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
3AE3120 AAFP - Chapter 3Sem 1-2021/2022
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
4AE3120 AAFP - Chapter 3Sem 1-2021/2022
• 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
5AE3120 AAFP - Chapter 3Sem 1-2021/2022
• 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
6AE3120 AAFP - Chapter 3Sem 1-2021/2022
• 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
7AE3120 AAFP - Chapter 3Sem 1-2021/2022
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…
9AE3120 AAFP - Chapter 3Sem 1-2021/2022
PERFORMANCE DIAGRAM OF AN AIRPLANE…
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PERFORMANCE DIAGRAM OF AN AIRPLANE…
11AE3120 AAFP - Chapter 3
Propeller efficiencyStandard power diagram
Sem 1-2021/2022
PERFORMANCE DIAGRAM OF AN AIRPLANE…
• 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
12AE3120 AAFP - Chapter 3Sem 1-2021/2022
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
PERFORMANCE DIAGRAM OF AN AIRPLANE…
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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
15AE3120 AAFP - Chapter 3Sem 1-2021/2022
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
AE3120 AAFP - Chapter 3Sem 1-2021/2022
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
AE3120 AAFP - Chapter 3Sem 1-2021/2022