Notes on Lab #4
Today's lab on falling and skydiving will start with a half-hour lecture by an
actual skydiver (and professional mountain guide), our own tech support guru
Steve Goryl. Then you will
spend about half an hour reading through the material in Module 4.1
(pp. 114-125). The actual work, Projects 4 and 5, should take you most
of the remaining hour. As usual, you will not build a model from scratch, but will instead modify
an existing model. To get started, download
this model of a skydiver's motion
under the influence of air friction. Save two copies of this:
When you are done, you will turn in these two modified models, along with your
Project 4 asks you to use air density values from an input graph. To learn
about input graphs, download
this tutorial from the second lab, and look on p. 11. Before making the
modification, run the original model with the original data set name at the top
(FallSkydiveDS). After you've made air density sensitive to
position, change the name of the data set name to
FallSkydiveDSDensity or something similar, and run the model again.
Then plotting position should give you an overlay graph comparing the
two different versions. Before copying and pasting this graph to your writeup,
modify it as follows: from the Options menu at the
top, change the color coding to
black-and-white numerical coding (because you can't count on print publications
being in color).
Include the labeled plot in your writeup, along with a brief
commentary on what it shows: does it should match your intuitions about the
effect of the more realistic air density model?
Project 5 asks you to have the skydiver jump at a 30 °
angle from an airplane moving
horizontally at 130 m/sec at a height of 600m,. Clearly, the interesting part
of this is the horizontal motion. As you may remember from
horizontal motion and vertical motion are independent of each other, and
horizontal motion is not (directly) affected by gravity. So you can
have separate components for horizontal velocity and position that will initially
be constant. Since the skydiver is not a projectile, it is probably also
safe to ignore the angle. So we'll focus on the forward motion.
To start, just use a simple three-variable model of horizontal position: a
box variable to accumulate it, a flow into the box variable for change in horizontal
position, and another box variable going into the flow, for horizontal
velocity (similar to vertical). This horizontal box variable velocity will
initially be a constant 130 m/sec. Once you've run the model, you can plot
horizontal position, which should come out as a straight, rising line. Then you
can use the control panel to build a plot of vertical position against
horizontal position; i.e., position in 2D space (ignoring lateral motion).
Because horizontal position is linearly increasing, this plot won't look
very different from the original plot of vertical position.
So what is it that slows the skydiver down horizontally? Air friction, of course!
Fortunately we have already modeled this, for vertical motion. So
duplicate the structure for vertical friction with a new horizontal friction
(it can share the drag coefficient, projected area, and air density
with the original, vertical friction). Just as vertical friction depends
on vertical velocity, horizontal friction should depend on horizontal velocity.
When you've got horizontal velocity working, your vertical/horizontal plot will
look something like a skydiver falling from a moving airplane, with the
horizontal axis magnified because of the relatively small horizontal
motion. Include this
plot in your writeup, and submit all three models and your writeup when you're
finished. Reward yourself by relaxing to the soothing sounds and visuals of
this beloved classic.