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Chapter 1 INTRODUCTION

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The most important factor for flying an aerial vehicle is the amount of lift generated. Again

the generation of lift depends on how much the flow is turned, which depends on the shape of

the object. In general, the lift is a very complex function of the shape. Thus optimising a

desired shape of aerofoil is a matter of great importance. This thesis involves such an

important topic and that is ―design of cambered aerofoil for unmanned aerial vehicle based on

subsonic wind tunnel test‖. The design of an Aerofoil usually starts with the definition of the

desired or required characteristics. These can be a certain range of lift coefficients, Reynolds

numbers, where the Aerofoil should perform best, moment coefficient, thickness, low drag,

high lift or any combination of such requirements. As there is no such an Aerofoil available,

which perfectly fits the desired conditions and fulfils all requirements, hence this effort was

attempted to design something new with improved performance.

The first section of this chapter provides with the description of aerofoil development, then

historical evolution and ends with a short description of aerofoil.

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1.1Aerofoil development

The earliest serious work on the development of Aerofoil sections began in the late 1800's.

Although it was known that flat plates would produce lift when set at an angle of incidence,

some suspected that shapes with curvature that more closely resembled bird wings would

produce more lift or do so more efficiently. H.F. Phillips patented a series of Aerofoil shapes

in 1884 after testing them in one of the earliest wind tunnels in which "artificial currents of

air (were) produced from induction by a steam jet in a wooden trunk or conduit." Octave

Chanute writes in 1893, ―It seems very desirable that further scientific experiments be made

on concavo-convex surfaces of varying shapes, for it is not impossible that the difference

between success and failure of a proposed flying machine will depend upon the sustaining

effect between a plane surface and one properly curved to get a maximum of 'lift'."

At nearly the same time Otto Lilienthal had similar ideas. After carefully measuring the

shapes of bird wings, he tested the Aerofoils shown here (reproduced from his 1894 book,

"Bird Flight as the Basis of Aviation") on a 7m diameter "whirling machine". Lilienthal

believed that the key to successful flight was wing curvature or camber. He also

experimented with different nose radii and thickness distributions.

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Fig 1.1: The earliest aerofoil design at last 19th century

Aerofoils used by the Wright Brothers closely resembled Lilienthal's sections: thin and highly

cambered. This was quite possibly because early tests of Aerofoil sections were done at

extremely low Reynolds number, where such sections behave much better than thicker ones.

The erroneous belief that efficient Aerofoils had to be thin and highly cambered was one

reason that some of the first airplanes were biplanes.

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A wide range of Aerofoils was developed, based primarily on trial and error Some of the more

successful sections such as the Clark Y and Gottingen 398 were used as the basis for a family of

sections tested by the NACA in the early 1920's.

Fig 1.2: Aerofoil variation before World War II

Unusual Aerofoil design constraints can sometimes arise, leading to some unconventional

shapes. The Aerofoil here was designed for an ultra light sailplane requiring very high

maximum lift coefficients with small pitching moments at high speed. One possible solution:

a variable geometry Aerofoil with flexible lower surface.

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1.2Historical evolution

A flat sheet makes a perfectly serviceable wing. That flat surfaces in the wind could produce

the sideways force that we now call lift was a very ancient observation. Two early

applications of it, the windmill and the fore-aft rigged sail, date back at least 800 years. It was

also perfectly evident to any thinking person that what kept birds and bats aloft were the large

flat surfaces attached to their arms. Neither the feathers of birds nor the fabric of sails and

windmill blades had any thickness to speak of, and so the earliest lifting surfaces were just

that: surfaces.

Thin surfaces restrained by a supporting structure naturally bellied out under air pressure,

assuming what we now call a "cambered" -- that is, arched -- shape. The fact that camber was

actually beneficial seems first to have been appreciated -- at least in writing -- by an English

civil engineer of the 18th century, John Smeaton, who noted that curving the surfaces of

their blades improved the performance of windmills.

For the next century and a half, nothing noteworthy occurred -- other than the invention of

the modern airplane, in 1804, by another Englishman, George Cayley.

When we arrive at the beginning of the 20th century, we find the Wrights conducting

systematic wind tunnel experiments to determine not only the best amount of camber to use,

but also the best fore-and-aft distribution of curvature. The Brazilian Santos-Dumont, whose

1906 Paris flights in his huge 14-bis ("Number 14 encore") are considered by some to have

been the first true powered flights because his airplane rolled and rose under its own power

(the Wrights employed a catapult and rail to get airborne in 1903), used very little camber,

perhaps because he knew that it made an airplane want to dive. On the other hand, the wings

of the Bleriot 11 that made the first aerial crossing of the English Channel had a great deal

more camber than they needed.

A number of early airplanes had sail-like wings, consisting of a single skin sewn to spars and

ribs. Such a wing lent itself to wing-warping, which was the earliest form of roll control.

Once ailerons appeared, wings had to be made rigid. By the time the First World War began,

well-streamlined biplanes of rather good performance were the rule; their wings had smooth

top and bottom surfaces with the structure hidden inside. Their cross-sections scarcely

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deserved the name of Aerofoils, however. They were actually just eel-like shapes, rounded at

the front and tapered more or less to a point at the back, and thickened just enough to envelop

the necessary internal structure.

Despite the random and ad hoc quality of these early Aerofoil designs, efforts were being

made to sort out the wheat from the chaff in wind tunnels. At first, unfortunately,

investigators did not recognize the importance of scale. They tested very small models at very

low speeds, and, because speed and size actually play important roles in the behaviour of

flowing air, their results supported the mistaken guess that thin Aerofoils were superior.

By 1917 the gray eminence of German aerodynamic research, Ludwig Prandtl, had a wind tunnel at

Göttingen large enough to allow testing of full-scale Aerofoil sections at realistic speeds. He also had

a mathematical method of creating Aerofoil-like curves. He quickly discovered the superiority of

thick sections, whose larger leading-edge radii allowed them to reach higher angles of attack, and

thus to produce more lift before stalling, than thin ones could. The long-held belief that thicker

sections must have greater drag also proved to be false. Anthony Fokker immediately adopted thick

Aerofoils for the triplane of Red Baron fame. The British and French builders persisted with their thin

Aerofoils through the end of the war, but then abandoned them.

The Wright brothers had done some of the earliest research on the most effective curvature,

or camber, of a wing, known as an Aerofoil. But during the early years of powered flight,

Aerofoils for aircraft were essentially hand-built for each airplane. Before World War I, there

had been little research to develop a standardized Aerofoil section for use on more than one

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aircraft. The British government had performed some work at the National Physical

Laboratory (NPL) that led to a series of Royal Aircraft Factory (RAF—not to be confused

with the Royal Air Force) Aerofoils. Aerofoils such as the RAF 6 were used on World War I

airplanes. Most American airplanes used either RAF sections or a shape designed by

Frenchman Alexandre Gustave Eiffel (best known for designing the Eiffel Tower).

The mean camber line shown in this illustration is the line that is equidistant at all points

between the upper and lower surfaces of the Aerofoil.

When the National Advisory Committee on Aeronautics (NACA) was established in 1915, its

members immediately recognized the need for better Aerofoils. The first NACA Annual

Report stated the need for "the evolution of more efficient wing sections of practical form,

embodying suitable dimensions for an economical structure, with moderate travel of the

centre of pressure and still affording a large angle of attack combined with efficient action."

NACA explained its first work with Aerofoils in 1917 NACA Technical Report No. 18,

"Aerofoils and Aerofoil Structural Combinations." The authors noted that mathematical

theory had not yet been applied to Aerofoil design and most of their work was trial and error.

They had tested a number of brass Aerofoil models with a span of 18 inches and a chord (or

maximum width) of 3 inches in a wind tunnel. With this report, they introduced the U.S.A.

series of Aerofoils and reported wind tunnel data for the U.S.A. 1 through U.S.A. 6 sections.

The authors stated that slight variations in Aerofoil design resulted in large differences in

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aerodynamic performance, a fact that required extensive and careful research in order to

obtain the best possible performance from an Aerofoil.

In 1933, NACA issued its monumental Technical Report No. 460, "The Characteristics of 78

Related Aerofoil Sections from Tests in the Variable-Density Wind Tunnel." The authors of

this report described the NACA four-digit Aerofoil series. The four digits defined the overall

shape of the Aerofoil. For instance, NACA Aerofoil 2412 had a maximum camber of 2

percent of the length of the chord, represented by the first digit; the maximum camber

occurred at a distance of 0.4 chord (or 4/10 or 40 percent) from the leading edge, indicated by

the second digit; and the maximum thickness of the Aerofoil was 12 percent (0.12) of the

overall width (or chord length) of the wing, represented by the last two digits. So if Aerofoil

2412 has a chord length of 10 feet, its maximum camber would be (0.02)10 = 0.2 feet; the

maximum camber would be located 40 percent (0.4) away from the leading edge – (0.4)10 =

4 feet; and the maximum thickness of the Aerofoil would be 0.12(10) = 1.2 feet.

Not all 78 Aerofoil sections would necessarily be used by airplane designers, but the testing

data gave aircraft manufacturers a wide selection. After this report was published, the NACA

Aerofoils became widely used, and the NACA 2412 continued in use on some light airplanes

more than half a century later.

NACA Technical Report 460 represented a major contribution to the development of the

Aerofoil. The information in the report eventually found its way into the designs of many

U.S. aircraft of the time, including a number of important aircraft during World War II. The

DC-3 transport, the B-17 Flying Fortress bomber, and the twin-tailed P-38 Lightning

interceptor airplane all relied upon the Aerofoil information in Report 460.

During the 1930s the U.S. National Advisory Committee for Aeronautics, or NACA,

developed and tested "families" of Aerofoils. Some of the most successful of these were the

NACA four-digit and five-digit series, which consisted of a "basic thickness form" -- a

symmetrical "teardrop" shape-superimposed on a "camber line" from which the profile

derived most of its aerodynamic characteristics, such as the amount of lift it produced at an

angle of attack of zero, and the strength of the "pitching moment" or diving tendency that

camber tended to produce. Many of those sections are still in use today and NACA's 23000

series, created in 1935, is probably the most widely used Aerofoil in history.

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Despite all the highly technical theoretical work done by NACA, there continued to be a

parallel tradition of what might be called barefoot Aerofoil design. It grew out of the

recognition that the Aerofoils on real wings, many of which were still skinned with fabric at

the time, did not bear much resemblance to idealized wind tunnel models. In practice,

anything that looked like an Aerofoil worked like an Aerofoil. The finest flower of the

barefoot school was the Clark Y, a 1922 invention of a Colonel Virginius Clark, who arrived

at it by the highly unscientific expedient of deforming one of the wartime Göttingen

Aerofoils to make the aft 70 percent of its bottom flat. The flat bottom turned out to be a very

attractive feature. It facilitated construction (especially for modellers, who flocked to the

Clark Y because it allowed them to make a wing straight by simply pinning it down to a flat

surface while the glue dried) and measurement of angle of attack, and it simplified the

carving of propeller blades. In spite of its possessing no special aerodynamic merit, the Clark

Y has been used in a great variety of airplanes.

By 1940, Aerofoil development had passed three milestones -- or at least what I think of as

milestones. The first was the general recognition, not due to any single investigator, that

camber aided the production of lift, and that if an Aerofoil had more than negligible thickness

it needed to be rounded in the front and somewhat sharp in the back. The next was the

discovery, due to Prandtl, that thickness -- meaning thickness greater than, say, a tenth of the

chord length -- was beneficial. The third milestone was the systematization of profiles --

largely the work of a NACA Langley researcher named Eastman Jacobs -- into "families"

with well-documented characteristics, which allowed designers to select suitable sections

from a catalogue. (By the way, the words "Aerofoil," "profile" and "section" are

synonymous)

The fourth milestone was a revolution in the relationship between mathematics and Aerofoil

design. From the early days, various kind of mathematical functions had been used to

generate Aerofoil shapes. But these procedures were not based on the physics of fluid flow;

they were just equations that happened to produce smoothly curved lines that looked like

Aerofoils. In 1931, another NACA aerodynamicist, Theodore Theodorsen, invented a

mathematical method of calculating the pressure distribution on any Aerofoil. The pressure

distribution is very important; it is the key to the Aerofoil's drag, lift and stalling behaviour.

Theodorsen was a confident fellow. When his calculated results did not precisely coincide

with wind-tunnel measurements, he airily dismissed the empirical results as unreliable.

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Relations between Theodorsen and the experimentalist Eastman Jacobs were prickly, and

when Jacobs, playing against type, proposed reversing Theodorsen's method in order to

obtain an Aerofoil shape that would generate a desired pressure distribution, Theodorsen

dismissed the idea as mathematically nonsensical. Jacobs persisted, however, and he

succeeded in creating the procedure used to design profiles in digital computers today.

The first fruit of Jacobs' work was the natural laminar flow Aerofoil. (Natural, in this context,

means that no powered method, such as boundary-layer suction, is used to maintain laminar

flow.) His work was based on the knowledge that the behaviour of the boundary layer -- the

thin layer of air, close to the Aerofoil surface, that the airplane drags along with it -- is

influenced by the pressure distribution. A laminar boundary layer, in which all air particles

follow paths parallel to the Aerofoil surface, could be sustained along the front of an

Aerofoil, as its upper and lower surfaces grew farther apart. But when the surfaces began to

converge, tiny turbulent eddies and vortices would appear in the boundary layer. The drag of

a laminar boundary layer is much less than that of a turbulent one. All Aerofoils have some

laminar flow, but the new family of laminar profiles developed by the NACA extended the

laminar boundary layer to as much as 60 percent of the Aerofoil's length, reducing drag by as

much as two-thirds.

As John Anderson notes in his History of Aerodynamics, the laminar Aerofoils, first used on

the P-51 Mustang, were successful in reducing drag in the wind tunnel but less successful in

the field because the irregularities of practical metal construction, along with general wear-

and-tear and unavoidable bug splatter, would disrupt the temperamental laminar boundary

layer. Yet they proved to be successful in an unexpected way; laminar-flow sections, with

their maximum thickness far aft, turned out to be well-suited for high-speed airplanes,

because they were less prone to early formation of transonic shock waves. Anderson might

have added that they had some success, even in the field and on low-speed airplanes, when

composite wings came into use. A high-performance sailplane with a non-laminar Aerofoil is

unthinkable today.

