Gust factor (2); Another approach is the use of a height dependent gust factor. In [9] A. Kareem refers to the following relationships (6), (7) where the phenomenon gust factor is defined:
Where:
t = averaging time interval [s],
g = peak factor [],
σ(z) = standard deviation at height z [m.s^{1}].
A different reading of formulae (6) and (7), the use of a reference time interval of 10 minutes and a required time interval of 1 minute lead to:
where g(10 min>1 min.z) = represents the peak factor and
represents the turbulence intensity.
According to Wieringa and Rijkoord [3] this turbulence intensity may be estimated by:
The Royal Netherlands Meteorological Institute provided us with data for the determination of the peak factor. These data and the formulae mentioned above should be used in combination with a vertical wind profile which is defined by a logarithmic function. Calculation results using this method show a remarkable difference in the increase of wind velocities for different roughness lengths. In the opinion of MPIN this is not surprising because of a higher turbulence intensity above rough land than above a flat sea surface. Using this approach formula (5) changes into:
Vertical wind profile + gust factor; An approach which combines the use of a logarithmic vertical wind profile and a gust factor is proposed by Det Norske Veritas (DNV) [10]:
Where:
tr = reference time interval (600 [s]),
Zr = reference height (10 [m]).
This approach is used by DNV for the determination of wind loads on offshore units.
Averaging time interval; With respect to wind loads on ships, given a defined height and geographical situation, the question arises which wind velocity, or rather the mean wind velocity of which duration, should be used in determining these loads. This depends for the greater part on the response of the vessel. In [8] PIANC states that intervals of more than 1 minute may be considered relevant for large vessels. This is an arbitrary value: two vessels with exactly the same lateral area (for instance a car carrier and a loaded tanker), will not respond in the same way to the same gust because of their different displacement and added mass.
In particular in case of wind velocities mentioned in weather forecasts (usually 10minute mean values), application of a gust factor may be of importance. Naturally the choice to use a gust factor is up to the user of the computer program.
Implementation of wind velocity formulae in the computer program; As can be seen from the previous paragraphs a wide selection of approaches is offered for the calculation of the wind velocity. It is impossible to go into detail about the considerations regarding a selection. The following choices were made: For 'normal' ships at open sea the power law profile is used in combination with the gust factor values of PIANC (formulae 4 and 5). The height exponent used in the power law is 0.1. For complex structures at open sea the method as proposed by DNV is used (formula 11). For both, 'normal' ships and complex structures in nonexposed harbor situations a logarithmic vertical wind profile is used in combination with a height dependent gust factor (formulae 3, 8, 9 and 10). For nonexposed harbor situations no data were found regarding standard roughness lengths or height exponents for the power law profile except the height exponent of 0.2 proposed by Blendermann [5]. For this reason we chose a (possibly arbitrary) roughness length of 0.2 [m] which appears to match reasonably with the use of a height exponent of 0.2 [] (see figure2). In all cases the equations are solved by numerical integration.
