a basic roughness. In addition to this roughness, the ship will be more or less fouled on her under water parts

dependent on quality and type of anti-fouling system,

trade, time in harbour, etc.

In Appendix I a method is given to calculate the

mean speed reduction on the basis of data in the abstract machinery Ioghcoks. In generai the speed reduction will

start at a certain time, t1, after the ship has entered

service and increase approximately linearly until time t2. A ship will generally be docked somewhere in the time period between t1 and t2. During this period the speed reduction will be approximately linear at an amount of b knots per month.

3.1. Minimum period between drydockings As seen, a ship's service speed generally decreases with time, so does also her potential earning, eq. (Sa). Antifouling paint may be renewed by drydocking, and

thereby the ship can gain a higher service speed. For

present purposes it can be assumed that the service speed

is restored to its original value at each drydocking. In practice this is not completely true because some

permanent increase in basic roughness takes place. This

roughness cari only be fully removed by sandblasting.

Total expenscs for the docking alone, renewal of the A/F-fIlm, including the cost of off-hire for the docking

time, deviation etc, but excluding expenses not ass ciated with treatment of the underNater hull, is called

DC (kr).

The sum of reduction

in annual earning potential and the annual docking expenses, as mentioned

above, then becomes:

/

TC = K V(t) + (DC/t) 12 (10)

where: t = (month)

time between drydockings

A necessary condition that must be satisfied if TC shall berninimized is:

aic

_-

_K\'(t)

i

Eq. (11) gives t = Tmin. V(kn)

The term, minimum docking interval, instead of "optimum" docking interval, is chosen because the

actual time interval, T, has to be greater than Trnin. This

because the docking expenses arc always paid by the shipowner, while the reduction in earning potential is

not always fully covered by the owner.

When V = -

f

V(t) dt is inserted into eq. (11), we

get for t = Tmin:

[i-f

AV(t)dt}_DC

12=0

KV(t) - K2(t)

- DC 12 = o

In appendix I it is shown that the speed reduction increases linearly with time:

From Figure 2:

(12)

where:

b = (kn!month)

speed reduction coefficient

t1 = (month)

time when speed reduction starts

V(kn)

-t(rnonth)

Fig. 2. Linear speed reduction as a function of time.

1f eq. (12) is combined with eq. (11) we get:

Tmin 2 DC

= i

(K/i2)(b/2)

The corresponding TCmin can be calculated from eq. (10). Eq. (13) is valid as long as Tmin is within the linear part of the speed reduction function, i.e.

t1 Trnint2, see Figure 3:

21

s t2

When tiF = t1 B = t eq. (14) becomes:

(b+b)

(tt1)2 _(t-t1)2

_2t

2t

f(rnomh)

Fig. 3. Linear speed reduction as a function of

time.

As the value of Tmin is generally less than t2, eq.

(13) can be applied in most cases.

In general, speed reduction when the ship is fully laden

and in

ballast is different. The mean speed

reduction with respect to time then becomes:

v

(FB)

(14)

bF(ttiF)2

_(14a)

btt1B)2

_(14h)

where

b = (knfmonth)

average speed reduction coefficient for fully laden and ballast condition

Eq. (13) will

gire the minimum time between

drydockings when b is replaced by b. Calculation of the

total cost. TC, by eq. (lO) may be performed without complications.

3.2. Sandblasting

Eq. (13) may i

principle also be applied to (13) calculate optimum periods between sandbiastings. The

sandbiasting effect is indicated in Figure 4.

Norwegian Maritime Research

No. 1/1974

Fig. 4. Effect of sandbiasting on speed reduction.

When total cost in connection with sandblasting,

including off hire, is known, Tmin sandbiasting can be calculated by eq. (13), when a sufficiently good estimate for b00, the slope corresponding to the basic deteriori-ation at the hull surface is known.

3.3. Underwater brushing

The effect of underwater brushing is indicated in Figure S.

