wind loads on marine structures

*Corresponding author. Tel.: 00351-1-841-7607; fax: 00351-1-847-4015.E-mail address: [email protected] (C. Guedes Soares)

Marine Structures 12 (1999) 199}209

Wind loads on marine structures

M.R. Haddara!, C. Guedes Soares",*!Memorial University of Newfoundland, Faculty of Engineering and Applied Science, St. John's, Nyd,

Canada A1B 3X5"Unit of Marine Technology and Engineering, Technical University of Lisbon, Instituto Superior Te&cnico,

Av. Rovisco Pais, 1049-001 Lisboa, Codex, Portugal

Received 29 January 1999; received in revised form 15 March 1999; accepted 9 April 1999

Abstract

A review of the available methods for the calculation of wind loads on ships and o!shorestructures is presented. Based on the review, four methods were selected and implementedin order to carry out a comparative study of the wind loads on ships. Namely, the ahead force,the side force and the yawing moment were calculated and compared. A large tanker bothin the loaded and ballast conditions was analysed using the four methods. In the secondpart, an expression for the estimation of wind loads on ships is proposed and compared withthe experimental data. A neural network technique was used to obtain this expression.( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Wind loads; Loads on ships

1. General

The wind loads do not usually play a major role in the structural design of ships ando!shore structures. The magnitude of the mean static forces and the moments causedby the wind amount to only a fraction of the total loading on the structure. However,there are instances when the e!ects of these forces and moments become critical.Cracks occurring in #are booms due to dynamic wind loading have been reported inthe literature [1]. Wind loads play important roles in the e$cient operation of a ship'spropulsion plant or on her manoeuvrability. Also in certain particular situations suchas the towing of ships, moored ships and dynamic positioning, wind loads play animportant role.

0951-8339/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 9 5 1 - 8 3 3 9 ( 9 9 ) 0 0 0 2 3 - 4

Wind tunnel tests are the most accurate procedure to estimate the wind forces onships and o!shore structures. However, these tests are time consuming and veryexpensive, thus the prediction methods are generally used complementary or alterna-tively to wind tunnel tests. Several numerical methods have been developed for theprediction of wind forces on #oating structures without recurring to direct modeltesting.

Isherwood [2] proposed expressions for the forces and moment coe$cients, derivedfrom multiple regression analysis of previously published experimental results. Thewind coe$cients are given by equations, depending on the basic characteristics of thewater above the hull. This method can be applied to a wide range of ship types andcon"gurations and for all angles of the wind relative to the bow.

Gould [3] presented a numerical procedure for the estimation of the windforces and moment on the superstructures of ships. The e!ect of wind speed overthe sea on the e!ective relative wind speed acting on the ship is discussed. In fact, thewind pro"le over the sea depends on the sea surface, which moves itself and presentsincreasing roughness with increasing wind speed. A logarithmic pro"le for windspeed is proposed by the author. The e!ective wind speed and the lateral centre ofpressure for a gradient wind, is then estimated by subdividing the frontal and lateralprojections into `universal elementsa. The wind tunnel data for ships covering a widerange of designs are given with advice on their application to other ships. This datacan be used to estimate the forces and moment coe$cients for a wide range of shiptypes.

Blendermann [4] has presented a systematic collection of wind load data. Continu-ing this work, Blendermann [5,6] derived expressions for the coe$cients of the windforces acting in the longitudinal and transverse directions and the yaw and rollingmoments. These expressions are functions of a drag coe$cient, the angle of attack, thefrontal and transverse areas subject to wind, the coordinates of the centre of area anda parameter called the cross-force parameter. This parameter is obtained statisticallyfrom the experimental data.

Blendermann [7] also proposed a method for the prediction of wind loads on shipsin a non-uniform air #ow using experimental data. The non-uniformity of the air #owis accounted for an e!ective dynamic pressure.

Brix [8,9] has presented a selection of the wind load data from Blendermann [4,5],together with methods for their use in manoeuvring problems.

Lee and Low [10] obtained results of wind tunnel tests on models of rigid o!shoreplatforms. The pressure transducers located at 141 locations on the 1 : 268 scale modelwere used to measure wind loads. The wind velocity was measured using hot wireanemometer. The wind tunnel results show an overriding in#uence of the legs. Theyaccounted for about 70% of all drag and about 80% of all over turning moments inthe #oating mode.

