UEE 306 Lecture1

UEE 306 Uçuş Teorisi

Ahmet AĞIRMAN

[email protected]

Erciyes Üniversitesi Sivil Havacılık Yüksek Okulu

Preliminaries

Lecture 1

UEE306-2013/2014

Overview and Definitions

The Atmospher

Basic Aerodynamics

Subsonic Airflow


The Atmospher

Basic Aerodynamics

Subsonic Airflow

Flight

• Ability to hover in as well as navigate through the air

• Not all but some living beings like eagles besides human-made systems like aircrafts

Overview & Definitions The atmospher Basic Aerodynamics Subsonic Airflow

Primary req’s of an a/c

• Wing: Generates a lift force




• Fuselage: Accomodates the payload





• Tail surfaces: Adds stability






• Control surfaces: Change direction of flight






• Control surfaces: Change direction of flight

• Engines: Make a/c go forward


The axis system

• x, y, z lines

• +x, -x, +y, -y, +z, –z directions

• A/c flight: combination of +x, y, z

• +x: due to engines

• -z: due to weight

• +z: due to ?

• y: due to ?


The four forces

• Stationary a/c: Only weight force at –z direction acts on it


The four forces


• In order to fly, a force ≥ W at +z direction needed, which is Lift, L


The four forces



• In order to get L, a force moves a/c at +x direction needed, which is Trust, T


The four forces



• In order to get L, a force moves a/c at +x direction needed, which is Trust, T

• Due to moving forward at +x direction, a force at –x direction created, which is Drag, D


Lift vs buoyancy

• Lift occurs due to motion

• Buoyancy does not occur due to motion


Mass, Force & Weight

• Mass – SI Unit: kilogram (kg) – Amount of a material – Can exist witout weight – A measure of effort putting an object in motion or rest


Mass, Force & Weight

• Mass – SI Unit: kilogram (kg) – Amount of a material – Can exist witout weight – A measure of effort putting an object in motion or rest

• Force & Weight – SI Unit: Newton (N) – Force: Universal reason for any physical change, i.e. in motion, in appereance, etc. – Weight: Gravitational force that objects apply to each other

– Force vs mass: 𝐹 = 𝑚. 𝑔 where 𝑔 = 9,81𝑚𝑠2 : gravitational acceleration, m: mass

• An aircarft with 60 tonnes of weight needs a minimum of lift:

𝐹 = 𝑚.𝑔 = 60000𝑥9,81 = 585600 𝑁 – Cannot exist without mass


Center of Gravity (CG)

• A location on aircraft through which the weight of a/c assumed to act

• A flying a/c assumed to rotate around its CG

• The CG of an a/c should remain in certain physical limits due to stability and controllability of the a/c


Work, Power, Energy

Work o SI Unit: Joule (J) o A net force does work if

the object moves in the direction of the force

o Work=Force x Distance, Nm or J

o Example: when 10 N force moves a body 2 metres away in the direction of it the work done is 20 J


Work, Power, Energy






Power

o SI Unit: Watt (W)

o The work has been done in unit time

o Power=ForcexDistance/Time, Nm/s or J/s or Watt

o Example: when 10 N force moves a body 2 metres away in the direction of it in 4 seconds, the power of that force is 5 W

Work, Power, Energy





o Imagine that work is the energy consumed, precisely the kinetic energy consumed.


Power

o SI Unit: Watt (W)

o The work has been done in unit time

o Power=ForcexDistance/Time, Nm/s or J/s or Watt

o Example: when 10 N force moves a body 2 metres away in the direction of it in 4 seconds, the power of that force is 5 W

Energy

o SI Unit: Joule (J)

o Ability to do work

Kinetic Energy


Kinetic Energy

o SI Unit: Joule (J)

o Energy possesed due to motion

o 𝐸𝑘 =1

2𝑚𝜗 2

o Example: 1 kg of air with 52 m/s (100 knots) velocity has 1352 J of (kinetic) energy

Newton’s first law of motion & Inertia


The law o Unless an external force applied,

o a body will rest if it was on rest OR o will keep its linear movement if was doing so.

Inertia o Resistance of a body against a change in its motion o Inertia is measured by mass of the body o The reason a body needs an external force to

experience a change in motion is inertia.

