faculty of engineering and information technology 1.1 mechanics of flight/fundamentals of flight...

Faculty of Engineering and Information Technology 1.1

Mechanics of Flight/Fundamentals of Flight

COURSE NOTES

John Baird


MILESTONES IN FLIGHT

GEORGE CAYLEY (1773 - 1857): WAS THE FIRST TO EXPLAIN HOW THE FORCE ON THE WIN CAN BE RESOLVED INTO TWO COMPONENTS OF

LIFT PERPENDICULAR TO THE FLIGHTDIRECTION

DRAG PARALLEL TO THE FLIGHTDIRECTION

WING SURFACEDRAG

LIFT

CAYLEY ALSO UNDERSTOOD THE FIRSTPRINCIPLES OF STABILITY AND CONTROL


WE TRY TO ANSWER THE THREE BASIC QUESTIONS

1. WHY AN AEROPLANE FLIES?

AERODYNAMICS

2. WHY DOES IT FLY - SO FAST? SO FAR? SO HIGH?

PERFORMANCE

3. WHY DOES IT BEHAVE THE WAY IT DOES AND HOW TO CONTROL IT?

STABILITY & CONTROL


Visualisation Examples


VISCOSITYTWO FEATURES OF LIQUIDS AND GASES ARE RESPONSIBLE FOR EXISTENCE OFVISCOSITY

LIQUIDS

COHESIVE OR ATTRACTIVE FORCESDOMINATE OVER INERTIA FORCES ANDLARGER THE COHESIVE FORCES (MORECLOSELY PACKED MOLECULES, GREATERTHE VISCOSITY.

GASESTHE BASIS OF VISCOSITY IS THE INTERNALRESISTANCE DUE TO COLLISION ANDTRANSFER OF MOMENTUM.

Fast drift

Slow drift

Fast molecules exchange with slow ones and vice versa. Slowing of fast molecules and vice versa is viscosity.


VISCOSITY WITH TEMP. BECAUSE BONDS BETWEEN MOLECULES WEAKEN OR CAN EVEN BREAK IN OTHER WORDS, COHESIVE FORCES WEAKEN.

VISCOSITY WITH TEMP. BECAUSE INCREASE IN TEMPERATURE CAUSES INCREASED MOLECULAR ACTIVITY WHICH IN TURN LEADS TO MORE COLLISIONS AND MORE TRANSFER OF MOMENTUM, THEREFORE MORE VISCOSITY.

FOR LIQUIDS

DECREASES

FOR GASES

INCREASES


NEWTON’S LAW OF VISCOSITY

THIS ESTABLISHES THE RELATION BETWEEN SHEAR FORCE (FRICTION FORCE) AND THE VISCOSITY.

IT STATES

SHEARING FORCE

A AREA OF INTERFACE

u VELOCITY DIFFERENCE BETWEEN ADJACENT

LAYERS OF FLUID.

h SEPARATION DISTANCE BETWEEN LAYERS OF

FLUID

PROPORTIONALITY CONST. CALLED THE

COEFFICIENT OF VISCOSITY.

Fs

Fs u

h

A

Fs

A

u

h

h

u1

Fs

u = u2- u1

u2


Moving plate

uA

BA’

B’

u

u=0 gradient

Fixed plate

Couette or channel flow

Fixed plate

y

Flow

velocity profile

A B

velocitygradient

h

DEFINITION OF VELOCITY GRADIENT

Boundary layer flow


UNITS OF SHEAR STRESS ARE N/m2 in SI.

FLUIDS OBEYING NEWTON’S LAW, ARE CALLED Newtonian Fluids

EXAMPLES : AIR, WATER, ALL FLUIDS WHICH HAVE SIMPLE MOLECULAR STRUCTURE.

THINK OF SOME FLUIDS WHICH ARE NOT NEWTONIAN!

