Foil (fluid mechanics)
A foil is a solid object with a shape such that when placed in a moving fluid at a suitable angle of attack the lift (force generated perpendicular to the fluid flow) is substantially larger than the drag (force generated parallel to the fluid flow). If the fluid is a gas, the foil is called an airfoil or aerofoil, and if the fluid is water the foil is called a hydrofoil.
Physics of foils
A foil generates lift primarily because of its shape and angle of attack. When oriented at a suitable angle, the foil deflects the oncoming fluid, resulting in a force on the foil in the direction opposite to the deflection. This force can be resolved into two components: lift and drag. This "turning" of the fluid in the vicinity of the foil creates curved streamlines which results in lower pressure on one side and higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flowfield about the foil has a higher average velocity on the upper surface than on the lower surface.
A more detailed description of the flowfield is given by the simplified Navier-Stokes equations, applicable when the fluid is incompressible. However, since the effects of the compressibility of air at low speeds is negligible, these simplified equations can be used for both airfoils and hydrofoils as long as the fluid flow is substantially less than the speed of sound (up to about Mach 0.3).
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 the plate will deflect the fluid passing over and under it, and this deflection will result in a lift force on the plate. However, while it does generate lift, it also generates a large amount of drag.
Since even a simple flat plate can generate lift, a significant factor in foil design is the minimization of drag. An example of this is the rudder of a boat or aircraft. When designing a rudder a key design factor is the minimization of drag in its neutral position, which is balanced with the need to produce sufficient lift with which to turn the craft at a reasonable rate. 
Other types of foils, both natural and man-made, seen both in air and water, have features that delay or control the onset of lift-induced drag, flow separation, and stall (see Bird flight, Fin, Airfoil, Placoid scale, Tubercle, Vortex generator, Canard (close-coupled), Blown flap, Leading edge slot, Leading edge slats), as well as Wingtip vortices (see Winglet).
Lifted weight is proportional to lift coefficient, density of fluid, wing area and true speed by square. A comparison of lifted weight as a function of altitude and depth reveals big differences by a factor of about 3’000 in total from 11 km above sea level to 10 km below sea level, divided into factors of: ~ 4 between summit and sea level, ~ 400 between flying close to the ground and planing on water, ~ 2 between planing on water and in a fully submerged state. The most dramatic changes are due to different fluids and levels of altitude. The most interesting sector to discuss lift is close to sea level: aircraft approaching the ground, plates planing on water and hydrofoils only barely submerged in water. There is one basic similarity across of these: Almost any shape, as long as it is not too thick, will work as an (air)foil and produce lift when the angle of attack is in the right range.
- "...the effect of the wing is to give the air stream a downward velocity component. The reaction force of the deflected air mass must then act on the wing to give it an equal and opposite upward component." In: Halliday, David; Resnick, Robert, Fundamentals of Physics 3rd Edition, John Wiley & Sons, p. 378
- "If the body is shaped, moved, or inclined in such a way as to produce a net deflection or turning of the flow, the local velocity is changed in magnitude, direction, or both. Changing the velocity creates a net force on the body" "Lift from Flow Turning". NASA Glenn Research Center. Retrieved 2011-06-29.
- "The cause of the aerodynamic lifting force is the downward acceleration of air by the airfoil..." Weltner, Klaus; Ingelman-Sundberg, Martin, Physics of Flight - reviewed, archived from the original on 2011-07-19
- "...if a streamline is curved, there must be a pressure gradient across the streamline..."Babinsky, Holger (November 2003), "How do wings work?" (PDF), Physics Education, 38 (6): 497–503, doi:10.1088/0031-9120/38/6/001
- "...the motion of objects in air and in water obeys identical laws until their speed approaches the speed of sound."(page 41) "... air too can be regarded as incompressible as long as flow speeds remain reasonably low. This assumption is roughly valid as long as airplanes fly slower than... about one-third of the speed of sound."(page 61) What Makes Airplanes Fly? Wegener, Peter P. Springer-Verlag 1991 ISBN 0-387-97513-6
- "...the low-speed flow of air, where V < 100 m/s (or V < 225 mi/hr) can also be assumed to be incompressible to a close approximation." in Anderson, John D. Jr. Introduction to Flight 4th ed McGraw-Hill 2000 ISBN 0-07-109282-X pg 114
- "A flat plate held at the proper angle of attack does generate lift, but also generates a lot of drag. Sir George Cayley and Otto Lilienthal during the 1800s showed that curved surfaces generate more lift and less drag than flat surfaces." http://quest.nasa.gov/aero/planetary/atmospheric/aerodynamiclift.html
- NASA. "What is lift?". Retrieved 7-5-2011. Check date values in:
- „Lifted_Weight_as_a_Function_of_Altitude_and_Depth_by_Rolf_Steinegger“ https://doi.org/10.21256/zhaw-4058