The fifth milestone in Aerofoil evolution comes with the development of foils especially

designed for flight below, but close to, the speed of sound. These so-called supercritical

Aerofoils have thick noses, flattish tops and aft camber, all characteristics designed to delay

the onset of shock waves due to local supersonic flow.

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You might suppose that supersonic Aerofoils would represent yet another great advance, but

in fact they are not Aerofoils in the normal sense at all. The laws of supersonic flight are

entirely different from those of subsonic flight, and purely supersonic wing sections dispense

with sophisticated camber and thickness distribution; a flattened diamond shape, or even, as

on the stabilizing surfaces of the X-15, a triangle with a bluff aft end, is sufficient. A knife

blade is as good a supersonic wing as anything else. The wings of supersonic airplanes do, in

fact, still have Aerofoils -- generally very thin ones -- but that is only because they take off

and land at subsonic speed.

In the late 1930s, the NACA performed more research on Aerofoils with the goal of

increasing maximum lift. This resulted in the NACA five-digit Aerofoil series and Aerofoils

such as the 23012, which is used on the Beech craft Bonanza aircraft. The first digit and the

last two digits in this series designate camber and thickness as in the four-digit series.

However, the second digit indicates twentieths of a chord rather than tenths as in the four-

digit series (3/20 in this example). And the middle digit is used to indicate either a straight

mean camber line (0) or a curved mean camber line (1). (The mean camber line is the line

that is equidistant at all points between the upper and lower surfaces of the Aerofoil. It is also

referred to as the "mean line.")

One of the problems with the NACA Aerofoil research performed up until the late 1930s was

that aerodynamicists could not test an entire wing section. They did not have a wind tunnel

big enough to mount an entire wing and so they tested only a part of the wing and then

extrapolated the data to a full wing. But the problem with this approach was that the

researchers could not determine the effects of the airflow at the tip of the wing, which was

often quite important to understanding its overall performance.

This changed in 1939 when the NACA constructed a new low-turbulence two-dimensional

wind tunnel at Langley Research Centre in Virginia. This wind tunnel was exclusively

dedicated to Aerofoil testing. Once it was constructed, NACA aerodynamicists conducted a

huge number of tests in the wind tunnel on a wide range of Aerofoil designs.

By the end of the 1930s, NACA aerodynamicists had turned their attention to laminar-flow

Aerofoils (laminar flow relates to the smooth flow of air over a structure). The laminar-flow

Aerofoils (NACA's six series) were shaped with their maximum thickness far back from the

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leading edge. The first aircraft to use the laminar-flow Aerofoils for their low-drag qualities

was North American's P-51 Mustang, and they are still used quite extensively today on many

high-speed aircraft. Although, in most cases, when used in actual flight outside of the wind

tunnel, these Aerofoils behaved much like traditional Aerofoils, they proved to have excellent

high-speed characteristics—an unexpected but welcome result.

The North American XP-51 Mustang was the first aircraft to incorporate a NACA laminar-

flow Aerofoil. It was used extensively during World War II.

NACA Aerofoil development was virtually halted in 1950 as the aerodynamicists switched

their attention to supersonic and hypersonic aerodynamics. But in 1965, Richard T.

Whitcomb developed the NASA supercritical Aerofoil. This was a revolutionary

development, for it allowed the design of wings with high critical Mach numbers, which can

operate at high speeds.

After Whitcomb's breakthrough, the National Aeronautics and Space Administration

(NASA), which was created in 1958 and absorbed the NACA, revived U.S. Aerofoil

research? It developed a low-speed Aerofoil series for use by general aviation on light

airplanes. These low-speed Aerofoils, designated LS (1), LS (2), and so on, have better lifting

characteristics than their predecessors and allow smaller wing areas—and hence less drag—

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for small private aircraft. But it is not uncommon to find aircraft in operation today that still

use the NACA four-digit and five-digit Aerofoil sections developed in the 1930s and 1940s.

In 1939, Eastman Jacobs at the NACA in Langley, designed and tested the first laminar flow

Aerofoil sections. These shapes had extremely low drag and the section shown here achieved

a lift to drag ratio of about 300.

A modern laminar flow section, used on sailplanes, illustrates that the concept is practical for

some applications. It was not thought to be practical for many years after Jacobs

demonstrated it in the wind tunnel. Even now, the utility of the concept is not wholly

accepted and the "Laminar Flow True-Believers Club" meets each year at the homebuilt

aircraft fly-in.

One of the reasons that modern Aerofoils look quite different from one another and designers

have not settled on the one best Aerofoil is that the flow conditions and design goals change

from one application to the next. On the right are some Aerofoils designed for low Reynolds

numbers.

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At very low Reynolds numbers (<10,000 based on chord length) efficient Aerofoil sections

can look rather peculiar as suggested by the sketch of a dragonfly wing. The thin, highly

cambered pigeon wing is similar to Lilienthal's designs. The Eppler 193 is a good section for

model airplanes. The Lissaman 7769 was designed for human-powered aircraft.

Unusual Aerofoil design constraints can sometimes arise, leading to some unconventional

shapes. The Aerofoil here was designed for an ultra light sailplane requiring very high

maximum lift coefficients with small pitching moments at high speed. One possible solution:

a variable geometry Aerofoil with flexible lower surface.

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The Aerofoil used on the Solar Challenger, an aircraft that flew across the English Channel

on solar power, was designed with a totally flat upper surface so that solar cells could be

easily mounted.

The wide range of operating conditions and constraints, generally makes the use of an

existing, "catalogue" section, not best. These days‘ Aerofoils are usually designed especially

for their intended application. The remaining parts of this chapter describe the basic ideas

behind how this is done.

.

Today, it is routine to custom-design the Aerofoils for each new airplane on a computer. In a

way, as Anderson remarks, Aerofoil design has come full circle. In the early years, each new

airplane might get a new Aerofoil. The same is true today-but today we no longer design new

Aerofoils in ignorance of how they work.

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CHAPTER 2

AEROFOIL THEORY

2.1 Aerofoil

An Aerofoil (in American English) or aerofoil (in British English) is the shape of a wing or

blade (of a propeller, rotor or turbine) or sail as seen in cross-section.

An Aerofoil-shaped body moved through a fluid produces an aerodynamic force. The

component of this force perpendicular to the direction of motion is called lift. The component

parallel to the direction of motion is called drag. Subsonic flight Aerofoils have a

characteristic shape with a rounded leading edge, followed by a sharp trailing edge, often

with asymmetric camber. Foils of similar function designed with water as the working fluid

are called hydrofoils.

The lift on an Aerofoil is primarily the result of its angle of attack and shape. When oriented

at a suitable angle, the Aerofoil deflects the oncoming air, resulting in a force on the Aerofoil

in the direction opposite to the deflection. This force is known as aerodynamic force and can

be resolved into two components: Lift and drag. Most foil shapes require a positive angle of

attack to generate lift, but cambered Aerofoils can generate lift at zero angle of attack. This

"turning" of the air in the vicinity of the Aerofoil creates curved streamlines which results in

lower pressure on one side and higher pressure on the other. This pressure difference is

accompanied by a velocity difference, via Bernoulli's principle, so the resulting flow field

about the Aerofoil has a higher average velocity on the upper surface than on the lower

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surface. The lift force can be related directly to the average top/bottom velocity difference

without computing the pressure by using the concept of circulation and the Kutta-Joukowski

theorem.

2.2 Aerofoil Design Characteristics

An Aerofoil is essentially a wing. While all Aerofoils share characteristics, not all of them are

used for flight. Some use the characteristics to have other aerodynamic effects. The primary

characteristic of the Aerofoil is a curve that causes a differential in air pressure on one side of

the Aerofoil.

Purpose

All Aerofoils are designed to affect the air and subsequently affect the car, boat,

airplane or other object they're attached to. Airplanes don't just use them for vertical

lift; they use them to navigate right and left and sometimes as stabilizers. Race cars

often employ an upside down wing. These foils press toward the ground, snugging the

car tight to the ground, improving traction. As with all Aerofoils, deign challenge is to

create an Aerofoil that will create adequate pressure differential while minimizing

drag, the pressure required to push the foil through the air.

Curve

Aerofoils are more complex than a flat plane angled in a direction to create deflection.

The foil or wing is curved. One side of the wing has a slightly exaggerated curve

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making it a longer distance from the leading edge of the foil to the trailing edge than

the other side of the foil.

Pressure Differential

This differential in distance causes a differential in pressure as air passes over each

side of the foil. Imagine still air hitting the leading edge of the foil at high speed. The

air wants to pass around the foil. The density of air on the longer plane of the foil

stretches out and speeds up the way water speeds through a garden hose nozzle. The

air on the shorter side creates an eddy. Pressure builds and it creates lift.

Leading Edge

Nearly all air foils have a sharp trailing edge and a relatively gentle radius on the

leading edge. This edge causes less disruption as the foil moves through the air,

letting air move around it gently with as little drag as possible. Imagine the difference

between a sharp-edged scraper moving across a surface and a smooth, rounded

surface. The rounded surface doesn't cut into the air the way a sharper edge would.

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2.3 Types

The cross-sectional shape or profile that is obtained by the intersection of an airplane wing

with a perpendicular plane is known as an Aerofoil. Aerofoils are of different shapes are sizes

depending on the specifications and configuration of the intended aircraft.

There are three basic types of Aerofoils.

1. Semi-symmetrical Aerofoils

2. Symmetrical Aerofoils

3. Flat Bottom Aerofoils

Fig 2.1: Three Basic types of Aerofoils

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2.4 Aerofoil terminology:

An Airfoil (in American English) or aerofoil (in British English) is the shape of a wing or

blade (of a propeller, rotor or turbine) or sail as seen in cross-section. Subsonic flight

Aerofoils have a characteristic shape with a rounded leading edge, followed by a sharp

trailing edge, often with asymmetric camber.

Figure 2.2: Aerofoil geometry

The various terms related to aerofoil:

The mean chamber line is the line drawn midway between upper and lower surface.

The most forward and rearward points of mean camber line are leading and trailing

edges respectively.

The straight line connecting the leading and trailing edges is the chord line of the

aerofoil.

The chord is the length of chord line.

Camber is the asymmetry between the top and the bottom surfaces of an aerofoil.

The thickness is the distance between upper and lower surface and measured

perpendicular to the chord line.

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2.5 Aerodynamic Forces

The aerodynamic forces acting on a body may be described by lift, drag and pitching moment.

Lift is the net vertical force and drag is the net horizontal force with respect to the direction of

the motion. The pitching moment reflects the tendency of the Aerofoil to pitch about a given

reference point. These quantities are derived from the normal force and axial force acting on

the Aerofoil by trigonometric relations (Eq. (1)).

FL Ncos𝛼 Asin𝛼

FD Acos𝛼 Nsin𝛼 (1)

The normal force (N) is defined as the force perpendicular to the Aerofoil chord and the axial

force (A) is the force acting parallel to the chord. It can be seen in these equations that the lift

force (FL) and the drag force (FD) are both derived from the same normal and axial force.

However, the angle of attack (α) determines how much of the normal and axial forces transfer

into lift and how much into drag. The pitching moment may be expressed by an integral of the

net moments acting on the Aerofoil (Eq. (2)).

M= 𝑑𝑀𝑈𝑇𝐸

𝐿𝐸 + 𝑑𝑀𝐿

𝑇𝐸

𝐿𝐸 (2)

In this equation, the differential moments are taken with respect to a given reference and then

integrated from the leading edge to the trailing edge. A graphical representation of these forces

is shown in Figure 2.3.

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Figure 2.3: Aerodynamic forces

2.6 Low-Speed Aerodynamics

In low-speed flows, where the free stream velocity is well under Mach 0.3, several

idealizations may be applied to simplify fluid dynamics analysis. One such idealization was

that the air density was assumed constant since it varies by only a few percent from speeds of

0 to 300 mph. This idealization is known as incompressible flow. Another idealization,

inviscid flow, was made by neglecting viscous effects such as friction, thermal conduction and

diffusion. Such effects are known to be minimal for low-speed air flow and this idealization is

well supported by current theory. The flow was assumed to be steady, and the body forces

acting on the working fluid were assumed to be minor compared to dynamic effects. These

idealized conditions are sufficient to allow the use of Bernoulli‘s equation, (Eq. (3)), in low-

speed flow analysis.

Bernoulli‘s equation may also be derived from the momentum equation by

considering a differential control volume and applying the assumptions made previously. The

resulting equation shows that the sum of the local pressure (p) and dynamic pressure (Eq. (4))

are constant throughout a given flow. From this equation, the local velocities may be

computed from knowledge of upstream data and local pressure so that all of the flow

characteristics may be obtained.

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P + 1

2𝜌𝑉∞

2 = constant = P + 𝑞∞ (3)

𝑞∞ = 1

2𝜌𝑉∞

2 (4)

Effects of the wind tunnel walls may be ignored by applying the inviscid flow approximation.

By doing so, the flow may be assumed to be uniform except over the Aerofoil. Uniform flow

simplifies control volume analysis, and allows the consideration of a full length Aerofoil as a

2D profile. The assumption of uniform flow is justified due to the smooth wind tunnel walls,

the filtered flow, and the controlled entry flow into the test section.

2.7 Characterizing Aerofoil Performance

Aerofoil performance may be characterized by quantities such as the lift, drag or pitching

moment produced under different operating conditions. These aerodynamic forces are often

computed from the total pressure over the planform area, and then normalized by the dynamic

pressure in order to produce non-dimensional quantities. For example, the lift coefficient may

be expressed as (Eq. (5)). The drag and normal force coefficients may also be expressed in a

similar manner as (Eq. (6)) and (Eq. (7)). The pitching moment must also be normalized by

the chord length in order to produce a non dimensional moment coefficient (Eq. (8)).

