Differential Equations
for Engineers:
the Essentials
Supplement to Class 14B
Homework Assignment 14:
Example Engineering Application of ODEs
Aircraft Flight Performance, Phase 2
Homework Assignment 14
Review:
Refresh your memory by skimming (the guide to the instructor’s or
student’s choice of numerical integration computer programs.)
Work :
We will use the numerical integration computer program to explore
aircraft flight performance. We will add realistic equations for angle
L
T
W
V
Variables for Aircraft Longitudinal Flight
Definition of Terms
=
=
V
h
altitude (ft)
speed (ft/sec)
Definition of Terms (2)
=
=
=
D
L
T
thrust (lbs)
drag (lbs)
lift (lbs)
Definition of Terms (3)
=
=
Temp
Temp
0
Air temperature (degrees R)
Air temperature at sea level (degrees R)
Equations to program
Basic equations of motion:
2
2
1
VSCL
La
=
Basic lift and drag equations:
gWm /=
Weight and mass:
Equations to program (2)
Constant parameters:
1060
1038.2
2.32
3
3
0
=
=
=
−
xW
x
g
a
slugs/ft^3
ft/sec^2
lbs
Graph 1: Air temperature vs altitude
Coordinates:
(altitude (k ft), TA (deg R))
0, 519
Equations to program (3)
Equations to program (4)
Graph 2: Air density reference
altitude vs altitude
)(/
0
hHh
aa e−
=
)(hH
Equations to program (5): drag coefficient
M
8.00
1D
C
0
C
D
M
Equations to program (6)
1
Drag coefficient at zero
lift vs Mach number