MVFS_Mooring_Analysis.pdf
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M/V FREEDON STAR
Mooring Analysis at SIU Paul Hall Center Piney Point Pier Facility Prepared for: Office of Ship Operations; Division of Sealift Operations & Response
(MAR-612)
Prepared by: Todd M. Hiller, P.E. - Department of Transportation; Maritime Administration;
Office of Shipyards & Marine Engineering (MAR-720)
Rev. A
MAR-720 September 28, 2015
Office of Shipyards & Marine Engineering
Maritime Administration
EXECUTIVE SUMMARY
Objective
Overview
REQUIREMENTS
RESULTS
CONCLUSION & RECOMMENDATIONS
REFERENCES
APPENDIX A
Minimum Number of Timber Cluster Piles required
APPENDIX B
0 deg Wind & 90 deg Current
APPENDIX C
45 deg Wind & 90 deg Current
APPENDIX D
90 deg Wind & 90 deg Current
APPENDIX E
135 deg Wind & 90 deg Current
APPENDIX F
180 deg Wind & 90 deg Current
APPENDIX G
Geometry of Mooring Arrangement
EXECUTIVE SUMMARY
Objective
MAR-720 was requested by MAR-612 to determine a mooring arrangement for the Merchant
Vessel Freedom Star (MVFS) at the SIU Paul Hall Center for Maritime Training and Education pier facility inside of Hodgson Point at the confluence of the Potomac River and St. Mary’s
River in Piney Point, Maryland. The vessel is proposed to be moored on the starboard side to the pier, Figure 1. The likelihood of vessel movement from passing ship wakes and sea wave action will be minimal due to her proximity and location relative to other vessel traffic on the St.
Mary’s River. The pier facility has ten (10) equally spaced timber pile clusters to serve as fendering to protect the vessel from any incidences of storms or hurricanes.
Overview
A mooring analysis was performed to the Unified Facilities Criteria (UFC), Ref.3-4. The Paul
Hall Center facility design criterion was a TYPE IIB Storm Mooring requirement. The analysis covers wind speeds set at 64 knots (varied directions) and transverse current of 2.0 knots. This criterion requirement is encouraged and used by the US Navy as a mooring design model for general home ports due to the short timeframe of sudden storms producing high winds.
Determining whether a facility is “exposed”, “moderate”, or “sheltered” depends on the environmental conditions at the site and is a matter for professional local judgment. Most inland facilities in the Unites States are considered “sheltered” due to their proximity in protected waters. The Paul Hall Center facility is considered a sheltered facility where wave impact to vessel mooring is negligible. Therefore, wave impact to mooring is not included in the results of this analysis.
Figure 1 – Arial view of SIU Piney Point pier facility and proposed location of MVFS
REQUIREMENTS
The MVFS will moor abreast in a southwesterly direction with the pier. The flat of side (FOS) portion of the MVFS can be viewed in Figure 2. The berthing arrangement proposed is shown in
Figure 3. Amidships for the vessel (Fr.42) was used as a reference when aligning the vessel to the pier. A combination of synthetic mooring lines provided by the MVFS was used for the analysis with additional (doubled up) mooring lines for 4, 5 & 10. The actual sizes and type of line was allocated for each mooring point and included in the analysis. The berthing energy calculations followed the methodology specified in Ref. 3 and is provided in Appendix A.
Vessel Description:
Hull Material: Steel
Length Overall (LOA): 176’
Length of Waterline: 166’
Beam, B: 37’
Mean Draft, T: 11’-6”
Displacement: 1,000 LT
Desired Spacing b/t pier & MVFS: 4’- 6’ @ DWL
Length of Flat-Of-Side (FOS): Fr. 40 to Fr. 83 ~ 86’
Sectional Projected Wind Area, AT (ft ): 980
Side Profile Projected Wind Area, AL (ft ): 3,674
Figure 2 - FOS Location, Approximately Frames 40-83 (S/P)
RESULTS
The revised results of the mooring analysis conducted to evaluate mooring line loads under specified design conditions are found in Appendix B-F. Appendix G shows a revised proposed geometry of the mooring lines between the MVFS and Paul Hall Center pier facility.
CONCLUSION & RECOMMENDATIONS
The original effort resulted in a revision of the original mooring arrangement based upon newly acquired 15T cleats and the existing mooring line inventory. Eight (8) cleats are now secured to the pier as shown in Appendix G. The acquisition of cleats led us to calculate the anticipated loads generated for a Type IIB mooring requirement. The results are shown in Appendix A.
Additionally, four (4) 50MT bollards are being ordered and will be placed in accordance with
Appendix G. Based upon the geometry and mooring configuration between the MVFS and pier, the remaining amount of mooring line provided by the ships force was approximately over 35 feet for the Amsteel and Poly and slightly over 50 feet for the Dacron lines. Unified Facilities
Criteria, Ref. 3-4 design methods was used to calculate associated loads applied, at various angles, to the vessels’ mooring arrangement.
This report addresses a conceptual arrangement for the MVFS to be staged and moored abreast the
Paul Hall Center pier facility at Piney Point. The ships master and MARAD Regional representative will make the final determination as to how the MVFS should be moored to ensure minimal adverse impact to the vessel and/or pier during any future hurricanes or inclement weather in the immediate region. Concluding the mooring of the MVFS at the Paul Hall Center pier, a post-mooring analysis/survey should be conducted to further verify the conceptual arrangement detailed in this report and/or reassess the final mooring arrangement.
REFERENCES
1 Naval Ships Technical Manual (NSTM) S9086-US-STM-010 , Chapter 611 FENDERS
AND SEPARATORS
2 Naval Facilities Engineering Command (NAVFAC), MO-104.1, Maintenance of Fender
Systems and Camels
3 Unified Facilities Criteria (UFC) 4-159-03, Design Moorings
4 Unified Facilities Criteria (UFC) 4-150-08, Inspection of Mooring Hardware
5 Unified Facilities Guide Specifications (UFGS), Division 35- Waterway and Marine
Construction, Section 35 59 13.16 Marine Fenders.
6 Randall, Robert E., Elements of Ocean Engineering, SNAME, 1997.
7 Milwee, William I., Modern Marine Salvage, Cornell Maritime Press, 1996.
8 USMMA, T/V Kings Pointer Heavy Weather Mooring Plan, August 2014.
9 Maritime International, Mooring Bollards Catalog, USA@maritime-international.com.
APPENDIX A
Minimum Number of Timber Cluster Piles required
Project:
M/V FS Mooring Analysis
@ Piney Point
Title: Job Number:
M/V Freedom Star Mooring Analysis MAR-720
Description:
Timber Pile Cluster Pressure on Hull:
Dimensions:
Length = 24.0 in
Width = 24.0 in
Depth = 48.0 in
Number of vertical pieces in contact w/ hull (est.) = 1 per timber pile cluster
TPC (Southern Pine) Compression Rating (est.) = 224,032 ft-lbs
Berthing Energy Applied = 406,035 ft-lbs
# of TPCs required to overcome Berthing Energy applied= 3 timber pile clusters
TPC Contact Area = 127 in2/fender
Total TPC Contact Area = 380 in2
Mooring - 64.0 knot wind @ 0 deg. and 2.0 knot current @ 90 deg. to the Piney Point Pier at a 11.5 draft
@ Piney Point
Title: Job Number:
Pier Cleat Calculations MAR-720
Description:
Loading Information:
Design Load: 30,000 lbf
Fitting Geometry:
Number of Bolts: 6
Size of Bolt: 0.875 in - dia.
