13.15_b_-_Presentation_-_Forces_experienced_by_winch_drums_and_reels_systems.pdf

Forces experienced by winch drums and reelssystems as a function of rope characteristics and varying line pull – a theoretical study The 18th North Sea Offshore Crane and Lifting Conference, Stavanger, Norway Marius Popa, FRINA, CEng, Ph.D. 25th April 2013 Summary This paper presents in Part A a theoretical study of internal line friction, line rigidity and their influence on drum and flange pressures on single drum winches, with varying line tension. It also develops in Part B, using the conclusion in Part A, an analysis of the effect of the rigidity of flange and line on the loads developed on the flange. The study in Part B was developed focusing on the structure of the reel flange however some conclusions may be of interest also for the structure of the winch flange. NOTE: This study is not intended and shall not be used to replace the basic requirements in section 5 of DNV Standard for the Certification of Lifting Appliances 2.22, with respect to design forces and stresses to be considered for winch drums and flanges; the concepts presented are intended to explore and stimulate a deeper understanding of two dominant phenomena involved. With further development and sufficient practical evidence, it may support the generation of “thorough documentation” as a means to alternative methods of design (reference is made to the DNV Standard for the Certification of Lifting Appliances 2.22 Ch. 2 Sec. 3 Guidance Note for the calculation of C coefficient for more than 2 layers). Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. All rights reserved. 2 3 . All rights reserved.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS A little bit of mathematics… (slide 1) T= tension in line FIGURE 1 – LOADS ACTING ON THE LINE’S RADIAL LAYER I SEGMENT DSI=DI/2*Dφ pi = pressure in each layer µ= friction coefficient Pp = product pitch n= number of radial layers l= number of windings along the drum D1 = external diameter (drum diameter + n*Pp) Ri= contribution of layer i to the total radial pressure on the drum Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. . the equation of equilibrium can be written as: Ti+Ff-i= Ti+dTi+Ff-(i-1) => Ff-i – Ff-(i-1) = dTi => -µ*(pi-pi-1)*dA = dTi [eq 2] Resulting: -µ*Ti* dφ = dTi By integration: T= T0*e-µφ Where φ is the angular length from the free end to the present position: φ= (n-1)*2*π*l + φ-l where n is the layer.). The equation developed below is a generalization of the “capstan effect” equation for a multi layers and multi windings arrangements (no surprise!. All rights reserved. 4 .PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS A little bit of mathematics… (slide 2) – Line pull variation In the vertical direction. the equation of equilibrium can be written as: pi*dA = pi-1*dA + (2*Ti+dTi)*sin(dφ/2) = …= (pi-pi-1)*dA = Ti* dφ [eq 1] In the horizontal direction. Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. l is the number of windings and φ-l is the “local” position on the layer n... 2 Sec. Considering dA= dφ*Di/2*Pp. 5 . [eq 1] becomes: (pi-pi-1)* dφ*Di/2*Pp = T0*e-µφ* dφ = (pi-pi-1) = 2* T0*e-µφi/Di/Pp [eq 3] [where Di= D1-(i-1)*Pp] The equation type 3 can be summed up for all n layers from the outside layer down to the drum… Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS A little bit of mathematics… (slide 3)… Pressure on the drum For one layer spooled onto the drum. All rights reserved.207.22 LA Ch. the pressure at the free end can be deduced as follows: p1*dA = 2*T* sin(dφ/2) and having dA= dφ*D1/2*Pp => p1*dφ*D1/2*Pp = T* dφ => p1 = 2*T/D1/Pp This formula can be deduced from DNV StC 2. 3 B. 6 .2] where φi+1= φi + 2*π*l This equation includes friction and the geometric effect Assuming that the variation in diameter does not significantly contribute to Ri (the coefficient of diameter may increase at a significantly lower rate than that due to the effect of friction) the equation above can be simplified: pdrum = Interesting to note: [eq 4. All rights reserved.