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Wings and Lift

How does a wing work?

Any object, whether it be a book sitting on a table or a rocket blasting into space, is acted

upon by some number of forces. The primary force most of us experience in our lives is our ownweight, the force holding us to the surface of the Earth. An aircraft in flight is acted upon by four

basic forces: weight that pulls the aircraft toward the ground, thrust that pushes the aircraft

forward, drag or the force of the air pushing against the motion of the aircraft, and lift that pullsthe aircraft up.

Four forces acting on an aircraft in flight

It is this lift force that is produced (primarily) by the wing, and I believe what thequestioner means to ask is "How does a wing generate lift?" Though this seems like a simpleenough question, the general public would probably be amazed to find out that engineers and

scientists still debate just how lift is produced even 100 years after flight became a reality. In

fact, it is quite easy to be drawn into charged debates on the subject, as I was when trying to

answer this question. So, to be fair to the proponents of each theory, I will discuss each in turn.But first, let us simplify our discussion slightly by thinking of the wing as only a two-

dimensional shape. Consider the cross-section of a wing created by a plane cutting through the

wing. This two-dimensional cross-sectional shape is called an airfoil (or aerofoil to our Britishfriends). An example of a common airfoil shape is the Clark Y.

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Clark Y airfoil

Bernoulli theory:

The most common explanation of the concept of lift is based upon the Bernoulli equation,

an equation that relates the pressures and velocites acting along the surface of a wing. What this

equation says, in simple terms, is that the sum of the pressures acting on a body is a constant.This sum consists of two types of pressures: 1) the static pressure, or the atmospheric pressure at

any point in a flowfield, and 2) the dynamic pressure, or the pressure created by the motion of abody through the air. Since dynamic pressure is a function of the velocity of the flow, theBernoulli equation relates the sum of pressures to the velocity of the flow past the body. So what

this equation tells us is that as velocity increases, pressure decreases and vice versa.

To understand why the flow velocity changes, we introduce a second relation called theContinuity equation. What this relationship tells us is that the velocity at which a flow passes

through an area is directly related to the size of that area. For example, if you blow through a

straw, the air will come out at a certain speed. If you then blow in with the same strength butnow squeeze the end of the straw, the air will come out faster.

So how do these equations relate to our two-dimensional airfoil? Look again at the Clark

Y and notice that an airfoil is a curved shape. While the bottom is relatively flat, the top surface

is thicker and more curved. Thus, when air passes over an airfoil, that flow over the top issqueezed into a smaller area than that airflow passing the lower surface. The Continuity equation

tells us that a flow squeezed into a smaller area must go faster, and the Bernoulli equation tells us

that when a flow moves faster, it creates a lower pressure. Thus, a higher pressure exists on thelower surface of an airfoil and a lower pressure on the upper surface. Whenever such a pressure

difference exists in nature, a force is created in the direction of the lower pressure (since pressure

is defined as force per unit area). Think of it as the upper surface being sucked upward. Thisupward force, of course, is lift. It is this theory that appears in most aerodynamic textbooks,

albeit sometimes with incorrect assumptions applied and conclusions drawn.

Newtonian theory:

A theory currently gaining in popularity and arguably more "fundamental" in origin is theNewtonian theory, so named because it is said to follow from Newton's third law of motion (for

every action there is an equal and opposite reaction). First, one most realize that any airfoilgenerating lift deflects the air flow behind it. Positive lift deflects the air downward, towards the

ground. Thus, the motion of any lifting surface through a flow accelerates that flow in a new

direction. Newton's second law tells us that force is directly proportional to acceleration (F=ma).Therefore, we must conclude from Newton's third law that the force accelerating the air

downward must be accompanied by an equal and opposite force pushing the airfoil upward. This

upward force is lift.

Circulation theory:

The most mathematical explanation for lift is the circulation theory. Circulation can bethought of as a component of velocity that rotates or swirls around an airfoil or any other shape.In a branch of aerodynamics called incompressible flow, we can usepotential flow relationships

to solve for this circulation for a desired shape. Once this quantity is known, the force of lift can

be solved for using the Kutta-Joukowski theorem that directly relates lift and circulation. Thisapproach tends to be more mathematically intense than I wish to get into here, and it's really

more of a method of calculating lift in an ideal flowfield than an explanation of the physical

origins of lift.

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Conclusion:

So the reader may be asking which of these theories is correct? In truth, each is valid insome respect and useful for certain applications, but the ultimate question is which is the most

fundamental explanation. Mathematicians would surely prefer the circulation theory, which is

certainly a very elegant approach firmly based on mathematical principles, but it fails to explain

what force of nature creates circulation or lift. Many would argue that the Newtonian explanationis most fundamental since it is "derived" from Newtonian laws of motion. While this is true to

some degree, the theory lacks an explanation as to why an airfoil deflects the flow downward inthe first place. Even accepting this principle, the idea that an airfoil deflects the flow andtherefore experiences lift also fails to capture the fundamental tools of nature (pressure and

friction) that create and exert that force on the body. Proponents of this explanation generally

deride the Bernoulli theory because it relies on less fundamental concepts, like the Bernoulli andContinuity equations. There is some truth to this complaint, and the theory may be more difficult

for the novice to understand as a result. However, both equations are derived from Newtonian

physics, and I would argue from more fundamental and more mathematically sound premisesthan the Newtonian theory. In the end, I leave it up to the reader to decide. The following are

some sources for further reading on the subject:

ALLSTAR Principles of Flight -- A much simplified description of the Bernoulli theory

Airfoil Misconception -- A site favoring the Newton theory A Physical Description of Flight -- The champions of the Newton theory

Bernoulli vs. Newton -- Good discussion of the two approaches

Remember that in answering this question, I considered only the two-dimensional cross-section of a wing, the airfoil, also known as an infinite wing. However, I did not adress any

issues regarding the design of the airfoil itself, like camber, thickness, orsymmetrical airfoils. In

addition, this discussion hasn't even touched on the aerodynamic properties of afinite wing, or awing with tips. As one might expect, such a wing has far different characteristics than does the

infinite wing. A discussion of finite wings involves addressing concepts like induced drag, tip

vortices, and aspect ratio as well as wing design issues like taper, sweep, twist, and high-lift

devices likeflaps and slats. Such a discussion goes far beyond the scope of this question, but we

look forward to receiving questions about these topics in the future.- answer byJeff Scott, 17 December 2000

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How Airplanes Fly: A Physical Description of Lift

Almost everyone today has flown in an airplane. Many ask the simple question "what

makes an airplane fly"? The answer one frequently gets is misleading and often just plain wrong.

We hope that the answers provided here will clarify many misconceptions about lift and that youwill adopt our explanation when explaining lift to others. We are going to show you that lift is

easier to understand if one starts with Newton rather than Bernoulli. We will also show you that

the popular explanation that most of us were taught is misleading at best and that lift is due to thewing diverting air down.

Let us start by defining three descriptions of lift commonly used in textbooks and training

manuals. The first we will call the Mathematical Aerodynamics Description which is used by

aeronautical engineers. This description uses complex mathematics and/or computer simulationsto calculate the lift of a wing. These are design tools which are powerful for computing lift but

do not lend themselves to an intuitive understanding of flight.

The second description we will call the Popular Explanation which is based on theBernoulli principle. The primary advantage of this description is that it is easy to understand and

has been taught for many years. Because of its simplicity, it is used to describe lift in most flight

training manuals. The major disadvantage is that it relies on the "principle of equal transit times"

which is wrong. This description focuses on the shape of the wing and prevents one fromunderstanding such important phenomena as inverted flight, power, ground effect, and the

dependence of lift on the angle of attack of the wing.

The third description, which we are advocating here, we will call the PhysicalDescription of lift. This description is based primarily on Newtons laws. The physical

description is useful for understanding flight, and is accessible to all that are curious. Little math

is needed to yield an estimate of many phenomena associated with flight. This description givesa clear, intuitive understanding of such phenomena as the power curve, ground effect, and high-

speed stalls. However, unlike the mathematical aerodynamics description, the physical

description has no design or simulation capabilities.

