Page 169 - The Complete Rigger’s Apprentice

Cruising sailors, though they’ll be interested the properties (modulus of elasticity) of the material
in good performance, will want to minimize the the mast is made of. The matters of wall thickness
expense, vulnerability, and intricacy of many sets of and mast radius will be dealt with later, on mast
spreaders, and will be less concerned about an abso-
lute minimum of wind-resistance. A cruising mast
section will have moderate radius, moderate wall Scantlings Recommended
thickness, and one or two sets of spreaders. And it by USSA Panel
will be built with a higher safety factor. The United States Sailing Association (USSA),
In sum, mast design involves juggling various formerly the United States Yacht Racing Union
stiffness-inducing factors along with cost, perfor- (USYRU), developed an alternative to Skene’s
mance, reliability, and even interior design. To mast scantling formulas for offshore racing yachts.
The two sets of formulas are based on the same
get the mast you want, you just have to be able to elements; the one from the USSA combines them
express those factors with numbers. in a different form, uses a lower safety factor, and
works with the righting moment at 40 degrees of
heel instead of 30 degrees. Resulting masts are con-
Mast Strength Formulas, Part 2 siderably lighter than ones designed by the Skene’s
All mast design formulas are variations and refine- method, but the USSA formulas do prevent the
ments on Euler’s Formula, an engineering corner- worst excesses of hold-your-breath spindliness in
stone which predicts the behavior of columns under offshore racing masts.
The formula for longitudinal inertia is:
compression, with allowances made for all the sig-
nificant variables. A predigested, easy-to-plug-into (Longitudinal Safety Factor 5 40 5 Righting
form appears in Skene’s Elements of Yacht Design. Moment (ft-lbs) at 1° heel 5 [Mast Height
(inches)]2) ÷ (End Fixity Factor 5 ⁄2 Beam
1
I like this version because it’s simple and conserva- (at chainplates) π 2 5 Modulus of Elasticity).
tive. For another, more race-oriented approach, see
the U.S. Sailing Association’s recommended scant- More concisely, that’s:
lings in the accompanying sidebar. FS 5 40 5 RMC 5 P 2
L
L
Meanwhile, let’s start with the formula for the F 5 CP 5 π 2 5 E
lateral, or transverse, plane. We’re looking for a With an inner forestay, the longitudinal safety
specific “transverse moment of inertia”—essentially factor is 1.5, if the forestay is attached to the mast
stiffness—which will be expressed, due to multiple between .651 and .701 of the mast height above
the sheer and is backed up with running backstays.
squarings hidden in the calculations, in inches to the Without a forestay, the safety factor is 2.
4
4
fourth (in. ). I (in. ) is our symbol. End fixity is 2 if the mast is keel-stepped, 1.5 if
tt
So: deck-stepped.
For minimum transverse inertia, the formula is:

I (in. 4 ) = C transv 5 L 2 (in. 2 ) 5 Load FS 5 40 5 RMC 5 P 2
t
tt
10,000 10,000 T F 5 CP x π 2 5 E T
Where C = a transverse constant Where P is the height of the mast to the lower
T
L = the length from deck spreaders.
t
The safety factor is 1.7 for a single-spreader
to lower spreader rig, 2 for a double-spreader, assuming the single
Load = RM 30 compression load. spreaders are more than halfway up the mast and
at least four-fifths of the boat’s one-half beam in
length, and the lower set of double spreaders is at
Stiffness varies inversely with the square of least .36 of the way up the mast and at least three-
unsupported length, so multiplying the load times fifths of the boat’s one-half beam. This spreader
the square of the longest unsupported length—deck placement proviso has the effect of keeping the
T
to spreaders—takes care of that relationship. The “P 2 ” measurement high, which results in a heavier,
safer mast section.
constant takes care of end fixity, a safety factor, and
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