Area of Bolt: 0.601 in2
Pitch: 6.00 in
Back Pitch: 6.00 in
Second moment of area about centroid, I: 119 in4
Height of load on cleat: 7.75 in
Calculations for Design Load, F:
Direct Load on Individual Bolt: 5,000 lbs
Direct Shear Stress td: 8,315 psi
Max moment applied per Bolt: 38,750 lbf-in tx: 2,929 psi ty: 976 psi td + ty: 9,291 psi tT: 9,742 total shear stress on bolt
Material Properties:
Yield Strength of F1554 Grade Bolt: 105,000 psi
Design Load Factor of Safety on Yield, nuw: 11
Direct Load on Individual Bolt: 9,494 lbs
Direct Shear Stress td: 15,789 psi
Max moment applied per Bolt: 73,579 lbf-in tx: 5,562 psi ty: 1,854 psi td + ty: 17,643 psi tT: 18,499 total shear stress on bolt
Material Properties:
Yield Strength of F1554 Grade Bolt: 105,000 psi
Implied Load Factor of Safety on Yield, nuw: 6
Office of Shipyards & Marine Engineering
Mooring - 64.0 knot wind @ 90 deg. and 2.0 knot current @ 90 deg. to the Piney Point Pier at a 11.5 draft
Calculations for Applied Load, 64.0 knot wind @ 90 deg. and 2.0 knot current @ 90 deg.
APPENDIX B
0 deg Wind & 90 deg Current
@ Piney Point
Title: Job Number:
MAR-720
Description:
Ship: M/V Freedom Star
Moored Draft:
Line 1 Displacement LT 1,000
L2 LWL ft 166.2
L3 Draft, T ft 11.5
L4 Beam, B ft 37.0
L5 Sectional Projected Wind Area, AT ft 2 980
L6 Side Profile Projected Wind Area, AL ft 2 3,674
L7 Wind Speed, Vw kt 64
L8 Current Speed, Vc kt 2
L9 Wind Angle, qw (180 o /bow & 0 o /stern) degrees 0
L10 Current Angle, qc (180 o /bow & 0 o /stern) degrees 90
L11 Water Depth, Wd ft 13
L12 Fyw = 0.5 r a Vw Ay Cyw fyw {q w} lbs 392
L13 r a = mass density of air slug/ft 3 0.00237
L14 Vw = wind speed ft-sec 108.02
L15 Ay = side profile projected area of the ship ft 2 3,674
L16 Cyw = Side Profile Wind Force Drag Coefficient 0.77
L17 C = empirical coefficient (Table 4-2) 0.92
L18 hR = reference height ft 32.8
L19 hH = AH / LwL = average height of hull ft 3.7
L20 AH = side profile wind area of hull ft 2 616
L21 hS = height of the superstructure above waterline ft 45.0
L22 AS = side profile wind area of superstructure ft 2 3,058
L23 fyw = side profile wind coefficient shape function 0.010
L24 Fxw = 0.5 r a Vw Ax Cxw fxw {q w} lbs 8,126
L25 Ax = sectional projected area of the ship ft 2 980
L26 CxwB = Bow Sectional Wind Force Drag Coefficient 0.700
L27 CxwS = Stern Sectional Wind Force Drag Coefficient 0.600
L28 Location of Superstructure Fwd of MS
L29 qx 100
L30 g = shape function for sectional wind loads degrees 90
L31 fxw = sectional wind coefficient shape function 1.000
L32 Cxw = Sectional Wind Force Drag Coefficient 0.600
L33 Mxyw = 0.5 ra Vw Ay LCxyw {qw} ft-lb 0
L34 Cxyw = Yaw Normalized Moment Coefficient 0.000
L35 qz 75
L36 a1 0.030
L37 a2 0.050
L38 l 0.000
L39 Total Side Profile Wind Forces lbs 392
L40 Total Sectional Wind Forces lbs 8,126
L41 Total Yaw Moment ft-lbs 0
Wind Force
Ship Particulars
Mooring - 64.0 knot wind @ 0 deg. and 2.0 knot current @ 90 deg. to the Piney Point Pier at a 11.5 draft
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
Prepared by: T.M. Hiller, P.E.
Date: 9/28/2015 UFC 4-159-03 Sheet 1 of 2
@ Piney Point
Title: Job Number:
MAR-720
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
L41 Fyc = 0.5 rw Vc LwL TCyc {qc} lb 57,222
L42 rw = mass density of water slug/ft 3 1.9905
L43 Vc = current speed ft-sec 3.38
L44 LWL ft 166.2
L45 Draft, T ft 11.5
L46 Water Depth, Wd ft 13.0
L47 Cyc = side profile current force drag coefficient 2.64
L48 CO = deepwater current force drag coefficient 0.62
L49 c = ship parameters 8.00
L50 Am = immersed cross-sectional area at midships ft 2 374.44
L51 Cm = midship coefficient 0.8800
L52 V = submerged volume ft 3 34,977
L53 C1 = shallow water current force drag coefficient 3.2
L54 K = dimensionless exponent 2
L55 Fxc = FxFORM + FxFRICTION + FxPROP 928
L56 FxFORM 483
L57 Cxcb= Sectional current force drag coefficient 0.1
L58 FxFRICTION 99
L59 Cxca= sectional skin friction coefficient 0.003
L60 S = wetted surface area ft 2 3,251
L61 RN= Reynolds Number 19,616,993
L62 v = Kinematic viscosity 1.2817E-05
L63 FxPROP 347
L64 Ap = propeller expanded blade area ft 2 30.6
L65 CPROP = propeller drag coefficient 1.0
L66 ATpp = Total projected propeller area 26
L67 Type of Ship Cargo
L68 AR = dimensionless area ratio for propellers 240
L69 Mxyc = Fyc(ec/LwL)LwL ft-lb -2,715,278
L70 Fyc = side profile current force 57,222
L71 e/Lwl = ratio of eccentricity to vessel waterline length -0.285
L72 Total Side Profile Current Forces lbs 57,222
L73 Total Sectional Current Forces lbs 928
L74 Total Yaw Moment ft-lbs -2,715,278
L75 Total Side Profile Forces lb 57,613
L76 Total Sectional Forces lb 9,054
L78 Total Yaw Moment ft-lb -2,715,278
Total Forces
Current Force
Date: 9/28/2015 UFC 4-159-03 Sheet 2 of 2
Job Number:
MAR-720
MOORING LINE INFORMATION
MOORING LINE STIFFNESS MATRIX DEFINITION AND MOORING LINE TENSION CALCULATION
Mooring Line
No.
dZi = Zch - Zbl cos qi =
(Ybl -Ych) /
Li sin qi =
(Xbl -Xch) /
Li fi = tan -1
(dZi/Li)
(degrees) cos fi LT = Lo +
Li/cos fi
1 10.8 0.646 0.764 17.2 0.955 44.3
2 10.8 0.971 -0.238 25.0 0.906 30.8
3 8.7 0.978 0.211 36.4 0.805 17.5
4 8.7 0.401 0.916 16.8 0.957 36.9
5 8.7 0.192 -0.981 7.0 0.992 87.6
6 -1.3 0.226 0.974 -1.3 1.000 67.6
7 -1.3 0.990 0.143 -7.0 0.993 13.0
8 -1.3 0.957 -0.289 -2.7 0.999 34.1
9 -1.3 0.562 -0.827 -1.6 1.000 58.0
10 -1.3 0.359 -0.933 -0.9 1.000 97.5
11 10.8 0.542 0.840 10.2 0.984 70.1
* (BS) = total line breaking strength = BSrope x (number of rope parts per line)
Mooring Line
No.
Mooring Line
Type
Nom. Line
Dia. (in.)
Load Area ai
(sq.in.)
