STYRELSEN FÖR
VINTERSJÖFARTSFORSKNING
WINTER NAVIGATION RESEARCH BOARD
Research Report No 67
Kaj Riska
FACTORS INFLUENCING THE POWER REQUIREMENT IN THE FINNISH-SWEDISH
ICE CLASS RULES
Finnish Transport Safety Agency
Swedish Maritime Administration
Finnish Transport Agency
Swedish Transport Agency
Finland
Sweden
Talvimerenkulun tutkimusraportit – Winter Navigation Research Reports
ISSN 2342-4303
ISBN 978-952-311-016-8
FOREWORD
In its report no 67, the Winter Navigation Research Board presents the outcome of the project on
factors influencing the power requirement in the Finnish-Swedish Ice Class Rules.
The focus of this report is on analysis of factors influencing, and development of the power
requirement in the Finnish-Swedish Ice Class Rules. The power requirement in these rules
included a radical change from the old practice where the propulsion power requirement was
based on the ship’s deadweight or displacement. The new requirement defined first of all a design
point for ships – an IA vessel must make at least 5 knots in a at centerline 1 m thick brash ice
channel. For the guidance of designers, an equation to calculate the brash ice resistance and also
the required power were given; but – most importantly – also other means like ice model tests were
allowed for verifying the adequate power. Because the design point is given in physical situation, it
is of importance that the equations given are physically correct, if not exact. This forms the
background of this report.
The Winter Navigation Research Board warmly thanks Professor Kaj Riska for this report.
Helsinki and Norrköping
June 2014
Jorma Kämäräinen
Peter Fyrby
Finnish Transport Safety Agency
Swedish Maritime Administration
Tiina Tuurnala
Stefan Eriksson
Finnish Transport Agency
Swedish Transport Agency
FACTORS INFLUENCING THE POWER
REQUIREMENT IN THE FINNISHSWEDISH ICE CLASS RULES
Kaj Riska
Helsinki 11.6.2006
ILS Oy Consulting Naval Architects & Marine Engineers
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1
CONTENTS
CONTENTS
1
EXECUTIVE SUMMARY
2
1.
INTRODUCTION
5
2.
THE POWER REQUIREMENT IN THE FINNISH-SWEDISH ICE
CLASS RULES
8
2.1
Brash Ice and Level Ice Resistance Formulation
8
2.2
Power Requirement in the Rules
10
3.
FACTORS INFLUENCING THE RULE ICE RESISTANCE
3.1
The Channel Profile
3.2
The Coefficient of Friction
3.3
The Question of Piece Size Influence
3.4
The Resistance from Consolidated Layer
3.5
The Influence of Side Ridges
14
14
18
22
25
27
4.
FACTORS INFLUENCING THE RULE POWER REQUIREMENT
4.1
The Power Provided by Main Engine
4.2
The Bollard Pull Formulation
4.3
The TNET Concept
4.4
The Shrouded Propellers
28
28
31
33
34
5.
MEASUREMENT RESULTS AVAILABLE
5.1
Measurements with Lunni – class
5.2
Measurements with Tervi – class
5.3
Measurements with Tempera – class
5.4
Measurements with Natura – class
5.5
Measurement with MS Birka Express
5.6
Measurements with Small Tonnage
36
36
39
41
41
42
42
6.
CALIBRATION OF THE POWER REQUIREMENT
6.1
Basic Analysis of the Data
6.2
Correction for the Accumulated Ice Thickness
6.3
Improvement of the Present Requirement
44
47
50
52
7
CONCLUSION
59
REFERENCES
61
Appendix 1
The ratio of calculated and measured propulsion power and ship
resistance plotted versus four parameters; L, B, HM and v.
Appendix 2
The plots of functions (47) versus the constants C3 and C4. The
model scale and full scale values are plotted separately.
Appendix 3
The proposed rule formulation.
Appendix 4
The ships used in the validation of the new power requirement
2
EXECUTIVE SUMMARY
The focus of the present report is on analysis of factors influencing, and development
of the power requirement in the Finnish-Swedish Ice Class Rules (FSICR 2002). The
power requirement in these rules included a radical change from the old practice
where the propulsion power requirement was based on the ship’s deadweight or
displacement. The new requirement defined first of all a design point for ships – an IA
vessel must make at least 5 knots in a at centerline 1 m thick brash ice channel. For
the guidance of designers, an equation to calculate the brash ice resistance and also
the required power were given; but – most importantly – also other means like ice
model tests were allowed for verifying the adequate power. Because the design point
is given in physical situation, it is of importance that the equations given are
physically correct, if not exact. This forms the background of this report.
The report contains essentially two parts. The first part (Chapters 3 and 4) contains an
analysis of factors influencing the formulation of the power requirement and the
second part contains the data available for verifying and/or developing the power
requirement (Chapters 5 and 6). The aim of the first part is to give background and
guidance for the development of the rule brash ice resistance and required power
formulation. The aim of the second part is to identify deviations from the rule power
or resistance and if any, suggest improvement(s).
The following conclusions emerged when an analysis of the rule brash ice resistance
formulation was carried out:
• The whole channel cross sectional profile in the model and full scale tests
should be taken into account up to the width where the ship passage influences
the channel. This width is called the effective channel width BE and is
approximately BE = 1.6B. Very often only the mid-channel thickness HM is –
erroneously – used.
• The coefficient of friction between ship hull and ice (µ) influences much the
resistance. The rule formulation uses a coefficient of friction value 0.15. The
formulation to correct the low value of coefficient of friction in model tests
given in Keinonen (1991) was shown to correspond well with one model test
series where the coefficient of friction value was varied.
• The properties of brash ice (internal friction, cohesion as well as the piece
size) have been found in earlier model tests to influence much the measured
resistance. Too large piece size results in too low resistance. No
comprehensive study of what are the proper brash ice parameters and how
these should be reproduced in model tests exists.
• The consolidated layer assumed to exist in the IA Super power requirement is
difficult to produce reliably or model in model tests. A recommendation thus
is that only the brash ice resistance is measured in model tests and the
resistance from the consolidated layer is calculated.
• The ice coverage in the brash ice channels in Nature is 100 %. Thus the brash
ice, as it cannot be compressed, retains its volume and must be wholly
displaced. The side ridges of channels hinder further the motion of brash ice.
These conditions should be reproduced in model tests.
3
The following conclusions emerged when an analysis of the rule power requirement
formulation was carried out:
• The slow speed engines with a FP propeller are not able to produce the
maximum power in ice, if the propeller design is based on open water
performance. This is because the limits of the engine restrict the engine power
output. This problem does not exist with CP propellers or diesel-electric
installations. This phenomenon is taken into account by changing the
propulsive factors in the rules.
• The power requirement is based on so called ‘quality factors’ of bollard pull.
A large set of measured bollard pull values was collected to verify the factors
used in the rules. The values of the propulsion constants were found to be
adequate, even if a large scatter exists.
• The power requirement is based on the TNET – concept in which the open
water resistance is taken into account approximately. TNET is defined to be the
thrust available to overcome the ice resistance i.e. the thrust available when
the thrust deduction factor is taken into account and open water resistance
subtracted. The used formulation was compared with model test results and
found to be adequate.
• A formulation how to take into account the additional thrust produced by the
nozzles was formulated.
The available full scale and model scale results for channel resistance and required
(used) power were collected. These were used to compare the actual power used and
resistance encountered (together with the measured speed and channel thickness) with
the calculated values. An error function describing the difference of the calculated and
measured resistance and/or power was developed. After the analysis of the factors
influencing the power requirement, it was decided that only the brash ice resistance
included in the power requirement needs to be developed – the power formulation is
thus adequate. The most promising avenue for improvement is in investigating the
channel thickness formulation. Thus the exact formulation of channel thickness was
introduced. Using this exact value in the calculations, it was noticed that the
difference between the calculated and measured values diminished. There was,
however, still room for improvement.
The dependency of the ice resistance on the hull angles assumes that the ice is
displaced down along the buttock lines and not sideways at all. If the bow is
cylindrical where the frames are practically vertical, the ice is displaced only
sideways. Thus the resistance formulation was improved so that the direction in which
the ice was assumed to be displaced was the mean direction between sideways and
downwards directions. The introduction of this amendment further decreased the error
between the measured and calculated resistance.
The theoretical dependency of the channel thickness quantities and resistance was
checked based on Mellor (1980). The correction of the exponents for the accumulated
thickness HF and mid-channel thickness HM did not improve much the situation
measured with the difference between calculated and measured resistance in full or
model scale.
4
As the theoretically based exponents did not diminish the error, the exponents on the
channel thickness in the ice resistance formulation were modified based only on
minimizing the error – and using the new dependency on hull lines and channel
thickness. Also the constants in the channel resistance formulation were adjusted. The
final rule formulation was observed to reduce much the large scatter between the
measured and calculated channel resistance and power used.
Based on the improved resistance formulation, a new propulsion power requirement
was developed. This gives much the same power requirements for ships below 20 000
t in displacement as the present one. A reduction of power requirement for larger
vessels in higher ice classes is, however, observed. This rule formulation must still be
verified taking into account the requirements for the traffic systems, as here only the
measurement values have been used in development.
5
1.
INTRODUCTION
The purpose of this report is to analyze factors influencing – and if possible, verify
with measured results in full and model scale - the rule requirement for propulsion
engine output of ships in the Finnish-Swedish ice class rules (FSICR 2002). The
requirement in the rules is set by stating the design point: The ship should reach at
least 5 knots speed in a brash ice channel of a specified thickness and a specified cross
sectional profile. The profile of the channel is specified in the rules as the thickness on
the centerline of the channel HM and the slope angle (2º) of the channel thickness
increasing towards the sides. Fig. 1 presents a typical brash ice channel from the
northern Baltic.
Measured cross section
Distance [m]
0
10
20
30
35
40
45
50
55
60
65
70
80
0.00
Depth [m]
-1.00
-2.00
Brash Ice
-3.00
Rect. Ice Bloks
-4.00
Rounded Ice Blocks
-5.00
Fast ice
Fig. 1. A photograph of a brash ice channel leading to the Finnish port Kemi and the
measured cross section of the channel (Riska et al. 2001).
The centreline thickness of the channel, HM, is an ice class factor. It is 1.0 m for ice
class IA, 0.8 m for IB and 0.6 m for IC. It is assumed that a consolidated ice layer of
thickness 0.1 m exists on top of the channel for ice class IA Super in addition to brash
ice with HM = 1 m.
6
The background of this design point is that ships bound to Finnish or Swedish ports
are not breaking ice – they are mostly escorted by icebreakers, especially when the ice
conditions get more severe. Thus only for the ice class IA Super there is a slight
requirement to break ice. The conclusion of operational modes of merchant vessels
and also the encountered ice conditions are based on a large survey made in the
beginning of 90’s (Veitch et al. 1991, Pöntynen 1992, Kujala & Sundell 1992,
Lehtinen 1993, 1994 and Miinala & Patey 2000).
As the fulfilment of the design point is not easy to show by other means than
calculations, the rules contain equations to calculate the rule brash ice resistance and
finally the required propulsion power. It is important here that the resistance and
propulsion are treated separately. The brash ice resistance equation is based on
analysing the deformation and displacement of the brash ice using methods developed
in soil mechanics (Keinonen 1979, Riska et al 1997). The resulting resistance
equation is semi-empirical and as such susceptible to giving erroneous results
especially outside the range of ship or ice parameters used in validation. The power
requirement formulation is based on the propulsion power required to produce enough
thrust to overcome the brash ice resistance. The relationship between propulsion
power and produced thrust is generalized from an average vessel with a single CP
propeller to twin and triple screw vessels with a direct drive FPP or other, more
advanced, propulsion systems..
In the development of equations to calculate the required propulsion power, several
assumptions have been used in the formulations. One assumption was already
mentioned above, the channel profile. Another assumption is that the coefficient of
friction, µ, between ship hull and ice is assumed in the rules to be 0.15. This
corresponds to an older vessel as for new vessels with intact hull coating the value
used is about 0.1. Further, the resistance equation in itself does not contain any margin
as is usual in power estimates (high friction naturally gives some margin). Finally it
has been assumed that ‘brash ice’ is an unambiguous concept – even if the
formulations have been mostly validated with tests in the channels leading to ports in
northern Finland. The present report presents an analysis about these assumptions.
The rules allow other methods to be used in assessing the performance and propulsion
power needed than calculation according to the equations given (FSICR 2002, §3.2.4).
Especially more detailed calculations or model tests are mentioned. The more detailed
calculations refer mainly to the propulsion i.e. assessment of the thrust given by the
propulsion unit. The rule resistance can be used in these calculations of performance.
Accepting more thorough calculations makes it possible to classify propulsion units
that do not fit into the rule assumptions – like tandem azimuthing propulsors (Are
these two propeller applications or one propeller applications?). The rule brash ice
resistance may be substituted by resistance obtained from model tests, provided that
some requirements for model tests are fulfilled (see Guidelines 2005).
Many of the model tests carried out to measure the ice resistance in brash ice channels
at five knots – in order to obtain the required propulsion power – have given lower
resistance values than the rule requirement. Usually the quantity that is lower in tests
is the ice resistance; the equations to calculate the required propulsion power from the
resistance give similar values as the measurements. To analyse the reasons for this
discrepancy is the main purpose of this report.
7
The reasons for the lower resistance values are not clear and as long as very limited
amount of reliable full scale results exist, the matter remains open. Some measured
full scale values are quite close to the rule propulsion power – it is important in the
full scale tests that the thickness of the brash ice channel has been measured and the
thickness measurements have been interpreted correctly. This is important as the rules
assume a channel profile where the channel is getting thicker from the mid-channel
towards the sides by a slope angle of 2o.
8
2.
THE POWER REQUIREMENT IN THE FINNISHSWEDISH ICE CLASS RULES
2.1
Brash Ice and Level Ice Resistance Formulation
Based on model and full-scale tests, the level ice resistance is often considered to be
linear with speed. Thus the level ice resistance Ri contains two constants C1 and C2
which are dependent on ship and ice parameters;
R i = C1 + C 2 ⋅ v
(1)
The constants’ C1 and C2 dependency on ship particulars is derived in the rule ice
resistance formulation by modifying the formulations of Ionov (1988) and Lindqvist
(1989), see Riska et al. 1997. The equations for C1 and C2 are
(
)
1
BL par h i + (1 + 0,021ϕ) f 2 Bh i2 + f 3 L bow h i2 + f 4 BL bow h i
T
2 +1
B
(2)
2
T B