The popular explanation of liftStudents of physics and aerodynamics are taught that airplanes fly as a result of

Bernoullis principle, which says that if air speeds up the pressure is lowered. Thus a wing

generates lift because the air goes faster over the top creating a region of low pressure, and thus

lift. This explanation usually satisfies the curious and few challenge the conclusions. Some may

wonder why the air goes faster over the top of the wing and this is where the popular explanationof lift falls apart.

In order to explain why the air goes faster over the top of the wing, many have resorted to the

geometric argument that the distance the air must travel is directly related to its speed. The usualclaim is that when the air separates at the leading edge, the part that goes over the top must

converge at the trailing edge with the part that goes under the bottom. This is the so-called

"principle of equal transit times".As discussed by Gale Craig (Stop Abusing Bernoulli! How Airplanes Really Fly.,

Regenerative Press, Anderson, Indiana, 1997), let us assume that this argument were true. The

average speeds of the air over and under the wing are easily determined because we can measure

the distances and thus the speeds can be calculated. From Bernoullis principle, we can thendetermine the pressure forces and thus lift. If we do a simple calculation we would find that in

order to generate the required lift for a typical small airplane, the distance over the top of the

wing must be about 50% longer than under the bottom. Figure 1 shows what such an airfoilwould look like. Now, imagine what a Boeing 747 wing would have to look like!

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Fig 1 Shape of wing predicted by principle of equal transit time.

If we look at the wing of a typical small plane, which has a top surface that is 1.5 - 2.5%

longer than the bottom, we discover that a Cessna 172 would have to fly at over 400 mph to

generate enough lift. Clearly, something in this description of lift is flawed.

But, who says the separated air must meet at the trailing edge at the same time? Figure 2shows the airflow over a wing in a simulated wind tunnel. In the simulation, colored smoke is

introduced periodically. One can see that the air that goes over the top of the wing gets to the

trailing edge considerably before the air that goes under the wing. In fact, close inspection showsthat the air going under the wing is slowed down from the "free-stream" velocity of the air. So

much for the principle of equal transit times.

Fig 2 Simulation of the airflow over a wing in a wind tunnel, with colored "smoke" to showthe acceleration and deceleration of the air.

The popular explanation also implies that inverted flight is impossible. It certainly does

not address acrobatic airplanes, with symmetric wings (the top and bottom surfaces are the sameshape), or how a wing adjusts for the great changes in load such as when pulling out of a dive or

in a steep turn?

So, why has the popular explanation prevailed for so long? One answer is that theBernoulli principleis easy to understand. There is nothing wrong with the Bernoulli principle, or

with the statement that the air goes faster over the top of the wing. But, as the above discussion

suggests, our understanding is not complete with this explanation. The problem is that we aremissing a vital piece when we apply Bernoullis principle. We can calculate the pressures around

the wing if we know the speed of the air over and under the wing, but how do we determine the

speed?

Another fundamental shortcoming of the popular explanation is that it ignores the work that isdone. Lift requires power (which is work per time). As will be seen later, an understanding of

power is key to the understanding of many of the interesting phenomena of lift.

Newtons laws and lift

So, how does a wing generate lift? To begin to understand lift we must return to high

school physics and review Newtons first and third laws. (We will introduce Newtons secondlaw a little later.) Newtons first law states a body at rest will remain at rest, or a body in motion

http://www.allstar.fiu.edu/aero/flight32.htmhttp://www.allstar.fiu.edu/aero/flight32.htmhttp://www.allstar.fiu.edu/aero/flight32.htm
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will continue in straight-line motion unless subjected to an external applied force. That means, if

one sees a bend in the flow of air, or if air originally at rest is accelerated into motion, there is aforce acting on it. Newtons third law states that for every action there is an equal and opposite

reaction. As an example, an object sitting on a table exerts a force on the table (its weight) and

the table puts an equal and opposite force on the object to hold it up. In order to generate lift a

wing must do something to the air. What the wing does to the air is the action while lift is thereaction.

Lets compare two figures used to show streams of air (streamlines) over a wing. Infigure 3 the air comes straight at the wing, bends around it, and then leaves straight behind thewing. We have all seen similar pictures, even in flight manuals. But, the air leaves the wing

exactly as it appeared ahead of the wing. There is no net action on the air so there can be no lift!

Figure 4 shows the streamlines, as they should be drawn. The air passes over the wing and isbent down. The bending of the air is the action. The reaction is the lift on the wing.

Fig 3 Common depiction of airflow over a wing. This wing has no lift.

Fig 4 True airflow over a wing with lift, showing upwash and downwash.The wing as a pump

As Newtons laws suggests, the wing must change something of the air to get lift.Changes in the airs momentum will result in forces on the wing. To generate lift a wing must

divert air down; lots of air.

The lift of a wing is equal to the change in momentum of the air it is diverting down.

Momentum is the product of mass and velocity. The lift of a wing is proportional to the amount

of air diverted down times the downward velocity of that air. Its that simple. (Here we have used

an alternate form of Newtons second law that relates the acceleration of an object to its mass

and to the force on it; F=ma) For more lift the wing can either divert more air (mass) or increaseits downward velocity. This downward velocity behind the wing is called "downwash". Figure 5

shows how the downwash appears to the pilot (or in a wind tunnel). The figure also shows howthe downwash appears to an observer on the ground watching the wing go by. To the pilot the airis coming off the wing at roughly the angle of attack. To the observer on the ground, if he or she

could see the air, it would be coming off the wing almost vertically. The greater the angle of

attack, the greater the vertical velocity. Likewise, for the same angle of attack, the greater the

speed of the wing the greater the vertical velocity. Both the increase in the speed and the increaseof the angle of attack increase the length of the vertical arrow. It is this vertical velocity that

gives the wing lift.

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Fig 5 How downwash appears to a pilot and to an observer on the ground.

As stated, an observer on the ground would see the air going almost straight down behindthe plane. This can be demonstrated by observing the tight column of air behind a propeller, a

household fan, or under the rotors of a helicopter; all of which are rotating wings. If the air were

coming off the blades at an angle the air would produce a cone rather than a tight column. If aplane were to fly over a very large scale, the scale would register the weight of the plane.

If we estimate that the average vertical component of the downwash of a Cessna 172traveling at 110 knots to be about 9 knots, then to generate the needed 2,300 lbs of lift the wingpumps a whopping 2.5 ton/sec of air! In fact, as will be discussed later, this estimate may be as

much as a factor of two too low. The amount of air pumped down for a Boeing 747 to create lift

for its roughly 800,000 pounds takeoff weight is incredible indeed.

Pumping, or diverting, so much air down is a strong argument against lift being just asurface effect as implied by the popular explanation. In fact, in order to pump 2.5 ton/sec the

wing of the Cessna 172 must accelerate all of the air within 9 feet above the wing. (Air weighs

about 2 pounds per cubic yard at sea level.) Figure 6 illustrates the effect of the air being diverteddown from a wing. A huge hole is punched through the fog by the downwash from the airplane

that has just flown over it.

Fig 6 Downwash and wing vortices in the fog.

(Photographer Paul Bowen, courtesy of Cessna Aircraft, Co.)

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So how does a thin wing divert so much air? When the air is bent around the top of the

wing, it pulls on the air above it accelerating that air down, otherwise there would be voids in theair left above the wing. Air is pulled from above to prevent voids. This pulling causes the

pressure to become lower above the wing. It is the acceleration of the air above the wing in the

downward direction that gives lift. (Why the wing bends the air with enough force to generate

lift will be discussed in the next section.)As seen in figure 4, a complication in the picture of a wing is the effect of "upwash" at

the leading edge of the wing. As the wing moves along, air is not only diverted down at the rearof the wing, but air is pulled up at the leading edge. This upwash actually contributes to negativelift and more air must be diverted down to compensate for it. This will be discussed later when

we consider ground effect.

