## Steel Sailboat Mast Design ...

an alternative

Saiboat Mast Design There is aluminum and wood, but did you know that there is also steel sailboat mast design?

The two greatest costs in building a sailboat are the hull and the rigging. I once read that rigging is nearly the cost of a hull. On limited funds, when I planned to build my boat, these were my concerns.

Since the cost of an aluminum mast and the hardware put a strain on my budget, I decided to compromise and use steel for the Notion's mast. In an attempt to research information on designs for self-constructed steel masts, books and the internet came up empty. I spoke with a designer who seemed unfamiliar with such a method, he recommended aluminum or wood for the mast material. Frustrated at no guidance available for steel sailboat mast design, I decided to apply my own knowledge and experience of sheet metal methods.

The mast that resulted from my effort stood on the Notion for almost 18 years, still does, as far as I know.

The formulas used in this article, I learned from Westlawn School of Yacht Design.

The construction methods I used in the fabrication of the steel mast for the Notion are cost effective and practical. It saved money, not only on the base mast, but on all the hardware too - most of which can be fabricated from materials commonly found around metal shops.

**Properties of Materials **

for Steel Sailboat Mast DesignThere are two "properties of material" understood by designers in sailboat mast design. First, "Moment of Inertia" next "Modules of elasticity". Now, I know what you're thinking - what the heck is this guy talking about? Let me explain what these are and why they are important ...

**Moment of Inertia**Moment of Inertia is an indication of stiffness. It's strength. It is affected by the SHAPE of the mast section, like, whether the mast is rectangle, circular or oval. Changes in such things as length, width and especially wall thickness will effect the inertia of that section. The chart at the bottom of this paper demonstrates that wall thickness has a greater effect on increasing inertia compared to small increases in length or width. Steel has the lowest moment of inertia, aluminum somewhat higher and wood rates the highest.

**Modules of Elasticity**The other property is "Modules of Elasticity". It is affected by the MATERIAL used. It is the stress/strain ratio of the material. You can think of it as the measurement of its ability to bend.

Stress is the amount of internal resistance offered by a material before it will yield or separate.

Strain, is the measure of deformation of material when placed under a load.

The yield point of a material is reached when the material no longer returns to its original shape after the load is removed (causing deformation).

If mast sections of two different materials are placed under equal loads, the section with the higher modules of elasticity will deform less. A good mast material is one that has a __high yield point__.

If the modules of elasticity for steel is at 29,000,000 psi - aluminum is at 10,000,000 psi - and wood is at 1,300,000 psi, it indicates that steel has three times a higher yield point than aluminum and twenty-two times higher than wood. From this, steel has better bending ability than aluminum or wood.

A balance between these two elements (strength and flexibility) are necessary for good mast design.

There are three accepted design formula's used in boat design - they are Euler's formula, USYRR (United States Yachting Racing Rules)and the Empirical formula.

To design a mast, a compression calculation is necessary. This factor is needed to enter into each of the three formulas: "Euler's", "USYRR" and "Empirical". These formulas calculate inertia - that is, the strength to support the compressive load. Several other factors are entered into this calculation but they are off topic so I'll end that here. Let me translate ...

"Euler's" is a formula that is used to calculate *inertia*. You remember inertia is discussed on the Properties of Materials, it indicates stiffness or strength. Alternately, the compression on a mast can be determined by the moment of inertia that the designer has calculated from the mast's physical size. A designer's compression calculations for a mast of aluminum or wood can also be used for steel.

Referring to the same chart, Euler's formula and the USYRR rules provide for all three materials; steel, aluminum and wood. But the Empirical formula provides for wood and aluminum only.

In general, for mast construction in any material, I prefer Euler's. It provides higher safety factors with little lost in stability over the other two formulas.

The important point here is that you need a compression calculation to convert an aluminum or wood designed mast into steel.

**Keel or Deck Stepped Masts**

United States Yacht Racing Rules (USYRR) and Empirical mast rules contain different factors for keel and deck stepped masts. The factors for a deck stepped mast results in a slightly heavier mast section than that of a keel stepped application using the same formula. The theory is that the end fixity is not as strong in deck stepping over placing it through to the keel.

Studying these formulas, a higher safety factor is apparent in Euler's formula. Also interesting, is that it results in a mast size that could be used in either a deck or keel application. So unless there is a specific design requirement, I prefer deck stepped a mast.

When constructing the Notion, I deck stepped the mast but there was no reason it could not have been keel stepped. It had a 2-1/2" pipe compression post in the cabin. I disguised this with a false mast section giving it the illusion of a keel stepped mast for better interior appearance.

**About Halyards** Interior or exterior, which to choose? Well, for cruising, the advantage of reduced wind resistance of an interior halyard proves minimal compared to the practical maintenance advantages of exterior halyards on a steel mast.

