Since the heat being lost is dependent on the temperature, which is changing, we needed a differential equation before (well actually since it's all been worked out before we didn't, but where's the fun in that?). This time, oxygen use is constant, so the math is much simpler. On the other hand, there are still plenty of variables to introduce uncertainty.

To begin, if you are sealed in a room with a normal mix of air you will not run out of oxygen. Rather CO

_{2}will build up to toxic levels, and you will die. It is possible to scrub CO

_{2}from the air. In fact, we currently do it on our spaceships. A major issue Apollo 13 faced was getting circular CO

_{2}filters to work with a square hole.

What this means for us is we need to look at time for CO

_{2}to build up to lethal levels, and for how long it would take to run out of O

_{2}if the CO

_{2}is being removed.

We also need to consider that people consume O

_{2}at different rates, and even at different rates at different times. VO

_{2}is a measure of what rate a person is consuming O

_{2}. Unfortunately, it is almost always used in the context of measuring peak VO

_{2}during exercise (as a measure of fitness). It was hard to get good numbers for a resting person, but I settled on about 0.018 cubic meters per hour. For the active rate, I still couldn't just use typical VO

_{2}numbers because they are for the max consumption rate during bursts of exercise. A person moving around attempting to repair a ship wouldn't be using as much air as a person sprinting. I found some good numbers from scuba diving forums and settled on 0.1 cubic meters per hour.

On the subject of the variation of people, different people will be able to tolerate different concentrations of CO

_{2}or levels of O

_{2}. It was hard finding a good number for lethal CO

_{2}concentration. Most sites were concerned with long term exposure at a work environment (years), or short term accidental exposure (minutes). I settled on 5% which is probably a bit low.

As for minimum O

_{2}concentration, similar problems apply. Here I settled on 11%, compared to about 21% normally. Ships could use slightly higher O

_{2}concentrations to begin with to help with loss of life support situations, but high O

_{2}levels have their own problems.

Additional issues are things like fires or venting atmosphere reducing the time. Also, the number of people on a ship is harder to estimate. On larger ships it is probably more constant. But on small shuttles it could vary quite a bit.

Working in our favor is the fact that the respiration equation:

`"C"_6"H"_12"O"_6 + 6"O"_2 to 6"CO"_2 + 6"H"_2"O"`

Has a one to one mole ratio between O

_{2}and CO

_{2}. Additonaly, a mole of any gas takes up about 24 liters at normal temperature and pressure. This means we can use the same formula for both O

_{2}consumption and CO

_{2}build up:

`t={V cdot Delta r}/{n cdot R}` Where: V is volume, `Delta r` is the change in the ratio of the gas, n is the number of people, and R is the rate that gas is changed. As an example:

`t = 36.1 " hours" = {26 "m"^3 cdot 0.05}/{2 cdot 0.018 "m"^3/"hour"}`

This is the formula for a 26 cubic meter shuttle craft, with 2 people. The change in concentration is 0.05 because CO

_{2}is effectively 0 normally. 0.018 cubic meters/hour is the resting CO

_{2}production rate.

I decided to give a range with worst case and best case scenarios. The best case is resting, and not worrying about CO

_{2}(because it's being scrubbed). The worst case is CO

_{2}build up will working to fix the ship.

As you can see there were some cases where heat loss was faster than the best case scenario. I didn't expect it to even be close.

Name | Volume (`"m"^3`) | Crew | Heat (days) | Oxygen, Resting (days) | CO2, Doing Work (days) |

Death Star II | 2,144,000,000,000,000 | 2,500,000 | 437,837 | 218,370,370 | 17,866,667 |

Super Star Destroyer | 12,645,900,000 | 300,000 | 967 | 10,733 | 878 |

Borg Cube | 28,000,000,000 | 130,000 | 25,585 | 54,843 | 4,487 |

Enterprise-D | 5,820,983 | 1,200 | 456 | 1,235 | 101 |

Enterprise | 211,248 | 430 | 161.0 | 125.1 | 10.2 |

Runabout | 569 | 3 | 11.3 | 48.3 | 4.0 |

Type 6 Shuttlecraft | 26 | 2 | 12.8 | 3.3 | 0.3 |

TIE Fighter | 8 | 1 | 0.7 | 2.0 | 0.2 |

## No comments:

## Post a Comment