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Turning Circle Diameter (TCD) Values for Vessels in Shallow Waters
CHAPTER 43
Turning Circle Diameter (TCD) Values for Vessels in Shallow Waters Introduction First of all, what exactly is a turning circle diameter (TCD)? It is measured on ship trials that are carried out in deep-water conditions. H/T is usually greater than 6.00. The vessel is turned completely through 360 with, say, starboard helm and then with port helm. This will produce two TCDs of different diameters. This hypothesis is for: 1. 2. 3. 4.
Single-screw merchant ships only Each ship fitted with a horizontal propeller shaft rotating within a shaft tunnel TCD maneuver carried out at full speed Turning maneuver conducted with a rudder helm held at 35 .
It should be observed in Figure 43.1 that at the beginning of the starboard turning maneuver, the ship turns initially to port. There are two reasons for this. Forces acting on the rudder itself will cause this move at first to port. Larger centrifugal forces acting on the ship’s hull will then cause the vessel to move the ship on a course to starboard (see Figure 43.1). The maximum angle of heel must be recorded. If the ship has port rudder helm this final angle of heel will be to starboard and vice versa. Again, this is due to centrifugal forces acting on the ship’s hull. During the TCD maneuver the ship will experience transfer, advance, drift angle, and angle of heel. With regard to grounding at the bilge plating, in deep water the angle of heel will present few or no problems. However, if the trials were undertaken in shallow waters there is an increased possibility of grounding at the bilge plating.
Updates of 1987 and 2002 In November 1987, the IMO regulation was that H/T should be greater than 4.00, where H is the water depth and T is the mean static draft of the vessel. In December 2002, further resolutions were made by the IMO (Ref A 601 (15). Ship Stability for Masters and Mates. http://dx.doi.org/10.1016/B978-0-08-097093-6.00043-8 Copyright Ó 2012 Elsevier Ltd. All rights reserved.
389
390
Chapter 43
TCD IN WATER WHERE H/T = 1.10
PATH WHEN H/T = 1.10 ADVANCE IN DEEP WATER
ADVANCE IF H/T = 1.10
PATH OF SHIP’S CTR OF GRAVITY
1
2
3
5
7
9
SHIP 10 LENGTHS PATH WHEN H/T = 2.46
PATH WHEN H/T = 5.75
TCD IN DEEP WATER
Figure 43.1: Variation of TCD with H/T Values for a Supertanker. Note how TCD in very shallow waters is approximately twice that when ship is in deep waters.
In their Section 4 on values of TCD in shallow water, they stated the following: For all ships of 100 m in length and over: 4.1.1 TCD is to be measured with the ship model and ship as for the fully loaded condition. 4.1.2 The initial speed of the ship should be at half-ahead speed. 4.1.3 Times and speeds at 90 , 180 , 270 , and 360 turning should be specifically shown, together with an outline of the ship. 4.1.4 Rudder angle should be at a maximum and H/T ratio to be 1.20.
The obtained information for the above should be presented (a) on a pilot card, (b) on a wheelhouse posting, and (c) in a maneuvering booklet. Angles of heel should be presented on a spreadsheet (see Tables 43.1e43.4).
Turning Circle Diameter (TCD) Values for Vessels in Shallow Waters
391
Table 43.1: Cb
(Fd 1.10)
Draft T Fd (m)
0.800 10.00 5.93
Fd (H/T)actual (H/T)actual Y2
4.83
4.63
1.30
0.07
K [ 1.00 e2.00
Ship Speed (knots)
Max. Squat (m)
Br. Mld. LBP (m) (m)
1.07
10.00
0.80
32.26 200
Table 43.2: Angle of heel ( ) ½bsin a (m)
0 0.00
2 0.56
4 1.13
6 1.69
8 2.24
10 2.80
Table 43.3: Meters at station 7.5 or 2.5 with ship at zero angle of heel and with trim or even keel. Kmbs
mbs
Trim Change
0.800 0.64 0.72 At 0 angle of heel, squat at station 2.5 or 7.5 is 0.72 m at the bilge strakes P and S At 2 angle of heel, squat at station 2.5 or 7.5 is 1.28 m at the bilge strakes P and S At 4 angle of heel, squat at station 2.5 or 7.5 is 1.85 m at the bilge strakes P and S At 6 angle of heel, squat at station 2.5 or 7.5 is 2.41 m at the bilge strakes P and S At 8 angle of heel, squat at station 2.5 or 7.5 is 2.96 m at the bilge strakes P and S At 10 angle of heel, squat at station 2.5 or 7.5 is 3.52 m at the bilge strakes P and S
Table 43.4: Heel Angle ( )
Squats (m)
0 2 4 6 8 10
0.72 1.28 1.85 2.41 2.96 3.52
Tanker’s speed is 10 knots.