𝐶𝐿 ≡𝐹𝐿

12𝜌∞𝑉∞

2 𝐴 (5)

𝐶𝐷 ≡𝐹𝐷

12𝜌∞𝑉∞

2 𝐴 (6)

𝐶𝑁 ≡𝐹𝑁

12𝜌∞𝑉∞

2 𝐴=

𝑃

𝑞∞ (7)

𝐶𝑀 ≡ ∆𝑃(𝑥)dc

𝑞∞𝑐 =

𝑀12𝜌∞𝑉∞

2 𝐴𝑐 (8)

These non-dimensional quantities are functions of the Reynolds number and the angle of

attack. The Reynolds influence may be seen by the inclusion of the density (𝜌∞) and velocity

(𝑉∞) terms. While the angle of attack (aoa) influences is implied through the force, moment

24

and area terms. Thus to in order appreciate the full range of responses of a given Aerofoil, it is

necessary to consider a range of Reynolds numbers and angles of attack. Variation in the

Reynolds number produces different lift curves, while variations in the angle of attack will

alter the lift-drag ratio.

25

CHAPTER 3

WIND TUNNEL THEORY

_________________________________________

3.1 Calibration of the Tunnel:

A suitable initial experiment to perform with the tunnel is to survey the velocity at the inlet to

the working section. This allows students to become familiar with the operation of the tunnel

and yield useful data for further work.

The velocity is surveyed at:

1. The working section centre line to establish a reference velocity.

2. Various distances from the floor to the ceiling of the working section to check

the uniformity of the velocity and show the height of the boundary layer.

3. Various planes along the length of the working section.

The pilot tube static wall tapping measure the stagnation pressure and the static

pressure at the wall. Referring to Bernoulli‘s equation, the difference between the stagnation

and static pressure are connected to each limb of either one of the manometers provided on

the Control and Instrumentation Frame.

26

The velocity at the point of measurement is given by:

V=√2×∆𝑃×9.81

𝜌 ; ρ=

𝑃×100

𝑅𝑇

Where:

∆𝑃 = 𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒

V= velocity

T= Ambient temperature

P= Ambient atmospheric pressure

R= Gas constant

3.2 Calibration of AFA3:

The AFA3 unit is delivered already set up and calibrated by TecQuipment; however, it may

sometimes be necessary to recheck the calibration of the apparatus.

To calibrate the AFA3 balance:

1. Fit the balance to its calibration/storage frame; place the assembly onto to a table so

that the back of the apparatus is close to the edge of the table.

2. Make sure the large pulley wheel is turned around to the rear of the frame (it may

have been shipped the other way round for easy packing.

3. Connect the cable from the balance to the display unit.

4. Use a spirit level across the top of the back plate to make sure that the balance is level,

adjust the four feet of the calibration frame if necessary. Also, place the spirit level up

the back of the back plate to check that it is vertical.

5. Slide the ‗T‘ shaped calibration arm from the top of the calibration frame and insert it

into the model holder from behind, with the bar roughly horizontal.

6. On the display module, press and hold the ‗zero‘ button. At the same time, switch on

the power. Wait a few seconds for the unit to settle. The display is now in the

27

calibration mode It will show the individual readings from the load cells as ‗FORE‘,

‗AFT‘ and ‗DRAG‘ (the display normally shows lift, drag and pitching moment).

7. Undo the centering clamps. The zero readings for each of the load cell should be 0 +/-

5 N. Make a note of the entire zero‘ readings.

8. Precede with the following calibration procedures.

3.3 Drag Calibration:

Fig 3.1: Drag Calibration

1. Unscrew and fit the small pulley to the central hole on the calibration arm.

2. Fit the looped end of the cord (supplied) around the small pulley.

3. Run the cord around the large pulley.

4. Hang a 5 kg mass from the ringed end of the cord.

5. Read the DRAG value; subtract the zero reading from earlier. The result should

49.10 N.

28

3.4 Fore/Aft Calibration:

.

Fig 3.2: Fore/Aft Calibration

1. Allow the cord to hang straight down from the small pulley.

2. Attach a 10 kg mass.

3. Read the FORE and AFT values. Subtract the ‗zero‘ readings from earlier. The result

should be 49.10 N.

29

3.5 Moment Calibration:

Fig 3.3: Moment Calibration

1. Move the small pulley to the left hand hole of the left hand hole of the calibration

arm; use a spirit level to ensure it is level.

2. Attach a 4 kg mass to the cord.

3. Read the FORE and AFT readings. Subtract the ‗zero‘ readings from earlier. The

results should be 39.2 N for the ‗FORE‘ load cell and 0N for the ‗AFT‘ load cell.

Remove the mass. Tap the frame and check that the readings return to zero +/- 0.2

N. If the readings are much greater or smaller than +/- 0.2 N, then contact

TecQuipment or your local agent for instructions.

30

CHAPTER 4

AEROFOIL SELECTION

_________________________________________

The aerofoil, in many respects, is the heart of the airplane. The aerofoil affects the cruise

speed, takeoff and landing distances, stall speed and overall aerodynamic efficiency during

all phases of flight.

4.1 Aerofoil Design Considerations:

Design considerations: 1-7(Daniel P. Raymer), 8, 17(Egbert Torenbeek), 9-16&18(Denis

Howe)

1. Aerofoil characteristics are strongly affected by the ―Reynolds numbers‖ at which

they are operating. Reynolds number, the ratio between the dynamic and the viscous

forces in a fluid, is equal to (ρVl/μ), where V is the velocity, l the length the fluid has

travelled down the surface, ρ the fluid density, and μ the fluid viscosity coefficient.

The Reynolds number influences whether the flow will be laminar or turbulent, and

whether flow separation will occur.

2. Another consideration in modern Aerofoil design is the desire to maintain laminar

flow over the greatest possible part of the Aerofoil.

3. thickness ratio has some effect upon the maximum lift coefficient

31

4. The drag increases with increasing thickness due to increased separation.

5. For initial selection of the thickness ratio, the historical trend shown in Fig. 4.14 can

be used. Note that a supercritical Aerofoil would tend to be about 10% thicker (i.e.,

conventional Aerofoil thickness ratio times1.1) than the historical trend.

6. In incompressible flow conditions relatively high thickness to chord ratios of up to 0.2

are acceptable

7. The basic Aerofoil must have a low profile drag coefficient for the range of lift

coefficients used in cruising flight.

8. The maximum lift coefficient both at low and higher Mach numbers

32

9. The stalling characteristics where a gentle loss of lift is preferable, especially for light

aircraft.

10. The aerofoil drag especially in aircraft climb and cruise conditions, when the lift

to drag ratio should be as high as possible

11. The aerofoil pitching moment characteristics which may be particularly important at

higher speeds. If it is unduly large there may be a significant trim drag penalty.

12. The nose radius, which should be relatively large to give good maximum lift

coefficient.

13. Trailing edge angle, which is often best made as small as is feasible.

14. The maximum lift coefficient of a basic, two dimensional, aerofoil can vary over a

wide range

15. In the case of a low speed aerofoil and an advanced one for use at high subsonic Mach

number a maximum lift coefficient of about 1.6 is typical.

16. Increase of thickness to chord ratio also results in a reduction of critical Mach

number. Various formulae and data sources have been derived to enable critical

Mach number to be evaluated. Subsonic airliner: MCRIT = 0.9 - (t/c) approx.

33

17. For preliminary design purposes the most critical aerofoil parameters are the

maximum lift coefficient and the related high speed drag characteristics, and lift curve

slope.

18. All these requirements cannot be satisfied by one single Aerofoil. Span wise variation

of the sectional shape and some measure of compromise will therefore generally be

accepted.

4.2 Performance Requirement:

On an air surveillance mission, purpose is to watch for ground or sea activity of various sorts,

or monitoring the path and characteristics of a hurricane. Our main concern is staying in the

air for the longest possible time. We want the airplane to have long endurance. A good

solution to the long endurance flight is to operate the aircraft at almost maximum lift

and lowest cruise speed with engine power just good enough to maintain the altitude

and against the wind, so as to reach the minimum fuel consumption and longest

mission endurance.

By definition, endurance is the amount of time that an airplane can stay in the air on one load

of fuel.

We know for a jet propelled airplane thrust specific fuel consumption is given by

34

[assuming Ct & L/D

=constant]

This is the general equation for endurance E of an airplane.

From above equation we see that (L/D) is the only aerodynamic parameter upon which

endurance depends upon and as our purpose is surveillance which requires best endurance. So

we will get best endurance for (L/D) max

Hence we should search for such an aerofoil which will gives us best (L/D)

Following are the requirements which are required to meet to develop new long-endurance

Aerofoils:

High operational lift coefficient, Cl>1;

High endurance factor Cl/Cd;

Less value of dCl/dα

Limited pitching moment coefficient Cm;

Large relative thickness t/c.

So we have to select such an aerofoil having the above characteristics.

35

CHAPTER 5

Experimental Investigation

_________________________________________

5.1 Data for Aerofoil-1

Air density=1.225

viscosity=1.83e-5 Pa-s

aerofoil chord=25 cm

Geometric Specification of Aerofoil-1:

