台灣海事安全與保安研究學刊-20120226-vol 3 no1
TRANSCRIPT
Microsoft Word - -20120226-Vol 3 No1Journal of Taiwan Maritime
Safety and Security Studies Vol 3, No 1
1
* Low, Fong-Yuan
CQA
Abstract
The close-quarters situation is the presage of ships collision. To prevent the collision is
to preclude the close-quarters situation. A concept of CQA (Close-Quarters Approaching)
and TCPA (Time of CQA) with a mathematics processing method on the basis of ship
manoeuvrability and turning circle are introduced in this paper. It can explicit point out own
ship’s position of the close-quarters situation by the CQA and TCQA. With some calculating
and simulation examples, the CQA method is examined and helpful for the navigator to
quantify and evaluate the situation of close-quarters.
Keywords: Ship collision, Close-quarters situation, Close-quarters approaching, Turning
circle
(Feb 2012)
Close-Quarters
()Close-Quarters Situation
()
(CPA=0)
(The inner route of the Great Barrier Reef) 1.5~2
14.32kts 14.06kts
150m(Accident)
Close-quarters situations(Incident)
B(container/21kts/17189GT)C(VLCC/16kts/160934GT)(BC )
(give-way vessel)
A Close-quarters
3
encyclopedia, Close Quarters Battle, http://en.wikipedia.org/, 2009.
2 The Australian Transport Safety Bureau, Maritime Safety Investigation Report - Final Close quarters between Blossom Forever & Pearl Prosperity (Occurrence No.59)1994, http://atsb.gov.au/publications/investigation_reports/ , 2009.
3 MAIB Report No.9/2007, Report on the investigation of the close-quarters situation between the ro-ro passenger ferry Maersk Dover the tanker Apollonia and the container vessel Maersk Vancouver in the Dover Strait on 17 October 2006, Marine Accident Investigation Branch, Southampton,U.K., 2007.
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
3
Identification System)
4 MAIB Report No.17/2005, Report on the investigation of the collision between Hyundai Dominion and
Sky Hope in the East China sea 21 June 2004, Marine Accident Investigation Branch, Southampton,U.K., 2005.
Ye
No
Close-Quarters
Situation
1961 Grepa-Verena ([1961] 2 Lloyds Rep. 127) Willmer
()(Size)(Characteristics)(speed)
6 360
(TCQA— Time of CQA)
O A
CQATCQA CQA
(CPA= 0) O’
O
O A CQA
5 A.N. Cockcroft & J.N.F. Lameijer, A Guide to The Collision Avoidance Rules-- 5th ed.,
Butterworth-Heinemann Publishing Ltd., Oxford, 2001, pp114-143.
6 Goodwin, E. M. , “A Statistical Study of Ship Domain,” Journal of Navigation, Vol. 28, 1975, pp. 328-344.
7 1998p43. 17 ()2
(so close)
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
5
(Rc)( Rc = ) O O
A CQA CQA
1.
2.
(Feb 2012)
90
()()
IMO(MSC.137(76))
(Maneuverability)
100m
Advance 4.5 ( Lpp)(tactical diameter)
5
--(Wheelhouse
( T90)
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
7
([3][4])
Re + R = V(T + t1 / 2)+ V / Kδ0 (1) K (1/s)
T (s) V (m/s) δ0 t1 δ0 (s) R Re ()
ReR
ta =(T + t1 / 2)= (Ad-Tf)/S1
(Feb 2012)
Kδ0= Ht = 90/(T90-ta)