392
Chapter 43
Some Observations • • • • • • •
A 1% increase in trim by the stern in deep water increases the TCD by 10%. Changes in a ship’s displacement do not alter changes in TCD values. Fine-form ships have greater TCD values than full-form ships. Hence container ships and passenger liners will have greater TCD values than supertankers. In deep water TCD for merchant ships is approximately three to four times ship’s LBP (see details in Figure 43.1). Ships with comparatively larger rudders have smaller TCD values. Any change in ship speed for another test run will not cause a change in TCD value. When H/T is 1.10, TCD can be double that for when ship is in deep waters (see details in Figure 43.1 and Table 43.5).
Calculations When a ship has a water depth greater than depth of influence, the ship is in deep water and the coefficient (KTCD) for TCD is 1.00. If the ship has a water depth of 1.10 times the ship’s mean draft, then the coefficient (KTCD) for TCD is about 2.00. So KTCD is 1.00e2.00. FD ¼ 4:44=ðCb Þ1:3 times each ship&s mean static even-keel draft
This will alter with each ship type. For a specific ship it will change with each condition of loading. A detailed study of this by the author produced the following equation: KTCD ¼ 1 þ fðFD H=Tactual Þ=ðFD 1:10Þg2
Figure 43.2 shows the values for KTCD against H/T, for several Cb values ranging from full-form to fine-form ships. Table 43.5: H/T
Cb
Water Depth
KTCD
5.75 2.46 1.10
0.820 0.820 0.820
Deep water Shallow Very shallow water
1.00 1.50 2.00
0.500
393
FD = 10.93
0.600
0.700
FD = 8.62
2
FD = 7.06
FD = 5.09 FD = 5.93
3
I.E. 10% UKG
H/T = 1.10
TCD COEFFICIENT
CB VALUES
0.900 0.800
Turning Circle Diameter (TCD) Values for Vessels in Shallow Waters
1
0
2
4
6
8
10
12
H/T VALUES
Figure 43.2: TCD Coefficient Plotted Against H/T. At H/T ¼ 1.10, KTCD ¼ 2.0 in very shallow water at each FD value; KTCD ¼ 1.0 in deep water. Hence, TCD is twice the the TCD in deep water. When H/T ¼ 1.00, the vessel has grounded. Each FD ¼ 4.44/C1.3 b , varying with ship type and Cb. H/T > FD means ship is in deep water; H/T FD means that the ship is in shallow waters, and KTCD will increase above 1.00. KTCD ¼ 1 þ {(FD H/Tactual)/ (FD 1.10)}2. Range of KTCD ¼ 1.00e2.00.
n
Worked Example Let us now consider one hull form, that of an oil tanker with LBP of 200 m and a Cb of 0.800. Let breadth molded be 32.26 m, the static mean draft be 10.00 m, the water depth be 46.30m, and the ship speed be 10 knots. TCD in deep waters z 3:25 LBP ¼ 650 m ðF D 1:10Þ ¼ 5:93 1:10 ¼ 4:83 m ðF D H=T actual Þ ¼ 5:93 4:63 ¼ 1:30 m fðF D H=Tactual Þ=ðFd 1:10Þg2 ¼ 0:07 KTCD ¼ 1 þ 0:07 ¼ 1:07
ðcolumn 4 in Table 43:1Þ ðcolumn 6 in Table 43:1Þ ðcolumn 7 in Table 43:1Þ
ðcolumn 8 in Table 43:1Þ
Consequently, at H/T of 4.63, the TCD is 1.07 650 ¼ 760.5 m instead of 650 m. Continuing: Maximum squat at the bow ¼ ðCb V2 Þ=100 ¼ 0:800 10 10=100 ¼ 0:80 m
394
Chapter 43 Loss of ukc at bilge plating ¼ 1=2 bsin a ¼ 16:13sin a
ðsee Table 43:2Þ
where a is the angle of heel, ranging from 0 to 10 . Mean bodily sinkage ¼ K mbs max: squat ¼ f1 20ð0:700 Cb Þ2 g 0:80 ¼ f1 20ð0:700 0:80Þ2 g 0:80 ¼ 0:80 0:80 ¼ 0:64 m from bow to stern
ðsee Table 43:3Þ
Trim at station 7:5 ¼ ðmbs þ max: squatÞ=2 ¼ 0:64 þ 0:80 ¼ 0:72m
ðsee column 3 in Table 43:3Þ
Transverse squat at the bilge plating at station 7:5 ¼ 0:72 þ 1=2 bsin a
ðTable 43:4Þ
where a is angle of heel ranging from 0 to 10 . n
Summary This oil tanker will go aground at the bilge plating port or starboard at an angle of heel of 4.82 . This is shown in graphical form in Figure 43.3, where the transverse squat due to mean bodily sinkage plus angle of heel is equal to the static ukc even keel of 2.00 m.