C 2 = (1 + 0,063ϕ) g1h1i,5 + g 2 Bh i + g 3 h i 1 + 1,2 
B L

C1 = f1
(
)
where hi is level ice thickness, B is ship breadth, T is ship draught, L is ship length
(between perpendiculars), Lpar is the length of the parallel midbody at waterline, Lbow
is the length of the foreship at waterline and φ (φ1 in the rules) is the stem angle at
CL. The coefficient of friction is assumed to be 0.1 and the bending strength of ice
500 kPa in the above equations.
The values for constants are based on model and full-scale data and these are
f1 = 0.23 kN/m3
f2 = 4.58 kN/m3
f3 = 1.47 kN/m3
f4 = 0.29 kN/m3
g1 = 18.9 kN/(m/s·m1,5)
g2 = 0.67 kN/(m/s·m2)
g3 = 1.55 kN/(m/s·m2,5)
The resistance formulation was validated using the performance of an array of ships
(see Riska et al. 1997). All these vessels are ice-strengthened cargo vessels and
therefore the resistance equation should be suited for vessels of this type. Overall the
comparison between calculated values and the observed performance is fair.
The brash ice resistance arises from displacing the brash ice present in the channel
both down and sideways. The sideways motion is limited because of the side ridges
which always are present in old navigation channels. The brash ice resistance is
normally studied using methods developed in soil mechanics. A speed dependant
formula for brash ice resistance Rch was derived based on results presented by
Englund (1996) and Wilhelmson (1996),
9
2
1 H  

1
1 
 (µ h cos ϕ + sin ψ sin α )
R ch = µ Bρ ∆ gH 2F K P  + M  B + 2H F  cos δ −
2
tan ψ 

 2 2H F  
+ µ Bρ ∆ gK 0 µ h L par H 2F
3
 LT 
+ ρ ∆ g   H M A WF Fn 2
 B2 
(3)
where µB = 1-p and p is porosity (µB = 0,8…0,9), ρ∆ the difference between the
densities of water and ice, g the gravity constant, KP the constant of passive stress – a
term used in soil mechanics, HM the thickness of the brash ice in the mid channel, δ
the slope angle of the displaced ice against the ship side (22,6o), µH the coefficient of
friction between the ice and the hull, φ the angle between the horizontal direction and
the vertical at B/4, K0 the coefficient of lateral stress at rest, Lpar the length of the
parallel midbody at the waterline, AWF the waterline area of the foreship and Fn the
Froude number. The soil mechanical values for the constants KP and K0 depend on the
properties of brash ice – typical values are KP = 6.5 and K0 = 0.27. HF describes the
thickness of the brash ice layer which is displaced by the bow and which moves to the
side against the parallel midbody. This is a function of ship breadth, channel thickness
and two slope angles, which are dependent of the inner properties of brash ice (γ=2o
and δ=22.6o are used).
HF = HM +
B
tan γ + (tan γ + tan δ )
2
B


BH M + tan γ 
4


tan γ + tan δ
(4)
This formula has been simplified by an approximation which is valid when B>10m
and HM>0.4m
H F = 0,26 + (BH M )0,5
(5)
The flare angle ψ may be calculated from the equations using the following
trigonometric identities
sin ψ =
tan ϕ
sin 2 α + tan 2 ϕ
 tan ϕ 
ψ = arctan 
 sin α 
.
The above equations are used subsequently in this report when investigating the ice
resistance.
10
2.2
Power Requirement in the Rules
The power requirement in the Finnish-Swedish ice class rules (FSICR 2002) is based
on an explicit performance requirement for different ice classes. The requirement is
stated as the ice condition where vessels of different ice class must be capable to
maintaining a certain minimum speed. These conditions are set based on the most
common operation modes and ice conditions encountered in the Northern Baltic. The
limit operability is stated as a minimum speed in commonly encountered navigation
channels.
The powering requirement in the Ice Class Rules is defined in the following manner.
The environmental requirements (channel thickness) and the speed requirement
(minimum 5 kn) define the rule channel resistance, which depends on ship geometry
and ship size. The resistance is calculated with equation presented in rules or it may
be determined directly by model tests etc. The required propulsion power is calculated
from the channel resistance as the power that gives the thrust which overcomes the
specified resistance. The required power is derived from a bollard pull equation. It
should be noted that the basic rule requirement is at least 5 knots speed in channels of
given thickness. This capability may be demonstrated by other means than
calculations using the given equations. Fig. 2 illustrates the rationale in the power
requirement.
Performance Requirement
Class
Speed
IAS
IA
IB
IC
5 kn
5 kn
5 kn
5 kn
Channel
thickness
Hm
1m
1m
0,8 m
0,6 m
Consolidated
layer
hi
0,1 m
0
0
0
Channel Resistance Rch
Rch = Rch (Hm , hi, ship geometry, ship size)
Propulsion Power Ps
Ps = Ps (Rch , Dp)
Fig. 2. The structure of the powering requirement
When values for brash ice material properties are inserted into the resistance
formulation used (see e.g. Riska 1997), the rule channel resistance for different ice
11
classes can be presented in the following form. The resistance equations contain the
bow angles φ and α. Usually these are measured at the stem from where most of the
icebreaking forces come. This is not correct for brash ice where the whole bow is
displacing ice. Thus an average value for angles α and φ would be suitable. To
calculate an average along the whole bow waterline is, however, not practical and thus
as a representative value for these angles the angels at waterline at a distance of B/4
from centerline are used (this is valid for α and φ2, φ1 is to be measured at centerline).
The rule resistance equation is thus the following:
[
3
]
 LT  A WF

R ch = C1 + C 2 + C 3 ⋅ (H F + H M )2 ⋅ B + C ψ H F ⋅ C µ + C 4 L par H 2F + C 5 ⋅ 
L
 B2 
(6)
where
H F = 0,26 + (H M B)1 / 2 ,
C µ = 0,15 cos ϕ 2 + sin ψ sin α ,
Cψ = 0,047ψ − 2,115 ,
(7)
(8)
min 0.45
min 0.0
(9)
 tan ϕ 2 
ψ = arctan

 sin α 
BL par
C1 = f1 ⋅
+ (1 + 0,021φ1 ) ⋅ (f 2 B + f 3 L bow + f 4 BL bow )
2T
+1
B
T  B2

C 2 = (1 + 0,063φ1 ) ⋅ (g1 + g 2 B) + g 3 1 + 1,2  ⋅
B L

(10)
(11)
(12)
The first two terms in Eq. (6) represent the level ice resistance and the three last ones
the brash ice resistance. The constants C1 and C2 apply only for ice class IA Super.
For lower classes they are to be taken as zero. For ships of ice class IA Super with a
bulb, the stem angle φ1 is to be taken as 90o. The stem angle must be between 0º and
90º. The values for constants used are:
C3 = 845.576 kg/(m2s2)
C4 = 41.74 kg/(m2s2)
C5 is given in Table 1.
f1 = 23 N/m2
f2 = 45.8 N/m
f3 = 14.7 N/m
f4 = 29 N/m2
3
g1 = 1537.3 N
g2 = 172.3 N/m
g3 = 398.7 N/m1,5
 LT 
 is to be taken as 20 if
The term 
 B2 
3
 LT 

 >20 or 5 if
 B2 
3
 LT 

 <5.
 B2 
12
For ships where the determination of certain parameters – especially angles - is
difficult due to e.g. lack of lines drawings, a simplified equation may be used for
calculating the rule channel resistance Rch. This equation is based on average or
slightly conservative values of the bow angles and lengths.
Table 1. The rule values for HM, hI and C5.
Ice class:
HM [m]
hi [m]
C5 [kg/s]
1AS
1,0
0,1
825,6
1A
1,0
0
825,6
1B
0,8
0
660,5
1C
0,6
0
495,4
The rule resistance is derived for a channel profile which contains the influence of the
side ridges. Thus the channel profile is assumed to get thicker moving from the
channel center line towards the edges by an angle δ = 2º. The brash ice is assumed to
be displaced sideways so that it comes to rest under the original brash ice. The angle
of repose of the brash ice material is assumed to be 22.6º. This way at the parallel
midbody of a vessel the brash ice thickness is given by a value HF. The assumed
geometry is given in Fig. 3.
Fig. 3. The rule brash ice channel before the ship passage and during the passage.
The required propulsion power is to be the power that gives high enough thrust to
exceed the ice resistance in the design ice conditions and at the design speed. The ship
speeds are low in the design ice conditions and therefore the requirement in the
Finnish-Swedish Ice Class Rules is derived from the bollard pull situation. The
resulting formulation for the required propulsion power PD is
PD = K e
(R ch )
Dp
3
2
(13)
13
where Ke is given in the Table 3, Dp is propeller diameter and Rch is the rule channel
resistance.
Table 3. Values of the constant Ke.
Propeller type or
machinery
1 propeller
2 propeller
3 propeller
CP or electric or hydraulic
propulsion machinery
2,03
1,44
1,18
FP propeller
2,26
1,6
1,31
The powering requirement formulation is the same for all ice classes. The difference
between the classes is included in the channel resistance formula.
14
3.
FACTORS INFLUENCING THE RULE ICE RESISTANCE
The analysis of factors influencing the propulsion power requirement is divided into
parts; some factors influence the resistance and some the determination of the
propulsion power, assuming that the resistance is known. The factors influencing the
brash ice resistance include the following:
1. The channel profile should reflect the thickening of the channel towards the edges
– thus the rule channel is not of uniform thickness.
2. The coefficient of friction influences the resistance much. This coefficient in full
scale is usually close to 0.1 for new ships but some model tests are made with a
coefficient of friction of 0.05 – because this value for friction is used in level ice
model tests.
3. The piece size in the brash ice is about 30 cm in diameter in full scale. Scaling
this down means a model scale piece size for larger ships – scale about 1:30 …
1:40 - 1 cm. This is not reached in any model tests, as the pieces are in relative
terms much larger in model scale.
4. The resistance for IA Super ice class includes a consolidated layer of thickness 10
cm on top of the brash ice.
5. The brash ice material is not compressed i.e the volume is constant but only
displaced by the ship bow in full scale. Thus the area of brash ice in a channel
cross section is not decreased when the ship passes. The ice coverage in brash ice
channels is 100 %, no open water is visible. Any open water patch in the channel
is likely to decrease the resistance.
6. In channels like the one presented in Fig. 1, the side ridges and the gradual
thickening towards the sides which in rule channels is defined as the slope hinder the brash ice motion sideways.
Some knowledge about factors 1 - 4 mentioned above exists. The background of these
factors is discussed below and, if possible, demonstrated by measurement results. The
influence of ice coverage and the compressibility of the brash ice on ice resistance are
difficult to assess as no data exist.
3.1
The Channel Profile
The rule channel profile was assumed to get thicker sideways with the slope angle of
δ = 2º which represent full scale channel profiles measured. When a ship passes
through this cross section, the brash ice must be pushed aside (and the cross sectional
area is not diminishing, as explained later). The displaced ice mass must be deposited
under the existing slope. The displaced brash ice will settle on a slope at the angle γ,
which is described by the angle of repose of the brash ice material (assumption is γ =
22.6º), see Fig. 3. The steepest angle of repose is usually equated to the angle of
internal friction φS. The angle γ determines the amount of ice that rests against the
parallel midbody – which is described by the thickness HF (see eqs. (4) and (5)). The
15
width up to which the channel is altered when ice is displaced, determines the
effective width of the channel, HE. This is the width of the cross section up to which
the ship passage influences the cross section. All cross sectional properties i.e.
channel thickness must be determined up to this width.
The effective width can be determined for the rule channel by setting the areas A1 and
A3 in Fig. 3 equal. The result is


