Definition of Terms
=
=
=
=
m
V
h
altitude (ft)
speed (ft/sec)
flight path angle (radians)
mass (slugs)
Definition of Terms (2)
=
=
=
D
L
T
thrust (lbs)
drag (lbs)
lift (lbs)
Basic Equations
sincos
WDT
dt
dV
m
−−=
Equations of motion:
Aerodynamic forces:
La
CSVL
2
2
1
=
Special Case
In the special case of low altitude, low speed flight along a constant
flight path, we may approximate
and the equation of motion along the flight path becomes
.
0
constTT
==
akV
dt
dV +−= 2
Special Case (2)
where
This is the same form as the equation of motion for the sounding
rocket on its descent. (See class 4.) We apply the results of that
analysis here and find that
=
00
2
m
SC
kDa
+=
))(tanh(/)(
0
ttkakatV
Special Case (3)
where is found from the initial condition
0
t
Homework Assignment 6
Read:
(Guide to numerical integration program of student’s or instructor’s
choice)
Work :
We will use the numerical integration program to explore aircraft
flight performance in this and in a later assignment. In this
assignment, number 6, we will program the basic equations of
Homework Assignment 6 (2)
In a second assignment later in the course we will program equations
for angle of attack, thrust, drag, and air density that more closely
resemble reality. At that time we will use the numerical integration
program to explore some fundamental measures of aircraft flight
performance:
Homework Assignment 6 (3)
Output:
Run the numerical integration program with the equations given
on the pages following. Terms are defined in today’s lecture. Run
the program for 25 seconds of flight time. You will know you have
programmed the equations correctly when the computed
fractional errors
/)(
Cerror
VVVfV
−=
Homework Assignment 6 (4)
Print out and hand in a copy of
(1) graphs of as a function of time
,, hV
Homework Assignment 6 (5)
sin/)cos(
sin
−−=
=
gmDTV
Vh
Basic equations of motion:
Homework Assignment 6(6)
Basic Lift and Drag Equations
2
2
2
1
2
1
VSCD
VSCL
Da
La
=
=
Homework Assignment 6 (7)
Constant parameters:
1038.2
2.32
3
0
=
=
=
−
W
x
g
a
slugs/ft^3
ft/sec^2
Different value for each student; see table
Homework Assignment 6 (8)
For this assignment only we will program the following
0
CC
DD
=
Homework Assignment 6 (9)
Also, for this assignment only we will program the following test
parameters
( )
ttka
kh
kaV
CC
C
0
0
)(
))cosh(/)ln(cosh()/(sin
tanh/
+=
=
=
sin
2
−=
=
C
Da
W
T
ga
m
SC
k
Homework Assignment 6 (10)
Helpful hints:
*Change color of graphs from red line on black background to black line on white
background (to save printer ink):
Right-click on graph
Left click on “edit”
Under “line attributes”, change color to black
Under “graph”, change color to white
Homework Assignment 6 (11)
Another helpful hint:
Computing Project #1:
Student Parameter Assignments
Student aircraft weight*
#1 56.0
#2 56.5
Student aircraft weight*
#9 60.5
#10 61.0
*in thousands of lbs