Squat values at Bilge plating
Angle of Heel in degrees 0 1 2 3 0.00 –1.00 –2.00 static ukc = 2m –3.00 –4.00
4
5
6
7
8
9
10
ship grounds at the Bilge plating
Figure 43.3: Squats at Bilge Plating.
Turning Circle Diameter (TCD) Values for Vessels in Shallow Waters n
395
Exercise 43 1. Estimate the turning circle diameters and TCD coefficients with respect to the LBP for the following vessels:
Ship Type
Br Mld (m)
LBP (m)
Water Depth H (m)
Draft T (m)
Cb Value
(a) Container vessel (b) General cargo ship (c) Supertanker
32.26 20.00 55.00
250 140 320
30.00 20.00 14.85
7.50 8.20 13.50
0.581 0.705 0.820
2. For the supertanker in Question 1, predict the angle of heel at which the bilge plating would just go aground at station 7.5 were her forward speed to be 9.00 knots. n
Reference Captain Eduardo O. Gilardoni (2006). Manejo del buque en aguas restringidas (2nd edn), p. 160. Instituto Iberoamericano De Derecho Maritimo, Lavalle, Argentine.
Turning Circle Diameter (TCD) Values for Vessels in Shallow Waters Introduction First of all, what exactly is a turning circle diameter (TCD)? It is measured on ship trials that are carried out in deep-water conditions. H/T is usually greater than 6.00. The vessel is turned completely through 360 with, say, starboard helm and then with port helm. This will produce two TCDs of different diameters. This hypothesis is for: 1. 2. 3. 4.
Single-screw merchant ships only Each ship fitted with a horizontal propeller shaft rotating within a shaft tunnel TCD maneuver carried out at full speed Turning maneuver conducted with a rudder helm held at 35 .
It should be observed in Figure 43.1 that at the beginning of the starboard turning maneuver, the ship turns initially to port. There are two reasons for this. Forces acting on the rudder itself will cause this move at first to port. Larger centrifugal forces acting on the ship’s hull will then cause the vessel to move the ship on a course to starboard (see Figure 43.1). The maximum angle of heel must be recorded. If the ship has port rudder helm this final angle of heel will be to starboard and vice versa. Again, this is due to centrifugal forces acting on the ship’s hull. During the TCD maneuver the ship will experience transfer, advance, drift angle, and angle of heel. With regard to grounding at the bilge plating, in deep water the angle of heel will present few or no problems. However, if the trials were undertaken in shallow waters there is an increased possibility of grounding at the bilge plating.
Updates of 1987 and 2002 In November 1987, the IMO regulation was that H/T should be greater than 4.00, where H is the water depth and T is the mean static draft of the vessel. In December 2002, further resolutions were made by the IMO (Ref A 601 (15). Ship Stability for Masters and Mates. http://dx.doi.org/10.1016/B978-0-08-097093-6.00043-8 Copyright Ó 2012 Elsevier Ltd. All rights reserved.
389
390
Chapter 43
TCD IN WATER WHERE H/T = 1.10
PATH WHEN H/T = 1.10 ADVANCE IN DEEP WATER
ADVANCE IF H/T = 1.10
PATH OF SHIP’S CTR OF GRAVITY
1
2
3
5
7
9
SHIP 10 LENGTHS PATH WHEN H/T = 2.46
PATH WHEN H/T = 5.75
TCD IN DEEP WATER
Figure 43.1: Variation of TCD with H/T Values for a Supertanker. Note how TCD in very shallow waters is approximately twice that when ship is in deep waters.