_{Experience today seems to indicate that}

underwater brushing may improve the service speed, at least for short periods of time. Tmin brushing may also

be calculated by means of eq. (13). Because the speed reduction is changed by brushing, brushing may also change Tmin. Brushing is, however, in practice done

after a service time greater than Trum as indicated in

Figure 5, and in such cases Tmiri is unchanged by the brushing, even though brushing reduces the economic

losses. A simple numerical example is ven in chapter 4.2.

TC = KV(t) + (DC/t) 12

Fig. 5. Effect of brushing on speed reduction.

4.1. General use of equivalent number of days off hire

As mentioned in chapter 3,

the actual docking interval,T, will normally be greater than Tmin. lt may therefore be of interest to investigate what happens

when T is different from Tmin. For this calculation it is

convenient to express all economic losses in terms of equivalent number of days off hire. The equation for

total cost is:

The corresponding equation based on equivalent number of days off hire becomes:

DOHTC

= P9v

+ DOHD

= DOH + (DOHD/t) 12

(15)

where: D5ÏITC = (day/year)

equivalent annual number of days off hire with respect to TC.

DOHV = (day/year)

V(t)

Vo (TSo Ao) (9)

= equivalent annual number of days

off hire with respect to speed

reduction

Norwegian Maritime Research

No. ¡/1974

22

DOHD =(day)

equivalent number of days off hire

with respect to docking expenses = DOHDT + DOHç'

(time part and cost part) (16)

V(t) =Í tW(t)dt

(4)

(kn)

mean value of speed reduction

with respect to time

This system of equations offers a general procedure

for finding Tmin and the development of costs as a

function of time.

Eq. (15) may be plotted as a function of time, the

minimum point corresponds to lnin.

Combination of eqs. (9) and (15), gives the following two general equations, which can be used to study the development of losses as functions of time:

DOHTç - DOHTC(Trni) DOHTC(Tmin) Vo 1 V(t) + (DOHD

TSo Ao/12

t Vo 1 V(Tmin) + (DOHD

(TSo Ao/12)' Tmin

DOHTC(t) - DOHTC (Tm4

365OH

-ISo

V(Tmin) ¡ ¿W(t) TSo + TH Vo

jV(Tmin)

-Vo (DOHD (TSo Ao/12) V(Tmm)

With linear reduction in speed, eq. (13) may be

rewritten in the form below, using substitution from eq. (7a) and (6a):

(10) _{Tmin +DOHD} Vo i

(TSoAo/12)

(b12)

In all cases, the DOHTC(t)-cune and the corre-sponding 1mm is independent of ship size, but indirectly dependent on freight rate because DOHDC may change with freight rate.

For similar sets of ¿W(t)-functions, all information

concerning Tmin and the DOHTC(t)-curve, can be condensed into one single diagram. We will have two main cases:

Vo

(

_{To Ao}

) = constant:

DOHv(t) can be drawn as a function of time, and Tmin marked on the curve as a function of DOHD

for each V(t)-function.

1 1

Tmin

(15 a)

(15b)

Vo

TSO Ao

vanes: Vo (DOHV _TSo

Ao can be drawn as a function of time, Tmin can be marked on the curve as a function of(DOHD

_TSo-Ao

for each V(t)-function.

Diagrams for sets of linear speed reduction functions will appear in chapter 4.3., Figures 10, 12, 14, 16, 18.

4.2.

Examples. Use of equivalent number of

days off hire, DOH

Reverting to chapter 3.3., underwater brushing. \Ve

assume that brushing restores speed as indicated by

Figure 5.

For ari actual ship the case may be:

1mm brushing _=1DOHD Vo

(TSo Ao/12) (b/2) = 1.85 (month)

i.e. about once for each round trip PG- Europe.

24 30 36 T (mont h)

Fig. 6. Equivalent annual number of days off

hire, DOHTa DQH and DOHD as

a

function of time.

