ISO 15016:2002

INTERNATIONAL ISO
STANDARD 15016
First edition
2002-06-15
Ships and marine technology — Guidelines
for the assessment of speed and power
performance by analysis of speed trial data
Navires et technologie maritime — Lignes directrices pour l'évaluation des
performances de vitesse et de puissance par analyse des données
d'essais de vitesse
Reference number
©
ISO 2002
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©  ISO 2002
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ii © ISO 2002 – All rights reserved

Contents Page
Foreword.iv
Introduction.v
1 Scope .1
2 Terms and definitions .1
3 Symbols and abbreviations.1
3.1 Symbols.1
3.2 Abbreviations.5
4 Trial conditions .5
4.1 Wind .5
4.2 Sea state .5
4.3 Water depth .6
4.4 Current.6
5 Speed and power measurement .6
5.1 Runs.6
5.2 Steering.6
5.3 Measured and observed data .6
6 Analysis procedure .8
6.1 Flow of trial analysis .8
6.2 Evaluation of acquired trial data .12
6.3 Correction of ship performance for resistance increase .16
6.4 Correction of ship performance for current .18
6.5 Correction of ship performance for air resistance.20
6.6 Correction of ship performance due to shallow water effects.21
6.7 Final ship performance .21
7 Example of method of analysis.21
Annex A (normative) Resistance increase due to wind.28
Annex B (normative) Resistance increase due to waves .31
Annex C (normative) Effect of steering .38
Annex D (normative) Effect of water temperature and salt content .40
Annex E (normative) Effect of vessel condition .42
Annex F (normative) Effect of shallow water .43
Bibliography.45

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO
member bodies). The work of preparing International Standards is normally carried out through ISO technical
committees. Each member body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, governmental and non-governmental, in
liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
The main task of technical committees is to prepare International Standards. Draft International Standards adopted
by the technical committees are circulated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this International Standard may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 15016 was prepared by Technical Committee ISO/TC 8, Ships and marine technology, Subcommittee SC 9,
General requirements.
Annexes A to F form a normative part of this International Standard.
iv © ISO 2002 – All rights reserved

Introduction
This International Standard concerns the method of analysing the results obtained from speed trials.
The primary purpose of speed trials is to determine ship performance in terms of speed, power and propeller
revolutions under prescribed ship conditions, and thereby verify the satisfactory attainment of the contractually
stipulated ship speed. Ship speed is that realized under the contractually stipulated conditions which usually are no
wind, no waves, no current, deep water, smooth hull and propeller surfaces.
Such stipulated conditions cannot normally all be expected to be met during the actual trials. In practice, certain
corrections for the environmental conditions have to be considered, as for water depth, wind, waves and current.
The purpose of this International Standard is to define basic requirements for the performance of speed trials, and
to provide procedures for evaluation and correction of speed trials covering all influences which may be relevant for
the individual trial runs based on sound scientific grounds, thus giving confidence to the customer with respect to
the final results.
The procedure specified in this International Standard has been derived largely on the basis of published data on
speed trials and on ship performance, the more important among them being listed in normative annexes A to F.
INTERNATIONAL STANDARD ISO 15016:2002(E)

Ships and marine technology — Guidelines for the assessment of
speed and power performance by analysis of speed trial data
1 Scope
This International Standard specifies the procedure to be applied in analysing the results of speed trials for ships,
with reference to the effects which may have an influence upon the speed-power-revolutions relationship.
The applicability of this International Standard is limited to commercial ships of the displacement type.
The instrumentation to be used in the speed trials is not specifically indicated, nor is the method of conducting the
trials. Calibrated instruments and their methods of use commonly adopted for such trials should be acceptable.
In this International Standard, it was decided that the unit to express the amount of an angle should be “rad”
(radian) and that the unit of speed should be “m/s” (metres per second). Nevertheless, “°” (degree) as a unit for an
angle and “kn” (knot) as a unit for speed may be used. However, the units for the angles and speeds which appear
in calculation formulas are to be “rad” and “m/s” without exception. Moreover, for the convenience of the users of
this standard, numerical values using the units of degree and knot are stated jointly at appropriate places.
2 Terms and definitions
For the purposes of this International Standard, the following terms and definitions apply.
2.1
propeller pitch
design pitch for controllable pitch propellers
2.2
brake power
power delivered by the output coupling of the propulsion machinery before passing through any speed-reducing
and transmission devices and with all continuously operating engine auxiliaries in use
2.3
shaft power
net power supplied by the propulsion machinery to the propulsion shafting after passing through all speed-reducing
and other transmission devices and after power for all attached auxiliaries has been taken off
3 Symbols and abbreviations
3.1 Symbols
A : area of midship section under water
M
A: rudder area
R
A : area of maximum transverse section exposed to wind (area of portion of ship above waterline
XV
projected normally to the longitudinal direction of ship)
B : breadth, moulded, of ship
b: rudder span
R
C : wind resistance coefficient
AA
C : wind resistance coefficient in head wind
AA0
C: block coefficient
B
C : frictional resistance coefficient
F
C : total resistance coefficient
T
D: propeller diameter
f: frequency
F: Froude number
n
g : acceleration due to gravity
h: water depth
H : total wave height
H : significant wave height of seas
1/ 3
H : significant wave height of swell
S1/ 3
J : propeller advance ratio
k: wave number
K ψ : directional coefficient of wind resistance
( )
WR
K: torque coefficient
Q
K : torque coefficient of propeller converted from behind to open water condition
QO
K: thrust coefficient
T
L : length of ship between perpendiculars
pp
m : mass in general
n : propeller frequency of revolutions
P: propeller pitch
P: brake power
B
P: delivered power
D
P : shaft power (= 2 pnQ)
S
Q: shaft torque
2 © ISO 2002 – All rights reserved

