The Maritime Engineering Reference Book: A Guide to Ship Design, Construction and Operation

The Maritime Engineering Reference Book: A Guide to Ship Design, Construction and Operation

by Anthony F. Molland

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The Maritime Engineering Reference Book is a one-stop source for engineers involved in marine engineering and naval architecture. In this essential reference, Anthony F. Molland has brought together the work of a number of the world's leading writers in the field to create an inclusive volume for a wide audience of marine engineers, naval architects and those involved


The Maritime Engineering Reference Book is a one-stop source for engineers involved in marine engineering and naval architecture. In this essential reference, Anthony F. Molland has brought together the work of a number of the world's leading writers in the field to create an inclusive volume for a wide audience of marine engineers, naval architects and those involved in marine operations, insurance and other related fields.

Coverage ranges from the basics to more advanced topics in ship design, construction and operation. All the key areas are covered, including ship flotation and stability, ship structures, propulsion, seakeeping and maneuvering. The marine environment and maritime safety are explored as well as new technologies, such as computer aided ship design and remotely operated vehicles (ROVs).

Facts, figures and data from world-leading experts makes this an invaluable ready-reference for those involved in the field of maritime engineering.

Professor A.F. Molland, BSc, MSc, PhD, CEng, FRINA. is Emeritus Professor of Ship Design at the University of Southampton, UK. He has lectured ship design and operation for many years. He has carried out extensive research and published widely on ship design and various aspects of ship hydrodynamics.

* A comprehensive overview from best-selling authors including Bryan Barrass, Rawson and Tupper, and David Eyres
* Covers basic and advanced material on marine engineering and Naval Architecture topics
* Have key facts, figures and data to hand in one complete reference book

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The Maritime Engineering Reference Book

A Guide to Ship Design, Construction and Operation


Copyright © 2008 Elsevier Ltd.
All right reserved.

ISBN: 978-0-08-056009-0

Chapter One

The marine environment


1.1 The ship in the marine environment

1.2 Wind

1.3 Variations in level of sea surface

1.4 Regular waves

1.5 The sinusoidal wave

1.6 Irregular waves

1.7 Spectrum formulae by Pierson/ Moskowitz and Bretschneider

1.8 The JONSWAP sea spectrum

1.9 Maximum wave height in a stationary random sea

1.10 Long-term statistics of irregular seaway

1.11 Wave data from observations

1.12 Wave climate

1.13 Freak waves

1.14 Oceanography

1.15 Ambient air

1.16 Climatic extremes

1.17 Marine pollution

References (Chapter 1)

The various Sections of this Chapter have been taken from the following books, with the permission of the authors:

Christ, R.D and Wernli, S.R. (2007) The ROV manual. Butterworth-Heinemann, Oxford, UK. [Section 1.14]

Kobylinski, L.K. and Kastner, S. (2003) Stability and Safety of Ships. Elsevier, Oxford, UK. [Sections 1.1–1.12]

Rawson K.J. and Tupper E.C. (2001) Basic Ship Theory. 5th Edition, Combined Volume. Butterworth-Heinemann, Oxford, UK. [Sections 1.15, 1.16]

Tupper, E.C. (2004) Introduction to Naval Architecture. 4th Edition. Butterworth-Heinemann, Oxford, UK. [Sections 1.13, 1.17]

1.1 The ship in the marine environment

A ship or any ocean vehicle or structure is exposed to the marine environment. It is a complicated and often hostile environment. Environmental forces at sea come from wind, seaway, current, tidal waves, and waves from earthquakes (tsunamis). From the practical point of view, the seafarer has to cope with wind and seaway. Generally, seaway is generated by the wind at the sea surface.

The occurrence and magnitude of wind and seaway depend on the sea area and on the time of the year. Wind and seaway vary randomly and can be described by statistical methods based on probability theory. In detail, we look at the rate of occurrence, the magnitude, and the time variations of wind and seaway.

It is convenient to make a distinction between long-term (in terms of days up to years) and short-term time (in terms of hours) variations of the seaway. While the long-term approach allows for the rate of occurrence and the severity of the seaway, the short-term time variations are important for the dynamic ship response in a particular seaway of constant energy. Seaway is represented by gravity waves of the water at the sea surface. The exciting wave forces vary in time. The ship responds to the oscillating external forces as a dynamic system.

Wind and wave data have been assembled by observation, by measurement, and by mathematical description. Goals of the near future are, for example, to apply the non-linear pattern of extreme irregular seas in ship operation, and to have sea on-line data on the bridge. The literature on the sea environment is abundant. This chapter gives a general insight into the physical features of the marine environment.

