Lecture 7Aircraft Trim

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Lecture 7

Aircraft Trim

Aspects of Aircraft Design and Control

with the kind input of Hamassala David Dicko Olivier Cleynen – April 2014

“Ride more than thou goest”

The fool — King Lear, I.4

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~ 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.

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Feedback is always appreciated:

olivier.cleynen ariadacapo.net

These course documents can be found at:

http://aircraft.ariadacapo.net/

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This document is published

under a Creative Commons license.

Some photos and illustrations have their author and specific license indicated on the bottom of the page.

You are encouraged to copy, modify,

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7.1 Trim: maintaining

longitudinal equilibrium

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7.1.1 A walk in an airliner

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CC by-sa Vincent Edlinger

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Longitudinal equilibrium:

balancing aircraft to maintain attitude

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trim

Engineer:

“set the aircraft in longitudinal equilibrium”

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trim Pilot:

“adjust the tail surfaces to obtain zero stick force”

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Maintaining attitude

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Two roles for the tail:

1. Allow longitudinal equilibrium 2. Allow longitudinal stability

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Problem #1

Whichever force is generated by the tail, affects the force to be generated at the wing

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Problem #2

The position of the lift force on the wing changes with lift coefficient

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7.1.2 Two conditions to attain trim

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Condition #1 for trim

the aircraft neither sinks nor rises:

  F

_vertical

=  0

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Condition #2 for trim

the aircraft does not move in pitch

  M

arbitrary point

=  0

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7.2 The aerodynamic center

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7.2.1 The aerodynamic center,

in a wind tunnel

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At constant speed, in the wind tunnel

CC-0 Olivier Cleynen

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The center of pressure of cambered airfoils

moves forward with increasing lift & lift coefficient

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Force, distance, and bending moment

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it so happens

that at constant speed, one point on the wing will “feel” constant bending moment (L×d)

→ the aerodynamic center

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At constant speed, the aerodynamic center sees constant bending moment

and lift force proportional to speed.

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But aircraft do not always fly at constant speed!

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7.2.2 The aerodynamic center,

in an aircraft slowing down

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At constant lift (aircraft slowing down)

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At constant lift, the bending moment

around the aerodynamic center is inversely proportional to the angle of attack.

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7.2.3 Wind tunnel and flight united:

the aerodynamic moment coefficient

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In both cases,

d seems to vary according to wing “effort”

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1 d ~ L ̃ ~ C ̃

_L

1 d ~ α ~ C ̃

_L

C ̃

_L

× d = cst

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Defining the aerodynamic moment coefficient

C_M ≡ M

1

2 ρ S _wing V ² ̄c

C_M = 1

̄c C _L d

C̃_M = 1

c C̃_L d

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C̃_M = cst

C ̃

_L

× d = cst

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In a wind tunnel, at constant speed

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In a wind tunnel, at constant speed

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In an aircraft, at constant lift

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In an aircraft, at constant lift:

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The aerodynamic center

● A useful model to position the lift force on an airfoil

● At this location:

● All of the lift force applies;

● A bending moment inversely proportional to lift coefficient applies (modeled with a constant moment coefficient).

● Usually found at quarter-chord position

● The greater the airfoil camber, the greater the moment coefficient

(Symmetrical airfoils have zero CM)

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The Aerodynamic Center

Varying CL,

Constant CM and position.

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Model validity limits

● Non-linear aerodynamics (stall)

→ CLmax

● Zero-lift (!)

The concept of the aerodynamic center

vanishes at the edges of the flight domain...

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7.3 Longitudinal Equilibrium

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7.3.1 Trimming at given conditions

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Sign conventions

Forces: positive upwards Moments: positive pitch up

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Condition #1: no sinking/rising

− W = L

_net

= F

_wing

 F

_stab

  F

_vertical

=  0

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Condition #2: no pitch movement

  M

arbitrary point

=  0

d

_CG

W + M

_wing

− d

_wing

F

_wing

− d

_tail

F

_tail

= 0

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_tail

= 0

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Trimming the aircraft

controlling l_wing (distance between CG and AC) is crucial to ensure safe flight

M

_wing

− l

_wing

 L

_net

 − b

_tail

F

_tail

= 0

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7.3.2 Trimming in any arbitrary condition

~ Coefficients to the rescue ~

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Why use coefficients?