23

Figure 6. shows for

a quite

representathe case

DOHTC, DOHV and DOHD as functions of time for a given speed reduction function V(t). The calculation is perfotmed with the equations in 4.1. I)ocking each 24th

month, gives DOHV 25.6 (day/year), i.e. 5L2 days in

the two year period. If the freight rate is 3($/(ton

month)) and dw 400 000 (ton). CON corresponds w about 226 000 (kr/day). This gives DOHv COH = 25.6

226 000 5.8 106 (kr/year)

Figure 6 indicates

a Tmin of 11

months. The

difference between 1mm

and T = 24 corresponds

to a difference in DOH' equal to 13.7 (day/year)

or 3.1 106 (kr/year)

13.7. (day/year) corresponds to 13.7/350 0.039 %

4% of the annual freight revenue. It should be noted that

DOH and DOH continues to increase after the speed reduction stops at t = 24 (month).

Figure 7 shows DOH for a linear speed reduction:

= 4

Fig. 7.

Figure 8 shows the influence on DOH from systems

that may delay the start of fouling and roughening of the underwater hull and thereby also delay the

corre-sponding speed ¡eduction. It may be seen that the

increase in Tmin with t1 is small, but the corresponding

reduction of DOHTC is considerable.

30 20 10 Fig. 8. lDOH.10 I F bO.15(kn/montj A.-Q0502121 -:

L(TTS1IIO J

Norwegian Maritime Research No. 111974

Vo 16 kn.

AV(t)= (t

t1) 0.10, t t1 t1

TSo _{Ao = (365 - 15) . (IO/il) = 318 (day) (Time}

at sea per year) DOH (doy)

b 0.15 (kn/month)

dw 400 000 (ton) _{ÌCOH 226 000 (kr/day)} 30

I DOH»0 r -I RT/C 3 ($/(ton month)) J 4400 (kr/h) TS.4.0050 oHT5 1 DOH (TH/TS.)l/l0 _J 20 tX5fl.. T.4 b0.15(Ln/rnor.ÑJ The brushing is estimated to cost about N.kr. 50 000

and to require fIve hours off hire, eq. (16):

DOHDT DOHDC 5/24 = 0.208 50000/220000 = 0.221 lo t,V(kfl)

DOHD = DOHDT + DOHDC = 0.429 (day)

4.3. Diagrams

for calculating the economic

consequences of different speed reductions The diagrams in this chapter are based on chapter 4.1

and use of the eqs. (15), (9), (16) and (4). Different

linear speed reduction functions are used.

Figures 9, 11, 13, 15 and 17 give Tmin according to

eq. (13a).

Eq. (16):

DOHD = DOHDT + DOHDC

Fig. 9, 11, 13, 15, 17:

Docking interval rmin, giving minimum DOHTC

Vo

according to eq. (13a). When _Ts0

_A/12

is different from 0.603, (e.g. Vo = 16, OH = 15,

(TH/TS0) = 1/10) Tmjn is a

function of

(DQHD

TSo

A0/i

and the lowest

hori-zontal scale should be used.

vertical scale to the far left, and Tmin ¡s given

Vo

as a function of (DOHD

TSo . Ao/121 rhe use of the figures is illustrated by Figure 12a.

Norwe'iwz Maritime Research

No. 1/1974

24

has a "time-part" and a

"cost-part". lt should be

noted that as the freight rate increases, DOH DT remains

the same, while DOHDC is gradually reduced. If the

freight rate R -

° then DOE! DC - 0, and DOHD

becomes equal to DOHDT i.e. the actual number of days used for the docking, including deviation etc.

In the Figures 10, 12, 14, 16 and 18, are condensed all information necessary to give Tmin and to construct the DOHTC (t) -- curve, for the given V(t). functions.

