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The final bit of information we need is the area of the mast at the partners and at the head – that is the area of actual timber. This is calculated as follows:

Area (A) = π(D^2-d^2)/4

Working this out for our Ø150 spar, we have:

A = 3.142(150^2-90^2)/4 = 11,309.734 mm^2

And the area (a) for the spar at the head:

Dhead = D•0.6 = 90 mm
dhead = Dhead-(Dhead*0.2*2) = 54 mm
a = 3.142(90^2-54^2)/4 = 4,071.504 mm^2

We use the areas to work out the average area over the tapered length, and thus the volume of the tapered length and the volume of the parallel length – which will lead us to the weight of the spar and the vertical centre of gravity. We don't need the areas to work out the strength of the spar – we simply use the Safety Factor for that.

Let's sum up now, all the figures we have (rounded off):

1,490 kg Calculated design value Displacement
GZ30 0.277 m Derived from GZ curve Righting arm at 30º
GZmax 0.481 m Derived from GZ curve Max righting arm
D 150 mm Starting value Outside Diameter of mast at partners
d 90 mm D-(D*0.2*2) Inside Diameter of mast at partners
RM30 4,049 Nm GZ30*∆*9.81 Righting Moment at 30º
RMmax 7,031 Nm GZmax*∆*9.81 Max Righting Moment
L 3.705 m Calculated value Length, CE of sail to partner
F30 1,093 N RM30/L Force at 30º
Fmax 1,898 N RMmax/L Max Force at 30º
y 75 mm D/2 Distance from extreme to Neutral Axis
I 21,629,865 mm^4 π(D^4-d^4)/64 Moment of Inertia
Z 288,398 mm^3 π(D^4-d^4)/32D Modulus of Section
A 11,309 mm^2 π(D^2-d^2)/4 Area at partner
a 4,072 mm^2 π(Dhead^2-dhead^2)/4 Area at head
W 480 kg/m^3 Average value at 12% moisture content Weight
E 13,400 N/mm^2 Average value clean Douglas Fir Modulus of Elasticity
R 69 N/mm^2 Average value clean Douglas Fir Modulus of Rupture

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© George Whisstock. This article is for information only and may not be commercially reproduced in any form or used in any way without permission. Do not use this material as the basis for designing a mast without professional advice.