Example Engineering Application of ODEs
A numerical integration project:
Numerical Integration of ODEs
Using the computer to calculate a solution time-step by time-step
Theory will be examined later in the course.
Homework Assignment 6
Read:
(Guide to numerical integration program of student’s or instructor’s
choice)
Work :
We will use a numerical integration program to explore further the
sounding rocket trajectory analyzed in Classes 3 and 4. This
Homework Assignment 6 (2)
We will employ the computer program to analyze the trajectory of a
small model rocket for which the simple model should work well.
In a second assignment later in the course we will program equations
for drag coefficient and air density that more closely resemble
Homework Assignment 6 (3)
Output:
Run the numerical integration program for rocket number 1 with the
equations given on the pages following. Print out and hand in a copy of
the computed rocket trajectory and your program, including user-
Due:
(date)
Homework Assignment 6:
Definition of Terms
=
=
=
m
V
h
Rocket altitude
Rocket vertical velocity
Rocket mass
Homework Assignment 6:
Definition of Terms (2)
=
=
=
0
W
D
T
Thrust (lbs)
Drag (lbs)
Rocket initial weight (lbs)
Homework Assignment 6:
Sounding Rocket Equations
Vh
=
Basic equations of motion:
Homework Assignment 6:
Sounding Rocket Equations (2)
Basic Thrust and Drag Equations
Thrust:
Drag:
2
2
1
VSCD
Da
=
0V
Homework Assignment 6:
Sounding Rocket Equations (3)
For this assignment we will program the following to describe the
drag coefficient and air density:
Homework Assignment 6:
Sounding Rocket Equations (4)
Constant parameters:
Parameters changing with rocket design:
2.32
=
g
ft/sec/sec
Homework Assignment 6:
Sounding Rocket Equations (5)
Rocket number
1 2 3
8120 1500
0
W
Initial weight (lbs)
* unique for each student
c
Homework Assignment 6: Helpful Hints
Expect numerically computed solutions to be within 2% or better of
closed-form-calculated values.
*Change color of graphs from red line on black background to black
line on white background (to save printer ink):
Homework Assignment 6: Helpful Hints (2)
*To print out an ODE Architect Tool page:
Press “Ctrl” and “PrntScn” keyboard keys simultaneously
Click on Tools and then on Report Writer
Homework Assignment 6: Student
Parameter Assignments
Rocket 1
Student gas exit speed
#1 4500
Rocket 1
Student gas exit speed
#6 5100