Modern Windships; Phase 2

Appendix 7. Wind Pressure Calculations

The calculations leading up to the chosen design criteria regarding the pressure imposed by the wind on the sails is explained in some detail below.

Survival Condition

Using the top gust wind speed calculated above we got a total Bernouilli pressure of:

[kN/m2]

Transferring to designers units we had:

[kg/m2]

The above pressure was assumed to be applied as uniform load on the local panels in case of extreme wind conditions, and the mast standing at a right angle towards the wind. This must definitely be considered as an extreme case. See the note below. If the mast can survive wind speeds of 80.8 m/s folded together and turned against the wind this was considered sufficient.

Note

Using a C_l of 3.2 we could now calculate the wind speed in sailing when it is advisable to fold the mast together in order not to exceed the local pressure maximum of the sandwich panels. Assuming that 2/3 of the force was generated by "suction" on the leeward side of the flap we get:

m/s

We now realised that using the survival criteria as design load for a sailing ship was very conservative. It was not reasonable to specify a sail that should withstand full storm without reefing. The resulting design would be far too heavy.

Full Sail Condition

Using the 3 sec. gust speed as design criteria, with a Cl of 3.2 (from the measurements described below) we got:

[kN/m2]

Recalculating to designers units we had:

[kg/m2]

But again we were designing the sails to withstand full storm conditions of 37 m/s wind speed. As mentioned above this would yield very heavy sails. The wing mast provides two mechanisms to prevent overloading of the panels. Designing for the average 10 min wind therefore seemed motivated. Any gusts above this limit would be taken care of by load relief from the mast.

As the design wind speed (25 m/s) is measured 10 m above the water surface it has to be corrected using a standard wind profile as the rig is positioned between 15 and 60 m above the surface. By averaging the wind speeds along the height of the mast we got a wind speed of 29.35 m/s. We had the wind speed variation with height z from DNV, see Ref. 16:

Equation 22

Using the heights 21.6, 32,3, 43.0 and 53.7 [m] we get:

[kN/m2]

Recalculating to designers units we had:

[kg/m2]

For comparison:

	The 10 min average speed of 25 m/s at a height of 10 m gave a pressure of 1250 N/m2, or 127 kg/m2.
	The 10 min average speed of 30.6 m/s at 45 m height gave a pressure of 1872 N/m2, or 191 kg/m2.

As can be seen from above, due to the quadratic dependence of the pressure with the wind speed, it was important to choose the correct design wind speed. See also Figure 86.

Figure 86. The wind pressure dependence on wind speed