Since friction acts parallel to the surface, there are only two small areas in which friction acts in the vertical direction. Not enough to matter, so it's ignored. So the only possible source for the forces to produce lift are the pressure differences around the airfoil. What we need to achieve looks something like this:
Now, one way of demonstrating the concept is by placing a disk that fits tightly in a cylinder and then evacuating the air above the disk, like so:
This creates a pressure difference between the top and bottom that produces a net force that lifts the weight. However, for generating lift on a wing, we could not evacuate the air fast enough to keep the surrounding air from rushing in, at least with this method.
The Bernoulli Equation says that the sum of static pressure and dynamic pressure is always the same. If you increase the dynamic pressure, then static pressure must go down; if dynamic pressure goes down, then static pressure goes up. If we assume that the density of the air remains the same, the only way to change dynamic pressure is via changing the velocity. One way to think of the Bernoulli Equation is that it says that the total energy of an airstream is a constant, since energy can never be created or destroyed. The static pressure is potential energy per unit volume of air and the dynamic pressure is the kinetic energy per unit volume. You can convert one to the other, but the total energy is a constant. The Bernoulli Equation acts like a roller coaster, as in the picture below. Car A is at the top of a hill; it has converted its velocity into altitude and arrives at the peak with high potential energy, but low kinetic energy. Momentarily, it will convert the potential energy (altitude) back into kinetic energy as it moves to the position of car B.
Now, the classic way to use the static pressure to speed up the air is a Venturi, as shown below:
Can we use the Venturi Effect to make the air go faster over the top of the airfoil? Let's put an airfoil into the airstream and find out:
Putting an airfoil into the airflow does indeed cause the Venturi effect to kick in. The airfoil impedes the flow of air, acting as one side of the Venturi, and the atmosphere above the airfoil cannot "bump up" in order to accommodate the air trying to make a detour. It speeds up because it must. The problem is that the airflow speeded up on both sides of the airfoil, creating the exact same pressure drop. They cancel either other out and there is no pressure difference between the top and bottom of the airfoil that we need for lift.
As you can see, it behaves pretty much like the airfoil above; the air speeds up on both sides of the cylinder, so no net lift is generated. But look what happens we start rotating the cylinder clockwise:
The rotating cylinder drags the air above along with it, speeding it up, but below the cylinder, the rotation fights against the airflow, slowing it down. The net result is a positive amount of lift. Although the Magnus Effect isn't a practical means of generating lift on a wing, it does suggest that imparting some overall rotation to the airflow in addition to the freestream flow could produce lift. Our goal, then, is to somehow produce this situation:
As you can see, there is a normal stagnation point on the leading edge, but the rear stagnation point is on the top. In order for the rear stagnation point to be there, the airflow must be like this:
This can't happen, except at very low airspeeds. The airflow simply cannot follow the rapid change in direction that would be required to negotiate the sharp trailing edge, and the airflow separates from the surface into a tight vortex:
This vortex, called the starting vortex is carried away down stream, but it leaves behind another vortex that has the same quantity of rotation, but in the opposite direction. The follow graphic uses the analogy of cogs to show how the starting vortex creates its opposite around the airfoil:
So what we're left with is a permanent vortex, called the bound vortex that speeds up the air on the top of the wing, and slows it down in the bottom, like this:
The air never flows backwards along the bottom of the airfoil as the bound vortex seems to show. Instead, it adds to the freestream; since the freestream is faster, the net result is movement in the freestream direction, just slower.
How can we explain this result?
The advantage of this technique, so proponents say, is that you get the turn but avoid the increase in stall speed associated with a loaded turn. So there is a free lunch after all.
Well, not really. There are two problems with this technique:
So is there any value at all in the technique? Let's run some numbers, using this diagram and formula as the basis of our calculations:
The entry highlighted in yellow is the unloaded turn. I show two values for some entries in the unloaded turn row, because the airspeed increases steadily during the maneuver.
Here are some interesting observations regarding the calculations:
The unloaded turn doesn't get the expected performance because it only generates half of the centripetal force that a true banked 60° turn would. So in terms of safety and performance, you're better off maneuvering at the proper airspeed for the bank angle you've chosen.
With the advent of the large slotted flaps in the C-170, C-180, and C-172 we encountered a nose down pitch in forward slips with the wing flaps deflected. In some cases it was severe enough to lift the pilot against his seat belt if he was slow in checking the motion. For this reason a caution note was placed in most of the owner's manuals under "Landings" reading "Slips should be avoided with flap settings greater than 30° due to a downward pitch encountered under certain combinations of airspeed, side-slip angle, and center of gravity loadings". Since wing-low drift correction in cross-wind landings is normally performed with a minimum flap setting (for better rudder control) this limitation did not apply to that maneuver. The cause of the pitching motion is the transition of a strong wing downwash over the tail in straight flight to a lessened downwash angle over part of the horizontal tail caused by the influence of a relative "upwash increment" from the upturned aileron in slipping flight. Although not stated in the owner's manuals, we privately encouraged flight instructors to explore these effects at high altitude, and to pass on the information to their students.
This phenomenon was elusive and sometimes hard to duplicate, but it was thought that a pilot should be aware of its existence and know how to counter-act it if it occurs close to the ground.
When the larger dorsal fin was adopted in the 1972 C-172L, this side-slip pitch phenomenon was eliminated, but the cautionary placard was retained. In the higher-powered C-172P and C-R172 the placard was applicable to a mild pitch "pumping" motion resulting from flap outboard-end vortex impingement on the horizontal tail at some combinations of side-slip angle, power, and airspeed.