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This chapter discusses the fundamental physical laws governing the forces acting
on an airplane in flight, and what effect these natural laws and forces have on
the performance characteristics of airplanes. To competently control the
airplane, the pilot must understand the principles involved and learn to utilize
or counteract these natural forces.


Modern general aviation airplanes have what may be considered high performance
characteristics. Therefore, it is increasingly necessary that pilots appreciate
and understand the principles upon which the art of flying is based.


STRUCTURE OF THE ATMOSPHERE



The atmosphere in which flight is conducted is an envelope of air that surrounds
the earth and rests upon its surface. It is as much a part of the earth as the
seas or the land. However, air differs from land and water inasmuch as it is a
mixture of gases. It has mass, weight, and indefinite shape.


Air, like any other fluid, is able to flow and change its shape when subjected
to even minute pressures because of the lack of strong molecular cohesion. For
example, gas will completely fill any container into which it is placed,
expanding or contracting to adjust its shape to the limits of the container.


The atmosphere is composed of 78 percent nitrogen, 21 percent oxygen, and 1
percent other gases, such as argon or helium. As some of these elements are
heavier than others, there is a natural tendency of these heavier elements, such
as oxygen, to settle to the surface of the earth, while the lighter elements are
lifted up to the region of higher altitude. This explains why most of the oxygen
is contained below 35,000 feet altitude.


Because air has mass and weight, it is a body, and as a body, it reacts to the
scientific laws of bodies in the same manner as other gaseous bodies. This body
of air resting upon the surface of the earth has weight and at sea level
develops an average pressure of 14.7 pounds on each square inch of surface, or
29.92 inches of mercury-but as its thickness is limited, the higher the
altitude, the less air there is above. For this reason, the weight of the
atmosphere at 18,000 feet is only one-half what it is at sea level. [Figure 2-1]






Figure 2-1. Standard sea level pressure.



ATMOSPHERIC PRESSURE



Though there are various kinds of pressure, this discussion is mainly concerned
with atmospheric pressure. It is one of the basic factors in weather changes,
helps to lift the airplane, and actuates some of the important flight
instruments in the airplane. These instruments are the altimeter, the airspeed
indicator, the rate-of-climb indicator, and the manifold pressure gauge.


Though air is very light, it has mass and is affected by the attraction of
gravity. Therefore, like any other substance, it has weight, and because of its
weight, it has force. Since it is a fluid substance, this force is exerted
equally in all directions, and its effect on bodies within the air is called
pressure. Under standard conditions at sea level, the average pressure exerted
on the human body by the weight of the atmosphere around it is approximately
14.7 lb./in. The density of air has significant effects on the airplane's
capability. As air becomes less dense, it reduces (1) power because the engine
takes in less air, (2) thrust because the propeller is less efficient in thin
air, and (3) lift because the thin air exerts less force on the airfoils.


EFFECTS OF PRESSURE ON DENSITY



Since air is a gas, it can be compressed or expanded. When air is compressed, a
greater amount of air can occupy a given volume. Conversely, when pressure on a
given volume of air is decreased, the air expands and occupies a greater space.
That is, the original column of air at a lower pressure contains a smaller mass
of air. In other words, the density is decreased. In fact, density is directly
proportional to pressure. If the pressure is doubled, the density is doubled,
and if the pressure is lowered, so is the density. This statement is true, only
at a constant temperature.


EFFECT OF TEMPERATURE ON DENSITY



The effect of increasing the temperature of a substance is to decrease its
density. Conversely, decreasing the temperature has the effect of increasing the
density. Thus, the density of air varies inversely as the absolute temperature
varies. This statement is true, only at a constant pressure.


In the atmosphere, both temperature and pressure decrease with altitude, and
have conflicting effects upon density. However, the fairly rapid drop in
pressure as altitude is increased usually has the dominating effect. Hence,
density can be expected to decrease with altitude.


EFFECT OF HUMIDITY ON DENSITY



The preceding paragraphs have assumed that the air was perfectly dry. In
reality, it is never completely dry. The small amount of water vapor suspended
in the atmosphere may be almost negligible under certain conditions, but in
other conditions humidity may become an important factor in the performance of
an airplane. Water vapor is lighter than air; consequently, moist air is lighter
than dry air. It is lightest or least dense when, in a given set of conditions,
it contains the maximum amount of water vapor. The higher the temperature, the
greater amount of water vapor the air can hold. When comparing two separate air
masses, the first warm and moist (both qualities tending to lighten the air) and
the second cold and dry (both qualities making it heavier), the first
necessarily must be less dense than the second. Pressure, temperature, and
humidity have a great influence on airplane performance, because of their effect
upon density.


