Aerodynamics concerns the motion of air and other gaseous fluids and other forces acting

on objects in motion through the air (gases). In effect, Aerodynamics is concerned with the
object (aircraft), the movement (Relative Wind), and the air (Atmosphere).

Newton's Laws Of Motion

Newton's three laws of motion are:

Inertia - A body at rest will remain at rest. and a body in motion will
remain in motion at the same speed and direction until affected by some
external force. Nothing starts or stops without an outside force to bring about or
prevent motion. Hence, the force with which a body offers resistance to change is
called the force of inertia.
Acceleration - The force required to produce a change in motion of a body
is directly proportional to its mass and the rate of change in its velocity.
Acceleration refers either to an increase or a decrease in velocity, although
Deceleration is commonly used to indicate a decrease.
Action / Reaction - For every action there is an equal and opposite
reaction. If an interaction occurs between two bodies, equal forces in opposite
directions will be imparted to each body.

Fluid Flow And Airspeed Measurement

(Bernoulli's Principle)

Daniel Bernoulli, a Swiss mathematician, stated a principle that describes the relationship
between internal fluid pressure and fluid velocity. His principle, essentially a statement of
the conversation of energy, explains at least in part why an airfoil develops an aerodynamic
force.

All of the forces acting on a surface over which there is a flow of air are the result of skin
friction or pressure. Friction forces are the result of viscosity and are confined to a very thin
layer of air near the surface. They usually are not dominant and, from the aviator's
perspective, can be discounted.
As an aid in visualizing what happens to pressure as air flows over an airfoil, it is helpful to
consider flow through a tube (Please see Figure above). The concept of conservation of
mass states that mass cannot be created or destroyed; so, what goes in one end of the tube
must come out the other end. If the flow through a tube is neither acccelerating or
decelerating at the input, then the mass of flow per unit of time at Station 1 must equal the
mass of flow per unit of time at Station 2, and so on, through Station 3. The mass of flow
per unit area (cross-sectional area of tube) is called the Mass Flow Rate.

At low flight speeds, air experiences relatively small changes in pressure and negligable
changes in density. This airflow is termed incompressable since the air may undergo
changes in pressure without apparent changes in density. Such airflow is similar to the flow
of water, hydraulic fluid, or any other incompressable fluid. This suggests that between any
two points in the tube, the velocity varies inversely with the area. Venturi effect is the
name used to describe this phenomenon. Fluid flow speeds up through the restricted area of
a venturi in direct proportion to the reduction in area. The Figure below suggests what
happens to the speed of the flow through the tube discussed.

The total energy in a given closed system does not change, but the form of the energy may
be altered. The pressure of the flowing air may be likened to energy in that the total
pressure of flowing air will always remain constant unless energy is added or taken from the
flow. In the previous examples there is no addition or subtraction of energy; therefore the
total pressure will remain constant.

Fluid flow pressure is made up of two componants - Static pressure and dynamic pressure.
The Static Pressure is that measured by an aneroid barometer placed in the flow but not
moving with the flow. The Dynamic Pressure of the flow is that componant of total
pressure due to motion of the air. It is difficult to measure directly, but a pitot-static tub
emeasures it indirectly. The sume of these two pressures is total pressure and is measured
by allowing the flow to impact against an open-end tube which is venter to an aneroid
barometer. This is the incompressible or slow-speed form of the Bernoulli equation.

Static pressure decreases as the velocity increases. This is what happens to air passing over
the curved top of an aircraft's airfoil. Consider only the bottom half of a venturi tube in the
Figure below. Notice how the shape of the restricted area at Station 2 resembles the top
surface of an airfoil. Even when the top half of the venturi tube is taken away, the air still
accelerates over the curved shape of the bottom half. This happens because the air layers
restrict the flow just as did the top half of the venturi tube. As a result, acceleration causes
decreased static pressure above the curved shape of the tube. A pressure differential force
is generated by the local variation of static and dynamic pressures on the curved surface.