Fs

A shear stress ' tau'

u

h shear rate

uh


SeaLevel

10

20

30

Altitude(km)

Temperature (degrees Centigrade)-56.5

Troposphere

Tropopause

Stratosphere

Mesosphere Ozone Layer

Balloons

Concorde

Large Jet Liners

General AviationHelicoptersBirdsInsects

U2 Spyplane

International Standard Atmosphere


THE SPEED OF SOUND IS RELATED TO THE PRESSURE & DENSITY BY THE ISENTROPIC RELATION

WHERE IS THE RATIO OF SPECIFIC HEATS IN AIR (CP/ CV) AND IS EQUAL TO 1.4

NOTE THAT THE SPEED OF SOUND IS A FUNCTION OF TEMPERATURE. THE SPEED OF SOUND DECREASES WITH INCREASING ALTITUDE (IE DECREASING TEMPERATURE)

R IS THE GAS CONSTANT FOR AIR AND IS 287.05 J/kg K

SPEED OF SOUND

a p

RT


PROPERTIES OF FLUIDS

FLUIDS CAN BE CLASSIFIED AS OR

.

IN A COMPRESSIBLE FLUID, PRESSURE & VELOCITY CHANGES ARE ACCOMPANIED BY SIGNIFICANT DENSITY CHANGES.

IN AN INCOMPRESSIBLE FLUID, PRESSURE & VELOCITY CHANGES DO NOT CAUSE ANY APPRECIABLE CHANGES IN DENSITY.

LIQUIDS ARE GENERALLY INCOMPRESSIBLE (Eg. WATER).

GASES ARE GENERALLY COMPRESSIBLE (Eg. AIR).

COMPRESSIBLE

INCOMPRESSIBLE


THE FLOW PARAMETER THAT BECOMES IMPORTANT UNDER SUCH CIRCUMSTANCES IS THE MACH NO. DISCUSSED EARLIER.

AT HIGH SPEEDS THEREFORE, WE CAN TALK IN TERMS OF:

SUBSONIC 0.3 < M < 0.7

TRANSONIC 0.7 < M < 1.4

SUPERSONIC 1.4 < M < 5

HYPERSONIC M > 5

PROPERTIES OF FLUIDS


FLOW REGIMES IN AIR

1 2 3 4 5 6 7 8 9 10 0

Su

bso

nic

Tra

nso

nic

Supersonic Hypersonic

TERMINOLOGY

0

Inco

mp

ress

ible

Compressible

No

n L

ine

ar

Linear

1 2 3 4 5 6 7 8 9 10

Oxygen dissociates (Chemical reactions important)


IN VISCOUS FLOWS THE EFFECTS OF VISCOSITY (WHICH PRODUCE FRICTIONAL OR SHEAR STRESSES) ARE CONFINED TO A VERY THIN LAYER OF FLUID CLOSE TO THE SURFACE. THIS THIN LAYER NEAR THE SURFACE IN WHICH VISCOSITY EFFECTS ARE CONFINED IS CALLED BOUNDARY LAYER, BECAUSE OF INTERNAL FRICTION DUE TO VISCOSITY, THE LAYER OF AIR CLOSEST TO THE BODY ‘STICKS’ TO THE SURFACE AND THE VELOCITY GRADUALLY INCREASES TILL AT THE ‘EDGE’ OF THE BOUNDARY LAYER, IT IS EQUAL TO THE VELOCITY IN THE ADJACENT EXTERNAL FLOW.

Fixed plate

y

Flow

velocity profile

A B

velocitygradient

BOUNDARY LAYERBOUNDARY LAYER DETAIL

BOUNDARY LAYERS


BECAUSE THE EFFECTS OF VISCOSITY ARE CONFINED TO THE BOUNDARY LAYER, IT HAS OFTEN BEEN POSSIBLE TO ANALYSE AERODYNAMIC PROBLEMS BY TREATING THE AIR AS IDEAL FLUID AND THIS HAS YIELDED QUITE ACCEPTABLE RESULTS ESPECIALLY AS REGARDS

. FOR TREATING THE PROBLEM OF AERODYNAMIC DRAG,

HOWEVER, WE NEED TO CONSIDER THE

WE ALSO NOTE THAT IN AN IDEAL FLUID, THAT HAS NO VISCOSITY, THE FLUID EXHIBITS NO SHEAR FORCES AND THERE WOULD BE NO RELATIVE MOTION BETWEEN ADJACENT LAYERS OF FLUID. SUCH A FLUID IS SAID TO

PAST THE SURFACE.

AERODYNAMIC LIFT

BOUNDARY LAYER

SLIP

BOUNDARY LAYERS


WITH REAL FLUIDS, ON THE OTHER HAND, THERE IS NO RELATIVE MOTION AT THE SURFACE. IN OTHER WORDS, AT THE SURFACE WE HAVE CONDITION.