In their Section 4 on values of TCD in shallow water, they stated the following: For all ships of 100 m in length and over: 4.1.1 TCD is to be measured with the ship model and ship as for the fully loaded condition. 4.1.2 The initial speed of the ship should be at half-ahead speed. 4.1.3 Times and speeds at 90 , 180 , 270 , and 360 turning should be specifically shown, together with an outline of the ship. 4.1.4 Rudder angle should be at a maximum and H/T ratio to be 1.20.
The obtained information for the above should be presented (a) on a pilot card, (b) on a wheelhouse posting, and (c) in a maneuvering booklet. Angles of heel should be presented on a spreadsheet (see Tables 43.1e43.4).
Turning Circle Diameter (TCD) Values for Vessels in Shallow Waters
391
Table 43.1: Cb
(Fd 1.10)
Draft T Fd (m)
0.800 10.00 5.93
Fd (H/T)actual (H/T)actual Y2
4.83
4.63
1.30
0.07
K [ 1.00 e2.00
Ship Speed (knots)
Max. Squat (m)
Br. Mld. LBP (m) (m)
1.07
10.00
0.80
32.26 200
Table 43.2: Angle of heel ( ) ½bsin a (m)
0 0.00
2 0.56
4 1.13
6 1.69
8 2.24
10 2.80
Table 43.3: Meters at station 7.5 or 2.5 with ship at zero angle of heel and with trim or even keel. Kmbs
mbs
Trim Change
0.800 0.64 0.72 At 0 angle of heel, squat at station 2.5 or 7.5 is 0.72 m at the bilge strakes P and S At 2 angle of heel, squat at station 2.5 or 7.5 is 1.28 m at the bilge strakes P and S At 4 angle of heel, squat at station 2.5 or 7.5 is 1.85 m at the bilge strakes P and S At 6 angle of heel, squat at station 2.5 or 7.5 is 2.41 m at the bilge strakes P and S At 8 angle of heel, squat at station 2.5 or 7.5 is 2.96 m at the bilge strakes P and S At 10 angle of heel, squat at station 2.5 or 7.5 is 3.52 m at the bilge strakes P and S
Table 43.4: Heel Angle ( )
Squats (m)
0 2 4 6 8 10
0.72 1.28 1.85 2.41 2.96 3.52
Tanker’s speed is 10 knots.
392
Chapter 43
Some Observations • • • • • • •
A 1% increase in trim by the stern in deep water increases the TCD by 10%. Changes in a ship’s displacement do not alter changes in TCD values. Fine-form ships have greater TCD values than full-form ships. Hence container ships and passenger liners will have greater TCD values than supertankers. In deep water TCD for merchant ships is approximately three to four times ship’s LBP (see details in Figure 43.1). Ships with comparatively larger rudders have smaller TCD values. Any change in ship speed for another test run will not cause a change in TCD value. When H/T is 1.10, TCD can be double that for when ship is in deep waters (see details in Figure 43.1 and Table 43.5).
Calculations When a ship has a water depth greater than depth of influence, the ship is in deep water and the coefficient (KTCD) for TCD is 1.00. If the ship has a water depth of 1.10 times the ship’s mean draft, then the coefficient (KTCD) for TCD is about 2.00. So KTCD is 1.00e2.00. FD ¼ 4:44=ðCb Þ1:3 times each ship&s mean static even-keel draft
This will alter with each ship type. For a specific ship it will change with each condition of loading. A detailed study of this by the author produced the following equation: KTCD ¼ 1 þ fðFD H=Tactual Þ=ðFD 1:10Þg2
Figure 43.2 shows the values for KTCD against H/T, for several Cb values ranging from full-form to fine-form ships. Table 43.5: H/T
Cb
Water Depth
KTCD
5.75 2.46 1.10
0.820 0.820 0.820
Deep water Shallow Very shallow water
1.00 1.50 2.00
0.500
393
FD = 10.93
0.600
0.700
FD = 8.62
2
FD = 7.06
FD = 5.09 FD = 5.93
3
I.E. 10% UKG
H/T = 1.10
TCD COEFFICIENT
CB VALUES
0.900 0.800
Turning Circle Diameter (TCD) Values for Vessels in Shallow Waters
1
0
2
4
6
8
10
12
H/T VALUES
Figure 43.2: TCD Coefficient Plotted Against H/T. At H/T ¼ 1.10, KTCD ¼ 2.0 in very shallow water at each FD value; KTCD ¼ 1.0 in deep water. Hence, TCD is twice the the TCD in deep water. When H/T ¼ 1.00, the vessel has grounded. Each FD ¼ 4.44/C1.3 b , varying with ship type and Cb. H/T > FD means ship is in deep water; H/T FD means that the ship is in shallow waters, and KTCD will increase above 1.00. KTCD ¼ 1 þ {(FD H/Tactual)/ (FD 1.10)}2. Range of KTCD ¼ 1.00e2.00.