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS A little bit of mathematics… (slide 4)… Pressure on the drum pdrum = [eq 4.1] Ri/Ri+1 = eµ*2π*l*(1 – (i-1)*α)/(1-i*α) With Pp/D1 = α Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. 3] Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. 7 . All rights reserved.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS A little bit of mathematics… (slide 5)… Pressure on the drum Straightening effect: Assuming that the rope/product needs a minimum pull Ks in order to be bended at the drum radius or at the present layer radius (no pressure is generated on the drum or between layers) the formulae for line tension variation and drum pressure can be updated as followings: T= (T0-Ks)*e-µ*φ +Ks pdrum = [eq 4. 8 . T. A. Lohrengel.March 2009 http://www. Wächter – “Problems related to the design of multi layer drums for synthetic and hybrid ropes”.pdf Hoop stress Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.imw.tu-clausthal. All rights reserved.de/fileadmin/Forschung/Veroeffentlichungen/Stuttgart_Seiltagung_IMW.Stuttgart . Dietz.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS EXISTING EXPERIMENTAL RESULTS (slide 1) Reference P. OIPEEC Conference / 3rd International Ropedays . Schwarzer and M. T.Stuttgart . Wächter – “Problems related to the design of multi layer drums for synthetic and hybrid ropes”. 9 . OIPEEC Conference / 3rd International Ropedays . Lohrengel. All rights reserved.March 2009 Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS EXISTING EXPERIMENTAL RESULTS (slide 2) The arrangement of the test stand in P. Dietz. Schwarzer and M. A. 25 => µ*l= ln(1.25 1.5m and 0. 10 .92m (say 1.25 dRi/dR(i+1) eµ*2π*l = 1.0013. Proportionally.0009 The drum length therefore is approximately 40*0.e. From the picture of the arrangement the approximate number of windings along length is approximately 40. All rights reserved. Considering also the geometrical effect the friction coefficient seems to be 0.25 1.27m (i. leading to a friction coefficient of 0. the outer diameter and the drum diameter is approximately 0.25)/2/π = 0. Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS EXISTING EXPERIMENTAL RESULTS (slide 3) The values taken from the diagram are approximated as follows: layer 1 2 3 4 5 R 100 180 224 295 336 dR 100 80 64 51 41 1.25 1.0m). arranged over 5 radial layers.023 = 0.023) respectively. 0.035 The reference paper states rope diameter is 23 mm.5 – 2*(5*0. 05 to 0. the values however are unknown. All rights reserved.0013) are extremely small in comparison with typical values (e. 11 . lubricated wire rope may of course exhibit lower coefficients of friction.10.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS The close correlation between experimental and theoretical values would appear to demonstrate the validity of equations above. All of these due to the nature of “hybrid rope” reported as used in the reference? The inclusion of diameter effects leads to an increase in coefficient of friction (approx. 0.513.30 for steel on steel). Rope anchorage design for winches. is based on a coefficient of friction µ = 0. Equations considering only the effect of friction however are simpler. [1] Ch.0. this value is about 100 times larger than those deduced from the results reported in reference. It is also noted that: Coefficients of friction considered above (i. 3 B. The equations accounting all three effects are more general and by their nature provide more conservative results.e. Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. 2 Sec.0009 . well-maintained. 50%) for same drum pressure. requiring no information with respect to geometrical characteristics and might therefore represent a reasonable initial approximation. 0.g. 014 1.605 1.002 1.285 1.285 1.000 1.007 1.000 1.533 1.995 1.828 1.001 1.250 1.750 1.750 1.533 1.750 1.043 1.20 code 1 2 3 4 5 10 50 2.730 1.285 1.750 2. All rights reserved.778 1.002 1.10 2 0.000 1. 