B E = B ⋅ 1 +




4H M
+ tan δ 
B
.
tan δ + tan γ 


(14)
The relationship (14) is plotted in Fig. 4a. For smaller ships the effective width is in
relative terms larger. For ships between the beam 15 to 50 m, the ratio lies between
1.5 to 1.8 as shown in Fig 4b where the relative effective width is plotted assuming
HM = 1.0 m. An average value of 1.6B for the effective width will be used in this
report when analysing of the full scale and model scale measurements.
Normalized Effective Width BE/B
B=
2,4
10 m
2,2
15 m
2,0
20 m
25 m
30 m
...
50 m
1,8
1,6
1,4
1,2
1,0
0,0
0,5
1,0
1,5
2,0
Channel Centerline Thickness HM [m]
Fig. 4a. The effective channel width versus the channel thickness with the ship beam
as a parameter.
16
2,0
BE/B
1,8
1,6
1,4
1,2
1,0
0
10
20
30
40
50
Ship Beam [m]
Fig. 4b. The effective width of the channel, when the mid channel thickness HM is 1.0
m.
If the channel profile is not similar to the rule profile, as is the case in measurements,
then an equivalent channel profile value (mid channel thickness HM) must be
determined from the measured cross section, see Ritvanen (2004). This equivalent
thickness used as a rule value HM can be determined by fitting the rule profile shape
on the shape of the actual channel profile. This is done by first determining the
channel profile cross sectional area versus the (half)width as
A CH = f (B E ) .
(15)
The measured actual area must be
A CH = A1 + A 2 + A 3
(
)
tan δ + tan γ
 H (B − B)  tan δ 2
(B E − B)2
= M E
+
BE − B2 +

2
8
8


1
= (B E − B)[4H M + (B E + B) tan δ + (B E − B)(tan δ + tan γ )]
8
These areas are depicted in Fig. 5.
(16)
17
Fig. 5. The conversion of the actual channel profile into the rule channel.
As the measured profile must correspond to the rule channel profile i.e. have the same
cross sectional area, we get the last equation as
A CH =
H M B E B 2E tan δ
.
+
2
8
(17)
There are three equations (15), (16) and (17) and three unknown quantities ACH, HM
and BE. If the two last equations are used to eliminate HM, then finally an equation to
determine BE is obtained:
A CH (B E ) =
BE
(B E − B)[B E tan δ + (B E − B) tan γ ]
8B
(18)
This formulation is cumbersome and, in view of many other uncertainties in
measurements, should be simplified. If the estimate BE = 1.6B is used, this gives
(Leiviskä 2004) a simplified version of Eq. (17) as
H M (B E = 1.6B) =
A CH − 0.32B 2 tan δ
.
0.8B
(19)
The usual way to estimate the channel thickness has been to use only the channel
profile up to the beam of the ship, and the HM is determined from the simplified
profile as
18
A
B tan δ
HM = 2 1 −
.
B
4
(20)
This method does not, however take into account the slope against which the brash ice
is displaced. In summary there are three ways to determine the mid channel thickness:
HM is determined as a function of the effective thicknesses HM(BE), HM(1.6B) or
HM(B). The simplification that BE = 1.6B is used in this report.
3.2
The Coefficient of Friction
The ice force acting on the ship hull is a pressure load which has a frictional
component in tangential plane opposing the motion at the ship/ice contact point. The
frictional force is described.by a coefficient of friction µ which relates the normal and
tangential forces acting at the contact point as
Fµ = µ(p, v) ⋅ Fn ,
(21)
where p is the average pressure acting on the contact surface and v the sliding speed.
Even if this is not generally the case, often the Amonton’s and Stokes’ laws are
assumed to be valid i.e. that the coefficient of friction is not a function of the contact
pressure nor of the sliding speed.
The importance of friction between ship hull and ice becomes clear if the force
components acting at a contact between ship hull and ice are investigated. The contact
situation is depicted in Fig. 6 where the ship side is assumed to be inclined. In the
figure also the equivalent force system is shown – this system is important in
investigating the bending failure of the ice cover.
Fn
Fz
Fµ
M0
Fx
Fig. 6. The force components at the ship/ice contact point and the equivalent force
system acting on the ice plate.
The equivalent force system acting on the ice plate can be derived from the force
components at the contact point. It is the following (βn is the normal frame angle,
complement of the flare angle ψ):
19
Fx = Fn cos β n + Fµ sin β n
Fz = Fn sin β n − Fµ conβ n
 u cr
h
u
M 0 = Fn 
+ cos β n  i − cr
 2 sin β n
 sin 2β n
(22)

