Lecture 1Lift and Drag

Lecture 1

Lift and Drag

Aspects of Aircraft Design and Control Olivier Cleynen – February 2014 – v1.4

~ foreword ~

●

The present notes serve as a support for in-class work, not the opposite!

Refer to the introductory course notes for explanations.

●

These notes are used as a succinct introduction to selected topics. They are purposefully

incomplete and must not be used for real-life

applications.

Feedback is always appreciated:

olivier.cleynen ariadacapo.net

These course documents can be found at:

http://aircraft.ariadacapo.net/

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1. Basic concepts in mechanics

energy time force distance

 t F

d

Weight

m g

Work

F × d

[J]

Power

 t

[W] or [hp]

F × d

Power

● Power and fuel economy are two different things!

● A more powerful car usually raises your fuel consumption

● A more powerful aircraft usually does not

● Aircraft are usually extremely powerful (×100)

~ 50 khp machine

Work

● The work spent and the work received are often very different

P

= F × V

P

= F × V

2. Power and speed

on the ground

Forces on a train

CC-0 Olivier Cleynen

No friction

F = 0

Voyager

Solid Friction

(rolling friction/resistance) (dry metal friction)

F = k

CC-0 Olivier Cleynen

If F = k

Friction with flexible materials

F = k × V

If F = k × V

Fluid Friction

F = k × V²

CC by-sa W:MorganaF1

If F = k × V²

If F = k × F²

Power spent to drive a train

● No friction?

→ infinite max. speed

● Solid friction?

→ there exists a max. speed

→ Fuel burn per km does not depend on speed

● Fluid friction?

→ Any 40% speed increase doubles fuel burn per km

Power and fuel economy are determined

by the speed dependence of drag

D = f ( V )

CC-0 Olivier Cleynen

CC by-sa Vincent Edlinger

3. Aircraft forces

Aircraft forces

Weight

CC by-sa Vincent Edlinger

Weight

MTOW MLW OWE

Aerodynamic reaction force

depends on a very large number of factors!

Thrust

≠ power

≠ energy expense

...but related to both

Lift and Drag

~ blessing and curse ~

Lift and Drag

Directions relative to speed, not fuselage An arbitrary (not “physical”) distinction

Finesse [the lift-to-drag ratio]

measures how “vertical” the reaction force is varies according to flight conditions...

f ≡ L

D

Finesse (the “lift-to-drag ratio”)

● “finesse” is often used to mean “maximum finesse”

● Finesse varies extensively during a flight, and aircraft rarely fly at f_max

● f_max is usually 10 on a jet fighter, 20 on a modern airliner or private aircraft, 40 for a competition sailplane

4. Quantifying aircraft forces

Experimenting: measuring lift

Experimenting: measuring lift

Experimenting: measuring lift

Experimenting: measuring lift

Lift

● Increases with speed squared

● Varies linearly with angle of attack (only in a certain range!)

Experimenting: measuring drag

Experimenting: measuring drag

Drag

● A strange behavior indeed!

● Increases with speed squared

● Increases with inverse of speed squared, too...

● At a given lift and altitude, drag will increase if you fly too slow. (≠ train!)

5. Lift and drag coefficients

How can we compare the ability to generate lift

for two wings of different shape and size ?

Wings generate lift

by imparting downward velocity on the air

A crude description of lift generation

CC-0 Olivier Cleynen

A crude description of lift generation

An idealized description of downwash

A crude description of lift generation

A crude description of lift generation

CC-0 Olivier Cleynen

An idealized description of downwash

How does an aircraft generate a force on air ?

Given a steady mass flow:

⃗ F

= d

d t ( ^m ⃗ v ) _{= ˙} ^m ⃗ v

mass flux × change in velocity

What flight parameters affect mass flux ?

● Proportional to air density

● Proportional to aircraft size (surface)

● Proportional to aircraft speed

● Depends on aircraft geometry

m ˙

m ˙ = ρ 1

S V g

What flight parameters

affect downwash velocity ?

● Proportional aircraft speed

● Depends on aircraft geometry

● Depends on aircraft attitude

v

v

= V

g

g

Quantifying lift:

= ρ 1

2 S V

g

g

g

L = ˙ m v

g

≡ C

The lift coefficient

The wing’s figure of merit

“influence of the wing geometry”

C

≡ L 1

2 ρ S V

And thus:

L = 1

2  S V

C

For a given C

(given flow pattern):

● Double the density?

→ lift doubled

● Double the wing surface?

→ lift doubled

● Double the velocity?

→ lift quadrupled

C

≡ L 1

2 ρ S V

For a given L (given aircraft)

● High speed, high density, high surface?

→ you want low CL

● Low speed, low density, low surface?

→ you want high CL

CC by-sa Vincent Edlinger

CC by-sa Vincent Edlinger

C_L ≡ L 1

2  S V²

The lift coefficient

● “Wing capability” for generating lift, independently of main conditions

● Controlled mainly with two parameters:

● Angle of attack

● Wing shape (esp. camber)

● Defined arbitrarily (but meaningfully) Dimensionless number (has no units)

Predicting the lift coefficient on a given wing

Extraordinary wing shapes have different behavior Linear aerodynamics: C_L,α is constant

Only true when the wing isn’t stalled!

C

= C

 ^{ − }



C

= k

  k

The drag coefficient

C

≡ D 1

2  S V

Predicting the drag coefficient on a given wing

Lift-independent drag (“viscous”)

Induced drag (“lift-induced”)

This equation only works in ideal conditions, i.e. high Re, low M, linear aerodynamics

C

= C

 K C

C

K C

6. Basic flight mechanics

C_D ≡ D 1

2  S V ²

Lift and Drag

● The equations we wrote have amazing consequences.

● Small wings, low density will increase your speed without an energy cost...

● … but you need higher power.

● Play around with the above notions and equations...

Beware:

● The equations we wrote have limited validity...

● Mach number dependence

● Reynolds number dependence

● No account for stall

● Never trust equations that “fall from the sky”.

Project 1

Flight speed range

Eclipse 500: the “$1,5m” jet

CC by-sa Alan Radecki

CC by-sa Josh Hallett

CC by-sa Josh Hallett

Pratt & Whitney Canada PW610F (Eclipse 500)

$150k D=37cm W= 120kg BPR=1,8 T=4kN

Project 1

● … is about putting together the concepts we explored today (in particular, drag)

● You are working for an aircraft manufacturer

● Data from a wind tunnel model series of tests is passed on to you – what do you think?

Project 1: tasks

● Choose a wing area that meets the design specifications ;

● Calculate the minimum and maximum flight speeds at low altitude ;

● Calculate the aircraft’s finesse and its optimal flight conditions.

Tools and help

● Use whatever software you wish (or none)

● Books, websites etc. in English are okay, but must be quoted.

Length

● Reports: 8 pages max (no longer!)

● Presentations: 15 minutes max, plus questions

How to Get the Project Done

● This is not a riddle that must be solved...

→ the solution is not hidden in the appendix

● Try to imagine the result first...

● Think about the data you need, then look for it

Key to a successful project:

Get a rough idea

of what the result looks like

as early as you can