Executive Summery For a specific voyage from Cabot Strait to the English Channel with departure February 23rd at 00 UTC the effect of six Flettner rotors is calculated to reduce the total main engine output by 28%. The results also show that the main engine output can be reduced by almost 40% (with 6 rotors) by optimizing the voyage planning in accordance with the Flettner rotor effect – instead of normal weather routeing. These results are of course specific for this voyage and averaging over geographical and seasonal weather conditions would most likely result in less pronounced, reduced main engine outputs. However, in rough conditions where normal weather routeing optimization will dictate a longer route than the shortest Great Circle route, the reduction percentage of the main engine output could be significantly higher.

1. Carsten Kofoed Page 1 of 9 Issued
Type of Report:
Performance analysis report
Title of Report:
Analysis of the effect of Flettner rotors
With and without Flettner rotor weather routeing optimization
Updated
Client:
Windagain
Client’s Ref.:
Jørn Winkler
Author(s):
Carsten Kofoed
Thomas Fredberg
Initials:
CNK
TF
Date:
25 March 2011.
Checked and approved by:
Tue Lippert TLI
Date:
25 March 2011.
Date of distribution: Date:
25 March 2011.
Keywords:
Flettner rotor
Apparent wind
Optimizing
DMI ref.-no.:
110559
DMI – Maritime Service Analysis of the effect of Flettner rotors - updated 25 March 2011

2. Carsten Kofoed Page 2 of 9 Issued
Analysis of the effect of the Flettner rotor
With and without Flettner rotor weather routeing optimization
Executive Summery
For a specific voyage from Cabot Strait to the English Channel with departure February
23rd
at 00 UTC the effect of six Flettner rotors is calculated to reduce the total main
engine output by 28%. The results also show that the main engine output can be reduced
by almost 40% (with 6 rotors) by optimizing the voyage planning in accordance with the
Flettner rotor effect – instead of normal weather routeing. These results are of course
specific for this voyage and averaging over geographical and seasonal weather conditions
would most likely result in less pronounced, reduced main engine outputs. However, in
rough conditions where normal weather routeing optimization will dictate a longer route
than the shortest Great Circle route, the reduction percentage of the main engine output
could be significantly higher.
Figure 1. Weather conditions February 24th
2011 12:00 UTC (model output).
DMI – Maritime Service Analysis of the effect of Flettner rotors - updated 25 March 2011

3. Carsten Kofoed Page 3 of 9 Issued
1. Introduction
The aim of this report is to analyse the effect of Flettner rotors for a specific voyage and
furthermore to examine how the Flettner rotor effect can be maximized by optimizing the
route planning in accordance with the Flettner rotor effect graph. The basis of this report
is a specific voyage from Cabot Strait (Newfoundland) to the English Channel with
departure February 23rd
2011 at 00:00 UTC. This voyage is being planned in two ways;
one where the route is optimized according to normal weather routeing and another
where the route is optimized to get the maximum effect of the Flettner rotors. For both
routes the same speed loss algorithm is used to account for speed loss caused by wind,
wave and surface current conditions along the routes.
Figure 2. Optimal route in accordance with normal weather routeing and weather conditions
during the planned voyage. This route is close to a direct Great Circle (GC) route.
Figure 3. Route optimized in accordance with the Flettner rotor effect. The route is more
northerly than a direct GC.
2. Basic assumptions for the calculations
The following assumptions are the basis of the calculations:
The voyages are planned for a Bulk Carrier of 110,000 tons Dwt and with a
Maximum Continuous Rating (MCR) of 15820 kW, resulting in a Calm Water
Speed of 14.0 kts.
DMI – Maritime Service Analysis of the effect of Flettner rotors - updated 25 March 2011