NEWTON'S LAWS OF MOTION AND FORCE



In the 17th century, a philosopher and mathematician, Sir Isaac Newton,
propounded three basic laws of motion. It is certain that he did not have the
airplane in mind when he did so, but almost everything known about motion goes
back to his three simple laws. These laws, named after Newton, are as follows:


Newton's first law states, in part, that: A body at rest tends to remain at
rest, and a body in motion tends to remain moving at the same speed and in the
same direction.



This simply means that, in nature, nothing starts or stops moving until some
outside force causes it to do so. An airplane at rest on the ramp will remain at
rest unless a force strong enough to overcome its inertia is applied. Once it is
moving, however, its inertia keeps it moving, subject to the various other
forces acting on it. These forces may add to its motion, slow it down, or change
its direction.


Newton's second law implies that: When a body is acted upon by a constant force,
its resulting acceleration is inversely proportional to the mass of the body and
is directly proportional to the applied force.


What is being dealt with here are the factors involved in overcoming Newton's
First Law of Inertia. It covers both changes in direction and speed, including
starting up from rest (positive acceleration) and coming to a stop (negative
acceleration, or deceleration).


Newton's third law states that: Whenever one body exerts a force on another, the
second body always exerts on the first, a force that is equal in magnitude but
opposite in direction.


The recoil of a gun as it is fired is a graphic example of Newton's third law.
The champion swimmer who pushes against the side of the pool during the
turnaround, or the infant learning to walk-both would fail but for the phenomena
expressed in this law. In an airplane, the propeller moves and pushes back the
air; consequently, the air pushes the propeller (and thus the airplane) in the
opposite direction-forward. In a jet airplane, the engine pushes a blast of hot
gases backward; the force of equal and opposite reaction pushes against the
engine and forces the airplane forward. The movement of all vehicles is a
graphic illustration of Newton's third law.


MAGNUS EFFECT



The explanation of lift can best be explained by looking at a cylinder rotating
in an airstream. The local velocity near the cylinder is composed of the
airstream velocity and the cylinder's rotational velocity, which decreases with
distance from the cylinder. On a cylinder, which is rotating in such a way that
the top surface area is rotating in the same direction as the airflow, the local
velocity at the surface is high on top and low on the bottom.


As shown in figure 2-2, at point "A," a stagnation point exists where the
airstream line that impinges on the surface splits; some air goes over and some
under. Another stagnation point exists at "B," where the two





Figure 2-2. Magnus Effect is a lifting force produced when a rotating cylinder
produces a pressure differential. This is the same effect that makes a baseball
curve or a golf ball slice.



airstreams rejoin and resume at identical velocities. We now have upwash ahead
of the rotating cylinder and downwash at the rear.


The difference in surface velocity accounts for a difference in pressure, with
the pressure being lower on the top than the bottom. This low pressure area
produces an upward force known as the "Magnus Effect." This mechanically induced
circulation illustrates the relationship between circulation and lift.


An airfoil with a positive angle of attack develops air circulation as its sharp
trailing edge forces the rear stagnation point to be aft of the trailing edge,
while the front stagnation point is below the leading edge. [Figure 2-3]





Figure 2-3. Air circulation around an airfoil occurs when the front stagnation
point is below the leading edge and the aft stagnation point is beyond the
trailing edge.



BERNOULLI'S PRINCIPLE OF PRESSURE



A half century after Sir Newton presented his laws, Mr. Daniel Bernoulli, a
Swiss mathematician, explained how the pressure of a moving fluid (liquid or
gas) varies with its speed of motion. Specifically, he stated that an increase
in the speed of movement or flow would cause a decrease in the fluid's pressure.
This is exactly what happens to air passing over the curved top of the airplane
wing.



An appropriate analogy can be made with water flowing through 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 is increased or
decreased, it is certain to change the pressure of the water at that point.
Suppose the hose was pinched, thereby 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.


