Saturday, October 4, 2014

Origami solar arrays in space

Origami?  In space?  That's right:  NASA is partnering with engineers to design collapsible solar arrays to be deployed in space.  Here's a polynomial optimization project for your high school math students using this theme.


"Bigger is better when it comes to space-based solar panels – but rockets have a very limited amount of room, so getting them into orbit can be a challenge. So where do NASA researchers turn when looking for solutions to this packing problem? Surprisingly, they look no further than the good, old-fashioned art of origami. Using an innovative folding technique, researchers at Brigham Young University (BYU) and NASA created an 82-foot solar array that can fold down to just 8.9 feet when closed..." - read more at Inhabitat.

Part 1:  
NASA has asked the engineers to design a box made of 16-gauge sheet metal to store materials related to this project.  If the area of the sheet is 60” x 144”, what size square should the fabricators cut from each corner in order to maximize the volume of the box?  Give both the size of the square and the maximum volume possible, and draw a sketch of the sheet metal indicating the sizes and locations of the cuts.
This is how the fabricators will fold the sheet metal into a box:

Part 2:
In a related project, NASA is developing a simple accordion-fold solar array (shown below) with a special type of polymer to be bonded around the edges and folds of the array.  Give the equation for the maximum area of array that can be built with any given length of this polymer.  (Hint:  use P to represent this length and give the equation in terms of P and x).

Part 3:
Try your hand at folding a cubesat using the following instructions for a Miura fold, which is the style of origami used by the engineers at BYU.  Make sure the aspect ratio of your sheet is 5:7 before you begin folding.

Deliverables:  submit your answers to parts 1 and 2 on a separate sheet of paper.

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