4 The propellerenvironment
4.8 Weather
The weather, or more fundamentally the air motion, caused by the dynamics of the Earth’s atmosphere, influences marine propulsion technology by giving rise to additional resistance caused by both the wind and resulting disturbances to the sea surface.
The principal physical properties of air which are of concern are density and viscosity. The density at sea level for dry air is given by the relationship:
ρ=0.4647 p
T
kg/m3 (4.3)
wherepis the barometric pressure (mmHg) andTis the local temperature (K).
For the viscosity of the air use can be made of the following relationship for dry air:
μ=170.9×10−6 393 120+T
T 273
3/2
poise (4.4) whereTis the temperature (K).
When the wind blows over a surface the air in con- tact with the surface has no relative velocity to that
Table 4.6Typical values of surface tension for sea and fresh water with temperature
Temperature(◦C) 0 5 10 15 20 25 30
Sea water
(dynes/cm) 76.41 75.69 74.97 74.25 73.55 72.81 72.09
Fresh water
(dynes/cm) 75.64 74.92 74.20 73.48 72.76 72.04 71.32
1 dyne=10−5N.
Figure 4.7 Wind speed definition
surface. Consequently, a velocity gradient exists close to the solid boundary in which the relative velocity of successive layers of the wind increases until the actual wind speed in the free stream is reached (Figure 4.7).
Indeed the flow pattern is analogous to the boundary layer velocity distribution measured over a flat plate. To overcome problems of definition in wind speed due to surface perturbations it is normal practice to measure wind speed at a height of 10 m above the surface of either the land or the sea: this speed is often referred to as the ‘10 metre wind’ (Figure 4.7).
As well as recording wind velocities, wind condi- tions are often related to the Beaufort scale, which was initially proposed by Admiral Beaufort in 1806. This scale has also been extended to give an indication of sea conditions for fully developed seas. The scale is not accurate enough for very detailed studies, since it was primarily intended as a guide to illustrate roughly what might be expected in the open sea. Nevertheless, the scale is sufficient for many purposes, both tech- nical and descriptive; however, great care should be exercised if it is used in the reverse way, that is for log- ging or reporting the state of the sea, since significant
The propeller environment 59
Table 4.7The Beaufort wind scale
Number Wind speed Wind Probable Noticeable effect At sea at 10 m (knots) description mean wave of wind on land
height (m)
0 Less than 1 Calm None Smoke vertical; Sea like a mirror.
flags still
1 1–3 Light air <0.1 Smoke drifts; Ripples with the appearance of scales vanes static are formed, but without foam crests.
2 4–6 Light breeze 0.2 Wind felt on face; Small wavelets, still short but more leaves, flags rustle; pronounced; crests have a glassy vanes move appearance and do not break.
3 7–10 Gentle breeze 0.6 Leaves and twigs in Large wavelets. Crests begin to break.
motion; light flags Foam of glassy appearance perhaps extended scattered white horses.
4 11–16 Moderate breeze 1.0 Raises dust; moves Small waves, becoming longer;
small branches fairly frequent white horses.
5 17–21 Fresh breeze 1.9 Small trees sway Moderate waves, taking a more pronounced long form, many white horses formed (chance of some spray).
6 22–27 Strong breeze 2.9 Large branches move; Large waves begin to form; the white telephone wire ‘sing’ foam crests are more extensive
everywhere (probably some spray).
7 28–33 Moderate gale 4.1 Whole trees in motion Sea heaps up and white foam from breaking waves begins to be blown in streaks along the direction of the wind (spindrift begins to be seen).
8 34–40 Fresh gale 5.5 Twigs break off; Moderately high waves of greater length;
progress impeded edge of crests break into spindrift. The foam is blown in well-marked streaks along the direction of the wind.
9 41–47 Strong gale 7.0 Chimney pots High waves. Dense streaks of foam removed along the direction of the wind. Sea
begins to roll. Spray may effect visibility.
10 48–55 Whole gale 8.8 Trees uprooted; Very high waves with long, overhanging structural damage crests. The resulting foam in great patches
is blown in dense white streaks along the direction of the wind. On the whole, the surface of the sea takes a white appearance.
The rolling of the sea becomes heavy and shock like. Visibility is affected.