El
(1,000 PSI)
(BS)*
(1,000 lb)
Number of
Parts/Line
Ki = ai Ei /
LT
1 Amsteel 1.50 1.77 1.8 15,229 205.0 1 607.4
2 Amsteel 1.50 1.77 1.8 15,229 205.0 1 875.0
3 Amsteel 1.50 1.77 1.8 15,229 205.0 1 1540.7
4 Dacron 2.25 3.98 8.0 2,176 179.9 2 469.2
5 Dacron 2.25 3.98 8.0 2,176 179.9 2 197.4
6 Poly 2.25 3.98 4.0 508 63.0 1 29.9
7 Poly 2.25 3.98 4.0 508 63.0 1 155.2
8 Poly 2.25 3.98 4.0 508 63.0 1 59.2
9 Amsteel 1.50 1.77 1.8 15,229 205.0 1 463.9
10 Amsteel 1.50 1.77 3.5 15,229 410.0 2 551.8
11 Amsteel 1.50 1.77 1.8 15,229 205.0 1 384.0
Mooring Line
No.
Kxi = Ki x sin qi x cos fi
Kyi = Ki x cos qi x cos fi
Kxi x lyi Kyi x lxi Kxi x ly
Kyi x lx
Fxi =
Kxi x dx +
Kxi x lyi x g
(1,000 lb)
Fyi =
Kyi x dy +
Kyi x lxi x g
(1,000 lb)
Mri = Kxi x lyi x dx+ Kyi x lxi x dy + (Kxi x ly + Kyi x lx ) x g)
(1,000 lb)
Ti = Fyi /
(cos qi x cos fi)
(1,000 lb)
FS= (BS)*
/ Ti
Percent
Strength (%)
1 0.0 374.5 0.0 33,326 2,965,672 0.0 1.2 -107 1.9 105.2 1%
2 -189.1 770.1 775.2 68,529 6,095,238 1.2 2.5 -225 2.8 73.0 1%
3 0.0 1,212.7 0.0 69,112 3,938,720 0.0 13.7 779 17.4 11.8 8%
4 0.0 180.1 0.0 10,264 584,961 0.0 2.0 0 5.3 34.0 3%
5 -192.3 37.6 2,864.7 2,144 79,509 0.3 0.4 20 2.2 80.8 1%
6 0.0 6.7 0.0 -223 7,348 0.0 0.4 0 1.6 40.5 2%
7 0.0 152.5 0.0 -5,034 166,159 0.0 7.9 0 8.1 7.8 13%
8 -17.1 56.6 0.0 -4,475 353,566 0.1 4.1 -326 4.3 14.6 7%
9 -383.5 260.6 0.0 -20,591 1,626,897 3.2 19.0 -1,499 33.8 6.1 16%
10 -514.8 198.3 0.0 -15,666 1,237,773 4.2 14.4 -1,141 40.2 10.2 10%
11 0.0 205.0 0.0 18,240 1,623,194 0.0 0.7 0 1.2 166.3 1%
Office of Shipyards & Marine Engineering
Title:
Mooring - 64.0 knot wind @ 0 deg. and 2.0 knot current @ 90 deg. to the Piney
Point Pier at a 11.5 draft
M/V FS Mooring Analysis @
Piney Point
Prepared by: Todd M. Hiller, P.E.
Date: 9/28/2015 Mooring Line CALC Sheet Sheet 1 of 1
APPENDIX C
45 deg Wind & 90 deg Current
@ Piney Point
Title: Job Number:
MAR-720
Description:
Ship: M/V Freedom Star
Moored Draft:
Line 1 Displacement LT 1,000
L2 LWL ft 166.2
L3 Draft, T ft 11.5
L4 Beam, B ft 37.0
L5 Sectional Projected Wind Area, AT ft 2 980
L6 Side Profile Projected Wind Area, AL ft 2 3,674
L7 Wind Speed, Vw kt 64
L8 Current Speed, Vc kt 2
L9 Wind Angle, qw (180 o /bow & 0 o /stern) degrees 45
L10 Current Angle, qc (180 o /bow & 0 o /stern) degrees 90
L11 Water Depth, Wd ft 13
L12 Fyw = 0.5 r a Vw Ay Cyw fyw {q w} lbs 31,005
L13 r a = mass density of air slug/ft 3 0.00237
L14 Vw = wind speed ft-sec 108.02
L15 Ay = side profile projected area of the ship ft 2 3,674
L16 Cyw = Side Profile Wind Force Drag Coefficient 0.77
L17 C = empirical coefficient (Table 4-2) 0.92
L18 hR = reference height ft 32.8
L19 hH = AH / LwL = average height of hull ft 3.7
L20 AH = side profile wind area of hull ft 2 616
L21 hS = height of the superstructure above waterline ft 45.0
L22 AS = side profile wind area of superstructure ft 2 3,058
L23 fyw = side profile wind coefficient shape function 0.792
L24 Fxw = 0.5 r a Vw Ax Cxw fxw {q w} lbs 7,296
L25 Ax = sectional projected area of the ship ft 2 980
L26 CxwB = Bow Sectional Wind Force Drag Coefficient 0.700
L27 CxwS = Stern Sectional Wind Force Drag Coefficient 0.600
L28 Location of Superstructure Fwd of MS
L29 qx 100
L30 g = shape function for sectional wind loads degrees 130.5
L31 fxw = sectional wind coefficient shape function 0.948
L32 Cxw = Sectional Wind Force Drag Coefficient 0.569
L33 Mxyw = 0.5 ra Vw Ay LCxyw {qw} ft-lb -240,914
L34 Cxyw = Yaw Normalized Moment Coefficient -0.029
L35 qz 75
L36 a1 0.030
L37 a2 0.050
L38 l 1.009
L39 Total Side Profile Wind Forces lbs 31,005
L40 Total Sectional Wind Forces lbs 7,296
L41 Total Yaw Moment ft-lbs -240,914
Wind Force
Ship Particulars
Mooring - 64.0 knot wind @ 45 deg. and 2.0 knot current @ 90 deg. to the Piney Point Pier at a 11.5 draft
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
@ Piney Point
Title: Job Number:
MAR-720
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
L41 Fyc = 0.5 rw Vc LwL TCyc {qc} lb 57,222
L42 rw = mass density of water slug/ft 3 1.9905
L43 Vc = current speed ft-sec 3.38
L44 LWL ft 166.2
L45 Draft, T ft 11.5
L46 Water Depth, Wd ft 13.0
L47 Cyc = side profile current force drag coefficient 2.64
L48 CO = deepwater current force drag coefficient 0.62
L49 c = ship parameters 8.00
L50 Am = immersed cross-sectional area at midships ft 2 374.44
L51 Cm = midship coefficient 0.8800
L52 V = submerged volume ft 3 34,977
L53 C1 = shallow water current force drag coefficient 3.2
L54 K = dimensionless exponent 2
L55 Fxc = FxFORM + FxFRICTION + FxPROP 928
L56 FxFORM 483
L57 Cxcb= Sectional current force drag coefficient 0.1
L58 FxFRICTION 99
L59 Cxca= sectional skin friction coefficient 0.003
L60 S = wetted surface area ft 2 3,251
L61 RN= Reynolds Number 19,616,993
L62 v = Kinematic viscosity 1.2817E-05
L63 FxPROP 347
L64 Ap = propeller expanded blade area ft 2 30.6
L65 CPROP = propeller drag coefficient 1.0
L66 ATpp = Total projected propeller area 26
L67 Type of Ship Cargo
L68 AR = dimensionless area ratio for propellers 240
L69 Mxyc = Fyc(ec/LwL)LwL ft-lb -2,715,278
L70 Fyc = side profile current force 57,222
L71 e/Lwl = ratio of eccentricity to vessel waterline length -0.285
L72 Total Side Profile Current Forces lbs 57,222
L73 Total Sectional Current Forces lbs 928
L74 Total Yaw Moment ft-lbs -2,715,278
L75 Total Side Profile Forces lb 88,227
L76 Total Sectional Forces lb 8,224
L78 Total Yaw Moment ft-lb -2,956,192
Total Forces
Current Force
MAR-720
MOORING LINE INFORMATION
MOORING LINE STIFFNESS MATRIX DEFINITION AND MOORING LINE TENSION CALCULATION
Mooring Line
No.
dZi = Zch - Zbl cos qi =
(Ybl -Ych) /
Li sin qi =
(Xbl -Xch) /
Li fi = tan -1
(dZi/Li)
(degrees) cos fi LT = Lo +
Li/cos fi
1 10.8 0.646 0.764 17.2 0.955 44.3
2 10.8 0.971 -0.238 25.0 0.906 30.8
3 8.7 0.978 0.211 36.4 0.805 17.5
4 8.7 0.401 0.916 16.8 0.957 36.9
5 8.7 0.192 -0.981 7.0 0.992 87.6
6 -1.3 0.226 0.974 -1.3 1.000 67.6
7 -1.3 0.990 0.143 -7.0 0.993 13.0
8 -1.3 0.957 -0.289 -2.7 0.999 34.1
9 -1.3 0.562 -0.827 -1.6 1.000 58.0
10 -1.3 0.359 -0.933 -0.9 1.000 97.5
11 10.8 0.542 0.840 10.2 0.984 70.1
* (BS) = total line breaking strength = BSrope x (number of rope parts per line)
Mooring Line
No.
