Capstone project: growing a Mars settlement from 30 to 100 people

Changing scale without simply multiplying by three: energy, water, habitat, food, health, maintenance, logistics and governance of a 100-resident settlement.
The problem to solve
Starting question. How can a settlement grow from thirty to one hundred residents without mechanically multiplying the equipment or creating new critical dependencies?
Intuition. For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
Concrete reference point. The initial architecture is treated as an existing system with its limits and its maintenance debt.
MASTERY MAP · MODULE 58
Four reference points to master — Capstone project: growing a Mars settlement from 30 to 100 people
Reference solution file: growth from 30 to 100 people over 1,000 sols
- Definition
- For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
- Intuition or concrete case
- The initial architecture is treated as an existing system with its limits and its maintenance debt.
- Quantitative reference point
- Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30.
- Limit or point of vigilance
- The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
Guided exercise — Reference solution file: growth from 30 to 100 people over 1,000 sols
Examine “Reference solution file: growth from 30 to 100 people over 1,000 sols” using the following reference point: Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30. Explain what you check, how you interpret the result and what decision follows. Then test the robustness of that decision against the following limit: The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
Reasoned answer — Reference solution file: growth from 30 to 100 people over 1,000 sols
- Starting point
- For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
- Clue from the case
- Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30.
- Caveat to apply
- The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
- Conclusion
- Finally, the hundred-person settlement must learn to correct itself.
Starting point at 30 residents
- Definition
- For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
- Intuition or concrete case
- The initial architecture is treated as an existing system with its limits and its maintenance debt.
- Quantitative reference point
- Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30.
- Limit or point of vigilance
- The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
Guided exercise — Starting point at 30 residents
In the case “Starting point at 30 residents,” use this reference point: Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30. Present the check to carry out, the margin to monitor and the resulting decision. Accept the conclusion only after taking this constraint into account: The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
Reasoned answer — Starting point at 30 residents
- Starting point
- For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
- Clue from the case
- Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30.
- Caveat to apply
- The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
- Conclusion
- Finally, the hundred-person settlement must learn to correct itself.
Population trajectory
- Definition
- For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
- Intuition or concrete case
- The initial architecture is treated as an existing system with its limits and its maintenance debt.
- Quantitative reference point
- Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30.
- Limit or point of vigilance
- The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
Guided exercise — Population trajectory
To master “Population trajectory,” connect the reasoning to this reference point: Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30. Say what it really proves, what it does not prove and the decision you would make. The answer must take this limit into account: The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
Reasoned answer — Population trajectory
- Starting point
- For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
- Clue from the case
- Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30.
- Caveat to apply
- The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
- Conclusion
- Finally, the hundred-person settlement must learn to correct itself.
Energy at the 100 scale
- Definition
- For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
- Intuition or concrete case
- The initial architecture is treated as an existing system with its limits and its maintenance debt.
- Quantitative reference point
- Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30.
- Limit or point of vigilance
- The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
Guided exercise — Energy at the 100 scale
Treat “Energy at the 100 scale” as a decision to be justified. The control reference point is: Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30. Explain how it is used, then conclude by stating the margin or threshold that would make you change your mind. Also check this limit: The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
Reasoned answer — Energy at the 100 scale
- Starting point
- For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
- Clue from the case
- Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30.
- Caveat to apply
- The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
- Conclusion
- Finally, the hundred-person settlement must learn to correct itself.
Mastery objectives
- Build a chain cause → observation → measurement for “Changing scale is not multiplying by 3.33.”
- Redo by hand the verification most useful for “Growth by stages.”
- Describe the failure, the uncertainty or the limit that threatens “Habitat and compartmentation.”
- Explain how “Water and atmosphere” changes the architecture or the operations.
1. Changing scale is not multiplying by 3.33
Some consumption grows almost in step with the number of residents, such as part of the water or the calories. Other functions benefit from pooling: laboratory, medical unit, a central control or workshop facility, heavy equipment. Conversely, new needs appear: several work shifts, separate quarters, greater emergency capacity, distributed storage and more formal governance. The project must identify these changes of regime.
2. Growth by stages
Going straight from 30 to 100 people makes errors hard to correct. The scenario chooses stages, for example 30 → 60 → 100, with authorization criteria before each arrival: power available, water reserve, ECLSS capacity, refuge beds, food production, medical stocks, vehicles and number of qualified technicians. People leave Earth only once the previous stage has been demonstrated.
3. Habitat and compartmentation
A population of 100 residents must not depend on a single large pressurized volume. The plan distributes sleeping quarters, work, refuge, care, agriculture and storage among isolatable zones. The connections allow daily circulation but can be closed in the event of fire, contamination or loss of pressure. The number of refuge places must be consistent with scenarios in which an entire quarter is unavailable.
4. Water and atmosphere
Flow rates increase, but above all the consequences of contamination. The loops are divided into trains or zones, with options for sampling, purging and controlled cross-feeding. Large tanks are useful as buffers, but distributing part of the stock keeps a single incident from making the whole reserve unavailable.
5. Power and microgrids
At 100 residents, a single network can become a path for failure propagation. The project provides several buses or microgrids able to support one another without being fully coupled. Vital loads have local autonomy. Large industrial loads take part in load shedding and are scheduled according to production, storage and maintenance.
6. Food and agriculture
Local production can cover a growing share of calories, but increasing the cultivated area adds light, water, nutrients, labor and heat. Imported stocks remain insurance against plant disease or loss of power. The project measures coverage in calories and nutrients, not just the mass harvested.
7. Health and population
A larger population increases the frequency of rare events. Medical skills, pharmacy, diagnostics and care spaces must therefore be expanded. Some capabilities can be pooled; others must be redundant, in particular the medical unit’s power supply, oxygen, sterilization and communications. Public health and epidemic management also become more important.