Normally, one looks at the air flowing over the wing in the frame of reference of thewing. In other words, to the pilot the air is moving and the wing is standing still. We have

already stated that an observer on the ground would see the air coming off the wing almost

vertically. But what is the air doing above and below the wing? Figure 7 shows an instantaneoussnapshot of how air molecules are moving as a wing passes by. Remember in this figure the air is

initially at rest and it is the wing moving. Ahead of the leading edge, air is moving up (upwash).

At the trailing edge, air is diverted down (downwash). Over the top the air is accelerated towards

the trailing edge. Underneath, the air is accelerated forward slightly, if at all.

Fig 7 Direction of air movement around a wing as seen by an observer on the ground.

In the mathematical aerodynamics description of lift this rotation of the air around thewing gives rise to the "bound vortex" or "circulation" model. The advent of this model, and the

complicated mathematical manipulations associated with it, leads to the direct understanding of

forces on a wing. But, the mathematics required typically takes students in aerodynamics sometime to master.

One observation that can be made from figure 7 is that the top surface of the wing does

much more to move the air than the bottom. So the top is the more critical surface. Thus,airplanes can carry external stores, such as drop tanks, under the wings but not on top where they

would interfere with lift. That is also why wing struts under the wing are common but struts on

the top of the wing have been historically rare. A strut, or any obstruction, on the top of the wingwould interfere with the lift.

Air has viscosity

The natural question is "how does the wing divert the air down?" When a moving fluid,such as air or water, comes into contact with a curved surface it will try to follow that surface. To

demonstrate this effect, hold a water glass horizontally under a faucet such that a small stream of

water just touches the side of the glass. Instead of flowing straight down, the presence of theglass causes the water to wrap around the glass as is shown in figure 8. This tendency of fluids to

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follow a curved surface is known as the Coanda effect. From Newtons first law we know that

for the fluid to bend there must be a force acting on it. From Newtons third law we know thatthe fluid must put an equal and opposite force on the object which caused the fluid to bend.

Fig 8 Coanda effect.

Why should a fluid follow a curved surface? The answer is viscosity; the resistance to

flow which also gives the air a kind of "stickiness". Viscosity in air is very small but it is enough

for the air molecules to want to stick to the surface. At the surface the relative velocity betweenthe surface and the nearest air molecules is exactly zero. (That is why one cannot hose the dust

off of a car and why there is dust on the backside of the fans in a wind tunnel.) Just above the

surface the fluid has some small velocity. The farther one goes from the surface the faster thefluid is moving until the external velocity is reached (note that this occurs in less than an inch).

Because the fluid near the surface has a change in velocity, the fluid flow is bent towards the

surface. Unless the bend is too tight, the fluid will follow the surface. This volume of air aroundthe wing that appears to be partially stuck to the wing is called the "boundary layer".

Lift as a function of angle of attack

There are many types of wing: conventional, symmetric, conventional in inverted flight,

the early biplane wings that looked like warped boards, and even the proverbial "barn door". Inall cases, the wing is forcing the air down, or more accurately pulling air down from above. What

each of these wings have in common is an angle of attack with respect to the oncoming air. It isthis angle of attack that is the primary parameter in determining lift. The inverted wing can be

explained by its angle of attack, despite the apparent contradiction with the popular explanation

involving the Bernoulli principle. A pilot adjusts the angle of attack to adjust the lift for thespeed and load. The popular explanation of lift which focuses on the shape of the wing gives the

pilot only the speed to adjust.

To better understand the role of the angle of attack it is useful to introduce an "effective" angle of

attack, defined such that the angle of the wing to the oncoming air that gives zero lift is definedto be zero degrees. If one then changes the angle of attack both up and down one finds that the

lift is proportional to the angle. Figure 9 shows the coefficient of lift (lift normalized for the sizeof the wing) for a typical wing as a function of the effective angle of attack. A similar lift versusangle of attack relationship is found for all wings, independent of their design. This is true for the

wing of a 747 or a barn door. The role of the angle of attack is more important than the details of

the airfoils shape in understanding lift.

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Fig 9 Coefficient of lift versus the effective angle of attack.

Typically, the lift begins to decrease at an angle of attack of about 15 degrees. The forces

necessary to bend the air to such a steep angle are greater than the viscosity of the air will

support, and the air begins to separate from the wing. This separation of the airflow from the topof the wing is a stall.

The wing as air "scoop"

We now would like to introduce a new mental image of a wing. One is used to thinking

of a wing as a thin blade that slices though the air and develops lift somewhat by magic. The new

image that we would like you to adopt is that of the wing as a scoop diverting a certain amount

of air from the horizontal to roughly the angle of attack, as depicted in figure 10. The scoop canbe pictured as an invisible structure put on the wing at the factory. The length of the scoop is

equal to the length of the wing and the height is somewhat related to the chord length (distance

from the leading edge of the wing to the trailing edge). The amount of air intercepted by thisscoop is proportional to the speed of the plane and the density of the air, and nothing else.

Fig 10 The wing as a scoop.

As stated before, the lift of a wing is proportional to the amount of air diverted down

times the vertical velocity of that air. As a plane increases speed, the scoop diverted more air.

Since the load on the wing, which is the weight of the plane, does not increase the vertical speedof the diverted air must be decreased proportionately. Thus, the angle of attack is reduced to

maintain a constant lift. When the plane goes higher, the air becomes less dense so the scoopdiverts less air for the same speed. Thus, to compensate the angle of attack must be increased.The concepts of this section will be used to understand lift in a way not possible with the popular

explanation.

Lift requires power

When a plane passes overhead the formally still air ends up with a downward velocity.

Thus, the air is left in motion after the plane leaves. The air has been given energy. Power is

energy, or work, per time. So, lift must require power. This power is supplied by the airplanesengine (or by gravity and thermals for a sailplane).

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How much power will we need to fly? The power needed for lift is the work (energy) per

unit time and so is proportional to the amount of air diverted down times the velocity squared ofthat diverted air. We have already stated that the lift of a wing is proportional to the amount of

air diverted down times the downward velocity of that air. Thus, the power needed to lift theairplane is proportional to the load (or weight) times the vertical velocity of the air. If the speed

of the plane is doubled the amount of air diverted down doubles. Thus the angle of attack mustbe reduced to give a vertical velocity that is half the original to give the same lift. The power

required for lift has been cut in half. This shows that the power required for lift becomes less asthe airplane's speed increases. In fact, we have shown that this power to create lift is proportionalto one over the speed of the plane.

But, we all know that to go faster (in cruise) we must apply more power. So there must be

more to power than the power required for lift. The power associated with lift, described above,is often called the "induced" power. Power is also needed to overcome what is called "parasitic"

drag, which is the drag associated with moving the wheels, struts, antenna, etc. through the air.

The energy the airplane imparts to an air molecule on impact is proportional to the speedsquared. The number of molecules struck per time is proportional to the speed. Thus the parasitic

power required to overcome parasitic drag increases as the speed cubed.

Figure 11 shows the power curves for induced power, parasitic power, and total power

which is the sum of induced power and parasitic power. Again, the induced power goes as oneover the speed and the parasitic power goes as the speed cubed. At low speed the power

requirements of flight are dominated by the induced power. The slower one flies the less air is

diverted and thus the angle of attack must be increased to maintain lift. Pilots practice flying onthe "backside of the power curve" so that they recognizes that the angle of attack and the power

required to stay in the air at very low speeds are considerable.

Fig 11 Power requirements versus speed.

At cruise, the power requirement is dominated by parasitic power. Since this goes as the

speed cubed an increase in engine size gives one a faster rate of climb but does little to improve

the cruise speed of the plane.