4. Carsten Kofoed Page 4 of 9 Issued
DMI – Maritime Service Analysis of the effect of Flettner rotors - updated 25 March 2011
The vessel is fitted with 6 Flettner rotors (type WA620) and the effect of these
rotors is supplied by Windagain and is used ‘as is’.
The maximum effect of the Flettner rotors can not exceed MCR. This ensures
that unrealistically high outputs can not be reached in very rough conditions.
The total effect of main engine and Flettner rotor combined is constant at
15820 kW throughout the voyage. This means that the main engine output has
to be continuously adjusted e.g. reduced below MCR equal to the effect of the
Flettner rotors.
Added wind resistance due to the Flettner rotor, especially in headwind
conditions, has not been taken into account. This is due to the fact that the
Flettner rotors can be deactivated and collapsed/lowered in these conditions.
The optimum route in accordance with the Flettner rotor effect have to be
carried out, so that the time of arrival is not significantly later than the time of
arrival for the standard weather routeing optimized route.
3. Results
The results for the two routes are as follows:
Normal (GC) – 6 rotors
Date and time Lat. Long. Course Dist.
(nm)
Steam
Hours
Speed
(kts)
Wind
dir
(deg)
Wind
(kts)
Sea
(m)
Swell
dir
Swell
(m)
Curr.
dir
(deg)
Curr.
(kts)
23-02-2011 00:00 47°16´N 059°36´W
23-02-2011 12:00 46°12´N 055°50´W 112 168 12 14.00 335 26 3.1 305 1.2 355 0.5
23-02-2011 20:30 46°08´N 053°07´W 92 113 8.5 13.29 340 22 2 275 1.6 50 0.8
24-02-2011 12:00 47°15´N 048°43´W 68 193 15.5 12.45 350 25 3.3 15 3.1 40 0.6
25-02-2011 12:00 48°57´N 041°19´W 73 313 24 13.04 310 18 1.6 355 4.5 0 0
26-02-2011 12:00 50°03´N 033°13´W 80 323 24 13.46 245 21 1.9 330 4 275 0.2
27-02-2011 12:00 50°41´N 024°37´W 86 331 24 13.79 210 17 1.4 290 3.5 250 0.1
28-02-2011 12:00 50°38´N 016°05´W 93 325 24 13.54 195 18 1.6 270 2.7 235 0.1
01-03-2011 12:00 49°52´N 007°28´W 100 334 24 13.92 120 3 0.3 285 2.3 0 0
01-03-2011 20:30 49°27´N 004°38´W 102 113 8.5 13.29 65 15 1.2 290 2.2 0 0
Table 1. Basic figures for the normal (GC) route. All values are averages since last position and
weather and ocean data are evaluated from model data and observations.
Normal (GC) – 6 rotors
Date and time W
(kts)
V
(kts)
Alpha
(rad)
A
(kts)
A
(Bf)
Beta
(deg)
kW % of
MCR
kWh
6 rotors
23-02-2011 00:00
23-02-2011 12:00 26 14.0 2.39 18.4 5 105.8 4420 27.9% 53040
23-02-2011 20:30 22 13.3 1.95 21.0 5 76.1 8580 54.2% 72930
24-02-2011 12:00 25 12.5 1.36 30.2 7 54.2 15820 100.0% 245210
25-02-2011 12:00 18 13.0 2.15 15.5 4 77.9 1690 10.7% 40560
26-02-2011 12:00 21 13.5 2.88 8.7 3 141.4 0 0.0% 0
27-02-2011 12:00 17 13.8 2.16 14.7 4 73.1 2600 16.4% 62400
28-02-2011 12:00 18 13.5 1.78 20.2 5 60.9 9750 61.6% 234000
01-03-2011 12:00 3 13.9 0.35 16.8 4 3.5 0 0.0% 0
01-03-2011 20:30 15 13.3 0.65 26.8 6 19.7 3510 22.2% 29835
Total 737975
Table 2. Results from the Apparent wind calculations and rotor effect results for the normal (GC)
route. The rotor effects are estimated from Apparent wind/Rotor effect curves provided by
Windagain.

