A foil is a surface designed to maximize lift (force generated perpendicular to the fluid flow) while minimizing drag (force generated in the direction of the fluid flow) in a given range of conditions. Foils may be designed to operate in any fluid, such as air or water. Lift consists of the sum of all the fluid dynamic forces on a body perpendicular to the direction of the external flow approaching that body. ... It has been suggested that Drag equation be merged into this article or section. ... A subset of the phases of matter, fluids include liquids, gases, plasmas and, to some extent, plastic solids. ...

Physics of foils

Foil design is strongly influenced by Bernoulli's principle, which states that high speed fluid flow results in lower pressure on surfaces parallel to the flow, and the related Coanda Effect, which states that a fluid stream will follow a surface that curves away. The traditional curved upper surface and nearly flat lower surface of a wing are designed to accelerate airflow over the curved top surface, and deflect it downwards at the rear. This downwards deflection of air is balanced (according to Newton's Third Law) by a matching upwards force on the foil, which is the lift. It is a common misconception that the pressure differential (caused by the Bernoulli principle) is the direct cause of lift, but the Bernoulli principle is only the means for generating the deflection. Examination of foils in operation shows a significant deflection of the fluid flow downstream of the foil. Bernoullis principle states that in fluid flow, an increase in velocity occurs simultaneously with decrease in pressure. ... The Coanda effect is the tendency of a stream of fluid to stay attached to a convex surface, rather than follow a straight line in its original direction. ... Newtons laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ...

The three mechanisms at work all work closely together to generate the greatest amount of lift. The faster the fluid flows over the foil's surface, the more suction is generated, resulting in a stronger Coanda Effect, which results in a greater deflection and more lift. When the forces are right to keep the fluid flow attached to the surface of the foil, it is called laminar flow. If there is insufficient suction to keep the fluid flow attached to the foil's surface, then the flow will separate and become turbulent. This turbulent flow often results in less deflection, loss of lift, and increased drag. Laminar flow (bottom) and turbulent flow (top) over a submarine hull. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ...

Basic design considerations

The degenerate case of a foil is a simple flat plate. When set at an angle (the angle of attack) to the flow of the fluid it works in, the plate will deflect the passing over and under it, and this deflection will result in a reacting force that pushes, or lifts the plate. In a perfect fluid, that has inertia but no viscosity, a flat plate would be a perfect airfoil, because it generates lift with no drag. However, once viscosity is added to the equation, drag appears, and the flat plate is no longer an ideal solution--while it does generate lift, it also generates a large amount of drag. In this diagram, the black arrow represents the direction of the wind. ... The principle of inertia is one of the fundamental laws of classical physics which are used to describe the motion of matter and how it is affected by applied forces. ... The pitch drop experiment at the University of Queensland. ...

Since even a simple flat plate can generate lift, the primary purpose of a foil designed for a given purpose is not the generation of lift, but rather the minimizing of drag under certain conditions. A good example of this is the rudder of a boat or aircraft. Under normal, non-steering conditions, the rudder is not producing any lift--if it were, the craft would turn in response to the lifting force. A primary goal when designing a rudder, therefore, is the minimization the amount of drag it produces when in its neutral state, which is balanced with the need to produce sufficient lift with increasing angle of attack to turn the craft at a reasonable rate at the speeds at which it will be operating. A good example of foils of this type are symmetric NACA 00xx foils, which have very low drag at zero angles of attack, and will generate lift equally well with positive or negative angles of attack. The worlds oldest depiction of a rudder. ... NACA official seal The National Advisory Committee for Aeronautics (NACA) was a U.S. federal agency founded on March 3, 1915 to undertake, promote, and institutionalize aeronautical research. ...

Plot of a NACA 0012 foil, generated from formula

The formula for a NACA 00xx foil, with "xx" being replaced by the percentage of thickness to chord, is: Image File history File links NACA_0012. ... Image File history File links NACA_0012. ...

where:

• x is the position along the chord from 0 to 1
• y is the thickness at a given value of x
• t is the maximum thickness as a fraction of the chord

The leading edge approximates a cylinder with a radius of:

Since wings generally are used primarily to generate lift in one direction, they are most often asymmetric, generating a better lift to drag ratio with positive angles of attack than with negative angles of attack (although they will work upside down, as stunt pilots often demonstrate when flying upside down). Asymmetric foils will generate some lift at a zero angle of attack. The word wing or wings has more than one use: In aeronautics a wing is an apparatus used to create lift. ...

Plot of a NACA 2312 foil, generated from formula

The simplest asymmetric foils are the NACA 4 digit series foils, which use the same formula as that used to generate the 00xx symmetric foils, but with the line of mean camber bent. The formula used to calculate the mean camber line is: Image File history File links NACA_2312. ... Image File history File links NACA_2312. ...

from x = 0 to x = p

from x = p to x = c

where:

• m is the maximum chamber in percentage of the chord
• p is the location of maximum camber in tenths of the chord

Reynold's numbers

Reynolds numbers are used to predict changes in scale or viscosity on a given foil shape. The Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L) and is used for determining whether a flow will be laminar or turbulent. ... The pitch drop experiment at the University of Queensland. ...

where:

• V is the velocity
• L is the chord of the foil
• v is the viscosity of the fluid

The viscosity is approximately 30000 m²/s for water and approximately 3000 m²/s for air.

SI units easy memorizable number example for airfoil at the transition between laminar and turbulent (Re = 10⁶) (could be a sailplane): laminar and turbulent water flow over the hull of a submarine In fluid dynamics, laminar flow is a flow regime characterized by high momentum diffusion, low momentum convection, and pressure and velocity independence from time. ... Turbulent flow around an obstacle; the flow further away is laminar Laminar and turbulent water flow over the hull of a submarine Turbulence creating a vortex on an airplane wing In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by low-momentum diffusion, high momentum convection, and...

Re = ((1 kg/m³)(17 m/s)(1 m))/(17×10^-6 N·s/m²) = 10⁶

Sometimes the transition is shifted to higher Re by means of a clean and smooth surface and sometimes it is shifted to lower Re by means of Vortex generators. The latter is unique to wings. 1967 Model Cessna 182K in flight showing after-market vortex generators on the wing leading edge A vortex generator is an aerodynamic surface, basically a small vane, that creates a vortex. ...

External links

• An overview by Paul Zander of information on foils for boating, compiled from rec.boats.building sources.
• Formulas for calculating NACA 4 and 5 digit foils.
• Formulas and explanations of NACA 4 and 5 digit foils.