20170219

In the Clinker Plywoord Boatbuilding Manual, Iain Oughtred proposes that the diameter of a solid unstayed round-sectioned wooden mast for a small boat should be 1:50 of LAD (length above deck). This is almost twice as big as the conventional mast of a racing dinghy. I guess the reason for this high value is that an unstayed mast should be extra stiff to cope with brutal downhaul needed in windy conditions.

Working from this assumption, the mast of Hatseflats should have a diameter of 86mm based on 450cm LAD. The area will be app 58 cm2 (pi * r2). The area moment of inertia (I) is (r^4 * pi/4) = 43^4 * pi/4 = 2685120 mm4. Given a density of 0.5 the weight will be 2.9kg/m or 14.5kg for a solid untapered mast of 500cm.

I like wood because it floats and is easy to work with. But nearly 15kgs for the mast alone is too much. 10-11kg would be acceptable but not much more.

A solid square section of 75x75mm results in a marginally less stiff mast (I=bh^3/12). But with a weight of 14kg (2.81kg/m) this alternative is still too heavy.

A hollow wooden mast with the top half tapered to 70% should be a lot lighter. This can be made with four tapered planks of 20mm around solid inserts. For a concentric hollow square I = (BH^3 - bh^3)/12
The net weight of this mast is around 11.6kg, but it requires a lot of work.

The alternative is an untapered aluminium tube with a internal doubling in the lower 100cm. The area moment of inertia of an annulus is (r2^4 - r1^4) * pi/4
The modulus of elasticity of aluminium is 69Gpa compared to 13GPa for wood. This means that the inner and outer diameters can be made smaller to achieve the same stiffness. The stiffness of the solid 75x75 wood section is EI (E=13, I=2636718) = 34277343. For an 80/74mm tube @2.04kg/m, I=(40^4 - 37^4) * pi/4 = 538656. Stiffness (EI) = 69 * 538656 = 37167311, even better.

Net weight is 5m * 2.04 = 10.2kg. With an inner sleeve for the lower 100cm, we arrive at 12.24kg. By using wood props in the ends we can even make it float.

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20170219_tirrik3_03.jpg Tirrik built by De Zeeg. Alloy hull, alloy spars