Therefore, if a portion of the hose is constricted, it not only increases the
speed of the flow, but also decreases the pressure at that point. Like results
could be achieved if streamlined solids (airfoils) were introduced at the same
point in the hose. This same principle is the basis for the measurement of
airspeed (fluid flow) and for analyzing the airfoil's ability to produce lift.


A practical application of Bernoulli's theorem is the venturi tube. The venturi
tube has an air inlet which narrows to a throat (constricted point) and an
outlet section which increases in diameter toward the rear. The diameter of the
outlet is the same as that of the inlet. At the throat, the airflow speeds up
and the pressure decreases; at the outlet, the airflow slows and the pressure
increases. [Figure 2-4]


If air is recognized as a body and it is accepted that it must follow the above
laws, one can begin to see how and why an airplane wing develops lift as it
moves through the air.


AIRFOIL DESIGN



In the sections devoted to Newton's and Bernoulli's discoveries, it has already
been discussed in general terms the question of how an airplane wing can sustain
flight when the airplane is heavier than air. Perhaps the explanation can best
be reduced to its most elementary concept by stating that lift (flight) is
simply the result of fluid flow (air) about an airfoil-or in everyday language,
the result of moving an airfoil (wing), by whatever means, through the air.


Since it is the airfoil which harnesses the force developed by its movement
through the air, a discussion and explanation of this structure, as well as some
of the material presented in previous discussions on Newton's and Bernoulli's
laws, will be presented.


An airfoil is a structure designed to obtain reaction upon its surface from the
air through which it moves or that moves past such a structure. Air acts in
various ways when submitted to different pressures and velocities; but this
discussion will be confined to the parts of an airplane that a pilot is most
concerned with in flight-namely, the airfoils designed to produce lift. By
looking at a typical airfoil profile, such as the cross section of a wing, one
can see several obvious characteristics of design. [Figure 2-5] Notice that
there is a difference in the curvatures of the upper and lower surfaces of the
airfoil (the curvature is called camber). The camber of the upper surface is
more pronounced than that of the lower surface, which is somewhat flat in most
instances.


In figure 2-5, note that the two extremities of the airfoil profile also differ
in appearance. The end which faces forward in flight is called the leading edge,
and is rounded; while the other end, the trailing edge, is quite narrow and
tapered. A reference line often used in discussing the airfoil is the chord
line, a straight line drawn through the profile connecting the extremities of
the leading and trailing edges. The distance from this chord line to the upper
and lower surfaces of the wing denotes the magnitude of the upper and lower
camber at any point. Another reference line, drawn from the leading edge to the
trailing edge, is the "mean camber line." This mean line is equidistant at all
points from the upper and lower contours.





Figure 2-5. Typical airfoil section.




Figure 2-4. Air pressure decreases in a venturi.




The construction of the wing, so as to provide actions greater than its weight,
is done by shaping the wing so that advantage can be taken of the air's response
to certain physical laws, and thus develop two actions from the air mass; a
positive pressure lifting action from the air mass below the wing, and a
negative pressure lifting action from lowered pressure above the wing.


As the airstream strikes the relatively flat lower surface of the wing when
inclined at a small angle to its direction of motion, the air is forced to
rebound downward and therefore causes an upward reaction in positive lift, while
at the same time airstream striking the upper curved section of the "leading
edge" of the wing is deflected upward. In other words, a wing shaped to cause an
action on the air, and forcing it downward, will provide an equal reaction from
the air, forcing the wing upward. If a wing is constructed in such form that it
will cause a lift force greater than the weight of the airplane, the airplane
will fly.


However, if all the lift required were obtained merely from the deflection of
air by the lower surface of the wing, an airplane would need only a flat wing
like a kite. This, of course, is not the case at all; under certain conditions
disturbed air currents circulating at the trailing edge of the wing could be so
excessive as to make the airplane lose speed and lift. The balance of the lift
needed to support the airplane comes from the flow of air above the wing. Herein
lies the key to flight. The fact that most lift is the result of the airflow's
downwash from above the wing, must be thoroughly understood in order to continue
further in the study of flight. It is neither accurate nor does it serve a
useful purpose, however, to assign specific values to the percentage of lift
generated by the upper surface of an airfoil versus that generated by the lower
surface. These are not constant values and will vary, not only with flight
conditions, but with different wing designs.