 h sin β n

  + Fµ  i
− u cr 

2



These equations are not investigated further here; the important fact for friction is that
higher friction decreases the bending force Fz so that if the friction is higher, larger
contact force is required to break the ice in bending. Higher friction, on the other
hand, increases the horizontal force component which contributes to resistance.
The coefficient of friction between different materials and ice vary much as Fig. 7
shows. The value of about 0.1 for the dynamic coefficient of friction seems to be an
appropriate value to use. A detailed measurement of the coefficient of friction
between ship hull and ice indicates, however, that the value 0.1 is appropriate when
ice is crushed at the contact and higher values should be used when investigating the
sliding friction (Liukkonen 1989, Mäkinen et al. 1994). Liukkonen (1989) also reports
coefficient of friction values of 0.05 at the waterline and 0.16 below waterline in
measurements carried out in brash ice channels.
Fig. 7. The coefficient of friction between ice and different materials (CRREL 2002).
20
The coefficient of friction to be used in model tests was evaluated by Liukkonen
(cited in Liukkonen 1989). Model tests were carried out using different coefficients of
friction and the resulting full scale predictions were compared with full scale
measurements, see Fig. 8. It was noted that if the model scale coefficient of friction is
low, comparison between full scale and model scale extrapolated results is good. This
observation has led to the use of low friction in level ice model tests. It should be
emphasized that this conclusion is made based on resistance tests in level ice.
Fig. 8. The full scale prediction of the ice resistance of IB Otso from model tests with
different coefficient of friction values and the corresponding full scale results
(Liukkonen 1989).
A coefficient of friction correction factor for ship total resistance in ice (RiT) has been
proposed by Keinonen (1991). If data about total resistance in ice exists with certain
coefficient of friction (R1,iT and µ1), then the resistance with another coefficient of
friction may be obtained from
R 2, iT =
0 .6 + 4 ⋅ µ 2
⋅ R 1, iT
0.6 + 4 ⋅ µ1
(23)
21
This correction leads to a change of about 20 % in resistance for coefficients of
friction 0.05 and 0.1 and to about 40 % corrections when the coefficients are 0.1 and
0.2. Here it should be noted that the rule ice resistance equation assumes a coefficient
of friction value 0.15.
In order to gain insight how the friction influences the brash ice resistance, the
normalized brash ice resistance is calculated for two vessels, MT Tervi and MT
Mastera, in the rule channel (HM = 1.0 m) with the rule speed (v = 5 knots). The result
is shown in Fig. 9. The resistance formulation is linear with the coefficient of friction
but the slope varies from ship to ship. The slope is relatively shallow for MT Mastera
as she has relatively short parallel midbody. Anyway, if a coefficient of friction 0.05
is used in the tests, about 20 % lower resistances are predicted as compared with the
calculated rule resistance.
1,8
RCH(µ)/RCH(µ = 0.15)
1,6
1,4
1,2
1,0
0,8
0,6
0,4
MT TERVI
MT MASTERA
0,2
0,0
0,0
0,1
0,2
0,3
0,4
Coefficient of Friction µ
Fig. 9. The normalized channel resistance of two vessels calculated with different
coefficients of friction.
Finally, the friction tests carried out with MT Tervi are investigated using the rule
channel resistance formulation. A plot of the calculated channel resistance with the
same input values as in the model tests using the coefficient of friction as a parameter
divided with the resistance when µ = 0.10 is shown in Fig. 10. In this figure the test
result where µ = 0.45 is also shown. The influence of friction is larger in the tests than
in the calculated channel resistance. Here it should be noted that the equation (25)
gives the resistance ratio of 2.24 when the tests give the ratio 2.26.
RCH(µ)/RCH(µ = 0.10)
22
2,0
1,5
1,0
HM = 0.92 m
v = 2.6 m/s
0,5
0,0
0,0
0,1
0,2
0,3
0,4
Coefficient of Friction µ
Fig. 10. The relative channel resistance and the one test point existing from model
tests with MT Tervi model. Input data shown in the figure.
3.3
The Question of Piece Size Influence
The ice piece size in the frequently transited navigation channels is quite small after
many freezing-breaking cycles. The resulting ice pieces are rounded and a typical
diameter is about 30 cm (Kujala & Sundell 1992). Fig. 11. presents a typical view of
these brash ice channels. The ice pieces in the channels are quite hard as they have
been milled around often by ship passages. Thus they form a tight packing with little
porosity at the middle of the channel, see Kujala & Sundell (1992). Usually the
porosity of the brash ice is taken to be about 10 %.
23
Fig. 11. An view from a typical frequently transited brash ice channel in the Baltic
with a close-up of the ice pieces (Photo: T. Leiviskä).
The mechanism how the piece size influences the brash ice resistance is uncertain at
the moment. There exists a clear indication that this influence may be large, see Fig.
12. The figure indicates that larger ice pieces induce a larger resistance. There is,
however, a limit to this as the mush ice – very small ice pieces, more like wet snow –
creates largest resistance, so the trend towards smaller and smaller resistance with
decreasing piece size is reversed at some point. The piece size given in Fig. 12 is in
model scale units. The ship used in the tests is 3.0 m long; if the full scale ship would
be 100 m long (a typical icebreaker), then the scale would be roughly 1:33. The
largest piece size would be then 3 m in diameter and the smallest 86 cm in diameter.
The mush ice pieces are stated to be about 12 mm in size, this gives in full scale 40
cm – thus the mush ice would resemble most closely the full scale conditions, at least
in what comes to piece size.
The brash ice resistance formulation given in Eq. (3) includes two parameters used in
soil mechanics, KP and K0. The first one of these depends on the internal friction
angel φs as
KP =
1 + sin ϕ s
1 − sin ϕ s
(24)
and the second constant depends on the Poisson’s ratio ν as
K0 =
ν
,
1− ν
(25)
24
see e.g. Mellor (1980). The values of these parameters in the rule resistance
formulation are assumed to be φs = 47.2º and ν = 0.21. The values reported for the
internal friction angle vary from about 43º to 58º. The Poisson’s ratio has been
measured in model scale and the result is the one used in the rule formulation. The
discussion of brash ice given above would lead to conclusion that the brash ice
material is practically incompressible – this would lead to Poisson’s ratio of 0.5 and
K0 = 1. Using the values from the higher end of the possible range would lead to more
than 100 % increase in calculated resistance – the resistance formula contains,
however, constants the value of which is determined by experiments. Thus a change
in the material constants should be reflected in a change in constants. The matter of
material constants is important in view of scaling and comparison between model
tests and full scale tests.
Fig. 12. The influence of piece size in brash ice on the total resistance in ice (Ettema
et al. 1986).
25
Coming back to the question of ice piece size and its influence on resistance, there has
been studies where the internal friction angle and piece size have shown some
influence on shear strength of brash ice. These results are given in Fig. 13. The results
in the left figure indicate that the friction angle would increase with increasing piece
size, a trend which is not found in the other results. At the moment there is not enough
data about the influence of ice piece size on the brash ice resistance to make any
definite conclusions.
The letters refer to piece size as follows;
IS
d = 18 mm
IM
d = 27 mm
IL
d = 70 mm
Fig. 13. Test results on the shear strength dependency on the normal stress applied.
The internal friction angle is given by the slope of the curves (Ettema & Urroz 1989,
Urroz & Ettema 1987).
3.4
The Resistance from Consolidated Layer
The rule resistance for IA Super vessels is calculated using the brash ice channel for
IA vessels (HM = 1 m) and additionally a layer of consolidated ice on top of the brash
ice. The thickness of the consolidated layer, hi, is assumed to be 10 cm. The
background for the layer thickness is that it forms from the brash ice in roughly half a
day when the air temperature is -10ºC. The consistency of this consolidated layer
material is somewhat uncertain but in view of the average piece size of brash ice, it
can be inferred that its thickness is not uniform.
The rule ice resistance formulation assumes that the resistance from the consolidated
layer can be given as the level ice resistance in ice thickness hi, Ri(hi). Further it is
assumed that to get the total ice resistance, the resistance from brash ice of thickness
at the channel centerline HM, RCH(HM), can be superimposed with the level ice
resistance. This gives the total ice resistance as
R iTOT (H M , h i ) = R CH (H M ) + R i (h i ) .
(26)
26
RiTOT(HM, hi)/RiTOT(HM,0)
This total ice resistance should not be mixed with the total resistance in ice, RTOT,i
which is the sum of ice and open water resistances. In order to investigate the
influence of the consolidated layer on the total ice resistance, the model test results
given in Table 8, Chapter 5, are compared with calculated resistance using the same
input parameters. Results are given in Fig. 14.
2,0
1,5
1,0
µ = 0.10
HM = 0.92 m
v = 2.6 m/s
0,5
0,0
0,0
0,1
0,2
0,3
0,4
0,5
Ice Thickness hi [m]
Fig. 14. The calculated relative ice resistance of MT Tervi shown using the thickness
of the consolidated layer as parameter. The cross shows the result of model tests with
the same input values.
Fig. 14 shows that the measured resistance from the consolidated layer is much higher
than the calculated one – even if the uncertainty of the layer thickness is taken into
account (estimates were between 7 and 11 cm).
Kitazawa & Ettema (1984) state that an increase of 29 % in resistance resulted from a
4 cm thick refrozen layer and 8 % increase in 12 cm refrozen layer in test where the
brash ice was 2.0 m and 6.1 m thick, respectively. These results are in full scale units
and the scale was 1:40. Both tests were made with 3.8 m/s speed and in a wide
channel – and the refrozen layer thickness was 2 % of the brash ice thickness in both
cases. In relative terms this is a smaller increase than in the tests with MT Tervi.
The reason of this discrepancy between calculated and measured ice resistance is
difficult to assess – especially because the increase in relatively thin consolidated ice
is large. One basic reason can be that the superposition of brash ice and level ice
resistance is not correct; the level ice lid could prohibit a proper movement of the
brash ice pieces causing an increase of resistance. Also the consolidated ice layer was
produced in this case by natural freezing of water. The resulting ice could be much
closer to natural ice instead of properly downscaled model ice. This matter is
27
discussed more when a general comparison of measured and calculated values is
made.
3.5
The Influence of Side Ridges
The brash ice material consists of rounded spherical pieces of solid ice with the
average size about 30 cm. There is a spread of sizes (see eg. Pöntynen 1992) and thus
the packing of ice pieces is likely to be tight. This results in a small porosity and the
fact that brash ice material cannot be compressed much without crushing the ice
pieces. This leads to the requirement that the areas A1 and A3 in Fig. 5 must be the
same. In model scale tests, however, the brash ice material is made of model ice – and
most model ice types suffer from the drawback that the compressive strength is too
low compared to the bending strength. Thus brash ice made from model ice can more
readily be compressed and this leads to, in proportion, a smaller area A3. However, no
research results exist about the compression of brash ice.
Another factor that should be mentioned in the context of compressing the brash ice
and its motion is the boundary between the channel and surrounding ice area. As the
brash ice channels form due to frequent ship traffic, ice is being pushed sideways and
thus the so called side ridges form. These are very prominent in the channel shown in
Fig. 1. The slope angle in the rule channel profile simulates the effects of the side
ridges and the measured gradual slope towards sides, at least in part. Brash ice motion
is further restricted by the surrounding immobile level ice sheet. Thus the brash ice
cannot be displaced sideways but must be piled up against and mainly below the
existing ice.
The effect of boundary conditions was studied by Kitazawa & Ettema (1984). They
used as the boundary a rigid wall and varied in the model tests the relative channel
width W/B. The result was that when the width between the walls was small
(W/B=1.2), the resistance increased by about 40 %. When the channel was wider than
the effective width (W>1.6B), then the resistance seemed to reach a uniform value
(two tests were carried out here; W=2B and W=3B). These results seem to endorse
the concept of an effective width, at least so that the effective width is bracketed
between BE = 1.2 B and 2B.
28
4.
FACTORS INFLUENCING THE RULE POWER
REQUIREMENT
The factors influencing the determination of the required propulsion power, once the
required thrust is set based on brash ice resistance, include:
1. Especially slow speed engines with FPP are not able to use all the engine power
for propulsion at slow speeds,
2. The bollard pull equation used in the rules (see Riska et al. 1997) may give too
conservative power requirement,
3. The treatment of the open water resistance is based on the TNET concept,
4. The thrust given by more advanced propulsion devices like shrouded propellers
may give higher thrust than assumed in the rule formulation.
The target of this report is to analyze some of the above factors in view of the full or
model scale data available. Before the data is presented and compared, most of the
above factors are analyzed in some detail.
4.1
The Power Provided by Main Engine
The working area of diesel engines given in the P – RPM – Q coordinates contains
many limits from different sources. One natural limit is the maximum engine power
related to torque and shaft revolutions by PD = 2πn Q, where n is RPM. Other limits
are depicted in Fig. 15a on P – RPM plane and in Fig. 15b on Q – RPM plane. The
diesel engine and the propeller curve are usually fitted together so that the propeller
operates most economically at the loading condition which is most common. For
majority of vessels this is open water speed at Maximum Continuous Rating (MCR).
This means that the propeller torque/power demand curve (see Fig. 15a) is tuned so
that it reaches the corner of MCR power at 100 % RPM. If a ship designed this way
encounters increased resistance e.g. due to ice, the propeller demand curve shifts left
and might cross one of the engine limits earlier than at MCR or 100 % power. One
situation of this kind is shown in Fig. 16 where the bollard pull propeller demand
curve crosses the engine torque limit at about 80 %.
The propulsion systems consisting of a Controllable Pitch Propeller (CPP) do not
suffer from this problem of not being able to mobilize the full power as both the RPM
and pitch are adjusted to match the demand. This is also true for Diesel-Electric
installations. Thus the propulsion factor Ke in the ice rules is increased by 10 % and
thus power for the FPP installations is increased compared with CPP or DE
installations. Whether this increase in the power requirement is adequate, depends on
the exact engine, propeller and ice resistance parameters but the Fig. 17 showing the
limits for a real engine (Wärtsilä 46) indicate that the drop of the power could be even
higher than that used in the rule formulation.
29
Fig. 15a. The engine limits on a P – RPM plot for a diesel engine (figure courtesy of
American Bureau of Shipping).
Torque %
100
80
60
Torque limit
Compressor
surge
Power limit
Optimum point
Smoke limit
Speed limit
40
20
Lowest torque using HFO:lla
10 20 30 40 50 60 70 80 90 100
RPM %
Fig. 15b. The engine limits on a Q – RPM plot for a diesel engine (figure courtesy of
Prof. Häkkinen).
30
Fig. 16. The engine limits and the propeller demand curve in open water and at
bollard pull.
Fig. 17. The engine limits of a Wärtsilä 46 engine (Wärtsilä 46 Project Guide).
31
4.2
The Bollard Pull Formulation
The power requirement in the ice rules is formulated so that the resistance which must
be overcome is given and then the power to give the necessary thrust is calculated.
This calculation could, in principle, be done if the propeller characteristics (KT - and
KQ – curves and the engine power) would be known. The propeller thrust can be
given as (see Juva & Riska 2002)
T=
K T (J )
2/3
KQ
(J )
⋅3
ρ
4π
2
(
)
⋅ PD D p 2 / 3 ,
(27)
where the advance number is J = (1-w)v/n·DP, w is the wake fraction and ρ water
density. DP is the propeller diameter. At the bollard pull situation the advance ratio is
J = 0. The bollard pull is thus – when the thrust deduction is taken into account by the
thrust deduction factor t
TB =
K T (J = 0)
2/3
KQ
(J
= 0)
⋅3
ρ
4π
2
(
)
⋅ (1 − t ) ⋅ PD D p 2 / 3 = K e ⋅ (PD D P )2 / 3 .
(28)
Here the factor Ke is called the quality factor for bollard pull. It should be noted that
this quantity is dimensional and the dimensions usually used for thrust, power and
propeller diameter in (30) are kN, kW and m, respectively. The commonly used value
for the Ke is 0.78 for single screw vessels, 0.98 for twin screw vessels and 1.12 for
triple screw vessels. These values are for CPP or diesel electric propulsion systems
and should be reduced by 10 % for FPP installations.
The above values for the quality factor were investigated using a literature survey
about data existing from bollard pull tests. The survey covered single, twin and triple
screw vessels, with a FPP or a CPP both in nozzles and open. In order to be able to
compare and analyze this large data set, the data is reduced to the CPP case by
increasing the FPP values by 10 % and decreasing the nozzle values by a factor of 1.3
– this represents the average increase of thrust at bollard by nozzles. The results of the
survey are given in Fig. 18. The survey results indicate that the quality factor is
dependent on propeller diameter, increasing towards smaller propellers. Overall the
selected Ke values in the ice rules seem to be reasonable, for single screw propeller
ships even a bit optimistic.
32
Single screw
1,4
1,2
1,0
Ke
0,8
0,6
0,4
Open, FPP
Nozzle, FPP
Open, CPP
Nozzle, CPP
Rule value
0,2
0,0
0
2
4
6
8
Propeller Diameter [m]
Twin screw
1,6
1,4
1,2
Ke
1,0
0,8
0,6
0,4
Open, FPP
Nozzle, FPP
Open, CPP
Nozzle, CPP
Rule value
0,2
0,0
0
2
4
6
8
Propeller Diameter [m]
Triple screw
1,6
1,4
1,2
Ke
1,0
0,8
0,6
0,4
Open, FPP
Nozzle, FPP
Open, CPP
Nozzle, CPP
Rule value
0,2
0,0
0
2
4
6
8
Propeller Diameter [m]
Fig. 18. The measured quality factor for bollard pull for a set of vessels.
33
4.3
The TNET Concept
The open water resistance is not given in the rule formulation as it is taken into
account using the concept of the net thrust TNET. The net thrust is defined to be the
thrust available to overcome the total ice resistance. At the self propulsion point the
thrust, including thrust deduction described by the thrust deduction factor t, equals the
total resistance at the ship speed v i.e.
T( v) ⋅ (1 − t ) = R TOT, i (h i , H M , v) = R iTOT (h i , H M , v) + R OW ( v) =
= R i (h i , v) + R CH (H M , v) + R OW ( v) .
(29)
From this expression above the definition of the net thrust is obtained as
TNET ( v) = T( v) ⋅ (1 − t ) − R OW ( v) .
(30)
At the self propulsion point this net thrust equals to total ice resistance. This definition
in itself does not make matters easier in view of taking the open water resistance into
account. Here use is made of the fact that at two speeds the net thrust is known: The
net thrust at zero speed is the bollard pull TB and at the open water speed vow the net
thrust is zero. The assumption that the net thrust is a second degree curve between
these points is made as follows
 1 v
2 v
− 
TNET ( v) = 1 −
 3 v ow 3  v ow




2
 ⋅ TB .