A comparison can be made with water flowing thru a garden hose. Water moving through a
hose of constant diameter exerts a uniform pressure on the hose; but if the diameter of a
section of the hose in increased or decreased, it is certain to change the pressure of the
water at this point. Suppose we were to pinch the hose, therby constricting the area
through which the water flows. Assuming that the same volume of water flows through the
constricted portion of the hose in the same period of time as before the hose was pinched, it
follows that the speed of flow must increase at that point. If we constrict a portion of the
hose, we not only increase the speed of the flow, but we also decrease the pressure at that
point. We could achieve like results if we were to introduce streamlined solids (airfoils) at
the same point in the hose. This principle is the basis for measuring airspeed (fluid flow)
and for analyzing the airfoil's ability to produce lift.
Scalar And Vector Quantities

A study of aircraft flight is further enhanced by understanding two types of quantities:

Scalar Quantities
Vector Quantities

Scalar quantities are those that can be described by size alone. Examples would be that of
area, volume, time, and mass.

Vector quantities are those that must be described by magnitude and direction.
Common examples would be that of velocity, acceleration, weight, lift, and drag. It is
important to note that the direction of these vector quantities is equally important as the
size or magnitude.

All forces, from whatever source, are vectors.

When an object is being acted upon by two or more forces, the combined effect of these
forces may be represented by the use of vectors. Vectors in the graphics used throughout
these pages are represented by a directed line segment capped with an arrow.

The arrow itself indicates the direction in which the force is acting, and the line segment
length in relation to a given scale represents the magnitude of that force. The vector is
drawn in relation to a reference line. Magnitude is drawn to whatever scale is conveniant to
the issue being addressed.

Common terms used to describe the helicopter rotor system are shown here. Although there
is some variation in systems between different aircraft, the terms shown are generally
accepted by most manufacturers.

The system below is an example of a Fully Articulated rotor system:

Semirigid Rotor Systems do not have vertical / horizontal hinge pins. Instead, the entire
rotor is allowed to teeter or flap by a trunnion bearing that connects the yoke to the mast
(this method iscommonly used on two blades rotor systems):

The Chord (1) is the longitudinal dimension of an airfoil section, measured from
the leading edge to the trailing edge.
The Span (2) is the length of the rotor blade from the point of rotation to the tip
of the blade.
The Vertical Hinge Pin (3) (drag hinge) is the axis which permits fore and aft
blade movement independent of the other blades in the system.
The Horizontal Hinge Pin (4) is the axis which permits up and down movement
of the blade independent of the other blades in the system.
The Trunnion (5) is splined to the mast and has two bearings through which it is
secured to the yoke. The blades are mounted to the yoke and are free to teeter
(flap)around the trunnion bearings.
The Yoke (6) is the structural member to which the blades are attached and
which fastens the rotor blades to the mast through the trunnion and trunnion
bearings.
The Blade Grip Retainer Bearings (7) is the bearing which permits rotation of
the blade about its spanwise axis so blade pitch can be changed (blade feathering).
Blade Twist is a characteristic built into the rotor blade so angle of incidence is
less near the tip than at the root. Blade twist helps distribute the lift evenly along the
blade by an increased angle of incidence near the root where blade speed is slower.
 Outboard portions of the blade that travel faster normally have lower angles of
incidence, so less lift is concentrated near the blade tip.

Aerofoil

An Airfoil is a structure, piece, or body designed to obtain a useful reaction upon itself in its
motion through the air. An airfoil may be no more than a flat plate (those darned
engineers !) but usually it has a cross section carefully contoured in accordance with its
intended application or function.
Airfoils are applied to aircraft, missles, or other aerial vehicles for:

Sustenation (A Wing or Rotor Blade)

For Stability (As a Fin)
For Control (A Flight Surface, such as a Rudder)
For Thrust (A Propeller or Rotor Blade)

Some airfoils combine some of these functions.