Mooring Line
Type
Nom. Line
Dia. (in.)
Load Area ai
(sq.in.)
El
(1,000 PSI)
(BS)*
(1,000 lb)
Number of
Parts/Line
Ki = ai Ei /
LT
1 Amsteel 1.50 1.77 1.8 15,229 205.0 1 607.4
2 Amsteel 1.50 1.77 1.8 15,229 205.0 1 875.0
3 Amsteel 1.50 1.77 1.8 15,229 205.0 1 1540.7
4 Dacron 2.25 3.98 8.0 2,176 179.9 2 469.2
5 Dacron 2.25 3.98 8.0 2,176 179.9 2 197.4
6 Poly 2.25 3.98 4.0 508 63.0 1 29.9
7 Poly 2.25 3.98 4.0 508 63.0 1 155.2
8 Poly 2.25 3.98 4.0 508 63.0 1 59.2
9 Amsteel 1.50 1.77 1.8 15,229 205.0 1 463.9
10 Amsteel 1.50 1.77 3.5 15,229 410.0 2 551.8
11 Amsteel 1.50 1.77 1.8 15,229 205.0 1 384.0
Mooring Line
No.
Kxi = Ki x sin qi x cos fi
Kyi = Ki x cos qi x cos fi
Kxi x lyi Kyi x lxi Kxi x ly
Kyi x lx
Fxi =
Kxi x dx +
Kxi x lyi x g
(1,000 lb)
Fyi =
Kyi x dy +
Kyi x lxi x g
(1,000 lb)
Mri = Kxi x lyi x dx+ Kyi x lxi x dy + (Kxi x ly + Kyi x lx ) x g)
(1,000 lb)
Ti = Fyi /
(cos qi x cos fi)
(1,000 lb)
FS= (BS)*
/ Ti
Percent
Strength (%)
1 0.0 374.5 0.0 33,326 2,965,672 0.0 0.2 -15 0.3 745.6 0%
2 -189.1 770.1 775.2 68,529 6,095,238 1.1 0.3 -35 0.4 517.6 0%
3 0.0 1,212.7 0.0 69,112 3,938,720 0.0 22.4 1,277 28.5 7.2 14%
4 0.0 180.1 0.0 10,264 584,961 0.0 3.3 0 8.7 20.8 5%
5 -192.3 37.6 2,864.7 2,144 79,509 -0.2 0.7 42 3.6 49.3 2%
6 0.0 6.7 0.0 -223 7,348 0.0 0.5 0 2.1 29.4 3%
7 0.0 152.5 0.0 -5,034 166,159 0.0 10.9 0 11.1 5.7 18%
8 -17.1 56.6 0.0 -4,475 353,566 0.1 5.6 -443 5.9 10.7 9%
9 -383.5 260.6 0.0 -20,591 1,626,897 3.1 25.8 -2,037 45.9 4.5 22%
10 -514.8 198.3 0.0 -15,666 1,237,773 4.1 19.6 -1,550 54.6 7.5 13%
11 0.0 205.0 0.0 18,240 1,623,194 0.0 0.1 0 0.2 1,179.4 0%
Office of Shipyards & Marine Engineering
Title:
Mooring - 64.0 knot wind @ 45 deg. and 2.0 knot current @ 90 deg. to the
Piney Point Pier at a 11.5 draft
M/V FS Mooring Analysis @
Piney Point
APPENDIX D
90 deg Wind & 90 deg Current
@ Piney Point
Title: Job Number:
MAR-720
Description:
Ship: M/V Freedom Star
Moored Draft:
Line 1 Displacement LT 1,000
L2 LWL ft 166.2
L3 Draft, T ft 11.5
L4 Beam, B ft 37.0
L5 Sectional Projected Wind Area, AT ft 2 980
L6 Side Profile Projected Wind Area, AL ft 2 3,674
L7 Wind Speed, Vw kt 64
L8 Current Speed, Vc kt 2
L9 Wind Angle, qw (180 o /bow & 0 o /stern) degrees 90
L10 Current Angle, qc (180 o /bow & 0 o /stern) degrees 90
L11 Water Depth, Wd ft 13
L12 Fyw = 0.5 r a Vw Ay Cyw fyw {q w} lbs 39,562
L13 r a = mass density of air slug/ft 3 0.00237
L14 Vw = wind speed ft-sec 108.02
L15 Ay = side profile projected area of the ship ft 2 3,674
L16 Cyw = Side Profile Wind Force Drag Coefficient 0.77
L17 C = empirical coefficient (Table 4-2) 0.92
L18 hR = reference height ft 32.8
L19 hH = AH / LwL = average height of hull ft 3.7
L20 AH = side profile wind area of hull ft 2 616
L21 hS = height of the superstructure above waterline ft 45.0
L22 AS = side profile wind area of superstructure ft 2 3,058
L23 fyw = side profile wind coefficient shape function 1.010
L24 Fxw = 0.5 r a Vw Ax Cxw fxw {q w} lbs 74
L25 Ax = sectional projected area of the ship ft 2 980
L26 CxwB = Bow Sectional Wind Force Drag Coefficient 0.700
L27 CxwS = Stern Sectional Wind Force Drag Coefficient 0.600
L28 Location of Superstructure Fwd of MS
L29 qx 100
L30 g = shape function for sectional wind loads degrees 171
L31 fxw = sectional wind coefficient shape function 0.095
L32 Cxw = Sectional Wind Force Drag Coefficient 0.057
L33 Mxyw = 0.5 ra Vw Ay LCxyw {qw} ft-lb 109,766
L34 Cxyw = Yaw Normalized Moment Coefficient 0.013
L35 qz 75
L36 a1 0.030
L37 a2 0.050
L38 l 1.005
L39 Total Side Profile Wind Forces lbs 39,562
L40 Total Sectional Wind Forces lbs 74
L41 Total Yaw Moment ft-lbs 109,766
Wind Force
Ship Particulars
Mooring - 64.0 knot wind @ 90 deg. and 2.0 knot current @ 90 deg. to the Piney Point Pier at a 11.5 draft
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
@ Piney Point
Title: Job Number:
MAR-720
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
L41 Fyc = 0.5 rw Vc LwL TCyc {qc} lb 57,222
L42 rw = mass density of water slug/ft 3 1.9905
L43 Vc = current speed ft-sec 3.38
L44 LWL ft 166.2
L45 Draft, T ft 11.5
L46 Water Depth, Wd ft 13.0
L47 Cyc = side profile current force drag coefficient 2.64
L48 CO = deepwater current force drag coefficient 0.62
L49 c = ship parameters 8.00
L50 Am = immersed cross-sectional area at midships ft 2 374.44
L51 Cm = midship coefficient 0.8800
L52 V = submerged volume ft 3 34,977
L53 C1 = shallow water current force drag coefficient 3.2
L54 K = dimensionless exponent 2
L55 Fxc = FxFORM + FxFRICTION + FxPROP 928
L56 FxFORM 483
L57 Cxcb= Sectional current force drag coefficient 0.1
L58 FxFRICTION 99
L59 Cxca= sectional skin friction coefficient 0.003
L60 S = wetted surface area ft 2 3,251
L61 RN= Reynolds Number 19,616,993
L62 v = Kinematic viscosity 1.2817E-05
L63 FxPROP 347
L64 Ap = propeller expanded blade area ft 2 30.6
L65 CPROP = propeller drag coefficient 1.0
L66 ATpp = Total projected propeller area 26
L67 Type of Ship Cargo
L68 AR = dimensionless area ratio for propellers 240
L69 Mxyc = Fyc(ec/LwL)LwL ft-lb -2,715,278
L70 Fyc = side profile current force 57,222
L71 e/Lwl = ratio of eccentricity to vessel waterline length -0.285
L72 Total Side Profile Current Forces lbs 57,222
L73 Total Sectional Current Forces lbs 928
L74 Total Yaw Moment ft-lbs -2,715,278
L75 Total Side Profile Forces lb 96,784
L76 Total Sectional Forces lb 1,002
L78 Total Yaw Moment ft-lb -2,605,511
Total Forces
Current Force
MAR-720
MOORING LINE INFORMATION
MOORING LINE STIFFNESS MATRIX DEFINITION AND MOORING LINE TENSION CALCULATION
Mooring Line
No.