8. Maintenance and specialization
With 100 residents, there are more specialists, but there is also more equipment. The organization must guarantee succession: no vital function depends on a single person. The maintenance teams manage configuration, inspections, parts and scheduled work while keeping an emergency response capability.
Deepening: logistics for a growing population
The manifest no longer carries only consumables: it must prepare the next phase. Cargo ships bring machines, structures, parts and materials that make it possible to increase local production before the new group arrives. A poorly sequenced growth stage can create several months in which the population has grown but the infrastructure has not.
Deepening: governance and common services
At 100 people, everyday decisions cannot all go up to a single commander. Responsibilities are organized by function and by quarter, with common safety and emergency rules. Governance must handle schedules, maintenance, resource allocation and disagreements without turning every technical trade-off into a political crisis.
9. Worked example: growth water reserve
At 3.5 L of direct drinking/food water needed per person per day, 100 residents represent 350 L/day. A 21-day stock requires 350 × 21 = 7,350 L. If the project wants to be able to isolate a tank without losing more than half the stock, two tanks of 3,675 L are not enough to keep 21 days after losing one of them; either more total volume or another available source is needed. Sizing redundancy is therefore not just a matter of nominal volume.
Calculated case study: going from 30 to 100 residents without simply multiplying by three
TEACHING ASSUMPTION — An infrastructure has 60 kW of fixed loads, independent of the number of residents, and 4 kW of variable load per person. 30% of contingency margin is added at the 100-person stage.
Let P_f be the fixed load, in kW; p the variable load, in kW/person; N the population; P(N) the power before margin; r the margin, with no unit.
At 30 people: P(30) = P_f + p × 30 = 60 + 4 × 30 = 180 kW. At 100 people: P(100) = 60 + 4 × 100 = 460 kW. With a 30% margin: P_plan = 460 × 1.30 = 598 kW.
Growth is not a simple factor of 100 ÷ 30, because part of the infrastructure is fixed and another part varies with the population. This distinction requires identifying what can be pooled before sizing the extension.
10. Integrated exercise
A 60-person base has an average of 900 kW and wants to take in 40 more people. Each new resident adds on average 4 kW of direct and indirect load at the stage considered. Calculate the new load and the margin if available production remains limited to 1.15 MW. Then identify why this calculation alone is not enough to authorize the arrival.
11. Reasoned solution
Forty new residents add 40 × 4 = 160 kW. The load rises to 1,060 kW, leaving a 90 kW margin out of 1,150 kW, or about 7.8% of capacity. This margin may be insufficient in the face of maintenance, dust, aging or peaks. Storage, water, ECLSS, refuge beds, food, health, mobility and skills must also be checked before deciding.
12. Final deliverable
Produce the 30 → 60 → 100 growth plan with zone architecture, capacities at each stage, go/no-go criteria, mass/energy/water/food budgets, medical strategy, maintenance organization, governance and ten residual dependencies on Earth. The file must also show what happens if a growth cargo ship is lost.
Deepening module 58: understand, calculate, verify and decide
Module goal — grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
1. Population trajectory and capacity
In this module, population trajectory and capacity serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- For “1. Population trajectory and capacity,” what is Growth when (N_end - N_start) is divided by duration?
- Reading aloud
- Full pronunciation: “Growth equals (N sub end minus N sub start) divided by duration.”
- Symbols, pronunciation and meaning
- Growth (“Growth”): average population growth; N_end (“N end”): final number; N_start (“N start”): initial number; duration (“duration”): time interval over which the calculation is made
- Units
- average population growth → people per unit of time; N end → count; N start → count; duration → duration expressed in the scenario’s unit.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- (N_end - N_start) plays the role of the numerator; duration serves as the reference in the denominator. The division (N_end - N_start) ÷ duration produces Growth, whereas duration ÷ (N_end - N_start) would answer a different question.
- Substitution and calculation
- Take only the values available for (N_end - N_start) and duration, harmonize their units or period, then form the quotient that gives Growth.
- Calculator entry
- Enter the parentheses for (N_end - N_start), the ÷ key, then the parentheses for duration. Check the displayed order before confirming Growth.
- Mental estimate
- Estimate how many times duration “fits” into (N_end - N_start); this estimate immediately gives the expected scale of Growth before the precise calculation.
- Independent check
- Independent check — Back-calculation: (Growth) × (duration) must reconstitute (N_end - N_start). This product tests the quotient by the inverse operation.
- Physical or operational interpretation
- The interpretation of “Growth = (N_end - N_start) / duration” belongs to the context “1. Population trajectory and capacity.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- Plain reading: Growth measures the amount of (N_end - N_start) per unit of duration for “1. Population trajectory and capacity.”
- Variation / sensitivity
- If only (N_end - N_start) varies, Growth varies in the same proportion. If only duration increases by 10%, Growth becomes about 0.909 times its initial value.
- Limit / assumption
- Validity condition: no division by zero for duration; the boundaries of (N_end - N_start) and duration must also be comparable in “1. Population trajectory and capacity.”
Now we inject the following event: population growth outpaces housing.
2. Power and microgrids at the 100 scale
In this module, power and microgrids at the 100 scale serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- For “2. Power and microgrids at the 100 scale,” what is Capacity_req when Demand × (1 + margin) is divided by A?
- Reading aloud
- Full pronunciation: “Capacity sub req equals Demand times (1 plus margin) divided by A.”
- Symbols, pronunciation and meaning
- Capacity_req (“required capacity”): installed capacity needed; Demand (“demand”): nominal need to be met; margin (“margin”): dimensionless sizing margin; A (“a”): availability of the system, a dimensionless fraction between 0 and 1.
- Units
- The same unit of capacity or power, depending on the subsystem, must be used for Capacity_req and Demand; margin and A are dimensionless. Dividing by A therefore does not change the unit.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- The demand is first increased by the factor 1 + margin, then divided by availability: a larger installed capacity is needed when the system is not available 100% of the time.
