AE3120 AIRPLANE AERODYNAMICS and FLIGHT PERFORMANCE ...

AE3120 AIRPLANE AERODYNAMICS and

FLIGHT PERFORMANCE

Chapter 3 – Equations of Force Equilibrium and

Performance Diagram

Prof. Hari Muhammad, Ph.D.

Ony Arifianto, Ph.D

Hendarko, M.Sc.

Study Program of Aerospace Engineering

Faculty of Mechanical and Aerospace Engineering

Institut Teknologi Bandung

Semester 1-2021/2022

1Sem 1-2021/2022 AE3120 AAFP - Chapter 3

3. EQUATIONS OF FORCE EQUILIBRIUM

AND PERFORMANCE DIAGRAM

3.1 INTRODUCTION

3.2 EQUATIONS OF FORCE EQUILIBRIUM

3.3 PERFORMANCE DIAGRAM

3.4 EXAMPLE OF PERFORMANCE DIAGRAM

2AE3120 AAFP - Chapter 3Sem 1-2021/2022

3. 1 INTRODUCTION

Motions of airplane include: translastional and rotational motion

Translational motion: as a respon to external forces acting on an

airplane: forward/backward motion; left/right motion; up/down

motion

Rotational motion: as a respon to external moments acting on an

airplane: roll; pitch; yaw


3.2 EQUATIONS OF FORCE EQUILIBRIUM

• Principle of force summation (vector):

• Scalar summation can be done if the forces are coordinated

on a chosen coordinate system. For instance, if they are

coordinated on wind axis system, then equations of force

equilibrium can be written as:

inersia aero prop weightF F F F

cos ( ) sin

sin ( ) cos

dVw dt

d

w dt

Onaxis X m D T W

Onaxis Z mV L T W

Inertia Aero Propulsion Weight


• If steady flight, then inertial force is zero, hence equations

of force equilibrium become:

0 cos ( ) sin

0 sin ( ) cos

w

w

Onaxis X D T W

Onaxis Z L T W


• For assumptions of angle of attack and engine incidence

angle zero, then equations of force equilibrium become:

• If gliding flight with T=0 dan <0, then equations of force

equilibrium become:

0 sin

0 cos

w

w

Onaxis X D T W

Onaxis Z L W

0 sin sin

0 cos cos

w

w

Onaxis X D W D W

Onaxis Z L W L W


• If cruise flight, then =0. If angle of attack and engine

incidence angle are small, then equations of force

equilibrium become:

0

0

w

w

Onaxis X D T D T

Onaxis Z L W L W

0max

2

2

2

21

12~maxmax

LCS

gmstall

CS

gm

L

CV

V

gmWWCSVL

L

L


3.3 PERFORMANCE DIAGRAM OF AN AIRPLANE

• Performance Diagram: relates thrust (power) required and thrust (power)

available of an aircraft with repect to airspeed in a certain flight

configurations and flight conditions.

8Sem 1-2020/2021 AE3120 AAFP - Chapter 3

PERFORMANCE DIAGRAM OF AN AIRPLANE…





11AE3120 AAFP - Chapter 3

Propeller efficiencyStandard power diagram

Sem 1-2021/2022


• In climbing flight with >0, equations of force equilibrium :

• If equilibrium force on Xw is multiplied by airspeed V, then

equation of power equilibrium is obtained as follow:

• or

sin

cos

w

w

Onaxis X T D W

Onaxis Z L W

sinVWVDVT

TV= power available = Pa

DV= power required = Pr

W sin is excess power = Pe

era PPP


PERFORMANCE DIAGRAM OF AN AIRPLANE …

13

For airplane with jet engine:Pa = T V (Thrust multipled by airspeed)

For airplane with piston propeller engine:

Pa is the power of propulsion system

AE3120 AAFP - Chapter 3Sem 1-2021/2022



3.4 EXAMPLE OF PERFORMANCE DIAGRAM

• The airplane N2XX:

• Drag D is computed from:

127PWx2:Engine

)upG/L;0(ionconfiguratClean

m65SsayapLuas;kg500.21m

flaps

2

D2

21 CSVD Drag coefficient CD is obtained from wind

tunnel test

D is varied with altitude H (in this case) and

airspeed V

Power available (dayatersedia) Pa is obtained from the data of 2 engine given from manufacturer


Performance Diagram of Airplane N2XX-R1

Maximum airspeed for cruising flight at flight condition of

m=21500 kg, H=20.000 ft, ISA+0 is 278 knots

16

Power available:

is obtained from

data of engine

Power required:

is computed from

data of drag

polar of the

airplane


Performance Diagram of Airplane N2XX-R2

17

Maximum airspeed for cruising flight at flight condition of

m=21500 kg, H=20.000 ft, ISA+0 is 294 knots

Power available:

is obtained from

data of engine

Power required:

is computed from

data of drag

polar of the

airplane


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