Newton’s second law of motion & Velocity, Acceleration


The law

o In order to change acceleration of a body, there needs to be a force proportional to mass of the body

𝐹 = 𝑚𝑎

o Velocity: The amount of distance the body takes in a unit of time. (m/s)

o Acceleration: The rate of change of velocity (m/s²)

Momentum


Which one requires a bigger force to get stopped in 1 sec?

10 kg of body with 3 m/s velocity vs 5 kg of body with 3 m/s velocity

10 kg of body with 5 m/s velocity vs 10 kg of body with 3 m/s velocity

1 tonnes of body with 1 m/s velocity vs 15 kg of body with 100 m/s velocity?

o Momentum: the amount of motion a body posseses: 𝑀=𝑚𝑣, kg-m/s

o Velocity: The amount of distance the body takes in a unit of time. (m/s) o Acceleration: The rate of change of velocity (m/s²)

Newton’s third law of motion


Every action has an equal and opposite reaction

UEE306-2013/2014


The Atmospher

Basic Aerodynamics

Subsonic Airflow

The atmosphere and air


• Envelope of the Earth • Has a mass and weight • Has an undetermined shape • Most important parameter is air density • If air density over airfoil decreases, then mass flow per

second decreases thus for the required lift force, speed should increase

• Air is compressible • Air flows from high pressure region to low pressure region • Air has a viscosity which is relatively very small

Static Pressure


• SI Unit: N/m², symbol: ‘p’ • 1 N/m² = 1 Pa, 100 Pa = 1 hPa = 1

milibar • 1013,25 milibar = 1.01325 bar = 1 atm • Result of weight of atmosphere • For a given altitude, all locations of

a/c have same static pressure • Static pressure decrases

exponentially by increase of altitude • Static pressure is always in precense

upon aircaft

Temperature


• SI Unit: C° or K°

• 1 K° = -273 C°

• Between 0 to 36000 ft, decreases almost linearly by increase of altitude as 6,4 C° for every 1000 meter

• After 36000 ft, it is constant at -56 C° for a while

Air Density


• SI Unit: kg/m³, symbol: ro (ρ)

• Depends on temperature, static pressure and humidity

• Ideal gas formula: 𝑝𝑉 = 𝑛𝑅𝑇

or

𝑝𝑉 =𝑚

𝑀𝑅𝑇

where M: molar mass in kg/mol

then

𝑝 =𝑚

𝑀

𝑅

𝑉𝑇

𝑝 = 𝜌𝑅𝑠𝑇

where ρ=m/M, density of dry air; 𝑅𝑠: Spesific dry air constant

hence

𝑝𝜌𝑇 = constant

Air Density


• SI Unit: kg/m³, symbol: ro (ρ) • Depends on temperature, static pressure and humidity • Ideal gas formula:

𝑝𝑉 = 𝑛𝑅𝑇 or

𝑝𝑉 =𝑚

𝑀𝑅𝑇

where M: molar mass in kg/mol then

𝑝 =𝑚

𝑀

𝑅

𝑉𝑇


where ρ=m/M, density of dry air; 𝑅𝑠: Spesific dry air constant hence


• Note: When altitude increases;

Air Density




𝑝𝑉 =𝑚

𝑀𝑅𝑇


𝑝 =𝑚

𝑀

𝑅

𝑉𝑇





Air Density




𝑝𝑉 =𝑚

𝑀𝑅𝑇


𝑝 =𝑚

𝑀

𝑅

𝑉𝑇





International Standard Atmosphere (ISA)


• Sea level values: – Temperature (𝑇0): 15 C°

– Static Air Pressure (𝑝0): 1013,25 hPa or 1 atm

– Dry air density (𝜌0): 1,225 kg/m³

• Temperature change is – 2 C° for each 1000 ft or

– 6,4 C° for each 1000 m untill 36000 ft

• Relative air density (𝜌𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒/𝜌0) decreases: For example, at 40000 ft altitude relative air density is 0,25

Dynamic Air Pressure


• Kinetic energy of incompressible air in unit volume, symbol is ‘q’ • Kinetic energy of air with mass m:

𝐸𝑘 =1

2𝑚𝜗2;