24 18 12 C V(kr) b.O5

-i

-2 f(month) 5 Fig. 10. 5 10

_{DOHîs,'(kn month)}

Fig. 9 /

tbv

h.25,'

,i

OHday/y ear) 1

.20'

/ /

I

f I ÖT-M5 , / I (TH/Ts)=i/10 /

,'

L--

---.J /

1.5 L // // Fig. 10, 12, 14, 16, 18:

_{fD_,'}

1.0

DOH, equivalent annual number of days off

hire due to speed reduction, as a function of

tíme. Tmfn (to be read off the horizontal scale) ¡s given on the DOHv (t)-curve as a function of

When is

DQHD.

_{TSQ. A0}

different from

0.05029, (e.g.

V0 = 16, OH = 15, (TH/TS0) =

Vo 05

1/10) (DOH,

_TSo

_Ao

's given on the

4. T(month) 24 18 12

/

Fig. 11. DOH _TSA0

5y/yecr)

/

[v

_=0.05029 i ' I /

'

30 _{v=i OH=15} /.231 '(TH/TS.)1/i0 / L / / F f / I / / / / / / / l-

-,i/I

/

/ ,, D 0H=,' F' 20

/ i'

//

I,

o 6 V(kn) -- b= .05 .10 .15

/

_{- -.20} 12 , / b=.25/

5/

[;-47

--

/

V. D0H0 TS;A.112j 12 18 24 T(mont-12 18 24 _T(rnnth) Fig. 12. 25 ,(month) -4 -2 D0RJTSA 20 Fig. 14. 6 v( kri)

fW;.-A-

.05029 30

--=0.05029

[\=16 0H=15

LdiT=lhb0

-12 5 lb 15 2b .10 it.=81 .05

io /

[11

12 18 24 T(month) 1 24 'T(rnonth)

Norwegian Maritime Research

No. 1/1974 10 15

20 DoHp;s.6o3

5 0

_DOHDçrS/)

5 Fig. 13.

EOH TSAI«m0rth)

1.5 1.0 Q5 t5 1.0 Q5

D0H TSA D0Hdcy/yecr) 50291 -1 ÖHrl5 1.5 -30

H/TS1/10

O0H 1.0 0.5 20 10 -2-V.

Norwegian j!antirne Research

No. ¡/1974

b0j5(kn/moi51

t,r12 8 4 o ib 15 20 _____ 5 lo _{DOHç12(kn.month)} b0.i5 (kn/month) tt 12 18 24 T(mont 26 24 L(month) 18

12<

1.0 0.5 5 12 18 24 T(rnonth) L. 5 12 18 24 T(rrnth) b 0.10 (kn/morlth)l t,12 8 4 o 2.0 TSA b0.10 (kn/month)] dcy/yecr)

r V

1.5 _-30

-o.?09

J

r'io CH=15 --

i 'ÇrH/TsJrl/lQ I L. 5 10 15 20 TS;1 5 lb month) Fig. 15. Fig. 17. AV(kn) 2-Fig. 16. Fig. 18.

n Fig. 10, the assumption is made that t1 =0, i.e. the

speed loss, starts as soon as the ship enters service. In this

special case the curves of Tmin (to be read off the

horizontal scale) will also be curves of DOUD; annual docking ex1penses (to be read off the vertical scale). This is because I)OHVDOHD when t=Tmin and t1 0.

The use of the diagrams is demonstrated by Figure

12a, suppose t'1 = 4 (month) and b = 0.15 (kn/month).

The docking expences - time and money -

corre-spond to DOHDIO(day).

The Tmin curve for DOHD = 10, intersects the

DOHV.curve for b = 0.15, at t = 1mm = 9.8 (month).