A helicopter flies for the same basic reason that any conventional aircraft flies, because
aerodynamic forces necessary to keep it aloft are produced when air passes about
the rotor blades. The rotor blade, or airfoil, is the structure that makes flight possible. Its
shape produces lift when it passes through the air. Helicopter blades have airfoil sections
designed for a specific set of flight characteristics. Usually the designer must compromise to
obtain an airfoil section that has the best flight characteristics for the mission the aircraft
will perform.

Airfoil sections are of two basic types, symmetrical and nonsymmetrical.

Symmetrical airfoils have identical upper and lower surfaces. They are suited to rotary-wing
applications because they have almost no center of pressure travel. Travel remains
relatively constant under varying angles of attack, affording the best lift-drag ratios for the
full range of velocities from rotor blade root to tip. However, the symmetrical airfoil
produces less lift than a nonsymmetrical airfoil and also has relatively undesirable stall
characteristics. The helicopter blade (airfoil) must adapt to a wide range of airspeeds and
angles of attack during each revolution of the rotor. The symmetrical airfoil delivers
acceptable performance under those alternating conditions. Other benefits are lower cost
and ease of construction as comparedto the nonsymmetrical airfoil.

Nonsymmetrical (cambered) airfoils may have a wide variety of upper and lower surface
designs. The advantages of the nonsymmetrical airfoil are increased lift-drag ratios and
more desirable stall characteristics. Nonsymmetrical airfoils were not used in earlier
helicopters because the center of pressure location moved too much when angle of attack
was changed. When center of pressure moves, a twisting force is exerted on the rotor
blades. Rotor system components had to be designed that would withstand the twisting
force. Recent design processes and new materials used to manufacture rotor systems have
partially overcome the problems associated with use of nonsymmetrical airfoils.
Airfoil Terminology
Rotary-wing airfoils operate under diverse conditions, because their speeds are a
combination of blade rotation and forward movement of the helicopter. An intelligent
discussion of the aerodynamic forces affecting rotor blade lift and drag requires a knowledge
of blade section geometry. Rotor blades are designed with specific geometry that adapts
them to the varying conditions of flight. Cross-section shapes of most rotor blades are not
the same throughout the span. Shapes are varied along the blade radius to take advantage
of the particular airspeed range experienced at each point on the blade, and to help balance
the load between the root and tip. The blade may be built with a twist, so an airfoil section
near the root has a larger pitch angle than a section near the tip.

The Chord Line (1) is a straight line connecting the leading and trailing edges of
the airfoil.
The Chord (2) is the length of the chordline from leading edge to trailing edge
and is the characteristic longitudinal dimension of an airfoil.
The Mean Camber Line (3) is a line drawn halfway between the upper and
lower surfaces. The chord line connects the ends of the mean camber line.
The shape of the mean camber is important in determining the aerodynamic
characteristics of an airfoil section. Maximum Camber (4) (displacement of the
mean camber line from the chord line) and where it is located (expressed as
fractions or percentages of the basic chord) help to define the shape of the mean
camber line.
The Maximum Thickness (5) of an airfoil andwhere it is located (expressed as a
percentage of the chord) help define the airfoil shape,and hence its performance.
The Leading Edge Radius (6) of the airfoil is the radius of curvature given the
leading edge shape.

The airfoil shown in the graphic is a Positive Cambered Airfoil because the mean camber
line is located above the chord line. The term "Camber" refers to the curvature of an airfoil
ot its surfaces. The mean camber of an airfoil may be considered as the curvature of the
median line (mean camber line) of the airfoil.

Distribution of pressure over an airfoil section may be a source of an aerodynamic twisting

force as well as lift. A typical example is illustrated by the pressure distribution pattern
developed by this cambered (nonsymmetrical) airfoil:

The upper surface has pressures

distributed which produce the upper
surface lift.
The lower surface has pressures
distributed which produce the lower
surface force. Net lift produced by the
airfoil is the difference between lift on
the upper surface and the force on the
lower surface. Net lift is effectively
concentrated at a point on the chord
called the Center Of Pressure.

