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Pilot's Handbook of Aeronautical Knowledge
Principles of Flight
Theories in the Production of Lift

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Pilot's Handbook of Aeronautical Knowledge



Table of Contents

Chapter 1, Introduction To Flying
Chapter 2, Aircraft Structure
Chapter 3, Principles of Flight
Chapter 4, Aerodynamics of Flight
Chapter 5, Flight Controls
Chapter 6, Aircraft Systems
Chapter 7, Flight Instruments
Chapter 8, Flight Manuals and Other Documents
Chapter 9, Weight and Balance
Chapter 10, Aircraft Performance
Chapter 11, Weather Theory
Chapter 12, Aviation Weather Services
Chapter 13, Airport Operation
Chapter 14, Airspace
Chapter 15, Navigation
Chapter 16, Aeromedical Factors
Chapter 17, Aeronautical Decision Making




Magnus Effect
In 1852, the German physicist and chemist, Heinrich Gustav
Magnus (1802–1870), made experimental studies of the
aerodynamic forces on spinning spheres and cylinders.
(The effect had already been mentioned by Newton in
1672, apparently in regard to spheres or tennis balls). These
experiments led to the discovery of the Magnus Effect, which
helps explain the theory of lift.

Flow of Air Against a Nonrotating Cylinder
If air flows against a cylinder that is not rotating, the flow of
air above and below the cylinder is identical and the forces
are the same. [Figure 3-3A]

A Rotating Cylinder in a Motionless Fluid
In Figure 3-3B, the cylinder is rotated clockwise and observed
from the side while immersed in a fluid The rotation of the
cylinder affects the fluid surrounding the cylinder. The flow
around the rotating cylinder differs from the flow around a
stationary cylinder due to resistance caused by two factors:
viscosity and friction.

Viscosity is the property of a fluid or semifluid that causes it
to resist flowing. This resistance to flow is measurable due
to the molecular tendency of fluids to adhere to each other to
some extent. High-viscosity fluids resist flow; low-viscosity
fluids flow easily.

Similar amounts of oil and water poured down two identical
ramps demonstrate the difference in viscosity. The water seems
to .ow freely while the oil flows much more slowly. (An
excellent website to demonstrate types of viscosity is found at
the Cornell University website on viscosity, located at http://

Since molecular resistance to motion underlies viscosity,
grease is very viscous because its molecules resist flow.
Hot lava is another example of a viscous fluid All fluids are
viscous and have a resistance to flow whether this resistance
is observed or not. Air is an example of a fluid whose
viscosity can not be observed.

Since air has viscosity properties, it will resist flow to some
extent. In the case of the rotating cylinder within an immersed
fluid (oil, water, or air), the fluid (no matter what it is) resists
flowing over the cylinder's surface.


Friction is the second factor at work when a fluid flows
around a rotating cylinder. Friction is the resistance one
surface or object encounters when moving over another and
exists between a fluid and the surface over which it flows

If identical fluids are poured down the ramp, they flow in the
same manner and at the same speed. If one ramp's surface
is coated with small pebbles, the flow down the two ramps
differs significantly. The rough surface ramp impedes the
flow of the fluid due to resistance from the surface (friction).
It is important to remember that all surfaces, no matter
how smooth they appear, are not smooth and impede the
flow of a fluid Both the surface of a wing and the rotating
cylinder have a certain roughness, albeit at a microscopic
level, causing resistance for a fluid to flow. This reduction
in velocity of the airflow about a surface is caused by skin
friction or drag.

When passing over a surface, molecules actually adhere
(stick, cling) to the surface, illustrated by the rotating cylinder
in a fluid that is not moving. Thus,
1. In the case of the rotating cylinder, air particles near
the surface that resist motion have a relative velocity
near zero. The roughness of the surface impedes their
2. Due to the viscosity of the fluid, the molecules on the
surface entrain, or pull, the surrounding flow above it
in the direction of rotation due to the adhesion of the
fluid to itself.

There is also a difference in flow around the rotating cylinder
and in .ow around a nonrotating cylinder. The molecules at
the surface of the rotating cylinder are not in motion relative
to the cylinder; they are moving clockwise with the cylinder.
Due to viscosity, these molecules entrain others above
them resulting in an increase in fluid flow in the clockwise
direction. Substituting air for other fluids results in a higher
velocity of air movement above the cylinder simply because
more molecules are moving in a clockwise direction.

A Rotating Cylinder in a Moving Fluid
When the cylinder rotates in a fluid that is also moving,
the result is a higher circulatory flow in the direction of the
rotating cylinder. [Figure 3-3C] By adding fluid motion, the
magnitude of the flow increases.

The highest differences of velocity are 90° from the relative
motion between the cylinder and the airflow Additionally,
and as shown in Figure 3-4, at point "A," a stagnation point
exists where the air stream impacts (impinges) on the front
of the airfoil's surface and splits; some air goes over and
some under. Another stagnation point exists at "B," where
the two airstreams rejoin and resume at identical velocities.
When viewed from the side, an upwash is created ahead of
the airfoil and downwash at the rear.

In the case of Figure 3-4, the highest velocity is at the top of
the airfoil with the lowest velocity at the bottom. Because
these velocities are associated with an object (in this case,
an airfoil) they are called local velocities as they do not exist
outside the lift-producing system, in this case an airfoil. This
concept can be readily applied to a wing or other lifting
surface. Because there is a difference of velocity above and
below the wing, the result is a a higher pressure at the bottom
of the wing and a lower pressure on the top of the wing.