Reference no: EM131413556

Introduction to Engineering Analysis Assignment - Red Bull Stratos Jump

Part 1:

Use ode45 and the simple freefall function from Section 10.3 of Physical Modeling in MATLAB to model Felix Baumgartner's altitude, velocity, and acceleration for the first minute after he jumped from 38,969.4 meters above sea level.  Compare by plotting modeled altitude, absolute value of velocity, and acceleration with the measured data*. Write a function that takes as parameters at least the end time (in seconds) for a plot (60 seconds for Part 1), a title, and the modelled altitude and velocity, and plots the altitude, absolute value of velocity, and acceleration for both the modeled and measured/calculated data. How accurate is the model for the first portion of the minute? How accurate is the model for the last portion of that first minute?  Comment on the acceleration calculated from the measured data.  Is there any way to smooth the acceleration calculated from the data?

Part 2:

Now consider section 10.4 on air resistance.  Use the modified acceleration function, but do some research to determine what mass, m, should be used in the function.  Estimate your uncertainty in the mass that you have chosen.  How sensitive is the velocity and altitude reached after 60 seconds to changes in the chosen mass?

Compare by plotting again the measured data with the modeled data.  Use your plotting function from Part 1 and plot for the first 60 seconds again.  How accurate is the revised model?  What is good and bad about the revised model?

Part 3:

Felix was wearing a pressure suit and carrying oxygen?  Why?  What can we say about the density of air in the stratosphere?  Exercise 10.6 on page 125 gives a more-complete model of drag due to air resistance, and gives a reference to a Wikipedia article. https://en.wikipedia.org/wiki/Drag_(physics)

How is the density of air different at around 39,000 meters than it is on the ground?

Can we include the changes in the density of air in our model?  Update the model by filling in a function to calculate the density of air.  Consider the product AC_d in the equation for drag due to air resistance.  What methods can we employ to estimate that product? Given the definitions of A and C_d, does the estimate seem reasonable?  Compare the measured data with our updated model by plotting for the first 4.5 minutes using your plotting function.  Now how accurate is the model?  

Updated notes on Part 3...  What are the factors involved in calculating the density of air?  How do those factors change when we end up at the ground but start at the stratosphere?  We are providing you with a function, stdatmo, that you can use to model the atmosphere up to at least the stratosphere, but please explain how calculating air density up to the stratosphere is more complicated than say just in the troposphere.

Part 4:  Improving our model in order to try to more closely match the actual data.  

What is the actual gravitational field strength around 39,000 meters?  (See Tipler Volume 1 6e page 369.)  How sensitive is the altitude reached after 4.5 minutes to simpler and more complicated ways of modelling the gravitational field strength?  What other changes could we make to our model?  Refer to, or at least attempt to explain, the physics behind any changes that you propose.  What is a change that we could make to our model that would result in insignificant changes to the altitude reached after 4.5 minutes?  How can we decide what change is significant and what change is insignificant? 

Part 5:

At what altitude does Felix pull the ripcord to deploy his parachute?  Recalculate the AC_d product with the parachute open, and modify your code so that you use one AC_d product before and one after this altitude.  Make a single acceleration-plot figure that includes, for each of the model and the acceleration calculated from measurements, the moment when the parachute opens and the following 10 or so seconds.  If you have trouble solving this version of the model, just plot the acceleration calculated from measurements.  According to this version of the model, what is the maximum magnitude of acceleration that Felix experiences?  How safe or unsafe would such an acceleration be for Felix? 

Part 6:

How long does it take for Felix's parachute to open? Try to adjust your code to reasonably model the period when the parachute opens.  A reasonable model will have a maximum magnitude of acceleration somewhat similar to that calculated from the measured data.  Redraw the acceleration figure from the previous Part but using the new model.  Also, using your plotting function from Part 1, plot the measured/calculated data and the model for the entire jump from stratosphere to ground.

Titles, labels and legends should be included in all figures.

* Measured data:  You will initially be provided with a draft spreadsheet containing data pulled out of the video below.  We would like some volunteers to fill in some data that we want to see.  Please let us know if you are willing to help.  The video is at: https://youtu.be/raiFrxbHxV0

Attachment:- Assignment Files.rar