There are many ways to approach the mast design, consider
moreover that the designer/builder always has to consider the building
process he intends to use as this often implies limitation to the design.
We will start from the loads that the mast has to carry. Most of these
loads are compressive loads. I could say: Ok i know these loads, i know
the compression values for this material i'll use, i know how much material
i need in my lay up. It isn't correct. When a so long and thin tube is
loaded on its top it undergoes first pure compression but quite instantaneously
under flexion. We will be able to use however a configuration of cables
that will distribute these flexural loads under compressive loads while
stabilising the mast.
We have to know how many kilograms the mast will substain. In a 2D world like that of the picture above, the mast will carry at the most only the crew weight plus the emiboat weight. By this way we are forgetting the sail drive force, it acts along the major axis of the boat at the sail's center of effort's height. For simplicity we could assume that this force is at its most equal to the maximum heeling force ( consider the max heeling force situation: here the sail drive is at its minimum, now if you consider the max drive force situation, the heel force is at its minimum, if you put the drive force equal to the maximum heeling force you are creating a very conservative overstimated loads situation).
By this way we could conclude that the mast will carry at the most the double of the weight we are considering, its obvious that if we add a gennaker the sail drive will arise, this should make us considering a different loads configuration, consider yet that sails works like a wing (two side of the sail works, one push while the other sucks the rig)in the upwind course, while in the downwind course the spinnaker (less the gennaker) works more like a parachute creating less lift on the sails than the same sail area in an upwind course situation, again consider that apparent wind decrease strongly in the downwind course thus diminishing the sail pressure-lift.
However we have to consider a safety factor, let's say 2 or 3. This means that the lay up have to be two or three times the calculated?!? one.
This seems to me a quite acceptable approach, i don't know if these results would lead really to a feasible mast at least since i will build a mast following these concepts. Uhmmmm it seem dangerous to me. For sure an exact value for all the vertical forces acting on the mast should be a good starting point for an engineer, but this is quite hard to match exactly, a easier yet safe methods could consist in creating a scaled lever model of the mast and sails rigged on a rigid platform where measure the loads with simple weights, this way should work well, it is easy in fact understand how a scaled lever gives scaled results. (weight*Arm=Weight1*Arm1=Weight*Arm/10=Weight1*Arm1/10) From them one could have a general idea of what it is needed to keep the mast straight to the sky, but what we really need is a safe, an existing mast to scale or to adapt to our material. So a more empirical yet safer method could be used. It's easy to scale down an existing aluminium section to one made of glass or carbon fiber in epoxy. A rule of thumb could be that one that says carbon mast tends to be 20% stiffer than the equivalent section in alloy. However the right way could be to bring from a material table of properties the flexural and compression properties of the alloy used in the existing mast and of the material one wants to use, then extract the equivalent weight of composite material, and finally plan a lay up that takes count of the fact that the alloy is an isotropic material while compisites is anisotropic, practically the most part of the fiber has to be laid along the major axis of the mast, while some plies of fiber has to be laid 0/90° and 0/45° to the major axis to give torsional and transverse resistance to the mast, this on the inside and on the outside faces of the tube.
I think that if the two approaches give similar results then it is probable that things are right. I hope i will have the time to compare with these two methods two types of mast used on the same platform (Bim A Class) one made from alloy and the other made from carbon epoxy.
Regarding the mast section it seems quite clear the fact that we are going to use a wingmast tipical section. It's very easy to shape this type of section.
Here i paste the method used from Thomas E. Speer in his wonderfoul pages of aerodynamics: (i hope this is not going to become a problem with the author)
Figure 4 shows the steps in the process. First, select an airfoil that has the characteristics you want, especially near the leading edge. It should be fairly thick or cambered, because this will determine the draft in the sail shape. It should also have the characteristic that the lee side laminar separation point (transition) moves smoothly toward the leading edge as angle of attack is increased. Next, set the percentage of the chord you want to use for the mast, and mark that on the upper surface.
Now draw a line from the mast-sail joint to just below
the leading edge. You'll want to place the end of the line so that it is
perpendicular to the airfoil contour. If it's too far up, you'll get a
sharp crease at the leading edge, and if it's too far down, you'll get
an indentation. Finally, measure off the distances perpendicular from the
line to the airfoil contour, and lay out points equally distant to the
other side of the line. This forms a reflection of the part of the airfoil
and completes the wingmast airfoil. That's all there is to it.
From the same Speer's pages come out the concept that the percentage of chord that is used is not determinant the absolute performances of the sail, instead it strongly changes the incidence of the sail to the wind direction allowance. This means that while in absolute terms a wider mast is not really different in terms of performance than a thinner one, it is instead more easily oriented in the right direction, towards the best incidence values therefore even when the wind or the boat change direction becouse of the waves or gusts or whatsoever.
It's important to say that thinner mast weights less, so they have less moment of inertia, on the other hand thicker mast are more tolerant towards structural mistakes and towards lay up mistakes.
We have not talked about the bend properties of the mast. It seems that many cat, especially bigger ones, doesn't have many possibilities of control on mast curvature, nevertheless this is a crucial point in mast design. I think that there are really few people that are able to define mathematically the exact bend propertiesof a mast, without at least any other example to follow and to refer to. So I don't expext to match the exact properties of my mast. For sure there are certain guidelines to follow, i wouldn't have realized at end neither a telegraph pole nor a fishing rod. I think that bending properties are easier to obtain in a wingmast than in a traditional mast, becouse of the fact that we are relatively interested in longitudinal flaxibility as this is in any case bigger than lateral one and becouse of this is modified and stted by the diamond tension. So we can focus on laterlal flexibility. This is what really interest us becouse our mast as rotative mast work most of the time "rotated". An engineer could relatively easily ( with a certain grade of approximation, given the variable loads situation of the sail) calculate the bending loads and then apply to a given material in a given section. The fact is that even if the grade of approximation is mantained low ( and this is very hard to do) the type of material that we are going to "create" cannot have a certain properties, by this way it easy to conclude that even professional mastbuilder, for little works arrive to a better results and in less time by going ahead with the try, miscalculate, correct and then retry method. I have made the idea that the mast i will realize should drive the sail design, as the sail is strongly and mainly influenced by the mast properties, of course a very bend mast should be corrected as there is no way to adapt a sail to too greater variation in the mast shape, the type of costruction that i intend to use should help me in this as it is made of two halves that are lately glued together. It should be a good idea to give the mast a certain type of bend, even if we don't know how much bend at the beginning, becouse we know what sort of curvature the mast should have under a fixed load (here are two picture taken from BIMare website, they shows the lateral and longitudinal flex of a carbon class a mast). We have to say that even if the mast bends in a certain manner and the sail is cutted to fit that curvature, it isn't only this that interest us. One of the best quality of carbon mast (apart their low weight) is their quick flex return, this means that even a if a glass or aluminium mast have the correct lateral and longitudinal flexibility it has not the same inverse reaction (the return to a normal position after a gust for example) . carbon has the best return flex properties, so if you want that your mast works in a good way even after a gust you should use as much carbon you can, even if this last is not sufficient to ensure the compressive loads of the forestay and backstay ( these loads can be easily taken by the glass even if at expense of more weight)