X(L) Y(L) X(U) Y(U) Thickness Camber Chord t/c

1 0 1 0.0012 0.0012 0.0006 1 0.0012

0.95 -0.00138 0.95 0.01352 0.0149 0.00607 0.95 0.015684

0.9 -0.00276 0.9 0.02524 0.028 0.01124 0.9 0.031111

36

0.8 -0.00552 0.8 0.04668 0.0522 0.02058 0.8 0.06525

0.7 -0.00828 0.7 0.06522 0.0735 0.02847 0.7 0.105

0.6 -0.01104 0.6 0.08046 0.0915 0.03471 0.6 0.1525

0.5 -0.0138 0.5 0.0916 0.1054 0.0389 0.5 0.2108

0.4 -0.01656 0.4 0.09774 0.1143 0.04059 0.4 0.28575

0.3 -0.01932 0.3 0.09818 0.1175 0.03943 0.3 0.391667

0.2 -0.02208 0.2 0.09052 0.1126 0.03422 0.2 0.563

0.15 -0.02346 0.15 0.08204 0.1055 0.02929 0.15 0.703333

0.1 -0.02454 0.1 0.06936 0.0939 0.02241 0.1 0.939

0.075 -0.02453 0.075 0.06097 0.0855 0.01822 0.075 1.14

0.05 -0.02352 0.05 0.05068 0.0742 0.01358 0.05 1.484

0.025 -0.02071 0.025 0.03559 0.0563 0.00744 0.025 2.252

0.0125 -0.01696 0.0125 0.02395 0.04091 0.003495 0.0125 3.2728

Table 5.1: Geometric Specification of Aerofoil-1

At wind speed 5.97m/s or Re=100000

α Cd Cl Cm L/D

-5 0.03535 1.548 -0.269 43.789

-3 0.05695 1.582 -0.292 27.772

-1 0.13793 1.62 -0.323 11.749

1 29.96728 1.694 -0.356 0.057

3 -0.97948 1.783 -0.394 -1.82

5 11.52364 1.94 -0.435 0.168

7 2.65337 2.084 -0.485 0.786

9 1.32001 2.24 -0.541 1.697

11 0.95062 2.408 -0.604 2.533

13 0.818 2.584 -0.672 3.16

15 0.09539 2.769 -0.747 29.028

17 0.09123 2.943 -0.826 32.256

19 0.24334 2.376 -0.993 9.764

21 3.88143 2.408 -1.089 0.62

23 0.17978 3.178 -1.091 17.677

25 0.21209 3.136 -1.187 14.784

Table 5.2: Experimental Data for Aerofoil-

37

Fig 5.1: Cl Vs α plot of Aerofoil-1 at Re=100000

Fig 5.2: Cd Vs α for aerofoil 1 at Re=100000

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

-5

0

5

10

15

20

25

30

35

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

38

Fig 5.3: Cm Vs α of Aerofoil-1 at Re=100000

Fig 5.4: L/D Vs α for Aerofoil-1 at Re=100000

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30

Cm

α

Cm Vs α

-10

0

10

20

30

40

50

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D

39

Fig 5.5: Cl Vs Cd of Aerofoil-1 at Re=100000

So for Aerofoil-1 at for Re=100000

(d Cl /dα)max = 0.085625

Cl max =3.178

(Cl /Cd )max = 43.789

At wind speed 11.95m/s or Re=200000

α Cd Cl Cm L/D

-5 0.03672 1.55 -0.269 42.198

-3 0.04447 1.582 -0.292 35.575

-1 0.10399 1.621 -0.323 15.583

1 21.19162 1.694 -0.356 0.08

3 -0.98054 1.783 -0.394 -1.818

5 8.14862 1.94 -0.435 0.238

7 1.87645 2.084 -0.485 1.111

9 0.9332 2.24 -0.541 2.401

11 0.67562 2.408 -0.604 3.564

13 0.57781 2.584 -0.672 4.473

15 0.07134 2.769 -0.747 38.814

17 0.07306 2.943 -0.826 40.278

0

0.5

1

1.5

2

2.5

3

3.5

-5 0 5 10 15 20 25 30 35

Cl

Cd

Cl Vs Cd

40

19 0.19918 2.376 -0.993 11.93

21 2.82043 2.408 -1.089 0.854

23 0.12857 3.178 -1.091 24.719

25 0.15126 3.136 -1.187 20.731

Table 5.3: Experimental data for Aerofoil-1 at Re=200000

Fig 5.6: Cl Vs α plot of Aerofoil-1 at Re=200000

Fig 5.7: Cd Vs α for aerofoil 1 at Re=200000

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

-5

0

5

10

15

20

25

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

41

Fig 5.8: Cm Vs α of Aerofoil-1 at Re=200000

Fig 5.9: L/D Vs α for aerofoil 1 at Re=200000

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-505

101520253035404550

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D Vs α

42

Fig 5.10: Cl Vs Cd of Aerofoil-1 at Re=200000

So for Aerofoil-1 at for Re=200000

(d Cl /dα)max = 0.08916

Cl max =3.178

(Cl /Cd )max = 42.198

At wind speed 17.575m/s or Re=300000

α Cd Cl Cm L/D

-5 0.03637 1.55 -0.269 42.619

-3 0.03892 1.582 -0.292 40.651

-1 0.08909 1.621 -0.323 18.191

1 17.30384 1.694 -0.356 0.098

3 -0.98186 1.783 -0.394 -1.816

5 6.65734 1.94 -0.435 0.291

7 1.53192 2.084 -0.485 1.361

9 0.76212 2.24 -0.541 2.94

11 0.54897 2.408 -0.604 4.386

13 0.47197 2.584 -0.672 5.476

15 0.0636 2.769 -0.747 43.535

17 0.0646 2.943 -0.826 45.554

0

0.5

1

1.5

2

2.5

3

3.5

-5 0 5 10 15 20 25

Cl

Cd

Cl Vs Cd

43

19 0.1641 2.376 -0.993 14.481

21 2.45185 2.408 -1.089 0.982

23 0.10651 3.178 -1.091 29.839

25 0.12498 3.136 -1.187 25.089

Table 5.4: Experimental data for Aerofoil-1 at Re=300000

Fig 5.11: Cl Vs α plot of Aerofoil-1 at Re=300000

Fig 5.12: Cd Vs α for Aerofoil 1 at Re=300000

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

-5

0

5

10

15

20

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

44

Fig 5.13: L/D Vs α for Aerofoil 1 at Re=300000

Fig 5.14: Cm Vs α of Aerofoil-1 at Re=300000

-10

0

10

20

30

40

50

60

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30

Cm

α

Cm Vs α

45

Fig 5.15: Cl Vs Cd of Aerofoil-1 at Re=300000

So for Aerofoil-1 at for Re=300000

(dCl/dα)max = 0.0805

Cl max =3.178

(Cl/Cd )max = 45.554

At wind speed 23.43m/s or Re=400000

α Cd Cl Cm L/D

-5 0.0366 1.551 -0.269 42.365

-3 0.03589 1.582 -0.292 44.087

-1 0.07749 1.621 -0.323 20.911

1 14.98754 1.694 -0.356 0.113

3 -0.98269 1.784 -0.394 -1.815

5 5.76641 1.94 -0.435 0.337

7 1.3315 2.084 -0.485 1.565

9 0.66008 2.24 -0.541 3.394

11 0.47471 2.408 -0.604 5.072

13 0.40902 2.584 -0.672 6.319

15 0.05879 2.769 -0.747 47.095

17 0.05937 2.943 -0.826 49.562

0

0.5

1

1.5

2

2.5

3

3.5

-5 0 5 10 15 20

Cl

Cd

Cl Vs Cd

46

19 0.15201 2.376 -0.993 15.632

21 2.24293 2.408 -1.089 1.074

23 0.09057 3.178 -1.091 35.09

25 0.10967 3.136 -1.187 28.592

Table 5.5: Experimental data for Aerofoil-1 at Re=400000

Fig 5.16: Cl Vs α plot of Aerofoil-1 at Re=400000

Fig 5.17: Cd Vs α for aerofoil-1 at Re=400000

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

-2

0

2

4

6

8

10

12

14

16

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

47

Fig 5.18: Cm Vs α of Aerofoil-1 at Re=400000

Fig 5.19: L/D Vs α for aerofoil-1 at Re=400000

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-10

0

10

20

30

40

50

60

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D Vs α

48

Fig 5.20: Cl Vs Cd of Aerofoil-1 at Re=400000

So for Aerofoil-1 at for Re=400000

(dCl/dα)max = 0.0829

Cl max =3.178

(Cl/Cd )max = 49.562

At wind speed 29.29m/s or Re=500000

α Cd Cl Cm L/D

-5 0.03618 1.551 -0.269 42.859

-3 0.02795 1.584 -0.293 56.677

-1 0.07179 1.621 -0.323 22.574

1 13.40587 1.694 -0.356 0.126

3 -0.98334 1.784 -0.394 -1.814

5 5.16037 1.94 -0.435 0.376

7 1.19261 2.084 -0.485 1.748

9 0.60152 2.24 -0.541 3.725

11 0.42448 2.408 -0.604 5.672

13 0.36611 2.584 -0.672 7.059

15 0.06136 2.769 -0.747 45.125

17 0.05571 2.943 -0.826 52.823

0

0.5

1

1.5

2

2.5

3

3.5

-5 0 5 10 15 20

Cl

Cd

Cl Vs Cd

49

19 0.14641 2.376 -0.993 16.232

21 0.15947 2.408 -1.089 15.103

23 0.08232 3.178 -1.091 38.607

25 0.09619 3.136 -1.187 32.6

Table 5.6: Experimental data for Aerofoil-1 at Re=500000

Fig 5.21: Cl Vs α plot of Aerofoil-1 at Re=500000

Fid 5.22: Cd Vs α for Aerofoil-1 at Re=500000

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

-2

0

2

4

6

8

10

12

14

16

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

50

Fig 5.23: Cm Vs α of Aerofoil-1 at Re=500000

Fig 5.24: L/D Vs α for aerofoil 1 at Re=500000

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-10

0

10

20

30

40

50

60

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D Vs α

51

Fig 5.25: Cl Vs Cd of Aerofoil-1 at Re=500000

So for Aerofoil-1 at for Re=500000

(dCl/dα)max = 0.0805

Cl max =3.178

(Cl/Cd )max = 56.677

Comparing Aerofoil-1 Performance at different Reynolds Number

Re 100000 200000 300000 400000 500000 Comments

Cl max 3.178 3.178 3.178 3.178 3.178 Same

(Cl)max at

Reynolds

Number

(Cl/Cd )max 43.789 42.198 45.554 49.562 56.677 maximum

(Cl/Cd)max

at

Re=500000

0

0.5

1

1.5

2

2.5

3

3.5

-2 0 2 4 6 8 10 12 14 16

Cl

Cd

Cl Vs Cd

52

(dCl/dα)max 0.085625 0.08916 0.0805 0.0829 0.0805 minimum

(dCl/dα)max

at

Re=300000

& 500000

Cm -0.269 -0.269 -0.269 -0.269 -0.269 -0.269

Table 5.7: Performance Comparison of Aerofoil-1

From our requirement and Aerofoil design consideration 8 & 9 design should be opted for

Maximum Cl max,

Maximum (Cl/Cd )max,

Minimum (dCl/dα)max

So from above table it can be decided that Aerofoil-1 performs well at Re= 500000 &

300000

53

5.2Data for Aerofoil-2

Air density=1.225

Viscosity=1.83e-5 Pa-s

aerofoil chord=25cm

Geometric Specification of Aerofoil-2:

X(L) Y(L) X(U) Y(U) Thickness Camber Chord t/c

1 0 1 0 0 0 1 0

0.99572 -0.00025 0.99572 0.00115 0.0014 0.00045 0.99572 0.001406

0.98296 -0.00094 0.98296 0.00448 0.00542 0.00177 0.98296 0.005514

0.96194 -0.0019 0.96194 0.00972 0.01162 0.00391 0.96194 0.01208

0.93301 -0.00302 0.93301 0.01656 0.01958 0.00677 0.93301 0.020986

0.89668 -0.00429 0.89668 0.02475 0.02904 0.01023 0.89668 0.032386

0.85355 -0.00575 0.85355 0.034 0.03975 0.014125 0.85355 0.04657

0.80438 -0.00741 0.80438 0.04394 0.05135 0.018265 0.80438 0.063838

0.75 -0.00928 0.75 0.05412 0.0634 0.02242 0.75 0.084533

0.69134 -0.01131 0.69134 0.06405 0.07536 0.02637 0.69134 0.109006

0.62941 -0.01345 0.62941 0.07319 0.08664 0.02987 0.62941 0.137653

0.56526 -0.01566 0.56526 0.08105 0.09671 0.032695 0.56526 0.171089

0.5 -0.01792 0.5 0.08719 0.10511 0.034635 0.5 0.21022

0.43474 -0.02018 0.43474 0.09128 0.11146 0.03555 0.43474 0.256383

0.37059 -0.02242 0.37059 0.09312 0.11554 0.03535 0.37059 0.311773

0.33928 -0.02351 0.33928 0.09318 0.11669 0.034835 0.33928 0.343934

54

0.30866 -0.02458 0.30866 0.09266 0.11724 0.03404 0.30866 0.379835

0.27886 -0.02559 0.27886 0.09158 0.11717 0.032995 0.27886 0.420175

0.25 -0.02653 0.25 0.08996 0.11649 0.031715 0.25 0.46596

0.22221 -0.02734 0.22221 0.08774 0.11508 0.0302 0.22221 0.517888

0.19562 -0.02795 0.19562 0.08483 0.11278 0.02844 0.19562 0.576526

0.17033 -0.02832 0.17033 0.08113 0.10945 0.026405 0.17033 0.642576

0.14645 -0.02839 0.14645 0.0766 0.10499 0.024105 0.14645 0.7169

0.12408 -0.02816 0.12408 0.07134 0.0995 0.02159 0.12408 0.801902

0.10332 -0.02763 0.10332 0.06552 0.09315 0.018945 0.10332 0.901568

0.08427 -0.0268 0.08427 0.05939 0.08619 0.016295 0.08427 1.022784

0.06699 -0.02567 0.06699 0.05313 0.0788 0.01373 0.06699 1.176295

0.05156 -0.02414 0.05156 0.04677 0.07091 0.011315 0.05156 1.375291

0.03806 -0.02214 0.03806 0.04027 0.06241 0.009065 0.03806 1.639779

0.02653 -0.01959 0.02653 0.03352 0.05311 0.006965 0.02653 2.001885

0.01704 -0.01651 0.01704 0.02652 0.04303 0.005005 0.01704 2.525235

0.00961 -0.01296 0.00961 0.01943 0.03239 0.003235 0.00961 3.370447

0.00428 -0.00898 0.00428 0.01254 0.02152 0.00178 0.00428 5.028037

0.00107 -0.00453 0.00107 0.00616 0.01069 0.000815 0.00107 9.990654

Table 5.8: Geometric Specification of Aerofoil-2

At wind speed 5.975m/s or Re=100000

α Cd Cl Cm L/D

-5 0.04226 -0.177 -0.059 -4.198

-3 0.03006 0.076 -0.085 2.522

-1 0.0304 0.317 -0.088 10.443

1 0.03176 0.548 -0.092 17.247

3 0.03193 0.778 -0.096 24.378

5 0.03368 0.999 -0.102 29.644

7 0.03976 1.19 -0.11 29.934

9 0.04797 1.345 -0.123 28.047

11 0.06228 1.425 -0.143 22.887

13 0.10049 1.299 -0.177 12.924

15 0.12953 1.335 -0.184 10.308

17 0.16297 1.35 -0.196 8.282

19 0.20481 1.305 -0.208 6.373

21 0.27111 1.221 -0.22 4.505

23 0.34773 1.115 -0.232 3.206

25 0.44065 0.999 -0.244 2.266

Table 5.9: Experimental Data for Aerofoil-2

55

Fig 5.26: Cl Vs α plot of Aerofoil-2 at Re=100000

Fig 5.27: Cd Vs α for aerofoil 2 at Re=100000

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

00.05

0.10.15

0.20.25

0.30.35

0.40.45

0.5

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

56

Fig 5.28: Cm Vs α of Aerofoil-2 at Re=100000

Fig 5.29: L/D Vs α for Aerofoil-2 at Re=100000

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-10

-5

0

5

10

15

20

25

30

35

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D Vs α

57

Fig 5.30: Cl Vs Cd of Aerofoil-2 at Re=100000

So for Aerofoil-2 at for Re=100000

(dCl/dα)max = 0.103

Cl max =1.485

(Cl/Cd )max = 29.934

At wind speed 11.95m/s or Re=200000

α Cd Cl Cm L/D

-5 0.02754 -0.163 -0.082 -5.909

-3 0.02845 0.076 -0.085 2.666

-1 0.02858 0.317 -0.088 11.108

1 0.02831 0.551 -0.092 19.456

3 0.02966 0.784 -0.096 26.447

5 0.03261 1.006 -0.101 30.865

7 0.03626 1.209 -0.108 33.342

9 0.04178 1.376 -0.12 32.928

11 0.05239 1.48 -0.137 28.256

13 0.07213 1.482 -0.162 20.539

15 0.11517 1.329 -0.191 11.543

17 0.15045 1.319 -0.198 8.77

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.1 0.2 0.3 0.4 0.5

Cl

Cd

Cl Vs Cd

58

19 0.19453 1.285 -0.209 6.605

21 0.23118 1.209 -0.221 5.228

23 0.29351 1.107 -0.233 3.772

25 0.37176 0.994 -0.245 2.673

Table 5.10: Experimental data for Aerofoil-2 at Re=200000

Fig 5.31: Cl Vs α plot of Aerofoil-2 at Re=200000

Fig 5.32: Cd Vs α for aerofoil 2 at Re=200000

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

59

Fig 5.33: Cm Vs α of Aerofoil-2 at Re=200000

Fig 5.34: L/D Vs α for aerofoil 2 at Re=200000

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-10

-5

0

5

10

15

20

25

30

35

40

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D

60

Fig 5.35: Cl Vs Cd of Aerofoil-2 at Re=200000

So for Aerofoil-2 at for Re=200000

(dCl/dα)max = 0.103125

Cl max =1.482

(Cl/Cd )max = 33.342

At wind speed 17.575m/s or Re=300000

α Cd Cl Cm L/D

-5 0.02704 -0.163 -0.082 -6.021

-3 0.02774 0.076 -0.085 2.734

-1 0.02766 0.317 -0.088 11.478

1 0.02717 0.553 -0.092 20.334

3 0.02798 0.787 -0.096 28.123

5 0.03132 1.01 -0.101 32.24

7 0.03451 1.217 -0.108 35.279

9 0.03979 1.391 -0.118 34.947

11 0.04896 1.501 -0.134 30.647

13 0.06473 1.524 -0.157 23.547

15 0.09687 1.413 -0.188 14.584

17 0.14118 1.311 -0.201 9.286

19 0.1786 1.277 -0.211 7.148

21 0.21643 1.2 -0.223 5.542

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Cl

Cd

Cl Vs Cd

61

23 0.26603 1.1 -0.234 4.135

25 0.33862 0.99 -0.245 2.922

Table 5.11: Experimental data for Aerofoil-2 at Re=300000

Fig 5.36: Cl Vs α plot of Aerofoil-2 at Re=300000

Fig 5.37: Cd Vs α for Aerofoil 2 at Re=300000

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

62

Fig 5.38: Cm Vs α of Aerofoil-2 at Re=300000

Fig 5.39: L/D Vs α for Aerofoil 2 at Re=300000

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-10

-5

0

5

10

15

20

25

30

35

40

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D Vs α

63

Fig 5.40: Cl Vs Cd of Aerofoil-2 at Re=300000

So for Aerofoil-2 at for Re=300000

(dCl/dα)max = 0.10066

Cl max =1.524

(Cl/Cd )max = 35.279

At wind speed 23.43m/s or Re=400000

α Cd Cl Cm L/D

-5 0.02692 -0.163 -0.082 -6.047

-3 0.02718 0.076 -0.085 2.79

-1 0.02713 0.317 -0.088 11.7

1 0.02672 0.554 -0.092 20.725

3 0.02718 0.788 -0.096 29.004

5 0.03055 1.013 -0.101 33.144

7 0.0334 1.223 -0.107 36.602

9 0.03856 1.399 -0.117 36.278

11 0.04728 1.515 -0.132 32.035

13 0.06082 1.548 -0.155 25.458

15 0.08643 1.467 -0.183 16.971

17 0.13296 1.324 -0.204 9.958

19 0.17015 1.274 -0.212 7.487

21 0.20821 1.197 -0.223 5.75

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Cl

Cd

Cl Vs Cd

64

23 0.25224 1.097 -0.235 4.349

25 0.3099 0.986 -0.246 3.183

Table 5.12: Experimental data for Aerofoil-2 at Re=400000

Fig 5.41: Cl Vs α plot of Aerofoil-2 at Re=400000

Fig 5.42: Cd Vs α for aerofoil-2 at Re=400000

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

65

Fig 5.43: Cm Vs α of Aerofoil-2 at Re=400000

Fig 5.44: Cl/Cd Vs α for aerofoil-2 at Re=400000

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-10

-5

0

5

10

15

20

25

30

35

40

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D Vs α

66

Fig 5.45: Cl Vs Cd of Aerofoil-2 at Re=400000

So for Aerofoil-2 at for Re=400000

(dCl/dα)max = 0.101833

Cl max =1.548

(Cl/Cd )max = 36.602

At wind speed 29.29m/s or Re=500000

α Cd Cl Cm L/D

-5 0.02659 -0.163 -0.082 -6.122

-3 0.02671 0.076 -0.085 2.839

-1 0.02671 0.317 -0.088 11.883

1 0.02645 0.554 -0.092 20.959

3 0.02731 0.788 -0.096 28.867

5 0.0297 1.015 -0.1 34.159

7 0.03261 1.227 -0.107 37.62

9 0.03759 1.405 -0.116 37.377

11 0.04573 1.525 -0.131 33.345

13 0.05863 1.566 -0.152 26.7

15 0.0806 1.497 -0.18 18.571

17 0.12608 1.338 -0.204 10.614

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Cl

Cd

Cl Vs Cd

67

19 0.16331 1.273 -0.212 7.794

21 0.20017 1.196 -0.224 5.975

23 0.23955 1.096 -0.235 4.573

25 0.29043 0.985 -0.247 3.39

Table 5.13: Experimental data for Aerofoil-2 at Re=500000

Fig 5.46: Cl Vs α plot of Aerofoil-2 at Re=500000

Fig 5.47: Cd Vs α for Aerofoil-2 at Re=500000

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

68

Fig 5.48: Cm Vs α of Aerofoil-2 at Re=500000

Fig 5.49: L/D Vs α for aerofoil 2 at Re=500000

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-10

-5

0

5

10

15

20

25

30

35

40

45

-10 -5 0 5 10 15 20 25 30

L/D

α

L/D Vs α

69

Fig 5.50: Cl Vs Cd of Aerofoil-2 at Re=500000

So for Aerofoil-2 at for Re=500000

(dCl/dα)max = 0.106375

Cl max =1.566

(Cl/Cd )max = 37.377

Comparing Aerofoil-2 Performance at different Reynolds Number

Re 100000 200000 300000 400000 500000 Comments

Cl max 1.485 1.482 1.524

1.548 1.566 Maximum

(Cl)max at

Re=500000

(Cl/Cd )max 29.934 33.342 35.279 36.602 37.377 maximum

(Cl/Cd)max

at

Re=500000

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Cl

Cd

Cl Vs Cd

70

(dCl/dα)max 0.103 0.103125 0.10066 0.101833 0.106375 minimum

(dCl/dα)max

at

Re=300000

Cm -0.059 -0.082 -0.082 -0.082 -0.082 -0.082

Table 5.14: Performance Comparison of Aerofoil-2

From our requirement and Aerofoil design consideration 8 & 9 design should be opted for

Maximum Cl max,

Maximum (Cl/Cd )max,

Minimum (dCl/dα)max

So from above table it can be decided that Aerofoil-2 performs well at Re= 500000

71

5.3 Data for Aerofoil-3

Air density=1.225

viscosity=1.83e-5 Pa-s

aerofoil chord=25.5cm

Geometric Specification of Aerofoil-3:

X(L) Y(L) X(U) Y(U) Thickness Camber Chord t/c

1 -0.0006 1 0.000599 0.001199 0 1 0.001199

0.99 -0.00097 0.99 0.002969 0.003936 0.001001 0.99 0.003975

0.98 -0.00133 0.98 0.005334 0.006667 0.002 0.98 0.006803

0.97 -0.0017 0.97 0.007687 0.009388 0.002993 0.97 0.009678

0.96 -0.00207 0.96 0.010023 0.012092 0.003977 0.96 0.012595

0.94 -0.0028 0.94 0.014624 0.017427 0.005911 0.94 0.018539

0.92 -0.00354 0.92 0.019116 0.022653 0.007789 0.92 0.024623

0.9 -0.00427 0.9 0.023503 0.027774 0.009615 0.9 0.03086

0.88 -0.00501 0.88 0.027789 0.032795 0.011391 0.88 0.037268

0.86 -0.00574 0.86 0.031974 0.037715 0.013117 0.86 0.043854

0.84 -0.00648 0.84 0.036054 0.042529 0.014789 0.84 0.05063

0.82 -0.00721 0.82 0.040025 0.047234 0.016407 0.82 0.057603

0.8 -0.00794 0.8 0.043884 0.051828 0.01797 0.8 0.064785

0.78 -0.00868 0.78 0.047628 0.056307 0.019475 0.78 0.072188

0.76 -0.00941 0.76 0.051257 0.06067 0.020922 0.76 0.079829

0.74 -0.01015 0.74 0.054768 0.064915 0.02231 0.74 0.087723

0.72 -0.01088 0.72 0.05816 0.069042 0.023639 0.72 0.095892

0.7 -0.01162 0.7 0.061433 0.07305 0.024908 0.7 0.104357

72

0.68 -0.01235 0.68 0.064584 0.076936 0.026116 0.68 0.113141

0.66 -0.01309 0.66 0.067605 0.080691 0.027259 0.66 0.122259

0.64 -0.01382 0.64 0.070482 0.084303 0.028331 0.64 0.131723

0.62 -0.01456 0.62 0.073206 0.087761 0.029325 0.62 0.141549

0.6 -0.01529 0.6 0.075763 0.091053 0.030237 0.6 0.151754

0.58 -0.01602 0.58 0.078145 0.094168 0.031061 0.58 0.162359

0.56 -0.01676 0.56 0.080348 0.097105 0.031795 0.56 0.173402

0.54 -0.01749 0.54 0.082371 0.099863 0.03244 0.54 0.184931

0.52 -0.01823 0.52 0.084215 0.102441 0.032994 0.52 0.197001

0.5 -0.01896 0.5 0.085877 0.104839 0.033458 0.5 0.209678

0.48 -0.0197 0.48 0.087357 0.107056 0.033829 0.48 0.223033

0.46 -0.02044 0.46 0.088643 0.109078 0.034104 0.46 0.237126

0.44 -0.02117 0.44 0.089718 0.110888 0.034273 0.44 0.252019

0.42 -0.0219 0.42 0.090566 0.11247 0.034331 0.42 0.267785

0.4 -0.02263 0.4 0.091171 0.113805 0.034269 0.4 0.284513

0.38 -0.02336 0.38 0.091521 0.114882 0.03408 0.38 0.302321

0.36 -0.02409 0.36 0.091627 0.115714 0.03377 0.36 0.321427

0.34 -0.02482 0.34 0.091508 0.116326 0.033345 0.34 0.342134

0.32 -0.02556 0.32 0.091186 0.116742 0.032815 0.32 0.364819

0.3 -0.02631 0.3 0.09068 0.116988 0.032186 0.3 0.389961

0.28 -0.02707 0.28 0.090002 0.117071 0.031466 0.28 0.418111

0.26 -0.02782 0.26 0.089084 0.1169 0.030634 0.26 0.449617

0.24 -0.02852 0.24 0.087831 0.116349 0.029656 0.24 0.484787

0.22 -0.02914 0.22 0.086143 0.115288 0.028499 0.22 0.524035

0.2 -0.02967 0.2 0.08392 0.113586 0.027127 0.2 0.567929

0.18 -0.03005 0.18 0.081069 0.111118 0.02551 0.18 0.617321

0.16 -0.03025 0.16 0.077571 0.107825 0.023658 0.16 0.673908

0.14 -0.03024 0.14 0.073436 0.103676 0.021598 0.14 0.740546

0.12 -0.02996 0.12 0.06862 0.098584 0.019329 0.12 0.821531

0.1 -0.02938 0.1 0.062998 0.092377 0.01681 0.1 0.923767

0.08 -0.02846 0.08 0.056431 0.08489 0.013986 0.08 1.061129

0.06 -0.02713 0.06 0.048757 0.075885 0.010815 0.06 1.264747

0.05 -0.02605 0.05 0.044275 0.070321 0.009115 0.05 1.40641

0.04 -0.02452 0.04 0.039128 0.063649 0.007304 0.04 1.591235

0.03 -0.02261 0.03 0.033022 0.055627 0.005208 0.03 1.854237

0.02 -0.02027 0.02 0.025374 0.045646 0.002551 0.02 2.28229

0.012 -0.01697 0.012 0.017858 0.034831 0.000442 0.012 2.902617

0.008 -0.01429 0.008 0.013735 0.028021 -0.00028 0.008 3.50265

0.004 -0.01051 0.004 0.008924 0.019436 -0.00079 0.004 4.8591

0.002 -0.00781 0.002 0.005803 0.013614 -0.001 0.002 6.8069

0.001 -0.00594 0.001 0.003727 0.009669 -0.00111 0.001 9.6689

0.0005 -0.00467 0.0005 0.002339 0.007009 -0.00117 0.0005 14.018

Table 5.15: Geometric Specification of Aerofoil-3

73

At wind speed 5.975m/s or Re=100000

α Cd Cl L/D Cm

-5 0.02613 1.451 55.523 -0.223

-3 0.02268 1.422 62.709 -0.24

-1 0.03989 1.376 34.502 -0.257

1 0.20173 1.408 6.981 -0.272

3 0.06183 1.452 23.485 -0.283

5 0.0564 1.311 23.25 -0.318

7 0.03357 1.284 38.238 -0.341

9 0.04139 1.244 30.048 -0.365

11 0.05039 1.177 23.363 -0.39

13 0.06309 1.076 17.058 -0.417

15 0.33161 0.945 2.85 -0.444

17 0.02728 1.196 43.839 -0.399

19 0.51349 0.658 1.282 -0.501

21 0.61265 0.533 0.871 -0.53

23 0.05639 0.691 12.257 -0.463

25 0.85201 0.347 0.407 -0.591

Table 5.16: Experimental Data for Aerofoil-3

Fig 5.51: Cl Vs α plot of Aerofoil-3 at Re=100000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

74

Fig 5.52: Cl Vs Cd of Aerofoil-3 at Re=100000

Fig 5.53: Cm Vs α of Aerofoil-3 at Re=100000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.2 0.4 0.6 0.8 1

Cl

Cd

Cl Vs Cd

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

-10 -5 0 5 10 15 20 25 30

Cm

α

Cm Vs α

75

Fig 5.54: Cl/Cd Vs α for aerofoil 3 at Re=100000

Fig 5.55: Cd Vs α for aerofoil 3 at Re=100000

So for Aerofoil-3at Re=100000

(dCl/dα)max = -0.0366

Cl max =1.452

(Cl/Cd )max = 62.709

-10

0

10

20

30

40

50

60

70

-10 -5 0 5 10 15 20 25 30

Cl/

Cd

α

Cl/Cd Vs α

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

76

At wind speed 11.95m/s or Re=200000

α Cd Cl Cm L/D

-5 0.02278 1.452 -0.224 63.744

-3 0.025 1.423 -0.24 56.916

-1 0.03178 1.376 -0.257 43.301

1 0.15019 1.408 -0.272 9.376

3 0.04807 1.452 -0.283 30.21

5 0.04488 1.311 -0.318 29.222

7 0.03093 1.284 -0.341 41.501

9 0.03859 1.244 -0.365 32.237

11 0.04698 1.177 -0.39 25.061

13 0.0592 1.076 -0.417 18.177

15 0.25735 0.945 -0.444 3.673

17 0.01945 1.196 -0.399 61.5

19 0.38518 0.658 -0.501 1.709

21 0.46691 0.534 -0.53 1.143

23 0.04199 0.691 -0.463 16.457

25 0.64338 0.347 -0.591 0.539

Table 5.17: Experimental data for Aerofoil-3 at Re=200000

Fig 5.56: Cl Vs α plot of Aerofoil-3 at Re=200000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

77

Fig 5.57: Cl Vs Cd of Aerofoil-3 at Re=200000

Fig 5.58: Cd Vs α for aerofoil 3 at Re=200000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cl