5. Carsten Kofoed Page 5 of 9 Issued
DMI – Maritime Service Analysis of the effect of Flettner rotors - updated 25 March 2011
Optimized – 6 rotors
Date and time Lat. Long. Course Dist.
(nm)
Steam
Hours
Speed
(kts)
Wind
dir
(deg)
Wind
(kts)
Sea
(m)
Swell
dir
(deg)
Swell
(m)
Curr.
dir
(deg)
Curr.
(kts)
23-02-2011 00:00 47°16´N 059°36´W
23-02-2011 12:15 46°12´N 055°50´W 112 168 12.25 13.71 335 26 3.1 290 1.0 5 0.3
23-02-2011 20:45 46°08´N 053°07´W 92 113 8.50 13.29 345 22 2.0 275 1.6 50 0.9
24-02-2011 10:00 46°59´N 049°29´W 70 158 13.25 11.92 355 26 3.4 15 2.9 45 0.7
24-02-2011 23:45 48°56´N 046°27´W 45 169 13.75 12.29 330 20 2.0 5 4.4 330 0.2
25-02-2011 12:45 51°28´N 045°01´W 20 161 13.00 12.38 270 20 2.1 350 4.3 95 0.1
26-02-2011 01:45 54°09´N 045°03´W 360 162 13.00 12.46 235 29 3.9 345 3.0 260 0.2
26-02-2011 13:15 54°04´N 040°32´W 90 159 11.50 13.83 245 28 4.3 245 3.7 250 0.1
27-02-2011 01:15 53°58´N 035°54´W 90 163 12.00 13.58 205 27 3.3 260 3.8 0 0
27-02-2011 13:15 53°53´N 031°28´W 90 156 12.00 13.00 175 31 3.6 260 3.0 210 0.3
28-02-2011 02:00 52°53´N 027°11´W 110 165 12.75 12.94 230 24 2.8 220 3.7 180 0.4
28-02-2011 13:30 51°31´N 023°32´W 120 157 11.50 13.65 255 18 1.6 255 4.6 300 0.2
01-03-2011 14:45 50°31´N 014°20´W 96 352 25.25 13.94 160 10 0.4 280 4.4 200 0.1
02-03-2011 17:45 49°27´N 004°38´W 96 379 27.00 14.04 80 6 0.5 290 3.4 0 0
Table 3. Basic figures for the Flettner rotor optimized route. All values are averages since last
position and weather and ocean data are evaluated from model data and observations.
Optimized – 6 rotors
Date and time W
(kts)
V
(kts)
Alpha
(rad)
A
(kts)
A
(Bf)
Beta
(deg)
kW % of
MCR
kWh
6 rotors
23-02-2011 00:00
23-02-2011 12:15 26 13.71 2.39 18.5 5 106.6 4420 27.9% 54145
23-02-2011 20:45 22 13.29 1.87 22.1 6 71.9 15470 97.8% 131495
24-02-2011 10:00 26 11.92 1.31 31.3 7 53.4 15820 100.0% 209615
24-02-2011 23:45 20 12.29 1.31 26.1 6 47.9 11960 75.6% 164450
25-02-2011 12:45 20 12.38 1.92 19.6 5 73.6 8840 55.9% 114920
26-02-2011 01:45 29 12.46 2.18 24.1 6 99.9 11180 70.7% 145340
26-02-2011 13:15 28 13.83 2.70 16.5 4 134.3 0 0.0% 0
27-02-2011 01:15 27 13.58 2.01 24.6 6 84.9 13780 87.1% 165360
27-02-2011 13:15 31 13.00 1.48 34.7 8 63.0 15820 100.0% 189840
28-02-2011 02:00 24 12.94 2.09 20.8 5 87.4 6630 41.9% 84532.5
28-02-2011 13:30 18 13.65 2.36 12.8 4 85.8 780 4.9% 8970
01-03-2011 14:45 10 13.94 1.12 20.4 5 26.1 3770 23.8% 95192.5
02-03-2011 17:45 6 14.04 0.28 19.9 5 4.8 0 0.0% 0
Total 1363860
Table 4. Results from the Apparent wind calculations and rotor effect results for the Flettner rotor
optimized route. The rotor effects are estimated from Apparent wind/Rotor effect curves provided
by Windagain.