x1(t) = Tf – Tf × cos(Ht × ( t-ta))
y1(t)= S1× ta + Tf× sin(Ht × (t-ta)) ------------------------- (2)
0 t T90, If t < ta then (ta = t)
If t < ta
2. (Lc--Collision Length)
(Xc) Lc
Lc
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
9
Lc =(L12+L22 – 2×L1×L2×cosXc)1/2/2 0 Xc 180 (3)
Lc (L1=200m, L2=100m) Xc 0 20 40 60 80 90 100 120 140 160 180
Lc/m 150 148 142 132 119 112 104 87 70 56 50
(L1-L2)/2 Lc (L1+L2)/2 L1=200mL2 =100m
Xc
3. CQA
O S2 Xc CQA
B O (x2(0),y2(0))
x2(0) =CQA × sin(B)
x2(t)= x2(0) – S2 × t ×sin(Xc) = CQA × sin(B) – S2 × t ×sin(Xc)
y2(t)= y2(0) + S2 × t ×cos(Xc) = CQA × cos(B) + S2 × t ×cos(Xc) (5)
0 t T90
(Feb 2012)
A×CQA2 + B×CQA + C = 0 (8)
A, B, C
A = 1 (8-1)
B = 2 (Tf × sin(B) × (cos(Ht × (t - ta)) - 1) – S2 × t × sin(B) × sin( X c) - cos(B) ×
(S1 × ta + Tf × sin(Ht × (t - ta)) - S2 × t × cos( X c))) (8-2)
C = 2Tf2 × (1 - cos(Ht × (t - ta)) × (Tf + S2 × t × sin( X c)) + (S2 × t)2 + S1 × ta × (S1
× ta + 2Tf × sin(Ht × (t - ta))) - 2S2 × t × cos( X c) × (S1 × ta + Tf × sin(Ht × (t - ta)))
– Lc2 (8-3)
CQA(t) = (-B+√(B2-4AC))/2A (10)
(10) 90 Lc CQA
(10)
0 t T90 , If t < ta then (ta = t)
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
11
3min 0.1min(6sec)( T90 1min
0.05min)
(11) CQA :
( S1 Lc Ad Tf90 T90)
( S2 Xc B)
4. CQA TCQA
CQA CQA TCQA
A C1 S1 B A (, )
C2 S2
A (r1,b1)C1S1
A (r1,b1) = (0,0)
(12)(13) t AB
Rs (13)[6]
Rs (t) = (Dx2+2Dx(S1×sinC1-S2×sinC2) × t + (S1×sinC1-S2×sinC2)2 × t2 + Dy2 +
2Dy(S1×cosC1-S2×cosC2) × t + (S1×cosC1-S2×cosC2)2× t2)1/2 (13)
CQA(13)
12
CQA= Rs (t) = (Dx2+2Dx(S1×sinC1-S2×sinC2) × t + (S1×sinC1-S2×sinC2)2 × t2 + Dy2
+ 2Dy(S1×cosC1-S2×cosC2) × t + (S1×cosC1-S2×cosC2)2× t2)1/2 (14)
t
t TCQA(-B+√(B2-4AC))/2A
TCQA = t = (-B-√(B2-4AC))/2A (17)
A = (S1×sinC1 – S2×sinC2)2 + (S1×cosC1 – S2×cosC2)2 (17-1)
B = 2(Dx (S1×sinC1 – S2×sinC2) + Dy (S1×cosC1 – S2×cosC2)) (17-2)
C = Dx2 + Dy2 - CQA2 (17-3)
5. TCQA
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
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Speed/kt LOA/m Advance/m Transfer/m T90/min DWT
Container 25 195 561 287 1.12 32,360 Bulk carrier 15.8 200 610 280 1.92 37,000
VLCC 16 339 1010 500 2.9 270,665
[15]
270T 15.8kts 45
CQA
CQA (Xc = 90, S1=S2/Buck) Time/ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 >1.2 CQA/ 0.08 0.106 0.124 0.137 0.129 xx 0.32 0.353 0.385 0.413 0.446 0.464 xx
xx Rc=Lc
CQA /m
/min CQA (Rc)/m
0.3 0.4 0.464 0.5 0.0 555.6 740.8 859.3 926.0 0.2 417.7 602.9 721.4 788.1 0.4 279.7 464.9 583.4 650.1 0.6 *92.9 278.1 396.6 463.3 0.8 *19.4 199.0 317.3 383.9 0.9 *59.1 137.4 254.4 320.7 1.0 127.4 *83.6 192.6 257.6 1.1 199.4 *72.7 138.7 198.6 1.2 274.0 122.4 *111.9 153.2 1.4 429.4 269.4 192.4 171.4 1.6 590.3 431.1 343.1 303.0 1.8 753.7 597.5 507.9 463.3 2.0 916.5 764.5 676.0 630.6
*(Rc Lc)
(S1=15.8Lc=112Ad=610Tf=280T90=1.92)
(S2=15.8Xc=90B=45)
(11) 0.1min CQA
CQA = 0.08 0.1min (Rc=Lc=112m) CQA = 0.106
0.2min ...... CQA 1.2 min 0.464 CQA
