Steel Mast Design:

To 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:

Euler's - Slender Column Formula

USYRR (United States Yacht Racing Rules)

Empirical Formula

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.


Formula Comparisons

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
  • Righting 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 conditions.
  • 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.