(31)
The assumption that the net thrust follows the second order polynomial of the above
shape is justified by that the fit is usually very good. This is shown in Fig. 19.
1400
1200
TNET -curve
TNET -curve, Calculated
TNET [kN]
1000
800
600
400
200
0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
V [m/s]
Fig. 19a. The TNET – curve for MT Tervi and corresponding measurement results
from model scale tests (Leiviskä 2006).
34
Fig. 19b. The theoretical TNET – curve for MT Uikku and corresponding measurement
results from model scale tests (Juva & Riska 2002).
4.4
The Shrouded Propellers
If the vessel is equipped with some propulsor which gives more thrust per power than
the usual propellers, then the relationship between thrust and power should be
investigated more thoroughly than just using the bollard pull relationship. The starting
point is that the vessel must fulfil the basic requirement of 5 knots in a specified brash
ice channel (the thickness of which varies with ice class), but the power used to
produce the thrust can be different from the one given with the rule equations. Here a
direct way to calculate or determine the thrust is examined for propellers in nozzles.
The force balance in ice at speed v1 is
(1 − t 1 )T(v1 ) = R OW (v1 ) + R CH (v1 ) ,
(32)
where t1 is the thrust deduction factor at speed v1. If the thrust and thrust deduction as
well as the open water resistance at speed v1 are known, then the definition of the net
thrust can now be used directly as
TNET = (1 − t1 ) ⋅ T( v1 ) − R OW ( v1 ) .
(33)
The basic requirement in the rules is that at 5 knots speed
TNET = R CH ,
from which the power can be calculated.
(34)
35
Now the question posed by propellers in nozzles may be tackled. At low speeds, the
nozzled propellers give higher thrust than open propellers of a corresponding size.
This extra thrust is, as a rule of thumb, given as 30 % of the corresponding open
propeller thrust. These facts can be cast in an equation if firstly the net thrust at speed
v, using e.g. (31), is denoted as
TNET ( v) = K ( v) ⋅ TB .
(35)
where the factor K(v) is the quadratic term in Eq. (33). The extra thrust given by the
nozzle is taken into account by the factor KN, where the bollard pull of the nozzle
propeller that otherwise is of the same size is
TB, N = K N ⋅ TB and
(36)
TNET ( v) = K ( v) ⋅ TB, N = K ( v) ⋅ K N ⋅ TB
(37)
Now, starting from the basic equation (36), the following chain, valid at speed v, is
obtained
R CH ( v) = TNET ( v)
= K ( v) ⋅ TB, N
= K ( v) ⋅ K N ⋅ TB
= K ( v) ⋅ K N ⋅ K e ⋅ (P ⋅ D P )2 / 3 .
(38)
where the subindex N refers to nozzle. In the rule formulation, v is 5 knots and thus
K(v) is assumed to be 0.8. Thus the power requirement for a nozzle propeller is
1
PN =
DP
 R CH

