Pro/DESKTOP® Tutorial
Gravity Toroid
Written
by
Tim Brotherhood
Copyright © 2003, Parametric Technology Corporation (PTC) -- All
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countries.
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Acknowledgements
Sheila Schencke, Executive Director, STARBASE Louisiana
Barbara Koscak, Executive Director, STARBASE Michigan
Rick Simms, Deputy Director, STARBASE Michigan
Feedback
In order to ensure these materials are of the highest
quality, users are asked to report errors to PTC at
[email protected].
Suggestions for improvements and other activities would
also be very welcome.
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2
T ABLE OF CONTENTS
INTRODUCTION .................................................................................................................. 4
Health on prolonged space flight................................................................................................4
What is gravity .....................................................................................................................................4
Artificial gravity...................................................................................................................................4
CREATING THE GRAVITY TOROID .......................................................................................... 7
Link corridor..........................................................................................................................................7
Vertical spokes .....................................................................................................................................9
Horizontal spokes ............................................................................................................................10
Rim.........................................................................................................................................................10
Toroid rim ............................................................................................................................................11
Shell.......................................................................................................................................................13
Assemble to space station ...........................................................................................................14
Further problems..............................................................................................................................14
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I NTRODUCTION
Health on prolonged space flight
There are several physiological problems associated with prolonged space travel including
loss of muscle function and reduced bone density. The human body puts its resources (i.e.
calories, minerals and proteins) where they are needed most. Since in a low gravity
environment the body does not have to work as hard as on the Earth’s surface, muscles and
bones begin to atrophy.
Experiments on US and Russian flights have shown that these effects can be reduced if
astronauts do regular, vigorous exercise. These are effective for short flights but journeys
to planets such as Mars and further will need a sustainable solution. Long term, the best
solution is to create some form of artificial gravity equivalent to that found on earth.
What is gravity
Gravity is the force that makes objects fall towards the ground. Gravity holds us down.
This force is proportional to the mass of an object; the greater mass an object is, the
greater the pull that object has on other objects. The average force of gravity acting on us
here on Earth is equivalent to 9.8 ms-2 . But small objects exert gravity too. Yes! Your body
exerts a small gravitational force on other objects.
Artificial gravity
Science fiction writers have come up with many ways to create gravity including magnetic
shoes and force fields. Most of these require materials that do not exist or huge energy
sources to operate and are unlikely to become reality. However, a simple solution has been
suggested since science fiction writing began.
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Werner von Braun design
Artwork © 1968 Robert McCall
Werner von Braun suggested the torus (above left) and Arthur C Clarke included a similar
design (above right) in 2001: A Space Odyssey.
If the diameter and rotational velocity of the large spinning wheel are carefully calculated,
a centripetal force equivalent to 1g can be generated at the rim.
Here are two examples that produce around 1g at the rim.
Example 1
Wheel diameter (m)
160
Rotation time (sec)
18
Rim velocity (ms-2)
28
Example 2
Wheel diameter (m)
640
Rotation time (sec)
32
Rim velocity (ms-2)
56
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Math of toroid size
How do we work out this?
The formula that allows us to calculate the force at the edge of a spinning space station is:
F = mw2 r
Where:
F = The centripetal reaction force needed to supporting the person
(assuming the force due to gravity on earth is 10 newtons)
m = The mass of the average person (typically 70kg)
w2 = Angular velocity (radians per second) of the rim squared
r = radius of the rim
Two things are unknown, the angular velocity and the radius. If we substitute numbers for
the values we know and use 40 meters for the radius we get:
700 = 70 x ω w2 x 40
Resolving this we see:
700 = ω w2 x 40
70
Cross section through space
station
Radius = r
10 = w2 x 40
Angular
velocity = ω
10 = ω w2
40
Sq root 0.25 = ω w
Or:
Mass = m
Centripetal
force = F
0.0625 radians per second angular velocity
1 radian = approximately 60 degrees
So, for a radius of 40 meters, an angular velocity of 3.75 degrees per second will create a
force at the edge equivalent to the gravity on earth.
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With this information we can create a toroidal module to add to the space station started
in the previous tutorial. At the same time we can teach you a new Pro/DESKTOP technique
for creating solid shapes, Revolve Profile.
CREATING THE GRAVITY T OROID
•
Start Pro/DESKTOP and begin a New design.
Link corridor
The hub will be an extrusion from a hexagon sketch on the Frontal workplane. This will be
similar to creating the corridor in the previous tutorial.
Hexagon shape
• Makes sure the palette is visible and the
Shapes tab selected.
• The browser should be set to show workplanes.
• Right click over the Frontal workplane and
click on Select workplane.
• Drag the hexagon shape onto the Frontal
workplane.
Make sure the frontal workplane is prehighlighted in light blue when you release the
mouse button.
•
View onto the workplane [Shift + W] and Autoscale [Shift + A].
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Changing the size of the hexagon
You might remember how to do this from the previous tutorial. Here is a reminder of the
key steps.
•
Remove the reference brackets from the diameter constraint.
•
Change the size of the construction circle to 2500mm.
•
Autoscale, [Shift + A].
