Tuesday, February 16, 2016

The Math of "The Martian" Sol 30

Mark needs to make water. As he says “fortunately I know the recipe: Mix 2 parts Hydrogen with 1 part oxygen and burn”

Mark plans to get the Hydrogen from The Mars Decent Vehicle (MDV). The MDV is a small space craft that was only designed to take them from their main spaceship, the Hermes, in orbit, to the surface of Mars. It uses Hydrazine (N2H4) to power its thrusters. Because Martinez, the mission pilot, did such a good job on his landing, the MDV has 292 Liters of Hydrazine left in the fuel tanks. Almost all of the Hydrazine can be broken down into N2 and H2 using the Iridium catalyst in the MDV’s thruster reaction chamber. Not all of the Hydrazine will convert to N2 and H2, a small portion will become ammonia.

If however we assume that all the Hydrazine is converted, then we can get an upper limit on how much water Mark can make. If Mark had an unlimited supply of Oxygen, how many Liters of water could he make with the Hydrazine he has, again, assuming all the Hydrazine reacts? What is the highest percentage of Hydrazine that can turn to ammonia will still yielding the amount of water Mark needs?

How much energy would be released if all the Hydrazine was converted to Nitrogen and Hydrogen in the absence of Oxygen all at once? I.E. If the hydrazine exploded outside the Hab. Express your answer in terms of Enthalpy. How many pounds of Trinitrotoluene (TNT) would be required for the same release of Enthalpy?

How much energy would be released if all the Hydrazine was converted to Nitrogen and Water in the presence of Oxygen all at once? I.E. If the hydrazine exploded inside the Hab. Express your answer in terms of Enthalpy. How many pounds of Trinitrotoluene (TNT) would be required for the same release of Enthalpy?

As for Oxygen, the Hab has an emergency supply of 50 Liters of O2 stored in Liquid from. How many Liters of Water could he make with that if he had an unlimited supply of Hydrogen?
That’s an emergency supply, and Mark would rather keep that for, you know, emergencies. He has a better idea for getting oxygen. The Hab has a machine that is designed to convert the CO2 that the crew exhales into solid carbon, and O2 gas, so all he needs to do is release extra CO2 into the Hab atmosphere. As long as he releases it at a slower rate then the environmental regulators can pull it out and process it he should be fine.

So now he needs to figure out how to get a bunch of CO2.
That’s where the Mars Accent Vehicle (MAV) comes in. The MAV takes the crew from the surface of Mars back up to the Hermes at the end of the mission. The MAV is arguably the most critical component of a Mars mission. Because of this, the MAV for Ares 3 was landed on Mars by the previous mission. So the crew of Ares 2 landed the Ares 3 MAV on Mars four years ago. (Martinez landed the Ares 4 MAV right before the crew descended to Mars.)

Because the MAV sits around for 4 years, it manufactures it’s own fuel from the Mars atmosphere through a complex series of chemical reactions. The first step of which is to pull CO2 from the Martian atmosphere.

To save weight, when the MAV takes off, as it did with the rest of his crew on SOL 6, it leaves behind unneeded components such as the landing gear and fuel plant to save weight for the ascent. So Mark can remove the CO2 collector from the MAV fuel plant, hook it up to the HAB’s power and collect as much CO2 as he needs.

If the Hab has 92m^2 of floor space, and is at least 3 meters tall, what is the minimum internal volume of the Hab? We can get a reasonable assumption of the maximum internal volume of the Hab if we assume it is in the shape of a half sphere. What would that volume be?

If the atmospheric regulator keeps the Hab CO2 concentration at 370ppm. If CO2 becomes dangerous at 10,000ppm how much CO2 can Mark release into the Hab at once before the concentration of CO2 becomes dangerous to him based on our calculation of the minimum internal volume of the hab?

If the MAV plant can collect 10 Liters of liquid CO2 in 15 hours, how long will it take to collect enough CO2 to create enough O2 to react with his entire Hydrazine supply?

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