Homework Assignment 14:
Example Engineering Application of ODEs
Sounding Rocket Performance
Phase 2
Homework Assignment 14
Read:
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 once again
to explore further the sounding rocket trajectory analyzed in Classes
Homework Assignment 14 (2)
Programming:
Either recover your own stored program or type in the program given
out by the instructor in reviewing Homework Assignment 6. Program
the equations for air density, drag coefficient and gravity as
described on the next charts.
Output:
Run the numerical integration computer program for each of the
three rocket designs. Hand in (1) a copy of your program, including
Due: (date)
Homework Assignment 14:
Definition of Key Terms
=+=
=
=
=
=
2
0))/((hRRgg
c
m
V
h
Rocket altitude
Rocket vertical velocity
Rocket mass
Speed of rocket exit gases
Acceleration of gravity
More definition of terms
in text and in
Supplement to Class
14A Notes
Homework Assignment 14:
Sounding Rocket Equations
/)(
gmDTV
Vh
−−=
=
Basic equations of motion (as before): More equations for
forces, speed of sound,
etc. in text and in
Supplement to Class
14A Notes
Homework Assignment 14:
Sounding Rocket Equations (2)
Equations given in text and
in Supplement to Class 14A
Notes
Homework Assignment 14:
Sounding Rocket Equations (3)
Graph 1: Air temperature vs altitude
Coordinates:
(altitude (k ft), temp (deg R))
0, 519
36, 390
82, 390
154, 509
Homework Assignment 14:
Sounding Rocket Equations (4)
Graph 2: Air density reference
altitude vs altitude
)(/
0
hHh
aa e−
=
)(hH
Homework Assignment 14:
Sounding Rocket Parameters
Rocket number
1 2 3
8120 1500
0.03 0.025 0.02
0
W
Initial weight (lbs)
0
D
C
Subsonic drag coefficient
* unique for each student
c
Homework Assignment 14: Student
Parameter Assignments
Rocket 1
Student gas exit speed
#1 4500
#2 4600
Rocket 1
Student gas exit speed
#6 5100
#7 5200
Homework Assignment 14:
Helpful Hints
In look-up tables, remember that data is given in kft, not feet.
*Example logic for User-Defined Function:
If X < 10 then
return 6
else
*This is for ODE Architect, given as an example to the instructor to replace with
appropriate guidance for his or her computing environment