Folienmaster ETH Zürich · 2015. 12. 3. · 3. Performance Considerations 4. Stability 5. Simplified Dynamic Model 6. UAV Control Approaches 7. Case Studies Lecture 1: Basics of

||Autonomous Systems Lab

151-0851-00 V

Marco Hutter, Michael Blösch, Roland Siegwart, Konrad Rudin and Thomas Stastny

Autonomous Systems Lab

23.11.2015Robot Dynamics - Fixed Wing UAS: Basics of Aerodynamics 1

Robot DynamicsFixed Wing UAS: Basics of Aerodynamics


1. Overview

2. Aerodynamic Basics

3. Performance

Considerations

4. Stability

5. Simplified Dynamic

Model

6. UAV Control

Approaches

7. Case Studies

Lecture 1:

Basics of Aerodynamics

1. Historical Overview

2. Aerodynamics

Basic Principles

Airfoil Lift/Drag/Moment

Induced Drag

Parasite Drag

Control Surfaces

3. Performance Considerations

Propulsion Systems

Power Required vs. Available

Maximum Range/Endurance

Contents:

Fixed Wing UAS



First Flight:

Montgolfier Brothers

1783

Ballon filled with hot air

First unmanned

demonstrations

Later with animals

Finally manned

Historical Overview

http://en.wikipedia.org/wiki/Montgolfier



Sir George Cayley:

First Design of modern

airplane configuration

1799

Discovery of aerodynamics

principles

First glider flight with an adult

in 1853

Historical Overview

http://en.wikipedia.org/wiki/George_Cayley



Jean-Marie Le Bris 1856

First to fly higher than his point of departure

towed by a horse

Height of 100 meters at a distance of 200 meters

Historical Overview

http://en.wikipedia.org/wiki/Jean-Marie_Le_Bris



Otto Lilienthal

First person to make repeated successful short flights

Used a fixed wing glider

Died after a crash in 1896, saying „Sacrifices must be made“

Historical Overview

http://en.wikipedia.org/wiki/Otto_Lilienthal



Wright brothers

Started as glider engineers and pilots

First engine powered flight in 1903

First to actively manipulate the plane by control surfaces

Historical Overview

http://en.wikipedia.org/wiki/Wright_Brothers



Analysis of a control volume

Conservation of mass:

Momentum conservation:

Linear

angular

Viscous forces

Aerodynamics: Basic Principles

0 dSS

nv

VSS

dVt

dSpdS vnnvvF )(

VS

dVt

dS )())(( rvnvrvM

0

y

wdy

du

V: Control Volume

S: Ctrl Volume Surface

n: Normal of S

: Air Densityv: Air flow velocity vector



Analysis on differential volumes:

with viscosity: Navier-Stokes Equation

Without viscosity: Euler Equation

Incompressible along streamline: Bernoulli Equation

Aerodynamics: Basic Principles

www.speedace.info/pito

t_tube.htm as on 29th

July 2009

constp

ghv

2

2



Aerodynamics: Basic Concepts

Forces

L : Lift

D : Drag

Y : Sideslip force

T : Thrust

G : Weight

Moments

L : Roll moment

M : Pitch moment

N : Yaw moment

Angles

a : Angle of attack

b : Sideslip angle

e : Thrust-vector angle

Background image:

http://upload.wikimedia.org/wikipe

dia/commons/

5/5c/C_172_line_drawing_oblique.

svg

z

x

y

T

e

M

L

N

G

vt

ab

D

L

Y

2

2VACL



Wing Geometry

Aerodynamics: Basic Concepts

b: Wingspan

c: Chord

c0: Root Chord

ct: Tip Chord

A: Reference Area

AR: Aspect Ratio

x

y

c

ct

c 0

b

A

A

bAR

2



Various types of wing

Biplanes & vertical composition of wing

Lift not proportional to the number of wings.