THE CONCEPT OF THE BOUNDARY LAYER WAS FIRST PROPOSED BY THE GERMAN AERODYNAMICIST LUDWIG PRANDTL (1875 - 1953) IN 1905.

IT WAS TRULY A MILESTONE IN AERODYNAMICS

NO SLIP

BOUNDARY LAYERS

y

VelocityZero velocity at wall, the no slip condition


TYPICAL BOUNDARY LAYER PROFILE

Free stream velocity, U

0.99U

Velocity gradient

Velocity Profile

Surface

Boundary layer thickness


WHEN THE BOUNDARY LAYER IS SUBJECTED TO

INCREASING PRESSURE IN THE FLOW DIRECTION, IT

BECOMES MORE AND MORE SLUGGISH AS IT HAS TO FLOW

AGAINST AN ADVERSE PRESSURE GRADIENT. IT

EVENTUALLY COMES OFF THE SURFACE. THE BOUNDARY

LAYER IS THEN SAID TO BE SEPARATED.

WHEN THE BOUNDARY LAYER ON AN AEROFOIL OR WING

SEPARATES, WE SAY THAT THE AEROFOIL OR WING HAS

ONCE THE BOUNDARY LAYER SEPARATES THE DRAG

INCREASES DRAMATICALLY AND WE CAN NO LONGER

ASSUME THAT FLOW OVER. THE AEROFOIL IS SMOOTH

(IDEAL).

STALLED

BOUNDARY LAYER BEHAVIOUR


A Separated Boundary Layer


B.L. BEHAVIOUR IN ADVERSE PRESSURE GRADIENT

Pressure force

Flow decelerating

Increasing Pressure

Point of separation Flow separated


PRESSURE DISTRIBUTION ON AN AEROFOIL

Negative pressure

Adverse Pressure Gradient


STALL ON AN AEROFOIL

Negative Pressure

NOTE RECIRCULATION REGION


DRAG ARISES DUE TO

SKIN FRICTION ON SURFACE OF BODY

PRESSURE DISTRIBUTION OVER BODY

SKIN FRICTION DRAG

PRESSURE DRAG

NATURE OF DRAG

(ALSO CALLED FORM DRAG)


REAL FLOWS AND AERODYNAMIC DRAG

VV

INCISCID FLOW VISCOUS FLOW


Pressure Drag on a Cylinder

degrees

p p01

2U2

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 30 60 90 120 150 180 210 240 270 300 330 360

Theoretical (potential flow)

Measured (R = 670000)

Measured (R=190000)


Skin Friction Drag

yU

y

wall

Dskin friction Awall AU

y

wall

Skin Friction Drag= Area x Shear Stress at wall


Total Drag

DRAG ON A TWO DIMENSIONAL OBJECT (PROFILE DRAG) IS A COMBINATION OF PRESSURE DRAG (ALSO CALLED FORM DRAG) AND SKIN FRICTION DRAG

PROFILE DRAG = PRESSURE DRAG + SKIN FRICTION DRAG


VELOCITY IS INVERSELY PROPORTIONAL TO THE CROSS-

SECTIONAL AREA. IN OTHER WORDS,

WHENEVER THERE IS ACCELERATION OF FLUID FLOW, THE

CROSS-SECTION IS NARROW AND THE STREAMLINES

CONVERGE.

WHEN THERE IS A DECELERATION, THE CROSS-SECTION IS

WIDER AND THE STREAMLINES DIVERGE.

Stream Tube


BERNOULLI’S EQN. RELATES CHANGES IN VELOCITY TO

CHANGES IN PRESSURE IN STEADY INCOMPRESSIBLE

INVISCID FLOW ALONG A STREAM LINE. IT IS THE MOST IMPORTANT EQUATION IN FLUID MECHANICS.

p 1

2V2 p0 constant

where p is the (static) pressure is the density, V is the local velocity and p0, the constant, is called the total pressure. The term is sometimes called the dynamic pressure.

1

2V2

Bernoulli’s Equation


Applications of Bernoulli’s Equation

One way of writing Bernoulli’s equation is:Total pressure = static pressure + dynamic pressure.

po p 1

2V2

If the velocity is zero the pressure is equal to the total pressure

p

To differential pressure gauged

4d

A PITOT TUBE

po p 1

2V2


FROM BERNOULLI’S EQN. WE HAVE

p 1

2V2 p0

or

V 2 p0 p

THEREFORE, BY MEASURING THE DIFFERENCE BETWEEN

THE TOTAL PRESSURE (Po) AND STATIC PRESSURE (), WE

CAN CALCULATE THE VELOCITY IN A FLOW.