R: resistance in general
R : resistance increase due to wind
AA
R : resistance increase due to displacement
ADIS
R : resistance increase due to temperature and salt content
AS
R: frictional resistance
F
R: total resistance
T
R : resistance increase due to waves
AW
R : resistance increase due to drifting
ββ
R : resistance increase due to steering
δδ
Sf : spectral density function of unidirectional waves
( )
S : real slip ratio
R
S : wetted surface area
W
t : thrust deduction fraction
T : period or temperature in general
T : average period from zeroth and first moment
T : average period from zeroth and second moment
T : mean wave period of seas
m
t : resistance deduction fraction due to steering
R
T : mean wave period of swell
Sm
T: water temperature
W
V : effective inflow velocity to rudder
eff
V: current velocity
F
V : ship's speed over the ground
G
V : ship's speed through the water
S
V : relative wind velocity
WR
V : true wind velocity
WT
w : Taylor wake fraction in general
β: drift angle
δ: rudder angle
R
∆: displacement force
∆R : total resistance increase
∆ r : response increase due to regular waves (=∆rr+∆ )
∆ r : resistance increase due to radiation in regular waves
∆r : resistance increase due to diffraction in regular waves
ζ: wave amplitude
A
η : efficiency in general
η: relative rotative efficiency
R
η : transmission efficiency: ratio PP/ or PP/
T DS DB
λ : aspect ratio of rudder
R
π : = 3,141 592 6
ρ : mass density in general
ρ : mass density of air
A
22 2
τ: load factor R/1ρDV −−w1 t=K/J
()( )
()ST
χ : incident angle of waves (head wave: χ = π rad)
ψ: yaw amplitude
A
ψ: course direction
ψ : relative wind direction: positive direction from which the wind is blowing; head wind = 0 (0°)
WR
ψ : true wind direction: positive direction from which the wind is blowing; wind from the north = 0 (0°)
WA
ν: kinematic viscosity
ω : circular frequency of incident waves
ω : circular frequency of encounter
e
4 © ISO 2002 – All rights reserved

3.2 Abbreviations
BSRA: The British Ship Research Association
ITTC: International Towing Tank Conference
JTTC: Japan Towing Tank Committee
KSNAJ: The Kansai Society of Naval Architects, Japan
RINA: Royal Institute of Naval Architects, UK
SNAJ: The Society of Naval Architects of Japan
SNAME: The Society of Naval Architects and Marine Engineers, USA
SRAJ: The Shipbuilding Research Association of Japan
WJSNAJ: The West — Japan Society of Naval Architects
4 Trial conditions
4.1 Wind
Wind speed and direction shall be measured as relative wind using the ship’s wind indicator. Continuous recording
of the relative wind during each run is recommended.
Whenever possible, wind force during the speed trials shall not be higher than
 Beaufort Number 6, L W 100 m, or
pp
 Beaufort Number 5, L < 100 m.
pp
4.2 Sea state
If possible, instruments should be used to determine the wave height, wave period and direction of seas and swell,
as buoys or instruments onboard the ships (e.g. seaway analysis radar). Wave characteristics may be determined
from observations by multiple observers, including the captain, preferably supported by hindcasting if the expected
effect of the seaway is significant.
The total wave height, H, which is the sum of significant wave heights of seas H and swell H , shall satisfy
1/ 3 S1/3
the following:
L W 100 m : the lower value of Hu 0,015L or 3 m (1)
pp pp
L < 100 m : Hu 1, 5 m
pp
where
H = HH+ (m); (2)
1/ 3 S1/ 3
L is the length of ship between perpendiculars, in metres.
pp
4.3 Water depth
Water depth in the trial area shall be obtained either from sea charts or by means of echo-sounder measurements.
To obtain satisfactory results, the water depth shall satisfy the following:
∆VV/0u,02 (3)
SS
where
V is the ship's speed, in metres/second;
S
∆V is the ship's speed loss due to shallow water, in metres/second
S
The ship's speed loss due to the effect of shallow water can be derived from normative annex F.
4.4 Current
Current speed and direction shall be obtained either as part of the evaluation of run and counter-run of each double
run or by direct measurement with a current gauge buoy.
5 Speed and power measurement
5.1 Runs
All speed trials shall be carried out using double runs, i.e. each run followed by a return run in the exact opposite
direction performed with the same engine settings. The number of such double runs shall not be less than three.
Preferably runs should be performed in head and following winds.
Each run shall be preceded by an approach run, which shall be of sufficient length to attain steady running
conditions.
5.2 Steering
The single amplitude of variation of heading angle, ψ , shall be within π/60 rad (3°).
A
The counter rudder to maintain a straight course shall be within π/36 rad (5°).
5.3 Measured and observed data
5.3.1 General data
Prior to the trial, the data specified below shall be recorded, based on measurements where relevant:
 date;
 area of trial;
 weather;
 mean water depth in area of trial;
 water temperature and density;
6 © ISO 2002 – All rights reserved