Biplane: factor ~ 1.5

Drag also increased

Advantage of higher stiffness and less Inertia around

x-axis (Aerobatics)

Wing Geometry



Suction

Overpressure

2-Dimensional Flow Analysis

Flow field (pressure distribution, laminar/turbulent) highly dependant

on angle of attack, Reynolds number and Mach number

Aerodynamics: Airfoil Lift and Drag

http://www.thuro.at/anims/abloesung.gifwww.thuro.at/aerodynamik2.htm http://www.thuro.at/anims/abloesung.gif

Laminar

boundary layer

Transition point Turbulent

boundary layer

Separated

boundary

layer

Stagnation point



Pressure distribution can be reduced to two forces and one moment

per unit length:

Aerodynamics: Airfoil Lift, Drag and Moment

v

Angle of attack

a

Leading edge

Trailing edge

Chord

c

25 % Chord Thickness

dL

dDdM

22

2VdycCdM m

2

2VdycCdD d

2

2VdycCdL l

Lift force

Drag force

Moment

: Density of fluid (air) [kg/m3]

c : Chord length [m]

V : Flight speed (w.r.t. air) [m/s]

Cl : Airfoil lift coefficient [-]

Cd : Airfoil drag coefficient [-]

Cm : Airfoil moment coefficient [-]



Coefficients Cl, Cd and Cm depend on

angle of attack a As long as flow is attached:

Cl – linear:

Cm – almost constant

At stall: flow separation

Cl – stops to increase

Cd – increases dramaticallyFlow field highly depending on Re (and Ma),

in particular:

Location of laminar/turbulent transition point

Separation point

Stall angle


Separation point

a

2d

dCl



Reynolds' number influence

at low speed, Re and Cd


Cl

Cd a

Polars of Airfoil we3.55-9.3

Re

cV Re

Forces Viscous

Forces Inertial

McMasters, J. H. and M. L. Henderson (1980). "Low Speed Single

Element Airfoil Synthesis." Technical Soaring 6(2): 1-21

W. Engel and A. Noth 2005



Mach Number (Ma)

dependency:

Measures to damp the drag increase:

Thin airfoils, supercritical airfoils

Sweep of the wing forward or back

Low-aspect-ratio wing

Aerodynamics:

Airfoil Lift, Drag and Moment

Grafics adapted from: Talay, T.A. (1975). „Introduction to the Aerodynamics of

Flight“. NASA Langley Research Center

The „Sound Barrier“

Drag-divergence Mach

Number

Win

g d

rag

co

eff

icie

nt

0 Mach Number 1

Due to wave

drag coefficient

Qualitatively only;

highly dependent

on airfoil and

wing geometry

Sound of Speed

Speed AirplaneMa



The choice of an airfoil depends on:

Flying speed

Wing loading

Construction method

Kind of flight (acrobatic, glide,…)

Placement on the airplane

Standard airfoils (some examples)

Goettingen

Eppler

Wortmann

NACA

Example: NACA 2412

Airfoils

Maximum camber deflection (% of chord)

Symmetric Airfoils

Semi-Symmetrical Airfoils

Under-Cambered Airfoils

Reflexed Airfoils

Flat-Bottom Airfoils

Thickness (% of chord)

Position of maximum camber deflection (tenths of chord)



Methods to determine airfoil lift, drag and

moment coefficients:

Theoretically using 2D-CFD software

Javafoil

http://www.mh-aerotools.de/

Xfoil

http://raphael.mit.edu/xfoil/

…

Experimentally in a wind tunnel

Extruded airfoil mounted on a

measurement system

Laminar flow produced by fans

Airfoil Lift, Drag

and Moment

www.uwal.org/publicdata/photos

Javafoil



From 2D to 3D: the wing is not

infinite…

Vortices are created at wing

extremities

Tip vortices induce

downward flow (w)

and thus reduce the

effective angle of attack

Approx. induced drag:

e: Oswald Factor < 1 for

non-elliptic lift distribution

Induced Drag

2

i

LD

CC

e AR

aerospaceweb.org

dL

V (free stream)

w

dDi


NASA Dryden Flight Research Center


Winglets: Less Induced Drag

www.aviationpartners.com

http://airpigz.com/blog/2010/8/27/poll-spiroids-funky-circular-

winglets-love-em-or-hate-em.html

Blended

Spiroids

Modern Glider

Designs



Ideally, winglets…

… reduce induced drag at

low speeds

… reduce spanwise flow

… increase the Reynolds

number near wing tip

… do not increase the

parasite drag too much

(relevant for high speed

performance)