OCIMF [11] presented coe$cients and procedures for computing wind loads onvery large crude carriers (VLCCs), i.e. tankers in the 150,000}500,000 DWT range.However, the coe$cients and procedures can be applied to smaller tankers withsimilar geometry. The wind coe$cients are based upon data obtained from windtunnel tests conducted at the University of Michigan in the 1960s.

200 M.R. Haddara, C. Guedes Soares / Marine Structures 12 (1999) 199}209

Table 1Main particulars of the tanker

Loaded In ballast

Overall length (m) 351.40Beam (m) 55.40Draft (m) 23.50 10.625Lateral projected area (m2) 3401.47 7839.63Height of centre of lateral area above 6.83 12.34Distance of centre of lateral from midship 24.45 (forward) 8.32 (forward)Transverse area (m2) 1131.79 1803.93

A very long mat-like platform was used to study the wind forces on a #oatingairport by Ohmatsu et al. [12]. Experiments were conducted in a closed-return windtunnel. A distorted model was used where only the fore and aft parts were accuratelyscaled. Wind pressure distribution, wind forces and wind velocity distribution aroundthe model were measured. It has been found that the total drag force coe$cientincreases with the increase in the model length and decreases with the increase in draft.

Chen et al. [13] carried out preliminary experiments to study the wind environmentover the helideck of an o!shore platform in the Beihai sea, China. Tests were carriedout in an atmospheric boundary layer wind tunnel using a 1 : 100 scale model. A hot-wire anemometer was used to measure the velocity over the helideck. The velocity wasmeasured at equally spaced stations, ten in the horizontal direction and eight in thevertical direction. The results for "ve di!erent angles of attack were obtained. Theseexperiments indicate that the distributions of the mean as well as the #uctuatingvelocities are quite sensitive to the direction of the wind. They also found that theseparation occurs generally at the front edge of the helideck. In some cases, the meanvelocity distribution at the centre of the deck has a turning point, which may suggestan instability.

The vibration characteristics of several Norwegian o!shore #are booms have beendiscussed by Oppen and Kvitrud [13]. A survey of the cracks produced by thisresonant vibration was also given. The cross wind vortex-induced vibration and wakeinteraction with the chord members were the main causes for cracks. The methods formitigating these e!ects were described and a recommended design practice wassuggested.

2. Comparative study on wind loads

Three methods available in the literature were used to estimate the wind loads ona 351.0 meter tanker, in the loaded and ballast conditions. Table 1 shows the principaldimensions of the tanker. The methods applied are those described in [2,3,11]. Theresults of the calculations are shown in Figs. 2}4 for the loaded tanker and in Figs. 5}7for the tanker in ballast. The experimental data obtained by Blendermann [4] isplotted together for comparative purposes.

M.R. Haddara, C. Guedes Soares / Marine Structures 12 (1999) 199}209 201

Fig. 1. Convention for positive quantities.

Fig. 2. Longitudinal force coe$cient, loaded tanker.

The convention for positive forces and moment are presented in Fig. 1, where Fx,

Fyand N represent, respectively, the longitudinal force, side force and yaw moment

and b is the angle between the wind speed and the ship bow.Fig. 2 represents the longitudinal force coe$cient for the loaded tanker. Although

one can observe some dispersion on the numerical results, in general the predictionscompare well with the experimental results. For wind coming from the stern, allmethods tend to overpredict the experimental results. Among the three methods, theOCIMF is the one which compares better with experiments.

Fig. 3, shows the results of the side force coe$cients for the loaded ship. One canobserve that both Isherwood's and the OCIMF methods agree with the experimentalvalues obtained for the side force by Blendermann over the whole range of the windangle. Values for the lateral force coe$cient obtained by Gould's method are highlyoverestimated.

In Fig. 4 the yaw moment coe$cients results are presented. One can "nd qualitativedi!erences between Blendermann's experimental results and OCIMF values for theyaw moment coe$cient on one side and estimates obtained by Gould's and Isher-wood's methods on the other side. The yaw moment coe$cients obtained using the"rst two methods have negative values over the whole range of the wind angle. The


Fig. 3. Side force coe$cient, loaded tanker.

Fig. 4. Yaw moment coe$cient, loaded tanker.

values obtained using Gould's and Isherwood's methods display a change in sign ofthe coe$cient around a wind angle of 703. Large quantitative discrepancies existbetween the results obtained using the three methods and Blendermann's experi-mental results.