“xx” Rc =Lc Rc<Lc Rc > Lc
0.6min < 112m 1.2min > 112m
CQA>0.464’ Rc Lc
CQA 90(1.92min)(Rc)”*”
Rc Lc CQA=0.464 111.9m
CQA=0.5
CQA=0.464
Lc()CQA CQA=0.5
Lc CQA
CQA
0
100
200
300
400
500
600
700
0.0 0.2 0.4 6.0 0.8 0.9 1.0 1.1 1.2 1.4 1.6 1.8 2.0
/min
Lc=112m
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
15
2. CQA
CQA(S1=S2)
Xc CQA/ CQA/Advance
Container Buck VLCC Con/561m Buck/610m VLCC/1010m 15 0.175 0.177 0.32 0.578 0.537 0.587 30 0.234 0.247 0.432 0.773 0.750 0.792 45 0.293 0.31 0.531 0.967 0.941 0.974 60 0.345 0.367 0.625 1.139 1.114 1.146 75 0.391 0.42 0.7 1.291 1.275 1.284 90 0.425 0.464 0.772 1.403 1.409 1.416
105 0.429 0.496 0.827 1.416 1.506 1.516 120 0.453 0.513 0.867 1.496 1.558 1.59 135 0.47 0.534 0.904 1.552 1.621 1.658 150 0.481 0.548 0.929 1.588 1.664 1.704 165 0.487 0.557 0.946 1.608 1.691 1.735 180 0.49 0.562 0.953 1.618 1.706 1.748
CQA (S1=S2)
(S1=S2)(Xc15°~ 180°)
CQA CQA
Xc CQA Xc
(Xc = 180°) CQA
CQA CQAClose-Quarters
()
CQA
0
0.2
0.4
0.6
0.8
1
1.2
15 30 45 60 75 90 105 120 135 150 165 180 (Xc)
C Q
A
/
CQA VLCC > Buck > Container
CQA CQA
CQA Xc
= 15°~ 60° CQA 0.6~1.2 Xc = 60°~120°
CQA 1.2~1.6 Xc = 120°~ 180° CQA
1.6~1.8
Container ship 3090120 CQA
CQAAdvance
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
15 30 45 60 75 90 105 120 135 150 165 180 (Xc)
C Q
A /A
dv an
ce
Con/561
Buck/610
VLCC/1010
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
17
(S2-S1) CQA/ CQA/Advance factor
Container Buck VLCC Con/561 Buck/610 VLCC/1010 -5 0.383 0.395 0.653 1.264 1.199 1.197 -4 0.391 0.407 0.675 1.291 1.236 1.238 -3 0.399 0.421 0.698 1.317 1.278 1.280 -2 0.408 0.434 0.722 1.347 1.318 1.324 -1 0.416 0.449 0.747 1.373 1.363 1.370 0 0.425 0.464 0.772 1.403 1.409 1.416 1 0.435 0.479 0.799 1.436 1.454 1.465 2 0.444 0.495 0.825 1.466 1.503 1.513 3 0.454 0.512 0.852 1.499 1.554 1.562 4 0.463 0.528 0.878 1.528 1.603 1.610 5 0.473 0.545 0.908 1.561 1.655 1.665
CQA
CQA
CQA Buck VLCC
(16kts) Container (25kts)
Xc = 90 (-5 +5 kts) CQA
1.2~1.7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-5 -4 -3 -2 -1 0 1 2 3 4 5 /knot
C Q
A
/
4. CQA
Xc Container Buck VLCC
R-turn L-turn R-turn L-turn R-turn L-turn 15 0.175 0.124 0.177 0.133 0.32 0.2 30 0.234 0.178 0.247 0.194 0.432 0.299 45 0.293 0.242 0.31 0.266 0.531 0.416 60 0.345 0.318 0.367 0.348 0.625 0.548 75 0.391 0.403 0.42 0.441 0.7 0.691 90 0.425 0.496 0.464 0.543 0.772 0.832
105 0.429 0.574 0.496 0.63 0.827 0.928 120 0.453 0.578 0.513 0.67 0.867 0.946 135 0.47 0.557 0.534 0.639 0.904 0.964 150 0.481 0.513 0.548 0.613 0.929 0.971 165 0.487 0.489 0.557 0.591 0.946 0.968 180 0.49 0.49 0.562 0.562 0.953 0.953
CQA CQA CQA
CQA(L-turn) < CQA(R-turn) CQA
CQAAdvance(Xc=90)
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
-5 -4 -3 -2 -1 0 1 2 3 4 5
/knot
ce
Con/561
Buck/610
VLCC/1010
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
19
CQA Xc > 70(VLCC > 75 )
CQA CQA
Xc > 70 CQA
Buck carrier Xc = 60 90 Xc = 60 CQA=