How to Reduce Induced Drag: Winglets

V (fre

e s

tream

)

v

Wing

Upward

winglet

Bound

vortex

Tip

vort

exTop view



Wing: integrate Cd along

the wing

Fuselage: highly Re number

and geometry depending…

Friction drag

Form drag

Interference drag

e.g. at the transition between

fuselage and wing

Can also be negative

Parasite Drag

Dra

g

Speed

total



For small airplanes,

the standard control surfaces are:

Ailerons (rolling)

Elevator (pitching)

Rudder (yawing)

For larger airplanes, they can be more complex…

Control surfaces


Ailerons:2. Low-Speed Aileron

3. High-Speed Aileron

Lift increasing flaps and slats:4. Flap track fairing

5. Krüger flaps

6. Slats

7. Three slotted inner flaps

8. Three slotted outer flaps

Spoilers:9. Spoilers

10. Spoilers-Air brakes


Turbojet engine

All air accelerated passes through the

compressor to the combustion

chamber and in the exhaust

Inefficient especially below Mach 2

Used in older fighter jets

Propulsion Group Types

Tiger F-5

www.luftfahrt.ch



Turbofan engine

Combination of ducted fan and jet exhaust nozzle

Modern airliners and fighters




Turboprop engine

Turbine engine is used to drive a propeller




Specific impulse at different speeds


I sp =T

m× g0



Propeller driven by piston engine or electrical motor




At the front

At the wings (various possibilities)

Placement of the Propulsion group

The placement defines where

the forces are introduced



At the tail (various possibilities)




Combined positions




The choice depends also on the conversion, i.e. the propulsion group!

Energy Storage:

Densities in Terms of Energy per Mass

Energy density of

some reactants

[kWh/kg](LHV Lower heating value)

Hydrogen 33.3

Methane 13.9

Propane 12.9

Gasoline 12.2

Diesel 11.7

Ethanol 7.5

Methanol 5.6

Best* 2015 Li-Ion Batt. 0.25

Sugar 4.4

Oil (Colza,…) 10.4

10 20 300



Given: drag coeff. as a funcion of lift coeff.: 𝐶𝐿 𝑉 =2𝑚𝑔

𝐴𝜌𝑉2, 𝐶𝐷 𝐶𝐿

Required power:

Specific Excess Power: 𝑆𝐸𝑃 = 𝑃𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 − 𝑃𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑚𝑔 ≈ 𝑉𝑐𝑙𝑖𝑚𝑏,𝑎𝑐ℎ𝑖𝑒𝑣𝑎𝑏𝑙𝑒


Power Required and Available for Level Flight

Drequired ACVVDP3

2

1

Pavailable

Prequired

Pexcess

Vstall Vmax Vne

Pow

er

True Airspeed

Vemax Vrmax

min

L

D

C

Cmg

L

DmgD

V

Pmax

D

L

C

C

Best glide ratio

max/

P

EVTVs

min/ P

max2

3

D

L

C

C

L

D

LL

D

C

Cmg

CA

mg

C

CmgVVDP

2

Minimum sink in

gliding mode

Max. Range*(vrmax):

Max. Endurance*(vemax):

* Assuming constant propulsive efficiency η

||Autonomous Systems Lab 23.11.2015Robot Dynamics - Fixed Wing UAS: Basics of Aerodynamics 35

6DoF Nonlinear Aircraft Equations of Motion

𝑈 = 𝑅𝑉 − 𝑄𝑊 − 𝑔𝑠𝑖𝑛𝜃 + 𝑿𝑻 + 𝑿𝑨 𝑚 𝑉 = −𝑅𝑈 + 𝑃𝑊 + 𝑔𝑠𝑖𝑛𝜙𝑐𝑜𝑠𝜃 + 𝒀𝑻 + 𝒀𝑨 𝑚 𝑊 = 𝑄𝑈 − 𝑃𝑉 + 𝑔𝑐𝑜𝑠𝜙𝑐𝑜𝑠𝜃 + 𝒁𝑻 + 𝒁𝑨 𝑚

