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 Key Terms
=
=
=
=
=
m
V
h
D
altitude
speed
flight path angle
mass
Additional definitions of
terms in text and in
Supplement to Class
14B Notes
desired flight path angle
Equations to program
Vh
=
sin
Basic differential equations to be integrated:
Basic equation for “autopilot” :
Ikk D210 )( −−−=
Comments on Equation for Angle of Attack
(Autopilot)
The model ignores “short period” dynamics. The pilot or autopilot
actually controls the elevator (a movable surface on the tail) to
control angle of attack. We will examine “short period” dynamics
later in the course.
Graph 1: Air temperature vs altitude
Coordinates:
(altitude (k ft), TA (deg R))
295, 298
344, 406
If altitude > 344 then TA = 406
Equations to program (2)
Equations to program (3)
Graph 2: Air density reference
altitude vs altitude
If altitude > 344 then = 23.0
)(/
0
hHh
aa e−
=
)(hH
)(hH
Equations to program (4)
Drag coefficient at zero lift vs Mach number
Equations in text and in
Supplement to Class 14B
Notes
Homework Assignment 14:
Run Objectives and Initial Conditions
Run 1: Test the program. Same trajectory as previously, in Phase 1. Start at
with desired flight path angle . Compare with Phase 1 results.
Run 2: Determine the ceiling. Start at with . Aircraft will eventually
cease increasing altitude.
25.0=
D
0=h
0=h
25.0=
D
*Helpful Hints on User-Defined Functions
For functions requiring “if then else” logic, taking the desired flight path
angle function as an example, write
If t < t1 then
return a
else
If t < t2 then
endif
endif
….
endif
end
f
end
*Helpful Hints on User-Defined Functions (2)
Ensure that the number of “If” statements equals the number of
“endif” statements.
Homework Assignment 14
Required Output:
Specified in text and in Supplement to Class 14B Notes