 air temperature;
 height of wind instrument above waterline;
 fore, midships and aft draughts;
 displacement;
 propeller pitch in the case of CPP.
It is recommended to retain a record of the following factors, which should prove useful for verifying the condition of
the ship at the time of the speed trial:
 time elapsed since last hull and propeller cleaning;
 surface condition of hull and propeller.
5.3.2 Data on each run
The following data shall be monitored and recorded on each run:
 clock time at commencement;
 time elapsed over the measured distance;
 course direction;
 ship's speed over ground;
 propeller frequency of revolutions;
 propeller shaft torque and/or brake power;
 relative wind velocity and direction;
 mean wave period, significant wave height and direction of waves (seas);
 mean wave period, significant wave height and direction of waves (swell);
 rudder angle;
 drift angle.
There are two kinds of power, one is shaft power and the other is brake power. Shaft power shall be calculated by
means of measuring shaft speed and torque of the shaft. Both types of power can be used to evaluate the speed
and power performance. The analysis procedure in clause 6 uses shaft power.
Data such as ship's speed, frequency of revolutions of the propeller, torque, rudder angle, and drift angle to be
used for analyses shall be the average values derived on the measured distance. If the draughts are needed for
each run, they may be estimated using a loading computer, based on the data prior to the trial and the fuel
consumption up to that time.
6 Analysis procedure
6.1 Flow of trial analysis
The analysis of trial data is basically divided into the following six steps, as shown in Figure 1.
a) Step 1: evaluation of acquired trial data.
b) Step 2: correction of ship's performance for resistance increase.
c) Step 3: correction of ship's performance for current.
d) Step 4: correction of ship's performance for air resistance.
e) Step 5: correction of ship's performance for shallow water.
f) Step 6: final ship's performance.
The procedure is described by reference to the numbered columns in Table 1.
8 © ISO 2002 – All rights reserved

a
P may be used alternatively.
B
Figure 1 — Flowchart of speed trial analysis
Table 1 — Format of speed trial data analysis (Part 1)
Hull Rudder Propeller
L
PP B d CB A A A b D P
trim ∆ M XV R R
Efficiency Depth Density Temperature

η η ρ
1− t h T
ρ W
T R A
1 Main engine output setting Remarks
i
2 Run number i +1
ψ
3 Course direction (rad)
Measured or observed data
V
4 Ship's speed over ground (m/s) G
5 Propeller frequency of revolutions (Hz)
n
P
6 Power measured (kW)
S
V
7 Relative wind velocity (m/s)
WR
ψ
8 Relative wind direction (rad)
WR
9 Directional coefficient of wind

resistance
K
VV=+V−2cV⋅V⋅os(ψ)
10 True wind velocity (m/s) V
WT WT WR G WR G WR
 
VVsinψψ+− sin ψ
() ()
 
−1 WR 0 WR G 0
ψ ψ = tan
11 True wind direction (rad)
WT WT  
VVcosψψ+− cos ψ
() ()
 WR 0 WR G 0 

In case of visual observations, the observed period value is
12 Mean wave period (Seas) (s)
T
m
to be used as T . When measured data are available, T
m
13 Significant wave height (Seas) (m) H
1/ 3
is to be used as T
m
χ
14 Incident angle of waves (Seas) (rad)
χ = π in head waves
15 Mean wave period (Swell) (s)
T
Sm
16 Significant wave height (Swell) (m) H
S1/ 3
χ
17 Incident angle of waves (Swell) (rad)
S
18 Rudder angle (rad)  Mean value during the measurement of ship's speed
δ
R
19 Drift angle (rad) β Mean value during the measurement of ship's speed

