Basic Principles of Flight Chapter 4

Chapter - 4

1 by Shiva U Asst. Prof. AAE Dept.

Significance of speed of sound, Air speed and Ground

Speed, Properties of Atmosphere, Bernoullis Equation, Forces on the Airplane, Airflow over wing section, pressure

distribution over a wing section, Generation of lift, Drag,

Pitching moments, Types of Drag, Lift curve, Drag curve,

Lift/Drag Ratio curve, Factors affecting lift and Drag, center

of pressure and its effects, Airfoil Nomenclature, Types of

Aerofoil, Wing section-Aerodynamic center, Aspect ratio,

Effects of lift, Drag, Speed, Air Density on Drag.


Significance of Speed of Sound

The speed of "sound" is actually the speed of transmission of a small disturbance through a medium.

Sound itself is a sensation created in the human brain in

response to sensory inputs from the inner ear.


As a general rule Air is compressible Medium. When a disturbance producing an infinitesimal pressure change

is generates at some point in the flow, this disturbance

will be propagated throughout the air as a pressure

wave travelling at the speed of sound.

Knowing the magnitude of the speed of the sound is important. If the flow velocity exceeds the propagation

speed of disturbances, these disturbances will pile up

to form strong waves, called shock waves.

These shock waves in turn produce large changes in flow properties. One important consequence of all this

is an increase in drag.


Pressure-pulse or compression-type wave (longitudinal wave) confined to a plane. This is the only type of sound

wave that travels in fluids (gases and liquids)


Transverse wave affecting atoms initially confined to a plane. This additional type of sound wave (additional type

of elastic wave) travels only in solids, and the sideways

shearing motion may take place in any direction at right

angles to the direction of wave-travel (only one shear

direction is shown here, at right angles to the plane).

Furthermore, the right-angle shear direction may change

over time and distance, resulting in different types of

polarization of shear-waves


Wave Simulation


Airspeed Airspeed is the speed of an aircraft relative to the air.

Among the common conventions for qualifying airspeed are: indicated airspeed ("IAS"), calibrated airspeed ("CAS"), true airspeed ("TAS"), equivalent airspeed ("EAS") and density airspeed.

Indicated airspeed (IAS) is the airspeed indicator reading (ASIR) uncorrected for instrument, position, and other errors.

Calibrated airspeed (CAS) is indicated airspeed corrected for instrument errors, position error (due to incorrect pressure at the static port) and installation errors.

Equivalent airspeed (EAS) is defined as the speed at sea level that would produce the same incompressible dynamic pressure as the true airspeed at the altitude at which the vehicle is flying.

True airspeed (TAS) is the speed of the aircraft relative to the atmosphere.


9

Ground Speed Groundspeed is the speed of the aircraft relative to the

ground rather than through the air, which can itself be

moving.

by Shiva U Asst. Prof. AAE Dept.

Standard Atmosphere

What we call a Standard Atmosphere is a mathematical abstraction of the real atmosphere

A standard atmosphere can be thought of as the mean or average conditions of temperature, pressure and

density for given altitudes

This model allows engineers to estimate atmospheric conditions for use in design and analysis

There are different standard atmospheres in use: 1959 ARDC Model Atmosphere

U.S. Standard Atmosphere, 1962

ICAO Standard Atmosphere


Need to define what we mean by altitude first

Absolute Altitude, ha, is the height above the earths center

Geometric Altitude, hG, is the height above sea level.

Geopotential Altitude, h A mathematical definition: the altitude for a given condition

(T, p and ), if the gravitation acceleration was constant at the sea level value.

By hydrostatics: dp = - g dhG or dp = - go dh

Knowing the variation of g with hG yields the relation

h= (r/ (r + hG)) hG Very little difference at normal airplane altitudes

We will use geopotential altitude almost exclusively!!


