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MBW:Modelling Components of a Lunar Life Support System

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  • This project is an extension of "Crop Growth and Associated Life Support for a Lunar Farm" by Tyler Volk 2.. This paper outlines a relatively simple model for crops growing in a moon base and a sample diet for astronauts. My project adds a harvesting cycle based on different diets, and a model of gas exchange between plants and humans. Gas exchange is a function of crop growth. I also design a controller for the atmosphere so as to not kill the humans or the plants.


Background

  • For any permanently occupied habitat on the moon, life support needs will have to be provided by more self sufficient means than with normal spacecraft. Constant resupply of a moon base is cost prohibitive. Therefore, food, water, air, waste, and hazard protection (such as radiation) must be dealt with using in-situ resources or a life support system that needs little resupply. To read more about understanding the long term effects of lunar gravity on blood flow for astronatus, see MBW:Gravitational Effects On Blood Flow.


  • One way to provide food for long durations is through Hydroponics [1]. There are hundreds of plants that can be grown hydroponically on the moon, but for the purposes of this project, I will study the four used in the Volk Paper[2] and in the NASA Controlled Ecological Life Support Systems (CELSS) program[3]: wheat, soybean, potato, and lettuce. These four crops have been closely studied for space flight purposes. It is known how to achieve near maximum planting density and lighting schedules in a hydroponic setting.


  • Since the Volk paper was written, the CELSS program has vastly expanded the number of crops studied for space agriculture purposes. There are many other plants that may be more efficient in both nutrition and sustainability. One of these food crops could be Quinoa[4]. This may be one area where this model can be expanded.


  • Based on the nutrient proportions of these four plants a proper diet for the astronauts can be devised. The major food types considered are protein, carbohydrates, and lipids. As I will show later, it is impossible to have a perfectly balanced diet with only these four crops because there will always be an excess of protein in order to fulfill the lipid requirement - however, a good diet can be found even if a perfect one is not possible with only four food sources. Since space flight is characterized by extremely tight mass restrictions, it will be worth eliminating any excess in diet (in this case, too much protein) for an actual moon base.


Project Categorization

  • The mathematics used for this model is separated into two categories, the logistic model for plant growth, and the flux modelling for the different chemical compounds. The logistic model uses six parameters for each of the four plants studied (wheat, soybean, potato and lettuce). There are two main differential equations used, one to represent the change of inedible mass growth, and the other representing the edible mass growth.
  • The logistics model begins as a logistic equation, depicting crop growth, which refers to an increasing biomass. This biomass can then be separated into edible biomass and inedible biomass. Furthermore, it these equations modeling growth of edible and inedible biomasses are turned into ordinary differential equations through the finite difference scheme.
  • The flux models are an enhancement of the logistic models for each plant type. The authors essentially broke down the mass into a fractional distribution of the different molecular compounds, CO2, H2O, O2, HNO3, and dry biomass, and plotted their respective distributions. The purpose of this is for future research that could potentially use this data to compare with actual measurements of these particular compounds from the plants.
  • The biological system studied is that of both humans and plants. The major portion of this study focused on the growth and development of plants in a specific environment similar to that found on a potential lunar base. The specific plants used here are wheat, soybeans, potato and lettuce.

Crop Model

  • The model used for the growth of crops in this paper is a logistic model with a couple kinks. A more sophisticated model is now used by NASA[5]. This more sophisticated model is an energy cascade model, and it is defined by many more parameters than the logistic model (for example, it models the process of photosynthesis along with crop growth). When I talk about crop growth, I refer to an increasing biomass. This biomass can be separated into edible biomass and inedible biomass. A project with a simple logistic model is APPM4390:Complement Modeling.


  • The logistic model is defined by six parameters that vary for each plant type. There are two exponential growth rates, r_ined and r_ed (referring to inedible and edible growth separately). This describes the exponential growth rate along the exponential part of the logistic curve. There are two carrying capacities, K_ined and K_ed. The carrying capacity is the asymtote that the edible and inedible masses will approach as they reach full size at the end of their growth cycle.


  • For wheat, soybean, and potato, the inedible mass starts to grow first followed later by the edible mass. The switch on time for edible growth is the parameter t*. Once the edible mass starts growing, it does so with the minimum edible mass "E_min". The initial conditions on the "M_ined" and "M_ed", which are the inedible and edible biomasses, respectively are also defined (and nonzero). These six parameters and two initial conditions for each plant type are gathered from experimental data[2]. A more sophisticated model would model photosynthesis and derive these parameters from that model.


  • Lettuce is slightly different than wheat, soybean, and potato. With lettuce, edible growth does not follow inedible growth like it does for the other crops. Instead, the inedible and edible biomasses grow together and the growth rate increases drastically after about eleven days. Therefore, "t*" is now taken as the time of increased growth rate and "r_1" is the first growth rate while "r_2" is the second growth rate. Each growth rate applies to both the inedible and edible parts of lettuce. The parameters are defined in the following figure.