10 © ISO 2002 – All rights reserved

Analysed data (Part 2)
20 Delivered power (kW) P PP= ⋅η
D DS T
21 Torque coefficient
K K=⋅500PDηρ/π / / /n
Q QDR
22 Propeller advance ratio
J
JK in Figure 2
( )
Q
23 Load factor
τ
τ J in Figure 2
( )
S
24 Slip ratio
SD=−1/JP
R
R
1/−=wnDJ V
25 Wake factor 1− w
G
26 Mean wake factor Mean value of data in both runs of a double run
()1− w
m
V
Vn=−DJ/1w
27 Mean speed through water (m/s) ()
S S
m
R
28 Total resistance (N) R=−ρDV11w−t τ
T ()( )
TS
m
Load correction
29 Resistance increase due to wind (N) R RC=⋅0,5ρψ⋅K ⋅A⋅V : see annex A
()
AA AA A AA0 WR XV WR
30 Resistance increase due to waves (N) R
: see annex B
AW
31 Resistance increase due to steering (N)
R Rt=−0,5ρ 1fλδAV : see annex C
() ( )
δδ
δδ Ra R ReffR
22 2
R Rd=π0,25ρβV : see annex C
32 Resistance increase due to drift (N)
ββ
ββ S
33 Resistance increase due
to temperature and salt content (N) R
: see annex D
AS
34 Resistance increase due
to displacement (N) R : see annex E.
ADIS
35 Total resistance increase (N)
∆R ∆=RR +R +R +R +R +R
AA AW δδ ββ AS ADIS
36 Correction for load factor ∆τ =∆RR/ ⋅τ τ : see [23]
∆τ
T
τ τ =ττ−∆
37 Load factor
1 1
J JJ= τ in Figure 2
38 Propeller advance ratio ( )
K KK= in Figure 2
39 Torque coefficient Q1 Q1
Q J
()
n
40 Propeller frequency of revolutions (Hz) 1 nn= J /J
1 1
41 Torque coefficient  ′
′ K =Kn in Figure 3
K ( )
QQ1
Q
42 Propeller advance ratio
′ ′ ′
J JJ= K in Figure 2
( )
Q
43 Load factor
′ ′′
τ ττ= J in Figure 2
( )
′
44 Correction of ship's speed (m/s) ∆V ∆=VaDn/1−w ⋅K −K
( ) ( )
G GQQ
m
′
V ′
45 Speed over ground (m/s) VV=+∆V
G
GG G
′ ′′
P P=⋅PK /K
46 Delivered power (kW)
D DD Q Q
′′
′ PP= /η
P
SD T
47 Shaft power (kW) S
Current (Part 3)
48 Time of day at middle of run t  ′
V : Speed at i +1 -th run with same power condition
i ( )
G(i+1)
as i -th run
49 Time at middle of serial runs t
50 Speed correction for RPM
′′
V ′′ ′ ′
difference (m/sec) VV=⋅n /n V : Speed at i -th run
G(i+1)
G(ii++1) G( 1) G(i)
ii+1
() ( )
′′ ′
V VV=−V /2
51 Mean current velocity (m/sec) ()
FM G(ii+1) G( )
FM
V
52 Current during each run (m/sec) VV= t in Figure 4
F ( )
FF i
′
V ′′
VV=+V
53 Speed without current (m/sec) S
SG F
Wind correction
54 Load factor increase ∆τ
∆=τρ0,5 AC /ρ/1()−t /1(−w) /D
A AAXVAA0
m
55 Load factor τ τ =+ττ′ ∆
2 2A
J
56 Propeller advance ratio JJ= (τ ) in Figure 2
2 22
K K =KJ in Figure 2
57 Torque coefficient ( )
Q2 Q2 Q 2
n nn=⋅J′/J
58 Propeller frequency of revolutions (Hz)
2 22
59 Torque coefficient K
K =Kn in Figure 3
Q0 ( )
Q0 Q2
′ ′ ′
∆V ′ ∆=VaDn/1−w ⋅K −K K : see [41]
60 Correction of ship's speed (m/sec) ()()
S SQ0Q Q
m
′′′ ′ ′
61 Ship's speed after correction (m/sec) V′′ VV=−∆V V : see [53]
S SS S S
′′
P =⋅PK /K K : see [21]
62 Delivered power (kW) P
D0 D Q0 Q Q
D0
PP= /η
63 Shaft power (kW) P
S0 D0 T
S0
Shallow water
′′ ′′′′ ′′ ′′ ′′′′
64 Speed loss (m/sec) ∆V ∆=VV+∆V V ∆VV/: see annex F
( )
S SS S S SS
′′′′
65 Ship's speed after correction (m/sec) VV=+∆V
V
S0 S S
S0
6.2 Evaluation of acquired trial data
6.2.1 Performance data
Each item shall be filled in Table 1 as follows:
 [1]: main engine output;
 [2]: run number;
 [3]: course (direction) of run;
 [4] to [6]: ship performance data:
ship's speed over the ground, propeller frequency of revolutions, measured power;
 [7] to [9]: wind data:
relative wind velocity and direction, directional coefficient of wind resistance;
12 © ISO 2002 – All rights reserved