The corresponding D0H-value is 5.2 (day/year):

DOHTC (9.8) = DOHV (9.8) ± DOHD (9.8)

=5.2+(l0/9.8)' 12

= 5.2 + 12.2 = 17.4 (day/year)

If the actual docking interval, T, is chosen equal to 18 months, and the speed reduction continues at last until

that point of time, we get that DOHV(18) =

(day/year)

-1.5 30 1.0- 20 T,.., curves for / _/ 05029

i','

20 / TS,'A, 00H0,' / 05- 10 1 f. ¿V (kn) / .15 o 00H, 12 18 24 T(month)

Fig. 12a. This figure ¡s equal to Figure 12, with the exception that a numerical example is marked ¡n the figure.

27

DOHTC(18) =D0I-1(l8)+ DOHD(18)

= 16.2 +(10/18)12

16.2 + 6.7 = 22.9 (day/year)

The difference between t = Tmin = 9.8 (month) and

T= 18(month)is:

DOHTC(18) - DOHTC(Tmin = 9.8) = 5.5 (day/year)

or about 1.6% of the ships annual freight revenue. As another example let us assume that a shipshall be

equipped with a new A/F-system giving t1 4 as before, but reducing b to 0.10 (kn/month).

Fig. 12 gives for DOHD = 10 andb 0.10; Tmin = 11.7 (month) and DOHV 5 (day/year)

DOHTC(1l.7)=5 ±(lO/ll.7)12

= S + 10.3 =l5.3(day/year) DOHTC(l8) = 10.8 + (10/18) 12

= 10.8 + 6.7 (day/year)

i.e. _{the savings are greatest when T is greater than} Tmin.

5. Short remarks on systems preventing fouling and roughening of the underwater hull.

Roughening of the hull is best prevented by means of

the best possible paint system, good corrosion control

and excellent cleaning and painting workmanship_when

dry docking. The effect of permanent roughening is

indicated in Fig. 4 as b00.

The fouling preventing systems can be divided into 3

groups:

- Conventional antifouling systems, i.e. use of

A/F-paint.

- Advanced A/F-systems, eq. ystems with

reacti-vating of the paint, and new types of A/F-paint.

- Other systems,

e.g. systems based on chlorine released by electrolyzing sea water or chlorine

from other sources.

In addition to these systems, mechanical brushing may be used as and additional aid. Ali these systems

should be judged by their ability to prevent service speed

reduction, and not only by their ability to prevent

fouling, as for example found by visual inspection. This means that the actual speed obtained in service must be

observed and economic calculations made should be based on these observations.

Today it is supposed that marine organisms settle on

Norwegian Maritime Research

No. 1/1974 20

0OH,.-0.05029) Speed permcx,thloss ¡¡ b.25 / .20, Examples r

Savings with the new system:

t = Tmin _{2.1 (day/year) or about 0.6% of the ships} ii'tuaI freight revenue

1= 18 5.4 (day/year) or about 1.5% of the ships

ival freight revenue. "DOH,rlO £ b =0j5,give DOH,=52 2.)r & b rO.15,g,ve 00H, Çday/year.i 00Hr 12 .05 -,.

-- __y

r.., curves for1 ., are dotted 6 12 18 24 Tfrr'onth) T.... 9.8 T,m bet wee/i dry dockings -4-

-the underwater hull only when -the ship speed is below

about 2 knots, i.e. normally only when the ship is in harbour, If the marine organisms have settled, fouling will continue both in harbour and at sea. If the marine organisms are prevented from settling no fouling will

occur, or, if settling is prevented in harbour, no fouling

will occur in harbour or at sea. This means that if the

fouling preventing system is sufficently effective in port, the system is not needed at sea.

A/F-paint seems today to be the most reliable fouling

preventive system. It has, however, two considerable drawbacks:

its fouling preventive effect, i.e. the poison

leakage, is greatest at sea when in principle it is of

least use.

- the A/F-paint itself deteriorates, and its increased roughness reduces speed.

Systems based on, for example, chlorine electrolyzed from sea water, can be used when they are most needed, i.e. in harbour, and not necessary at sea. The roughening from deteriorating A/F-paint will disappear.