Since we now know how the power requirements vary with speed, we can understand drag,which is a force. Drag is simply power divided by speed. Figure 12 shows the induced, parasitic,

and total drag as a function of speed. Here the induced drag varies as one over speed squared and

parasitic drag varies as the speed squared. Taking a look at these curves one can deduce a fewthings about how airplanes are designed. Slower airplanes, such as gliders, are designed to

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minimize induced drag (or induced power), which dominates at lower speeds. Faster airplanes

are more concerned with parasite drag (or parasitic power).

Fig 12 Drag versus speed.

Wing efficiency

At cruise, a non-negligible amount of the drag of a modern wing is induced drag.

Parasitic drag, which dominates at cruise, of a Boeing 747 wing is only equivalent to that of a1/2-inch cable of the same length. One might ask what effects the efficiency of a wing. We saw

that the induced power of a wing is proportional to the vertical velocity of the air. If the length of

a wing were to be doubled, the size of our scoop would also double, diverting twice as much air.So, for the same lift the vertical velocity (and thus the angle of attack) would have to be halved.

Since the induced power is proportional to the vertical velocity of the air, it too is reduced by

half. Thus, the lifting efficiency of a wing is proportional to one over the length of the wing. Thelonger the wing the less induced power required to produce the same lift, though this is achieved

with and increase in parasitic drag. Low speed airplanes are effected more by induced drag thanfast airplanes and so have longer wings. That is why sailplanes, which fly at low speeds, have

such long wings. High-speed fighters, on the other hand, feel the effects of parasite drag morethan our low speed trainers. Therefore, fast airplanes have shorter wings to lower parasite drag.

There is a misconception by some that lift does not require power. This comes from

aeronautics in the study of the idealized theory of wing sections (airfoils). When dealing with anairfoil, the picture is actually that of a wing with infinite span. Since we have seen that the power

necessary for lift is proportional to one over the length of the wing, a wing of infinite span does

not require power for lift. If lift did not require power airplanes would have the same range fullas they do empty, and helicopters could hover at any altitude and load. Best of all, propellers

(which are rotating wings) would not require power to produce thrust. Unfortunately, we live in

the real world where both lift and propulsion require power.

Let us now consider the relationship between wing loading and power. Does it take more

power to fly more passengers and cargo? And, does loading affect stall speed? At a constantspeed, if the wing loading is increased the vertical velocity must be increased to compensate.

This is done by increasing the angle of attack. If the total weight of the airplane were doubled

(say, in a 2g turn) the vertical velocity of the air is doubled to compensate for the increased wingloading. The induced power is proportional to the load times the vertical velocity of the diverted

air, which have both doubled. Thus the induced power requirement has increased by a factor of

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four! The same thing would be true if the airplanes weight were doubled by adding more fuel,

etc.One way to measure the total power is to look at the rate of fuel consumption. Figure 13

shows the fuel consumption versus gross weight for a large transport airplane traveling at a

constant speed (obtained from actual data). Since the speed is constant the change in fuel

consumption is due to the change in induced power. The data are fitted by a constant (parasiticpower) and a term that goes as the load squared. This second term is just what was predicted in

our Newtonian discussion of the effect of load on induced power.

Fig 13 Fuel consumption versus load for a large transport airplane

traveling at a constant speed.

The increase in the angle of attack with increased load has a downside other than just theneed for more power. As shown in figure 9 a wing will eventually stall when the air can no

longer follow the upper surface. That is, when the critical angle is reached. Figure 14 shows the

angle of attack as a function of airspeed for a fixed load and for a 2-g turn. The angle of attack at

which the plane stalls is constant and is not a function of wing loading. The stall speed increasesas the square root of the load. Thus, increasing the load in a 2-g turn increases the speed at which

the wing will stall by 40%. An increase in altitude will further increase the angle of attack in a 2-g turn. This is why pilots practice "accelerated stalls" which illustrates that an airplane can stall

at any speed. For any speed there is a load that will induce a stall.

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Fig 14 Angle of attack versus speed

for straight and level flight and for a 2-g turn.

Wing vortices

One might ask what the downwash from a wing looks like. The downwash comes off the

wing as a sheet and is related to the details on the load distribution on the wing. Figure 15 shows,through condensation, the distribution of lift on an airplane during a high-g maneuver. From the

figure one can see that the distribution of load changes from the root of the wing to the tip. Thus,the amount of air in the downwash must also change along the wing. The wing near the root is"scooping" up much more air than the tip. Since the root is diverting so much air the net effect is

that the downwash sheet will begin to curl outward around itself, just as the air bends around the

top of the wing because of the change in the velocity of the air. This is the wing vortex. Thetightness of the curling of the wing vortex is proportional to the rate of change in lift along the

wing. At the wing tip the lift must rapidly become zero causing the tightest curl. This is the wing

tip vortex and is just a small (though often most visible) part of the wing vortex. Returning tofigure 6 one can clearly see the development of the wing vortices in the downwash as well as the

wing tip vortices.

Fig 15 Condensation showing the distribution of lift along a wing.

The wingtip vortices are also seen.

(from Patterns in the Sky, J.F. Campbell and J.R. Chambers, NASA SP-514.)

Winglets (those small vertical extensions on the tips of some wings) are used to improve

the efficiency of the wing by increasing the effective length of the wing. The lift of a normal

wing must go to zero at the tip because the bottom and the top communicate around the end. Thewinglets blocks this communication so the lift can extend farther out on the wing. Since the

efficiency of a wing increases with length, this gives increased efficiency. One caveat is that

winglet design is tricky and winglets can actually be detrimental if not properly designed.

Ground effect

Another common phenomenon that is misunderstood is that of ground effect. That is theincreased efficiency of a wing when flying within a wing length of the ground. A low-wing

airplane will experience a reduction in drag by 50% just before it touches down. There is a great

deal of confusion about ground effect. Many pilots (and the FAA VFR Exam-O-Gram No. 47)

mistakenly believe that ground effect is the result of air being compressed between the wing andthe ground.

To understand ground effect it is necessary to have an understanding of upwash. For the

pressures involved in low speed flight, air is considered to be non-compressible. When the air isaccelerated over the top of the wing and down, it must be replaced. So some air must shift

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around the wing (below and forward, and then up) to compensate, similar to the flow of water

around a canoe paddle when rowing. This is the cause of upwash.As stated earlier, upwash is accelerating air in the wrong direction for lift. Thus a greater

amount of downwash is necessary to compensate for the upwash as well as to provide the

necessary lift. Thus more work is done and more power required. Near the ground the upwash is

reduced because the ground inhibits the circulation of the air under the wing. So less downwashis necessary to provide the lift. The angle of attack is reduced and so is the induced power,

making the wing more efficient.Earlier, we estimated that a Cessna 172 flying at 110 knots must divert about 2.5 ton/sec

to provide lift. In our calculations we neglected the upwash. From the magnitude of ground

effect, it is clear that the amount of air diverted is probably more like 5 ton/sec.

Conclusions

Let us review what we have learned and get some idea of how the physical description has given

us a greater ability to understand flight. First what have we learned:

The amount of air diverted by the wing is proportional to the speed of the wing and theair density.

The vertical velocity of the diverted air is proportional to the speed of the wing and the

angle of attack.

The lift is proportional to the amount of air diverted times the vertical velocity of the air. The power needed for lift is proportional to the lift times the vertical velocity of the air.

Now let us look at some situations from the physical point of view and from the perspective of

the popular explanation.

The planes speed is reduced . The physical view says that the amount of air diverted is

reduced so the angle of attack is increased to compensate. The power needed for lift is

also increased. The popular explanation cannot address this.

The load of the plane is increased . The physical view says that the amount of air diverted

is the same but the angle of attack must be increased to give additional lift. The power

needed for lift has also increased. Again, the popular explanation cannot address this.

A plane flies upside down . The physical view has no problem with this. The plane adjusts

the angle of attack of the inverted wing to give the desired lift. The popular explanationimplies that inverted flight is impossible.

As one can see, the popular explanation, which fixates on the shape of the wing, may satisfymany but it does not give one the tools to really understand flight. The physical description of lift

is easy to understand and much more powerful.