 [10]: true wind velocity.
True wind velocity, V , in metres per second, is calculated by
WT
VV=+V−2cV⋅V⋅os(ψ) (4)
WT WR G WR G WR
where
V is the ship's speed over the ground, in metres per second;
G
V is the relative wind velocity, in metres per second;
WR
ψ is the relative wind direction, in radians;
WR
 [11]: true wind direction.
True wind direction, ψ , in radians, is calculated by
WT
 )
VVsin(ψψ+−) sin(ψ
−1 WR 0 WR G 0
ψ = tan (5)

WT
VVcos(ψψ+−) cos(ψ )

 WR 0 WR G 0
where
ψ is the ship's course direction, in radians
 [12] to [17]: wave data (seas and swell).
Significant height and mean period of waves for seas and swell shall be noted when appropriate. Wave data shall
be determined as described in 4.2. When the measured data are available, the averaged period from zeroth and
second moment, T , shall be noted and equation (B.6) shall be applied. The incident angle of waves, χ, is defined
in Figure B.2.
 [18] and [19]: Steering data:
rudder angle, drift angle.
6.2.2 Working point of propeller in measurement
[20] to [23]: power data shall be filled in Table 1 as follows.
The torque coefficient, K , is calculated from the delivered power and propeller frequency of revolutions as
Q
follows:
1 000 P
D
K=× ×η (6)
QR
2π
ρnD
where
PP=×η , in kilowatts; (7)
DS T
D is the propeller diameter, in metres;
n is the propeller frequency of revolution, in hertz;
P is the shaft power, in kilowatts;
S
P is the delivered power, in kilowatts;
D
η is the relative rotative efficiency (η may be determined from either the design data base or preferably by
R R
model tests);
η is the transmission efficiency (η may be determined from either the design data base or mechanical
T T
tests);
ρ is the mass density of sea water, in kilograms per cubic metre.
The propeller advance ratio, J, and load factor, τ, are then determined by making use of a diagram of propeller
characteristics in open water as shown in Figure 2.

Key
1 Torque coefficient
2 Load factor
Figure 2 — Propeller characteristic curves and working point
14 © ISO 2002 – All rights reserved

6.2.3 Calculation of wake factor
Each item shall be filled in Table 1 as follows:
a) [24]: slip ratio.
The real slip ratio, S , from measurement is calculated by
R
DJ
S =−1 (8)
R
P
where
J is the propeller advance ratio;
P is the propeller pitch, in metres.
b) [25]: wake factor.
For both runs of a double run, the wake factor 1− w is determined from the ship's speed over the ground, V ,
( )
G
and the propeller advance ratio, J, based on the torque identity and on the open water diagram of the propeller.
nD
1−=wJ× (9)
V
G
c) [26]: mean wake factor.
The mean wake factor (1− w) is determined as the mean of the wake factors obtained for the individual runs of a
m
double run.
d) [27]: ship's speed through the water.
The ship's speed, through the water, V , in metres per second, is approximated by
S
nD
VJ=× (10)
S
(1− w)
m
e) [28]: total resistance of ship.
The total resistance of a ship, R , in newtons, is calculated by
T
R =⋅ρDV⋅ (1−w) (1−t)⋅τ (11)
TS m
where
1− t is the thrust deduction factor;
τ is the load factor;
1− t may be determined from either the design data base or model tests.
6.3 Correction of ship performance for resistance increase
6.3.1 Effect of resistance increase on load factor
Environmental and external disturbances, such as sea water conditions, wind, waves and steering, increase the
resistance of a ship, and corrections of the ship resistance for these disturbances should be made. The ship
resistance should also be corrected for the deviation of the actual displacement from the specified displacement.
Resistance increases due to the disturbances and the deviations are calculated by the procedures specified in
annexes A, B, C,D and E. The methods and procedures presented in these annexes are the latest available today.
Other scientifically based methods may be adopted as agreed between the shipyard and owner. Some of these
resistance increases can also be determined from model tests.
[29] to [35] in Table 1 concern the total resistance increase.
The total resistance increase, ∆ R, in newtons, is given by
∆=RR +R +R +R +R +R (12)
AA AW δδ ββ AS ADIS
where
R is the resistance increase due to wind, in newtons;
AA
R is the resistance increase due to waves, in newtons;
AW
R is the resistance increase due to steering, in newtons;
δδ
R is the resistance increase due to drifting, in newtons;
ββ
R is the resistance increase due to water temperature and salt content, in newtons;
AS
R is the resistance increase due to deviation of displacement, in newtons.
ADIS
[36] in Table 1 concerns the correction for load factor;
The effect of resistance increases on load factor ∆τ is given by
∆ R
∆=τ ×τ (13)
R
T
6.3.2 Torque curve
[37] in Table 1 concerns the corrected load factor.
The load factor corrected by resistance increase, τ , is given by
τ =−ττ∆ (14)
[38] and [39] in Table 1 concern the propeller advance ratio and torque coefficient, respectively.
The propeller advance ratio, J , and torque coefficient, K , are obtained by using a diagram of propeller
1 Q1
characteristics in open water as shown in Figure 2.
[40] in Table 1 concerns the propeller frequency of revolutions.
16 © ISO 2002 – All rights reserved