dZi = Zch - Zbl cos qi =
(Ybl -Ych) /
Li sin qi =
(Xbl -Xch) /
Li fi = tan -1
(dZi/Li)
(degrees) cos fi LT = Lo +
Li/cos fi
1 10.8 0.646 0.764 17.2 0.955 44.3
2 10.8 0.971 -0.238 25.0 0.906 30.8
3 8.7 0.978 0.211 36.4 0.805 17.5
4 8.7 0.401 0.916 16.8 0.957 36.9
5 8.7 0.192 -0.981 7.0 0.992 87.6
6 -1.3 0.226 0.974 -1.3 1.000 67.6
7 -1.3 0.990 0.143 -7.0 0.993 13.0
8 -1.3 0.957 -0.289 -2.7 0.999 34.1
9 -1.3 0.562 -0.827 -1.6 1.000 58.0
10 -1.3 0.359 -0.933 -0.9 1.000 97.5
11 10.8 0.542 0.840 10.2 0.984 70.1
* (BS) = total line breaking strength = BSrope x (number of rope parts per line)
Mooring Line
No.
Mooring Line
Type
Nom. Line
Dia. (in.)
Load Area ai
(sq.in.)
El
(1,000 PSI)
(BS)*
(1,000 lb)
Number of
Parts/Line
Ki = ai Ei /
LT
1 Amsteel 1.50 1.77 1.8 15,229 205.0 1 607.4
2 Amsteel 1.50 1.77 1.8 15,229 205.0 1 875.0
3 Amsteel 1.50 1.77 1.8 15,229 205.0 1 1540.7
4 Dacron 2.25 3.98 8.0 2,176 179.9 2 469.2
5 Dacron 2.25 3.98 8.0 2,176 179.9 2 197.4
6 Poly 2.25 3.98 4.0 508 63.0 1 29.9
7 Poly 2.25 3.98 4.0 508 63.0 1 155.2
8 Poly 2.25 3.98 4.0 508 63.0 1 59.2
9 Amsteel 1.50 1.77 1.8 15,229 205.0 1 463.9
10 Amsteel 1.50 1.77 3.5 15,229 410.0 2 551.8
11 Amsteel 1.50 1.77 1.8 15,229 205.0 1 384.0
Mooring Line
No.
Kxi = Ki x sin qi x cos fi
Kyi = Ki x cos qi x cos fi
Kxi x lyi Kyi x lxi Kxi x ly
Kyi x lx
Fxi =
Kxi x dx +
Kxi x lyi x g
(1,000 lb)
Fyi =
Kyi x dy +
Kyi x lxi x g
(1,000 lb)
Mri = Kxi x lyi x dx+ Kyi x lxi x dy + (Kxi x ly + Kyi x lx ) x g)
(1,000 lb)
Ti = Fyi /
(cos qi x cos fi)
(1,000 lb)
FS= (BS)*
/ Ti
Percent
Strength (%)
1 0.0 374.5 0.0 33,326 2,965,672 0.0 0.7 61 1.1 185.8 1%
2 -189.1 770.1 775.2 68,529 6,095,238 0.0 1.4 125 1.6 128.9 1%
3 0.0 1,212.7 0.0 69,112 3,938,720 0.0 25.3 1,444 32.2 6.4 16%
4 0.0 180.1 0.0 10,264 584,961 0.0 3.8 0 9.8 18.3 5%
5 -192.3 37.6 2,864.7 2,144 79,509 -1.2 0.8 63 4.1 43.6 2%
6 0.0 6.7 0.0 -223 7,348 0.0 0.5 0 2.2 28.3 4%
7 0.0 152.5 0.0 -5,034 166,159 0.0 11.4 0 11.6 5.4 18%
8 -17.1 56.6 0.0 -4,475 353,566 0.0 5.8 -456 6.0 10.4 10%
9 -383.5 260.6 0.0 -20,591 1,626,897 0.9 26.6 -2,100 47.3 4.3 23%
10 -514.8 198.3 0.0 -15,666 1,237,773 1.3 20.2 -1,598 56.3 7.3 14%
11 0.0 205.0 0.0 18,240 1,623,194 0.0 0.4 0 0.7 293.8 0%
Office of Shipyards & Marine Engineering
Title:
Mooring - 64.0 knot wind @ 90 deg. and 2.0 knot current @ 90 deg. to the
Piney Point Pier at a 11.5 draft
M/V FS Mooring Analysis @
Piney Point
APPENDIX E
135 deg Wind & 90 deg Current
@ Piney Point
Title: Job Number:
MAR-720
Description:
Ship: M/V Freedom Star
Moored Draft:
Line 1 Displacement LT 1,000
L2 LWL ft 166.2
L3 Draft, T ft 11.5
L4 Beam, B ft 37.0
L5 Sectional Projected Wind Area, AT ft 2 980
L6 Side Profile Projected Wind Area, AL ft 2 3,674
L7 Wind Speed, Vw kt 64
L8 Current Speed, Vc kt 2
L9 Wind Angle, qw (180 o /bow & 0 o /stern) degrees 135
L10 Current Angle, qc (180 o /bow & 0 o /stern) degrees 90
L11 Water Depth, Wd ft 13
L12 Fyw = 0.5 r a Vw Ay Cyw fyw {q w} lbs 31,005
L13 r a = mass density of air slug/ft 3 0.00237
L14 Vw = wind speed ft-sec 108.02
L15 Ay = side profile projected area of the ship ft 2 3,674
L16 Cyw = Side Profile Wind Force Drag Coefficient 0.77
L17 C = empirical coefficient (Table 4-2) 0.92
L18 hR = reference height ft 32.8
L19 hH = AH / LwL = average height of hull ft 3.7
L20 AH = side profile wind area of hull ft 2 616
L21 hS = height of the superstructure above waterline ft 45.0
L22 AS = side profile wind area of superstructure ft 2 3,058
L23 fyw = side profile wind coefficient shape function 0.792
L24 Fxw = 0.5 r a Vw Ax Cxw fxw {q w} lbs 2,352
L25 Ax = sectional projected area of the ship ft 2 980
L26 CxwB = Bow Sectional Wind Force Drag Coefficient 0.700
L27 CxwS = Stern Sectional Wind Force Drag Coefficient 0.600
L28 Location of Superstructure Fwd of MS
L29 qx 100
L30 g = shape function for sectional wind loads degrees 211.5
L31 fxw = sectional wind coefficient shape function -0.538
L32 Cxw = Sectional Wind Force Drag Coefficient -0.323
L33 Mxyw = 0.5 ra Vw Ay LCxyw {qw} ft-lb 366,307
L34 Cxyw = Yaw Normalized Moment Coefficient 0.043
L35 qz 75
L36 a1 0.030
L37 a2 0.050
L38 l 1.003
L39 Total Side Profile Wind Forces lbs 31,005
L40 Total Sectional Wind Forces lbs 2,352
L41 Total Yaw Moment ft-lbs 366,307
Wind Force
Ship Particulars
Mooring - 64.0 knot wind @ 135 deg. and 2.0 knot current @ 90 deg. to the Piney Point Pier at a 11.5 draft
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
@ Piney Point
Title: Job Number:
MAR-720
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