- Substitution and calculation
- Take only the values available for Demand × (1 + margin) and A, harmonize their units or period, then form the quotient that gives Capacity_req.
- Calculator entry
- Enter the parentheses for Demand × (1 + margin), the ÷ key, then the parentheses for A. Check the displayed order before confirming Capacity_req.
- Mental estimate
- Estimate how many times A “fits” into Demand × (1 + margin); this estimate immediately gives the expected scale of Capacity_req before the precise calculation.
- Independent check
- Inverse check: Capacity_req × A / (1 + margin) must give back Demand. For A = 1 and margin = 0, Capacity_req must equal Demand.
- Physical or operational interpretation
- The interpretation of “Capacity_req = Demand × (1 + margin) / A” belongs to the context “2. Power and microgrids at the 100 scale.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- Said without notation: the demand is first increased by the factor 1 + margin, then divided by availability; a larger installed capacity is needed when the system is not available 100% of the time.
- Variation / sensitivity
- With demand and margin fixed, a relative +10% in A divides Capacity_req by 1.10; with A fixed, +10% in Demand increases Capacity_req by 10%.
- Limit / assumption
- A here is an availability, not an area. A must be strictly positive and defined over the same period as the demand and the capacity.
Now we inject the following event: heat-rejection capacity becomes the limiting factor.
3. Water, sanitation and storage
In this module, water, sanitation and storage serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- What value of Water_stock results from the product given by “Water_stock = Q_day × autonomy”?
- Reading aloud
- Full pronunciation: “Water sub stock equals Q sub day times autonomy.”
- Symbols, pronunciation and meaning
- Water_stock (“water stock”): quantity of water to store; Q_day (“Q day”): the settlement’s net water consumption or need per day; autonomy (“autonomy”): number of days or sols the stock must cover.
- Units
- Q_day in L/day or kg/day; autonomy in days on the same basis; Water_stock in L or kg. If autonomy is expressed in sols, convert Q_day to a per-sol basis or convert the duration.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- A daily flow multiplied by the number of days to be covered gives the total quantity to store.
- Substitution and calculation
- Prepare the values corresponding to Q_day × autonomy separately, with their conversions visible, then form their product to obtain Water_stock.
- Calculator entry
- Enter each prepared factor of Q_day × autonomy separately if necessary, then use “×” between their values; round Water_stock at the last step.
- Mental estimate
- Before the exact value, round each factor of Q_day × autonomy to one significant figure and form the product. This approximation places Water_stock in the right order of magnitude.
- Independent check
- Inverse check: Water_stock / autonomy must give back Q_day. Dimensional check: L/day × day = L.
- Physical or operational interpretation
- The interpretation of “Water_stock = Q_day × autonomy” belongs to the context “3. Water, sanitation and storage.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- Plain reading: to obtain Water_stock, the quantities in Q_day × autonomy are taken together as a product, in line with the model of “3. Water, sanitation and storage.”
- Variation / sensitivity
- The sensitivity is multiplicative: doubling a single factor of Q_day × autonomy doubles Water_stock if the others do not change; changing two factors compounds their variations.
- Limit / assumption
- Validity: the model “Water_stock = Q_day × autonomy” must remain applicable over the domain studied. If two factors of Q_day × autonomy are not independent in the assumed sense, their simple product may be insufficient.
— “Water, sanitation and storage.”
Now we inject the following event: a critical imported flow is delayed.
4. Food and stock security
In this module, food and stock security serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- What value of Food_stock results from the product given by “Food_stock = N × q_food × t × (1 + margin)”?
- Reading aloud
- Full pronunciation: “Food sub stock equals N times q sub food times t times (1 plus margin).”
- Symbols, pronunciation and meaning
- Food_stock: total mass of food to plan for; N: number of people; q_food: food consumption per person per unit of time; t: duration covered; margin: additional safety fraction.
- Units
- N in people; q_food for example in kg/(person·day); t in days in this case; margin dimensionless; Food_stock in kg.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- N × q_food × t turns an individual daily consumption into a total mass for the whole population and the whole duration; 1 + margin adds a proportional reserve.
- Substitution and calculation
- Prepare the values corresponding to N × q_food × t × (1 + margin) separately, with their conversions visible, then form their product to obtain Food_stock.
- Calculator entry
- Enter each prepared factor of N × q_food × t × (1 + margin) separately if necessary, then use “×” between their values; round Food_stock at the last step.
- Mental estimate
- Before the exact value, round each factor of N × q_food × t × (1 + margin) to one significant figure and form the product. This approximation places Food_stock in the right order of magnitude.
- Independent check
- Dimensional check: people × kg/(person·day) × day × dimensionless = kg.
- Physical or operational interpretation
- The interpretation of “Food_stock = N × q_food × t × (1 + margin)” belongs to the context “4. Food and stock security.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- Plain reading: to obtain Food_stock, the quantities in N × q_food × t × (1 + margin) are taken together as a product, in line with the model of “4. Food and stock security.”
- Variation / sensitivity
- The sensitivity is multiplicative: doubling a single factor of N × q_food × t × (1 + margin) doubles Food_stock if the others do not change; changing two factors compounds their variations.
- Limit / assumption
- Validity: the model “Food_stock = N × q_food × t × (1 + margin)” must remain applicable over the domain studied. If two factors of N × q_food × t × (1 + margin) are not independent in the assumed sense, their simple product may be insufficient.
Now we inject the following event: the local workshop cannot qualify a vital part.
5. Habitat, zoning and refuges
In this module, habitat, zoning and refuges serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- What value of V_refuge results from the product given by “V_refuge = N × v_refuge_pp”?
