Basically, *hydro*foils are like *air*foils, just used in water.
They can be used on propeller blades, as lifting surfaces or in keels and
rudders. In most of these applications a high lift to drag ratio is required,
which usually drives the design to higher lift coefficients.

Water can change from a liquid to a gaseous state - under certain conditions
it starts to boil. While it is demonstrated in millions of kitchens each day
that water starts to boil when it is heated to about 100 degrees Celsius, this
process also depends on the pressure. When some water is enclosed in a container
and the container is evacuated, the water will boil even at room temperature.
The state change occurs, whenever the environmental pressure is dropping below
the so called *"vapor pressure"*. Heating does not change the environmental
pressure, but reduces the vapor pressure of water until it drops below the
environmental pressure. When water flows around an airfoil shape, the local
pressure drops below the undisturbed pressure (pressure coefficient C_{P}
< 0). If this pressure drop is large enough, the vapor pressure can be reached
on the surface of the airfoil and a small vapor bubble starts to develop, which
can grow into a large "cave" of vapor. This process is called "cavitation".
Similar to a separation bubble in air, cavitation largely increases drag and
often also reduces lift. A loss of lift can even lead to disaster, e.g. provoke
a *spinout* of a surfboard, a situation in which the lift (side force) of
the fin is lost. Additionally, the collapse of larger vapor bubbles may lead to
vibrations and even structural damage (remember that the density of water is
1000 times as large as the density of air). Damage due to cavitation often is a
problem for marine propellers, turbines and pumps.

Therefore it is very advisable to use airfoils only in a certain angle of attack range to avoid cavitation.

__Remark:__ a second effect may occur on hydrofoils, which are operated
close to the free surface: "ventilation" occurs, when the suction region on the
foil is strong enough to suck air from the free surface down to the foil's
surface. The result is similar to cavitation: a rapid loss of lift. Ventilation
can be avoided by means like fences or by unloading the root region of a fin
which operates close to the surface.

The critical pressure coefficient C_{P, crit} depends mainly on the
vapor pressure of the water, the flow velocity and the immersion depth of the
foil:

If the pressure coefficient in any region of the airfoil becomes
lower than C_{P, crit}, cavitation will occur. The graph below shows
critical C_{P} values for three speeds and three depths.

*Limiting C _{P, crit} values over flow velocity for
different water depths. The curves show clearly, that the additional pressure
due to depth allows for lower C_{P, crit} values and thus higher loads
at the same speed. In all cases the critical pressure coefficients drop fairly
fast with increasing speed.*

The analysis of the pressure distribution of an airfoil at various angles of
attack yields the lift coefficient and the minimum pressure coefficient on the
surface of the airfoil for each angle of attack. This minimum pressure often
occurs close to the leading edge. A plot of this minimum pressure coefficient Cp^{*}
versus lift coefficient is shown below. The graph also contains horizontal lines
corresponding to forward speeds of 15 and 20 knots for a depth of 0. The
corresponding C_{P} values are taken from the graph above.

*C _{p}* envelopes for two airfoils and comparison
with the C_{P, crit} values for different speeds. *

Intersecting these airfoil specific curves with the critical pressure coefficient according to a certain flow velocity and water depth yields the useable range of lift coefficients. If the lift coefficient or angle of attack drives Cp* to lower values (more negative or upwards in the graph) than the critical pressure coefficient, the local vapor pressure will be reached and the water will begin to boil - cavitation occurs.

The 5% thin NACA 4405 shows suction peaks much earlier than the thicker NACA
4410, which results in a wider range of lift coefficients for the thicker
airfoil. It can also be seen that the usable range of lift coefficients shrinks
with increasing forward speed. There is a speed limit above which no cavitation
free flow is possible. The only way to move that fast is to accept cavitation
and switch to *"super-cavitating"* sections. These have different shapes,
similar to airfoils for supersonic flow (e.g. wedges). Any flow with cavitation
requires different numerical models, capable of handling *"multi-phase"*
flows (water + steam); you can use JavaFoil only up to the onset of cavitation.

Cavitation free airfoils for a wide range of lift coefficients must avoid suction peaks and will usually have large regions of almost constant velocity - similar to high speed airfoils designed to keep the local Mach number just below the sonic limit M = 1.

[Considerations for Hydroprops]

*Last modification of this page:
16.02.08*

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