When the angle of attack is increased:

Upper surface lift increases

relative to the lower surface force.
Since the two vectors are not
located at the same point along the
chord line, a twisting force is
exerted about the center of
pressure. Center of pressure also
moves along the chord line when
angle of attack changes, because
the two vectors are separated. This
characteristic of nonsymmetrical
airfoils results in undesirable
control forces that must be
compensated for if the airfoil is
 used in rotary wing applications.

The pressure patterns for symmetrical airfoils are distributed differently than for
nonsymmetrical airfoils:

Upper surface lift and lower surface lift vectors are opposite each other instead of being
separated along the chord line as in the cambered airfoil.

When the angle of attack is increased to develop positive lift, the vectors remain essentially
opposite each other and the twisting force is not exerted. Center of pressure remains
relatively constant even when angle of attack is changed. This is a desirable characteristic
for a rotor blade, because it changes angle of attack constantly during each revolution.

A knowledge of relative wind is particularly essential for an understanding of aerodynamics

of rotary-wing flight because relative wind may be composed of multiple components.
Relative wind is defined as the airflow relative to an airfoil:

Relative wind is created by movement of an airfoil through the air. As an example, consider
a person sitting in an automobile on a no-wind day with a hand extended out the window.
There is no airflow about the hand since the automobile is not moving. However, if the
automobile is driven at 50 miles per hour, the air will flow under and over the hand at 50
miles per hour. A relative wind has been created by moving the hand through the air.
Relative wind flows in the opposite direction that the hand is moving. The velocity of airflow
around the hand in motion is the hand's airspeed.

When the helicopter is stationary on a no-wind day, Resultant Relative Wind is produced
by rotation of the rotor blades. Since the rotor is moving horizontally, the effect is to
displace some of the air downward. The blades travel along the same path and pass a given
point in rapid succession (a three-bladed system rotating at 320 revolutions per minute
passes a given point in the tip-path plane 16 times per second).

The graphic illustrates how still air is changed to a column of descending air by rotor blade
action:

This flow of air is called an Induced Flow (downwash). It is most predominant at a hover
under still wind conditions. Because the rotor system circulates the airflow down through
the rotor disk, the rotational relative wind is modified by the induced flow. Airflow from
rotation, modified by induced flow, produces the Resultant Relative Wind.
In this graphic, angle of attack is reduced by induced flow, causing the airfoil to produce
less lift:

When the helicopter has horizontal motion, the resultant relative wind discussed above is
further changed by the helicopter airspeed. Airspeed component of relative wind results
from the helicopter moving through the air. It is added to or subtracted from the rotational
relative wind, depending on whether the blade is advancing or retreating in relation to the
helicopter movement. Induced flow is also modified by introduction of airspeed relative
wind. The pattern of air circulation through the disk changes when the aircraft has
movement. Generally the downward velocity of induced flow is reduced. The helicopter
moves continually into an undisturbed airmass, resulting in less time to develop a vertical
airflow pattern. As a result, additional lift is produced from a given blade pitch setting.

A total aerodynamic force is generated when a stream of air flows over and under an airfoil
that is moving through the air. The point at which the air separates to flow about the airfoil
is called the point of impact:
A high pressure area or stagnation point is formed at the point of impact. Normally the high
pressure area is located at the lower portion of the leading edge, depending on angle of
attack. This high pressure area contributes to the overall force produced by the blade.

This picture also shows airflow lines that illustrate how the air moves about the airfoil
section. Notice that the air is deflected downward as it passes under the airfoil and leaves
the trailing edge. Remember Newton's third law which states "every action has an equal and
opposite reaction." Since the air is being deflected downward, an equal and opposite force
must be acting upward on the airfoil. This force adds to the total aerodynamic force
developed by the airfoil. At very low or zero angles of attack, the deflection force or impact
pressure may exert a zero positive force, or even a downward or negative force.

Air passing over the top of the airfoil produces aerodynamic force in another way. The shape
of the airfoil causes a low pressure area above the airfoil according to Bernoulli's Principle,
and the decrease in pressure on top of the airfoil exerts an upward aerodynamic force.
Pressure differential between the upper and lower surface of the airfoil is quite small - in the
vicinity of 1 percent. Even a small pressure differential produces substantial force when
applied to the large area of a rotor blade.