12 .390 1.533 1.882 1.023 1.250 2.958 1.686 1.000 0 5 10 15 20 25 30 35 40 45 50 Winding -l Radial Friction layer 2 0.778 1.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS VARIATION OF DRUM PRESSURE WITH COEFFICIENT OF FRICTION (EFFECT OF DIAMETER INCLUDED) – REEL CONFIGURATION R-OUT= 5.000 1.000 1.208 1.533 1.750 2.750 1.730 1.882 1.750 Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.500 1.002 1.0 / PP=0.01 2 0.750 1.05 2 0.043 1.939 1.02 2 0.745 1.1 M / 2 LAYERS 2.043 1.989 1.152 1.001 2 0.285 1.008 1.081 1.081 1. 500 2.051 1.938 2.603 2.395 1.10 0.219 2.147 4.051 1.000 1.025 1.000 .1 M / 5 LAYERS 5.500 5.500 1.000 1.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS VARIATION OF DRUM PRESSURE WITH COEFFICIENT OF FRICTION (EFFECT OF DIAMETER INCLUDED) – REEL CONFIGURATION R-OUT= 5.326 1.951 2.000 3.700 1.000 0 10 20 30 40 50 Winding-l layer 5 5 5 5 5 5 Frictio n 0.951 3.051 1.000 3.000 4.395 1.05 0.955 3.002 1.500 4.000 50 3.624 1.000 3.000 2.894 2.938 2.262 1.000 2 5.000 4 4.002 1.000 1.051 1.20 code 1 5.427 3.045 1.007 3. All rights reserved.024 3.000 Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.018 3.0 / PP=0.01 0.002 3.553 2.000 10 4.395 1.02 0.088 1.219 2.000 5 4.088 3.179 1.395 3. 13 3 5.045 1.001 0.082 3.045 1.500 3. Gordon. Pearlman – “Winch Technology . reducing the pressure and hoop stresses experienced by it. Stephen M.3 shows that spooling with a tension approximating or lower than the spring (straightening) characteristic of the line may generate less pressure on the drum and indeed offer a degree of ‘protection’ to the structure of the drum. cumulative damage experienced by the wire due to heating/friction and pressures applied to the winch drum is a fine one and needs to be considered. All rights reserved. maintenance routines. These first layers will act in effect like a protective ‘cage’ for the drum. Pearlman.com/winch_article. Information contained in InterOcean source below proposes an alternative method to minimize the pressure experienced by winch drums for deep subsea arrangements. being normal practise for subsea applications.htm Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. David R. reducing the coefficient of friction might lead to more load on the drum.interoceansystems. Inc. the balance between operating procedures. Michael D. For deep sea applications in particular. financial and technical constraints imposed on the design of such winches.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS It is interesting to note that a reduction in the coefficient of friction may result from welllubricated lines.e. spooling the first layers on the drum with a reduced tension. in terms of safety. site http://www. As can be observed however. 14 . Equation 4. i. used to minimize the amount of the heat dissipation from friction and prolong product life.Past Present and Future A Summary of Winch Design Principles and Developments” Paper on InterOcean Systems. All rights reserved. 15 . However. the diagram below from an Australian mines code seems to support the idea. No sufficient data was available to validate these equations and deductions . ODN 0901. OIPEEC Conference – Oxford – March 2013 (correspondence with Mr. Maljaars “An axi-symmetric FEM model of drum with multi-layer rope winding”. van den Bos. de Ruiter and S.firm conclusions in relation to this aspect are therefore not possible at the time of writing.PART A: THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS And some caveat not in the paper… In the paper: The relationship between increased line rigidity and a reduced coefficient of friction between layers does not appear to be available in the literature. C. Source: W. van de Bos) Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. 16 . Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS. CONSIDERING THE INFLUENCE OF LINE ELASTICITY. All rights reserved. Simple 2D FE models were done to study these effects. 