● Lift coefficients allow us to quantify the limits for the wing and tail → stall

● Moment coefficients allow us to easily describe the movement of the center of pressure

● Coefficients help answer questions such as

“what if we were 30% higher and 20% faster?”

→ so bear with me for a few more slides...

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M

_wing

− l

_wing

( L

_net

) − b

_tail

F

_tail

= 0

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Introducing coefficients

ugh!

M _wing 1

2 ρ S_wing V ² ̄c

− l_wing 1

̄c

L_net 1

2 ρ S _wing V ²

− b_tail 1

̄c

S _tail S _wing

F_tail 1

2 ρ S _tail V ²

= 0

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_wing

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The main trim equation

States “the aircraft does not pitch up or down”

Perfect place to start when trim data needs to be quantified (elevator angles, CG position, ability to move in pitch)

C

_M_wing

− l

_wing

 c C

_L

−  V C

_{F tail}

= 0

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Limitations

● Small angles only

(drag & thrust influence pitch at high angles)

● Linear aerodynamics only

(the AC moves when stall occurs)

● No downwash of the wing on the tail

→ Do not design a real aircraft with this single equation!

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7.4 A pilot’s perspective on trim

~ “who designed that airplane?” ~

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7.4.1 The trim tab

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CC by-sa Markus Sümnick

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The trim tab relieves pilot effort on the controls

by generating a moment on the elevator hinge

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7.4.2 Trim setting and speed

~ don’t touch that button ~

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Cruise condition (datum)

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Reducing speed, but maintaining altitude

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Trimmed elevator at cruise conditions

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Untrimmed elevator at reduced speed conditions (note: speed still horizontal)

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Untrimmed elevator at reduced speed (detail)

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Trimmed elevator at reduced speed conditions (note: speed still horizontal)

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For any given speed,

there corresponds a specific trim tab setting

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Detail of untrimmed elevator at low speed

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Untrimmed elevator at low speed, with controls released:

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With controls released:

→ yoke/stick moves to neutral point,

where elevator hinge moments all balance out

→ reduced negative tail on aircraft

→ aircraft pitches down!

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The pilot’s perspective on trim

If the trim tab is not set

to the current aircraft speed, the aircraft will tend to pitch

“towards” its trim tab setting speed

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For precise piloting, any desired change in speed will require a new trim tab setting

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7.4.3 The trimmable horizontal stabilizer [THS]

~ large aircraft do it their way ~

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CC by-sa Olivier Cleynen

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CC by-sa Olivier Cleynen

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For any given speed, there corresponds a specific optimal THS setting

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For any change in speed, the changing THS vertical force must be compensated with a

new elevator position

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To maintain minimum drag, any desired change in speed will require a new THS setting

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Beware:

an improperly-adjusted THS can generate enough force

that equilibrium cannot be reached with elevators alone!

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● The THS is automatically trimmed to changes in flap setting, thrust, and speed

● The pilot’s stick position

commands a desired vertical G around the neutral position of 1 G

● The THS is automatically trimmed to changes in flap setting and

thrust

● The pilot must manually trim the THS according to speed

● The pilot’s yoke position

commands an elevator deflection angle around the neutral angle behind the THS

Airbus and Boeing : Two different strategies to obtain equilibrium when flying manually (using side-stick or yoke)

What are the advantages and disadvantages of each strategy?

Airbus Boeing

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Project 7

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Your 777 is on the go

● How will you organize the freight containers?

● Will you be able to trim when landing?

● Objectives:

● Play with main notions around aircraft trim

● Explore the practical importance of trim calculations