It should be understood that different airfoils have different flight
characteristics. Many thousands of airfoils have been tested in wind tunnels and
in actual flight, but no one airfoil has been found that satisfies every flight
requirement. The weight, speed, and purpose of each airplane dictate the shape
of its airfoil. It was learned many years ago that the most efficient airfoil
for producing the greatest lift was one that had a concave, or "scooped out"
lower surface. Later it was also learned that as a fixed design, this type of
airfoil sacrificed too much speed while producing lift and, therefore, was not
suitable for high-speed flight. It is interesting to note, however, that through
advanced progress in engineering, today's high-speed jets can again take
advantage of the concave airfoil's high lift characteristics. Leading edge
(Kreuger) flaps and trailing edge (Fowler) flaps, when extended from the basic
wing structure, literally change the airfoil shape into the classic concave
form, thereby generating much greater lift during slow flight conditions.


On the other hand, an airfoil that is perfectly streamlined and offers little
wind resistance sometimes does not have enough lifting power to take the
airplane off the ground. Thus, modern airplanes have airfoils which strike a
medium between extremes in design, the shape varying according to the needs of
the airplane for which it is designed. Figure 2-6 shows some of the more common
airfoil sections.


LOW PRESSURE ABOVE



In a wind tunnel or in flight, an airfoil is simply a streamlined object
inserted into a moving stream of air. If the airfoil profile were in the shape
of a teardrop, the speed and the pressure changes of the air passing over the
top and bottom would be the same on both sides. But if the teardrop shaped
airfoil were cut in half lengthwise, a form resembling the basic airfoil (wing)
section would result. If the airfoil were then inclined so the airflow strikes
it at an angle (angle of attack), the air molecules moving over the upper
surface would be forced to move faster than would the molecules moving along the
bottom of the airfoil, since the upper molecules must travel a greater distance
due to the curvature of the upper surface. This increased velocity reduces the
pressure above the airfoil. Bernoulli's principle of pressure by itself does not
explain the distribution of pressure over the upper surface of the airfoil. A
discussion of the influence of momentum of the air as it flows in various curved
paths near the airfoil will be presented. [Figure 2-7] Momentum is the
resistance a moving body offers to having its direction or amount of motion
changed. When a body is forced to move in a circular path, it offers resistance
in the direction away from the center of the curved path. This is "centrifugal
force." While the particles of air move in the curved path AB ,centrifugal force
tends to throw them in the direction of the arrows between A and B and hence,
causes the air to exert more than normal pressure on the leading edge of the
airfoil. But after the air particles pass B (the point of reversal of the
curvature of the path) the centrifugal force tends to throw them in the
direction of the arrows between B and C (causing reduced pressure on the
airfoil). This effect is held until the particles reach C ,the second point of
reversal of curvature of the airflow. Again the centrifugal force is reversed
and the particles may even tend to give slightly more than normal pressure on
the trailing edge of the airfoil, as indicated by the short arrows between C and
D .





Figure 2-6. Airfoil designs.





Figure 2-7. Momentum influences airflow over an airfoil.



Therefore, the air pressure on the upper surface of the airfoil is distributed
so that the pressure is much greater on the leading edge than the surrounding
atmospheric pressure, causing strong resistance to forward motion; but the air
pressure is less than surrounding atmospheric pressure over a large portion of
the top surface (B to C).


As seen in the application of Bernoulli's theorem to a venturi, the speedup of
air on the top of an airfoil produces a drop in pressure. This lowered pressure
is a component of total lift. It is a mistake, however, to assume that the
pressure difference between the upper and lower surface of a wing alone accounts
for the total lift force produced.


One must also bear in mind that associated with the lowered pressure is
downwash; a downward backward flow from the top surface of the wing. As already
seen from previous discussions relative to the dynamic action of the air as it
strikes the lower surface of the wing, the reaction of this downward backward
flow results in an upward forward force on the wing. This same reaction applies
to the flow of air over the top of the airfoil as well as to the bottom, and
Newton's third law is again in the picture.