Parameters.png
Taken from Volk Paper[2]


  • The equations for the growth of edible and inedible biomasses are given below. These a set of ordinary differential equations. Note that the growth of edible biomass is dependent on both the edible biomass and inedible biomass. The top three equations are for wheat, soybean, and potato while the bottom three contain modifications for lettuce growth. These equations were evolved using a finite difference scheme.


Eqns1.png
Taken from Volk Paper[2]


Eqns2.png
Taken from Volk Paper[2]


  • Below are plots for the biomass growth of wheat, soybean, potato, and lettuce. Notice that the scales on the axes are different. This is not surprising: each crop has a different growth time and biomass yield. Also, notice that the relations of inedible and edible biomasses are different for each crop. At the end of each cycle, the biomasses are returned to zero as they are harvested. Harvesting is discussed more in a later section. Note that each mass is per square meter. The area of a necessary crop is determined in a later section.


Growth of Wheat


Growth of Soybean


Growth of Potato


Growth of Lettuce


Harvesting Schedule

  • As noted above, the biomass of each crop returns to zero at the end of each cycle in the above four plots. This is intended to model a harvesting cycle. The time of harvest of harvest is determined by a percent difference between the current biomass and the specified carrying capacity of the edible biomass.


  • There are several assumptions behind this method. I assume that the plant is fully developed when it is fully grown. This might not be the case, and furthermore, it is plant dependent. The plant might not have the correct food groups (protein, carbs, lipids) at an earlier stage. Despite this, it is in the astronauts best interest to harvest as soon as possible. The longer they wait to harvest, the more food they will need from each harvest - this drives up the area requirements for the crops.

Diet Determination

  • The crop growth curves shown in the previous section are calculated per square meter of space. But how many crops, and of which variety, are required to feed an astronaut indefinitely? I assume that food supplies will be provided until first harvest. After each plant is harvested, I model how many plants are needed to feed an astronaut indefinitely without further food supplies.


  • The first step in this process is to come up with a good diet for an astronaut. There are three food groups considered: protein, carbohydrates, and lipids. The body needs a certain amount of each group every day. The proportions of these groups that the astronauts eats is defined as his diet. Furthermore, each crop contains different proportions of each food group within its edible mass. This is shown in the following figure.


Nuts.png
Taken from Volk Paper[2]


  • As an aside, there are also psychological considerations as well as health considerations. Astronauts will need more than four types of foods to eat to stay happy. While this might not sound significant, over long time periods, a boring diet can have an impact on moral and work efficiency, especially when it is combined with being isolated in a confined space away from home.


Normal Diet

  • A normal diet for an astronaut would consist of 110 grams/day of protein, 375 grams/day of carbohydrates, and 95 grams/day of lipids. This is fundamentally and optimization problem. There are many variables that one could optimize, including the necessary space for crops, the mass of crops, the amount of power needed for lighting, the impact of oxygen-carbon dioxide exchange on the atmosphere, or the necessary resupplies to grow the crops. In real life, a cost function containing all of these variables will be minimized.


  • For my project, I minimized the area that the crops took. This turned out to be a non optimized system for the following reason. Immediately it can be seen that there is a problem with the four selected crops. Looking at the above figure, there is no way to achieve a proper amount of lipids without going over on protein. This excess should be eliminated for a more sophisticated diet model in the future by including more types of plants. This diet also provides a sufficient amount of total energy per day (2700 calories) for astronauts who are most likely performing manual labor for part of their day.


  • Under this diet, each astronaut needs 43.1 square meters of space for crops to feed himself indefinitely. This is broken up into 35 square meters for soybean, 8 square meters for wheat, 3.2 square meters for potato, and 0.2 square meters for lettuce.

Atkins Diet

  • Looking at the proportions of food groups in the above figure, one might be tempted to eliminate the carbohydrates with an Atkins diet[6]. This turns out to be a profoundly bad idea. The astronauts are getting energy (calories) from the carbohydrate portions of the four crops. If the carbohydrates are taken away, this energy must still be obtained by other means.


  • Assuming a strict Atkins diet of 20 grams of carbohydrates each day, in order to still get 2700 calories each day, the necessary area of the crops rises to over 80 square meters. Furthermore, this only includes lettuce and soybean plants since the carbohydrate proportion of potato and wheat is considerably higher. It is difficult to get enough protein and lipids to make 2700 calories without going over on carbohydrates with only these four plants as well. This is similar to the protein problem in the normal diet, except more severe.


  • On top of all the engineering considerations (a higher area of crops will raise the cost function for the life support system), there is also health considerations. The human body already has many problems staying in microgravity for long periods of time (although this would be mitigated on the moon). The effect of microgravity on the body is understood but the mechanisms are not explained. Adding another health consideration with the Atkins diet would not be wise without a significant amount of further study.

Gas Exchange

  • Gas exchange between humans and plants is a new consideration in life support on the moon. In normal spacecraft, carbon dioxide is scrubbed out of the atmosphere and oxygen and nitrogen are added back in to maintain pressure. Humans produce CO2 and consume O2, while plants produce O2 and consume CO2.


  • The humans' gas exchange is constant (for active humans, 2241 grams/day CO2 produced and 1852 grams/day O2 consumed)[7] but the plants' CO2 consumption and O2 production is a function of their biomasses. The edible and inedible portions of their biomasses produce at different rates as well.