L41 Fyc = 0.5 rw Vc LwL TCyc {qc} lb 57,222
L42 rw = mass density of water slug/ft 3 1.9905
L43 Vc = current speed ft-sec 3.38
L44 LWL ft 166.2
L45 Draft, T ft 11.5
L46 Water Depth, Wd ft 13.0
L47 Cyc = side profile current force drag coefficient 2.64
L48 CO = deepwater current force drag coefficient 0.62
L49 c = ship parameters 8.00
L50 Am = immersed cross-sectional area at midships ft 2 374.44
L51 Cm = midship coefficient 0.8800
L52 V = submerged volume ft 3 34,977
L53 C1 = shallow water current force drag coefficient 3.2
L54 K = dimensionless exponent 2
L55 Fxc = FxFORM + FxFRICTION + FxPROP 928
L56 FxFORM 483
L57 Cxcb= Sectional current force drag coefficient 0.1
L58 FxFRICTION 99
L59 Cxca= sectional skin friction coefficient 0.003
L60 S = wetted surface area ft 2 3,251
L61 RN= Reynolds Number 19,616,993
L62 v = Kinematic viscosity 1.2817E-05
L63 FxPROP 347
L64 Ap = propeller expanded blade area ft 2 30.6
L65 CPROP = propeller drag coefficient 1.0
L66 ATpp = Total projected propeller area 26
L67 Type of Ship Cargo
L68 AR = dimensionless area ratio for propellers 240
L69 Mxyc = Fyc(ec/LwL)LwL ft-lb -2,715,278
L70 Fyc = side profile current force 57,222
L71 e/Lwl = ratio of eccentricity to vessel waterline length -0.285
L72 Total Side Profile Current Forces lbs 57,222
L73 Total Sectional Current Forces lbs 928
L74 Total Yaw Moment ft-lbs -2,715,278
L75 Total Side Profile Forces lb 88,227
L76 Total Sectional Forces lb 3,280
L78 Total Yaw Moment ft-lb -2,348,971
Total Forces
Current Force
MAR-720
MOORING LINE INFORMATION
MOORING LINE STIFFNESS MATRIX DEFINITION AND MOORING LINE TENSION CALCULATION
Mooring Line
No.
dZi = Zch - Zbl cos qi =
(Ybl -Ych) /
Li sin qi =
(Xbl -Xch) /
Li fi = tan -1
(dZi/Li)
(degrees) cos fi LT = Lo +
Li/cos fi
1 10.8 0.646 0.764 17.2 0.955 44.3
2 10.8 0.971 -0.238 25.0 0.906 30.8
3 8.7 0.978 0.211 36.4 0.805 17.5
4 8.7 0.401 0.916 16.8 0.957 36.9
5 8.7 0.192 -0.981 7.0 0.992 87.6
6 -1.3 0.226 0.974 -1.3 1.000 67.6
7 -1.3 0.990 0.143 -7.0 0.993 13.0
8 -1.3 0.957 -0.289 -2.7 0.999 34.1
9 -1.3 0.562 -0.827 -1.6 1.000 58.0
10 -1.3 0.359 -0.933 -0.9 1.000 97.5
11 10.8 0.542 0.840 10.2 0.984 70.1
* (BS) = total line breaking strength = BSrope x (number of rope parts per line)
Mooring Line
No.
Mooring Line
Type
Nom. Line
Dia. (in.)
Load Area ai
(sq.in.)
El
(1,000 PSI)
(BS)*
(1,000 lb)
Number of
Parts/Line
Ki = ai Ei /
LT
1 Amsteel 1.50 1.77 1.8 15,229 205.0 1 607.4
2 Amsteel 1.50 1.77 1.8 15,229 205.0 1 875.0
3 Amsteel 1.50 1.77 1.8 15,229 205.0 1 1540.7
4 Dacron 2.25 3.98 8.0 2,176 179.9 2 469.2
5 Dacron 2.25 3.98 8.0 2,176 179.9 2 197.4
6 Poly 2.25 3.98 4.0 508 63.0 1 29.9
7 Poly 2.25 3.98 4.0 508 63.0 1 155.2
8 Poly 2.25 3.98 4.0 508 63.0 1 59.2
9 Amsteel 1.50 1.77 1.8 15,229 205.0 1 463.9
10 Amsteel 1.50 1.77 3.5 15,229 410.0 2 551.8
11 Amsteel 1.50 1.77 1.8 15,229 205.0 1 384.0
Mooring Line
No.
Kxi = Ki x sin qi x cos fi
Kyi = Ki x cos qi x cos fi
Kxi x lyi Kyi x lxi Kxi x ly
Kyi x lx
Fxi =
Kxi x dx +
Kxi x lyi x g
(1,000 lb)
Fyi =
Kyi x dy +
Kyi x lxi x g
(1,000 lb)
Mri = Kxi x lyi x dx+ Kyi x lxi x dy + (Kxi x ly + Kyi x lx ) x g)
(1,000 lb)
Ti = Fyi /
(cos qi x cos fi)
(1,000 lb)
FS= (BS)*
/ Ti
Percent
Strength (%)
1 0.0 374.5 0.0 33,326 2,965,672 0.0 0.7 59 1.1 189.6 1%
2 -189.1 770.1 775.2 68,529 6,095,238 0.3 1.4 121 1.6 131.6 1%
3 0.0 1,212.7 0.0 69,112 3,938,720 0.0 23.1 1,319 29.4 7.0 14%
4 0.0 180.1 0.0 10,264 584,961 0.0 3.4 0 9.0 20.1 5%
5 -192.3 37.6 2,864.7 2,144 79,509 -0.8 0.7 52 3.8 47.8 2%
6 0.0 6.7 0.0 -223 7,348 0.0 0.5 0 2.0 31.1 3%
7 0.0 152.5 0.0 -5,034 166,159 0.0 10.3 0 10.5 6.0 17%
8 -17.1 56.6 0.0 -4,475 353,566 0.1 5.2 -414 5.5 11.5 9%
9 -383.5 260.6 0.0 -20,591 1,626,897 1.6 24.1 -1,907 43.0 4.8 21%
10 -514.8 198.3 0.0 -15,666 1,237,773 2.1 18.4 -1,451 51.1 8.0 12%
11 0.0 205.0 0.0 18,240 1,623,194 0.0 0.4 0 0.7 300.0 0%
Office of Shipyards & Marine Engineering
Title:
Mooring - 64.0 knot wind @ 135 deg. and 2.0 knot current @ 90 deg. to the
Piney Point Pier at a 11.5 draft
M/V FS Mooring Analysis @
Piney Point
APPENDIX F
180 deg Wind & 90 deg Current
@ Piney Point
Title: Job Number:
MAR-720
Description:
Ship: M/V Freedom Star
Moored Draft:
Line 1 Displacement LT 1,000
L2 LWL ft 166.2
L3 Draft, T ft 11.5
L4 Beam, B ft 37.0
L5 Sectional Projected Wind Area, AT ft 2 980
L6 Side Profile Projected Wind Area, AL ft 2 3,674
L7 Wind Speed, Vw kt 64
L8 Current Speed, Vc kt 2
L9 Wind Angle, qw (180 o /bow & 0 o /stern) degrees 180
L10 Current Angle, qc (180 o /bow & 0 o /stern) degrees 90