0.367 (CQA(L-turn)= 0.348 < CQA(R-turn)= 0.367)
Xc = 90CQA= 0.464 (CQA(L-turn)= 0.543 >
CQA(R-turn)= 0.464)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
15 30 45 60 75 90 105 120 135 150 165 180 (Xc)
C Q
A /
VLCC 000 16kts0900 ARPA
75 6.2 305T 20kts CPA= 0, TCPA= 22
LOA+200m CQA
TCQA
Xc = 000- 305= 55 Lc= 339m+200m= 539m
(11)
(S1=16ktsLc=539m Ad=1010m Tf=500mT90=2.9min)
(S2=20ktsXc=55B=75)
0.1min CQA = 1.11
(17) TCQA
(B=0Rs =0S1=16C1=0CQA=1.11’)
(B=75Rs = 6.2’S2=20C2=305)
TCQA= 18min
0900+18=0918 1.11
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
21
0918 2.7min 0920.7
350m/0.19 CQA CPA 1.04
4min
TCQACPATCPA
CQATCQA
CQA
CQA
1961 Willmer
……()()
(Feb 2012)
CQA TCQA
( S1 Lc Ad Tf90 T90)
( S2 Xc B)
(90) ARPA
AIS
= () +
4. CQA CQA
( 6 )
5. CQA CQA Xc < 90
1.5 Xc 90 2
)
7. CQA CQA ( CQA )
Xc< 70° Xc > 70 CQA
(
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
23
CQA)
CQA Close Quarters of Approaching
TCQA Time of CQA Ad Advance Tf Transfer
T90 Turning period from Initial to 90 90 ta Rudder effect time = (Ad-Tf)/S1
Rc Range of target ship and own ship during turning period
Lc Collision length Xc Cross course angle = C1-C2 Ht Turning angle per minute = 90/(T90-ta)
(x1, y1) Own ship position S1 Own ship speed C1 Own ship course L1 LOA of own ship
(x2, y2) Target ship position S2 Target ship speed C2 Target ship course L2 LOA of target ship Rs Target ship range B Target ship Bearing K (1/s) T (s) V (m/s) δ0 t1 δ0 (s) R Re ()
1. ( OO )2003
2. 1998p43
3. 1996pp.9-20
4. 2008pp.11-71
5. 33 1 2007
pp.17-33
22 3 2007pp.243-252
7.
(Feb 2012)
1999 3 pp.29-33
8. A.N.Cockcroft & J.N.F.Lameijer, A Guide to The Collision Avoidance Rules-- 5th ed.,
Butterworth-Heinemann Publishing Ltd., 2001, Oxford, pp.114-143.
9. Goodwin, E. M., “A Statistical Study of Ship Domain,” Journal of Navigation, Vol. 28,
1975, pp.328-344.
10. IMO Resolution MSC.137(76), Standards for ship Manoeuvrability, 4 December 2002.
11. Marine Accident Investigation Branch, MAIB Report No.9/2007, Report on the
investigation of the close-quarters situation between the ro-ro passenger ferry Maersk
Dover the tanker Apollonia and the container vessel Maersk Vancouver in the Dover
Strait on 17 October 2006, Southampton, U.K., 2007.
12. Marine Accident Investigation Branch, MAIB Report No.17/2005, Report on the
investigation of the collision between Hyundai Dominion and Sky Hope in the East
China Sea 21 June 2004, Southampton, U.K., 2005.
13. The Australian Transport Safety Bureau, Maritime Safety Investigation Report - Final
Close quarters between Blossom Forever & Pearl Prosperity (Occurrence No.59) 1994,
http://atsb.gov.au/publications/investigation_reports/, 2009.
Wikipedia the free encyclopaedia, Close Quarters Battle, http://en.wikipedia.org/, 2009.
15. U.S. Coast Guard Report No.CG-D-25-79, “Rules of the Road Training Investigation”,
National Maritime Research Centre, New York, 1978, pp.23-28.