Figure of standard atmosphere variation


Mathematical Model

The standard atmosphere defines the temperature variation

with altitude as shown

Now need to find pressure and density as functions of either T or h

Begin with the hydrostatic equation, divided by the equation of state for a perfect gas

dp / p= -godh/RT

Can integrate this equation for pressure when we know the P relationship between T and h


Gradient Layers, T varies linearly with h

Define a lapse rate, a, by: dT/dh = a

Define the conditions at the layer base by h1, p1, 1, and T1 In previous equation, replace dh with dT/a and integrate

w.r.t. temperature to get:

P/P1= (T/T1)-g

o/aR

And since p/p1 = (T)/(1T1)

/1=(T/T1)-[(g

0/aR)+1]


Isothermal Layers, T is constant

Start at the base of the layer where we will define the conditions as h1, p1, 1, and T

Integrate the previous equation W.R.T. h holding T Constant

P/P1= e (go/RT)( hh

1) = /1


Other Altitudes

Most flight instruments do not directly measure altitude -they measure pressure and deduce altitude.

If we know the local air pressure and use the standard atmosphere tables to look up the corresponding altitude, we call this the pressure altitude.

Similarly, knowing the local density, we could look up the density altitude, or knowing the temperature, the temperature altitude.

Remember, however, that since the local air rarely matches the standard atmosphere model, these altitudes rarely equal the geometric altitude - or even each other.


Daniel Bernoulli (1700 -1782) Bernoulli's Principle is a physical phenomenon

that was named after the

Swiss scientist Daniel

Bernoulli who lived

during the eighteenth

century. Bernoulli studied

the relationship of the

speed of a fluid and

pressure.

18

Bernoullis Principle


Bernoulli's Principle (top) says that increased air velocity produces decreased pressure.

Lift (bottom) is produced by an airfoil through a combination of decreased pressure above the airfoil and increased pressure beneath it.

Flow Over an Airfoil

19

Flow over an Airfoil


Bernoulli's Equation


Forces on the Airplane


During flight the four forces acting on the airplane are:

Lift is the upward force created by the effect of airflow as it passes over and under the wings. It supports the

airplane in flight.

Weight is a downward force caused by the pull of gravity. It opposes lift.

Thrust is the forward force generated by the propeller and engine which propels the airplane through the air.

Drag is the rearward force that limits the speed of the airplane.


Airfoil Geometry

23

An airfoil is the 2D cross-

section shape of the wing,

which creates sufficient lift

with minimal drag


HOW DOES AN AIRFOIL GENERATE LIFT?

Lift due to imbalance of pressure distribution over top and bottom surfaces of airfoil (or wing) o If pressure on top is lower than pressure on bottom surface, lift is generated

o Why is pressure lower on top surface?

We can understand answer from basic physics: o Continuity (Mass Conservation)

o Newtons 2nd law (Euler or Bernoulli Equation)

24

Lift = PA



1. Flow velocity over top of airfoil is faster than over bottom surface

o Streamtube A senses upper portion of airfoil as an obstruction

o Streamtube A is squashed to smaller cross-sectional area

o Mass continuity rAV=constant: If A THEN V

25

Streamtube A is squashed

most in nose region

(ahead of maximum thickness)

A B



2. As V p

o Incompressible: Bernoullis Equation

o Compressible: Eulers Equation

o Called Bernoulli Effect

3. With lower pressure over upper surface and higher pressure over bottom surface, airfoil feels a net force in upward direction Lift

VdVdp

Vp

r

r

constant2

1 2

26

Most of lift is produced

in first 20-30% of wing

(just downstream of leading edge)


Ty

p

i

c

a

l

S

t

r

e

a

m

l

i

n

e

s

27

Angle of Attack

chord lineV


Pressure Distribution

99500

99550

99600

99650

99700

99750

99800

99850

99900

99950

100000

0 0.2 0.4 0.6 0.8 1

Chordwise Distance, x, m

Su

rfa

ce

Pre

ss

ue

, P

, N

/sq

m

Net Normal Force

Upper Surface Pressure

Lower Surface Pressure

n P P dxlc

u ( )0


Pressure Coefficient Distribution

02

2

1

V

ppcp

r

2

2

1

V

ppcp

r

12

2

1

2

2

1

2

2

1

0

0

V

V

V

ppcp

r

r

r

30

In free-stream:

At stagnation point (V=0):

Positive Cp means the pressure is higher than the free-

stream (atmospheric) pressure, and negative Cp means

suction relative to free-stream pressure. The maximum,

which occurs at the stagnation point, is always 1. by Shiva U Asst. Prof. AAE Dept.