Cd

Cl Vs Cd

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

78

Fig 5.59: Cm Vs α of Aerofoil-3 at Re=200000

Fig 5.60: Cl/Cd Vs α for aerofoil 3 at Re=200000

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-10

0

10

20

30

40

50

60

70

-10 -5 0 5 10 15 20 25 30

Cl/

Cd

α

Cl/Cd Vs α

79

So for Aerofoil-3at Re=200000

(dCl/dα)max = -0.0366

Cl max =1.452

(Cl/Cd )max = 63.744

At wind speed 17.575m/s or Re=300000

α Cd Cl Cm L/D

-5 0.02167 1.452 -0.224 67.017

-3 0.02304 1.423 -0.24 61.765

-1 0.02821 1.376 -0.257 48.791

1 0.1286 1.408 -0.272 10.951

3 0.04199 1.452 -0.283 34.584

5 0.0403 1.311 -0.318 32.542

7 0.02972 1.284 -0.341 43.197

9 0.03724 1.244 -0.365 33.4

11 0.0455 1.177 -0.39 25.88

13 0.05777 1.076 -0.417 18.63

15 0.06712 0.945 -0.444 14.082

17 0.01639 1.196 -0.399 72.964

19 0.32729 0.659 -0.501 2.012

21 0.39536 0.534 -0.53 1.35

23 0.03449 0.691 -0.463 20.041

25 0.54332 0.347 -0.591 0.639

Table 5.18: Experimental data for Aerofoil-3 at Re=300000

80

Fig 5.61: Cl Vs α plot of Aerofoil-3 at Re=300000

Fig 5.62: Cd Vs α for aerofoil 3 at Re=300000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

0

0.1

0.2

0.3

0.4

0.5

0.6

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

81

Fig 5.63: Cm Vs α of Aerofoil-3 at Re=300000

Fig 5.64: Cl Vs Cd of Aerofoil-3 at Re=300000

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.1 0.2 0.3 0.4 0.5 0.6

Cl

Cd

Cl Vs Cd

82

Fig 5.65: Cl/Cd Vs α for aerofoil 3 at Re=300000

So for Aerofoil-3at Re=300000

(dCl/dα)max = -0.0366

Cl max =1.452

(Cl/Cd )max = 67.017

At wind speed 23.43m/s or Re=400000

α Cd Cl Cm L/D

-5 0.02742 1.452 -0.224 52.969

-3 0.02287 1.423 -0.24 62.228

-1 0.02674 1.376 -0.257 51.469

1 0.11544 1.408 -0.272 12.199

3 0.03816 1.452 -0.283 38.06

5 0.02528 1.311 -0.318 51.877

7 0.02962 1.284 -0.341 43.349

9 0.03646 1.244 -0.365 34.117

11 0.04451 1.177 -0.39 26.454

13 0.0566 1.076 -0.417 19.014

15 0.06561 0.945 -0.444 14.407

17 0.01431 1.196 -0.399 83.566

19 0.29909 0.659 -0.501 2.203

21 0.35527 0.534 -0.53 1.503

-10

0

10

20

30

40

50

60

70

80

-10 -5 0 5 10 15 20 25 30

Cl/

Cd

α

Cl/Cd Vs α

83

23 0.032 0.691 -0.463 21.6

25 0.49815 0.348 -0.591 0.698

Table 5.19: Experimental data for Aerofoil-3 at Re=400000

Fig 5.66: Cl Vs α plot of Aerofoil-3 at Re=400000

Fig 5.67: Cd Vs α for aerofoil 3 at Re=400000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

0

0.1

0.2

0.3

0.4

0.5

0.6

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

84

Fig 5.68: Cm Vs α of Aerofoil-3 at Re=400000

Fig 5.69: Cl/Cd Vs α for aerofoil 3 at Re=400000

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-10

0

10

20

30

40

50

60

70

80

90

-10 -5 0 5 10 15 20 25 30

Cl/

Cd

α

Cl/Cd Vs α

85

Fig 5.70: Cl Vs Cd of Aerofoil-3 at Re=400000

So for Aerofoil-3at Re=400000

(dCl/dα)max = -0.02675

Cl max =1.452

(Cl/Cd )max = 62.228

At wind speed 29.29m/s or Re=500000

α Cd Cl Cm L/D

-5 0.02718 1.453 -0.224 53.442

-3 0.02227 1.423 -0.24 63.91

-1 0.0254 1.376 -0.257 54.182

1 0.10571 1.408 -0.272 13.322

3 0.03556 1.452 -0.283 40.833

5 0.02444 1.311 -0.318 53.669

7 0.02942 1.284 -0.341 43.637

9 0.03601 1.244 -0.365 34.542

11 0.04394 1.178 -0.39 26.797

13 0.05579 1.076 -0.417 19.29

15 0.06518 0.945 -0.444 14.506

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.1 0.2 0.3 0.4 0.5 0.6

Cl

Cd

Cl Vs Cd

86

17 0.01343 1.196 -0.399 89.06

19 0.27642 0.659 -0.501 2.384

21 0.33202 0.534 -0.53 1.609

23 0.03018 0.691 -0.463 22.898

25 0.45125 0.348 -0.591 0.771

Table 5.20: Experimental data for Aerofoil-3 at Re=500000

Fig 5.71: Cl Vs α plot of Aerofoil-3 at Re=500000

Fig 5.72: Cd Vs α for aerofoil 3 at Re=500000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

0

0.1

0.2

0.3

0.4

0.5

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

87

Fig 5.73: Cm Vs α of Aerofoil-3 at Re=500000

Fig 5.74: Cl/Cd Vs α for aerofoil 3 at Re=500000

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

-20

0

20

40

60

80

100

-10 -5 0 5 10 15 20 25 30

Cl/C

d

α

Cl/Cd Vs α

88

Fig 5.75: Cl Vs Cd of Aerofoil-3 at Re=500000

So for Aerofoil-3at Re=500000

(dCl/dα)max = -0.029375

Cl max =1.453

(Cl/Cd )max = 54.182

Comparing Aerofoil-3 Performance at different Reynolds Number

Re 100000 200000 300000 400000 500000 Comments

Cl max 1.452 1.452 1.452 1.452 1.453 almost

same at all

Re

(Cl/Cd )max 62.709 63.744 67.017 62.228 54.182 maximum

(Cl/Cd)max

at

Re=300000

(dCl/dα)max -0.0366 -0.0366 -0.0366 -0.02675 -0.029375 minimum

(dCl/dα)max

at

Re=400000

Cm -0.223 -0.224 -0.224 -0.224 -0.224 -0.224

Table 5.21: Performance Comparison of Aerofoil-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.1 0.2 0.3 0.4 0.5

Cl

Cd

Cl Vs Cd

89

From our requirement and Aerofoil design consideration 8 & 9 design should be opted for

Maximum Cl max,

Maximum (Cl/Cd )max,

Minimum (dCl/dα)max

So from above table it can be decided that Aerofoil-3 performs well at Re= 300000 & 400000

Summary:

Aerofoil-1 is suitable for UAV operating at Re= 500000 & 300000

Aerofoil-2 is suitable for UAV operating at Re= 500000

Aerofoil-3 is suitable for UAV operating at Re= 300000 & 400000

90

CHAPTER 6

ADDITIONAL INVESTIGATION

_________________________________________

6.1 Investigation of Variation of Pitching Moment Co-Efficient with the

Variation of Angle of Attack:

At Reynolds Number = 100000

Cm

α A-1 A-2 A-3

-5 -0.269 -0.059 -0.223

-3 -0.292 -0.085 -0.24

-1 -0.323 -0.088 -0.257

1 -0.356 -0.092 -0.272

3 -0.394 -0.096 -0.283

5 -0.435 -0.102 -0.318

7 -0.485 -0.11 -0.341

9 -0.541 -0.123 -0.365

11 -0.604 -0.143 -0.39

13 -0.672 -0.177 -0.417

15 -0.747 -0.184 -0.444

17 -0.826 -0.196 -0.399

19 -0.993 -0.208 -0.501

21 -1.089 -0.22 -0.53

23 -1.091 -0.232 -0.463

25 -1.187 -0.244 -0.591

Table 6.1: Variation of Cm with α at: Re = 100000

91

Fig 6.1: Graphical plot of variation of Cm with α at: Re = 100000

At Reynolds Number = 200000

Table 6.2: Variation of Cm with α at: Re = 200000

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30

Cm

α

Cm Vs α

A-1

A-2

A-3

Cm

α A-1 A-2 A-3

-5 -0.269 -0.082 -0.224

-3 -0.292 -0.085 -0.24

-1 -0.323 -0.088 -0.257

1 -0.356 -0.092 -0.272

3 -0.394 -0.096 -0.283

5 -0.435 -0.101 -0.318

7 -0.485 -0.108 -0.341

9 -0.541 -0.12 -0.365

11 -0.604 -0.137 -0.39

13 -0.672 -0.162 -0.417

15 -0.747 -0.191 -0.444

17 -0.826 -0.198 -0.399

19 -0.993 -0.209 -0.501

21 -1.089 -0.221 -0.53

23 -1.091 -0.233 -0.463

25 -1.187 -0.245 -0.591

92

Fig 6.2: Graphical plot of variation of Cm with α at: Re = 200000

At Reynolds Number = 300000

Cm

α A-1 A-2 A-3

-5 -0.269 -0.082 -0.224

-3 -0.292 -0.085 -0.24

-1 -0.323 -0.088 -0.257

1 -0.356 -0.092 -0.272

3 -0.394 -0.096 -0.283

5 -0.435 -0.101 -0.318

7 -0.485 -0.108 -0.341

9 -0.541 -0.118 -0.365

11 -0.604 -0.134 -0.39

13 -0.672 -0.157 -0.417

15 -0.747 -0.188 -0.444

17 -0.826 -0.201 -0.399

19 -0.993 -0.211 -0.501

21 -1.089 -0.223 -0.53

23 -1.091 -0.234 -0.463

25 -1.187 -0.245 -0.591

Table 6.3: Variation of Cm with α at: Re = 300000

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

A-1

A-2

A-3

93

Fig 6.3: Graphical plot of variation of Cm with α at: Re = 300000

At Reynolds Number = 400000

Cm

α A-1 A-2 A-3

-5 -0.269 -0.082 -0.224

-3 -0.292 -0.085 -0.24

-1 -0.323 -0.088 -0.257

1 -0.356 -0.092 -0.272

3 -0.394 -0.096 -0.283

5 -0.435 -0.101 -0.318

7 -0.485 -0.107 -0.341

9 -0.541 -0.117 -0.365

11 -0.604 -0.132 -0.39

13 -0.672 -0.155 -0.417

15 -0.747 -0.183 -0.444

17 -0.826 -0.204 -0.399

19 -0.993 -0.212 -0.501

21 -1.089 -0.223 -0.53

23 -1.091 -0.235 -0.463

25 -1.187 -0.246 -0.591

Table 6.4: Variation of Cm with α at: Re = 400000

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30

Cm

α

Cm Vs α

A-1

A-2

A-3

94

Fig 6.4: Graphical plot of variation of Cm with α at: Re = 400000

At Reynolds Number = 500000

Cm

α A-1 A-2 A-3

-5 -0.269 -0.082 -0.224

-3 -0.293 -0.085 -0.24

-1 -0.323 -0.088 -0.257

1 -0.356 -0.092 -0.272

3 -0.394 -0.096 -0.283

5 -0.435 -0.1 -0.318

7 -0.485 -0.107 -0.341

9 -0.541 -0.116 -0.365

11 -0.604 -0.131 -0.39

13 -0.672 -0.152 -0.417

15 -0.747 -0.18 -0.444

17 -0.826 -0.204 -0.399

19 -0.993 -0.212 -0.501

21 -1.089 -0.224 -0.53

23 -1.091 -0.235 -0.463

25 -1.187 -0.247 -0.591

Table 6.5: Variation of Cm with α at: Re = 500000

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

A-1

A-2

A-3

95

Fig 6.5: Graphical plot of variation of Cm with α at: Re = 500000

From above graphs and tables it is clearly visible that moment co-efficient varies with angle

of attack. It has been observed that at all Reynolds Number Aerofoil-1 and Aerofoil-2 fail to

maintain stability due to severe changes in pitching moment co-efficient with the increase in

angle of attack. But Aerofoil-2 has better stability.

So from this point of view Aerofoil-2 performs best.