1
* Low, Fong-Yuan
CQA
Abstract
The close-quarters situation is the presage of ships collision. To prevent the collision is
to preclude the close-quarters situation. A concept of CQA (Close-Quarters Approaching)
and TCPA (Time of CQA) with a mathematics processing method on the basis of ship
manoeuvrability and turning circle are introduced in this paper. It can explicit point out own
ship’s position of the close-quarters situation by the CQA and TCQA. With some calculating
and simulation examples, the CQA method is examined and helpful for the navigator to
quantify and evaluate the situation of close-quarters.
Keywords: Ship collision, Close-quarters situation, Close-quarters approaching, Turning
circle
(Feb 2012)
Close-Quarters
()Close-Quarters Situation
()
(CPA=0)
(The inner route of the Great Barrier Reef) 1.5~2
14.32kts 14.06kts
150m(Accident)
Close-quarters situations(Incident)
B(container/21kts/17189GT)C(VLCC/16kts/160934GT)(BC )
(give-way vessel)
A Close-quarters
3
encyclopedia, Close Quarters Battle, http://en.wikipedia.org/, 2009.
2 The Australian Transport Safety Bureau, Maritime Safety Investigation Report - Final Close quarters between Blossom Forever & Pearl Prosperity (Occurrence No.59)1994, http://atsb.gov.au/publications/investigation_reports/ , 2009.
3 MAIB Report No.9/2007, Report on the investigation of the close-quarters situation between the ro-ro passenger ferry Maersk Dover the tanker Apollonia and the container vessel Maersk Vancouver in the Dover Strait on 17 October 2006, Marine Accident Investigation Branch, Southampton,U.K., 2007.
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
3
Identification System)
4 MAIB Report No.17/2005, Report on the investigation of the collision between Hyundai Dominion and
Sky Hope in the East China sea 21 June 2004, Marine Accident Investigation Branch, Southampton,U.K., 2005.
Ye
No
Close-Quarters
Situation
1961 Grepa-Verena ([1961] 2 Lloyds Rep. 127) Willmer
()(Size)(Characteristics)(speed)
6 360
(TCQA— Time of CQA)
O A
CQATCQA CQA
(CPA= 0) O’
O
O A CQA
5 A.N. Cockcroft & J.N.F. Lameijer, A Guide to The Collision Avoidance Rules-- 5th ed.,
Butterworth-Heinemann Publishing Ltd., Oxford, 2001, pp114-143.
6 Goodwin, E. M. , “A Statistical Study of Ship Domain,” Journal of Navigation, Vol. 28, 1975, pp. 328-344.
7 1998p43. 17 ()2
(so close)
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
5
(Rc)( Rc = ) O O
A CQA CQA
1.
2.
(Feb 2012)
90
()()
IMO(MSC.137(76))
(Maneuverability)
100m
Advance 4.5 ( Lpp)(tactical diameter)
5
--(Wheelhouse
( T90)
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
7
([3][4])
Re + R = V(T + t1 / 2)+ V / Kδ0 (1) K (1/s)
T (s) V (m/s) δ0 t1 δ0 (s) R Re ()
ReR
ta =(T + t1 / 2)= (Ad-Tf)/S1
(Feb 2012)
Kδ0= Ht = 90/(T90-ta)
x1(t) = Tf – Tf × cos(Ht × ( t-ta))
y1(t)= S1× ta + Tf× sin(Ht × (t-ta)) ------------------------- (2)
0 t T90, If t < ta then (ta = t)
If t < ta