1.2 Wind

By tradition, the magnitude of the wind is defined by the Beaufort Scale (Admiral Beaufort, England, 1806). The Beaufort wind scale is based on observation of the sea, by way of a rough grouping from 1 to 12Bft. The observed wave pattern in deep sea is related to the generating wind force. Storm at Bft. 11 is described as 'Waves are so high that ships within sight are hidden in the troughs; visibility poor'. Beaufort 12 means a hurricane, with the deep sea criterion describing the sea status as follows, de Beurs (1957): 'The sea is white with streaky foam as covered by a dense white curtain; air filled with spray; visibility very poor'.

The Beaufort numbers also correspond to a rating of wind according to ascending wind velocity. Each Bft. number relates to a range of wind velocities. Any wind above 32.5m/s (63.2kn.) is Bft. 12. The Beaufort scale is given in Table 1.1 where wind velocity is given at a height of z1 = 6m. The scale is also depicted in Figure 1.1.

The upper and lower limits of the Beaufort wind regions are approximated by a quadratic polynomial function, with n as Bft. number, vw1 upper limit and vw2 lower limit of the velocity range:

vw1 = 0.1424 • n2 + 1.4127 • n - 0.0434 (1.1)

vw2 = 0.1569 • n2 + 0.9112 • n - 0.0434 (1.1)

The Bft. wind velocities are average values of the horizontal wind at sea. A detailed analysis of the wind profile above the sea surface shows an increase of wind velocity with respect to the vertical distance from the sea surface, see Figure 1.2. The wind velocity at z0 = 10m above sea level has been used as a reference or characteristic wind speed, van Koten (1976).

Only for detailed analysis and calculation of wind forces the vertical wind distribution must be taken into account. The wind profile is approximated by

Vz = V0 • (z/z0)α (1.3)

The exponent is 0.12 for wind at sea surface.

In order to look at the time variation of the wind speed, we can plot the mean energy versus the average occurrence cycle in time. Figure 1.3 gives an example of the so-called spectrum of the ocean wind velocity, data taken from van Koten (1976), see also Price and Bishop (1974). We see four energy peaks, which define four distinctly different ranges of wind energy with respect to their time variation:

(1) In the first peak, the repetition cycle of the wind is only a few minutes and less than a minute (about 0.5 to 3 minutes). This shorttest time variation of the wind is of interest for the wind action on the ship and her dynamic response. A wind with its rapid time varation taken into account is called a "gust". In gusts, the maximum wind speed can be about 50% more than the mean wind speed. Davenport (l964) developed a gust spectrum.

The sudden occurrence of gusts has caused ship losses. Sailing ships are in particular endangered from extreme wind and gust. The German sailing vessel NIOBE capsized in the Baltic Sea caused by a thunderstorm gust in 1928, see Horn et al. (1953). In 1956, the German training vessel PAMIR, under sails, capsized in a hurricane in the Atlantic. Extreme wind, seaway, and shifting of grain cargo caused the loss, see Wendel and Platzoeder (1958).

Peaks 2, 3 and 4 show, whether the ship meets severe wind in the time of the year (4), and how long these prevailing wind conditions will last (2 and 3), see Figure 1.4. However, these long periods of excitation have no effect on the dynamic ship response:

(2) Peak 2 shows the daily cycles. (1/2) The mean velocity taken as the average constant wind velocity is small between peak 1 and 2, with periods of 10 to 60 minutes. This again is not critical for a dynamic excitation of ship motion by the wind.

(3) The repetition cycle of the wind is from one day up to one week. This accounts for the well-known time length of storm conditions.

(4) The repetition cycle of the wind is one year, showing the dependence of the wind on the time of the year.

Extensive research has been put into the problem of seaway generation. Hasselmann et al. (1973, 1976) showed mathematically the non-linear transfer of energy.

1.3 Variations in level of sea surface

A cyclic rise and fall of the sea level is called a wave. However, we must keep in mind that rise and fall of wind-generated waves are due to the progressive orbital motion of wave particles. Figure 1.4 shows the relative energy of the variations in the level of the sea surface, plotted versus the frequency of the orbital motion. We see pronounced peaks in the energy distribution of the sea level, which correspond to well-known phenomena at sea.

Surge, at small frequencies less than 0.001Hz (1Hz = cycle per second): This corresponds to a wave period of >1000s (>15min).