Measurement of Velocity:


PITOT TUBE USED IN A WIND TUNNEL TO MEASURE VELOCITY

po

V

To micromanometer

Pitot-static tube

Test Section


PITOT TUBE USED TO MEASURE BOUNDARY LAYER PROFILE

V

Boundary layer velocity

profile

Staticorifice

To manometer

Pitot tube fixed to manometer traverse


po p 1

2V2

Total energy per unit volume

pressure energy per unit volume

kinetic energy per unit volume

ALTERNATIVE VIEW OF BERNOULLI’S EQUATION


Pressure and Velocity

Negative pressure

How Lift is Generated


THEREFORE, BY NOTING THE EQUIVALENT AIRSPEED FROMASI AT ANY ALTITUDE, WE CAN DETERMINE THE TRUE AIRSPEED BY THE KNOWLEDGE OF RELATIVE DENSITY .

USUALLY, THE AIRSPEED INDICATOR IS CALIBRATED SOTHAT IT READS DIRECTLY THE SPEED EITHER IN KNOTS ORkm/hr.

Static pressure measured by port on fuselage

Using Bernoulli’s Equation to Measure Velocity of Aircraft

Dynamic pressure measured by pitot probe


Flow Examples

Flow accelerates and pressure reduced

Dividing streamlinep=p0 at stagnation point


Flow Examples

All objects in a flow have a stagnation point


Flow Examples

Distance along aerofoil

Pressureand

Velocityp

V

Free streamVp

s s’

s’s

p

V

Vp

T

FF’


TRANSITION TO TURBULENCE

Smooth entry

(a) Laminar Flow

Dye filament Control valve

dWater

Filament becomes unstable

Filament breakup and turbulent flow

(b) Turbulent Flow

V

V

Osborne Reynolds in the 1880s investigated the behaviour of flow that was either direct (laminar) or sinuous (turbulent).


Transition to Turbulence

Whether the flow is turbulent or laminar depends on the relative magnitude of the viscous forces and the kinetic forces (momentum) of the flow.

When viscous forces are large, small irregularities are removed by ‘viscous damping’. This is characterised by slow flow, and/or high viscosity.

When the flow has sufficient momentum such that the viscous forces are relatively small, it becomes turbulent.


Example of a Turbulent Boundary Layer


Stability of Shear Flow

Splitter Plate Dividing stream line

Consider the flow above in which viscosity is very small. Consider what happens if the dividing stream line is disturbed a small amount.

Note that, if the velocity difference is high enough the pressure differences will act to increase the divergence of the streamline.

IT WILL BECOME TURBULENT

p,V1

p,V2V P

V P

V P

V P


Stability of Shear Flow

p,U1

p,U2U P

U P

U P

U P

IF VISCOUS FORCES DOMINATE, DISTURBANCE ENERGY WILL DISSIPATE. IF KINETIC FORCES DOMINATE THE DISTURBANCES WILL GROW AND FLOW WILL BECOME TURBULENCE. WHETHER A FLOW IS TURBULENT OR NOT DEPENDS ON:

KineticForces

Viscous Forces

1

2U2

dUdy

U2

U

D

UD

D

= REYNOLDS NUMBER


REYNOLDS NUMBER

= FLUID DENSITYV = A VELOCITY - USUALLY THE FREE STREAM VELOCITYD = A REPRESENTATIVE LENGTH SCALE = THE FLUID VISCOSITY

R UD

EXAMPLES

U

D

R UC

CHORD C

For a given configuration and definition the Re determines when the transition to turbulence occurs.