000 600 2.333 1000 52.247 30798 10.507 197239 12.054 168645 224861 281073 1867797 5.573 0.445 0. All rights reserved.770 100kN= ks=1e5/dy= 20964 ln(ks)= 9.756 56948 10.951 5 2 5796 4750 3 8776 5300 4 11443 5700 5 (rigid) 42817 8800 4.352 5.950 1.667 200 kp=1e5/dy= 17416 ln(kp)= 4.593 0.080 2500 0.271 Spokes properties Section 1 (soft) Spoke Iy= 2873 Spoke A= 4000 Square dy for 100kN= 9.449 6. 17 6 (rigid) 2.05 1 3 4 Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. Line (product) properties Section 1 (soft) Line Iy= Line A= dy for 100kN= 0.401 71378 11.559 39078 10.192 .241 5. CONSIDERING THE INFLUENCE OF LINE ELASTICITY.170 ks=1e5/dy= 10905 ln(ks)= 9.587 1.525 39612 10.356 0.852 117371 11.88 9 1124 29 5.335 2.33 3 400 0.747 21064 9.176 0.742 2 1.297 Triangular dy for 4.667 800 3.673 2.227 5.955 3.PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS. Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. 18 . CONSIDERING THE INFLUENCE OF LINE ELASTICITY. All rights reserved.PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS. All rights reserved. increasing in stiffness from left to right.PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS. CONSIDERING THE INFLUENCE OF LINE ELASTICITY. 19 . Rectangular arrangement: Typical shear force and bending moments diagrams for the spoke elements Product characteristics are represented. Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS. CONSIDERING THE INFLUENCE OF LINE ELASTICITY. 20 . T arrangement :Typical shear force and bending moment diagrams for the spoke elements Product characteristics are represented. increasing in stiffness from left to right. All rights reserved. Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. 316 1.881 0.250 3.250 2.418 0.250 0.488 0.631 0.435 0.454 0.623 0.495 1.182 0.227 5.851 0.500 .000 3.000 2.032 2.205 0.269 4.465 3.532 1.250 1.514 0.000 4.500 2.750 2.109 0.449 6.755 0.000 5.271 2.413 0.365 3.500 3.218 0.250 4.785 1.000 6.000 1.750 1.390 0.289 2. CONSIDERING THE INFLUENCE OF LINE ELASTICITY.399 1.051 5.501 0.000 0.296 0.479 0.686 1.206 1.487 0.536 0.026 1.352 5.750 3.752 1.495 0.PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS.091 1.500 Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.580 0.588 0.938 0.241 5.568 0.500 1.750 0.424 1.567 2.556 2.622 1. F-COMPUTED/F-CODE ks-1 ks-2 ks-3 ks-4 ks-5 ks-1 ks-2 ks-3 ks-4 ks-5 F/F-code log(kp) R R R R R T T T T T Kp-1 Kp-2 Kp-3 Kp-4 Kp-5 Kp-6 4.803 1.468 0.453 0.665 0.533 0.000 4.547 0.918 1.196 1.686 0.821 0. All rights reserved.500 0.426 3.528 1.443 0.227 0. 21 5.492 4.500 6. 271 0.000 4.500 0.241 2.467 kp-3 5.142 0.080 6.180 0. M-COMPUTED/M-CODE ks-1 ks-2 ks-3 ks-4 ks-5 ks-1 ks-2 ks-3 ks-4 ks-5 M/M-code log(kp) R R R R R T T T T T 5.733 0.205 0.161 0.250 0.223 0.277 kp-6 6. All rights reserved.750 0.250 5.317 0.500 2.014 1.530 0. 22 kp-4 5.843 1.623 3.163 0.500 .754 4.245 0.288 0.774 kp-2 5.500 4.125 0.031 0.346 2.750 4.051 0.449 0.750 1.098 0.610 0.000 2.000 4.500 3.190 0.512 1.925 1.500 kp-5 5. CONSIDERING THE INFLUENCE OF LINE ELASTICITY.670 2.107 0.133 1.269 1.500 1.250 4.737 0.000 Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.194 0.000 kp-1 4.352 0.580 0.000 0.247 0.579 0.883 0.250 3.500 5.000 3.051 0.000 6.139 0.250 1.351 3.989 1.847 0.750 2.164 0.188 0.PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS.150 0.623 0.793 0.935 0.250 2.368 0.728 1.006 1.303 0.202 1.040 0.180 0.135 0.227 0.006 4.375 4.000 1.046 0.318 5.750 3. 316 0.366 0.173 0.768 0.212 0.325 0.276 0.051 0. Z-COMPUTED/Z-CODE ks-1 ks-2 ks-3 ks-4 ks-5 ks-1 ks-2 ks-3 ks-4 ks-5 Z/Z-code log(kp) R R R R R T T T T T kp-1 4.045 1.789 0.126 1.601 kp-4 5.434 0.225 0.096 1.623 0.507 0.227 0.878 kp-2 5.539 0.250 0.500 5.897 0.554 0.658 0.936 1.449 0.241 0.837 0. All rights reserved.360 0.500 6.345 0.384 0. CONSIDERING THE INFLUENCE OF LINE ELASTICITY.224 0.196 0.352 0.659 0.883 0.PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS.398 0.500 0.000 6.661 0.000 4.000 0. 