Chapter 1 - Structure of an Airplane

At the end of this block of study, you should be able to:Label the parts of an airplane.

Describe the five types of stress which act on an aircraft in flight and give an example of

where each applies to an airplane.Describe both truss and semimonocoque types of fuselages.

Describe the basic structure of a wing.

Explain the structure and function of the empennage.Identify the three types of landing gear.

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Most aircraft are composed of the fuselage (body), wings, empennage (tail assembly),

landing gear, and power plant (see figure 1-1). Locate these parts in the diagram as they are

discussed.

Sections in this Chapter:

Section 1.1 - THE FUSELAGE STRUCTURE

Section 1.2 - WINGS

Section 1.3 -EMPENNAGE

Section 1.4 -LANDING GEAR

Section 1.5 -POWER PLANT

Section 1.6 -REVIEW EXERCISE

Section 1.1 - The Fuselage Structure

The word fuselage is based on the French word fuseler, which means "to streamline."

The fuselage must be strong and streamlined since it must withstand the forces that are created in

flight. It houses the flight crew, passengers, and cargo.

Fuselages are classified according to the arrangement of their force-resisting structure.The types of fuselages we will study are the truss and the semimonocoque. Five types of stress

act on an aircraft in flight: tension, compression, bending, shear, and torsion. Let's look at each

one individually

Tension:

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Tension is the stress which tends to pull things apart. When you try to break a length

of rope, you exert a type of stress which is called tension. (see animation or figure 1-2a)

Compression:

Compression is the opposite of tension.It is the stress which tends to push materials

together. When you grasp a football at both endsand push, the ball is subject to compression. The

landing gear struts of an aircraft are also subject to

compression. (see animation or figure 1-2b)

Bending:

This type of stress combines tension and

compression. You put a bending stress on a bar

when you grasp it with both hands and push theends together or when you bend a paper clip. Thewing spars (interior structural members) are

subjected to bending while the aircraft is in flight.

The lower side of the spar is subjected to tension, while the upper side is subjected tocompression. Obviously, some materials will break before they bend and often are unacceptable

for aircraft construction. (see animation or figure 1-2c which shows the upper side as the tensile

side)

Shear:

Shear stress is caused by forces

tending to slip or slide one part of a materialin respect to another part. This is the stressthat is placed on a piece of wood clamped in a

vise and you Chip away at it with a hammer and

chisel. This type of stress is also exerted when

two pieces of metal, bolted together, are pulledapart by sliding one over the other or when you

sharpen a pencil with a knife. The rivets in an

aircraft are intended to carry only shear. Bolts, as a rule, carry only shear, but sometimes theycarry both shear and tension. (see animation or figure 1-2d)

Torsion: Torsion is the stress which tends to

distort by twisting. You produce a torsional

force when you tighten a nut on a bolt. The

aircraft engine exerts a torsional force on thecrankshaft or turbine axis.

All the members (or major portions) of

an aircraft are subjected to one or more of these stresses. Sometimes a member has alternatestresses, such as compression one instant and tension the next. Some members can carry only

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one type of stress. Wire and cables, for example, normally carry only tension.(see animation or

figure 1-2e)

Since any member is stronger in compression or tension than in bending, members carryend loads better than side loads. In order to do this,

designers arrange the members in the form of a truss, or

rigid framework (see figure 1-3). In order for a truss to be

rigid, it must be composed entirely of triangles. When theload on a truss acts in one direction, every alternate

member carries tension while the other members carrycompression. When the load is reversed, the members

which were carrying compression now are subjected to

tension and those which were carrying tension are under

compression. The truss itself consists of a welded tubularsteel structure with longerons (horizontal members) and

diagonal braces. These features make it rigid, strong, and

light.

The truss is covered with a metal or fabric cover so that less drag will be generated. Toproduce a smooth surface, the fabric cover is put on fairing strips, which are thin flat strips of

wood or metal. These fairing strips run the length of the fuselage in line with the direction of

flight.

The semimonocoque is the most often used construction for modern, high-performance

aircraft. Semimonocoque literally means half a single

shell. Here, internal braces as well as the skin itself carry

the stress (see figure 1-4). The internal braces includelongitudinal (lengthwise) members called stringers and

The semimonocoque structure is easier to

streamline than the truss structure. Since the skin of thesemimonocoque structure must carry much of the fuselage's

strength, it will be thicker in some places than at other

places. In other words, it will be thicker at those pointswhere the stress on it is the greatest.

Section 1.2 - The Wings

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Wing construction is basically the same in all types of aircraft. Most modern aircraft have

all metal wings, but many older aircraft had wood and fabric wings. Ailerons and flaps will bestudied later in this chapter.

To maintain its all-important aerodynamic shape, a wing must be designed and built to

hold its shape even under extreme stress. Basically, the wing is a framework composed chiefly

of spars, ribs, and (possibly) stringers (see figure 1-5). Spars are the main members of thewing. They extend lengthwise of the wing (crosswise of the fuselage). All the load carried by the

wing is ultimately taken by the spars. In flight, the force of the air acts against the skin. From the

skin, this force is transmitted to the ribs and then to the spars.Most wing structures have two spars, the front spar and the rear spar. The front spar is

found near the leading edge while the rear spar is about two-thirds the distance to the trailing

edge. Depending on the design of the flight loads, some of the all-metal wings have as many asfive spars. In addition to the main spars, there is a short structural member which is called an

aileron spar.

The ribs are the parts of a wing which support the covering and provide the airfoil shape.These ribs are called forming ribs. and their primary purpose is to provide shape. Some may have

an additional purpose of bearing flight stress, and these are called compression ribs.The most simple wing structures will be found on light civilian aircraft. High-stress types

of military aircraft will have the most complex and strongest wing structure.

Three systems are used to determine how wings are attached to the aircraft fuselagedepending on the strength of a wing's internal structure. The strongest wing structure is the full

cantilever which is attached directly to the fuselage and does not have any type of external,

stress-bearing structures. The semicantilever usually has one, or perhaps two, supporting wires orstruts attached to each wing and the fuselage. The externally braced wing is typical of the biplane

(two wings placed one above the other) with its struts and flying and landing wires (see figure 1-

6).

Section 1.3 - Empennage

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The empennage, commonly called the tail assembly (see figure 1-7), is the rearsection of the body of the airplane. Its main purpose is to give stability to the aircraft. Thefixed parts are the horizontal stabilizer and the vertical stabilizer or fin.

The front, fixed section is called the horizontal stabilizer and is used to prevent the airplanefrom pitching up or down.

The rear section is called the elevator and is usuallyhinged to the horizontal stabilizer. The elevator is a movable

airfoil that controls the up-and-down motion of theaircraft's nose.

The vertical tail structure is divided into the verticalstabilizer and the rudder. The front section is called the

vertical stabilizer and is used to prevent the aircraft from

yawing back and forth. The principle behind its operation is

much like the principle of a deep keel on a sailboat. In light,

single-engine aircraft, it also serves to offset the tendency ofthe aircraft to roll in the opposite direction in which the propeller is rotating.

The rear section of the vertical structure is the rudder. It is a movable airfoil that is used

to turn the aircraft.

Section 1.4 - Landing Gear

Airplanes require landing gear for taxiing, takeoff, and landing. The earliest airplane of

all--the Wright Flyer--used skids as its landing gear. Soon, wheels were attached to the skids.

Since that time, various arrangements have been used for wheels and structures to connect themto the airplane. Today, there are three common types of landing gear: conventional, tricycle,and tandem (see figure 1-8).

Conventional landing gear consists of two wheels forward of the aircraft's center ofgravity and a third small wheel at the tail. This type of landing gear is most often seen in older

general aviation airplanes. The two main wheels are fastened to the fuselage by struts. Without a

wheel at the nose of the plane, it easily pitches over if brakes are applied too soon. Because thetailwheel is castered--free to move in any direction--the plane is very difficult to control when

landing or taking off.