 K vKgK N





3/ 2
K
= e
DP
 R CH

 KN



3/ 2
=
1
K 3N/ 2
⋅ POPEN .
(39)
This equation shows that in theory, if the open water propeller has a diameter which is
KN3/2 times larger than (i.e. about 1.48 times) the nozzled propeller diameter, then the
thrusts are the same. Or to put it in different terms, the power of nozzled propulsion
can be about 70 % of the corresponding open propulsion, and the performances are
the same – all these assuming that KN = 1.3.
36
5.
MEASUREMENT RESULTS AVAILABLE
The basis for evaluating the channel ice resistance and the propulsion power required
is formed by the measurement results obtained from various ships. Most results – both
from full scale and model scale - exist from the tanker Uikku (or her sister ships
Lunni, Sotka or Tiira) and from the tanker Tervi (and her sister ship Palva). In the
following the results available are briefly described. Special attention is given to note
down the ice conditions measured.
5.1
Measurements with Lunni-class
The dimensions of MT Uikku used in calculating the power requirement and also the
ice resistances are given in Table 4. In this table as well as in the subsequent similar
tables, some values are estimated (these are marked in bold) and some are measured
from the lines plan available. Two Lunni-class vessels were converted to Azipod
vessels, so dimensions for both the original and converted versions are given in Table
4. Some discrepancy exists in literature in the measured values as measuring the
length of bow area, for example, is sometimes not easy. The values given in the
following tables are, however, those that are used in the calculations performed for
this report.
Table 4. The main particulars of MT Uikku before and after the conversion to Azipod
vessel.
Lpar
m
LWL
m
DP
m
Awf
m2
vow
m/s
no.
type
of
FP/CP
props
1 FP/DE
Load
condition
α
deg
φ1
deg
φ2
deg
Lbow
m
BWL
m
T
m
Loaded
24
29
29
32.9 76.3 155.2 21.5
9.5
5.65 490.0 8.8
Ballast
Loaded,
old
Ballast,
old
24
29
33
31.4 71.1 137.9 20.3
6.1
5.65 441.0 7.5
1
FP/DE
24
29
29
32.9 76.3 155.2 21.5
9.5
5.45 490.0 8.8
1
CP
24
29
33
31.4 71.1 137.9 20.3
6.1
5.45 441.0 7.5
1
CP
Full scale trial results include tests in level ice and in brash ice close after the ships
were delivered (Grönqvist 1979, Kannari 1982). These references give the results
shown in Table 5. It should be noted that these results are with the tankers before
conversion to Azipod-ships. The diameter of the original CP propeller was 5.45 m
with the same machinery power. The results given by Kannari (1982) seem to be very
low – actually the speed used in the full scale brash ice tests exceeds in one case the
open water speed. Thus these measurement points are somewhat suspect. This matter
is treated when the data is used for verification later in this report.
37
Table 5. Early full scale results with Lunni class tankers.
Test
Level ice
resistance
(Grönqvist
1979)
Result
Resistances
RiTOT = 300 kN, v = 0.9 kn
RiTOT = 700 kN, v = 10.9 kn
hi – v curve
hi = 90 cm, v = 3.9 kn
hi = 40 cm, v = 12.6 kn
Brash ice Resistance
resistance RCH,TOT = 650 kN, v = 10.5 kn
(Grönqvist
1979)
Brash ice Resistance, ballast (Tav = 6.2
resistance m)
(Kannari
PD = 6.1 MW, RCH,TOT = 425
1982)
kN,
ROW = 260 kN, v = 6.8 m/s
Resistance, loaded (Tav = 9.6
m)
PD = 5.8 MW, RCH,TOT = 525
kN,
ROW = 185 kN, v = 5.8 m/s
PD = 7.7 MW, RCH,TOT = 625
kN,
ROW = 265 kN v = 6.7 m/s
Resistance, ballast (Tav = 6.0
m)
PD = 3.3 MW, RCH,TOT = 380
kN,
ROW = 180 kN, v = 6.0 m/s
PD = 7.1 MW, RCH,TOT = 500
kN,
ROW = 325 kN, v = 7.8 m/s
Resistance, loaded (Tav = 8.9
m)
PD = 5.7 MW, RCH,TOT = 500
kN,
ROW = 200 kN, v = 6.0 m/s
PD = 6.8 MW, RCH,TOT = 560
kN,
ROW = 250 kN, v = 6.5 m/s
Ice conditions
Notes
hi = 50 cm
Resistance
deduced
from
propeller curves
One thicker field
measured also
Channel
maximum
thickness 2 m
HT = 1.22 m
Ballast
HM = 1.01 m
Loaded
HM = 0.99 m
HT = 1.18 m
The
channel
profiles
exist.
The
thickness
value used as a
reference
thickness is the
effective channel
thickness.
This
is
the
effective channel
thickness
i.e.
average thickness
over the channel
width of 1.2B
Ballast
HM = 1.03 m
Loaded
HM = 1.01 m
The problem with the channel thickness to be associated with the test results is
described later but for the future reference, here a fit to the channel cross section data
available is done so that the rule channel thickness at the center line HM is obtained.
This is done using the effective channel width of 1.6B. Values for the centerline
thickness are included in Table 5.
38
Another, more recent full scale test series exists with MT Uikku in full load (NortalaHoikkanen 1999). This gave the results of channel resistance RCH = 420 – 500 kN in
the speed range of 3.5 – 5.1 m/s. Channel profiles were measured in detail and the
measurements gave an average channel thickness over the effective breadth between
1.21 – 1.89 m and the resulting channel thickness at the centerline of HM = 0.92 – 1.59
m. In the subsequent analysis the average values from the ranges above are used i.e.
RCH = 455 kN, v = 4.3 m/s and HM = 1.30 m.
Several tests series have been carried out in model scale to measure the brash ice
resistance of MT Uikku. Before describing these, the open water resistance in forward
motion in full scale units is given as (Rodenheber 2002, Leiviskä & Tuhkuri 2000,
Leiviskä 2002, Leiviskä 2004)
R OW = 0.52 ⋅ v 3 + 0.91 ⋅ v 2 + 8.53 ⋅ v [kN], [v] = m/s.
(40)
An extensive set of model tests was carried out at the Helsinki University of
Technology in 1999 using MT Uikku model of scale 1:20. This model was already the
Azipod-version of the ships. The ship was in loaded condition and the coefficient of
friction between the model hull and ice was low, µ = 0.03. These tests were done in
repeatedly running the vessel in the same channel and it was stated that only for the
first tests the measured channel profile was reliable. Thus only the two or three first
points for each channel are accepted here. The results are given in Table 6, where also
the calculated mid-channel thickness HM is shown. The tests were propulsion tests
except the last ones in channel 6.
Table 6. The results of channel tests with MT Uikku model.
Test
Speed
[m/s]
Channel 1
3.26
HM =2.53 m
2.82
Channel 3
0.54
HM =3.82 m
2.24
Channel 5
2.19
HM =2.71 m
3.13
4.56
Resistance
RCH [kN]
434
444
797
645
633
795
973
Test
Speed
[m/s]
1.83
Channel 2
HM =4.18 m
2.46
3.40
Channel 4
HM =1.85 m
3.40
2.33
Channel 6
HM =3.08 m
3.18
Towing test
4.70
Resistance
RCH [kN]
658
604
430
444
627
679
750
Another model test series with MT Uikku in brash ice exists (Leiviskä 2004). Here
only one point relevant to this report is given. The model was the Azipod version of
MT Uikku and the scale was 1:31.56. The result, in full scale units, was at v = 0.56
m/s RCH,TOT = 1330 kN where the mid channel thickness was HM = 4.70 m. This gives
the channel resistance of RCH = 1325 kN.
39
5.2
Measurements with Tervi-class
There are two tankers of Tervi-class; MT Tervi and MT Palva. The main particulars
of them are shown in Table 7. The stem angle is relatively blunt but her bow is still an
ice breaking bow in the sense that she does not have a bulb.
Table 7. The main particulars of MT Tervi.
Load
condition
α
deg
φ1
deg
φ2
deg
Lbow
m
Lpar
m
LWL
m
BWL
m
T
m
Loaded
37
41
39
33.8 132.2 198.3 30.2 12.5
7.1 745.0 7.5
Ballast
37
41
39
34.2 114.5 180.9 30.2
7.1 745.0 7.5
7.3
DP
m
Awf
m2
vow
m/s
no.
type
of
FP/CP
props
1
CP
1
Many of the model test results for MT Tervi has been reported in Ritvanen (2004).
There exists additionally model test results from tests where the coefficient of friction
of the hull was varied and also where tests with consolidated channels were made
(NN 2005). These model scale results are summarized in full scale units in Table 8. In
this table the mid channel ice thickness is calculated - as also above with Lunni
results - using BE = 1.6B. The open water resistance is accounted for as a ratio
between the total resistance and open water resistance as described by Ritvanen
(2004).
The tests with a consolidated layer targeted at 10 cm thick consolidated layer. The
layer thickness was very difficult to measure and thus a calculated value is used. It is
calculated using the Zubov equation for ice thickness
h i2 + 50 ⋅ h i − 8 ⋅ θ = 0
(41)
where the cold sum term is
T
θ=
∫ (Tf − Ta )dt
0
and Tf is water freezing temperature (0oC in this case) and Ta air temperature; units oC
and day. Using this equation, the measured cold sum and the porosity of brash ice (cf.
Riska et al 1997), a thickness value of 7 cm in full scale units is obtained.
CP
40
Table 8. The results from model tests in full scale units of Tervi-class.
Source
Leiviskä &
Kiili (2004)
Wilhelmson
(1996)
NN (2005)
V [m/s]
3.31
3.42
1.52
1.58
1.89
0.95
0.98
1.16
1.07
2.72
2.74
1.03
2.59
4.11
1.01
2.60
2.60
4.29
2.60
2.60
2.60
2.60
HM [m]
2.16
1.79
1.66
1.30
2.50
2.50
2.01
2.55
2.44
3.77
2.66
1.78
1.78
1.78
1.05
1.05
1.03
1.03
0.82
0.89
0.82
0.89
RCH
[kN]
818
830
827
689
1046
1234
1455
1157
1485
775
916
861
1001
1336
381
1063
833
1044
836
1089
1582
1776
PD [kW]
11130
10857
7121
11835
12426
11573
14313
-
Notes
Both resistance and
propulsion tests.
µ = 0.10
Fully loaded
Model the same as
above.
µ = 0.10
Fully loaded in all
tests
µ = 0.10
Consolidated
layer,
o
cold sum 17 C ⋅ h
2.60
2.60
2.60
2.60
2.60
2.60
0.86
0.86
0.94
0.86
0.86
0.94
2296
1971
2210
2776
2300
2691
-
µ = 0.41
µ = 0.41
Consolidated
layer,
o
cold sum 17 C ⋅ h
Four test results exist from MT Tervi in full scale. These measurements are described
in Leiviskä (2006). These results are given in Table 9.
Table 9. The results from full scale tests of MT Tervi (Leiviskä 2006).
Source
Leiviskä
(2006)
V [m/s]
5.80
6.30
2.88
1.59
HM [m]
0.52
0.79
0.79
0.33
RCH [kN]
411
438
397
474
PD [kW]
6346
7688
2760
2530
Notes
Ballast
Loaded
41
5.3
Measurements with Tempera - class
There are two tankers of Tempera – class, MT Tempera and MT Mastera. These
tankers are called DAT as they are planned to go astern in ice. This mode of operation
is not interesting here so that only test results where the ships went forward are dealt
with here. The particulars of Tempera-class tankers in ballast and loaded are given in
Table 10.
Table 10. The main particulars of Tempera – class tankers.
Load
condition
α
deg
φ1
deg
φ2
deg
Lbow
m
Loaded
41
90
66
Ballast
32
90
67
Lpar
m
LWL
m
BWL
m
T
m
DP
m
Awf
m2
vow
m/s
49.2 124.2 242.8 44.0 14.5
7.5
1370
7.8
56.5 108.6 239.3 44.0
7.5
1570
7.0
8.9
no.
type
of
FP/CP
props
1 FP/DE
1
FP/DE
There are not any model test results available from these tankers, so only the full scale
results available are given in Table 11.
Table 11. The results from full scale tests of MT Mastera or MT Mastera.
Source
Leiviskä
(2006)
v [m/s]
5.30
3.03
2.68
Wilkman et
3.8
al (2004)
4.4
4.7
5.4
HM [m]
0.26
0.12
0.12
0.29
0.29
0.29
RCH [kN]
NA
NA
NA
NA
NA
NA
PD [kW]
6500
1750
2800
5000
7000
9200
Notes
Loaded
Loaded
Ballast
Ballast
Ballast
Ballast
Measurements with Natura - class
There are two tankers of Natura – class, MT Natura and MT Futura. These tankers
have an ice class IC, and a cylindrical bow with a bulb. The main particulars are
shown in Table 12. The full scale test result is given in Table 13.
Table 12. The main particulars of MT Futura and MT Natura.
Load
condition
α
deg
φ1
deg
φ2
deg
Lbow
m
Lpar
m
LWL
m
BWL
m
T
m
DP
m
Awf
m2
vow
m/s
Loaded
34
90
90
53.7 136.6 242.4 40.0 13.87 8.0
1600
7.1
Ballast
25
90
90
49.7 126.5 231.2 40.0 8.15
1561
7.1
8.0
no.
type
of
FP/CP
props
1
CP
1
CP
42
Table 13. The results from full scale tests of MT Futura.
Source
Leiviskä
(2006)
5.5
v [m/s]
5.81
HM [m]
0.34
RCH [kN]
PD [kW]
Notes
NA
6800
Ballast
Measurement with MS Birka Express
The design point of IA Super ice class where there is 10 cm of refrozen ice on top of
the brash ice channel has proved to be difficult to model in model tests. In order to
have some verification point from the refrozen channel, one test voyage has been
done onboard MS Birka Express. The main particulars of MS Birka Express are
shown in Table 14 – many of the shape parameters are estimated from the available
material. The data point from the archipelago fairway channel between Kemi and
Oulu is given in Table 15. This channel had refrozen and an estimate of the thickness
of the consolidated layer is 8.9 cm (Leiviskä 2006).
Table 14. The main particulars of MS Birka Express.
Load
condition
Loaded
α
deg
φ1
deg
φ2
deg
24.0 90.0 60.0
Lbow
m
Lpar
m
LWL
m
BWL
m
40.0 80.0 140.0 22.7
T
m
DP
m
Awf
m2
6.95
4.2
530
no.
type
of
FP/CP
props
10.3
1
CP
vow
m/s
Table 15. The results from full scale test of MS Birka Express.
Source
Leiviskä
(2006)
5.6
v [m/s]
2.37
HM [m]
0.76
RCH [kN]
PD [kW]
NA
6084
Notes
consolidated
layer
hi = 8.9 cm
Measurements with Small Tonnage
The power requirement in the 2002 ice class rules seemed to increase much the
requirements for smaller ships. Thus it was decided to make a special study of the
power required by smaller vessels. In a study of these smaller vessels the power used
of five vessels was measured and at the same time the channel profiles were
determined (Leiviskä 2004c). The data of these ships (the ships remain anonymous) is
given in Table 16. The results of the observations are given in Table 17 where the mid
channel thickness is calculated assuming the effective channel width to be 1.6B.
43
Table 16. The main particulars of ships included in the study of small tonnage.
no.
type
of
FP/CP
props
1
CP
Ship no.
α
deg
φ1
deg
φ2
deg
Lbow
m
BWL
m
T
m
DP
m
Awf
m2
vow
m/s
B
34
NA
90
15.0 60.6 78.9 12.5
5.3
2.8
102
6.3
C
29
NA
61
17.1 44.9 78.8 12.6
5.4
2.7
146
6.1
1
CP
D
36
NA
64
12.2 52.1 80.2 12.5
5.0
2.4
98
5.7
1
CP
E
32
NA
70
16.0 63.0
92.4 13.6
6.0
2.9
155
7.1
1
CP
G
30
NA
47
15.5 53.0 85.0 12.5
5.3
2.6
126
6.5
1
FP
Lpar
m
LWL
m
Table 17. The results from full scale test of the small tonnage.
Source
Leiviskä
(2004c)
Ship
B
C
C
D
E
G
G
v [m/s]
4.6
3.9
4.4
3.6
5.4
4.4
5.1
HM [m]
0.28
0.32
0.24
0.34
0.42
0.58
0.43
RCH [kN] PD [kW]
NA
1800
NA
1840
NA
1840
NA
1700
NA
2640
NA
1845
NA
1845
Notes
Full
power
assumed
in each
case
44
6.
CALIBRATION OF THE POWER REQUIREMENT
The measurement results available from different ships were described in the previous
chapter. Now these results are used to compare the calculated and measured ice
resistance and propulsion power used. The comparison is done based on the ratio
between the calculated and measured ice resistance or power used. The effective
width of the channel is 1.6B in all measurements and the measured or calculated mid
channel thickness HM as well as the actual ship speed is used also in calculations. The
coefficient of friction is assumed to be 0.15 if the value is not known (it is only known
in model scale measurements). The basic data, divided into tables per ship, are shown
in Tables 18a-f. The Lunni-class data given by Kannari (1982) is corrected so that the
points given in the reports are thought to refer to speed in knots, not in m/s. The
corrected values are given in Table 18a.
Table 18a. The compilation of the basic data from Lunni – class for analysis.
Test data
Full
scale
results, first
seven values
corrected,
µ = 0.15
Model scale
results,
µ = 0.03
L
[m]
B
[m]
HM
[m]
v
[m/s]
137.9
155.2
155.2
137.9
137.9
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
155.2
20.3
21.5
21.5
20.3
20.3
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
21.5
1.01
0.99
0.99
1.03
1.03
1.01
1.01
1.30
2.53
2,53
4.18
4.18
3.82
3.82
1.85
2.71
2.71
2.71
3.08
3.08
3.08
4.70
3.5
3.0
3.4
3.1
4.0
3.1
3.3
4.3
3.26
2.82
1.83
2.46
0.54
2.24
3.40
2.19
3.13
4.56
2.33
3.18
4.70
0.56
Measured
RCH
PD
[kN]
[kW]
365
6100
475
5800
555
7700
345
3300
460
7100
445
5700
490
6800
455
NA
434
NA
444
NA
658
NA
604
NA
797
NA
645
NA
437
NA
633
NA
795
NA
973
NA
627
NA
679
NA
750
NA
1325
NA
Calculated
RCH
PD
[kN]
[kW]
341
3166
460
3993
480
4568
420
3907
441
5414
475
4263
486
4559
721
1218
1164
2050
2139
1728
1871
848
1200
1307
1542
1427
1541
1832
2285
-
45
Table 18b. The compilation of the basic data from Tervi – class for analysis.
Test data
Full
scale
result,
µ = 0.15
Model
test
result,
µ = 0.10
Model
test
results,
µ = 0.41
L
[m]
B
[m]
HM
[m]
v
[m/s]
180.9
180.9
180.9
198.3
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
180.9
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
30.2
0.52
0.79
0.79
0.33
2.16
1.79
1.66
1.30
2.50
2.50
2.01
2.55
2.44
3.77
2.66
1.78
1.78
1.78
1.05
1.05
1.03
1.03
0.82
0.89
0.86
0.86
0.86
5.8
6.3
2.88
1.59
3.31
3.42
1.52
1.58
1.89
0.95
0.98
1.16
1.07
2.72
2.74
1.03
2.59
4.11
1.01
2.60
2.60
4.29
2.60
2.60
2.60
2.60
2.60
Measured
RCH
PD
[kN]
[kW]
411
6350
438
7688
397
2760
474
2530
818
11130
830
10860
827
7120
689
NA
1046 11840
1234 12430
1455
NA
1157 11570
1485
NA
775
14313
916
NA
861
NA
1001
NA
1336
NA
381
NA
1063
NA
833
NA
1044
NA
836
NA
1089
NA
2296
NA
1971
NA
2210
NA
Calculated
RCH
PD
[kN]
[kW]
494
12328
784
39726
720
6408
297
1358
2229 38650
1803 28933
1507 15337
1140
2476 34079
2414 29055
1860
2483 31028
2349
4240 88536
2768
1613
1708
1878
882
938
918
1031
715
782
1338
1338
1338
-
Table 18b-continued. The compilation of the basic data from Tervi – class for
analysis, the tests for ice class IA Super.
Model tests
µ = 0.10,
hi = 7 cm
µ = 0.41,
hi = 7 cm
L
[m]
B
[m]
HM
[m]
v
[m/s]
180.9
180.9
180.9
180.9
180.9
30.2
30.2
30.2
30.2
30.2
0.82
0.89
0.86
0.86
0.94
2.60
2.60
2.60
2.60
2.60
Measured
RCH
PD
[kN]
[kW]
1582
NA
1776
NA
2776
NA
2300
NA
2691
NA
Calculated
RiTOT
PD
[kN]
[kW]
834
901
1457
1457
1591
-
46
Table 18c. The compilation of the basic data from Tempera – class for analysis.
Test data
Full
scale
results,
µ = 0.15
L
[m]
B
[m]
HM
[m]
v
[m/s]
242.8
242.8
239.3
239.3
239.3
239.3
44.0
44.0
44.0
44.0
44.0
44.0
0.26
0.12
0.12
0.29
0.29
0.29
5.3
3.03
2.68
3.8
4.4
4.7
Measured
RCH
PD
[kN]
[kW]
NA
6500
NA
1750
NA
2800
NA
5000
NA
7000
NA
9200
Calculated
RCH
PD
[kN]
[kW]
8331
1159
1111
5975
7788
9161
Table 18d. The compilation of the basic data from Natura – class for analysis.
Test data
Full
scale
results,
µ = 0.15
L
[m]
B
[m]
HM
[m]
v
[m/s]
Measured
RCH
PD
[kN]
[kW]
126.5
40.0
0.34
5.81
NA
6800
Calculated
RCH
PD
[kN]
[kW]
-
13708
Table 18e. The compilation of the basic data from MS Birka Express for analysis,
note that this is a case of IA Super ice class.
Test data
Full
scale
results,
µ = 0.15,
hi = 8.9 cm
L
[m]
B
[m]
HM
[m]
v
[m/s]
Measured
RCH
PD
[kN]
[kW]
140.0
22.7
0.76
2.37
NA
6084
Calculated
RiTOT
PD
[kN]
[kW]
-
5309
Table 18f. The compilation of the basic data from small tonnage analysis.
Test data
Full
scale
results,
µ = 0.15
L
[m]
B
[m]
HM
[m]
v
[m/s]
78.9
78.8
78.8
80.2
92.4
85.0
85.0
12.5
12.6
12.6
12.5
13.6
12.5
12.5
0.28
0.32
0.24
0.34
0.42
0.58
0.43
4.6
3.9
4.4
3.6
5.4
4.4
5.1
Measured
RCH
PD
[kN]
[kW]
NA
1800
NA
1840
NA
1840
NA
1700
NA
2640
NA
1845
NA
1845
Calculated
RCH
PD
[kN]
[kW]
1513
1147
1136
1318
4746
3549
4299
47
6.1
Basic Analysis of the Data
The basic data of the ratio between measured and calculated power and channel
resistance can be plotted versus the parameters L, B, HM and v. These plots are shown
in Appendix 1. These plots show for that the power required from a IA Super vessel is
almost exactly the same as the observed power. The model tests with a consolidated
layer show, however, higher measured resistance than the rule resistance. This shows
that the production of the consolidated layer is not straightforward – as discussed in
Section 3.4. For pure channel resistance (resistance required from IC, IB and IA
vessels) there is much scatter. High values of both the power and resistance have been
measured both in model tests and in full scale tests. Not the ship size (L or B) nor the
speed do show any trend. The only observation that can be made from the basic data
is that in higher speeds the measured full scale power seems to increase compared
with the calculated value. The mid channel thickness HM influences somewhat the
ratio between calculated and measured resistance or power. The full scale values are,
however, from thinner channels.
Both the mid channel ice thickness and ship beam influence the piling up of ice at the
ship side. The total height of the ice at the ship side is, for the rule channel profile
H TOT = H M +
tan δ
B+
2
(tan δ + tan γ ) ⋅  H M B + tan δ B 2  .