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-10 -5 0 5 10 15 20 25 30C

m

α

Cm Vs α

A-1

A-2

A-3

96

6.2 Investigation of Cd-α curves at different Reynolds Number :

At Reynolds Number = 100000

Cd

α A-1 A-2 A-3

-5 0.03535 0.04226 0.02613

-3 0.05695 0.03006 0.02268

-1 0.13793 0.0304 0.03989

1 29.96728 0.03176 0.20173

3 -0.97948 0.03193 0.06183

5 11.52364 0.03368 0.0564

7 2.65337 0.03976 0.03357

9 1.32001 0.04797 0.04139

11 0.95062 0.06228 0.05039

13 0.818 0.10049 0.06309

15 0.09539 0.12953 0.33161

17 0.09123 0.16297 0.02728

19 0.24334 0.20481 0.51349

21 3.88143 0.27111 0.61265

23 0.17978 0.34773 0.05639

25 0.21209 0.44065 0.85201

Table 6.6: Variation of Cd with α at: Re = 100000

97

Fig 6.6: Graphical plot of variation of Cd with α at: Re = 100000

At Reynolds Number = 200000

Cd

α A-1 A-2 A-3

-5 0.03672 0.02754 0.02278

-3 0.04447 0.02845 0.025

-1 0.10399 0.02858 0.03178

1 21.19162 0.02831 0.15019

3 -0.98054 0.02966 0.04807

5 8.14862 0.03261 0.04488

7 1.87645 0.03626 0.03093

9 0.9332 0.04178 0.03859

11 0.67562 0.05239 0.04698

13 0.57781 0.07213 0.0592

15 0.07134 0.11517 0.25735

17 0.07306 0.15045 0.01945

19 0.19918 0.19453 0.38518

21 2.82043 0.23118 0.46691

23 0.12857 0.29351 0.04199

25 0.15126 0.37176 0.64338

Table 6.7: Variation of Cd with α at: Re = 200000

-5

0

5

10

15

20

25

30

35

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

A-1

A-2

A-3

98

Fig 6.7: Graphical plot of variation of Cd with α at: Re = 200000

At Reynolds Number = 300000

Cd

α A-1 A-2 A-3

-5 0.03637 0.02704 0.02167

-3 0.03892 0.02774 0.02304

-1 0.08909 0.02766 0.02821

1 17.30384 0.02717 0.1286

3 -0.98186 0.02798 0.04199

5 6.65734 0.03132 0.0403

7 1.53192 0.03451 0.02972

9 0.76212 0.03979 0.03724

11 0.54897 0.04896 0.0455

13 0.47197 0.06473 0.05777

15 0.0636 0.09687 0.06712

17 0.0646 0.14118 0.01639

19 0.1641 0.1786 0.32729

21 2.45185 0.21643 0.39536

23 0.10651 0.26603 0.03449

25 0.12498 0.33862 0.54332

Table 6.8: Variation of Cd with α at: Re = 300000

-5

0

5

10

15

20

25

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

A-1

A-2

A-3

99

Fig 6.8: Graphical plot of variation of Cd with α at: Re = 300000

At Reynolds Number = 400000

Cd

α A-1 A-2 A-3

-5 0.0366 0.02692 0.02742

-3 0.03589 0.02718 0.02287

-1 0.07749 0.02713 0.02674

1 14.98754 0.02672 0.11544

3 -0.98269 0.02718 0.03816

5 5.76641 0.03055 0.02528

7 1.3315 0.0334 0.02962

9 0.66008 0.03856 0.03646

11 0.47471 0.04728 0.04451

13 0.40902 0.06082 0.0566

15 0.05879 0.08643 0.06561

17 0.05937 0.13296 0.01431

19 0.15201 0.17015 0.29909

21 2.24293 0.20821 0.35527

23 0.09057 0.25224 0.032

25 0.10967 0.3099 0.49815

Table 6.9: Variation of Cd with α at: Re = 400000

-5

0

5

10

15

20

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

A-1

A-2

A-3

100

Fig 6.9: Graphical plot of variation of Cd with α at: Re = 400000

At Reynolds Number = 500000

Cd

α A-1 A-2 A-3

-5 0.03618 0.02659 0.02718

-3 0.02795 0.02671 0.02227

-1 0.07179 0.02671 0.0254

1 13.40587 0.02645 0.10571

3 -0.98334 0.02731 0.03556

5 5.16037 0.0297 0.02444

7 1.19261 0.03261 0.02942

9 0.60152 0.03759 0.03601

11 0.42448 0.04573 0.04394

13 0.36611 0.05863 0.05579

15 0.06136 0.0806 0.06518

17 0.05571 0.12608 0.01343

19 0.14641 0.16331 0.27642

21 0.15947 0.20017 0.33202

23 0.08232 0.23955 0.03018

25 0.09619 0.29043 0.45125

Table 6.10: Variation of Cd with α at: Re = 500000

-2

0

2

4

6

8

10

12

14

16

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

A-1

A-2

A-3

101

Fig 6.10: Graphical plot of variation of Cd with α at: Re = 500000

From above graphs and tables it is clearly visible that moment co-efficient varies with angle

of attack. It has been observed that at all Reynolds Number, Aerofoil-1 gives the maximum

drag co-efficient where Aerofoil-2 gives lowest drag co-efficient.

So from this point of view Aerofoil-2 performs best.

-2

0

2

4

6

8

10

12

14

16

-10 -5 0 5 10 15 20 25 30

Cd

α

Cd Vs α

A-1

A-2

A-3

102

6.3 Investigation of Cl-α curves at different Reynolds Number :

At Reynolds Number = 100000

Cl

α A-1 A-2 A-3

-5 1.548 -0.177 1.451

-3 1.582 0.076 1.422

-1 1.62 0.317 1.376

1 1.694 0.548 1.408

3 1.783 0.778 1.452

5 1.94 0.999 1.311

7 2.084 1.19 1.284

9 2.24 1.345 1.244

11 2.408 1.425 1.177

13 2.584 1.299 1.076

15 2.769 1.335 0.945

17 2.943 1.35 1.196

19 2.376 1.305 0.658

21 2.408 1.221 0.533

23 3.178 1.115 0.691

25 3.136 0.999 0.347

Table 6.11: Variation of Cl with α at: Re = 100000

103

Fig 6.11: Graphical plot of variation of Cl with α at: Re = 100000

At Reynolds Number = 200000

Cl

α A-1 A-2 A-3

-5 1.55 -0.163 1.452

-3 1.582 0.076 1.423

-1 1.621 0.317 1.376

1 1.694 0.551 1.408

3 1.783 0.784 1.452

5 1.94 1.006 1.311

7 2.084 1.209 1.284

9 2.24 1.376 1.244

11 2.408 1.48 1.177

13 2.584 1.482 1.076

15 2.769 1.329 0.945

17 2.943 1.319 1.196

19 2.376 1.285 0.658

21 2.408 1.209 0.534

23 3.178 1.107 0.691

25 3.136 0.994 0.347

Table 6.12: Variation of Cl with α at: Re = 200000

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

A-1

A-2

A-3

104

Fig 6.12: Graphical plot of variation of Cl with α at: Re = 200000

At Reynolds Number = 300000

Cl

α A-1 A-2 A-3

-5 1.55 -0.163 1.452

-3 1.582 0.076 1.423

-1 1.621 0.317 1.376

1 1.694 0.553 1.408

3 1.783 0.787 1.452

5 1.94 1.01 1.311

7 2.084 1.217 1.284

9 2.24 1.391 1.244

11 2.408 1.501 1.177

13 2.584 1.524 1.076

15 2.769 1.413 0.945

17 2.943 1.311 1.196

19 2.376 1.277 0.659

21 2.408 1.2 0.534

23 3.178 1.1 0.691

25 3.136 0.99 0.347

Table 6.13: Variation of Cl with α at: Re = 30000

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

A-1

A-2

A-3

105

Fig 6.13: Graphical plot of variation of Cl with α at: Re = 300000

At Reynolds Number = 400000

Cl

α A-1 A-2 A-3

-5 1.551 -0.163 1.452

-3 1.582 0.076 1.423

-1 1.621 0.317 1.376

1 1.694 0.554 1.408

3 1.784 0.788 1.452

5 1.94 1.013 1.311

7 2.084 1.223 1.284

9 2.24 1.399 1.244

11 2.408 1.515 1.177

13 2.584 1.548 1.076

15 2.769 1.467 0.945

17 2.943 1.324 1.196

19 2.376 1.274 0.659

21 2.408 1.197 0.534

23 3.178 1.097 0.691

25 3.136 0.986 0.348

Table 6.14: Variation of Cl with α at: Re = 400000

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

A-1

A-2

A-3

106

Fig 6.14: Graphical plot of variation of Cl with α at: Re = 400000

At Reynolds Number = 400000

Table 6.15: Variation of Cl with α at: Re = 500000

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

A-1

A-2

A-3

Cl

α A-1 A-2 A-3

-5 1.551 -0.163 1.453

-3 1.584 0.076 1.423

-1 1.621 0.317 1.376

1 1.694 0.554 1.408

3 1.784 0.788 1.452

5 1.94 1.015 1.311

7 2.084 1.227 1.284

9 2.24 1.405 1.244

11 2.408 1.525 1.178

13 2.584 1.566 1.076

15 2.769 1.497 0.945

17 2.943 1.338 1.196

19 2.376 1.273 0.659

21 2.408 1.196 0.534

23 3.178 1.096 0.691

25 3.136 0.985 0.348

107

Fig 6.15: Graphical plot of variation of Cl with α at: Re = 500000

From the investigation of all the graphs and tables it has been observed that in

all Reynolds Number Cl increases with the increase of α.

So according to the investigation of Cl-α curve, Aerofoil-1 performs best.

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30

Cl

α

Cl Vs α

A-1

A-2

A-3

108

6.4 Investigation of Variation Maximum Lift Co-Efficient With Maximum

Camber of the 3 Aerofoils:

At Reynolds Number = 100000:

Aerofoil C max Cl max

A-1 0.04059 3.178

A-2 0.03555 1.425

A-3 0.034331 1.452

Table 6.16: Variation of Cl max with camber at Re = 100000

Fig 6.16: Graphical plot of variation of Cl max with camber at Re = 100000

0

0.5

1

1.5

2

2.5

3

3.5

0.034 0.035 0.036 0.037 0.038 0.039 0.04 0.041

Cl m

ax

Camber(%Chord)

Cl max Vs Camber

109

At Reynolds Number = 200000:

Aerofoil C max Cl max

A-1 0.04059 3.178

A-2 0.03555 1.482

A-3 0.034331 1.452

Table 6.17: Variation of Cl max with camber at Re = 200000

Fig 6.17: Graphical plot of variation of Cl max with camber at Re = 200000

0

0.5

1

1.5

2

2.5

3

3.5

0.034 0.036 0.038 0.04 0.042

Cl

max

Camber(%Chord)

Cl max Vs Camber

110

At Reynolds Number = 300000:

Aerofoil C max Cl max

A-1 0.04059 3.178

A-2 0.03555 1.524

A-3 0.034331 1.452

Table 6.18: Variation of Cl max with camber at Re = 300000

Fig 6.18: Graphical plot of variation of Cl max with camber at Re = 300000

0

0.5

1

1.5

2

2.5

3

3.5

0.034 0.036 0.038 0.04 0.042

Cl m

ax

Camber(%Chord)

Cl max Vs Camber

111

At Reynolds Number = 400000:

Aerofoil C max Cl max

A-1 0.04059 3.178

A-2 0.03555 1.548

A-3 0.034331 1.452

Table 6.19: Variation of Cl max with camber at Re = 400000

Fig 6.19: Graphical plot of variation of Cl max with camber at Re = 400000

0

0.5

1

1.5

2

2.5

3

3.5

0.034 0.036 0.038 0.04 0.042

Cl m

ax

Camber(%Chord)

Cl max Vs Camber

112

At Reynolds Number = 500000:

Aerofoil C max Cl max

A-1 0.04059 3.178

A-2 0.03555 1.566

A-3 0.034331 1.452

Table 6.20: Variation of Cl max with camber at Re = 500000

Fig 6.20: Graphical plot of variation of Cl max with camber at Re = 500000

After investigation of all the graphs and tables it can be decided that the trend of variation of

maximum lift coefficient with maximum camber is same at all the five Reynolds number and

that is Clmax increases steadily as camber increases.

From this point of view, Aerofoil-1 performs best but Aerofoil-2 may be chosen also as it

performs better than Aerofoil-3.

0

0.5

1

1.5

2

2.5

3

3.5

0.034 0.036 0.038 0.04 0.042

Cl m

ax

Camber(%Chord)

Cl max Vs Camber

113

6.5 Investigation of Variation Maximum Lift Co-Efficient With Maximum

Thickness of the 3 Aerofoils:

At Reynolds Number: 100000:

Aerofoil Tmax Cl max

A-1 0.1175 3.178

A-2 0.11724 1.425

A-3 0.117071 1.452

Table 6.21: Variation of Cl max with maximum thickness at Re = 100000

Fig 6.21: Graphical plot of variation of Cl max with maximum thickness at Re = 100000

0

0.5

1

1.5

2

2.5

3

3.5

0.117 0.1171 0.1172 0.1173 0.1174 0.1175 0.1176

Cl m

ax

Thickness(Maximum)

Cl max Vs Thickness(Maximum)

114

At Reynolds Number: 200000:

Aerofoil Tmax Cl max

A-1 0.1175 3.178

A-2 0.11724 1.482

A-3 0.117071 1.452

Table 6.22: Variation of Cl max with maximum thickness at Re = 200000

Fig 6.22: Graphical plot of variation of Cl max with maximum thickness at Re = 200000

0

0.5

1

1.5

2

2.5

3

3.5

0.117 0.1171 0.1172 0.1173 0.1174 0.1175 0.1176

Cl m

ax

Thickness(Maximum)

Cl max Vs Thickness(Maximum)

115

At Reynolds Number: 300000:

Aerofoil Tmax Cl max

A-1 0.1175 3.178

A-2 0.11724 1.524

A-3 0.117071 1.452

Table 6.23: Variation of Cl max with maximum thickness at Re = 300000

Fig 6.23: Graphical plot of variation of Cl max with maximum thickness at Re = 300000

0

0.5

1

1.5

2

2.5

3

3.5

0.117 0.1171 0.1172 0.1173 0.1174 0.1175 0.1176

Cl m

ax

Thickness(Maximum)

Cl max Vs Thickness(Maximum)

116

At Reynolds Number: 400000:

Aerofoil Tmax Cl max

A-1 0.1175 3.178

A-2 0.11724 1.548

A-3 0.117071 1.452

Table 6.24: Variation of Cl max with maximum thickness at Re = 400000

Fig 6.24: Graphical plot of variation of Cl max with maximum thickness at Re = 400000

0

0.5

1

1.5

2

2.5

3

3.5

0.117 0.1171 0.1172 0.1173 0.1174 0.1175 0.1176

Cl m

ax

Thickness(Maximum)

Cl max Vs Thickness(Maximum)

117

At Reynolds Number: 500000:

Aerofoil Tmax Cl max

A-1 0.1175 3.178

A-2 0.11724 1.566

A-3 0.117071 1.452

Table 6.25: Variation of Cl max with maximum thickness at Re = 500000

Fig 6.25: Graphical plot of variation of Cl max with maximum thickness at Re = 500000

After investigation of all the graphs and tables it can be decided that the trend of variation of

maximum lift coefficient with maximum camber is same at all the five Reynolds number and

that is Clmax increases steadily as camber increases.

From this point of view, Aerofoil-1 performs best but Aerofoil-2 may be chosen also as it

performs better than Aerofoil-3.