L11 Water Depth, Wd ft 13
L12 Fyw = 0.5 r a Vw Ay Cyw fyw {q w} lbs 392
L13 r a = mass density of air slug/ft 3 0.00237
L14 Vw = wind speed ft-sec 108.02
L15 Ay = side profile projected area of the ship ft 2 3,674
L16 Cyw = Side Profile Wind Force Drag Coefficient 0.77
L17 C = empirical coefficient (Table 4-2) 0.92
L18 hR = reference height ft 32.8
L19 hH = AH / LwL = average height of hull ft 3.7
L20 AH = side profile wind area of hull ft 2 616
L21 hS = height of the superstructure above waterline ft 45.0
L22 AS = side profile wind area of superstructure ft 2 3,058
L23 fyw = side profile wind coefficient shape function 0.010
L24 Fxw = 0.5 r a Vw Ax Cxw fxw {q w} lbs 9,074
L25 Ax = sectional projected area of the ship ft 2 980
L26 CxwB = Bow Sectional Wind Force Drag Coefficient 0.700
L27 CxwS = Stern Sectional Wind Force Drag Coefficient 0.600
L28 Location of Superstructure Fwd of MS
L29 qx 100
L30 g = shape function for sectional wind loads degrees 252
L31 fxw = sectional wind coefficient shape function -1.057
L32 Cxw = Sectional Wind Force Drag Coefficient -0.634
L33 Mxyw = 0.5 ra Vw Ay LCxyw {qw} ft-lb 407,333
L34 Cxyw = Yaw Normalized Moment Coefficient 0.048
L35 qz 75
L36 a1 0.030
L37 a2 0.050
L38 l 1.002
L39 Total Side Profile Wind Forces lbs 392
L40 Total Sectional Wind Forces lbs 9,074
L41 Total Yaw Moment ft-lbs 407,333
Wind Force
Ship Particulars
Mooring - 64.0 knot wind @ 180 deg. and 2.0 knot current @ 90 deg. to the Piney Point Pier at a 11.5 draft
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
@ Piney Point
Title: Job Number:
MAR-720
Office of Shipyards & Marine Engineering
M/V Freedom Star Mooring Analysis
L41 Fyc = 0.5 rw Vc LwL TCyc {qc} lb 57,222
L42 rw = mass density of water slug/ft 3 1.9905
L43 Vc = current speed ft-sec 3.38
L44 LWL ft 166.2
L45 Draft, T ft 11.5
L46 Water Depth, Wd ft 13.0
L47 Cyc = side profile current force drag coefficient 2.64
L48 CO = deepwater current force drag coefficient 0.62
L49 c = ship parameters 8.00
L50 Am = immersed cross-sectional area at midships ft 2 374.44
L51 Cm = midship coefficient 0.8800
L52 V = submerged volume ft 3 34,977
L53 C1 = shallow water current force drag coefficient 3.2
L54 K = dimensionless exponent 2
L55 Fxc = FxFORM + FxFRICTION + FxPROP 928
L56 FxFORM 483
L57 Cxcb= Sectional current force drag coefficient 0.1
L58 FxFRICTION 99
L59 Cxca= sectional skin friction coefficient 0.003
L60 S = wetted surface area ft 2 3,251
L61 RN= Reynolds Number 19,616,993
L62 v = Kinematic viscosity 1.2817E-05
L63 FxPROP 347
L64 Ap = propeller expanded blade area ft 2 30.6
L65 CPROP = propeller drag coefficient 1.0
L66 ATpp = Total projected propeller area 26
L67 Type of Ship Cargo
L68 AR = dimensionless area ratio for propellers 240
L69 Mxyc = Fyc(ec/LwL)LwL ft-lb -2,715,278
L70 Fyc = side profile current force 57,222
L71 e/Lwl = ratio of eccentricity to vessel waterline length -0.285
L72 Total Side Profile Current Forces lbs 57,222
L73 Total Sectional Current Forces lbs 928
L74 Total Yaw Moment ft-lbs -2,715,278
L75 Total Side Profile Forces lb 57,613
L76 Total Sectional Forces lb 10,002
L78 Total Yaw Moment ft-lb -2,307,945
Total Forces
Current Force
MAR-720
MOORING LINE INFORMATION
MOORING LINE STIFFNESS MATRIX DEFINITION AND MOORING LINE TENSION CALCULATION
Mooring Line
No.
dZi = Zch - Zbl cos qi =
(Ybl -Ych) /
Li sin qi =
(Xbl -Xch) /
Li fi = tan -1
(dZi/Li)
(degrees) cos fi LT = Lo +
Li/cos fi
1 10.8 0.646 0.764 17.2 0.955 44.3
2 10.8 0.971 -0.238 25.0 0.906 30.8
3 8.7 0.978 0.211 36.4 0.805 17.5
4 8.7 0.401 0.916 16.8 0.957 36.9
5 8.7 0.192 -0.981 7.0 0.992 87.6
6 -1.3 0.226 0.974 -1.3 1.000 67.6
7 -1.3 0.990 0.143 -7.0 0.993 13.0
8 -1.3 0.957 -0.289 -2.7 0.999 34.1
9 -1.3 0.562 -0.827 -1.6 1.000 58.0
10 -1.3 0.359 -0.933 -0.9 1.000 97.5
11 10.8 0.542 0.840 10.2 0.984 70.1
* (BS) = total line breaking strength = BSrope x (number of rope parts per line)
Mooring Line
No.
Mooring Line
Type
Nom. Line
Dia. (in.)
Load Area ai
(sq.in.)
El
(1,000 PSI)
(BS)*
(1,000 lb)
Number of
Parts/Line
Ki = ai Ei /
LT
1 Amsteel 1.50 1.77 1.8 15,229 205.0 1 607.4
2 Amsteel 1.50 1.77 1.8 15,229 205.0 1 875.0
3 Amsteel 1.50 1.77 1.8 15,229 205.0 1 1540.7
4 Dacron 2.25 3.98 8.0 2,176 179.9 2 469.2
5 Dacron 2.25 3.98 8.0 2,176 179.9 2 197.4
6 Poly 2.25 3.98 4.0 508 63.0 1 29.9
7 Poly 2.25 3.98 4.0 508 63.0 1 155.2
8 Poly 2.25 3.98 4.0 508 63.0 1 59.2
9 Amsteel 1.50 1.77 1.8 15,229 205.0 1 463.9
10 Amsteel 1.50 1.77 3.5 15,229 410.0 2 551.8
11 Amsteel 1.50 1.77 1.8 15,229 205.0 1 384.0
Mooring Line
No.