- Reading aloud
- Full pronunciation: “V sub refuge equals N times v sub refuge sub pp.”
- Symbols, pronunciation and meaning
- V_refuge (“vee refuge”): total volume needed for the refuge; N (“en”): number of people; v_refuge_pp (“vee refuge per person”): volume planned per person in the refuge.
- Units
- V_refuge in m³; N as a count; v_refuge_pp in m³/person.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- To obtain V_refuge, the relationship combines N × v_refuge_pp multiplicatively. Each factor brings its unit or coefficient; the final product must be dimensionally compatible with the left-hand side.
- Substitution and calculation
- Prepare the values corresponding to N × v_refuge_pp separately, with their conversions visible, then form their product to obtain V_refuge.
- Calculator entry
- Enter each prepared factor of N × v_refuge_pp separately if necessary, then use “×” between their values; round V_refuge at the last step.
- Mental estimate
- Before the exact value, round each factor of N × v_refuge_pp to one significant figure and form the product. This approximation places V_refuge in the right order of magnitude.
- Independent check
- Independent check — Cross-check: remove one factor from the product N × v_refuge_pp; V_refuge divided by this factor must reconstitute the combination of all the others.
- Physical or operational interpretation
- The interpretation of “V_refuge = N × v_refuge_pp” belongs to the context “5. Habitat, zoning and refuges.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- Plain reading: to obtain V_refuge, the quantities in N × v_refuge_pp are taken together as a product, in line with the model of “5. Habitat, zoning and refuges.”
- Variation / sensitivity
- The sensitivity is multiplicative: doubling a single factor of N × v_refuge_pp doubles V_refuge if the others do not change; changing two factors compounds their variations.
- Limit / assumption
- Validity: the model “V_refuge = N × v_refuge_pp” must remain applicable over the domain studied. If two factors of N × v_refuge_pp are not independent in the assumed sense, their simple product may be insufficient.
Now we inject the following event: the health system is overwhelmed by an incident.
6. Industry and local maintenance
In this module, industry and local maintenance serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- For “6. Industry and local maintenance,” what is f_local when Local_mass is divided by Total_mass?
- Reading aloud
- Full pronunciation: “f sub local equals Mass sub local divided by Mass sub total.”
- Symbols, pronunciation and meaning
- f_local: fraction of the total mass supplied locally; Local_mass: mass produced or extracted locally within the boundary; Total_mass: corresponding total mass, local plus imported according to the definition of the balance.
- Units
- Both masses in the same unit; f_local dimensionless, between 0 and 1.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- The quotient measures the share of mass covered locally.
- Substitution and calculation
- Take only the values available for Local_mass and Total_mass, harmonize their units or period, then form the quotient that gives f_local.
- Calculator entry
- Enter the parentheses for Local_mass, the ÷ key, then the parentheses for Total_mass. Check the displayed order before confirming f_local.
- Mental estimate
- Estimate how many times Total_mass “fits” into Local_mass; this estimate immediately gives the expected scale of f_local before the precise calculation.
- Independent check
- f_local × Total_mass must give back Local_mass.
- Physical or operational interpretation
- The interpretation of “f_local = Local_mass / Total_mass” belongs to the context “6. Industry and local maintenance.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- Plain reading: f_local measures the amount of Local_mass per unit of Total_mass for “6. Industry and local maintenance.”
- Variation / sensitivity
- If only Local_mass varies, f_local varies in the same proportion. If only Total_mass increases by 10%, f_local becomes about 0.909 times its initial value.
- Limit / assumption
- Validity condition: no division by zero for Total_mass; the boundaries of Local_mass and Total_mass must also be comparable in “6. Industry and local maintenance.”
Now we inject the following event: an electrical extension reduces the reserve margin.
7. Mobility and surface logistics
In this module, mobility and surface logistics serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- What value of Fleet_capacity results from the product given by “Fleet_capacity = N_vehicles × unit_capacity × A”?
- Reading aloud
- Full pronunciation: “Capacity sub fleet equals N sub vehicles times capacity sub unit times A.”
- Symbols, pronunciation and meaning
- Fleet_capacity (“fleet capacity”): total usable capacity actually available; N_vehicles (“N vehicles”): number of vehicles in the fleet; unit_capacity (“unit capacity”): usable capacity of one vehicle; A (“a”): average availability of the fleet, a dimensionless fraction.
- Units
- N_vehicles is a dimensionless count; unit_capacity and Fleet_capacity have the same unit of capacity; A is dimensionless. The product keeps the unit of capacity.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- N_vehicles × unit_capacity gives the total nominal capacity; multiplying by the availability A estimates the share that is actually accessible.
- Substitution and calculation
- Prepare the values corresponding to N_vehicles × unit_capacity × A separately, with their conversions visible, then form their product to obtain Fleet_capacity.
- Calculator entry
- Enter each prepared factor of N_vehicles × unit_capacity × A separately if necessary, then use “×” between their values; round Fleet_capacity at the last step.
- Mental estimate
- Before the exact value, round each factor of N_vehicles × unit_capacity × A to one significant figure and form the product. This approximation places Fleet_capacity in the right order of magnitude.
- Independent check
- Inverse check: Fleet_capacity / (N_vehicles × unit_capacity) must give back A. With A = 1, the usable capacity must equal the nominal capacity of the fleet.
- Physical or operational interpretation
- The interpretation of “Fleet_capacity = N_vehicles × unit_capacity × A” belongs to the context “7. Mobility and surface logistics.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- In this calculation, N_vehicles × unit_capacity gives the total nominal capacity; multiplying by the availability A estimates the share that is actually accessible.
- Variation / sensitivity
- With unit capacity and availability fixed, adding 10% more vehicles adds 10% capacity. With the fleet fixed, usable capacity varies linearly with A.