0

0.5

1

1.5

2

2.5

3

3.5

0.117 0.1171 0.1172 0.1173 0.1174 0.1175 0.1176

Cl m

ax

Thickness(Maximum)

Cl max Vs Thickness(Maximum)

118

6.6 Investigation of Variation Maximum Lift Co-Efficient With Reynolds

Number:

Aerofoil-1:

Re Cl max

1.00E+05 3.178

2.00E+05 3.178

3.00E+05 3.178

4.00E+05 3.178

5.00E+05 3.178

Table 6.26: Variation of Cl max with Reynolds Number of Aerofoil-1

Fig 6.26: Graphical Plot of Variation of Cl max with Reynolds Number of Aerofoil-1

0

0.5

1

1.5

2

2.5

3

3.5

0.00E+00 2.00E+05 4.00E+05 6.00E+05

Cl m

ax

Re

Cl max Vs Re

119

Aerofoil-2:

Re Cl max

1.00E+05 1.425

2.00E+05 1.482

3.00E+05 1.524

4.00E+05 1.548

5.00E+05 1.566

Table 6.27: Variation of Cl max with Reynolds Number of Aerofoil-2

Fig 6.27: Graphical Plot of Variation of Cl max with Reynolds Number of Aerofoil-2

1.4

1.42

1.44

1.46

1.48

1.5

1.52

1.54

1.56

1.58

0.00E+00 2.00E+05 4.00E+05 6.00E+05

Cl m

ax

Re

Cl max Vs Re

120

Aerofoil-3:

Re Cl max

1.00E+05 1.452

2.00E+05 1.452

3.00E+05 1.452

4.00E+05 1.452

5.00E+05 1.452

Table 6.28: Variation of Cl max with Reynolds Number of Aerofoil-3

Fig 6.28: Graphical Plot of Variation of Cl max with Reynolds Number of Aerofoil-3

From the above graphs and tables it has been observed that Cl max increases with Reynolds

Number only in case of Aerofoil-2.

So according to this investigation Aerofoil-2 performs best.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0.00E+00 1.00E+05 2.00E+05 3.00E+05 4.00E+05 5.00E+05 6.00E+05

Cl m

ax

Re

Cl max Vs Re

121

6.7 Investigation of Cl Values At Different Angles of Attack:

At 7 degree AOA

Cl values

Re. No A-1 A-2 A-3

1.00E+05 2.084 1.19 1.284

2.00E+05 2.084 1.209 1.284

3.00E+05 2.084 1.217 1.284

4.00E+05 2.084 1.223 1.284

5.00E+05 2.084 1.227 1.284

constant 3.1%

increase

constant

Table 6.29: Variation of Cl values with Reynolds Number for the 3 Aerofoils at 7° AOA

At 5 degree AOA

Cl values

Re. No A-1 A-2 A-3

1.00E+05 1.94 0.999 1.311

2.00E+05 1.94 1.006 1.311

3.00E+05 1.94 1.01 1.311

4.00E+05 1.94 1.013 1.311

5.00E+05 1.94 1.015 1.311

constant 1.6%

increase

constant

Table 6.30: Variation of Cl values with Reynolds Number for the 3 Aerofoils at 5° AOA

122

At 11 degree AOA

Cl values

Re. No A-1 A-2 A-3

1.00E+05 2.408 1.425 1.177

2.00E+05 2.408 1.48 1.177

3.00E+05 2.408 1.501 1.177

4.00E+05 2.408 1.515 1.177

5.00E+05 2.408 1.525 1.178

constant 7% increase constant

Table 6.31: Variation of Cl values with Reynolds Number for the 3 Aerofoils at 11°

AOA

From above graphs and tables it has been observed that at 5°, 7°, 11° angles of attack Cl

increases only for Aerofoil-2. But as the surveillance UAV optimizes for maximum

endurance i.e, maximum L/D and according to previous decision Aerofoil-2 is the optimized

aerofoil which gives maximum L/D at 7 degree. So the optimized angle of attack is 7°

123

6.8 Investigation of variation of Cl/Cd values at different Angles of Attack:

At Reynolds Number: 100000:

Cl/Cd

α A-1 A-2 A-3

-5 43.789 -4.198 55.523

-3 27.772 2.522 62.709

-1 11.749 10.443 34.502

1 0.057 17.247 6.981

3 -1.82 24.378 23.485

5 0.168 29.644 23.25

7 0.786 29.934 38.238

9 1.697 28.047 30.048

11 2.533 22.887 23.363

13 3.16 12.924 17.058

15 29.028 10.308 2.85

17 32.256 8.282 43.839

19 9.764 6.373 1.282

21 0.62 4.505 0.871

23 17.677 3.206 12.257

25 14.784 2.266 0.407

Table 6.32: variation of Cl/Cd values at different Angles of Attack at Re= 100000

124

Figure 6.29: Graphical Plot of variation of Cl/Cd values at different AOA at Re= 100000

At Reynolds Number: 200000:

Cl/Cd

α A-1 A-2 A-3

-5 42.198 -5.909 63.744

-3 35.575 2.666 56.916

-1 15.583 11.108 43.301

1 0.08 19.456 9.376

3 -1.818 26.447 30.21

5 0.238 30.865 29.222

7 1.111 33.342 41.501

9 2.401 32.928 32.237

11 3.564 28.256 25.061

13 4.473 20.539 18.177

15 38.814 11.543 3.673

17 40.278 8.77 61.5

19 11.93 6.605 1.709

21 0.854 5.228 1.143

23 24.719 3.772 16.457

25 20.731 2.673 0.539

Table 6.33: variation of Cl/Cd values at different Angles of Attack at Re= 200000

-10

0

10

20

30

40

50

60

70

-10 0 10 20 30

Cl/

Cd

α

Cl/Cd Vs α

A-1

A-2

A-3

125

Figure 6.30: Graphical Plot of variation of Cl/Cd values at different AOA at Re= 200000

At Reynolds Number: 300000:

Cl/Cd

α A-1 A-2 A-3

-5 42.619 -6.021 67.017

-3 40.651 2.734 61.765

-1 18.191 11.478 48.791

1 0.098 20.334 10.951

3 -1.816 28.123 34.584

5 0.291 32.24 32.542

7 1.361 35.279 43.197

9 2.94 34.947 33.4

11 4.386 30.647 25.88

13 5.476 23.547 18.63

15 43.535 14.584 14.082

17 45.554 9.286 72.964

19 14.481 7.148 2.012

21 0.982 5.542 1.35

23 29.839 4.135 20.041

25 25.089 2.922 0.639

Table 6.34: variation of Cl/Cd values at different Angles of Attack at Re= 300000

-10

0

10

20

30

40

50

60

70

-10 -5 0 5 10 15 20 25 30

Cl/

Cd

α

Cl/Cd Vs α

A-1

A-2

A-3

126

Figure 6.31: Graphical Plot of variation of Cl/Cd values at different AOA at Re= 300000

At Reynolds Number: 400000:

Cl/Cd

α A-1 A-2 A-3

-5 42.365 -6.047 52.969

-3 44.087 2.79 62.228

-1 20.911 11.7 51.469

1 0.113 20.725 12.199

3 -1.815 29.004 38.06

5 0.337 33.144 51.877

7 1.565 36.602 43.349

9 3.394 36.278 34.117

11 5.072 32.035 26.454

13 6.319 25.458 19.014

15 47.095 16.971 14.407

17 49.562 9.958 83.566

19 15.632 7.487 2.203

21 1.074 5.75 1.503

23 35.09 4.349 21.6

25 28.592 3.183 0.698

Table 6.35: variation of Cl/Cd values at different Angles of Attack at Re= 400000

-10

0

10

20

30

40

50

60

70

80

-10 -5 0 5 10 15 20 25 30

Cl/

Cd

α

Cl/Cd Vs α

A-1

A-2

A-3

127

Figure 6.32: Graphical Plot of variation of Cl/Cd values at different AOA at Re= 400000

At Reynolds Number: 500000:

Cl/Cd

α A-1 A-2 A-3

-5 42.859 -6.122 53.442

-3 56.677 2.839 63.91

-1 22.574 11.883 54.182

1 0.126 20.959 13.322

3 -1.814 28.867 40.833

5 0.376 34.159 53.669

7 1.748 37.62 43.637

9 3.725 37.377 34.542

11 5.672 33.345 26.797

13 7.059 26.7 19.29

15 45.125 18.571 14.506

17 52.823 10.614 89.06

19 16.232 7.794 2.384

21 15.103 5.975 1.609

23 38.607 4.573 22.898

25 32.6 3.39 0.771

Table 6.36: variation of Cl/Cd values at different Angles of Attack at Re= 500000

-20

-10

0

10

20

30

40

50

60

70

80

90

-10 -5 0 5 10 15 20 25 30

Cl/

Cd

α

Cl/Cd Vs α

A-1

A-2

A-3

128

Figure 6.33: Graphical Plot of variation of Cl/Cd values at different AOA at Re= 500000

From the above graphs and tables it is visible that Aerofoil-3 gives maximum value but it is

in the stall region. But within the acceptable range of angle of attack Aerofoil-2 and Aerofoil-

3 give suitable value from which we can take Aerofoil-2 as it meets other performance

requirements. Thus it is the acceptable one.

-20

0

20

40

60

80

100

-10 -5 0 5 10 15 20 25 30

Cl/

Cd

α

Cl/Cd Vs α

A-1

A-2

A-3

129

CHAPTER 7

DISCUSSIONS & RECOMMENDATION

_________________________________________

7.1 Discussions

In this thesis three aerofoils have been developed for experimental investigation by subsonic

wind tunnel. A number of conclusions can be drawn from the tests and investigations that

have been done such as

At all Reynolds Number Aerofoil-2 performs best while investigating the variation of

drag co-efficient with the variation of angle of attack and it gives the minimum drag

co-efficient.

At all Reynolds Number Aerofoil-1 performs best while investigating the variation of

lift co-efficient with the variation of angle of attack.

Aerofoil-2 performs best while investigating the variation of pitching moment co-

efficient with the variation of angle of attack.

Aerofoil-1 performs best but Aerofoil-2 may be chosen also as it performs better than

Aerofoil-3 in case of investigation of variation maximum lift co-efficient with

maximum camber and maximum thickness.

Aerofoil-2 performs best in the investigation of variation of maximum lift co-efficient

with Reynolds number.

Aerofoil-3 gives maximum Cl/Cd values at different AOA and it is in the stall region.

But within the acceptable range of angle of attack Aerofoil-2 and Aerofoil-3 give

130

suitable value from which we can take Aerofoil-2 as the desired aerofoil, as it meets

other performance requirements. Thus Aerofoil-2 is the acceptable one.

After discussing the comparative performance of Aerofoils individually it has been

decided that Aerofoil-2 can best meet performance requirements. Although in some

cases Aerofoil-1 performs best but Aerofoil-1 failed to maintain a stable variation of

pitching moment with angle of attack which is one of our major performance

requirements. Again Aerofoil-1 gives maximum drag co-efficient. On the other hand

Aerofoil-2 gives minimum drag co-efficient as well as it can maintain a stable

variation of pitching moment co-efficient with angle of attack i.e. it meets major

performance requirement.

So, Aerofoil-2 best meet the performance requirements and it is the optimised

aerofoil.

.

131

7.2 Recommendations for future work:

Future work should focus on developing more detailed wind tunnel testing

results.

The same analysis can be done with the other types of aerofoil like semi-symmetrical

aerofoil, symmetrical aerofoil.

In future a step can be taken which will be useful in improving the aerodynamics of

cambered Aerofoils through improving the lower surface boundary layer

performance by designing an optimised leading edge.

Using the optimised aerofoil of this thesis, wing for unmanned aerial vehicle can be

constructed.

Applying this methodology, comparison of performance among different aerofoil can

be made in future.

132

References

_________________________________________

1. Daniel P. Raymer, Aircraft Design: A Conceptual Approach, AIAA Education Series,

1992

2. Egbert Torenbeek, Synthesis of Subsonic Airplane Design, Delft University, 1976

3. Denis Howe, Aircraft Conceptual Design Synthesis, Professional Engineering

Publishing, 2000

4. John D. Anderson Jr., Fundamentals of Aerodynamics, 2001

5. L J Clancy, Aerodynamics

6. Jan Roskam, Chuan-Tau Edward Lan, Airplane Aerodynamics and Performance

7. John Dreese, The Dreese Airfoil Primer

8. Dr.Ing. Luca Cistriani, UAV Design Engineer , Falco UAV Low Reynolds Airfoil

Design and Testing at Galileo Avionica

9. Michael R. Reid, Thin/Cambered/Reflexed Airfoil Development for Micro-Air

Vehicles at Reynolds Numbers Of 60,000 To 150,000

10. G Manikandan, M Ananda Rao, Effect of Maximum Thickness Location of An

Aerofoil on Aerodynamic Characteristics.

11. Nicholas K. Borer, Design and Analysis of Low Reynolds Number Airfoils

12. Kyoungwoo Park, Ji-Won Han, Hyo-Jae Lim, Byeong-Sam Kim, and Juhee Lee,

Optimal Design of Airfoil with High Aspect Ratio in Unmanned Aerial Vehicles

13. Shawn E. Gano, John E. Renaud, Stephen M. Batill, Andr es Tovar, Shape

Optimization for Conforming Airfoils

14. J. Hua, F.M. Kong, Po-yang Jay Liu, D.W. Zingg, Optimization Of Long-Endurance

Airfoils

15. Luis E. Casas, Jon M. Hall, Sean A. Montgomery, Hiren G. Patel, Sanjeev S. Samra,

Joe Si Tou, Omar Quijano, Nikos J. Mourtos, Periklis P. Papadopoulos; Preliminary

Design and CFD Analysis of a Fire Surveillance Unmanned Aerial Vehicle

16. Neal Allgood, Kevin Albarado, Elizabeth Barrett, Grace Colonell, Brian Dennig,

Jayme Howsman, and Ajay Madhav; Design, Fabrication, and Testing of a

Surveillance/Attack UAV

133

Bibliography

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4. http://scienceofaircraft.blogspot.com/2010_08_01_archive.html

5. http://www.dreesecode.com/primer/airfoil1.html

6. http://www.ae.illinois.edu/m-selig/uiuc_lsat/Airfoils-at-Low-Speeds.pdf

7. https://ritdml.rit.edu/bitstream/handle/1850/2607/MReidThesis09?sequence=1

8. http://mail.tku.edu.tw/095980/airfoil%20design.pdf

9. http://www.disasterzone.net/projects/docs/mae171a/wind_tunnel_experiment.pdf

10. https://ritdml.rit.edu/bitstream/handle/1850/2607/MReidThesis09?sequence=1

11. http://faculty.dwc.edu/sadraey/Chapter%205.%20Wing%20Design.pdf

12. http://people.clarkson.edu/~pmarzocc/AE429/The%20NACA%20airfoil%20series.pd

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