Figs. 5}7 represent comparisons between the numerical predictions and experi-mental results, respectively of the longitudinal force, side force and yaw momentcoe$cients for the tanker in the ballast condition. The conclusions for the longitudi-nal force coe$cients are similar to those obtained for the loaded condition. Again theOCIMF method tends to agree better with the experiments than the other methods.In the case of the side force coe$cients all methods overestimate the experimentaldata, the Isherwood results being closer to the experiments than the Gould andOCIMF results. The numerical results for the yaw moment coe$cients agree qualitat-ively with those obtained from Blendermann's experimental values. For wind anglesbelow 803, OCIMF is the closest to Blendermann's experimental values. For anglesabove 803, Gould's estimates are the closest.


Fig. 5. Longitudinal force coe$cient, tanker in ballast.

Fig. 6. Side force coe$cient, tanker in ballast.

Fig. 7. Yaw moment coe$cient, tanker in ballast.


In conclusion, it seems that this comparative study indicates that there is no generalagreement between the four methods available for the estimation of wind forces onships. The discrepancy between the estimates obtained using the other three methodsand Blendermann's experimental results may be caused by the limited range ofexperiments carried out in these studies and the statistical analysis carried on the datato obtain formulas for the estimation of the forces.

3. An universal model for the estimation of wind loads on ships

The trend of using neural network techniques in the parametric identi"cation ofmathematical models using measured input and output of the system is growing. Oneof the main advantages of this method is that no functional relationship between thedependent and the independent variables has to be assumed a priori. This techniquewas used to obtain a universal expression for the wind loads. Blendermann's [4]experimental data were used for training a feed-forward neural network. Optimisationof the network was obtained using the back-propagation method. The data fora tanker, which were not used in the training of the network, was used to test theability of the network to predict wind loads for a new ship. This approach yieldsa mathematical expression which can be used to estimate loads on any ship. Thismeans that this is a universal mathematical expression which does not depend on thetype of ship.

The following expressions are used to calculate the coe$cients of the wind forces:

Ck"

m+i/1

ckiH

ki, k"1, 2, 3, (1)

where k"1, 2, 3 refer to the longitudinal force, transverse force and yaw moment,respectively, and

Hki"

[1!e~Gki]

[1#e~Gki],

Gki"

5+j/l

wkij

xj, k"1, 2, 3 (2)

and

x-"

AL

¸2, x

2"

Ar

B2, x

3"

¸

B,

x4"

S

¸

, x5"e, x

6"1, (3)

where AL

is the lateral projected area, AT

is the transverse projected area, s is thedistance between the centre of the lateral projected area and the midship section ofthe ship, e is the angle between the centre line of the ship and the wind velocity, ¸ is


Table 2Ships used in the training of the neural network

Ship Load (m) B (m) D (m)

Container ship (full) 210.75 30.50 11.6Container ship (empty) 210.75 30.50 9.6Container ship (loaded) 210.75 30.50 9.6Container ship (empty) 216.40 23.77 6.94Drill ship 150.1 21.35 7.00Cruise ship 143.90 17.35 5.90Cruise ship 161.00 29.00 6.05Cutter 25.05 5.80 2.50Cargo ship (loaded) 141.1 18.50 7.32Cargo ship (empty) 141.1 18.50 4.43Cargo ship (loaded) 155.45 23.10 8.69Cargo ship (container on deck) 155.45 23.10 8.69Research vessel: Wind from Port 55.00 12.50 3.95Research vessel: Wind from Starboard 55.00 12.50 3.95Speed boat 53.60 9.20 2.50O!shore supply vessel 61.95 13.00 4.85O!shore supply vessel 61.00 13.00 4.85Gas tanker (loaded) 274.00 47.20 10.95Gas tanker (ballast) 274.00 47.20 8.04

the ship's length and B is the ship's beam. The values for the weights, cki

and wkij

, arecalculated by the neural network.

A neural network having one hidden layer was used. The input layer has six inputsas shown in Eq. (3). The hidden layer has 11 nodes. The experimental data for 19 shipswere used to train the network. Table 2 shows a list of the ships used in the training ofthe network. The weights, which were calculated by the neural network, are used topredict the wind forces acting on the same tanker that has been used in the compara-tive study in the previous section. This ship was not included in the data used to trainthe network. It should be noted that the training data did not include any tankers.Furthermore, all the ships used in the training of the network were smaller than thetanker used to test the generalisation ability of the network.

