102 lab4

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 3.1 (pp. 61-72). 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, go to your downloaded folder of Vensim models and copy the FallSkyDive.mdl model into two copies: username_FallSkyDive4.mdl and username_FallSkyDive5.mdl. When you are done, you will turn in these two modified models, along with your PDF writeup.

Project 4 asks you to use air density values from an input graph. To learn about input graphs, (re)download the instructions 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 physics class, 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, realize that you’ve already got a good model of the skydiver’s vertical motion; indeed, that is all that we’ve modeled so far. So now you’ll add some new, standalone components to your existing (username_FallSkyDive5.mdl) model to create 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. This box variable horizontal velocity will have an initial value of 130 and an equation that’s just zero, to start off. You can initialize horizontal position to whatever you like, because it’s arbitrary. 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). To make the plot sensible, you’ll eventually want to rename the original position and velocity variables to vertical position and vertical velocity, but I recommending making a backup copy of your model somewhere before doing this, so you can backtrack if something goes wrong. Because horizontal position is linearly increasing, this plot won’t look very different from the original plot of vertical position, but make sure to keep the X and Y axes the same size, to get a realistic view.

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 both models and your writeup when you’re finished.