6. Carsten Kofoed Page 6 of 9 Issued
Route
Steam
hours
Total
rotor
output
(MWh)
Total
engine
output
(MWh)
Saved engine output rel.
to normal GC without
rotors
(MWh)
Saved
%
Normal (GC) - no rotors 164.50 0 2602.390 0 0%
Normal (GC) - 6 rotors 164.50 737.975 1864.415 737.975 28.36%
Optimized - 6 rotors 185.75 1363.860 1574.705 1027.685 39.49%
Table 5. Saved total main engine output relative to the engine output for the normal GC-route
with no Flettner rotors. The total main engine output for the optimized route without rotors is
185.75 hours * 15820 kWh (MCR*hours) = 2938.565 MWh.
The total Flettner rotor effect varies with the number of rotors as follows:
Route Steam
hours
Total
rotor
output
(MWh)
Total
engine
output
(MWh)
Saved engine output rel.
to normal GC without
rotors
(MWh)
Saved
%
Normal (GC) - no rotors 164.50 0 2602.390 0 0%
Normal (GC) - 4 rotors 164.50 495.083 2107.307 495.083 19.02%
Normal (GC) - 5 rotors 164.50 618.854 1983.536 618.854 23.78%
Normal (GC) - 6 rotors 164.50 737.975 1864.415 737.975 28.36%
Optimized - 4 rotors 185.75 956.822 1981.743 620.647 23.85%
Optimized - 5 rotors 185.75 1170.067 1768.498 833.892 32.04%
Optimized - 6 rotors 185.75 1363.860 1574.705 1027.685 39.49%
Table 6. Variation of the total effect of the Flettner rotors relative to the number of rotors. See
detailed results in the Appendix.
4. Method
The effect of the Flettner rotors is a function of the apparent wind affecting the vessel
enroute. The apparent wind velocity, A, is wind experienced onboard a moving
object/vessel and is defined by the following vector subtraction: the Velocity of the
wind, W minus the Velocity of the vessel, V.
Figure 4. Apparent wind definition, source Wikipedia.
The apparent wind velocity vector, A, and the apparent wind angle, ß, to the vessel
velocity, V, is defined as follows:
DMI – Maritime Service Analysis of the effect of Flettner rotors - updated 25 March 2011

7. Carsten Kofoed Page 7 of 9 Issued
DMI – Maritime Service Analysis of the effect of Flettner rotors - updated 25 March 2011
)cos(222
VWVWA
)cos(2
)cos(
arccos 22
VWVW
VW
where:
W = true wind velocity
V = vessel velocity, |V| (=vessel speed) = sailed distance / steaming hours
= true pointing angle
A = true wind velocity

8. Carsten Kofoed Page 8 of 9 Issued
DMI – Maritime Service Analysis of the effect of Flettner rotors - updated 25 March 2011
5. Appendix
Results for 4 and 5 Flettner rotors:
Normal (GC) – 4 rotors
Date and time W
(kts)
V
(kts)
Alpha
(rad)
A
(kts)
A
(Bf)
Beta
(degrees)
kW % of
MCR
kWh
4 rotors
23-02-2011 00:00
23-02-2011 12:00 26 14.0 2.39 18.4 5 105.7 2947 18.6% 35360
23-02-2011 20:30 22 13.3 1.95 21.0 5 76.1 5720 36.2% 48620
24-02-2011 12:00 25 12.5 1.36 30.2 7 54.2 10747 67.9% 166573
25-02-2011 12:00 18 13.0 2.15 15.5 4 77.9 1127 7.1% 27040
26-02-2011 12:00 21 13.5 2.88 8.7 3 141.4 0 0.0% 0
27-02-2011 12:00 17 13.8 2.16 14.7 4 73.1 1733 11.0% 41600
28-02-2011 12:00 18 13.5 1.78 20.2 5 60.9 6500 41.1% 156000
01-03-2011 12:00 3 13.9 0.35 16.8 4 3.5 0 0.0% 0
01-03-2011 20:30 15 13.3 0.65 26.8 6 19.7 2340 14.8% 19890
Total 495083
Normal (GC) – 5 rotors
Date and time W
(kts)
V
(kts)
Alpha
(rad)
A
(kts)
A
(Bf)
Beta
(degrees)
kW % of
MCR
kWh
5 rotors
23-02-2011 00:00
23-02-2011 12:00 26 14.0 2.39 18.4 5 105.7 3683 23.3% 44200
23-02-2011 20:30 22 13.3 1.95 21.0 5 76.1 7150 45.2% 60775
24-02-2011 12:00 25 12.5 1.36 30.2 7 54.2 13433 84.9% 208217
25-02-2011 12:00 18 13.0 2.15 15.5 4 77.9 1408 8.9% 33800
26-02-2011 12:00 21 13.5 2.88 8.7 3 141.4 0 0.0% 0
27-02-2011 12:00 17 13.8 2.16 14.7 4 73.1 2167 13.7% 52000
28-02-2011 12:00 18 13.5 1.78 20.2 5 60.9 8125 51.4% 195000
01-03-2011 12:00 3 13.9 0.35 16.8 4 3.5 0 0.0% 0
01-03-2011 20:30 15 13.3 0.65 26.8 6 19.7 2925 18.5% 24863
Total 618854