Pressure Distribution on

Cambered Airfoil


by Shiva U Asst. Prof. AAE Dept. 32

Computation Fluid Dynamics Simulation


CFD Simulation: Near stall


CFD Simulation: Fully Stalled


Evolution of

Airfoil Design

Laminar boundary

layer creates less skin

friction drag


Airfoils

1- Geometric characteristics of the airfoils.

2- Aerodynamic characteristics of the airfoils.

Airfoil Geometric Characteristics


40

Airfoil geometric characteristics include:

1- Mean camber line : The locus of points halfway between

the upper and lower surfaces as measured perpendicular

to the mean camber line.

2- Leading & trailing edges: The most forward and rearward

points of the mean camber line.

3- Chord line: The straight line connecting the leading and

trailing edges.


4- Chord C : The distance from the leading to trailing edge

measured along the chord line.

5- Camber : The maximum distance between the mean

camber line and the chord line.

6- Leading edge radius and its shape through the leading

edge.

7- The thickness distribution: The distance from the upper

surface to the lower surface, measured perpendicular

to chord line


NACA Airfoil Series

1- NACA 4-digit series

2- NACA 5-digit series

3- NACA 1-series or 16-series

4- NACA 6- series


NACA Four-Digit Series

Example: NACA 2412

NACA 2 4 12

43

Camber in

percentage of chord

yc = 0.02 C

Position of camber

in tenths of chord xc = 0.4 C

Maximum thickness (t )

in percentage of chord

(t/c)max = 0.12

xc yc C


NACA Five-Digit Series

Example: NACA 23012

NACA 2 30 12

45

When multiplied by 3/2

yields the design lift

coefficient Cl in tenths.

Cl = 0.3

When divided by 2, gives

the position of the

camber in percent of

chord xc = 0.15 C

Maximum thickness

(t ) in percentage of

chord (t/c)max = 0.12


way2v_000Sticky NoteNational Advisory Committee for Aeronautics (NACA)

NACA Six- Series

Example: NACA 64-212

NACA 6 4 - 2 12

46

Series

designation 6

Location of minimum

pressure in tenths of

chord (0.4 C)

Design lift

coefficient in

tenths (0.2)

Maximum thickness (t )

in percentage of chord

(t/c)max = 0.12

Note that this is the series of laminar airfoils .


The component of the total aerodynamic force that acts at right angles to the resultant relative wind

The two factors that most affect the coefficient of lift and the coefficient of drag are:

1. Shape of the airfoil &

2. Angle of Attack

49

LIFT


L= CL 1/2 S V2

L ~ Lift force

CL ~ Coefficient of lift

~ density of the air in slugs S ~ total wing area in square feet

V ~ airspeed (in feet per second)


D= CD 1/2 S V2

D ~ Drag force

CD ~ Coefficient of lift

~ density of the air in slugs

S ~ total wing area in square feet



Mcg = CM,cg1/2 S V2c

Mcg ~Moment about center of gravity

~ density of the air in slugs

S ~ total wing area in square feet


c ~ chord length


Types of Drag


Form or pressure drag is caused by the

separation of air that is flowing over the aircraft

or airfoil.


Flow over flat plate


Flow over Cylinder

Flow over Airfoil

The leading edge of a wing will always produce a certain amount

of friction drag.


Induced drag is a byproduct of lift.


Aspect Ratio


Center of Pressure

Center or pressure : The point of intersection

between the chord line and the line of action of

the resultant aerodynamic force R.


Moment on an Aircraft


63

Aerodynamic Center


Aerodynamic Center The aerodynamic center is the point at which the

pitching moment coefficient for the airfoil does not

vary with lift coefficient i.e. angle of attack.


Lift Curve


Drag Curve


Lift/Drag Ratio Curve


Factors Affecting Lift & Drag


Effect of lift, drag, Speed & Air Density

on Drag


Basic Principles of Flight Chapter 4

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