4

(42)
The total height HTOT is estimated in the present rules to be HTOT = HM + HF where the
HF (defined as HTOT – HM) is a function of both the mid channel thickness and ship
breadth as
H F = 0.26m + H M ⋅ B .
(43)
The quantity HF could be defined both for the correct height given in (42) and the
estimate in the 2002 rules. These pile up heights are plotted in Fig. 20 assuming the
mid channel thickness to be 1.0 m. The first term in the expression (42) under the
square root dominates the thickness and thus the height HF is proportional to H M B .
The estimate given by (43) is, however, noticeably higher than the actual value.
48
HM = 1.0 m
8
HF [m]
6
H F = 0.26m + H M ⋅ B
4
HF =
tan δ
B+
2
(tan δ + tan γ ) H M B + tan δ B2 
4


2
0
0
10
20
30
40
50
B [m]
Fig. 20. The estimated and exact height of the pile up against the ship beam.
The measurement results are plotted versus the exact expression for the height (42)
and the approximate square root expression in Figs. 21a and 21b. Now a clear trend of
higher calculated value with thicker ice emerges.
49
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
2,5
2,0
1,5
1,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
0,5
0,0
0
2
4
6
8
HF [m]
Fig. 21a. The ratio between calculated and measured power and channel resistance
plotted versus the pile up height defined in (42).
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
2,5
2,0
1,5
1,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
0,5
0,0
0
2
4
6
8
SQRT(HM B) [m]
Fig. 21b. The ratio between calculated and measured power and channel resistance
plotted versus the approximate additional pile up height.
50
6.2
Correction for the Accumulated Ice Thickness
The difference between the estimated pile-up depth at the ship side HF and the more
exact height results in a difference between the measured channel resistance and
required propulsion power as compared with the calculated ones. If the resistance
equation is corrected so that instead of the estimated HF the correct value in Eq. (42)
is used, the results given in Fig. 22 are obtained.
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
2,5
2,0
1,5
1,0
0,5
0,0
0
10
20
30
40
50
B [m]
Fig. 22a. A comparison between the calculated and measured resistance and
propulsion power values when using the correct pile-up depth HF plotted versus ship
beam.
51
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
2,5
2,0
1,5
1,0
0,5
0,0
0
2
4
6
v [m/s]
Fig. 22b. A comparison between the calculated and measured resistance and
propulsion power values when using the correct pile-up depth HF plotted versus ship
speed in the test.
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
2,5
2,0
1,5
1,0
0,5
0,0
0
2
4
6
8
HF,Correct [m]
Fig. 22c. A comparison between the calculated and measured resistance and
propulsion power values when using the correct pile-up depth HF plotted versus the
total pile-up depth.
52
6.3
Improvement of the Present Requirement
The Figs. 22a. and 22c. show a clear trend and Fig. 22b. shows a large scatter and thus
there is obviously a reason to search for an improved formulation of the power
requirement. In order to improve the formulation of the power requirement, the
measurement results are used as a set of test data. Based on the initial analysis of these
data, some indications for the development work can be gathered. These indications
include the following:
•
•
•
•
•
•
The level ice resistance formulation in the present 2002 rules is not changed
The change is implemented in the channel resistance i.e. the power calculation
is not changed
As the speed dependency is small in the channel resistance, see e.g. Leiviskä
(1998), only the two first factors are kept in the channel resistance. Initial
regressions on the measurement data suggest also this.
The bow resistance (first factor of RCH) is about 25 to 30 % of the total
resistance, see Leiviskä (1998), this is borne in mind when determining the
constants
The shape factor Cµ is modified. At present the frictional force factor is based
on the assumption that the brash ice is displaced following the buttock lines
(verticals). This is shown in the first factor of Cµ which contains the term
µ·sinφ2.
The actual HF is used instead of the estimate. Some thicknesses are also
modified to better reflect the intent in the formulation, see e.g. Mellor (1980).
The frictional part of the shape factor Cµ is modified so that the brash ice motion has
two components; one sideways along the waterline and one down following the
vertical. Thus the first component of the coefficient Cµ is to be
µ⋅
cos α + cos ϕ2
.
2(1 + cos α cos ϕ2 )
Further, as the dependency of the resistance on the waterline entrance angle α is not
clear, the average value of this angle is used (α = 30º). This results in the shape factor
Cµ = µ
0.87 + cos ϕ 2
sin ϕ 2
+
.
2 + 1.7 cos ϕ2
1 + 3 sin 2 ϕ2
(44)
The final formulation of the channel resistance selected is thus
(
)
R CH = C 3 ⋅ C µ ⋅ H AV ⋅ B + C ψ H M + C 4 ⋅ µ ⋅ L PAR ⋅ H TOT 2
(45)
where Cψ is given in (9), HTOT in (42), Cµ in (44) and the average channel thickness is
H AV = H M +
tan δ
⋅ B E ≈ H M + 0.014 ⋅ B
4
(46)
53
where the approximation based on the approximate effective width is also shown.
Now it remains to determine the constants C3 and C4. This is done using a regression
on the measured resistance and power points, described above. The regression is done
based on least squares method by minimizing the following quantities. If the
measured channel resistances and powers are denoted as Ri and Pi and the
corresponding calculated values as Rci and Pci, then the quantities to be minimized are
∆P2 =
NP
P
∑ ( Pci − 1) 2
i =1
and
i
(47)
∆R 2 =
NR
R
∑ ( Rci − 1) 2
i =1
i
The regression is done separately on the model scale and full scale results. The
functions (47) are shown in App. 2. The minimum is quite shallow and shows also a
dependency between C3 and C4. The following values are selected for the constants:
C3 = 16.8 kN/m2 and C4 = 0.5 kN/m3.
The resulting plots of the channel resistance and power are shown in Fig. 23. Clearly,
the trends versus the accumulated depth of ice or the ship beam decreased and the
scatter versus the ship speed also decreased when the formula (45) was used.
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
2,5
2,0
1,5
1,0
0,5
0,0
0
10
20
30
40
50
B [m]
Fig. 23a. A comparison between the calculated and measured resistance and
propulsion power values when using the correct pile-up depth HF and using the new
equation (46) plotted versus ship beam.
54
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
2,5
2,0
1,5
1,0
0,5
0,0
0
2
4
6
v [m/s]
Fig. 23b. A comparison between the calculated and measured resistance and
propulsion power values when using the correct pile-up depth HF and using the new
equation (46) plotted versus ship speed.
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
2,5
2,0
1,5
1,0
0,5
0,0
0
2
4
6
8
HF,Correct [m]
Fig. 23c. A comparison between the calculated and measured resistance and
propulsion power values when using the correct pile-up depth HF and using the new
equation (46) plotted versus correct pile-up depth.
55
The final aim of this work is the formulation of the rule equation. The regression with
power values contains the measured ship power which often in full scale results is the
main engine power PE instead of the delivered power PD which is used in the
calculations. Thus some reserve is prudent to take in the rule power requirement. This
is done by using the values for the constants as C3 = 18.4 kN/m2 and C4 = 0.55 kN/m3.
The definitions and equations for the final rule formulation are collected in Appendix
3. The rule requirement is based on, as in the 2002 rules, that speed to be attained is 5
knots in a HM = 1 m thick channel for IA ice class. For the IA Super requirement, the
new brash ice resistance formulation is used and the consolidated ice resistance is
calculated using the old formulation (constants C1 and C2). The IB requirement
corresponds, as earlier, to HM = 0.8 m and IC requirement to HM = 0.6 m. The impact
on the validation vessels of the new power requirement is studied with an array of
ships presented in Appendix 4. First the new power requirement divided by the
installed power is shown versus the ship size, Figs. 24.
2,0
IA Super
IA
IB
IC
Pnew/Pinst
1,5
1,0
0,5
0,0
0
10
20
30
40
B [m]
Fig. 24a. The new power requirement divided by the installed power plotted versus
the ship length and using the array of validation ships.
56
2,0
IA Super
IA
IB
IC
Pnew/Pinst
1,5
1,0
0,5
0,0
0
50
100
150
200
250
L [m]
Fig. 24b. The new power requirement divided by the installed power plotted versus
the ship length and using the array of validation ships.
A clear trend seems to emerge of low requirement in the mid-range of ships, but this
is an illusion as most of the vessels in the range of 20 to 30 m breadth are ships with
high open water speed. Thus their need for propulsion power is driven by the open
water resistance. A better view may be obtained if the new power requirement is
divided by the present one and plotted versus ship size, see Figs. 25.
57
2,0
IA Super
IA
IB
IC
Pnew/P2002
1,5
1,0
0,5
0,0
0
10
20
30
40
B [m]
Fig. 25a. The new power requirement divided by the rule power according to 2002
rules plotted versus the ship beam and using the array of validation ships.
2,0
IA Super
IA
IB
IC
Pnew/P2002
1,5
1,0
0,5
0,0
0
50
100
150
200
250
L [m]
Fig. 25b. The new power requirement divided by the rule power according to 2002
rules plotted versus the ship length and using the array of validation ships.
58
The new and present power requirement correlate well – only for larger vessels (MT
Mastera and Tervi) the new requirement is clearly less than the present requirement.
Thus the developed formulation fulfills one the targets set in the beginning.
59
7.
CONCLUSION
The aim of the present report is to analyze the propulsion power requirement in the
present Finnish-Swedish ice class rules. The present requirement is stated to have
some drawbacks which are analyzed in the report. The following conclusions emerged
when an analysis of the rule brash ice resistance formulation was carried out:
• The whole channel cross sectional profile in the model and full scale tests
should be taken into account up to the width where the ship passage influences
the channel. This width is called the effective channel width BE and is
approximately BE = 1.6B. Very often only the mid-channel thickness is –
erroneously – used.
• The coefficient of friction between ship hull and ice influence much the
resistance. The rule formulation uses a coefficient of friction value 0.15. The
formulation to correct the low value of coefficient of friction in model tests
given in Keinonen (1991) was shown to correspond well with one model test
series where the coefficient of friction value was varied.
• The properties of brash ice (internal friction, cohesion as well as the piece
size) have been found in earlier model tests to influence much the measured
resistance. Too large piece size results in too low resistance. No
comprehensive study of what are the proper brash ice parameters and how
these should be reproduced in model tests exists.
• The consolidated layer assumed to exist in the IA Super power requirement is
difficult to produce reliably or model in model tests. A recommendation thus
is that only the brash ice resistance is measured in model tests and the
resistance from the consolidated layer is calculated.
• The ice coverage in the brash ice channels in Nature is 100 %. Thus the brash
ice, as it cannot be compressed, retains its volume and must be displaced. The
side ridges of channels hinder further the motion of brash ice. These
conditions should be reproduced in model tests.
The following conclusions emerged when an analysis of the rule power requirement
formulation was carried out:
• The slow speed engines with a FPP are not able to produce the maximum
power in ice, if the propeller design is based on open water performance. This
is because the limits of the engine restrict the engine power output. This
problem does not exist with CP propellers or diesel-electric installations. This
phenomenon is taken into account by changing the propulsive factors in the
rules.
• The power requirement is based on so called ‘quality factors’ of bollard pull.
A large set of measured bollard pull values was used to verify the factors used
in the rules. The values of the propulsion constants were found to be adequate,
even if a large scatter exists.
• The power requirement is based on the TNET – concept in which the open
water resistance is taken into account approximately. TNET is defined to be the
thrust available to overcome the ice resistance i.e. the thrust available when
the thrust deduction factor is taken into account and open water resistance
60
subtracted. The used formulation was compared with model test results and
found to be adequate.
• A formulation how to take into account the additional thrust produced by the
nozzles was formulated.
The analysis of power requirement in the Finnish-Swedish ice class rules was
analyzed using an array of measurement points for power and resistance obtained by
full scale and model scale tests. The analysis suggested that instead of the
approximation for the accumulated ice depth HF, the exact formula is to be used.
Further, the influence of hull angles on the resistance was changed to better reflect the
direction where the brash ice is displaced. Finally, the form of the resistance equation
was simplified. The new proposed rule power requirement showed that for ships of
beam about 20 m, no major change resulted but for ships of larger beam in higher ice
class, some decrease of the power requirement was noticed. It should be stated here,
that the development of the power requirement was carried out here based on the
measured ice resistance and power values. The final power requirement depends also
on the needs of the winter navigation system where the number of icebreakers,
fairway taxes and transit times of merchant vessels are balanced. After this analysis is
carried out, the final rule formulation can be proposed.
61
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Leiviskä, T. 2006: The Comparison between the Measured and Calculated Ice
Channel Resistance of Large Vessels – Winters 2003 and 2004. Helsinki University of
Technology, Ship Laboratory, Rpt. D-91, 38 p.
Lindqvist, G. 1989: A Straightforward Method for Calculation of Ice Resistance of
Ships. Proc. Of the POAC ’89, Luleå, Sweden, 12-16 June, pp. 722-735.
Liukkonen, S. 1989: About Physical Modelling of Kinetic Friction between Ice and
Ship. Proc. Of the POAC ’89, Vol. 2, pp.736 – 749.
63
Mellor, M. 1980: Ship Resistance in Thick Brash Ice. Cold Regions Science and
Technology, 3(1980), pp. 305-321.
Miinala, M. & Patey, M. 2000: Performance of Ice-Navigating Ships in the Northern
Baltic in Winter 1999. Helsinki University of Technology, Ship Laboratory, Rpt. M249, 27 p. + App.
Mäkinen, E. et al. 1994: Friction and Hull Coatings in Ice Operations. Proc.
ICETECH ’94, SNAME, pp. E1-E22.
Nortala-Hoikkanen, A. 1999: Channel Tests with MT Uikku close to Kemi 24.26.3.1999 [in Finnish]. MARC Rpt. B-145, 20 s. + liitteet.
Nortala-Hoikkanen, A. & Bäckström, M. 1999: Model Tests in Brash Ice Channels
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Winter 1992. Helsinki University of Technology, Laboratory of Naval Architecture
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Merchant Vessels in Ice in the Baltic. Winter Navigation Research Board, Research
Rpt. No. 52, 68 p. + App.
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64
Appendix 1. The ratio of calculated and measured propulsion power and ship ice
resistance plotted versus four parameters; L, B, HM and v, for both the tests when
there was no consolidated layer and when there was a consolidated layer. The
calculation is done according to the rule 2002 formulation.
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
2,5
2,0
1,5
1,0
0,5
0,0
0
50
100
150
200
250
L [m]
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
2,5
2,0
1,5
1,0
0,5
0,0
0
10
20
30
B [m]
40
50
65
Brash ice resistance
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
2,5
2,0
1,5
1,0
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
0,5
0,0
0
1
2
3
4
5
HM [m]
Brash ice resistance
Power, Full scale
Resistance, Full scale
Power, Model scale
Resistance, Model scale
PDcalc/PDmeas , RCHcalc/RCHmeas
3,0
2,5
2,0
1,5
1,0
0,5
0,0
0
2
4
v [m/s]
6
PDcalc/PDmeas , RiTOT,calc /RiTOT,meas
66
Brash ice and consolidated ice resistance
3,0
Power, full scale results
Resistance, model scale results
2,5
2,0
1,5
1,0
0,5
0,0
0
50
100
150
200
PDcalc/PDmeas , RiTOT,calc/RiTOT,meas
L [m]
Brash ice and consolidated ice resistance
3,0
Power, Full Scale Results
Resistance, Model Scale Results
2,5
2,0
1,5
1,0
0,5
0,0
0
10
20
30
B [m]
40
50
PDcalc/PDmeas , RiTOT,calc/RiTOT,meas
67
Brash ice and consolidated ice resistance
3,0
Power, full scale results
Resistance, model scale results
2,5
2,0
1,5
1,0
0,5
0,0
0
1
2
3
4
PDcalc/PDmeas , RiTOT,calc/RiTOT,meas
HM [m]
Brash ice and consolidated ice resistance
3,0
Power, full scale results
Resistance, model scale results
2,5
2,0
1,5
1,0
0,5
0,0
0
2
4
v [m/s]
6
68
Appendix 2 The plots of functions (47) versus the constants C3 and C4. The model
scale and full scale values are plotted separately.
Model scale data
0,7
0,6
0,5
∆P2
0,4
0,3
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,2
20
19
0,1
18
0,0
0,6
17
0,5
0,4
C4
C3
16
0,3
0,2
15
Model scale data
0,35
0,30
∆R
0,10
0,15
0,20
0,25
0,30
0,35
2
0,25
0,20
20
0,15
19
18
0,10
0,6
17
0,5
0,4
C4
16
0,3
0,2
15
C3
69
Full scale results
1,2
1,0
0,6
0,4
20
19
0,2
18
0,0
0,6
0,5
0,4
C4
3
17
C
0,0
0,2
0,4
0,6
0,8
1,0
1,2
∆ P2
0,8
16
0,3
0,2
15
Full scale data
0,14
0,12
∆R2
0,04
0,06
0,08
0,10
0,12
0,14
0,10
0,08
20
0,06
19
18
0,04
0,6
17
0,5
0,4
C4
16
0,3
0,2
15
C3
70
Appendix 3. The proposed rule formulation.
The rule resistance equation is thus the following:
(
)
R CH = C1 + C 2 + C 3 ⋅ C µ ⋅ H AV ⋅ B + C ψ H M + C 4 ⋅ µ ⋅ L PAR ⋅ H TOT 2
(3.1)
where
(
H TOT = H M + 0.0175 ⋅ B + 0.451 ⋅ H M B + 0.0087 ⋅ B 2
H AV = H M + 0.014 ⋅ B
0.87 + cos ϕ 2
sin ϕ 2
+
,
Cµ = µ
2 + 1.7 cos ϕ 2
1 + 3 sin 2 ϕ
)
(3.2)
(3.3)
(3.4)
2
Cψ = 0,047ψ − 2,115 ,
min 0.0
(3.5)
 tan ϕ 2 
ψ = arctan