LAMINAR AND TURBULENT FLOW

LAMINAR FLOW

SMOOTH STEADY SMALLER SHEAR STRESS

TYPICALLY STREAMLINEDBODIES

LESS SKIN FRICTION DRAG. MORE PRESSURE DRAGLaminar profile

Turbulent mean profile


TURBULENT FLOW

HIGHLY DISORGANISED BASICALLY LARGEUNSTEADY SHEAR STRESS

MORE SKIN FRICTION DRAG.LESS PRESSURE DRAG

TYPICALLYBLUFF BODIES

Laminar profile

Turbulent mean profile

LAMINAR AND TURBULENT FLOW


Transition to Turbulence

Smoke visualisation of a boundary layer. The laminar boundary layer on the left is ‘tripped’ by a grid and becomes turbulent


Boundary Layer Profiles

Y

U

Laminar Profile

Streamlines

Momentum exchange by viscous forces only

Turbulent Profile

Momentum exchanged more effectively by mass transport into lower layers


(a)

(b)

The laminar boundary layer (a) encourages separation and leads to a wide wake and high form drag. In (b) a trip is used to cause transition to turbulence in the boundary layer, separation is delayed, the wake narrows and the form drag decreases.


Turbulent Boundary Layer on a Flat Plate

Free stream velocity V

Boundary layeredge

L

Vertical dimension exaggerated

t

s

tL

Laminar Transition Turbulent

turbulent eddies


Four Fluid Phenomena: Number 1Pressure force

Flow decelerating


1. Adverse pressure gradients cause separation

(Separation cannot occur in favourable gradients)


Four Fluid Phenomena: Number 2


2. Turbulence inhibits or delays separation

Pressure force

Laminar flow

Energy deep in boundary layer is resistant to separation

Turbulent flow



3. In a certain Re range adverse pressure gradients can encourage turbulence, and favourable gradients can relaminarise flow.

Pressure force



4. In a certain Re range surface roughness encourages turbulence.


Cricket Ball Swing

Laminar Flow

Turbulent Flowtripped by seam and maintained by rough surface

Roughened side

Polished Side

Asymmetric wake

Angle (degrees)

Pressure

0 180

1/2 V2

TurbulentLaminar

LIFT


REYNOLDS NUMBER & ITS SIGNIFICANCE

WE HAVE SEEN THAT THE TURBULENT MOTION IS MORE

VIGOROUS AND ENERGETIC. ALSO, THE VELOCITY

FLUCTUATIONS IN TURBULENT FLOW IMPOSE STRESSES

ADDITIONAL TO THOSE SHEAR STRESSES THAT RESULT

FROM MOLECULAR MOTIONS. THESE ADDITIONAL

STRESSES ARISING PURELY OUT OF TURBULENT

FLUCTUATIONS ARE CALLED OR

SOMETIMES REFERRED TO AS EDDY STRESSES.

THEREFORE:

TOTAL SHEAR STRESS VISCOUS SHEAR STRESS

IN TURBULENT FLOW

REYNOLDS STRESSES

REYNOLDS STRESSES


More on Reynolds Number and Scaling

IN FLUID MECHANICS IT IS MORE CONVENIENT TO USE NON-DIMENSIONAL NUMBERS SUCH AS THE REYNOLDS NUMBER IN DESCRIBING FLOW. LET US FIND A NON-DIMENSIONAL NUMBER RELATED TO DRAG.

DRAG IS A FORCE WHICH, IN MANY CASES, IS RELATED TO THE KINETIC ENERGY OF THE FLOW (SEE BELOW)

Gauge pressure of 1/2 U2

Gauge pressure near zero

IN THE CASE SHOWN, THE DRAG IS LIKELY TO BE PROPORTIONAL TO THE DYNAMIC PRESSURE 1/2 U2

THEREFORE WE DEFINE THE DRAG COEFFICIENT AS

CD D

12U2A

DRAG

U

Area A


More on Reynolds Number and Scaling

SIMILARLY THE LIFT COEFFICIENT IS

CL L

1

2U2A

WHERE L IS THE LIFT GENERATED BY AN AEROFOIL OF PLAN AREA A

Wing Planform (A)

Air Flow

(V)

Chord

(c)

Span (b)


WHY USE COEFFICIENTS ?IMAGINE THAT YOU HAVE MEASURED THE LIFT ON AN AEROFOIL IN A WIND TUNNEL AT VARIOUS VELOCITIES

ANGLE OF ATTACK

LIF

T

ANGLE OF ATTACKLI

FT

NOW WE VARY THE SIZE OF THE AEROFOIL

U1

U2

U4

U3

C1

C4

C3

C4

THE RESULTS ARE FAR TOO COMPLEX


WHY USE COEFFICIENTS ?

