Structural considerations in sailboat design

Blue sloop-rigged yacht standing on land in a small harbor on a clear winter day. Waiting for the new sailing season.

Strength and stiffness requirements

All boats shall have adequate strength (ability to withstand an applied load without failure or permanent deformation) to keep the hull watertight and withstand hydrostatic and hydrodynamic loads without breaking. Besides these water-generated forces, several other loads, like the rig loads, may also affect the hull and deck of a sailing boat.

Checking the strength can be regarded as a basic task in structural design to ensure safety, but the stiffness (capacity of a mechanical system to sustain external loads without excessive changes of its geometry) of the structures is often an important factor also for the performance of sailing boats and yachts. This is mainly due to the requirements to keep sail shape under control. Too much flexibility in the forestay, shrouds, halyards, or sheets leads to inefficient profile shape or wrong angle of attack in hard wind. For example, halyard thicknesses are often dictated by the stiffness requirement, and the ropes are thus over-dimensioned regarding their strength. As the rigging is attached to the hull and deck, their stiffness also plays a major role in keeping sail shape as desired.

The requirement of structural stability of some elements also requires additional stiffness to keep their shape within certain limits when loaded. For example, the angle between shrouds and mast decreases if the standing rigging is too loose and flexible. The smaller angle increases the compressive force in the mast, making it more prone to buckling, see figure below.

In some areas, additional stiffness is also needed for the “feel” of the boat. For example, if the deck is too flexible when walking on it, or if hull panels often vibrate in waves, the boat may be regarded as unreliable.

Decreasing angle between a shroud and mast when loaded
Figure 1. Decreasing angle between a shroud and mast when loaded

Elements of structural dimensioning (scantlings determination)

In the following, we will focus on the principles of scantlings determination of hull, deck, and rig.

The structural calculations can be divided into three different areas:

  • load determination (pressures, forces);
  • material properties (modulus of elasticity, allowable stress);
  • structural modeling (response calculation).

Loads

Loads affecting a sailboat hull are mainly due to the effects of water, waves, rigging, rudder, and keel (or other fins). While the water and wave loads affecting the hull panels are relatively local (they act in specific areas), the rig and ballast keel loads typically tend to bend the whole hull structure and are thus called global loads (see Figure 2).

Figure 2. Typical loadings of a sailboat hull (based on Larsson, Eliasson)

Material properties

The most common material properties needed for scantlings determination are:

  • Tensile strength and tensile stiffness.
  • Compressive strength and compressive stiffness.
  • Bending strength and bending stiffness.
  • In-plane and interlaminar shear strength (for composite materials).
  • Core shear strenght and compressive strength (for sandwich structures).

Material properties are usually well determined in the case of metals, as the alloys are carefully standardized and documented. Their toughness (i.e., the ability of a material to absorb energy and plastically deform without fracturing) gives extra safety against catastrophic failures, and welding and fatigue loading effects are well understood.

Composites are more complicated, as the material is anisotropic, i.e., its properties change in different directions. In fact, the mechanical properties have significant variations due to fiber orientation and its proportional amount. Additionally, the boatyards’ manufacturing environment (temperature, humidity, dustiness, etc.) affects the final material values.

Structural modeling

The structural analysis method can be a simple formula or a detailed finite element model.

The standard ISO 12215 provides good guidelines and equations for the scantlings chain. The standard includes the main equations for panel thicknesses and stiffener section moduli within its part “Part 5: Design pressures for monohulls, design stresses, scantlings determination.

ISO 12215 also contains equations and curves for limited areas and individual parts, like panels, stiffeners, rudder posts, or rigs. However, a finite element analysis (FEA) is needed to achieve reliable results for a complicated geometry. It shall be noted that the loadings and allowable stresses in simplified models are often interconnected and do not necessarily represent real values if taken separately as inputs for an FEA.

FRP as primary structural material

Fiber reinforced plastics are composite materials made of a plastic component or matrix that is reinforced by fibers in one or more directions. The reinforcing fibers are typically glass, aramid, or carbon fibers. The matrix usually is made of thermoset plastics, typically based on polyester, vinyl, or epoxy resins. Reinforced thermoplastics or bio-based resins are still very rare in boatbuilding production.

The stiffness of FRP is mainly determined by the fibers’ direction, proportion, and characters; this is also the case for most of the strength, especially in tension. The matrix affects mainly the bending strength, the interlaminar shear strength (ILSS), the compression strength (fiber buckling), and the impact strength. The manufacturing method affects the strength and the stiffness through fiber content, porosity, and quality uniformness. The compatibility of the fibers and the matrix also plays an important role.

Typical reinforcement types are:

  • Unidirectional reinforcements (UD): the fibers are positioned pointing almost entirely into a single direction (0˚).
  • Chopped strand mat (CSM): 30-50 mm long fibers pointing in all directions.
  • Continuous fiber rovingswoven roving (WR), biaxial roving (BR, two UD stitched perpendiculary at 0˚ and 90˚), or multiaxial roving (multiple directions).
  • For spray laminates: roving strands chopped to 20-30 mm length (see CSM above).

The laminates are composed of several reinforcement layers impregnated with resin (plastic matrix). The matrix transfers the loads from one fiber to another but usually is much more flexible than the fibers. The stiffness is calculated using the rule of mixture:

E = Φ × Ef + (1 – Φ) × Em

Where:

  • Φ = volume fraction of the fibres;
  • Ef = Young’s modulus of the fibres (in their direction);
  • Em = Young’s modulus of the matrix.

Because Em is much lower than Ef, we can often simplify the equation:

E = Φ × Ef

The strength of laminates is more complicated to calculate, and testing is still the most reliable way to determine it. Typical breaking tensile strength values are 80-100 Mpa for CSM (glass) but much more for WR and UD laminates in the direction of fibers. The standard ISO 12215-5 includes a comprehensive table of the ultimate strength of FRP laminates as a function of fiber content.

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