 sin α 
BL par
C1 = f1 ⋅
+ (1 + 0.021ϕ1 ) ⋅ (f 2 B + f 3 L bow + f 4 BL bow )
2T
+1
B
T  B2

C 2 = (1 + 0.063φ1 ) ⋅ (g1 + g 2 B) + g 3 1 + 1.2  ⋅
B L

(3.6)
(3.7)
(3.8)
The first two terms in Eq. (3.1) represent the level ice resistance and the two last ones
the brash ice resistance. The constants C1 and C2 apply only for ice class IA Super.
For lower classes they are to be taken as zero. For ships of ice class IA Super with a
bulb, the stem angle φ1 is to be taken as 90o. The stem angle must be between 0º and
90º. The values for constants used are:
C3 = 18.4 kN/m2
C4 = 0.55 kN/m3
f1 = 23 N/m2
f2 = 45.8 N/m
f3 = 14.7 N/m
f4 = 29 N/m2
g1 = 1537.3 N
g2 = 172.3 N/m
g3 = 398.7 N/m1.5
Table 3.1. The rule values for HM, hI and C5.
Ice class:
HM [m]
hi [m]
IAS
1,0
0,1
IA
1,0
0
IB
0,8
0
IC
0,6
0
The rule resistance is derived for a channel profile which contains the influence of the
side ridges. Thus the channel profile is assumed to get thicker moving from the
channel center line towards the edges by an angle δ = 2º. The brash ice is assumed to
be displaced sideways so that it comes to rest under the original brash ice. The angle
of repose of the brash ice material is assumed to be 22.6º. The channel dimensions
used in the rule formulation are given in Fig. 3.1.
71
BE/2
B/2
BE/4
HM
δ = 2º
HTOT
HAV
γ = 22.6º
Fig. 3.1. The rule brash ice channel dimensions. In the rule proposal, BE = 1.6B.
The required propulsion power is the power that gives high enough thrust to exceed
the ice resistance in the design ice conditions and speed. The resulting formulation for
the required propulsion power PD is
PD = K e
(R ch )
3
2
(3.9)
Dp
where Ke is given in the Table 3.2, Dp is propeller diameter and Rch is the rule channel
resistance.
Table 3.2. Values of the constant Ke.
Propeller type or
machinery
1 propeller
2 propeller
3 propeller
CP or electric or hydraulic
propulsion machinery
2,03
1,44
1,18
FP propeller
2,26
1,6
1,31
The powering requirement formulation is the same for all ice classes. The difference
between the classes is included in the channel resistance formula.
72
Appendix 4. The ships used in the validation of the new power requirement.
α
[o]
ϕ1
[o]
ϕ2
[o]
L
[m]
B
[m]
T
[m]
Lbow
[m]
Lpar
[m]
Awf
[m2]
Dp
[m]
prop.
no/type
Pinst
[kW]
P2002
[kW]
Pnew
[kW]
38.0
39.0
39.0
92.0
16.2
5.2
24.4
38.0
310.0
3.05
1/CP
2740
4582
3913
22.0
35.0
35.0
105.0
17.0
6.6
32.3
41.0
420.0
4.15
1/CP
4120
3556
3227
23.0
90.0
41.0
102.7
17.0
5.8
29.4
44.0
340.0
3.60
1/CP
2960
2991
2910
23.0
31.0
29.0
116.3
21.0
6.2
33.4
51.0
440.0
3.80
1/CP
5520
3768
3571
19.0
47.0
35.0
105.3
17.6
6.6
33.5
37.0
400.0
3.70
1/CP
3680
3037
2694
24.0
29.0
29.0
155.2
21.5
9.5
32.9
76.3
490.0
5.65
1/DE
11470
4494
4068
19.0
90.0
35.0
116.2
19.0
6.1
43.1
50.0
490.0
3.70
1/CP
5920
5917
5641
23.0
31.0
60.0
97.4
16.0
5.8
25.0
33.0
280.0
3.60
1/CP
2960
2788
2704
Finnmerchant/IAS
ex: Arcturus
17.0
90.0
24.0
146.0
25.0
8.3
52.9
73.0
710.0
5.70
1/CP
13200
7152
6170
Tervi/IA
37.0
41.0
39.0
198.3
30.2
12.5
33.8
132.2
745.0
7.10
1/CP
10800
8996
6479
Finnhansa/IAS
26.0
90.0
28.0
171.3
28.7
6.8
48.5
78.5
890.0
5.0
2/CP
23040
7561
6608
Mariella/IAS
22.0
90.0
11.0
159.6
28.4
6.78
52.0
104.2
886.0
4.5
2/CP
23000
8347
6557
Birka Princess/IA
21.0
90.0
19.0
129.1
24.7
5.6
50.5
28.6
803.0
2.8
2/CP
17600
4475
2983
Ship/ice class
Envik/IAS
Kemira/IAS
Link Star/IA
Solano/IA
Atserot/IA
ex: Tebostar
Uikku/IAS
Finnoak/IAS
ex: Ahtela
Aila/IA
73
Futura/IC
25.0
90.0
90.0
231.2
40.0
14.0
49.7
126.5
1560.
8.0
1/CP
10860
6063
6069
Arkadia/IC
37.0
90.0
67.0
184.5
32.2
11.7
27.1
126.4
585.0
5.4
1/CP
9267
7284
5817
Windia/IC
23.0
66.0
39.0
68.3
11.9
4.1
20.4
25.2
161.0
2.1
1/FP
1100
1012
1314
ex. Sirius/IB
19.0
61.0
47.0
79.0
12.0
4.6
24.9
38.4
138.0
2.2
1/FP
1300
1877
2252
Nossan/IB
35.0
90.0
73.0
84.9
13.2
5.5
14.8
54.9
148.0
3.2
1/CP
1470
2321
1935
Shuttle
Göteborg/IA
50.0
90.0
25.0
82.5
13.0
3.6
6.6
74.2
46.7
3.2
1/CP
2000
1636
2127
Mastera/IAS
41.0
90.0
66.0
242.8
44.0
14.5
49.2
124.2
1370.
7.5
1/DE
16000
36067
19199
Nikar G/IA
34.0
45.0
90.0
78.9
12.5
5.3
15.0
60.6
102.0
2.8
1/CP
1800
3400
2975
Cleopatra/IA
29.0
45.0
61.0
78.8
12.6
5.4
17.1
44.9
146.0
2.7
1/CP
1840
2914
2698
Rijnborg/IA
36.0
45.0
64.0
80.2
12.5
5.0
12.2
52.1
98.0
2.4
1/CP
1700
3653
3156
Atria/IA
32.0
45.0
70.0
92.4
13.6
6.0
16.0
63.0
155.0
2.96
1/CP
1975
3644
3193
Kirsten/IA
30.0
45.0
47.0
85.0
12.5
5.3
15.5
53.0
126.0
2.6
1/FP
1845
3031
3036