ANGLE OF ATTACK

LIF

T C

OE

FF

ICIE

NT

IF WE PLOT NON-DIMENSIONAL NUMBERS SUCH AS LIFT COEFFICIENT VS ANGLE OF ATTACK ALMOST ALL DATA COLLAPSES TO ONE LINE

THE RESULTS ARE NOW SIMPLIFIED

SLIGHT VARIATION CAUSED BY CHANGING REYNOLDS NUMBER


ANOTHER EXAMPLEDRAG ON A CYLINDER

VELOCITY

DR

AG

VARIABLE DIAMETERS

Log

(DR

AG

CO

EF

FIC

IEN

T)

Log (REYNOLDS NUMBER)

ON A NON-DIMENSIONAL PLOT OF APPROPRIATE PARAMETERS ALL DATA COLLAPSES TO ONE GRAPH


SCALING LAWS & DIMENSIONAL ANALYSIS

IN FLUID FLOWS, WE CAN ALWAYS IDENTIFY A

CHARACTERISTIC DIMENSION FOR A BODY OVER OR

THROUGH WHICH FLUID FLOWS. THIS CAN BE, FOR

EXAMPLE, THE CHORD OF AN AEROFOIL, DIAMETER OF A

PIPE, HEIGHT OF A CHANNEL, ETC.

IN A SIMILAR VEIN, WE CAN DEFINE A CHARACTERISTIC

VELOCITY SCALE WHICH IS TYPICAL FOR A GIVEN PROBLEM.

FOR EXAMPLE, THE FLIGHT SPEED OF AN AIRCRAFT, OR

TEST SECTION VELOCITY IN A WIND TUNNEL, OR FREE-

STREAM VELOCITY EXTERNAL TO THE BOUNDARY LAYER.


REYNOLDS NUMBER

UL

REYNOLDS NUMBER IS THE MOST IMPORTANT PARAMETER IN AERODYNAMICS.

is the density of the fluid

U is a characteristic velocity, typically free stream velocity

L is a characteristic dimension, typically the diameter of a cylinder or pipe or the chord of an aerofoil

is the fluid viscosity.


Drag & Lift CoefficientsThe main aim of aerodynamics is to predict drag and lift.

Drag has the units of force mass x acceration ML

T2

The drag is likely to be related to the pressure experienced by the aerofoil which is typified by the Stagnation Pressure 1/2 U2

1

2U2 has units of

M

L3

L2

T2

M

LT2

1

2U2A has units of

M

L3

L2

T2

L2

ML

T2

We can multiply by an area ( L2) to get the same units as Force

ThereforeD

1

2U2A

is dimensionless and is called the Drag Coefficient


DRAG ON A CYLINDER

Re < 1 Viscous flow, drag is proportional to velocity, skin friction drag dominates

10 < Re < 5x105 Viscous flow, drag is proportional to the square of velocity, pressure drag dominates.

Re > 5x105 Boundary layer is turbulent and separation is delayed. Thus the wake is narrower and there is a greater area of pressure recovery on the rearward surfaces. Thus drag is reduced.


0.01

0.1

1

10

100

1000

1 2 3 4 5 6 7 8 9

Series1

log10(Reynolds number)

Spe

ed (

m/s

)

dust particles

insects

models

birds & bats

human-powered aircraft

hang gliders

sailplanes

general aviationjet transports

dirigibles

0.001

0.0001

0.01

0.050.10.2

0.51.0

Mac

h nu

mbe

r

Approximate Reynolds number ranges of aerodynamic objects in nature and technology.


0.05 90.05 5

10000 95 9

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

0.01 0.1 1 10

Take-offCruise

Vstol, cargo.

Large Jet transport

L= 4 m

Concorde L = 20 m

US SST L = 32 m

Hypersonic Aircraft L = 32m

ICBM

IRBM

Gemini GT-3L = 2.1 m

Space FerryL = 10.7 m

Velocity (km/s)

RL

Low Speed Compressible

Transonic

Supersonic Hypersonic

M - 0.3 0.8 1.2 5

Subsonic

Reynolds number and speed (Mach number) regimes for various vehicles (Poisson-Quinton, 1968)


How does Streamlining work?

Re<1

A B

Consider two bodies of revolution A and B. At low Re, skin friction drag is much larger than pressure drag. Viscous forces dominate. Note that B has a much larger surface area than A.

The drag on B will be much larger than the drag on A. Streamlining will not work.


Re>100

A

B

Pressure drag dominates.