11 56–64 Storm 11.0 Widespread damage Exceptionally high waves. (Small- and medium-sized ships might, for a long time, be lost to view behind the waves.) The sea is completely covered with long white patches of foam lying along the direction of the wind. Everywhere the edges of the wave crests are blown into froth. Visibility is affected.
12 65–71 Hurricane Over 13.0 Countryside The air is filled with foam and spray.
devastated Sea completely white with driving spray; visibility very seriously affected.
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60 Marine propellers and propulsion
Figure 4.8 Typical wave spectra for varying wind speed
errors can be introduced into the analysis. This is partic- ularly true in confined and restricted sea areas, such as the North Sea or English Channel, since the sea gener- ally has two components: a surface perturbation and an underlying swell component, both of which may have differing directional bearings. Table 4.7 defines the Beaufort scale up to force 12. Above force 12 there are further levels defined: 13, 14, 15, 16 and 17, with associated wind-speed bands of 72–80, 81–89, 90–99, 100–108 and 109–118 knots, respectively. For these higher states descriptions generally fail except to note that conditions become progressively worse.
Until comparatively recently the only tools available to describe the sea conditions were, for example, the Beaufort scale, which as discussed relates overall sea state to observed wind, and formulae such as Stevens’
formula:
Z=1.5√
F (4.5)
whereZis the maximum wave height in feet andFis the fetch in miles.
However, from wave records it is possible to stat- istically represent the sea. Using these techniques an energy spectrum indicating the relative importance of the large number of different component waves can be produced for a given sea state. Figure 4.8 shows one such example, for illustration purposes, based on the Neumann spectrum for different wind speeds and for fully developed seas. From Figure 4.8 it will be seen that as the wind speed increases, the frequency about which the maximum spectra energy is concentrated, termed the modal frequencyf0, is reduced. Many spectra have been advanced by different authorities and these will give differing results; partly because of the dependence of wave energy on the wind duration and fetch which leads to the problem of defining a fully developed sea.
When the wind begins to blow short, low amplitude waves are initially formed. These develop into larger and
Figure 4.9 Growth of a wave spectra with wind duration
Table 4.8World Meteorological Organization (WMO) sea state code
Sea state Significant wave height (m) Description code
Range Mean
0 0 0 Calm (glassy)
1 0–0.1 0.05 Calm (rippled)
2 0.1–0.5 0.30 Smooth (wavelets)
3 0.5–1.25 0.875 Slight
4 1.25–2.5 1.875 Moderate
5 2.5–4.0 3.250 Rough
6 4.0–6.0 5.000 Very rough
7 6.0–9.0 7.500 High
8 9.0–14.0 11.500 Very high
9 Over 14.0 Over 14.00 Phenomenal
longer waves if the wind continues to blow for a longer period of time. This leads to a time-dependent set of spectra for different wind duration, as seen in Figure 4.9.
An analogous, but opposite, situation is seen when the wind dies down as the longer waves, due to their greater velocity, move out of the area, leaving only the smaller shorter waves. For continuous spectra the area under the spectrum can be shown to be equal to the mean square of the surface elevation of the water surface.
In order to study the effects of waves the energy spectrum concept provides the most convenient and rig- orous of approaches. However, for many applications, the simpler approach of appealing directly to wave data will suffice. Typical of such data is that given by Dar- byshire (Reference 5) or more recently that produced by Hogbenet al. (Reference 6) which provides a wave atlas based on some 55 million visual observations from ships during the period 1854 to 1984. Furthermore the World Meteorological Organization (WMO) produced a standard sea state code in 1970; this is reproduced in Table 4.8. In the context of this table, the significant wave height is the mean value of the highest third of a
The propeller environment 61 Table 4.9 Port classification for fouling according to (Reference 7)
Clean ports Fouling ports Cleaning ports
Light Heavy Non-scouring Scouring
Most UK Ports Alexandria Freetown Bremen Calcutta
Auckland Bombay Macassar Brisbane Shanghai
Cape Town Colombo Mauritius Buenos Aires Yangtze Ports
Chittagong Madras Rio de Janeiro E. London
Halifax Mombasa Sourabaya Hamburg
Melbourne Negapatam Lagos Hudson Ports
Valparaiso Karadii La Plata
Wellington Pernambuco St Lawrence Ports
Sydney* Santos Manchester
Singapore Suez Tuticorin Yokohama
* Variable conditions.
large number of peak to trough wave heights. It should, however, be noted that wave period does not feature in this well-established sea state definition.