Kxi = Ki x sin qi x cos fi
Kyi = Ki x cos qi x cos fi
Kxi x lyi Kyi x lxi Kxi x ly
Kyi x lx
Fxi =
Kxi x dx +
Kxi x lyi x g
(1,000 lb)
Fyi =
Kyi x dy +
Kyi x lxi x g
(1,000 lb)
Mri = Kxi x lyi x dx+ Kyi x lxi x dy + (Kxi x ly + Kyi x lx ) x g)
(1,000 lb)
Ti = Fyi /
(cos qi x cos fi)
(1,000 lb)
FS= (BS)*
/ Ti
Percent
Strength (%)
1 0.0 374.5 0.0 33,326 2,965,672 0.0 0.6 -56 1.0 202.5 0%
2 -189.1 770.1 775.2 68,529 6,095,238 1.4 1.3 -120 1.5 140.5 1%
3 0.0 1,212.7 0.0 69,112 3,938,720 0.0 14.2 808 18.0 11.4 9%
4 0.0 180.1 0.0 10,264 584,961 0.0 2.1 0 5.5 32.8 3%
5 -192.3 37.6 2,864.7 2,144 79,509 0.5 0.4 17 2.3 77.9 1%
6 0.0 6.7 0.0 -223 7,348 0.0 0.3 0 1.5 42.8 2%
7 0.0 152.5 0.0 -5,034 166,159 0.0 7.5 0 7.6 8.2 12%
8 -17.1 56.6 0.0 -4,475 353,566 0.2 3.9 -306 4.1 15.5 6%
9 -383.5 260.6 0.0 -20,591 1,626,897 3.4 17.8 -1,410 31.8 6.5 15%
10 -514.8 198.3 0.0 -15,666 1,237,773 4.6 13.6 -1,073 37.8 10.9 9%
11 0.0 205.0 0.0 18,240 1,623,194 0.0 0.3 0 0.6 320.3 0%
Office of Shipyards & Marine Engineering
Title:
Mooring - 64.0 knot wind @ 180 deg. and 2.0 knot current @ 90 deg. to the
Piney Point Pier at a 11.5 draft
M/V FS Mooring Analysis @
Piney Point
APPENDIX G
Geometry of Mooring Arrangement
MAR-720
Ship: M/V Freedom Star Units: (Foot-Pound Units)
MOORING GEOMETRY (Shaded Fields are manual input) LCG = 3.99A ft (est) - Midship
Mooring Line
No.
Vessel
Chock #
Xch
(ft)
Ych
(ft)
Zch
(ft)
Mooring
Cleat/
Bollard
Xbl
(ft)
Ybl
(ft)
Zbl
(ft)
Li = [(Xch-
Xbl)2+(Ych-
Ybl)2]1/2
Lo
(ft) lxi = Xcg -
Xch lyi =Ycg - Ych
(note Ycg=0)
1 1 85.0 -4.1 16.8 2 111.5 -26.5 6.0 34.70 8.0 88.99 -4.1
2 1 85.0 -4.1 16.8 3 79.5 -26.5 6.0 23.07 5.3 88.99 -4.1
3 2 53.0 -14.9 14.7 4 55.5 -26.5 6.0 11.87 2.7 56.99 -14.9
4 2 53.0 -14.9 14.7 3 79.5 -26.5 6.0 28.93 6.7 56.99 -14.9
5 2 53.0 -14.9 14.7 7 -16.5 -28.5 6.0 70.82 16.3 56.99 -14.9
6 3 -37.0 -16.1 4.7 6 16.5 -28.5 6.0 54.92 12.6 -33.01 -16.1
7 3 -37.0 -16.1 4.7 8 -35.5 -26.5 6.0 10.51 2.4 -33.01 -16.1
8 5 -83.0 0.0 4.7 10 -91.0 -26.5 6.0 27.68 6.4 -79.01 0.0
9 5 -83.0 0.0 4.7 11 -122.0 -26.5 6.0 47.15 10.8 -79.01 0.0
10 5 -83.0 0.0 4.7 12 -157.0 -28.5 6.0 79.30 18.2 -79.01 0.0
11 6 85.0 4.1 16.8 1 135.5 -28.5 6.0 60.11 9.0 88.99 4.1
Cartesian Coordinate System, Forward Perpendicular of the Vessel is 0,0,0; x is positive aft, y is positive to starboard and z is positive up.
Nomenclature:
Chock Coordinates Lt = Total mooring line length M ri = Total external moment about vert axis
Bollard Coordinates ai = Total section area of mooring line Ti = Tension in a mooring line
Li = Length from Chock to Bollard Ei = M odulus of Elasticity o f line FS = Factor o f Safety
Lo = Length from Chock to Bitt BS = Breaking Strength of line dx = Vessel movement in x direction lxi = Long'l distance from Chock to Xcg Ki = Spring constant along length of line dy = Vessel movement in y direction lyi = Transverse dist. From Chock to Centerline Kxi = effective spring const o f line in x-dir. g = Vessel ro tation about vertical axis dz = Difference in Elevation from Bollard to Chock Kyi = effective spring const o f line in y dir. Xcg = Vessel longitudinal center o f gravity qi = Angle in horiz. plane from chock to bollard Fx = Total external force in x direction Rope Area = area of a circle of the nominal diameter o f the rope fi = Angle in vert. P lane from chock to bollard Fy = Total external force in y direction Load Area = Philystrand effective area
26.5
Office of Shipyards & Marine Engineering
M/V Freedom Star Chocks Lundeburg Facility
Xch, Ych and Zch =
Xbl, Ybl and Zbl =
M/V Freedom Star Mooring AnalysisTitle:
M/V FS Mooring Analysis @
Piney Point
123456789101112
Wind @ 64.0 knots/90 deg.
Current @ 2.0 knots/90 deg.
-40
-30
-20
-10
-180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160
23456
89101112
Pier, 4.97
WL WL
-1.0
4.0
9.0
14.0
19.0
160.00 A 110.00 A 60.00 A 10.00 A 40.00 F 90.00 F 140.00 F
H e ig h ts A b o ve V e ss e l
W at e rl in e ft
Profile View
Figure 3 - Conceptual Mooring Arrangement between M/V FREEDOM STAR w/ new bollard configuration and pier
N o m e n c la tu re
C h o c k C o o rd in a te s L t
T o ta l m o o ri n g li n e le n g th
M ri
T o ta l e xt e rn a l m o m e n t a b o u t v e rt a xi s
B o lla rd
C o o rd in a te s a i =
T o ta l s e c ti o n a re a o f m o o ri n g li n e
T i =
T e n s io n in a m o o ri n g li n e
L i = e n g th f ro m C h o c k t o
B o lla rd
E i =
M o d u lu s o f E la s ti c it y o f lin e F
S
F a c to r o f S a fe ty o
L e n g th f ro m C h o c k t o
B it t
B S
B re a k in g S tr e n g th o f lin e dx
V e s s e l m o v e m e n t in x d ir e c ti n lx
L o n g 'l d is ta n c e f ro m C h o c k t o
X c g
K i =
S p ri n g c o n s ta n t a lo n g le n g th o f lin e dy
V e s s e l m o v e m e n t in y d ir e c ti ly
T ra n s v e rs e d is t.
F ro m
C h o c k t o
C e n te rl in e K xi e ff e c ti v e s p ri n g c o n s t o f lin e in x -d ir g
V e s s e l r o ta ti o n a b o u t v e rt ic a l a xi s dz
D if fe re n c e in
E le v a ti o n f ro m B o lla rd t o
C h o c k
K yi e ff e c ti v e s p ri n g c o n s t o f lin e in y d ir
X c g
V e s s e l l o n g it u d in a l c e n te r o f g ra v it y q i =
A n g le in h o ri z.
p la n e f ro m c h o c k t o b o lla rd
F x
T o ta l e xt e rn a l f o rc e in x d ir e c ti
R p e A re a a re a o f a c ir c le o f th e n o m in a l d ia m e te r o f th e r o p e f i =
A n g le in v e rt
. P la n e f ro m c h o c k t o b o lla rd
F y
T o ta l e xt e rn a l f o rc e in y d ir e c ti a d A re a
P h ily s tr a n d e ff e c ti v e a re a
.5
X c h , Y c h a n d Z c h
X b l, Y b l a n d Z b l =
W in d
.0 k n o ts /9 d e g.
C u rr e n t
.0 k n o ts /9 d e g.
-4
-3
-2
-1
-1
-1
-1
-1
-1
-8
-6
-4
-2
P ie r, .9
W L
W L
-1 .0
.0
.0
.0
.0
0.
A
0.
A
.0
A
.0
A
.0
F
.0
F
0.
F
Heights Above Vessel Waterline (ft.)
P ro fi le
V ie w
File details come from the government source that posted it.