n
Worked Example Let us now consider one hull form, that of an oil tanker with LBP of 200 m and a Cb of 0.800. Let breadth molded be 32.26 m, the static mean draft be 10.00 m, the water depth be 46.30m, and the ship speed be 10 knots. TCD in deep waters z 3:25 LBP ¼ 650 m ðF D 1:10Þ ¼ 5:93 1:10 ¼ 4:83 m ðF D H=T actual Þ ¼ 5:93 4:63 ¼ 1:30 m fðF D H=Tactual Þ=ðFd 1:10Þg2 ¼ 0:07 KTCD ¼ 1 þ 0:07 ¼ 1:07
ðcolumn 4 in Table 43:1Þ ðcolumn 6 in Table 43:1Þ ðcolumn 7 in Table 43:1Þ
ðcolumn 8 in Table 43:1Þ
Consequently, at H/T of 4.63, the TCD is 1.07 650 ¼ 760.5 m instead of 650 m. Continuing: Maximum squat at the bow ¼ ðCb V2 Þ=100 ¼ 0:800 10 10=100 ¼ 0:80 m
394
Chapter 43 Loss of ukc at bilge plating ¼ 1=2 bsin a ¼ 16:13sin a
ðsee Table 43:2Þ
where a is the angle of heel, ranging from 0 to 10 . Mean bodily sinkage ¼ K mbs max: squat ¼ f1 20ð0:700 Cb Þ2 g 0:80 ¼ f1 20ð0:700 0:80Þ2 g 0:80 ¼ 0:80 0:80 ¼ 0:64 m from bow to stern
ðsee Table 43:3Þ
Trim at station 7:5 ¼ ðmbs þ max: squatÞ=2 ¼ 0:64 þ 0:80 ¼ 0:72m
ðsee column 3 in Table 43:3Þ
Transverse squat at the bilge plating at station 7:5 ¼ 0:72 þ 1=2 bsin a
ðTable 43:4Þ
where a is angle of heel ranging from 0 to 10 . n
Summary This oil tanker will go aground at the bilge plating port or starboard at an angle of heel of 4.82 . This is shown in graphical form in Figure 43.3, where the transverse squat due to mean bodily sinkage plus angle of heel is equal to the static ukc even keel of 2.00 m.
Squat values at Bilge plating
Angle of Heel in degrees 0 1 2 3 0.00 –1.00 –2.00 static ukc = 2m –3.00 –4.00
4
5
6
7
8
9
10
ship grounds at the Bilge plating
Figure 43.3: Squats at Bilge Plating.
Turning Circle Diameter (TCD) Values for Vessels in Shallow Waters n
395
Exercise 43 1. Estimate the turning circle diameters and TCD coefficients with respect to the LBP for the following vessels:
Ship Type
Br Mld (m)
LBP (m)
Water Depth H (m)
Draft T (m)
Cb Value
(a) Container vessel (b) General cargo ship (c) Supertanker
32.26 20.00 55.00
250 140 320
30.00 20.00 14.85
7.50 8.20 13.50
0.581 0.705 0.820
2. For the supertanker in Question 1, predict the angle of heel at which the bilge plating would just go aground at station 7.5 were her forward speed to be 9.00 knots. n
Reference Captain Eduardo O. Gilardoni (2006). Manejo del buque en aguas restringidas (2nd edn), p. 160. Instituto Iberoamericano De Derecho Maritimo, Lavalle, Argentine.