Surf beat: peak at about 0.016Hz. This corresponds to a wave period of 1min, and wavelength of 6km.

Swell: peak at about 0.056Hz, period 18s, wavelength 500m.

Wind sea: peak at 0.13Hz, period 7.5s, wavelength 90 m.

Capillaries: The lowest peak at the large frequency tail of the spectral curve marks the capillary waves.

1.4 Regular waves

1.4.1 The trochoid

The wave contour is given by a trochoid function, based on the kinetic motion of a point inside a wheel at a smaller radius fixed to the rolling motion of the wheel, Figure 1.5. Equations (1.4) and (1.5) give the parametric x and [xi] Cartesian co-ordinates of the trochoidal wave.


[xi] = - Hw/2 • cos α (1.5)

For hydrostatic calculations, the trochoid is applied to estimate the underwater shape of the ship hull in a longitudinal wave, see e.g. the stability regulations of the German Navy, Arndt et al. (1982). However, sine waves can include the orbital motion of the water particles, as discussed in the next Sections.

1.4.2 Higher order waves. Stokes and Airy Theory

The first people to treat surface waves in deep water mathematically were Airy (1845) and Stokes (1849, 1880). In applying potential theory, Stokes developed formulae not only for the exact wave contour, but also for the motion of the water particles in the wave. Parameters in the equations are the wave steepness Hw / Lw and the relative water depth d/Lw. A detailed account of all related formulae can be found in Wiegel (1964). Wehausen and Laitone (1960) gave the fundamental status of potential theory in surface waves. Ever since, many more researchers have contributed to the field of ocean waves.

For a large water depth from d/Lw between 1 and 0.5, the wave contour by Stokes to the third order is:




Figure 1.6 shows the profile of a regular Stokes wave by the sum of two sinusoidal components. The second order component increases the wave crest and raises the level in the wave trough. The third component is too small to contribute (here 0.5mm). The wave crest shows a sharper peak than the sinusoidal wave, and the wave trough is wider and flat. This is closer to reality.

The wave length by StokeTs depending on wave steepness Hw/Lw and relative water depth d/Lw is Wiegel (1964):



Lw0 = gT2w/2π (1.8)

For waves of small wave steepness Hw/Lw Equation (1.7) simplifies to:

Lw = Lw0 tanh 2πd/Lw (1.9)

With tanh x = ex - e-x/ex + e-x

The hyperbolic tangent varies between zero and 1. In general, the deeper the water and the less steep the wave, the closer the Stokes wave comes to a sinusoidal wave. This results from Equation (1.7), by d/Lw approaching infinity and Hw/Lw approaching zero. The simplified first order Stokes wave coincides with the sinusoidal wave already derived by Airy (1845).

For decreasing water depth d, the more complicated mathematical description with elliptical functions is applied (so-called cnoidal waves). The solitary wave is the limiting case for very shallow water. Figure 1.7 compares the different wave contours, according to Wiegel (1964). With less relative water depth, the wave crest becomes larger, while the wave trough is widened and raised.

The maximum steepness of a wave according to Michell (1893) is:

Lw = Lw0 tanh 2πd/Lw (1.9)

Max (Hw/Lw) = 0.142 • tanh (2πd/Lw) (1.10)

For deep water waves, this results in a maximum wave steepness of 0.142 or 1/7. In other words, a wave cannot be higher than 1/7 of the wave length. When the wave reaches a steepness of 1/7, the wave breaks. Figure 1.8 shows the profile of a breaking wave as calculated by Longuet-Higgins and Cokelet (1976).

1.5 The sinusoidal wave

1.5.1 Basic relationships to describe regular waves in deep water

The wave pattern we observe at the water surface results from orbital motions of water particles generated by wind energy transfer. We speak of gravity waves, as gravity acceleration acts on the mass of the water particles and tries to smooth the water surface. In the most simplified fashion, we only look at regular sinusoidal waves in a two-dimensional space for unidirectional waves in deep water. Figure 1.9 shows a regular sinusoidal wave with the orbital wave motion.


Excerpted from The Maritime Engineering Reference Book Copyright © 2008 by Elsevier Ltd.. Excerpted by permission of Butterworth-Heinemann. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Meet the Author

Anthony Molland, MSc, PhD, CEng, FRINA is Emeritus Professor of Ship Design at the University of Southampton. He has carried out extensive experimental research and published widely on ship design and ship hydrodynamics including ship rudders and control surfaces, propellers and ship resistance components.

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