Steel Mast Design:
illustrate the practically of steel as a mast material, I will be calculating
the dimensions of a mast for a 34-foot steel sailboat in steel, aluminum,
and wood. The design results will than be compared to aluminum and wood
designs. The formulas that I will be using are:
- Slender Column Formula
(United States Yacht Racing Rules)
Euler's and USYRR have provision for Aluminum,
wood, and Steel, while the Empirical Formula only has provision for Aluminum
and Wood. I will include it anyway.
The comparison chart will show: Mast
Section - Shape, Calculated Wall Thickness, Longitudinal and Transverse
Dimensions, Weight per Foot, Longitudinal and Transverse Inertias, Longitudinal
and Transvers Safety Factors.
Additionally, the Negative Stability Angle and
Righting Moment at Thirty Degrees is given to gage the results of the
different mast materials on the stability of the boat.
Negative Stability Angle - The angle at which the
boat when heeled will not return to an upright position.
Right Moment at Thirty Degrees - The righting
force in pounds, at a heel angle of thirty-degree, that return the boat
to an upright position.
Rectangular sections have slightly higher inertials than oval sections of the same overall length and width.
- USYRU-IMS and Empirical formulas both reach nearly the same results but the Empirical formula is somewhat higher.
- Of the three formulas, Euler's has a higher inertia.
- Wood is the heaviest mast section for their required inertia.
- Of the three formulas, Euler's has a higher safety factor.
- Ultimate/Negative stability (the angle of heel to which the boat
will no longer be able to right itself), is between 122 degrees and 127
degrees. Comparing wood, steel and aluminum, the following applies:
1. Wood masts have the lowest stability at 122 degrees;
2. Steel masts show a little more stability at 125 degrees; and
3. Aluminum has the greatest stability at 126 degrees.
Mast material has little effect on the ultimate stability - there is only 1 degree difference between steel and aluminum
moment is only a slightly less at an angle of heel of 30 degrees. In
this regard, all formulas are between 30,600 lbs. - 32,500 lbs of
righting moment at this angle. A steel mast at 31,356 pounds using
Euler's formula is no real loss to stability under normal sailing
- The steel mast section is somewhat smaller which aids wind
resistance. The rectangular shape however, is less aerodynamic than
that of an oval but considered minimal to the crusing sailor.
- Overall, Euler's formula is preferable resulting in a higher safety factor and no real negatives.
- Since the highest inertia is seen for wood sections, accordingly,
the moment of inertia for aluminum is much less than wood. Steel
sections however, have the lowest value of the three materials. Wall
thickness accounts for this - steel masts have a thin wall - aluminum
slightly thicker and wood the most dense.