The propeller frequency of revolutions, n , in hertz, is calculated by
J
nn=× (15)
J
A graph shall be plotted with the values of n and K as shown in Figure 3, and the mean curve Kn∼ (•) is
1 Q1 Q1 1
then determined using the least-squares method or alternatives.

Figure 3 — Torque coefficient curves and propeller frequency of revolutions
6.3.3 Working point of the propeller taking account of resistance increase
[41] in Table 1 concerns the torque coefficients.
Making use of the mean curve of K ∼ n , torque coefficient K′ ()n is determined.
Q1 1 Q
[42] and [43] in Table 1 concern the propeller advance ratio and load factor.
′′ ′′
The propeller advance ratio JK and load factor τ K are obtained from Figure 2.
( ) ()
Q Q
6.3.4 Ship performance in no air and no waves
[44] in Table 1 concerns the correction of ship's speed.
The correction of ship's speed over the ground due to resistance increases ∆V , in metres per second, is
G
calculated using equations (16) and (17).
aD⋅⋅n⋅()K′ −K
QQ
∆=V (16)
G
(1− w)
m
where
JJ−
HL
a = (17)
()KK−
QH QL
where
J is the propeller advance ratio at K obtained from a diagram of propeller characteristics;
H QH
J is the propeller advance ratio at K obtained from a diagram of propeller characteristics;
L QL
K are higher values over the maximum measured value of K ;
QH Q
K are lower values below the minimum measured value of K .
QL Q
′
[45] to [47] in Table 1 concern ship's speed over the ground, V , in metres per second, delivered power at
G
propeller, P′ , in kilowatts, and shaft power, P′ , in kilowatts, when a ship runs at n in no air and no waves are
D S
calculated using equations (18), (19) and (20), respectively.
′
VV=+∆V (18)
GG G
′
K
Q
′
PP=⋅ (19)
DD
K
Q
P′
D
′
P = (20)
S
η
T
6.4 Correction of ship performance for current
6.4.1 Time history of current
[48] and [49] in Table 1 concern time.
The time at middle of run and time at middle of serial runs are noted.
′′
[50] in Table 1, ship's speed at i +1 th run, V , in metres per second, at the propeller frequency of revolutions
( )
G(i+1)
n is calculated by
i
()
n
i
()
′′ ′
VV=× (21)
G(ii++1) G( 1)
n
i+1
()
where
n is the propeller frequency of revolutions at i th run, in hertz;
( )
()i
n is the propeller frequency of revolutions at i +1 th run, in hertz;
( )
()i+1
′
V is the ship's speed over the ground at (i +1) th run, in metres per second.
G(i+1)
Equation (21) is applicable if the engine(s) are not operated in constant frequency mode during double runs.
18 © ISO 2002 – All rights reserved

[51] in Table 1, the mean current velocity, V , in metres per second, at the intermediate time of each series of
FM
measurements is calculated by
′′ ′
VV−
G1ii+ G
() ()
V = (22)
FM
where V ′ is the ship's speed over the ground at i th run, in metres per second.
( )
G(i)
The time history of current is illustrated in Figure 4.