The drag on A will be much larger than the drag on B. Streamlining reduces the drag

substantially

How does Streamlining work?

Angle (degrees)

Pre

ssur

e

0 180

1/2 V2

Distance from leading edge

Pre

ssur

e

1/2 V2


The Effect of Streamlining

NACA 64-421 airfoil compared with a circular wire having the same drag. The diameter of the wire is one tenth of the thickness of the aerofoil.

Thickness

Wire


MORE ON REYNOLDS NUMBER

If we want to model the flow over an object we should try to get the Reynolds number of the model and the full size object as close as possible.

Re mod el Re full size

UL

mod el

UL

full size

if model full size and model full size , then

Umodel L full size

LmodelUfull size

Lmodel Lfull size


MORE ON REYNOLDS NUMBER

IF (Re )model= (Re )full size

Then (Cd )model= (Cd )full size

and (CL )model= (CL )full size

IN PRACTICE THIS CAN RARELY BE ACHIEVED


V

W

L AF

DT

Primary forces acting on an aircraft in steady level flight.


V

L

D

L/D=2

V

L

D

L/D=3.3

V

L

D

L/D=4

Lift to drag ratio for a flat plate, a cambered plate and an aerofoil at incidence.


0

2

4

6

8

10

12

14

16

18

-2 0 2 4 6 8 10 12

Wright Brothers (1903)

A modern Aerofoil

Angle of Attack (degrees)

Lif

t to

Dra

g R

atio

Variation of Lift to Drag ratios.


Wing Planform (S)

Span (b)

Air Flow

(V)

Leading edge

Trainling edge

Chord

(c)

Thickness

Camber

Camber line

Trailing edge

Leading edge radius

Air Flow

Chord line

AoA()

Chord (c)

A

A

Section A-AWing and aerofoil nomenclature


Sweep angle (

b

c

Rectangular wing Swept wing

c

Root cord (cr)

Elliptic wing

Tapered wing

Tip cord(ct)

b

cr

cr

Delta wing

Ogive wing(Concorde)

Figure 8.4a Typical wing planforms


Conventional low speed aerofoil

Low speed symmetric aerofoil

Laminar flow aerofoil

Transoinc ‘supercritical’ aerofoil

Thin supersonic ‘biconvex’ aerofoil

Multi-element ‘high lift’ aerofoil

Typical aerofoil sections


-2

-1.5

-1

-0.5

0

0.5

1

0.0 0.2 0.4 0.6 0.8 1.0x/c

Cp

Pressure loss due to viscosity

Pressure distribution on a lifting aerofoil


0

0.2

0.4

0.6

0.8

1

1.2

1.4

-5 0 5 10 15 20

A

B

C

Angle of Attack ( degrees)

Lif

t Coe

ffic

ient

(C

L)

Maximum lift coefficient

Moderate angle of attack

Lift curve slope(ideal value 2)

Linear or operationalsection of the lift curve

Lift curve showing changes in pressure distribution and the flow around the aerofoil


Ways of Plotting Aerofoil Performance

Angle of Attack

Lift

Coe

ffic

ient

Angle of AttackD

rag

Coe

ffic

ient

or

Drag Coefficient

Lift

Coe

ffic

ient

Polar Plot


Lift and Drag Curves

Angle of Attack

Lift

Coe

ffic

ient

Angle of AttackD

rag

Coe

ffic

ient

CLmax

dCL

d

CDmin

Shape of curve indicates sudden stall or gentle stall

Offset indicates asymmetric aerofoil


Polar Plots

Drag Coefficient

Lift

Coe

ffic

ient

dCL

dCD

max

CLmax


Measurement of Profile Drag

Up till now we have been talking about the behaviour of infinitely long aerofoil sections (or ‘profiles’). These are measured in an wind tunnel with the aeorfoils being terminated in the walls. Real wings are not infinite

Testing Aerofoil ProfilesTesting three dimensional wings

Wing Tip Vortex


Induced Drag

Wing Tip

Low Pressure

High Pressure

Wing Tip Vortex

Note that a downwards velocity is generated


Induced Drag

Airspeed

Lift

Drag

Two Dimensional Flow(infinite aspect ratio)

Local Airspeed

Local Lift

Drag

Three Dimensional Flow(finite aspect ratio)

Induced downwards airflow

Induced Drag


Induced DragInduced Drag is proportional to the square of the Lift Coefficient.