- Limit / assumption
- A is an availability, not an area. An average availability does not necessarily represent correlated failures or simultaneous unavailability.
Now we inject the following event: population growth outpaces housing. In module 58, this point must be reread from the section “7 — Mobility and surface logistics”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
8. Health and organization of care
In this module, health and organization of care serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- For “8. Health and organization of care,” what is Care_load when Care_hours is divided by Caregiver_hours?
- Reading aloud
- Full pronunciation: “Load sub care equals Hours sub care divided by Hours sub caregivers.”
- Symbols, pronunciation and meaning
- Care_load (“care load”): fraction of caregiver hours taken up by care; Care_hours (“care hours”): total care time to be provided over the period; Caregiver_hours (“caregiver hours”): caregiver working time available over the period
- Units
- Care load → dimensionless, often expressed as a fraction or %; Care hours → h; Caregiver hours → h.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- Care_hours plays the role of the numerator; Caregiver_hours serves as the reference in the denominator. The division Care_hours ÷ Caregiver_hours produces Care_load, whereas Caregiver_hours ÷ Care_hours would answer a different question.
- Substitution and calculation
- Take only the values available for Care_hours and Caregiver_hours, harmonize their units or period, then form the quotient that gives Care_load.
- Calculator entry
- Enter the parentheses for Care_hours, the ÷ key, then the parentheses for Caregiver_hours. Check the displayed order before confirming Care_load.
- Mental estimate
- Estimate how many times Caregiver_hours “fits” into Care_hours; this estimate immediately gives the expected scale of Care_load before the precise calculation.
- Independent check
- Independent check — Back-calculation: (Care_load) × (Caregiver_hours) must reconstitute Care_hours. This product tests the quotient by the inverse operation.
- Physical or operational interpretation
- The interpretation of “Care_load = Care_hours / Caregiver_hours” belongs to the context “8. Health and organization of care.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- Plain reading: Care_load measures the amount of Care_hours per unit of Caregiver_hours for “8. Health and organization of care.”
- Variation / sensitivity
- If only Care_hours varies, Care_load varies in the same proportion. If only Caregiver_hours increases by 10%, Care_load becomes about 0.909 times its initial value.
- Limit / assumption
- Validity condition: no division by zero for Caregiver_hours; the boundaries of Care_hours and Caregiver_hours must also be comparable in “8. Health and organization of care.”
— “Health and organization of care.”
Now we inject the following event: heat-rejection capacity becomes the limiting factor. In module 58, this point must be reread from the section “8 — Health and organization of care”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
9. Governance and specialization of roles
In this module, governance and specialization of roles serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- For “9. Governance and specialization of roles,” what is Role_load when Task_hours is divided by Available_hours?
- Reading aloud
- Full pronunciation: “Load sub roles equals Hours sub tasks divided by Hours sub available.”
- Symbols, pronunciation and meaning
- Role_load (“role load”): fraction of available time taken up by the assigned tasks; Task_hours (“task hours”): cumulative time required by the tasks considered; Available_hours (“available hours”): total time available to carry out the tasks
- Units
- Role load → dimensionless, often expressed as a fraction or %; Task hours → h; Available hours → h.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- Task_hours plays the role of the numerator; Available_hours serves as the reference in the denominator. The division Task_hours ÷ Available_hours produces Role_load, whereas Available_hours ÷ Task_hours would answer a different question.
- Substitution and calculation
- Take only the values available for Task_hours and Available_hours, harmonize their units or period, then form the quotient that gives Role_load.
- Calculator entry
- Enter the parentheses for Task_hours, the ÷ key, then the parentheses for Available_hours. Check the displayed order before confirming Role_load.
- Mental estimate
- Estimate how many times Available_hours “fits” into Task_hours; this estimate immediately gives the expected scale of Role_load before the precise calculation.
- Independent check
- Independent check — Back-calculation: (Role_load) × (Available_hours) must reconstitute Task_hours. This product tests the quotient by the inverse operation.
- Physical or operational interpretation
- The interpretation of “Role_load = Task_hours / Available_hours” belongs to the context “9. Governance and specialization of roles.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- Plain reading: Role_load measures the amount of Task_hours per unit of Available_hours for “9. Governance and specialization of roles.”
- Variation / sensitivity
- If only Task_hours varies, Role_load varies in the same proportion. If only Available_hours increases by 10%, Role_load becomes about 0.909 times its initial value.
- Limit / assumption
- Validity condition: no division by zero for Available_hours; the boundaries of Task_hours and Available_hours must also be comparable in “9. Governance and specialization of roles.”
Now we inject the following event: a critical imported flow is delayed. In module 58, this point must be reread from the section “9 — Governance and specialization of roles”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
10. Science, production and priorities
In this module, science, production and priorities serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- In “10. Science, production and priorities,” how are the indexed contributions of “Priority_score = Σ(w_i × s_i)” added up to rebuild Priority_score?
- Reading aloud
- Full pronunciation: “priority score equals the sum, over all criteria i, of the weight w sub i times the score s sub i.”
- Symbols, pronunciation and meaning
- Σ (“sigma”): add up; Priority_score ranks a growth or safety action. w_i (“w sub i”) expresses the importance of a dependency; s_i (“s sub i”) describes the action’s standing on this criterion. The criteria can cover criticality, autonomy gained, lead time and local capability.
- Units
- The score, weights and ratings are dimensionless. The settlement’s physical balances — power, mass, days of stock or production rate — must be converted through documented thresholds before being turned into ratings.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration.
- Why this operation
- The symbol Σ means that the rule is applied to each index and the contributions are then added up. The total rebuilt in this way is Priority_score.
- Substitution and calculation
- List the indexed terms provided by the case, calculate each with its own index, then add these values; no missing term is invented.
- Calculator entry
- Calculator: keep a list of the contributions, add them up once in index order and a second time in reverse order.
