**Kitefoil introduction**

Foil is a technology that allows a hull (propelled by a motor or in this case a sail) to **emerge totally from the water**, thanks to the hydrodynamic action of the submerged surface.

In fact, the pressure of the water under the **wings**, combined with the depression that forms above them, generates a force of lift opposed to the weight, and allows a great **reduction of resistance** to motion and consequently an increase in efficiency.

The curve in figure shows qualitatively the **rapid reduction of the resistance**, once, reached a certain speed, the **hull comes out of the water**.

Kitefoil is composed of the following elements:

**Fuselage**: It extends in length in the direction of motion and transmits the sustaining force to the hull through the mast, to which it is connected;

**Mast or Keel**: It transmits the sustaining force to the hull, connecting it to the fuselage and to the immersed surfaces that create the lift;**Supporting and stabilizing wings:**These are the surfaces that create lift. The first is able to give all the lift required to separate the hull from the surface of the water, while the second balances the moment provided by the first, with a consequent stabilization effects.

**History of the hydrofoil**

Hydrofoils have been used in different types of boats for over 100 years.

The first person that designed and built an hydrofoil was an Italian named Enrico **Forlanini**, in **1906**. For his hydrofoil Forlanini used a system of 4 groups of parallel wings (a pair in the bow and a pair in the stert) of decreasing width, unlike the single hydrofoil wings in use today.

Forlanini’s design was resumed and improved by various other inventors over the following decades (in particular Alexander Graham Bell and Casey Baldwin), until around the** 50’s** the world **began to invest massively** **in boats using hydrofoil fins**, for both military and commercial use. The boom was reached in the **60 ‘s- 70’s **but **since then their use in motor boats has gradually decreased**, due to various problems; not only due to **construction and maintenance costs**, but also **safety and environmental issues**. Materials for hydrofoils were in fact metallic, the same used for the structure of the boat.

The same problems occurred for hydrofoils used in the sailing or hobby disciplines, that began in the 60s, but was soon abandoned.

Since the turn of the century **investments in this technology have resumed**. Mainly because **new composite materials** made it possible to produce extremely **light and resistant** appendages, different hydrofoil researches began again, in order to identify the best shape and structure for every hull and wind.

**A wide interest **in hydrofoil sailing technology spread trough the **media **thanks to its use in the 2010 **America’s Cup**. Some sectors in which the foil has developed, however, are only now becoming popular. Unfortunately research has already reached a moment of stationarity, because the significant risks involved in the sector do not attract investors’ interest.

**Hydrofoil in kitesurfing**

The application of hydrofoil to kitesurfing dates back to the 2000s. The design of modern hydrofoil for kitesurfing varies in geometry based on its type of use. The main categories are:

- beginner;
- freestyle;
- racing boards.

**Kitefoils for beginners** are designed to be **stable at low speeds**.

Those for **freestyle** instead are more suitable for performing acrobatics and jumps and therefore **have greater maneuverability**, in addition to being structurally **more resistant**, in order to be able to **withstand impacts on landing jumps**.

**Racing kitefoils** are designed to reach the **highest**** possible ****speeds with the greatest stability** for all the different wind conditions. To do this, the latter have a minimal design and are made of carbon fiber, to be as light and resistant as possible.

Hydrofoil for kitesurfing (also called kitefoil) is a combination of various components, each with a very precise function . Although it is easy to design a single fin suitable to a certain sea condition, it is far more complicated to create a kitefoil that is best suited to a wide range of wind conditions, and therefore to a larger speed range.

To best explain the operation of the components of a hydrofoil fin, it is important initially to understand the most important **moments** to which the board is subjected: **roll**, **pitch** and** yaw**.

Pitch Yaw and Roll in a Hydrofoil

To understand how kitesurf works we can consider just the first 2, roll and pitch. Yaw can be ignored because load conditions are approximately simmetric and the mast twist can therefore be denied.

Kitefoils must produce enough lift to rise out of the water, giving support to the kitesurfer, and at the same time produce a moment of such magnitude as to allow balancing. The lift created must be sufficient in a wide range of speeds from the starting speed (“take off” speed) to the maximum speed (“top” speed).

The **take-off speed** is the speed at which lift begins to be such as to allow the kitesurfer and the board to separate from the water. As resistance decreases, due to the fact that the board is now no longer in contact with water, but in the air (which density is about 1000 times lower than that of water), there is an increase in speed; this increase in speed corresponds to an increase in lift for the main foil, and a change in lift capacity of the stabilizer, which may vary depending on the type used, as will be discussed below.

There are two different functioning systems of the **stabilizer**, which can have a positive bearing capacity and a negative bearing capacity.

**In the case of the positive flow stabilizer**, in order to balance the moment of force Fp (Force weight of the kiter minus the force exerted by the kite) must have a arm smaller than the second case and therefore the kiter must have a greater ability to stay in equilibrium. The balance of the moment becomes evident in the behavior of each kitesurfer who uses kitefoils, which centers the back foot on the mast and uses the front foot to apply a force that balances the moment. In simplified terms, the board represents a lever on which the rider applies a force, while he **balances the strength of the stabilizer with his front foot, **counteracting the moment generated by load-bearing and resistant forces.

The stabilizer moment and the rider’s need to counterbalance it, leads to a more stable equilibrium, and the rider’s **ability lies in maintaining the balance** in situations of **variable winds** and during **maneuvers such as** **tacks or jibes**.

Contrary to its name **n****egative flow stabilizer **improves stability because the proportion of the fin / lift ratio is reduced and therefore its **efficiency decreases**. The task of the kitefoil designer is to create a geometry that** allows at the same time both:**

- A
**sufficient bearing capacity in a wide range of windy conditions;** - Produce a stabilizing moment sufficient to allow the achievement of equilibrium.

So, ultimately it is required to **maximize Lift / Resistance ratio without unduly compromising stability**. The design of a kitefoil is subject to a number of constraints that must be considered in the optimization phase. If one wants to design a kitefoil for racing, he should consider the rules imposed by the IKA (International Kitefoil Association) which specifies that the maximum length of a kitefoil, (measured perpendicularly to the board) **cannot exceed 5000 mm** (in the **current state of the art** foils are about **1.2m long**, that is far from 5 m). Furthermore, the **appendices can be up to one, and their purpose must be mainly to create lift**. **No limitations** are imposed regarding the **materials**. Other limitations that must be considered in the design of a kitefoil are imposed on the structural design, since the kitefoil must have an optimized geometry that has to be easy to build and at the same time must be able to withstand the stresses to which it is subjected.

**Theoretical bases**

To understand the functioning of the hydrofoil, we have to analyze the physics of a easy wing profile. The wing of the hydrofoil creates a lift force, perpendicular to the flow direction, and a drag force, oriented with flow direction. The angle of attack α is the angle between the flow direction and the contour string.

The lift produced by a profile is directly proportional to the area of the wing surface “A_L” and proportional to the square of the relative velocity of the flow “v”; it also depends on the density of the fluid “ρ” and the on the lift coefficient “C_L”:

F_L=lift=\frac{1}{2}\rho A_mC_Lv^2

Resistence is a function of:

- wing surface “A_R”;
- relative speed of the water “v”;
- drag Coefficient “C_D”;
- water density “ρ”:

F_D=drag=\frac{1}{2}\rho A_mC_Dv^2

The lift and drag dimensionless coefficients C_L and C_D respectively, could be analytically, numerically or experimentally calculated, and are function of the profile shape.

C_L=\frac{L}{\frac{1}{2}\rhoA_mv^2}

C_D=\frac{D}{\frac{1}{2}\rhoA_mv^2}

\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}