  • Adding this into the crop growth model, the following figure is made. Note that it appears symmetric but isn't exactly symmetric (across the horizontal axis). At the start, humans dominate the gas exchange since no crops are grown yet. Quickly the crops take over and produce more O2 and consume more CO2. The discontinuous jumps represent the harvesting cycles. Remember that each harvesting period is different for each crop. This figure also assumes the normal diet presented in a previous section. The largest discontinuities are the soybean harvest, since soybean makes up such a large portion of the normal diet. It would be advantageous to smooth this curve out, by staggering harvests for example. This will reduce the load and requirements on the atmospheric controller, discussed in the next section.


Exchange of carbon dioxide and oxygen between plants and humans

Atmosphere Control

  • It can be seen from the above plot that CO2 must be replenished and O2 removed (or stored for another use, like extra vehicular activity). This is backwards of other spacecraft where CO2 must be removed. A chain of PID controllers was used to control the atmosphere. The partial pressure is what is important. The plants require a certain CO2 partial pressure to grow their best, while humans can't have too much CO2 or they will die. O2 partial pressure is also important since humans will suffer from hypoxia or hyperoxia and die if the partial pressure of oxygen goes too low or too high, respectively[8]. The atmosphere was assumed to be 70.3 kPa (about 70% of atmospheric pressure). CO2 partial pressure needs to be around 0.12 kPa, and oxygen partial pressure between 18 kPa and 23.1 kPa. This plot shows the controllers adjusting the grams of each component in the atmosphere and thus the partial pressure with certain volume assumptions. This has engineering applications, such as the necessary resupply rate of the gasses.


Partial Pressures of Atmospheric Gasses

Conclusions

  • In this project I have presented a model for hydroponically growing crops on the moon for the purposes of self sufficient life support. A crop model was developed from a previous paper. The purpose of the crop model was to tie it into other life support systems, and this project has combined the atmospheric life support system with the food life support system. Gas exchange between plants and humans was modeled based on the necessary amount of plants to feed an astronaut with a good diet indefinitely on the moon.


  • Each astronaut will double the food required but will also contribute to the atmosphere himself. Therefore, the gas exchange plot will take the same shape no matter how many astronauts there are, but the values will be multiplied by the number of crew members. The atmospheric control model will have to correct the partial pressures more rapidly for additional crew, since the atmosphere partial pressures will be more volatile with the increased number of plants and humans. The model, and my extensions, have important engineering applications to the ultimate design of a moon base.


Further Reading

  • An excellent, engineering oriented overview of spacecraft life support is the NASA Advanced Life Support Baseline Values and Assumptions Document [5]. Many assumptions about life support system properties were taken from this document.
  • For further reading, the paper "Approach to Crop Modeling with the Energy Cascade," by Tyler Volk, Bruce Bugbee, and Raymond Wheeler, cites the paper used in this project. It allows for a more sophisticated mathematical model through the use of an energy cascade model, which is now being used by NASA. In the paper, they model crop growth to analyze data to predict gas exchange and evaluates areas for improvement in design and engineering, using data from a wheat crop. The crop was examined for time dependance of the major three components in the energy cascade: photosynthetic photon absorption, canopy quantum yield, and carbon use efficiency. In the end, this paper cited the work of Volk and later created models to be generally expanded to predict and analyze crops for which data on gas exchange is available (i.e. lettuce, white potatoes, and soybeans).
  • In addition, a secondary paper that references this paper is "An Optimal Control Strategy for Crop Growth in Advanced Life Support Systems" Fleisher, D, and Baruh H. Life Support & Biosphere Science, Vol. 8 pp. 43-53. This paper used the crop growth model derived from the Volk paper and considered it with another crop growth model developed by the NASA Ames Reseach Center. By using these two growth models, they derived an elementary method for controlling crop growth in an Advanced Life Support System. The control strategies they devised use feedback control to compensate for the effects of environmental disturbances in the crop growth chambers to maintain desired crop growth rates. Their work considered small-order matehmatical error inputs to the system and evaluation of their control system errors. They show that the proposed approach is a potentially viable way of controlling crop growth.

External Links

  • Check out the guidelines for an average American's diet, according to the US Department of Agriculture, and compare it to the hypothesized diet of an Astronaut!

References

  1. Wikipedia - Hydroponics
  2. 2.0 2.1 2.2 2.3 2.4 2.5 Volk, T. & Cullingford, H. "Crop Growth and Associated Life Support for a Lunar Farm" The Second Conference on Lunar Bases and Space Activities of the 21st Century, 1992., p.525
  3. NASA Controlled Ecological Life Support Systems (CELSS) program
  4. Quinoa: An Emerging "New" Crop with Potential for CELSS
  5. 5.0 5.1 Hanford, Anthony and NASA. "Advanced Life Support Baseline Values and Assumptions Document" 2004
  6. Wikipeda - Atkins Diet
  7. Wikipedia - Human Gas Exchange
  8. Wikipedia - Oxygen Toxicity in Humans