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The tricycle landing gear, as you can guess from its name, has three wheels--two main

wheels and a nosewheel (see figure 1-9). Thistype of landing gear makes the aircraft easier to

handle on the ground and it also makes landings

much safer. An aircraft equipped with tricycle

landing gear is less apt to pitch forward.The tandem landing gear is used for

very large aircraft like the B-52 bomber and theU-2 reconnaissance/research aircraft. The mainlanding gear is in two sets that are located one

behind the other on the fuselage. The tandem

landing gear allows the use of a highly flexiblewing, but it may also require the use of small

wheels on the tips of the wings to keep the wings from scraping the ground.

Section 1.6 - Review Exercise

1. Label the parts of the aircraft shown below.

A. B.

C. D.

E. F.

G. H.

I. J.

K. L.

M.

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2. Complete the chart of landing gear types by filling in the first column with the correct term:

conventional, tricycle, or tandem. Use the description to guide you.

A. Easiest for pilot to make a safe landing.

B. The landing gear is in two sets on the fuselage. Allows the

use of highly flexible wing.

C. Most difficult for pilot to control the plane. Used in earlier aircraft; would often pitch over.

3. Match the following statements with the BEST response. Choose the appropriate answer from

A. Structure on a wing that supports the skin and provides theairfoil shape.

B. The type of fuselage where the skin and internal braces carry

the flight stresses.C. Movable section of the horizontal stabilizer that pitches nose up

or down.

D. Type of stress that pulls things apart.

E. Vertical structure that prevents an airplane from rolling over.

F. Movement up and down, back and forth.

G. Type of stress which is caused by twisting.

H. Structure bearing the major part of the wing's load.

I. Body of a plane that must be strong and streamlined.

J. Strongest type of system for attaching the wings to the fuselage.

Chapter 2-Characteristics of the Flight Atmosphere

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At the end of this block of study, you should be able to:

Describe the composition of the atmosphere.

Describe why air has weight and how this is related toatmospheric pressure.

Describe how changes in air temperature affect

atmospheric pressure and density.

Define relative humidity.Convert temperatures between the Fahrenheit and

the Celsius scales.

The atmosphere is composed of a mixture of gases.Nitrogen is by far the largest component of air, accounting

for 78 percent; the next largest component is oxygen

which consists of 21 percent. The remainder consists ofsmall portions of other gases. All gases, regardless of

where they are found, have certain characteristics such as

weight, density, temperature, pressure, and mass. To

understand how an airplane flies within the atmosphere,you must first understand some of the features of the

atmosphere.

Sections in this Chapter:

Section 2.1 - WEIGHT

Section 2.2 -DENSITY

Section 2.3 -PRESSURE

Section 2.4 -HUMIDITY

Section 2.5 - TEMPERATURE

Section 2.6 -REVIEW EXERCISE

Section 2.1 - WEIGHT

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Because we cannot see air we may think of it as nothing, but you need only to stand in

front of a fan or pedal your bicycle into the wind to know that air has substance. Air has weightbecause it is matter and is attracted by the Earth's gravity. Weight is explained in Figure 2-1a.

Notice that the direction of the atmosphere's weight is toward Earth's center, which is thecenter of gravity. Refer to the 1 inch x 1 inch x 60 miles column of air shown in Figure 2-1a.

This column of air has a weight of 14.7 pounds. This is caused by gravity pulling all air

molecules within the column toward Earth's center with that many pounds of force. It is theweight of the air which produces atmospheric pressure.

Always remember that WEIGHT is in one direction, while PRESSURE is in all directions.

Mass:

Mass is the amount of material as shown in Figure 2-1b.

Section 2.2 - DENSITY

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Density is illustrated in Figure 2-2a and is the amount of material contained in a unit of

volume. Density is constant in solids because more material cannot be forced into a givenvolume of a solid. Solids will remain almost unchanged in density as long as the temperature

doesn't become high enough to cause the solids to melt or burn. With air, however, the story is

quite different.

Density: Amount of material PER UNIT VOLUME.

Figure 2-2a shows two small one-inch cubes on the right side. One of them weighs only

one pound, and the other, with tightly packed molecules, weighs ten pounds Although the

volume is the same, the weight is very different because the molecules are packed closertogether. The density of the air and the changes that temperature produce upon the density of air

play an important role in an aircraft's flight.

Temperature: ENERGY of motion.

Since air is a gas, it is free to expand or contract as its temperature changes. Notice inFigure 2-2b how the five molecules of air increase their range of motion with each 20-degree

increase in temperature. Since the molecules are not confined in a container, the air expands as

the temperature increases. This also means that the range of particle motion decreases with

decreases in temperature. Comparing the temperature and

density of a unit of air, you can see that as temperature

increases the density will decrease, and as the temperature

decreases the density increases. As you will understand later,this constantly changing air density is very significant to flight.

Section 2.3 - PRESSURE

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The atmosphere extends upward for hundreds of miles. The pull of the Earth's gravity on

air molecules (see figure 2-3a) creates a pressure that pushes in all directions and amounts to

about 14.7 pounds per square inch (psi) at sea level. This is air pressure on a standard day at sealevel. This pressure will support 29.92 inches of mercury in a barometer, which is the instrument

that provides the local atmospheric pressure that you hear on your daily television weather

bulletins.

As you know, pressure changes take place at Earth's surface as high- and low-pressurecells form and move across the surface. However, changes in atmospheric pressure occur for

aviators not only as they fly into or out of high- and low-pressure cells but also as they climb or

descend in their airplanes. This is because atmospheric pressure changes with altitude (higher

altitude - less pressure, lower altitude - more pressure).

Let us consider Earth's total atmosphere. We find that it extends from the surface outward

into what we call space. As we travel outward (upward) there is less pressure because there are

fewer air molecules above us. At 18,000 feet the pressure is about one-half as that at the surface.If we continue to travel outward, the pressure continues to reduce until there is no measurable

pressure and, for all practical purposes, we are in space. Few aviators are concerned with highaltitudes and consequent extreme low pressures, because the maximum operating altitude

(ceiling) for most small air planes is 20,000 feet or less. Even at the relatively low altitude of12,500 feet, pilots are required by regulation to breathe supplemental oxygen.

The factors of weight, density, temperature, and pressure of the atmosphere interact and

one does not change without affecting the others. However, temperature change is the main

reason the atmospheric pressure and density change. Let's look at how the temperature causesthese changes. To do this, we must use a starting point and the accepted starting point is known

as the standard atmosphere. The standard atmosphere is based on average conditions at 40 north

latitude where the average pressure is 29.92 inches of mercury and the average temperature is

59 Fahrenheit (F) or 15 Celsius (C).

Under standard conditions, temperature decreases about 2 C or 3.5 F. for each 1,000-

foot increase in altitude. Variations to this standard are common and the standard decrease is not

always found. For example, what is called a temperature inversion may actually cause anincrease rather than a decrease in temperature at some locations.

Section 2.4 - HUMIDITY

The air contains water vapor in addition to the gases we have mentioned. This will vary

from a very small amount up to a maximum of four or five percent. The air gets this moisture byevaporation from bodies of water and from vegetation. The capacity of air for holding water

vapor is directly related to the temperature of the air; the warmer the air, the more water vapor itcan hold. When the air contains all the vapor it can for its temperature and pressure, it is said to

be saturated. Weather forecasts provide us with the relative humidity which is the ratio ofamount of water vapor which a sample of air holds to the amount it can hold when

saturated (see figure 2-5). It may be surprising to you that water vapor (composed mainly of

hydrogen) is lighter than air (composed mainly of nitrogen). Thus, air which feels damp and

heavy is actually lighter than dry air. Its density is also less.

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Temperature: ENERGY of motion.