There are a couple of important advantages to exterior halyards. Construction is much simpler and the interior of the mast does not require paint since the mast is welded water and air tight. Rust does not form when oxygen is not present.

**Formula Comparisons**To demonstrate the results of different mast materials, review the chart at the bottom of this article.

This chart compares the three recognized formulas used in mast design:

- Euler's - slender column formula;
- USYRR (United States Yacht Racing Rules); and
- the Empirical formula.

Euler's formula is the base of the analysis, the other two formulas extend the comparison. The sample mast, for the subject comparison, is one of my current designs for a steel cutter.

The chart compares:

- overall dimensions;

- inertia for these dimensions

- safety factors compared to Euler's formula

- mast weight per foot

- righting moment in pounds - with the boat heeled at 30 degrees

- the negative stability of the boat. Negative stability is the angle of the heel where the boat loses all force to right itself.

**Chart Results**

In studying the results of all the charts there are several conclusions that emerge between the different formulas and mast materials.

- 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 (according to Euler).

- 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 amuminum, the following applies:
1. Wood masts have the lowest stability at 122 degrees;

2. Steel masts show a little more stablity at 125 degrees; and

3. Aluminum has the greatest stability at 126 degrees.

Mast material has little effect on the ultimate stability - ther 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.

**EMPERICAL FORMULA** **MAST** MATERIAL | **MAST** SECTION | **WALL** THICKNESS | **LONG.** DIM'S | **TRANS** DIM'S | **WEIGHT** FOOT | **LONG.** INERTIA | **TRANS** INERTIA | **LONG.** SAFETY FACTOR | **TRANS** SAFETY FACTOR | **%LIGHTER** THAN EULER'S | **NEGATIVE** RA-30 |

ALUMIMUM | OVAL | .187 | 8.250 | 4.875 | 4.390 | 25.170 | 11.620 | 2.410 | 2.010 | 14.800 | 127 31,062 |

- | - | - | - | - | - | - | - | - | - | - | - |

WOOD | OVAL | 20% | 9.000 | 6.000 | 5.420 | 184.170 | 83.840 | 2.220 | 1.860 | 28.700 | 125 31,500 |

**EULER'S FORMULA** **MAST** MATERIAL | **MAST** SECTION | **WALL** THICKNESS | **LONG.** DIM'S | **TRANS** DIM'S | **WEIGHT** FOOT | **WEIGHT** MAST | **LONG.** INERTIA | **TRANS** inertia | **LONG.** SAFETY FACTOR | **TRANS** SAFETY FACTOR | **NEGATIVE** RA-30 |

ALUMIMUM | OVAL | .187 | 9.000 | 6.000 | 5.04 | 219.730 | 37.450 | 20.020 | 3.230 | 3.260 | 126 31,759 |

- | - | - | - | - | - | - | - | - | - | - | - |

WOOD | OVAL | 20% | 9.750 | 7.125 | 6.980 | 304.380 | 282.150 | 150.670 | 3.170 | 3.190 | 123 30,537 |

WOOD | RECT | 20% | 8.625 | 6.250 | 6.900 | 300.720 | 290.86 | 152.730 | 3.260 | 3.230 | 122 30,620 |

- | - | - | - | - | - | - | - | - | - | - | - |

STEEL | OVAL | .074 | 8.625 | 5.500 | 5.416 | 265.030 | 13.190 | 6.640 | 3.300 | 3.140 | 125 31,155 |

STEEL | RECT | .074 | 7.125 | 4.750 | 5.780 | 281.130 | 12.927 | 6.960 | 3.240 | 3.290 | 124 30,953 |

- | - | - | - | - | - | - | - | - | - | - | - |

STEEL | RECT | .062 | 7.500 | 5.000 | 5.110 | 251.940 | 12.720 | 6.680 | 3.190 | 3.240 | 125 31.356 |

**UNITED STATES YACHT RACING RULES** **MAST** MATERIAL | **MAST** SECTION | **WALL** THICKNESS | **LONG.** DIM'S | **TRANS** DIM'S | **WEIGHT** FOOT | **LONG.** INERTIA | **TRANS** INERTIA | **LONG** SAFETY FACTOR | **TRANS** SAFETY FACTOR | **%LIGHTER** THAN EULER | **NEGATIVE** RA-30 |

ALUMIMUM | OVAL | .187 | 7.875 | 4.750 | 4.220 | 23.730 | 10.670 | 2.120 | 1.820 | 19.400 | 127 32,362 |

- | - | - | - | - | - | - | - | - | - | - | - |

WOOD | OVAL | 20% | 8.750 | 5.875 | 5.160 | 169.530 | 76.460 | 1.990 | 1.690 | 35.2 | 126 32.061 |

- | - | - | - | - | - | - | - | - | - | - | - |

STEEL | OVAL | .074 | 7.500 | 4.375 | 4.500 | 8.180 | 3.680 | 2.150 | 1.780 | 20.300 | 127 32,500 |

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