Di12U2S

CL

2

ARwhere

Di

S AR

the Induced Drag

the wing area

the aspect ratio, span divided by chord

CL

Infinite wing

Finite wing

Note, curves cross at zero lift point


Basic Flight Mechanics

V

W

L AF

DT

Note that for steady level flight, the Lift L is equal to the Weight W (=mg). If we assume that the lift is generated entirely by the wing, we can write

CL L

1

2U2S

mg

1

2U2S

or

U mg12S

.1

CL

To maintain steady level flight at low speeds the CLmust be increased (by increasing angle of attack). In high speed flight CL must be decreased (by decreasing angle of attack).


Basic Flight Mechanics

L

D

T

W

Angle of attack Small ( 3-4 degrees)

W

L

D

Angle of attack Large ( 20-25 degrees)

Umin mg12S

.1

CL max

Note: an aircraft’s minimum speed (landing speed) is determined by CLmax and the wing area.


Total Drag on an AircraftThe total drag on an aircraft is a combination of drag caused by appendages, skin friction drag, pressure drag (collectively called parasite drag) and induced drag. Induced drag is high at low speeds (high CL) and low at high speeds ( low CL).

Drag

Velocity (steady and level)

CD CD,e CL

2

eARCD

CL2

eAR

CD,e


Total Drag on an Aircraft

CD CD,e CL

2

eAR

Total Drag

Parasite Drag: Includes profile drag, (pressure drag and skin friction drag on wing), skin friction and pressure drag on fuselage, empennage, engine necelles, landing gear etc.

Induced Drag


High Lift DevicesUmin

mg12S

.1

CL max

The minimum controllable speed at which an aircraft can fly determines the landing speed. From the above equation, the landing speed can be reduced by increasing CLmax ( ie by delaying stall) or by increasing the wing area. Most modern high lift devices work on a combination of:• Delaying stall by increasing camber,• Delaying stall by re-energising the boundary layers inhibiting separation,• Increasing the total effective wing area.

Chord Increased

Boundary Layers re-energised


The Effect of Flaps

CL

=0

=30

=15

CLmax increases with

Zero lift point changes with camber

Modern aerofoils have a CLmax of 1.4. Multi-element flaps can increase that to 3.2


Elementary Flight Mechanics

V

1.

S21W

bV.S2

1aDVP

V

1.

S21W

bV.S2

1aD

drag induced drag parasite bCaC

SV21

DC

23

req

2

22

2LD

2D


Power and Drag

Velocity

Stall SpeedP

D

Vmp VmD


As Weight Increases

Velocity

Stall Speed

D

VmD

DragWeight W1

Weight W2


Increasing Weight

• W=L and as W increases L increases

• If CL and the AoA are unchanged V must increase as W1/2

• At a given AoA, L/D is constant and D is proportional to W

• At a given AoA, Preq =DV and is proportional to W3/2


Power Requirements

Velocity

Stall Speed

Preq

Power

Pavail

Max climb rate Max speed

Take-off and Landing speed


Maximum Payload

Velocity

Preq

Drag

Pavail

Minimum workable manoevre range


Pitching Moment

Pitching Moments: Cm=M/(1/2 V2Sc)=Cm0+ k CL

(Nose up is positive)

CL (or AoA)Cm

Aft point of reference

Forward point of reference

Aerodynamic Centre ref point


Aerodynamic Centre

O A C

L

M

O A

L

M0= constant

O A C

L

C

Centre of Pressure

Position of C varies with

Position of Aerodynamic Centre(A) remains fixed


Stability of Wing Alone

CG moving aft

Highly unstable

Unstable

Neutrally stable

Stable (desirable)

Unresponsive

Pitching Moment

CL


Longitudinal StabilityLw

LT

WC

G

Lw

LT

W

G

M0= constant

A


Stability of Wing and Tailplane

Wing Alone

Pitching Moment

Tail Alone

Aircraft

CL

Trim Point

• Movement aft of CofG makes aircraft less stable.• Neutral point is point of CofG where aircraft is neutrally stable (Cm constant)• Static margin is distance CofG is ahead of neutral point

faculty of engineering and information technology 1.1 mechanics of flight/fundamentals of flight...

Documents

faculty of engineering

information technology

u2u2 slide

basis of viscosity

coefficient of viscosity

stability control slide

gases increases slide

newtons law of viscosity