J or Nm • Kinetic energy of air in unit volume:

(𝐸𝑘)𝑉 = (

1

2𝑚𝜗2)/𝑉;

Nm/m³=N/m²=F/A=p≜Pressure

𝐸𝑘−𝑢𝑛𝑖𝑡 𝑣𝑜𝑙𝑢𝑚𝑒 =1

2𝜌𝜗2, N/m²

• Example: An aircrafts flies with 100 m/s velocity at sea level. Then the dynamic pressure over the body is

𝑞 =1

2𝜌𝜗2 =

1

21,225𝑥1002 = 61,25ℎ𝑃𝑎

• If you know the total surface A the dynamic pressure applies, then the total force the a/c under will be

𝐹 = 𝑝𝐴

Measurement of Dynamic Air Pressure

Overview & Definitions The Atmospher Basic Aerodynamics Subsonic Airflow

• Pitot tube receives the total pressure:

𝑝𝑡𝑜𝑡𝑎𝑙 = 𝑝𝑠𝑡𝑎𝑡𝑖𝑐 +1

2𝜌𝜗2

• Static port receives only the static pressure • Air Speed Indicator (ASI) substracts the static pressure from the total:

𝑞 = 𝑝𝑡𝑜𝑡𝑎𝑙 − 𝑝𝑠𝑡𝑎𝑡𝑖𝑐 then

𝜗 =2(𝑝𝑡𝑜𝑡𝑎𝑙 − 𝑝𝑠𝑡𝑎𝑡𝑖𝑐)

𝜌

Problem: ASI is calibrated to sea level conditions: 𝜌 = 𝜌0 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 for all altitudes

Air speed you read from ASI at altitudes other then sea level is not REAL air spead and so called Indicated Air Speed (IAS)

Good news: The speed change you read from ASI is accurate at all altitudes! If you see from ASI you twiced your speed, then a/c really twiced its speed.

Indicated Air Speed (IAS)


• The speed you directly read from ASI.

• Assume that

– you are at a non-sea-level altitude

– with air density 𝜌𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒,

– then dynamic pressure at that altitude be 𝑞𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒,

– and sea level air density be 𝜌0.

• The aircraft should have a true air speed or TAS.

• Then, the dynamic pressure can be expressed as

𝑞𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 =1

2𝜌0𝐼𝐴𝑆

2 =1

2𝜌𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑇𝐴𝑆

2

Calibrated Air Speed (CAS)


• The air speed when position or pressure errors eliminated from IAS at low speed flights (<320m/s)

• Sometimes you cannot read true pressure levels at pitot tube and static port due to: – Positions of pitot tube and static vents on aircraft

– Effects of flaps and landing gears, or even a/c, etc.

– Manevours and angle of attact

– Incorrect alignment of pitot tube according to air stream

• After elimination of pressure or positin errors we get CAS

CAS=IAS−𝐸𝑟𝑟𝑜𝑟𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛

Equivalent Air Speed (EAS)


• The air speed when position and compressibility errors eliminated from IAS at high speed flights (>320m/s)

• If a/c flies at high speeds, then compressibility effects are the case

• The dynamic pressure ASI measures (𝑞𝑐) is not the actual 𝑞 but a higher value:

𝑞𝑐 = 𝑞(1 +𝑀2

4+

𝑀4

40 +

𝑀6

1600+⋯) > 𝑞

• After elimination of pressure and compressibility errors we get EAS

EAS=IAS−𝐸𝑟𝑟𝑜𝑟𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 −𝐸𝑟𝑟𝑜𝑟𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦

True Air Speed (TAS)


• The air speed when position and compressibility errors eliminated and sea-level

calibration fixed • Assume that

– you are at a non-sea-level altitude – with air density 𝜌𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 , – then dynamic pressure at that altitude be 𝑞𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 , – and sea level air density be 𝜌0 – You read EAS from ASI at that altitude

• After elimination of pressure and compressibility errors we get EAS

TAS=𝑓(IAS−𝐸𝑟𝑟𝑜𝑟𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛−𝐸𝑟𝑟𝑜𝑟𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦) = 𝑓(𝐸𝐴𝑆)

or

𝑞𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 =1

2𝜌0𝐸𝐴𝑆

2 =1

2𝜌𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒𝑇𝐴𝑆

2

thus 𝑻𝑨𝑺 = 𝑬𝑨𝑺/ 𝝈, where 𝜎 = 𝜌𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒/𝜌0

• EAS=TAS only at sea levels since 𝜎 = 1 at sea level. • Remember: at 40000 ft 𝜎 = 0,25. That implies

– if at sea level you read EAS=100 knots, TAS is 100 knots – if at 40000 ft you read EAS=100 knots, TAS is 200 knots!