- Mental estimate
- Estimate the largest term and the number of contributions; for positive values, Priority_score must at least equal the individual maximum without grossly exceeding their number multiplied by that maximum.
- Independent check
- Removal check: remove one contribution from Priority_score; the difference must be exactly the sum of the other calculated terms.
- Physical or operational interpretation
- The interpretation of “Priority_score = Σ(w_i × s_i)” belongs to the context “10. Science, production and priorities.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- In words, Priority_score gathers all the contributions to which the index of Σ requires the same rule to be applied.
- Variation / sensitivity
- Varying a single contribution by Δ changes Priority_score by the same Δ, possibly multiplied by its coefficient.
- Limit / assumption
- Check that the set of indices is complete, free of duplicates and defined on the same boundary before any summation.
Now we inject the following event: the local workshop cannot qualify a vital part. In module 58, this point must be reread from the section “10 — Science, production and priorities”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
11. Dependence on Earth and progressive autonomy
In this module, dependence on Earth and progressive autonomy serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- For “11. Dependence on Earth and progressive autonomy,” what is Dependence when Imported_mass is divided by Total_mass_consumed?
- Reading aloud
- Full pronunciation: “Dependence equals Mass sub imported divided by Mass sub total sub consumed.”
- Symbols, pronunciation and meaning
- Dependence (“dependence”): fraction of the total mass consumed that must be imported; Imported_mass (“imported mass”): mass coming from outside the settlement over the period; Total_mass_consumed (“total mass consumed”): total mass consumed over the same period and within the same boundary.
- Units
- Imported_mass and Total_mass_consumed must use a common mass scale, for example kg; Dependence is dimensionless, often expressed as a percentage.
- Origin and status of values
- Each number used keeps an explicit status — measurement, constant, mission value or exercise assumption — so as not to confuse reality and demonstration. The course links these inputs to: the needs, capacities, margins and balances of the 100-person scenario.
- Why this operation
- Dividing the imported mass by the total mass consumed gives the share of consumption that depends on imports.
- Substitution and calculation
- Take only the values available for Imported_mass and Total_mass_consumed, harmonize their units or period, then form the quotient that gives Dependence.
- Calculator entry
- Enter the parentheses for Imported_mass, the ÷ key, then the parentheses for Total_mass_consumed. Check the displayed order before confirming Dependence.
- Mental estimate
- Estimate how many times Total_mass_consumed “fits” into Imported_mass; this estimate immediately gives the expected scale of Dependence before the precise calculation.
- Independent check
- Inverse check: Dependence × Total_mass_consumed must give back Imported_mass.
- Physical or operational interpretation
- The interpretation of “Dependence = Imported_mass / Total_mass_consumed” belongs to the context “11. Dependence on Earth and progressive autonomy.” The number obtained must be linked to its unit, to the calculation boundary and to the conditions under which the relationship remains valid.
- In plain English
- Plain reading: Dependence measures the amount of Imported_mass per unit of Total_mass_consumed for “11. Dependence on Earth and progressive autonomy.”
- Variation / sensitivity
- If only Imported_mass varies, Dependence varies in the same proportion. If only Total_mass_consumed increases by 10%, Dependence becomes about 0.909 times its initial value.
- Limit / assumption
- Both masses must cover the same period and the same material boundary. A dependence measured by mass does not necessarily describe dependence in terms of criticality or value.
Now we inject the following event: the health system is overwhelmed by an incident. In module 58, this point must be reread from the section “11 — Dependence on Earth and progressive autonomy”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
12. Cautious growth versus accelerated growth
In this module, cautious growth versus accelerated growth serves directly to grow a settlement from 30 to 100 residents by turning mission systems into infrastructure able to grow, be maintained and support new activities.
- Starting question
- What compound growth rate per period links N_start to N_end over t periods?
- Reading aloud
- Reading: “g equals the ratio N end over N start, raised to the power one over t, minus one.”
- Symbols, pronunciation and meaning
- g (“gee”): compound growth rate per period; N_end: final headcount; N_start: initial headcount; t (“tee”): number of periods of equal length. The power 1/t corresponds to the t-th root of the overall ratio.
- Units
- N_end and N_start use the same counting unit, so their ratio is dimensionless. t is a number of periods. g is dimensionless per period and is often expressed as a percentage per period.
- Origin and status of values
- The headcounts and the duration come from the population scenario studied. The periods must have a uniform length — for example years — and that length must be stated.
- Why this operation
- The ratio N_end/N_start measures the total growth factor. Taking the power 1/t looks for the identical factor that, repeated t times, reproduces this total factor. Finally, subtracting 1 turns this periodic factor into the rate g.
- Substitution and calculation
- Mandatory order: 1) calculate the ratio N_end/N_start; 2) raise this ratio to the power 1/t, or take its t-th root; 3) subtract 1. The result is the compound rate per period.
- Calculator entry
- Enter (N_end / N_start)^(1 / t) - 1 with the parentheses. Check the ratio and the exponent 1/t separately before the power, then convert g to a percentage if necessary.
- Mental estimate
- If N_end > N_start, g must be positive; if they are equal, g = 0; if N_end < N_start, g is negative. For the same total growth, spreading the change over more periods reduces the rate per period.
- Independent check
- Rebuild the final headcount with N_start × (1 + g)^t. The result must give back N_end to within rounding.
- Physical or operational interpretation
- g describes an equivalent constant compound rate. It does not mean that the real population must grow by exactly the same percentage in every period.
- In plain English
- We are looking for the same growth factor, repeated in each period, that takes the initial headcount to the final headcount.
- Variation / sensitivity
- For a fixed t, increasing N_end/N_start increases g. For a ratio greater than 1, increasing t lowers the rate needed per period, since the total growth is spread over more periods.
