Comp1211 Modelling and Simulation. Worksheet 2 (Saturn V).
[CBPrice. 26-02-13]
Color Coding for this Worksheet
General Information
Information you will need for the activities
The Activities!
Purpose
(a) To get to know the CBP74 Simulation Engine and how to use it. (b) To learn how to grab data from the
simulation and to plot this in graphs using Excel. (c) To learn how to interpret these graphs. (d) To learn
how to make some visual observations of the behaviour of a Saturn V rocket and describe these in Simple
English. (e) To understand the differences between “parameters” and “variables”. (f) To understand the
concepts of a model and of a simulation.
Background Information
PARAMETERS concerning the actual Saturn V launch vehicle are summarised in the table below (“scaled”
version). These are used in the model and simulation you will use.
Total mass of the Saturn V vehicle
Mass of the fuel in the first-stage
Total engine thrust (5 engines)
1st Stage burn time
dMdT
vGas
28 kg
20 kg
345.5 N
2.5 kg/s
138.2 m/s
LAUNCH SEQUENCE This sequence replicates the actual Saturn V launch sequence, though the times
have been made a little easier:
1.
2.
3.
4.
Sequence starts at t = 0 secs. The engines are being prepared for ignition
Engines ignite at t = 5 secs and their thrust builds up gradually
The maximum engine thrust is achieved at t = 7 secs
The Saturn V vehicle is released at t = 8 secs, but only if
a. The thrust has reached the maximum
b. The thrust is greater than the weight of the vehicle
ONE BIT OF THE UNDERLYING MATHEMATICAL MODEL:
The thrust of the engines is calculated as follows : Thrust = VGas * dMdT, where VGas is the speed of the
burnt gas leaving the engines and dMdT is the rate of consumption of the fuel.
Remember also that the mass of the rocket at any time is the sum of the vehicle structure mass plus the mass
of the fuel. While the vehicle structure mass remains constant, the mass of the fuel changes with time as it is
used up.
Console Commands
The following console commands are available for this simulation. Here “X” refers to a number which you
will be asked to input. Remember to include spaces as indicated below.
Console Command
Effect
setparam pitchAngle X
The rocket is launched vertically, but after a certain time it will
pitch over at the angle you provide here.
This is the rate of consumption of fuel. The higher it is the more
thrust is developed by the engines. But the fuel gets used up faster
This sets the initial mass of fuel in the rocket before launch
This sets the exhaust velocity of the engine gas. The higher this
then the larger the thrust.
setparam dMdT X
setparam initmassFuel X
setparam vGas X
Activities
1
Getting to Know the Simulation Engine (Part 1).
(a) Double Click the UDK icon on the desktop and shut down any additional windows. You will see
a white landscape with a cube. Make sure you maximise the window.
(b) Choose File > Open then navigate to UDKGame > Content > CBP74_Content and select the
level CBP74_SaturnV_level.udk, You will find an EIE with a rocket in view.
(c) Start the level by selecting the blue arrow at the bottom of the toolbar, you should see a red
cross-hair on the screen.
(d) Move the cross-hair over the rocket and left-click. It will glow nuclear-green for a moment. A
load of information will appear top-right on the HUD. Look at the top three lines of information.
This should make sense.
(e) Hit F1 to start the simulation running with the default parameters. Observe the motion of the
rocket as it rises and falls
(f) When the rocket has landed (line 2 on the HUD will indicate “touch down”) then press F2 to
reset the simulation.
(g) Repeat (e) and (f) a couple of times until you are familiar with the basic controls
(h) Press “Exc” to exit the engine.
You may choose to make notes.
2
Getting to Know the Simulation Engine (Part 2).
Here we shall explore how to change one “parameter” of the model, the pitchAngle and to run the
simulation several times with different values of this parameter and so to try to understand what is
the effect of this parameter on the behaviour of the rocket.
(a) Open up the level as above and select the rocket as in 1(d).
(b) Now hit the tab key which will bring up the console window at the bottom of your screen (a one
row black bar).
(c) Type here the following: setparam pitchAngle 80 Please type the spaces as indicated, then hit
return. This will set the angle of pitch of the rocket to 80 degrees after it has lifted off. This angle is
measured with respect to the vertical, so 90 degrees means changing to horizontal flight.
(d) Observe the motion of the rocket and how it has changed, from the default angle of pitch of 10
degrees. Write down your observations
(e) Repeat (b) to (d) with various pitch angles (which you can choose, but be sensible!) and reflect
on what you see. Is there any pattern here? Write down your observations
3
Importing data into Excel and Interpreting the data
(a) Open up the level and set the pitch angle to zero, so the rocket is constrained to move vertically,
up and down. [Hint: setparam pitchAngle 0].
(b) Now run the simulation and reset it when the rocket returns to Earth. Now hit Esc to exit the
level and close the log file.
(c) Open up an Excel file. You can click on the icon in the level to open the Excel file, else navigate
to C:\UDK\UDK-2012-10\UDKGame\Content\CBP74_Content\TextFiles and open up the file
SaturnV.xlsx
(d) Import the latest data SaturnV_X (where X is the version number) from the location
C:\UDK\UDK-2012-10\UDKGame\Logs. (See separate document or movie clip for help)
(d) Plot a graph of “totalMass” versus “time” (See separate document or movie clip for help)
Now answer the following questions based on your graph of total mass (remember the total mass is
the mass of the rocket structure plus the mass of the fuel.
1.
2.
3.
4.
5.
4
What is the total mass at the start and end of the flight? What has caused this change?
At what time did the engines ignite?
At what time was the fuel used up?
At what time did the rocket hit the ground? You can also get this from the HUD
Describe in simple English how the total rocket mass changes with time.
More data interpretation
Make a plot of velyZ (vertical velocity) against time and answer the following questions
1. Work out at what time the rocket lifts off. Explain.
2. What is happening to the velocity between 8 and 13 seconds? What causes this change?
3. What is the velocity around 21 secs? Describe the behaviour of the rocket at this point in
time.
4. The velocity after 21 seconds is negative. What is the rocket doing in this time interval?
5. What time does the rocket hit the ground? Check with your above answers
6. Describe in simple English how the velocity of the rocket changes with time.
5
Conducting your first Simulation
Here we are going to ask a what-if question. What would happen if one or more SaturnV engines
failed on launch (SaturnV has 5 engines)? Would the rocket launch? What happens to the maximum
height reached?
One way of simulating this is to reduce the parameter dMdT from its value of 2.5 when all five
engines are working. Remember dMdT is the rate of fuel consumption. So when five engines are
running dMdT is 2.5, but if four engines are running then dMdT is 2.0, three engines would mean
dMdT is 1,5 and so on.
So here’s what you could do. First gather some data
(a) Start the level and set a value of dMdT by using the console command setparam dMdT 2.5
(b) Run the simulation by pressing F1 and wait until the rocket crashes
(c) Record the maximum height as displayed on the HUD
(d) Reset, change dMdT and repeat (b) and (c) to simulate the effect of losing 1,2,3 and 4 engines on
launch.
Now you must analyse the data. Here’s a suggestion
(e) You have a series of data pairs, (i) value of dMdT, (ii) corresponding value of max height. So
enter these manually into Excel and create a table and perhaps draw a graph.
(f) Look at the table and the graph and describe in simple English how the value of dMdT
determines the maximum height
(g) How many engines can be lost to achieve some sort of launch? How many engines can be lost so
that the maximum height is within 20% of the desired height.