HIGH PRESSURE BELOW



In the section dealing with Newton's laws as they apply to lift, it has already
been discussed how a certain amount of lift is generated by pressure conditions
underneath the wing. Because of the manner in which air flows underneath the
wing, a positive pressure results, particularly at higher angles of attack. But
there is another aspect to this airflow that must be considered. At a point
close to the leading edge, the airflow is virtually stopped (stagnation point)
and then gradually increases speed. At some point near the trailing edge, it has
again reached a velocity equal to that on the upper surface. In conformance with
Bernoulli's principles, where the airflow was slowed beneath the wing, a
positive upward pressure was created against the wing; i.e., as the fluid speed
decreases, the pressure must increase. In essence, this simply "accentuates the
positive" since it increases the pressure differential between the upper and
lower surface of the airfoil, and therefore increases total lift over that which
would have resulted had there been no increase of pressure at the lower surface.
Both Bernoulli's principle and Newton's laws are in operation whenever lift is
being generated by an airfoil.


Fluid flow or airflow then, is the basis for flight in airplanes, and is a
product of the velocity of the airplane. The velocity of the airplane is very
important to the pilot since it affects the lift and drag forces of the
airplane. The pilot uses the velocity (airspeed) to fly at a minimum glide
angle, at maximum endurance, and for a number of other flight maneuvers.
Airspeed is the velocity of the airplane relative to the air mass through which
it is flying.


PRESSURE DISTRIBUTION



From experiments conducted on wind tunnel models and on full size airplanes, it
has been determined that as air flows along the surface of a wing at different
angles of attack, there are regions along the surface where the pressure is
negative, or less than atmospheric, and regions where the pressure is positive,
or greater than atmospheric. This negative pressure on the upper surface creates
a relatively larger force on the wing than is caused by the positive pressure
resulting from the air striking the lower wing surface. Figure 2-8 shows the
pressure distribution along an airfoil at three different angles of attack. In
general, at high angles of attack the






Figure 2-8. Pressure distribution on an airfoil.



center of pressure moves forward, while at low angles of attack the center of
pressure moves aft. In the design of wing structures, this center of pressure
travel is very important, since it affects the position of the airloads imposed
on the wing structure in low angle-of-attack conditions and high angle-of-attack
conditions. The airplane's aerodynamic balance and controllability are governed
by changes in the center of pressure.


The center of pressure is determined through calculation and wind tunnel tests
by varying the airfoil's angle of attack through normal operating extremes. As
the angle of attack is changed, so are the various pressure distribution
characteristics. [Figure 2-8] Positive (+) and negative (-) pressure forces are
totaled for each angle of attack and the resultant force is obtained. The total
resultant pressure is represented by the resultant force vector shown in figure
2-9.


The point of application of this force vector is termed the "center of pressure"
(CP). For any given angle of attack, the center of pressure is the point where
the resultant force crosses the chord line. This point is expressed as a
percentage of the chord of the airfoil. A center of pressure at 30 percent of a
60- inch chord would be 18 inches aft of the wing's leading edge. It would
appear then that if the designer would place the wing so that its center of
pressure was at the airplane's center of gravity, the airplane would always
balance. The difficulty arises, however, that the location of the center of
pressure changes with change in the airfoil's angle of attack. [Figure 2-10]





Figure 2-9. Force vectors on an airfoil.




Figure 2-10. CP changes with an angle of attack.



In the airplane's normal range of flight attitudes, if the angle of attack is
increased, the center of pressure moves forward; and if decreased, it moves
rearward. Since the center of gravity is fixed at one point, it is evident that
as the angle of attack increases, the center of lift (CL) moves ahead of the
center of gravity, creating a force which tends to raise the nose of the
airplane or tends to increase the angle of attack still more. On the other hand,
if the angle of attack is decreased, the center of lift (CL) moves aft and tends
to decrease the angle a greater amount. It is seen then, that the ordinary
airfoil is inherently unstable, and that an auxiliary device, such as the
horizontal tail surface, must be added to make the airplane balance
longitudinally.


The balance of an airplane in flight depends, therefore, on the relative
position of the center of gravity (CG) and the center of pressure(CP)of the
airfoil. Experience has shown that an airplane with the center of gravity in the
vicinity of 20 percent of the wing chord can be made to balance and fly
satisfactorily.







The tapered wing presents a variety of wing chords throughout the span of the
wing. It becomes necessary then, to specify some chord about which the point of
balance can be expressed. This chord, known as the mean aerodynamic chord (MAC),
usually is defined as the chord of an imaginary untapered wing, which would have
the same center of pressure characteristics as the wing in question.


Airplane loading and weight distribution also affect center of gravity and cause
additional forces, which in turn affect airplane balance.