- Limit / assumption
- N_start > 0, N_end > 0 and t > 0 are required. The model describes an equivalent compound rate and does not capture irregular variations, capacity limits or discrete events.
Now we inject the following event: an electrical extension reduces the reserve margin. In module 58, this point must be reread from the section “12 — Cautious growth versus accelerated growth”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
Progressive exercises with one-to-one answers
Exercise 1: Population trajectory and capacity
For “Population trajectory and capacity,” explain which quantities enter “Capacity_req = Demand × (1 + margin) / A” and how you would check the result. Then apply the same reasoning to the following degraded case: heat-rejection capacity becomes the limiting factor. Your conclusion must state what remains certain, what becomes uncertain and the decision to make.
Answer — Exercise 1: Population trajectory and capacity
- Case data
- The exercise is about “Population trajectory and capacity” and uses the relationship “Capacity_req = Demand × (1 + margin) / A.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: heat-rejection capacity becomes the limiting factor.
- Relationship
- Capacity_req = Demand × (1 + margin) / A — the control relationship used for this exercise.
- Reasoning
- The method consists in translating “Population trajectory and capacity” into quantities compatible with “Capacity_req = Demand × (1 + margin) / A,” checking the units and then comparing the result with an order of magnitude or an operational threshold. The case “heat-rejection capacity becomes the limiting factor” must then be used as a sensitivity test of the decision.
- Result
- For “Population trajectory and capacity,” the result is acceptable only if the data used and the unit check can be traced. The relationship “Capacity_req = Demand × (1 + margin) / A” provides the framework for the calculation; the case “heat-rejection capacity becomes the limiting factor” then determines whether the margin remains sufficient to keep the decision.
Exercise 2: Power and microgrids at the 100 scale
Analyze “Power and microgrids at the 100 scale” using “Growth = (N_end - N_start) / duration” as the reference relationship. Present the useful data and their units, then check the result by an independent check or an order of magnitude. Finally, take this degradation into account: a critical imported flow is delayed.
Answer — Exercise 2: Power and microgrids at the 100 scale
- Case data
- The exercise is about “Power and microgrids at the 100 scale” and uses the relationship “Growth = (N_end - N_start) / duration.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: a critical imported flow is delayed.
- Relationship
- Growth = (N_end - N_start) / duration — the control relationship used for this exercise.
- Reasoning
- To avoid an automatic answer, separate three steps: build the data for “Growth = (N_end - N_start) / duration,” check the calculation and its unit, then interpret the margin. The scenario “a critical imported flow is delayed” is a second case to analyze: it can change the margin without necessarily changing the relationship itself.
- Result
- The answer must lead to a decision justified by “Growth = (N_end - N_start) / duration” and not to a generic sentence. In the absence of imposed values, no single numerical value is required. The conclusion remains valid only if the scenario “a critical imported flow is delayed” destroys neither the consistency of the data nor the safety margin.
Exercise 3: Water, sanitation and storage
On “Water, sanitation and storage,” use “Load_pp = Total_load / N” to build a traceable line of reasoning. Explain the assumptions, the meaning of the result and the margin available. Then revisit the conclusion if the following case occurs: the local workshop cannot qualify a vital part.
Answer — Exercise 3: Water, sanitation and storage
- Case data
- The exercise is about “Water, sanitation and storage” and uses the relationship “Load_pp = Total_load / N.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: the local workshop cannot qualify a vital part.
- Relationship
- Load_pp = Total_load / N — the control relationship used for this exercise.
- Reasoning
- First identify the variables of “Load_pp = Total_load / N” and put them in consistent units. Then apply the relationship keeping the assumptions visible, and check the order of magnitude. Finally, repeat the reasoning taking into account the degraded case “the local workshop cannot qualify a vital part” to see whether the margin or the decision changes.
- Result
- This exercise does not set a single number as long as the case-specific data are not provided. A correct answer therefore gives a traceable calculation or check, its unit, and then an explicit decision. If “the local workshop cannot qualify a vital part” makes an input unreliable or removes the available margin, the decision must be reviewed rather than kept by default.
Exercise 4: Food and stock security
The case “Food and stock security” must be handled with the relationship “Dependence = Imported_mass / Total_mass_consumed.” Start by identifying the data and units needed, then say how the result would be checked. Finally, test the decision in this degraded situation: the health system is overwhelmed by an incident.
Answer — Exercise 4: Food and stock security
- Case data
- The exercise is about “Food and stock security” and uses the relationship “Dependence = Imported_mass / Total_mass_consumed.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: the health system is overwhelmed by an incident.
- Relationship
- Dependence = Imported_mass / Total_mass_consumed — the control relationship used for this exercise.
- Reasoning
- The reasoning must start from the quantities actually available for “Dependence = Imported_mass / Total_mass_consumed.” Once the units are harmonized, carry out the calculation or the symbolic check, then verify the result by an independent estimate. The scenario “the health system is overwhelmed by an incident” is then used to test the robustness of the conclusion.
- Result
- The expected result is a checked conclusion, not an invented value. For “Food and stock security,” the calculation based on “Dependence = Imported_mass / Total_mass_consumed” must come with its unit and the useful margin. The scenario “the health system is overwhelmed by an incident” must lead to changing the decision if this margin becomes insufficient or if a piece of data ceases to be credible.
Numerical reference points kept. 40%.
Exercise 5: Habitat, zoning and refuges
To examine “Habitat, zoning and refuges,” link the relevant data to “Capacity_req = Demand × (1 + margin) / A.” Justify each step of the reasoning, check the consistency of the units and make the margin explicit; then test the decision with this scenario: an electrical extension reduces the reserve margin.
Answer — Exercise 5: Habitat, zoning and refuges
- Case data
- The exercise is about “Habitat, zoning and refuges” and uses the relationship “Capacity_req = Demand × (1 + margin) / A.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: an electrical extension reduces the reserve margin.