Temperature also changes horizontally as well as vertically in the atmosphere (see figure

2-2b). How much it changes in any direction is partially based on the extent to which Earth'ssurface area is exposed to the Sun, our primary source of heat. The Sun's rays penetrate the

atmosphere and heat Earth's surface, which in turn heats the atmosphere next to it. Atmospheric

temperature is based on the amount of heat absorbed or reflected by the Earth's surface. Sand,water, and forested surfaces differ in the amount of heat they absorb and reflect so the air over

them will be heated differently.

Pressure: Omnidirectional. FORCE of motion PER UNIT AREA.

The relationship of temperature to density and pressure can be confusing (see figure

2-3b). If a cubic foot of air on the Earth's surface is heated, the air will expand and rise in theatmosphere. This cubic foot of air may then occupy two cubic feet. Both its pressure and density

will have decreased. As the air rises and expands, the heat it contains is spread over a larger area,

and its temperature decreases with altitude. Also, as the air rises it receives less and less

additional heat from the Earth's surface.

Section 2.5 - TEMPERATURE

We have mentioned Fahrenheit and Celsius temperatures. The different figures result

merely from using different scales or units of measurement. The military services and scientistsusually use the Celsius scale, while civilian aviation primarily uses the Fahrenheit scale. The

Celsius scale runs from 0 for freezing to 100 for boiling water; these same events occur at 32

and 212 on the Fahrenheit scale. The average standard day temperature at sea level for most ofthe United States is 15 C and 59 F.

To convert from one to the other, you can use the appropriate formula:

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C = (F-32) x 5/9

F = (9/5 x C) + 32For example: 15C = (59F - 32) x 5/9

or

59F=(9/5 x 15C)+32

Section 2.6 - REVIEW EXERCISE

Choose the BEST option that completes the statement.

1. On the Celsius scale water boils at

2. 41 degrees F is equal to about

3. What percentage of the Earth's atmosphere is made up of oxygen?

4. As the altitude increases the atmospheric pressure

5. As the temperature of a parcel of air decreases, its density

6. As the temperature of a parcel of air increases, its pressure

7. Relative humidity is the measurement of the total percentage of water vapor in the air.

Chapter 3 - Principles of Flight - Level 2

At the end of this block of study, you should be able to:

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Define airfoil, camber, and chord.

Identify the parts of an airfoil.Describe Bernoulli's principle and tell how it relates to lift on an airfoil.

Define relative wind, angle of incidence, and angle of attack.

Aeronautics is

the term applied to the

flight of an aircraft throughthe atmosphere. As

defined in Webster's NewCollegiate Dictionary,

aeronautics is "the science

dealing with the operation of

aircraft" or "the art or science offlight." We will begin the study of aeronautics in this section by discussing airfoils, relative

wind, angle of attack, and the four forces of flight. these are the basics of aeronautics.

Sections in this Chapter:

Section 3.1 -AIRFOILS

Section 3.2 -BERNOULLI'S PRINCIPLE

Section 3.3 -RELATIVE WIND

Section 3.4 -REVIEW EXERCISE

Section 3.1 - AIRFOILS

An airfoil is any part of an airplane that is designed to produce lift. Those parts of

the airplane specifically designed to produce lift include the wing and the tail surface. In modernaircraft, the designers usually provide an airfoil shape to even the fuselage. A fuselage may not

produce much lift, and this lift may not be produced until the aircraft is flying relatively fast, but

every bit of lift helps.

Figure 3-1 shows a cross section of a wing, but it could be a tail surface or a propeller

because they are all essentially the same. Locate the leading edge, the trailing edge, the chord,

and the upper and lower camber on Figure 3-1.

The leading edge of an airfoil is the portion that meets the air first. The shape of theleading edge depends upon the function of the airfoil. If the airfoil is designed to operate at high

speed, its leading edge will be very sharp, as on most current fighter aircraft. If the airfoil is

designed to produce a greater amount of lift at a relatively low rate of speed, as in a Cessna 150or a Cherokee 140, the leading edge will be thick and fat. Actually, the supersonic fighter aircraft

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and the light propeller-driven aircraft are virtually two ends of a spectrum. Most other aircraft lie

between these two.

Trailing Edge:

The trailing edge is the back of the airfoil, the portion at which the airflow over the

upper surface joins the airflow over the lower surface. The design of this portion of the airfoil is

just as important as the design of the leading edge. This is because the air flowing over the upperand lower surfaces of the airfoil must be directed to meet with as little turbulence as possible,regardless of the position of the airfoil in the air.

Chord:

The chord of an airfoil is an imaginary straight line drawn through the airfoil from

its leading edge to its trailing edge. We might think of this chord line as the starting point fordrawing or designing an airfoil in cross section. It is from this baseline that we determine how

much upper or lower camber there is and how wide the wing is at any point along the wingspan.

The chord also provides a reference for certain other measurements as we shall see.

Camber:

The camber of an airfoil is the characteristic curve of its upper or lower surface . The

camber determines the airfoil's thickness. But, more important, the camber determines the

amount of lift that a wing produces as air flows around it. A high-speed, low-lift airfoil has verylittle camber. A low-speed, high-lift airfoil, like that on the Cessna 150, has a very pronounced

camber.

You may also encounter the terms upper camberand lower camber. Upper camber refers

to the curve of the upper surface of the airfoil, while lower camber refers to the curve of thelower surface of the airfoil. In the great majority of airfoils, upper and lower cambers differ from

one another.

Bernoullis Principle:

Daniel Bernoulli, an eighteenth-century Swiss scientist, discovered that as the velocity of

a fluid increases, its pressure decreases. How and why does this work, and what does it have to

do with aircraft in flight?Bernoulli's principle can be seen most easily through the use of a venturi tube (see

Animation or Figure 3-2). The venturi will be discussed again in the unit on propulsion systems,

since a venturi is an extremely important part of a carburetor. A venturi tube is simply a tube

which is narrower in the middle than it is at the ends. When the fluid passing through the tubereaches the narrow part, it speeds up. According to Bernoulli's principle, it then should exert less

pressure. Let's see how this works.

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As the fluid passes over the central part of

the tube, shown in Animation or Figure 3-2,more energy is used up as the molecules

accelerate. This leaves less energy to exert

pressure, and the pressure thus decreases. Oneway to describe this decrease in pressure is to

call it a differential pressure. This simply

means that the pressure at one point is differentfrom the pressure at another point. For thisreason, the principle is sometimes called

Bernoulli's Law of Pressure Differential.

Bernoulli's principle applies to any fluid, and since air is a fluid, it applies to air. The

camber of an airfoil causes an increase in the velocity of the air passing over the airfoil.

This results in a decrease in the pressure in the stream of air moving over the airfoil. This

decrease in pressure on the top of the airfoil causes lift.

Section 3.3 - RELATIVE WIND

In order to discuss how an airfoil produces lift or why it stalls, there are three terms we

must understand. These are relative

wind, angle of incidence, and angle of

attack.

There is a noticeable motion

when an object moves through a fluidor as a fluid moves around an object. If

a thick stick is moved through stillwater or the same stick is held still in a

moving creek, relative motion is produced. It does not matter whether the stick or the water ismoving. This relative motion has a speed and direction.

Now let's replace the water with air as our fluid and the stick with an airplane as our

object. Here again, it doesn't matter whether the airplane or the air is moving, there is a relative

motion called relative wind. The relative wind will be abbreviated with the initials RW (seefigure 3-3). Since an airplane is a rather large object, we will use a reference line to help in

explaining the effects of relative wind. This reference is the aircraft's longitudinal axis, an

imaginary line running from the center of the propeller, through the aircraft to the center of the

tail cone.

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Note in Figure 3-4 that the relative wind can theoretically be at any angle to the

longitudinal axis. However, to maintain controlled flight, the relative wind must be from adirection that will produce lift as it flows over the wing. The relative wind, therefore, is the

airflow produced by the aircraft moving through the air. The relative wind is in a direction

parallel with and opposite to the direction of flight.

