# Hydrofoils

In this work a mechanical lift control system for the daggerboard of a hydrofoil sailboat was investigated. Parameters of the mechanical components of the system were determined on a simplified model so that the system is stable and so that the lift of the hydrofoil remains constant over a given speed range of the boat.

The simplified model can be seen in the following picture:

It was obtained that the system is feasibly on this simplified model. A simplified motion equation of the system is displayed for exemplary parameters in the following diagram:

The grey lines show the angular acceleration of the system depending on the freestream velocity.

The red line shows the moment of the mechanical components which depends on the angle divided by the mass moment of inertia of wing and frame. This line is independent of the freestream velocity.

The blue lines show the sum of all moments the water exerts on the wing around the point P divided by the mass moment of inertia of wing and frame.

The sum of the red and blue lines give the resultant angular acceleration (grey lines) of the system.

The angle dependent mechanical moment (red line) is chosen so that the lift at the equilibrium positions (EP) of the system is constant and that these equilibrium positions are stable. Note that another unstable equilibrium position which is independent of the freestream velocity exists at a higher angle in the diagram above.

In the work it was shown that the motion equation of the system yields diagrams qualitatively similar to the one above for most practically relevant cases.

Realization possibilities for the moment of the mechanical components were presented in this wok. It seems that a linear spring, a non-linear spring, and a damper may suffice. Two potential ways of realizing the required moment are shown below:

The influence of the parameter A on the stability of the system is remarkable. When the constant-lift equilibrium position of a system with otherwise fixed parameters is unstable it can always be made stable by simply increasing A. Disadvantages which may arise when increasing A are a higher required pre-loading of the springs, and a lower required stiffness of the springs. Also, the influence of theoretically difficult to predict unsteady effects of the flow may increase. The parameter A may be of particular interest for the real lift control system because this parameter may be easy to manipulate independent from other parameters of the hydrofoil or the entire boat.

Additional considerations indicate that possibilities may exist to integrate the lift control system into a conventional two surface layout and achieve constant lift over a given speed range and longitudinal stability. It further seems that if the system is designed so that it seeks to keep constant a certain lift at a certain depth below the free surface this lift starts to decrease when the distance to the free surface is slowly decreased. This means that the investigated system may not only be used to keep the lift constant, but also to achieve heave stability.

Exemplary considerations made in this work also indicate that the main findings above may even be transferable to a more detailed model of the system with a curved daggerboard rather than just a simple straight wing. Future work will be needed to investigate this matter.

Finally, it shall be emphasized how sophisticated the real case is. The unsteady motion of the water around a curved wing in close proximity to the water surface is very difficult to model. Ultimately, reliable results may only be obtained with experiments or time-consuming simulations. It is argued though, that the study of a simplified system and the knowledge of the simplifications and their implications leads to a basic preliminary understanding of the system and the ability pass a first judgement on its feasibility.

In this work it could be concluded that the lift control system seems feasible. If the system may also provide heave stability will have to be studied more thoroughly in future work. Results obtained in this work indicate that this might be possible.

For more information on the used simplifications and assumptions in this work and for more details on the obtained results just write a quick message.