Figs. 8}13 show a comparison between the experimental and the predicted windforces coe$cients for the tanker. The predicted data agreed qualitatively with theexperimental data in all cases. The errors in estimating the maximum forces on thetanker using the neural network are much smaller than those produced by the othermethods. These results show that this method produces much better predictions thanthat given by the methods currently available in the literature.

4. Conclusions

A review of the available methods for the calculation of wind loads on ships ando!shore structures is presented. A comparative study was carried out, where the


Fig. 8. Predicted and measured longitudinal force coe$cient (loaded tanker).

Fig. 9. Predicted and measured side force coe$cient (loaded tanker).

Fig. 10. Predicted and measured yaw moment coe$cient (loaded tanker).


Fig. 11. Predicted and measured longitudinal force coe$cient (tanker in ballast).

Fig. 12. Predicted and measured side force coe$cient (tanker in ballast).

Fig. 13. Predicted and measured yaw moment coe$cient (tanker in ballast).


ahead force, side force and yawing moment were calculated for a tanker in loaded andballast conditions using four methods. The quality of the predictions is assessed bycomparing the numerical results with experimentally obtained results.

Generally speaking the comparative study indicates that there is no general agree-ment between the methods used for the estimation of wind forces on ships. Theexperimental results obtained by Blendermann are the most comprehensive andreliable among the four methods. The discrepancy between the estimates obtainedusing the other three methods and Blendermann's experimental results may be causedby the limited range of experiments carried out in these studies and the statisticalanalysis carried on the data to obtain formulas for the estimation of the forces.

In the second part of the paper, a neural network technique was used to obtaina universal expression for the estimation of wind loads on ships. The tanker, whichwas used for the comparative study, was chosen to test the ability of the network topredict wind loads on ships. It should be noted that this tanker was not used in thetraining of the network. It was found that the numerical predictions agree well withthe experimental results, suggesting that the neural network technique can be used togenerate expressions, which produce better results than those given by the methodscurrently available in the literature.

References

[1] Oppen, AN, Kvitrud A. Wind induced resonant cross #ow vibrations on Norwegian o!shore #arebooms. Proceedings of the 14th International Conference on O!shore Mechanics and Arctic Engin-eering (OMAE), v1-A, New York: ASME, 1995, p. 341}54.

[2] Isherwood RM. Wind resistance of merchant ships. Trans. Roy. Inst. Naval Architects 1972;114:327}38.

[3] Gould RWF. The estimation of wind loads on ship superstructures. The Royal Institution of NavalArchitects, monograph, No. 8, 1982. p. 34.

[4] Blendermann W. Schi!sform und Windlast-Korrelations-undRegressionanalyse von Windkanalmes-sungen am Modell. Report No. 533. Institut fur Schi!bau der Universitat Hamburg, 1993a. 99 pagesplus Appendix.

[5] Blendermann W. Wind loads on moored and manoeuvring vessels. Proceedings 12th InternationalConference on O!shore Mechanics and Arctic Engineering (OMAE), New York: ASME, 1993, v1, p. 183.

[6] Blendermann W. Parameter identi"cation of wind loads on ships. J. Wind Engng. Ind. Aerodyn.1994;51:339}51.

[7] Blendermann W. Estimation of wind loads on ships in wind with a strong gradient. Proceedings of the14th International Conference on O!shore Mechanics and Arctic Engineering (OMAE), New York:ASME, 1995, v1-A, p. 271}7.

[8] Brix J. editor. Manoeuvring Technical Manual. Appendix I: Wind forces and moments in dimension-less form, Part 1, Schi! & Hafen 42, 1990. No 2, p. 41, No 3, p. 55, No 4, p. 47.

[9] Brix J. editor. Manoeuvring technical manual. Hamburg: Seehafen, 1993. p. 147 and 236.[10] Lee TS, Low HT. Wind e!ects on o!shore platforms: a wind tunnel model study. Proceedings of the

Third International O!shore and Polar Engineering Conference, Singapore, 1993. p. 466}470.[11] OCIMF. Prediction of wind loads and current loads on VLCCs. 1994.[12] Ohmatsu S, Takai R, Sato H. On the wind and current forces acting on a ultra large #oating platform.

Proceedings of the 14th International Conference on O!shore Mechanics and Arctic Engineering(OMAE), New York: ASME, 1995, v1-A, p. 475}81.

[13] Chen Q, Gu Z, Sun T, Song S. Wind environment over the Helideck of an o!shore platform. J WindEngng Ind Aerodyn. 1995;54/55:621}31.


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