2. (Lc--Collision Length)
(Xc) Lc
Lc
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
9
Lc =(L12+L22 – 2×L1×L2×cosXc)1/2/2 0 Xc 180 (3)
Lc (L1=200m, L2=100m) Xc 0 20 40 60 80 90 100 120 140 160 180
Lc/m 150 148 142 132 119 112 104 87 70 56 50
(L1-L2)/2 Lc (L1+L2)/2 L1=200mL2 =100m
Xc
3. CQA
O S2 Xc CQA
B O (x2(0),y2(0))
x2(0) =CQA × sin(B)
x2(t)= x2(0) – S2 × t ×sin(Xc) = CQA × sin(B) – S2 × t ×sin(Xc)
y2(t)= y2(0) + S2 × t ×cos(Xc) = CQA × cos(B) + S2 × t ×cos(Xc) (5)
0 t T90
(Feb 2012)
A×CQA2 + B×CQA + C = 0 (8)
A, B, C
A = 1 (8-1)
B = 2 (Tf × sin(B) × (cos(Ht × (t - ta)) - 1) – S2 × t × sin(B) × sin( X c) - cos(B) ×
(S1 × ta + Tf × sin(Ht × (t - ta)) - S2 × t × cos( X c))) (8-2)
C = 2Tf2 × (1 - cos(Ht × (t - ta)) × (Tf + S2 × t × sin( X c)) + (S2 × t)2 + S1 × ta × (S1
× ta + 2Tf × sin(Ht × (t - ta))) - 2S2 × t × cos( X c) × (S1 × ta + Tf × sin(Ht × (t - ta)))
– Lc2 (8-3)
CQA(t) = (-B+√(B2-4AC))/2A (10)
(10) 90 Lc CQA
(10)
0 t T90 , If t < ta then (ta = t)
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
11
3min 0.1min(6sec)( T90 1min
0.05min)
(11) CQA :
( S1 Lc Ad Tf90 T90)
( S2 Xc B)
4. CQA TCQA
CQA CQA TCQA
A C1 S1 B A (, )
C2 S2
A (r1,b1)C1S1
A (r1,b1) = (0,0)
(12)(13) t AB
Rs (13)[6]
Rs (t) = (Dx2+2Dx(S1×sinC1-S2×sinC2) × t + (S1×sinC1-S2×sinC2)2 × t2 + Dy2 +
2Dy(S1×cosC1-S2×cosC2) × t + (S1×cosC1-S2×cosC2)2× t2)1/2 (13)
CQA(13)
12
CQA= Rs (t) = (Dx2+2Dx(S1×sinC1-S2×sinC2) × t + (S1×sinC1-S2×sinC2)2 × t2 + Dy2
+ 2Dy(S1×cosC1-S2×cosC2) × t + (S1×cosC1-S2×cosC2)2× t2)1/2 (14)
t
t TCQA(-B+√(B2-4AC))/2A
TCQA = t = (-B-√(B2-4AC))/2A (17)
A = (S1×sinC1 – S2×sinC2)2 + (S1×cosC1 – S2×cosC2)2 (17-1)
B = 2(Dx (S1×sinC1 – S2×sinC2) + Dy (S1×cosC1 – S2×cosC2)) (17-2)
C = Dx2 + Dy2 - CQA2 (17-3)
5. TCQA
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
13
Speed/kt LOA/m Advance/m Transfer/m T90/min DWT
Container 25 195 561 287 1.12 32,360 Bulk carrier 15.8 200 610 280 1.92 37,000
VLCC 16 339 1010 500 2.9 270,665
[15]
270T 15.8kts 45
CQA
CQA (Xc = 90, S1=S2/Buck) Time/ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 >1.2 CQA/ 0.08 0.106 0.124 0.137 0.129 xx 0.32 0.353 0.385 0.413 0.446 0.464 xx
xx Rc=Lc
CQA /m
/min CQA (Rc)/m
0.3 0.4 0.464 0.5 0.0 555.6 740.8 859.3 926.0 0.2 417.7 602.9 721.4 788.1 0.4 279.7 464.9 583.4 650.1 0.6 *92.9 278.1 396.6 463.3 0.8 *19.4 199.0 317.3 383.9 0.9 *59.1 137.4 254.4 320.7 1.0 127.4 *83.6 192.6 257.6 1.1 199.4 *72.7 138.7 198.6 1.2 274.0 122.4 *111.9 153.2 1.4 429.4 269.4 192.4 171.4 1.6 590.3 431.1 343.1 303.0 1.8 753.7 597.5 507.9 463.3 2.0 916.5 764.5 676.0 630.6
*(Rc Lc)
(S1=15.8Lc=112Ad=610Tf=280T90=1.92)
(S2=15.8Xc=90B=45)
(11) 0.1min CQA
CQA = 0.08 0.1min (Rc=Lc=112m) CQA = 0.106
0.2min ...... CQA 1.2 min 0.464 CQA
“xx” Rc =Lc Rc<Lc Rc > Lc
0.6min < 112m 1.2min > 112m
CQA>0.464’ Rc Lc
CQA 90(1.92min)(Rc)”*”
Rc Lc CQA=0.464 111.9m
CQA=0.5
CQA=0.464
Lc()CQA CQA=0.5
Lc CQA
CQA
0
100
200
300
400
500
600