𝜙 = 𝑃 + 𝑄𝑠𝑖𝑛𝜙 + 𝑅𝑐𝑜𝑠𝜙 𝑡𝑎𝑛𝜃

𝜃 = 𝑄𝑐𝑜𝑠𝜙 − 𝑅𝑠𝑖𝑛𝜙

𝜓 = 𝑄𝑠𝑖𝑛𝜙 + 𝑅𝑐𝑜𝑠𝜙 𝑠𝑒𝑐𝜃

𝑛 = 𝑈𝑐𝑜𝑠𝜃𝑐𝑜𝑠𝜓 + 𝑉 −𝑐𝑜𝑠𝜙𝑠𝑖𝑛𝜓 + 𝑠𝑖𝑛𝜙𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜓 +𝑊 𝑠𝑖𝑛𝜙𝑠𝑖𝑛𝜓 + 𝑐𝑜𝑠𝜙𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜓

𝑒 = 𝑈𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜓 + 𝑉 𝑐𝑜𝑠𝜙𝑐𝑜𝑠𝜓 + 𝑠𝑖𝑛𝜙𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜓 +𝑊 −𝑠𝑖𝑛𝜙𝑐𝑜𝑠𝜓 + 𝑐𝑜𝑠𝜙𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜓

𝑑 = −𝑈𝑠𝑖𝑛𝜃 + 𝑉𝑠𝑖𝑛𝜙𝑐𝑜𝑠𝜃 +𝑊𝑐𝑜𝑠𝜙𝑐𝑜𝑠𝜃

𝑃 = 𝐼𝑥𝑧 𝐼𝑥 − 𝐼𝑦 + 𝐼𝑧 𝑃𝑄 − 𝐼𝑧 𝐼𝑧 − 𝐼𝑦 + 𝐼𝑥𝑧2 𝑄𝑅 + 𝐼𝑧 𝑳𝑻 + 𝑳𝑨 + 𝐼𝑥𝑧 𝑵𝑻 +𝑵𝑨 𝐼𝑥𝐼𝑧 − 𝐼𝑥𝑧

2

𝑄 = 𝐼𝑧 − 𝐼𝑥 𝑃𝑅 − 𝐼𝑥𝑧 𝑃2 − 𝑅2 + 𝑴𝑻 +𝑴𝑨 𝐼𝑥𝐼𝑧 − 𝐼𝑥𝑧

2

𝑅 = −𝐼𝑥𝑧 𝐼𝑥 − 𝐼𝑦 + 𝐼𝑧 𝑄𝑅 + 𝐼𝑥 𝐼𝑥 − 𝐼𝑦 + 𝐼𝑥𝑧2 𝑃𝑄 + 𝐼𝑥 𝑵𝑻 + 𝑵𝑨 + 𝐼𝑥𝑧 𝑳𝑻 + 𝑳𝑨 𝐼𝑥𝐼𝑧 − 𝐼𝑥𝑧

2


B.W. McCormick. Aerodynamics, Aeronautics, and Flight

Mechanics. Wiley, 1979. ISBN: 9780471030324.

B. Etkin. Dynamics of Atmospheric Flight . Wiley, 1972.

ISBN: 9780471246206.

G.J.J. Ducard. Fault-Tolerant Flight Control and Guidance

Systems: Practical Methods for Small Unmanned Aerial

Vehicles . Advances in Industrial Control. Springer, 2009.

ISBN: 9781848825611.

R.W. Beard and T.W. McLain. Small Unmanned Aircraft:

Theory and Practice. Princeton University Press, 2012.

ISBN: 9780691149219.


References


See you next week!


Documents

Folienmaster ETH Zürich · 2015. 12. 3. · 3. Performance Considerations 4. Stability 5. Simplified Dynamic Model 6. UAV Control Approaches 7. Case Studies Lecture 1: Basics of