An alternative could be to use chlorine at the end of the harbour period to kill the marine organisms already settled, and also, if possible, to use mechanical brushing to remove the most of the dead marine organisms. The results will be that almost no further fouling and speed loss will occur at sea. The system could be kept onboard,

but it would be better utilized if kept in port at e.g.

tanker terminals. In Fig. 19, is indicated possible speed

reductions for given shaft horse power as function of

time for the different systems.

(D No protection

Ø Cooveotior1 A/F-system

(D "Leaving port. chlorine syste (D

4 Perfect'-chl orine system

Norwegian Maririnie Research

No. 1/1974

©

(D.

t (month)

28

prevented, long docking intervals should be avoided.

Great effort should be made to develop systems that can prevent ship service speed reduction caused by fouling

and roughening of the underwater hull. The

corre-sponding savings will be considerable.

Appendix I

Determination of service speed reduction due to

fouling and roughening of the underwater hull

We assume that the intention is to run the ship at con-stant horsepower, i.e. at 100 per cent utilization of the

propulsive machinery and at constant (machinery and

propeller) efficiency. Service speed will the be gradually reduced as a function of time. As a ship's earning poten-tial is directly related to the speed, it is of importance to make the best possible estimate of the service speed loss

due to fouled and rough underwater hull. A simple

manual method giving quite good results will be briefly

described.

As the service speed reduction is due to many causes, all causes except speed reduction due to fouled and rough underwater hull should be eliminated. The

method consists of the following steps:

Speed data is taken from the abstract machinery logbooks.

Special speed trials at sea are ordinarily done by the ship's standard equipment and especially good recordings may not be expected. It is better to use

data from the logbook because the great number of observations in the logbook will cancel out observation errors and factors that may obscure

the recordings of individual speed trials at sea.

Speeds measured with the log for the fully laden and the ballast condition are treated separately for

each voyage.

Select speed data for days without stop in the

engine and for the most frequent weather, and find

the mean speed for each voyage.

Find the mean observation time corresponding to

the mean speed and the mean wind direction

relative to the ship corresponding to the mean speed.

Adjust the speed to correspond to the nominal horsepower, SHPo.

Plot SHP versus speed from the ship's trial or

model tests on log-linear paper, see Figure Al.a.

As a matter of experience, the SHP-speed _curve

will be a straight line over a great range of speed. The corresponding equation is:

SHPo=(1 + x)

VVo

= (1 + x)'

I SHP

ln(l±x)

The SHP may be assumed to be proportional to F,

fuel consumption, which gives:

ln(1 ±x)

ln(--)

SHP

1H 1H

Fig. 19. 6. Conclusion.

The concept "equivalent annual number of days off

hire", can be used with great advantage to measure losses due to speed reduction and costs of docking.

Equivalent annual number of days off hire with

respect to speed reduction may be of considerable magnitude, If speed reduction cannot be sufficiently

SHP

FULLY LADEW

BALLAST

V(kn)

Fig. A 1. 1 Typical SHP-speed curves for trial conditions (log-linear paper).

This formula may be used to correct an observed speed to correspond to the nominal fuel

consump-tion (correcconsump-tion: - LV).

Correct the mean speed for each voyage to a

nominal draught and plot

the resulting speed values versus time on lineai paper. A curve similar

to the one in Figure Al. 2 is normally the result. From the curve determine the initial value of speed at fully laden and in ballast condition, i.e.

for t O.

Determine the slopes b (kn/rnonth) of the curves

for t > t1 either by simply drawing straight lines

through the points or preferably by linear

regres-sion analysis.

As a final check compare the speed data measured by the log against speed data observed by nautical observations over a period of time. Special notice

should be given to possible boundaiy layer in.

fluence on the log.

The objective of the method is to calculate speed reduction as such caused by change in wetted surface condition, and not to try to explain exactly why the speed starts falling.