700
0.0 0.2 0.4 6.0 0.8 0.9 1.0 1.1 1.2 1.4 1.6 1.8 2.0
/min
Lc=112m
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
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2. CQA
CQA(S1=S2)
Xc CQA/ CQA/Advance
Container Buck VLCC Con/561m Buck/610m VLCC/1010m 15 0.175 0.177 0.32 0.578 0.537 0.587 30 0.234 0.247 0.432 0.773 0.750 0.792 45 0.293 0.31 0.531 0.967 0.941 0.974 60 0.345 0.367 0.625 1.139 1.114 1.146 75 0.391 0.42 0.7 1.291 1.275 1.284 90 0.425 0.464 0.772 1.403 1.409 1.416
105 0.429 0.496 0.827 1.416 1.506 1.516 120 0.453 0.513 0.867 1.496 1.558 1.59 135 0.47 0.534 0.904 1.552 1.621 1.658 150 0.481 0.548 0.929 1.588 1.664 1.704 165 0.487 0.557 0.946 1.608 1.691 1.735 180 0.49 0.562 0.953 1.618 1.706 1.748
CQA (S1=S2)
(S1=S2)(Xc15°~ 180°)
CQA CQA
Xc CQA Xc
(Xc = 180°) CQA
CQA CQAClose-Quarters
()
CQA
0
0.2
0.4
0.6
0.8
1
1.2
15 30 45 60 75 90 105 120 135 150 165 180 (Xc)
C Q
A
/
CQA VLCC > Buck > Container
CQA CQA
CQA Xc
= 15°~ 60° CQA 0.6~1.2 Xc = 60°~120°
CQA 1.2~1.6 Xc = 120°~ 180° CQA
1.6~1.8
Container ship 3090120 CQA
CQAAdvance
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
15 30 45 60 75 90 105 120 135 150 165 180 (Xc)
C Q
A /A
dv an
ce
Con/561
Buck/610
VLCC/1010
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
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(S2-S1) CQA/ CQA/Advance factor
Container Buck VLCC Con/561 Buck/610 VLCC/1010 -5 0.383 0.395 0.653 1.264 1.199 1.197 -4 0.391 0.407 0.675 1.291 1.236 1.238 -3 0.399 0.421 0.698 1.317 1.278 1.280 -2 0.408 0.434 0.722 1.347 1.318 1.324 -1 0.416 0.449 0.747 1.373 1.363 1.370 0 0.425 0.464 0.772 1.403 1.409 1.416 1 0.435 0.479 0.799 1.436 1.454 1.465 2 0.444 0.495 0.825 1.466 1.503 1.513 3 0.454 0.512 0.852 1.499 1.554 1.562 4 0.463 0.528 0.878 1.528 1.603 1.610 5 0.473 0.545 0.908 1.561 1.655 1.665
CQA
CQA
CQA Buck VLCC
(16kts) Container (25kts)
Xc = 90 (-5 +5 kts) CQA
1.2~1.7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-5 -4 -3 -2 -1 0 1 2 3 4 5 /knot
C Q
A
/
4. CQA
Xc Container Buck VLCC
R-turn L-turn R-turn L-turn R-turn L-turn 15 0.175 0.124 0.177 0.133 0.32 0.2 30 0.234 0.178 0.247 0.194 0.432 0.299 45 0.293 0.242 0.31 0.266 0.531 0.416 60 0.345 0.318 0.367 0.348 0.625 0.548 75 0.391 0.403 0.42 0.441 0.7 0.691 90 0.425 0.496 0.464 0.543 0.772 0.832
105 0.429 0.574 0.496 0.63 0.827 0.928 120 0.453 0.578 0.513 0.67 0.867 0.946 135 0.47 0.557 0.534 0.639 0.904 0.964 150 0.481 0.513 0.548 0.613 0.929 0.971 165 0.487 0.489 0.557 0.591 0.946 0.968 180 0.49 0.49 0.562 0.562 0.953 0.953
CQA CQA CQA
CQA(L-turn) < CQA(R-turn) CQA
CQAAdvance(Xc=90)
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
-5 -4 -3 -2 -1 0 1 2 3 4 5
/knot
ce
Con/561
Buck/610
VLCC/1010
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
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CQA Xc > 70(VLCC > 75 )
CQA CQA
Xc > 70 CQA
Buck carrier Xc = 60 90 Xc = 60 CQA=