Figure 4 — Tidal current curve
6.4.2 Ship's speed corrected with current effect
[52] and [53] in Table 1:
The time history of current gives current velocity, V , at each intermediate time of running, t .
F i
The ship's speed corrected with current effect, V ′ , in metres per second, is given by
S
VV′′=+V (23)
SG F
When the current is measured by a current meter, the data can be used directly.
6.5 Correction of ship performance for air resistance
6.5.1 Torque curve
The ship's performance in no wind, no waves and no current is obtained by taking account of the effect of air
resistance due to the ship running in no wind conditions on the load factor and torque coefficient.
[54] in Table 1: Change of load factor for a ship running in no wind.
∆τ is given by
A
ρ⋅⋅AC
A XV AA0
∆=τ (24)
A
2(ρ⋅−Dt1)(1−w)
m
where
A is the above-water cross-sectional area of the ship (area of portion of ship above waterline projected
XV
normally to the longitudinal direction of ship), in square metres;
C is the wind resistance coefficient in a head wind;
AA0
ρ is the mass density of air, in kilograms per cubic metre.
Α
If the contract stipulates a certain head wind and/or wave conditions, equation (24) is modified accordingly.
′
[55] in Table 1: Load factor, τ , is calculated using ∆τ and τ :
2 A
′
τ = τ + ∆τ (25)
2 A
[56] and [57] in Table 1: The propeller advance ratio, J , and torque coefficient, K , corresponding to τ is
2 Q2 2
obtained from the propeller characteristic curves shown in Figure 2.
[58] in Table 1: The propeller frequency of revolutions, n , in hertz, corresponding to J is calculated by
2 2
′
J
nn=× (26)
J
and each calculated n gives a point as shown in Figure 3, by which means a curve of torque coefficient versus
propeller frequency of revolutions ( ) is determined using the least-squares method or alternatives.
6.5.2 Ship performance in no wind, no waves and no current, or other stipulated conditions
[59] in Table 1: The torque coefficient, K , which corresponds to the propeller frequency of revolutions, n, is
Q0
determined from the torque coefficient curves as shown in Figure 3.
[60] in Table 1: Correction of ship's speed, ∆V ′ , in metres per second, for a ship running in no wind is calculated
S
by
′
aD⋅⋅n⋅()K −K
Q0 Q
′
∆=V (27)
S
(1− w)
m
′′
[61] to [63] in Table 1: Ship's speed, V , in metres per second, delivered power at propeller, P , in kilowatts, and
S D0
shaft power, P , in kilowatts, when a ship runs at n in no wind, no waves and no current are calculated by
S0
20 © ISO 2002 – All rights reserved

VV′′=−′ ∆V ′ (28)
SS S
K
Q0
PP=× (29)
D0 D
K
Q
P
D0
P = (30)
S0
η
T
6.6 Correction of ship performance due to shallow water effects
′′
[64]: Speed loss, ∆V , due to shallow-water effects is determined using Figure F.1 in normative annex F.
S
[65]: Ship's speed, V , in metres per second, corrected for shallow water is calculated by
S0
′′ ′′
VV=+∆V (31)
S0 S S
6.7 Final ship performance
Ship performance for each run in no wind, no waves, no current and deep water is obtained by the above analysis;
delivered power at propeller, P , shaft power, P , and ship's speed, V , at propeller frequency of revolutions,
D0 S0 S0
n, are calculated by equations (29), (30) and (31), respectively.
The final ship performance is determined as the mean of the performance of the individual runs of a double run.
7 Example of method of analysis
This example is based on data obtained during speed trials with a single-screw, large, oil tanker (VLCC) in the full
load condition. The ship dimensions are listed in Table 2.
Five double runs were carried out. A torsionmeter was used and an anemometer was equipped on the fore-mast in
the trial. Wave data were obtained from observation by eye.
The data measured during the trial are listed in Table 2 (from item 1 to 19).
a) The measured shaft power and propeller frequency revolutions are plotted against the ship speed in Figure 5
( ∆ mark).
b) The speed of the true wind during the trial varied from 8 m/s to 11 m/s, and it was a north wind. The wind
direction changed from south to north one day before the trial, therefore the sea was slight (wave height: 0,5 m
to speed of the 1,0 m). The resistance increase caused by the wind was calculated using the method specified
in annex A.
c) The swell varied from 2 m to 3 m, which developed as a typhoon approached. The trial was stopped for a while
after 6 runs were finished because the swell height became large, but it was resumed later. The resistance
increase caused by the waves was calculated using the method specified in annex B.
d) The rudder angle and drift angle were less than 0,01 rad (0,6°), so that the resistance increases are negligible.
e) The actual displacement was about 500 tonnes larger than the specified value, and the actual water density
was 0,1 % smaller than the specified value. The resistance increase due to these deviations is also negligible.
f) The depth of water was 500 m, so that the speed loss due to shallow water is negligible.
The analysed data are listed in Table 2 (from item 20 to item 65).
The load correction (from item 29 to 47 in Table 2) produced satisfactory results. Figure 6 shows the diagram of
torque coefficient versus propeller frequency of revolutions.
The tide analysis (from item 48 to 53) also produced satisfactory results. Figure 7 shows the tidal current curve.
The final performance in still air conditions is plotted in Figure 5 ({ mark).
Other data used in the analysis are described below:
a) propeller open-water characteristics:
J 0,550 0 0,600 0 0,650 0 0,700 0
K 0,211 9 0,190 7 0,168 9 0,146 5
T
10K 0,311 4 0,289 3 0,266 0 0,241 5
Q
b) C = 1, 0
AA0
c) Directional coefficient of wind resistance: Standard of JTTC (see Figure A.2)
22 © ISO 2002 – All rights reserved