Although the method is simple, it has proved quite

reliable to the extent that it is possible to control it. The determination of the speed reduction is of vital

impor-tance for calculating the optimum time between

dry-dockings and it

is, of course, possible to use more

advanced statistical methods to improve the accuracy, but this may be unnecessary in most cases.

29

Nori,egia'i %fanrirne Research

No. 1/1974

° Ballist

Fully !cden

V(kn) tip tf

ti

t(m3nh)

Fig. A 1.2 Typical curve for speed reduction due to

_{fouling and roughening of the}

underwater hull with constant shaft

horsepower.

Appendix U

Integration of eq. (lb)

I

RdwÄ

=Rdw fA(t)dt

_T0

(lb)

Combination with eq. (2a) gives:

T

l=Rdw

365OH

dt

(lc)

+TH

For simplicity we will here assume a linear decrease in speed with time, see Fig. A2.

V=V0--bt

where;

b _(kn/month)

speed reduction coefficient Eq. (le) becomes:

l=R dw

_j

365OH

dt _(Id) TH Integration gives: 365 - OH

1R dw

l+Q

1 (J

bTisx

TH TH bt TH

Expansion of eq. (le) gives

TS0

IRdw AO.{l_

TS0+TH

bi

2

TS0TH

V ( k,,)

-V=V - bt

Eq. (5):

AJbT

TS0 LiA IO Vo TS0+TH

-

0.l

24 ₃₀

=0.06818 (-)

16

30+3

Eq. the reduction in annual freight capacity or annual earning potential corresponds to about 6.8%.

= R/C dw

12 (from eq. 6a)

3. 5.5

400 000 12 = 79.2 106 (kr/year) which ves: Al = 0.06818 79.2V 106 = 5.4 106 (kr/year) Eq. (1 f): From eq. (1f):

A0ÄAAbT

IS0

A0 A

V0 TS0+TH

bI 2 TS0TH

(TS0+TH)2

Norwegian ,%íaritipne Research

No. 1/1974

T

t(month)

Fig. A2.

when further terms are neglected. It should be noted

that the first two ternis in the paranthesis corresponds to

eq. (5). If the V(t) function is too complicated for an analytical solution of eq. (lb), then the integration can

in principle be solved numerically. Because of the good

approximation which eq. (5) gives, this should not be necessaiy. Numerical example:

0H = 15 (day)

TH = 3 (day) TS0 30(day) V0

=16(kn)

b = q.i (kn/month) T = 24 (month)

RT/C = 3 $ ¡(ton month), exchange rate

dw = 400 000 (ton)

(17)

30

which is equal to eq. (5). with the exception of the

last term. This term is numerically equal to + 0.00062 or 0.00062/0.06818= 0.009 1%

i.e. eq. (5) gives, with linear reduction in speed and b = 0.1, a reduction in annual earning potential that is about

1% too small. This is, of course without any practical significance.

Appendix Ill

The following is a model for calculating annual

earning potential taking into account variations in voyage distance, freight rate, deadweight and speed.

The model is

described by the following set of

equations: 12 n t

-(

₎ dwR1 (18) month(n) n month(n) = At 3t;.4 (19) 1=1 D ₍₂₀₎ Liti

=THj+24V

AI

=Io-1

(21) where: = (kr/year)

annual earning potential

=(-)

number of voyages in the time rnonth(n)

dw = (ton)

carrying capacity on voyage; (Instead of ton, cft. container etc. can he used, with corresponding change in R)

R = (kr/ton)

net freight rate on voyage i

mon th(n) = (month)

time for n voyages

12

rnonth(n)

) (year)

a factor to correct Ito an annual basis = (day)

total time for voyage i

D 24V1

_____ = TS1 = (day) time at sea voyage

(kn)

the mean value of speed with respect to

time on voyage i, i.e. mean speed in the time interval TS.

As V1 is a function of the length of the time interval

IS, eq.

