Redesign the Hab Project, GSE Honors Geometry, Fall 2016

Airlock 1 slowly depressurized to 0.006 atmospheres. Watney, wearing an EVA suit, stood inside it waiting for the cycle to complete. He had done it literally hundreds of times. Any apprehension he may have had on Sol 1 was long gone. Now it was merely a boring chore before exiting to the surface.

As the depressurization continued, the Hab’s atmosphere compressed the airlock, and AL102 stretched for the last time.

On Sol 119, the Hab breached.

The initial tear was less than one millimeter. The perpendicular carbon fibers should have prevented the rip from growing. But countless abuses had stretched the vertical fibers apart and weakened the horizontal ones beyond use.

The full force of the Hab’s atmosphere rushed through the breach. Within a tenth of a second, the rip was a meter long, running parallel to the seal-strip. It propagated all the way around until it met its starting point. The airlock was no longer attached to the Hab.

The unopposed pressure launched the airlock like a cannonball as the Hab’s atmosphere explosively escaped through the breach. Inside, the surprised Watney slammed against the airlock’s back door with the force of the expulsion.

The airlock flew forth meters before hitting the ground. Watney, barely recovered from the earlier shock, now endured another as he hit the front door, face-first.

Andy Weir, The Martian, p. 156

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After Mark Watney’s disastrous mission to Mars, NASA is looking to make some improvements before the next mission. One of the improvements that must be made is a redesign of the Hab that will include more resilient airlocks. NASA has hired you to create the floorplans and model for the new Hab. You are restricted by the amount of tarping that will be available to build with on Mars: 4000 m2. Each of the new airlocks will require 20 m2. Your goal is to maximize the area inside the Hab given the materials that you use.

The Hab must be comprised of 3 separate buildings: sleeping quarters, living quarters, and working quarters. The sleeping quarters must fit 6 beds that have dimensions of 2 meters long x .75 meters wide x .5 meters tall. If bunked, the beds are 1.5 meters tall and need a 1 meter head clearance. The other buildings should show the dimensions for necessities such as a shower, bathroom, kitchen area, and work space.

First, you must come up with a floor plan for the new Hab. Each piece of the floorplan must be expressed in the equation of a circle or a line with domain restrictions. An example, a line segment AB can be described as “y = 2x – 3 for [-2, 3]” which would use the line from the coordinates (-2, -7) to (3, 3). The bases of the three buildings must be 3 different shapes including one circle and one polygon with more than 4 sides. The floorplan should be constructed on a grid with a scale for the astronauts to follow when constructing it on Mars. The buildings will be connected with airlocks and must be externally tangent to be linked. You must also have an external airlock on each building for emergency egress. Please indicate all of these points on your floorplan.

Second, you must come up with the 3-dimensional model for each building. At least one building must be a composition of two different geometric figures (pyramid, prism, cone, etc). Each building must be tall enough to accommodate astronauts as tall as 1.9 m. You need to provide the dimensions for the height component of each building based on the base from the floorplan.

Next, calculate the surface area to ensure that you will have enough materials. Don’t forget to include the amount for each airlock. Also, calculate the volume of the entire Hab. Find the ratio of volume to surface area to see how efficiently you have used the materials to maximize the space in the Hab.

Volume to Surface Area = Volume ÷ Surface Area

When turning in your proposal, the Hab committee needs the following documents:

The gridded floorplan with scale. Each vertex should be distinctly labeled.
The equation of each of the figures for your floorplan labeled by piece. For example, AB: y = 2x + 3 for [-1, 3]
The 3-dimensional model of your buildings - can be computer generated or physically constructed.
The calculation of each building’s surface area and volume.
The calculation for total surface area, total volume, and volume to surface area ratio.

Grading Rubric

Requirement / Fulfilled / Partially Fulfilled / Lacking or Missing / Points Earned
The Hab has 3 buildings that meet all dimension requirements / 9-10 points
The Hab has 3 different shaped buildings that meet the requirements / 6-8 points
The Hab has 3 buildings but are not all different shapes or don’t meet a minor requirement / 0-5 points
The Hab has less than 3 buildings and/or is missing other major requirements / /10
The floorplan is drawn accurately to scale and labeled clearly / 16-20 points
The floorplan is represented on a grid, each vertex is labeled, and an accurate scale is included. / 11-15 points
The floorplan is represented on a grid, but the plan is missing labels or the design is not to scale / 0-10 points
The floorplan is poorly drawn and/or lacking in proper scale or labels / /20
The floorplan has accurate equations and domain restrictions / 16-20 points
Each line segment or circle on the plan has the correct equation with domain restrictions / 11-15 points
There are more than 4 mistakes in equations or domain restrictions. / 0-10 points
The floorplan is missing equations and domain restrictions or the equations and restrictions are consistently wrong. / /20
The 3-dimensional model is an accurate representation of the Hab design / 9-10 points
The 3-dimensional model shows an accurate layout and shape of each of the Hab’s components / 6-8 points
The 3-dimensional model is inaccurate but shows the shape of each of the Hab’s components / 0-5 points
The 3-dimensional model is lacking or does not clearly represent the Hab design / /10
The calculation for surface area and volume is correct / 9-10 points per building
The calculations are accurate / 6-8 points per building
The calculations take the correct approach but are incorrect / 0-5 points per building
The calculations are missing or use the incorrect formula / /30
The Hab design is within the given material restrictions / 5 points
The Hab requires at most 4000 m2 of tarp to construct. / 3 points
The Hab requires between 4000 and 5000 m2 of tarp to construct / 0 points
The Hab requires more than 5000 m2 of tarp to construct. / /5
The calculation for volume to surface area is correct / 5 points
The calculation for volume to surface area is accurate to the hundredths place. / 3 points
The calculation for volume to surface area is set up correctly but not accurate to the hundredths place. / 0 points
The calculation is missing or not calculated correctly. / /5
FINAL GRADE / /100