If necessary, you can refer back to the Space station tutorial for the detailed instructions.
Moving the hexagon
It will be much easier to center the spokes and rim if this hexagon is located on the origin.
•
Make sure
, the Select line tool is selected.
• Open the Edit pull-down menu and click on
Select all.
All of the lines in the hexagon sketch will be
highlighted.
• Move the mouse over the center of the hexagon.
• Left mouse click and drag the hexagon over the
origin (0,0).
Renaming
In complex designs it can be very difficult to locate which sketch is the basis for a
particular feature. To help, you should always give sketches names that indicate their
purpose. You have already done this in previous tutorials when creating a new sketch but
existing sketches (and workplanes) can also be renamed.
• Move the mouse cursor over the text for the Lateral
workplane and left mouse click.
• Pause, then left mouse click again.
The sketch name will highlight in black and the text cursor
will appear.
• Type a new sketch name of Link profile
• Click
.
You are now ready to extrude a solid to form the basis of the connecting link corridor.
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Extruding the link corridor
•
Click on
•
Change the dialog settings to match those in this dialogue box.
, the Extrude Profile... tool.
Notice that the Symmetric about workplane option
has been checked. This ensures that the link corridor
extends an equal distance on either side of the
frontal workplane making it easier to center the
spokes and rim.
• Click on
dialog box.
to close the Extrude Profile
Vertical spokes
The vertical spokes are created in exactly the same way as the link corridor with a hexagon
sketch on the Base workplane and a longer extrusion.
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The main stages are listed below. Refer back to creating the link corridor if you need more
detailed steps.
• Select the Base workplane.
• Add a hexagon shape from the palette.
• Alter the size to 2500mm diameter (remove reference first).
• Center the hexagon on the origin.
• Rename the hexagon sketch to Vspoke profile.
• Create an Extrusion named Vertical spoke, symmetrical
about the workplane and 76000mm long.
Horizontal spokes
• Repeat the above steps to create the horizontal spokes from a
hexagonal sketch on the Lateral workplane.
Rim
The rim is created using a new technique called Revolve Profile... Unlike extrude – which
needs only one sketch – revolve needs two.
The revolve principle
In Pro/DESKTOP a revolved shape requires two sketches, an axis sketch with a single
straight line and a profile sketch of the shape of the object.
Axis
sketch
Sketches
(separated for clarity)
Gravity Toroid
Profile
sketch
Sketches
(ready to revolve)
Completed
revolve
10
Toroid rim
Axis sketch
• On the Frontal workplane create a new
sketch called Rim axis.
• View onto workplane [shift + W] and
zoom in on the hub of the station.
• Draw line horizontally through centre of
airlock corridor (Shown in red).
• With the axis line selected.
Fixing the axis line
To provide a fixed reference for the revolve. The axis line will be fixed in position.
•
Make sure the axis line is selected.
•
Open the Constraint pull-down menu.
•
Select the Toggle Fixed option.
•
A small triangle appears on the axis line to show it is fixed.
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Rim profile sketch
The profile sketch must be on the same workplane as the axis
sketch. For the rim profile you will use another hexagonal sketch.
• Zoom out to see the whole design.
• Drag a hexagon sketch onto the Frontal workplane.
• Rename the hexagon sketch Rim profile.
• Resize the hexagon to be 6000mm.
• Move the hexagon to the top of the vertical spokes, aligning it with
the spoke.
• Constrain the top line in the hexagon to be 40,000mm from the
axis line.
Revolve rim
The next bit is simple, to create the Revolved rim.
•
Select
•
Make sure the correct profile and axis sketches are selected.
•
Type in 360 for the Angle.
•
Click on
, the Revolve Profile... tool from the features toolbar.
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12
You should now have a rim on your model
Shell
The final step is to hollow the toroid.
• Select the end face of the central airlock
corridor.
• From the Features pull-down menu or from the
features tool bar select
, the Shell tool.
• Enter 50 for the Offset.
This will become the wall thickness for the
toroid.
Click on
•
to see the result.
Don't forget to save your model.
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Assemble to space station
The skills learned in the previous tutorial should enable you to assemble this
toroid module to your space station assembly.
Why not create an album image of your space station against a space
background?
Further problems
This image is from the film 2001: A Space Odyssey. It shows an astronaut exercising by
running around the perimeter of the rotating space station.
Unfortunately life isn't as simple as we would like. Other effects are at work.
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Varied perimeter speed
If we assume the astronaut is running in
the direction of spin, his angular velocity is
faster than before. The effect is to increase
the apparent gravity. He will feel as though
he is running up-hill.
What do you think he would feel if he ran
against the direction of spin?
Coriolis effect
Have you ever tried to hold the axle of a spinning bicycle wheel? If you have, what
happens when you try to change the axis of rotation? The wheel resists being turned and
tries to lie down!
Attempt to turn the wheel…
And the wheel will try to lie down!
This is called the Coriolis effect. It is the same thing that makes the water spin as it
disappears down the drain in a bathtub or sink.
A detailed examination of the problems associated with artificial gravity can be found at
http://mars.complete-isp.com/aero2.htm
Now you are ready to publish your space station to your school network or even the
Internet!
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