Figure 5 — Examples of trial performance curves
Figure 6 — Example of torque coefficient curves and propeller frequency of revolution

Figure 7 — Example of tidal current curve
24 © ISO 2002 – All rights reserved

Table 2 — Example of speed trial data analysis
Hull  Rudder Propeller Efficiency, etc. Depth  Density Temperature
L C A A A b K K U T
Bd trim ' DP 1-th U
PP B M XV R R t R A W
2 2 2 3 3
m m m m ton mm m m °C
m m m kg/m kg/m
318,0 58,0 18,5 0,0 273 740 0,78 1 070 1 132 95,5 14,2 9,5 8,3 0,971 1,0 0,87 500,0 1 024,0 1 225 20,0
1 Main engine output setting 25 % 50 % 75 % NOR MCR
2 Run number 1 2 3 4 56789 10
3 Course direction (°) 355,0 175,0 355,0 175,0 355,0 175,0 175,0 355,0 175,0 355,0
\
(rad) 6,196 3,054 6,196 3,0546,196 3,0543,0546,196 3,0546,196
Measured or observed data
4 Ship's speed over ground (kn) V 8,57 10,81 11,76 13,96 14,03 15,71 16,36 15,11 16,40 15,40
G
(m/s) 4,409 5,561 6,050 7,182 7,218 8,082 8,416 7,773 8,437 7,922
5 Propeller frequency of revolutions (Hz) n 0,731 7 0,730 0 0,926 7 0,926 7 1,046 7 1,046 7 1,093 3 1,095 0 1,116 7 1,113 3
6 Power measured (kW) P 5 711 5 533 11 349 11 140 16 200 16 190 18 500 18 330 19 450 19 756
S
7 Relative wind velocity (m/s) V 15,3 4,0 15,0 2,8 16,0 0,7 0,4 16,5 0,0 16,5
WR
8 Relative wind direction (°) < 10,0 215,0 10,0 225,0 355,0 210,0 225,0 355,0 215,0 10,0
WR
(rad) 0,174 5 3,752 5 0,174 5 3,927 0 6,195 9 3,665 2 3,927 0 6,195 9 3,752 5 0,174 5
9 Directional coefficient of wind resistance K 1,040 – 0,980 1,040 – 0,820 1,020 – 1,040 – 0,820 1,020 – 0,980 1,040
V
10 True wind velocity (m/s) 10,98 9,13 9,10 9,37 8,83 8,70 8,70 8,78 8,44 8,81
WT
11 True wind direction (rad) < 0,157 0 0,166 7 0,202 9 0,125 6 6,037 46,236 2 6,228 46,031 46,195 9 0,244 1
WT
(°) 9,0 9,6 11,6 7,2 345,9 357,3 356,9 345,6 355,0 14,0
12 Mean wave period (Seas) (s) T 3,90 3,90 3,90 3,90 3,90 3,90 2,80 2,80 2,80 2,80
m
13 Significant wave height (Seas) (m) H 1,00 1,00 1,00 1,00 1,00 1,00 0,50 0,50 0,50 0,50
1/3
14Incident angle of wave (Seas) (°) x 170,0 350,0 170,0 350,0 170,0 350,0 350,0 170,0 350,0 170,0
(rad) 2,97 6,11 2,97 6,11 2,97 6,11 6,11 2,97 6,11 2,97
15 Mean wave period (Swell) (s) T 10,59 10,59 10,59 10,59 11,32 11,32 11,32 11,32 11,32 11,32
Sm
H
16 Significant wave height (Swell) (m) 2,0 2,0 2,0 2,0 2,5 2,5 2,5 2,5 3,0 3,0
S1/3
X
17 Incident angle of wave (Swell) (°) 40,0 220,0 40,0 220,0 40,0 220,0 220,0 40,0 220,0 40,0
S
(rad) 0,698 1 3,839 7 0,698 1 3,839 7 0,698 1 3,839 7 3,839 7 0,698 1 3,839 7 0,698 1
18 Rudder angle (°) G 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00
R
(rad) 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00
...