Front sail link plate FEM analysis
Study of the possible causes for structural failure
The interest for creating this project comes from the curiosity of finding out the reason why the forestay plates failed structurally, and understanding the stresses acting on it.
1. General description
The element to be studied in this report is the part that connects the deck to the forestay, which is a pair of stainless link plates. To provide some background, the forestay function is to keep the mast in a vertical position, and at the same time, to serve as a guide and attach point for the front sail, in this case a genoa.
2.1 Load cases
In order to calculate the stresses on the link plates, the loads acting on it must be determined first. This load will be mainly produced by the aerodynamic pressure on the sail, which will be then transferred via de forestay to the link plates. To calculate this load, several factos need to be considered, including the following:
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Axial force acting on the link plates, in Newtons.
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Torsional force acting in the link plates. (to be estimated), in Newtons*meter
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Wind speed, in meters per second.
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Front sail total area, in square meters.
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Forestay length, in meters.
2.1.1 Lift force
In order to determine the loads acting on the sail, it is first required to obtain the lift. Lift is dependent on the density of the air, the square of the velocity, the air's viscosity and compressibility, the surface area over which the air flows, the shape of the body, and the body's inclination to the flow.
Figure 2.1.1-1 Pressure distribution around a wing section (Ref. 1)
The lift force is calculated according to the following equation:
Where:
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cl = lift coefficient
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A = sail area, which is 23 m2
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ρ = air density, which is 1.225 kg/m3
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V = apparent wind speed, which is assumed to be 20 knots (10.3 m/s)
Note that the part of the equation that involves 0.5 * ρ * V^2 is called dynamic pressure and refers to Bernoulli equations.
The amount of lift that is generated by an airfoil dependes on how much the flow is turned. The turning of the flow will vary with the shape of the airfoil, and in this case, we have a variable shape airfoil, since the sail shape and curvature can by modified to match the wind conditions and the attack angle. However, it is not always possible to obtain the optimal shape or curvature due to physical limitations, such as the existence of a mast in front of the sail, or in the case of the front sail, the presence of the sail rail, that also induces an effect as can be seen in the figure below:
Figure 2.1.1-2 Flow around a mast/sail combination (Ref. 1)
The presence of this elements such as the mast in front of the sail generate separations. Theses must be avoided for two main reasons. First, in order not to reduce the pressure differences between the two sides of the sail, which would cause a reduction in lift and driving force. Secondly, because separation itself causes a drag increase.
The lift coefficient depends greatly on the angle of attack on the leading edge. When sailing, the angle of attack of the sails regarding the wind flow can be adjusted and therefore different lift coefficients are obtained. For this study, an average lift coefficient is used that takes into account different sail configurations. In the figure below a typical pressure distribution for a certain angle of attack is presented.
Figure 2.1.1- 3 Flow around a sail
In order to define the lift coefficient, the Reynolds number needs to be calculated.
Where:
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v: flow speed (10.3 m/s)
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L: characteristic length (chord length) (3.5m)
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V: kinematic viscosity (1.511*10^-5 [m2/s] for 20 deg. Celsius and 1 atm)
Introducing the numbers, the Re number results in : Re=2385837.19
To obtain the lift and drag coefficients according to the calculated Reynolds number, the website Airfoiltools is used, that provides plots for different airfoil shapes and Re numbers. The profile that is simulated due to its similitude to an actual sail is the EPPLER 376 AIRFOIL (e376-il). Find the profile properties and drawing below:
Figure 2.1.1-4 EPPLER 376 AIRFOIL (e376-il) (Airfoiltools)
Max thickness 2.5% at 4.3% chord.
Max camber 9% at 32.7% chord
Find below the plots for Reynolds numbers of 500000 and 1000000:
Figure 2.1.1-5 Lift and drag coefficients (Airfoiltools)
From the figure above it has been concluded that the maximum lift coefficient achievable with the current profile is 1.65. However, conservatively a lift coefficient of 1.5 is selected. Therefore, the Lift generated is by the total area of the sail is:
L = 2241.8 N >> 2.242 kN
2.2 Load cases
To obtain the tension acting on the forestay, some assumptions are made aiming to simplify the calculations. First, the lift on the 2D sail section on the centroid will be considered as a punctual load as shown below:
Figure 2.2-1 Forces on sail - Section a-a
Figure 2.2-2 Forces on forestay
FEM analysis >> Work in progress
