The freestanding mast is only supported at deck level and at the bottom of the hull. The distance between the deck bearing and the bottom bearing is around 2 metres. The distance from the deck to the top of the mast is around 17 metres.
To estimate the forces and bending moments I will first assume the mast must be able to deal with a righting moment of 60 kNm.
I will use two methods/models. Model A puts the full force of the wind at the top of the mast. Model B is more realistic and assumes the wind force is distributed evenly along the entire mast (above deck ofcourse).
The drawings below show the forces in equilibrium. Note that the maximum bending moment (60 kNm at deck level) and the load on the bottom bearing (60 kNm / 2 m = 30 kN) do not depend on the model. These are determined by the 60 kNm righting moment of the yacht.
Also note that model B allows a higher wind force (17 m x 0.42 kN/m = 7 kN) than model A (3.5 kN) and, as a result, causes a higher load on the deck bearing (37 kN versus 33.5 kN).
To calculate an efficient (not too heavy and expensive) carbon laminate of the mast at different locations I need more bending moments than the maximum of 60 kNm at deck level.
Luckily, using model A, these bending moments are very easy to calculate: the bending moments decrease linearly from 60 kNm at deck level to zero towards the bottom and the top of the mast. Using model B the calculations are more complicated (I will probably add two bending moment diagrams later to illustrate this point).
However, because the (above deck) bending moments in model B are equal to or lower than in model A, I can also choose to just ignore model B. Using model A will automatically create a safety factor AND make my life easier.
Model A: 3.5 kN point load at top of mast
Model B: 0.42 kN/m distributed load