Speed of Sound (a)


• Sound is a mechanical wave emiting through air spherically • Speed of sound is function of temperature:

𝑎 = 𝛾𝑅∗𝑇

• When air temperature is low, then sound is slow • Mach number is a simple ratio of

𝑀 =𝑇𝐴𝑆

𝑎

• Critical Mach number, (𝑀𝑐𝑟𝑖𝑡), is the number before an a/c

reaches speed of sound; at some areas of the a/c, air speed reaches the speed of sound.

How to Fix These Errors?


• Read the notes

UEE306-2013/2014


The Atmospher

Basic Aerodynamics

Subsonic Airflow

The Principle of Continuity


From a given cross area (A), at a given velocity (v), with air density ρ, mass of air flowing at a unit of time is constant at all cross areas of the system:

𝐴1𝑥𝜗1𝑥𝜌 = 𝐴2𝑥𝜗2𝑥𝜌 = ⋯ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (𝑘𝑔

𝑠)

Bernoulli's Theorem


An ideal incompressible fluid with zero viscosity satisfies the following:

𝑝 +1

2𝜌𝜗2 = 𝑝𝑡𝑜𝑡𝑎𝑙 = 𝑝𝑝𝑖𝑡𝑜𝑡 = 𝑝𝑠𝑡𝑎𝑔𝑛𝑎𝑡𝑖𝑜𝑛 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

Streamlines and the Streamtube


• Streamline : the path traced by a particle of air in a steady airflow • Streamlines cannot cross • Close together streamlines: increased velocity • Diverging streamlines: decelerating airflow and resultant increasing pressure • Converging streamlines: accelerating airflow, with resultant decreasing

pressure

• Streamtube: an imaginary tube made of streamlines • No flow into or out of the streamtube through the

"walls", only a flow along the tube

UEE306-2013/2014


The Atmospher

Basic Aerodynamics

Subsonic Airflow

Wing Geometry


Wing Geometry


• Airfoil: A shape capable of producing lift with relatively high efficiency • Chord Line: A straight line joining the centers of curvature of the leading and

trailing edges of an aerofoil • Chord: The distance between the leading and trailing edges measured along

the chord line • Angle of Incidence: The angle between the chord line and the horizontal

datum of the aircraft • Mean Line or Camber Line: A line joining the leading and trailing edges of an

aerofoil, equidistant from the upper and lower surfaces • Maximum Camber: The maximum distance of the mean line from the chord

line. • Thickness/Chord ratio: The maximum thickness or depth of an aerofoil section

expressed as a percentage of the chord, with its location as a percentages of the chord aft of the leading edge

• Leading edge radius: The radius of curvature of the leading edge

Air Flow Terminology


• Total Reaction: The resultant of all the aerodynamic forces acting on the aero foil section

• Centre of Pressure (CP): The point on the chord line, through which Lift is considered to act

• Lift: The aerodynamic force which acts at 90o,to the Relative Air Flow. • Drag: The aerodynamic force which acts parallel to and in the same direction

as the Relative Air Flow (or opposite to the aircraft flight path) • Angle of Attack (𝛼 or alpha) (can also be referred to as Aerodynamic

Incidence): The angle between the chord line and the Relative Air Flow

Air Flow around an Airfoil


Influence of Dynamic Pressure


• "If the static pressure on one side of a body is reduced more than on the other side, a pressure differential will exist «

• "If the dynamic pressure is increased, the pressure differential will increase« • "If the dynamic pressure (lAS) is increased, the upward force will increase"

Influence of Angle of Attack


How to create an airfoil? (For geeks)

End of

Lecture 1

UEE306-2013/2014

Documents

UEE 306 Lecture1