(20) should be solved by iteration. The

convergence is, however, very fast. On Fig. A.3 the possible service speed V(t) with constant shaft horse

power is indicated as a function oft. The actual effective speed V based on V(t) in the interval TS is marked on

the figure.

Only in very special cases should it be necessary to use the above equations to calculate the effect of service speed reduction. The equations can, however, be used for many other purposes.

5.5 (kr/$) n

Nomenclature

dw (ton)

ship deadweight ship capacity or actually carried amount of cargo

C (ton/year)

annual transportation capacity A

(yea(')

annual number of voyages

t (month)

time

Tmjn (month)

docking interval that corresponds to min. of

the sum of annual docking expenses and

annual potential net freight revenue

T (month)

actual docking interval

V (knot) = (kn)

ship speed

V0 (kn)

constant speed

charter speed or initial speed

AV (kn)

speed reduction

AV (kn)

mean speed reduction with respect to time

E. Telfer: "Some aspects of the external maintenance of tankers". Trans. RINA 1971

B. A. Hilliard: "Optimum periods between dry dockings". The University of Michigan 1966.

Just. Fr. Storm and B. Matzon Sorensen: "Máling av

motstandvariasjoner i service". (In Norwegian) NSTM 1967.

F. Borchsenius: "Noen eksempler pá teknisk tilstands-kontroll av skrog og maskineri". (In Norwegian) NSTM

1967.

B. _{Matzon Sorensen: "Begroningskontroll med enkle}

midler". (In Norwegian) NSFI-nytt 2-1972.

B. Matzon Sorensen: "Har De grobunn for beregninger" (In Norwegian) SF1-nyu 4-1970.

A. Yazaki, T. Iwata, S. Takezawa: "Some Analysis on Sea Margin By Using Abstract - Logbooks".

Japan Shipbuilding and Marine Engineering, Nov. 1967. P. H. Benson, D.L. Brining and D. W. Perrin: "Marine Fouling and Its Prevention". Marine Technology, Jan. 1973.

R. Scott: "Voyage performance of MV Protesilaus", Trans. RINA 1970. 1H IS IS0 R

RI/c

Al CON365 COH (ton/day)

fuel consumption corresponding to SHP. (day)

time in harbour for each voyage (day)

time at sea for each voyage

time at sea for each voyage with V= V0

(kr/ton) net freight rate

(kr/(ton- month))

net "time charter" freight rate (kr/year)

potential annual net freight revenue = annual earning potential

(kr)

reduction in I corresponding to AV (kr/day)

cost of off hire with respect to 365 days (kr/day)

cost of off hire with respect to annual

effective

time of the ship ((TS0+IH) A

365

-OH).

Norwegian Man time Research

No. 1/1974

SUP (hp)

shaft horse power _{" Here: day = 24 hours.}

31 Fig. A3.

Possible ship speed versus time for

constant shaft horsepower and

dead-weigh t.

References

E.V. Telfer: "On taking the rough with the smooth"

01-1 DOH DOH DOHV DOE-ID DOHDT (day)

annual number of days off hire caused by machinery damage, yard repair, drydocking etc.

(day)

equivalent number of days off hire (day/year) = (

- )

equivalent annual number of days off hire (day/year)

equivalent annual number of days off hire

with respect to speed reduction (day)

equivalent number of days off hire with

respect to docking

DOHDT + DOHDC

(day)

time used for docking including deviation and waiting time

time-part of DOHD

Type Matter: Ja-Du Offset-Service, :Vesodden. Lay-out: Brvnjulf Saastad, Nesodden. Printed by: Euro Trykk A/S. Oslo, Norway.

32

Norwegian Maritime Research

No. 1/1974 DOHDC DOHD DOHTC DC TC (day)

number of days equivalent to the cost of docking

(day/year)

equivalent annual number of days off lure

with respect to docking (day/year)

equivalent annual number of days off hire

with respect to docking and speed reduction (kr)

cost of docking including off hire costs (kr)

DC + zI

sum of docking costs and annual earning