9. Carsten Kofoed Page 9 of 9 Issued
DMI – Maritime Service Analysis of the effect of Flettner rotors - updated 25 March 2011
Optimized route – 4 rotors
Date and time W
(kts)
V
(kts)
Alpha
(rad)
A
(kts)
A
(Bf)
Beta
(degrees)
kW % of
MCR
kWh
4 rotors
23-02-2011 00:00
23-02-2011 12:15 26 13.71 2.39 18.5 5 106.6 2947 18.6% 36097
23-02-2011 20:45 22 13.29 1.87 22.1 6 71.9 10313 65.2% 87663
24-02-2011 10:00 26 11.92 1.31 31.3 7 53.4 10660 67.4% 141245
24-02-2011 23:45 20 12.29 1.31 26.0 6 47.9 7973 50.4% 109633
25-02-2011 12:45 20 12.38 1.92 19.6 5 73.6 5893 37.3% 76613
26-02-2011 01:45 29 12.46 2.18 24.1 6 99.9 7453 47.1% 96893
26-02-2011 13:15 28 13.83 2.70 16.5 4 134.3 0 0.0% 0
27-02-2011 01:15 27 13.58 2.01 24.6 6 84.9 9187 58.1% 110240
27-02-2011 13:15 31 13.00 1.48 34.6 8 63.0 14387 90.9% 172640
28-02-2011 02:00 24 12.94 2.09 20.8 5 87.4 4420 27.9% 56355
28-02-2011 13:30 18 13.65 2.36 12.8 4 85.8 520 3.3% 5980
01-03-2011 14:45 10 13.94 1.12 20.4 5 26.1 2513 15.9% 63462
02-03-2011 17:45 6 14.04 0.28 19.9 5 4.8 0 0.0% 0
Total 956822
Optimized route – 5 rotors
Date and time W
(kts)
V
(kts)
Alpha
(rad)
A
(kts)
A
(Bf)
Beta
(degrees)
kW % of
MCR
kWh
5 rotors
23-02-2011 00:00
23-02-2011 12:15 26 13.71 2.39 18.5 5 106.6 3683 23.3% 45121
23-02-2011 20:45 22 13.29 1.87 22.1 6 71.9 12892 81.5% 109579
24-02-2011 10:00 26 11.92 1.31 31.3 7 53.4 13325 84.2% 176556
24-02-2011 23:45 20 12.29 1.31 26.0 6 47.9 9967 63.0% 137042
25-02-2011 12:45 20 12.38 1.92 19.6 5 73.6 7367 46.6% 95767
26-02-2011 01:45 29 12.46 2.18 24.1 6 99.9 9317 58.9% 121117
26-02-2011 13:15 28 13.83 2.70 16.5 4 134.3 0 0.0% 0
27-02-2011 01:15 27 13.58 2.01 24.6 6 84.9 11483 72.6% 137800
27-02-2011 13:15 31 13.00 1.48 34.6 8 63.0 15820 100.0% 189840
28-02-2011 02:00 24 12.94 2.09 20.8 5 87.4 5525 34.9% 70444
28-02-2011 13:30 18 13.65 2.36 12.8 4 85.8 650 4.1% 7475
01-03-2011 14:45 10 13.94 1.12 20.4 5 26.1 3142 19.9% 79327
02-03-2011 17:45 6 14.04 0.28 19.9 5 4.8 0 0.0% 0
Total 1170067