The total aerodynamic force, sometimes called the resultant force, may be divided into two
components called lift and drag. Lift acts on the airfoil in a direction perpendicular to the
relative wind. Drag is the resistance or force that opposes the motion of the airfoil through
the air. It acts on the airfoil in a direction parallel to the relative wind:
Many factors contribute to the total lift produced by an airfoil. Increased speed causes
increased lift because a larger pressure differential is produced between the upper and
lower surfaces. Lift does not increase in direct proportion to speed, but varies as the square
of the speed. Thus, a blade traveling at 500 knots has four times the lift of the same blade
traveling at only 250 knots. Lift also varies with the area of the blade. A blade area of 100
square feet will produce twice as much lift as a blade area of only 50 square feet. Angle of
attack also has an effect on the lift produced. Lift increases as the angle of attack increases
up to the stalling angle of attack. Stall angle varies with different blades and is the point at
which airflow no longer follows the camber of the blade smoothly. Air density is another
factor that directly influences lift.

Two design factors, Airfoil Shape and Airfoil Area are primary elements that determine
how much lift and drag a blade will produce. Any change in these design factors will affect
the forces produced.

Normally an increase in lift will also produce an increase in drag. Therefore, the airfoil is
designed to produce the most lift and the least drag within normal speed ranges.

Helicopter rotor systems depend primarily on rotation to produce relative wind which
develops the aerodynamic force required for flight. Because of its rotation and weight, the
rotor system is subject to forces and moments peculiar to all rotating masses. One of the
forces produced is Centrifugal Force.

It is defined as the force that tends to make rotating bodies move away from the center of
rotation. Another force produced in the rotor system is Centripetal Force. It is the force
that counteracts centrifugal force by keeping an object a certain radius from the axis of
rotation.

The rotating blades of a helicopter produce very high centrifugal loads on the rotor head and
blade attachement assemblies. As a matter of interest, centrifugal loads may be from 6 to
12 tons at the blade root of two to four passenger helicopters. Larger helicopters may
develop up to 40 tons of centrifugal load on each blade root. In rotary-wing aircraft,
centrifugal force is the dominant force affecting the rotor system. All other forces act to
modify this force.

When the rotor blades are at rest, they droop due to their weight and span. In fully
articulated systems, they rest against a static or droop stop which prevents the blade from
descending so low it will strike the aircraft (or ground!). When the rotor system begins to
turn, the blade starts to rise from the static position because of the centrifugal force. At
operating speed, the blades extend straight out even though they are at flat pitch and are
not producing lift.

As the helicopter develops lift during takeoff and flight, the blades rise above the "straight
out" position and assume a coned position. Amount of coning depends on RPM, gross
weight, and G-Forces experienced during flight. If RPM is held constant, coning increases as
gross weight and G-force increase. If gross weight and G-forces are constant, decreasing
RPM will cause increased coning. Excessive coning can occur if RPM gets too low, gross
weight is too high, or if excessive G-forces are experienced. Excessive coning can cause
undesirable stresses on the blade and a decrease of total lift because of a decrease in
effective disk area:

Notice that the effective diameter of the rotor disk with increased coning is less than the
diameter of the other disk with less coning. A smaller disk diameter has less potential to
produce lift.

Centrifugal force and lift effects on the blade can be illustrated best by a vector. First look at
a rotor shaft and blade just rotating:

Now look at the same rotor shaft and blade when a vertical force is pushing up on the tip of
the blade:

The vertical force is lift produced when the blades assume a positive angle of attack. The
horizontal force is caused by the centrifugal force due to rotation. Since one end of the
blade is attached to the rotor shaft, it is not free to move. The other end can move and will
assume a position that is the resultant of the forces acting on it:
The blade position is now "coned" and its position is a resultant of the two forces, lift and
centrifugal force, acting on it.