23 5.363 0.681 kp-3 5.549 kp-5 5.750 0.298 1.754 0.698 0.500 .413 0.935 0.566 0.510 0.553 0.603 0.271 0.480 0.478 0.619 0.724 0.464 0.005 0.456 0.393 0.268 0.390 0.302 0.000 4.932 0.000 Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.338 0.713 0.825 1.506 kp-6 6.250 1. It may be of course that actual spooling procedures differ from the assumptions made herein. It is not a naturally stable one. Such information would obviously be valuable for the purposes of validating these theories.PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS. this study indicates that the loads and forces experienced by the flanges at least are in effect significantly lower than the values typically used for the purposes of design. suggest at least that there are situations when it is specified / requested by the end-user. Assuming a square arrangement for a spooled-on product may or may not be realistic.g. 24 . partitions in various combinations with flexible filling materials may in some cases be used between windings along the drum. e. The triangular arrangement is obviously the more natural and therefore stable one. perhaps partly as a result of these two phenomena cancelling one another out. This study does however consider a ‘perfect fit’ between the ring arrangement and the drum length. All rights reserved. associated with controlled constant tension onshore spooling). as were representative measurements taken from actual reel assemblies (e. strain gauge measurements or flange tip deflections.g. Figures relating to the transverse rigidity of actual product were unfortunately unavailable for the purposes of this study. it does not therefore account for the well-known increase in load associated with a side-ring arranged in an imperfect triangular cell (angle between line of rings’ centre and horizontal less than 60º). This brief study attempts to demonstrate the influence of product elasticity on the forces imparted into the offshore reels that are used to transport them. CONSIDERING THE INFLUENCE OF LINE ELASTICITY. Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. Structural failure of offshore reels does not appear to have been reported in the literature. but the information received from industrial users of reel structures. perhaps more appropriate design methodology for reels structures. Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS. For this equipment the inertia effects might have at least the same strength effect as the effect of the line spooling tension. considered by the designer as a kind of ‘mega-winch’. The effects studied in Part A together with those in part B should provide the designer with a more thorough understanding of the phenomena at work and it is hoped some stimulation for further investigation and work towards a different. At the same time. Part A however demonstrates the relative importance of friction and the spring/straightening effect for the better understanding of loads acting on the system and the necessity for these effects to be considered for the development of in some cases more optimum and safer winch arrangements. Part B also has significant limitations due to the simplistic analysis methods employed for assessing the effects of product and flange elasticity. with empirical measurements and data being the major exponents missing from the development of final conclusions and incorporation of them into relevant codes and standards. It is the opinion of the Author that both directions explored in parts A and B are worthy of further work. For example. 25 . CONSIDERING THE INFLUENCE OF LINE ELASTICITY.PART B: AN ESTIMATION OF THE FORCES EXPERIENCED BY THE FLANGES OF REELS. All rights reserved. axial elasticity can have a significant effect on the pressure experienced by a winch drum. CONCLUSIONS Part A of this study does not consider various characteristics associated with the line (whatever it may be) spooled onto a drum. part B demonstrates the importance of understanding the effects that relative elasticity has on the design of offshore reel structures and possible for winches too. dnv. property and the environment www. 26 . All rights reserved.Safeguarding life.com Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study 25th April 2013 © Det Norske Veritas AS.