0.367 (CQA(L-turn)= 0.348 < CQA(R-turn)= 0.367)
Xc = 90CQA= 0.464 (CQA(L-turn)= 0.543 >
CQA(R-turn)= 0.464)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
15 30 45 60 75 90 105 120 135 150 165 180 (Xc)
C Q
A /
VLCC 000 16kts0900 ARPA
75 6.2 305T 20kts CPA= 0, TCPA= 22
LOA+200m CQA
TCQA
Xc = 000- 305= 55 Lc= 339m+200m= 539m
(11)
(S1=16ktsLc=539m Ad=1010m Tf=500mT90=2.9min)
(S2=20ktsXc=55B=75)
0.1min CQA = 1.11
(17) TCQA
(B=0Rs =0S1=16C1=0CQA=1.11’)
(B=75Rs = 6.2’S2=20C2=305)
TCQA= 18min
0900+18=0918 1.11
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
21
0918 2.7min 0920.7
350m/0.19 CQA CPA 1.04
4min
TCQACPATCPA
CQATCQA
CQA
CQA
1961 Willmer
……()()
(Feb 2012)
CQA TCQA
( S1 Lc Ad Tf90 T90)
( S2 Xc B)
(90) ARPA
AIS
= () +
4. CQA CQA
( 6 )
5. CQA CQA Xc < 90
1.5 Xc 90 2
)
7. CQA CQA ( CQA )
Xc< 70° Xc > 70 CQA
(
Journal of Taiwan Maritime Safety and Security Studies Vol 3, No 1
23
CQA)
CQA Close Quarters of Approaching
TCQA Time of CQA Ad Advance Tf Transfer
T90 Turning period from Initial to 90 90 ta Rudder effect time = (Ad-Tf)/S1
Rc Range of target ship and own ship during turning period
Lc Collision length Xc Cross course angle = C1-C2 Ht Turning angle per minute = 90/(T90-ta)
(x1, y1) Own ship position S1 Own ship speed C1 Own ship course L1 LOA of own ship
(x2, y2) Target ship position S2 Target ship speed C2 Target ship course L2 LOA of target ship Rs Target ship range B Target ship Bearing K (1/s) T (s) V (m/s) δ0 t1 δ0 (s) R Re ()
1. ( OO )2003
2. 1998p43
3. 1996pp.9-20
4. 2008pp.11-71
5. 33 1 2007
pp.17-33
22 3 2007pp.243-252
7.
(Feb 2012)
1999 3 pp.29-33
8. A.N.Cockcroft & J.N.F.Lameijer, A Guide to The Collision Avoidance Rules-- 5th ed.,
Butterworth-Heinemann Publishing Ltd., 2001, Oxford, pp.114-143.
9. Goodwin, E. M., “A Statistical Study of Ship Domain,” Journal of Navigation, Vol. 28,
1975, pp.328-344.
10. IMO Resolution MSC.137(76), Standards for ship Manoeuvrability, 4 December 2002.
11. Marine Accident Investigation Branch, MAIB Report No.9/2007, Report on the
investigation of the close-quarters situation between the ro-ro passenger ferry Maersk
Dover the tanker Apollonia and the container vessel Maersk Vancouver in the Dover
Strait on 17 October 2006, Southampton, U.K., 2007.
12. Marine Accident Investigation Branch, MAIB Report No.17/2005, Report on the
investigation of the collision between Hyundai Dominion and Sky Hope in the East
China Sea 21 June 2004, Southampton, U.K., 2005.
13. The Australian Transport Safety Bureau, Maritime Safety Investigation Report - Final
Close quarters between Blossom Forever & Pearl Prosperity (Occurrence No.59) 1994,
http://atsb.gov.au/publications/investigation_reports/, 2009.
Wikipedia the free encyclopaedia, Close Quarters Battle, http://en.wikipedia.org/, 2009.
15. U.S. Coast Guard Report No.CG-D-25-79, “Rules of the Road Training Investigation”,
National Maritime Research Centre, New York, 1978, pp.23-28.