Let's look a little closer at how relative wind affects an airplane and its wings. As shown

in Figure 3-3, the chord line of the wing is not parallel to the longitudinal axis of the

aircraft. The wing is attached so that there is an angle between the chord line and the

longitudinal axis. (We call this difference the angle of incidence.) Since we describe relative

wind (relative motion) as having velocity (speed and direction), the relative wind's direction forthe wing is different from that of the fuselage. It should be easy to see that the direction of the

relative wind can also be different for the other parts of the airplane.

Very briefly, angle of attack is a term used to express the relationship between an

airfoil's chord and the direction of its encounter with the relative wind. This angle can beeither positive, negative, or zero. When speaking of the angle of attack, we normally think of the

relative wind striking the airfoil from straight ahead. In practice, however, this is true only during

stabilized flight which is in a constant direction.

Section 3.4 - REVIEW EXERCISE

1. The part of an airplane that produces lift is called a(n) .

2. The baseline for designing an airfoil in cross section is determined from the

.

3. The amount of lift that a wing can produce is determined by the .

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4. Bernoulli's principle states that as the velocity of a fluid increases, its pressure

.

5. Lift is produced by the in pressure on top of an airfoil as the air

passing over the top of the airfoil is speeded up.

6. Name the parts of the airfoil shown by the arrows.

A.

B.

C.

D.

E.

F.

7. The relative wind is airflow produced by the moving through the air.

8. The relative wind flows in a direction with and to the

direction of flight.

9. The angle between the chord of the wing and the longitudinal axis of the aircraft is called

the

.

10. The is the angle between the chord of the

wing and the relative wind.

Chapter 4 - The four forces of flight - Level 2

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At the end of this block of study, you should be able to:

Define lift.State the relationship between airspeed, camber, angle of attack, and lift.

Give the four forces of flight and tell which of these forces oppose each other.

Describe maximum gross weight, empty weight, center of gravity, center of lift, and usefulload with relation to an airplane.

Define induced drag and parasite drag and give two examples of each.

Four forces of flight in balance.

Sections in this Chapter:

Section 4.1 -LIFT

Section 4.2 -AIRSPEED, CAMBER, AND LIFT

Section 4.3 -LIFT AND WEIGHT

Section 4.4 -DRAG

Section 4.5 -INDUCED DRAG

Section 4.6 -PARASITE DRAG

Section 4.7 -REVIEW EXERCISE

Section 4.1 - LIFT

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We know that we can cause reduced pressure in a fluid if the velocity of its flow is increased

(Based on Bernoulli's principle - section 3-2 ).

The camber of an airfoil's upper surface makes the

air flowing over it move faster than the air flowing

under the wing. This increase in velocity reduces

the pressure (P1>P2) on the top of the wing so lift is

produced. (See Figure 4-1).

Lift is also called airfoil lift or Bernoulli's lift.Lift will continue as long as the airfoil is moving

through the air and the air remains smooth rather than

turbulent.

Every airfoil, no matter what its camber or chord, willlose its smooth flow at some point along the upper

surface. The perfect airfoil, if there were such a thing,

would have turbulent flow at its trailing edge where thedivided airstream comes together again. The regular

airfoil has turbulence somewhere forward of the trailing

edge even though level flight is maintained. With every

increase in angle of attack (See Figure 4-2), thisturbulent flow moves farther and farther toward the

leading edge. The increase in angle of attack increases

lift. This is true up to a point because we also must consider the power needed to force the craftthrough the air. If we had unlimited power, angle of attack would be of no concern, but this is not

the normal situation so the turbulent flow continues forward until there is no more lift available.

Dynamic lift

It may interest you to know, at this point, that lift can also be created by an airfoil without any

camber at all.

This lift, however, is completely different from the lift we have been talking about. This

type of lift is called dynamic lift and is caused by the pressure of impact air against the

lower surface of the airfoil.A kite flying on a balmy spring day is an excellent example of an airfoil without camber being

sustained in flight by dynamic lift. Similar to the airfoil in the wind tunnel, it makes nodifference to the kite whether it is moving forward through the air or the air is moving past it. It

simply goes on and hangs up there in the spring sky. (If you have flown a kite, however, you

know there's a difference. You know that when the wind is light, you have to run your legs off attimes to get the kite airborne.)

This same kind of lift also helps hold the aircraft in the air and can be explained by Newton's

third law of motion.Newton's third law of motion states that for every action there is an equal and opposite

reaction. A popular example of this law is the gun and the bullet shown in Figure 4-3. When the

trigger is pulled and the gun fires, the bullet leaving the barrel is the action and the recoil of thegun is the reaction. If we can ignore friction and air resistance, the force of the bullet striking thewall and the force of the gun striking the opposite wall will be equal.

Section 4.2

AIRSPEED, CAMBER, AND LIFT

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The energy factors at the upper surface of a wing, as we have said, are velocity and pressurehigher velocity, lower pressure. If the velocity of the relative wind is normally very high during

cruising flight of an airplane, it is not necessary for its wings to have much camber. This is one

of the reasons why fighter-type military aircraft have thin wings. At slower speeds, such asduring takeoffs or landings, the loss of induced lift because of the low camber is compensated for

by using a high angle of attack. As you can see, this high angle of attack causes an increase in the

dynamic lift. Even so, the airplane with low-camber airfoils must use much higher takeoff andlanding speeds than the more conventional airplane.

To further illustrate these points, note in the top portion

of Figure 4-4 that we have two examples of airfoils with

the same relative wind velocity and the same dynamic lift.However, by thickening and increasing the camber of the

wing, wing B's total lift is increased because of the

increased induced lift.In the lower portion of Figure 4-4, you are looking at

two wings which are producing the same mount of total

lift even though one wing has less amber than the other.

Both wings are at the same angle of attack so they havethe same amount of dynamic lift for any given airspeed

(velocity of the relative wind). The only way to make the

thin wing produce as much lift as the thick wing is tospeed it up, and this is what we attempt to show in the

figure. Wing C's relative wind is ten miles per hour faster

than D's relative wind, this additional speed is needed toincrease both the dynamic and induced lift so that its total

lift can equal that of Wing D. We want you to understand

that the examples in Figure 4-4 are just that.We have discussed the atmosphere and how airfoils

produce lift because of their movement through theatmosphere. We also mentioned that lift is the force that

counteracts the force of gravity to allow flight. At thispoint, you may have concluded that lift and gravity are the

only forces involved with flight. Actually there are two

others, thrust and drag, which complete the three-dimensional forces acting upon an aircraft in flight. Figure

4-5 shows the basic directions of all four forces when an

aircraft is in straight and level flight at a constant speed.Now, you should be able to see that, in this situation, the

four forces are in balance. The force of total lift equals the

force of total weight, so there is no upward or downwardmovement. The force of thrust equals the force of drag, so

there is no increase or decrease in the speed of the

airplane. You should also be able to see that the moment one of these forces becomes stronger or

weaker than the others, some type of reaction must take place.

Section 4.3 - LIFT AND WEIGHT

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With these two forces in opposition to each other, it is obvious that increased lift and

decreased weight are objectives in both the designing and flying of aircraft.Induced lift can be increased, as has been mentioned before, by changing the camber, or

curvature, of the airfoil. Work continues in an effort to achieve the most efficient designs

possible. But more important, at least to the person who is flying an airplane, is the angle of the

airfoil as it encounters the relative wind (angle of attack). As indicated earlier, lift is increased asthe angle of attack is increased because there is more relative wind striking the airfoil's bottom

surface, creating higher pressure. There is also an increase in the induced lift, because at a higherangle of attack the air has to travel even farther over the top surface of the wing.

There is a point in this relationship of airfoil to angle of attack where lift is destroyed and the

force of gravity (weight) takes command. This is called stall. The air can no longer flow

smoothly over the wing's upper surface. Instead, the air burbles over the wing and lift is lost.You might wonder why the force of power from the engine can't take the place of the loss of lift

from the airfoil. Very simply, there just isn't enou