- Relationship
- Capacity_req = Demand × (1 + margin) / A — the control relationship used for this exercise.
- Reasoning
- Use “Capacity_req = Demand × (1 + margin) / A” as a chain of control: input data, units, operation, result, then interpretation. Do not mix a measured value with an assumption. The degraded case “an electrical extension reduces the reserve margin” must be handled separately to determine whether it reduces the margin or invalidates a piece of data.
- Result
- The right answer links the result of “Capacity_req = Demand × (1 + margin) / A” to an operational decision. Without imposed numerical data, the result must be kept in symbolic form or explicitly stated values must be used as assumptions. The case “an electrical extension reduces the reserve margin” serves to decide whether the conclusion remains robust.
Exercise 6: Industry and local maintenance
On “Industry and local maintenance,” use “Growth = (N_end - N_start) / duration” as a verification tool rather than as an isolated formula. Describe the quantities, the check of the result and the associated decision, then integrate this degraded situation: population growth outpaces housing.
Answer — Exercise 6: Industry and local maintenance
- Case data
- The exercise is about “Industry and local maintenance” and uses the relationship “Growth = (N_end - N_start) / duration.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: population growth outpaces housing.
- Relationship
- Growth = (N_end - N_start) / duration — the control relationship used for this exercise.
- Reasoning
- Start by explaining what each term of “Growth = (N_end - N_start) / duration” represents. Check the units before any substitution, then interpret the result in the context of “Industry and local maintenance.” Finally, revisit the decision when the scenario “population growth outpaces housing” is imposed.
- Result
- Precision that is absent from the problem statement must not be manufactured. A valid answer presents the data chosen, the application of “Growth = (N_end - N_start) / duration,” the unit and the margin, then explains what changes under “population growth outpaces housing.” If the degraded case breaks the main assumption, the conclusion must be put on hold or recalculated.
Exercise 7: Mobility and surface logistics
Handle “Mobility and surface logistics” by showing how “Load_pp = Total_load / N” informs the decision. The units and assumptions must remain visible. After checking the result, reassess the margin in this situation: heat-rejection capacity becomes the limiting factor.
Answer — Exercise 7: Mobility and surface logistics
- Case data
- The exercise is about “Mobility and surface logistics” and uses the relationship “Load_pp = Total_load / N.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: heat-rejection capacity becomes the limiting factor.
- Relationship
- Load_pp = Total_load / N — the control relationship used for this exercise.
- Reasoning
- The method consists in translating “Mobility and surface logistics” into quantities compatible with “Load_pp = Total_load / N,” checking the units and then comparing the result with an order of magnitude or an operational threshold. The case “heat-rejection capacity becomes the limiting factor” must then be used as a sensitivity test of the decision.
- Result
- For “Mobility and surface logistics,” the result is acceptable only if the data used and the unit check can be traced. The relationship “Load_pp = Total_load / N” provides the framework for the calculation; the case “heat-rejection capacity becomes the limiting factor” then determines whether the margin remains sufficient to keep the decision.
Exercise 8: Health and organization of care
Build a complete answer for “Health and organization of care” around “Dependence = Imported_mass / Total_mass_consumed.” Say which data are required, how the result would be checked and what decision follows. Then check that this decision remains valid in the following case: a critical imported flow is delayed.
Answer — Exercise 8: Health and organization of care
- Case data
- The exercise is about “Health and organization of care” and uses the relationship “Dependence = Imported_mass / Total_mass_consumed.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: a critical imported flow is delayed.
- Relationship
- Dependence = Imported_mass / Total_mass_consumed — the control relationship used for this exercise.
- Reasoning
- To avoid an automatic answer, separate three steps: build the data for “Dependence = Imported_mass / Total_mass_consumed,” check the calculation and its unit, then interpret the margin. The scenario “a critical imported flow is delayed” is a second case to analyze: it can change the margin without necessarily changing the relationship itself.
- Result
- The answer must lead to a decision justified by “Dependence = Imported_mass / Total_mass_consumed” and not to a generic sentence. In the absence of imposed values, no single numerical value is required. The conclusion remains valid only if the scenario “a critical imported flow is delayed” destroys neither the consistency of the data nor the safety margin.
Numerical reference points kept. 40%.
Exercise 9: Governance and specialization of roles
To work on “Governance and specialization of roles,” use the relationship “Capacity_req = Demand × (1 + margin) / A” to structure the reasoning. Identify the quantities needed and their units, then explain what the result allows you to decide. Finally, test the robustness of this decision in the following degraded case: the local workshop cannot qualify a vital part.
Answer — Exercise 9: Governance and specialization of roles
- Case data
- The exercise is about “Governance and specialization of roles” and uses the relationship “Capacity_req = Demand × (1 + margin) / A.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: the local workshop cannot qualify a vital part.
- Relationship
- Capacity_req = Demand × (1 + margin) / A — the control relationship used for this exercise.
- Reasoning
- First identify the variables of “Capacity_req = Demand × (1 + margin) / A” and put them in consistent units. Then apply the relationship keeping the assumptions visible, and check the order of magnitude. Finally, repeat the reasoning taking into account the degraded case “the local workshop cannot qualify a vital part” to see whether the margin or the decision changes.
- Result
- This exercise does not set a single number as long as the case-specific data are not provided. A correct answer therefore gives a traceable calculation or check, its unit, and then an explicit decision. If “the local workshop cannot qualify a vital part” makes an input unreliable or removes the available margin, the decision must be reviewed rather than kept by default.
Exercise 10: Science, production and priorities
Study “Science, production and priorities” with the help of “Growth = (N_end - N_start) / duration.” Specify the data that would need to be measured or known, check the units and the order of magnitude, then examine what changes in this situation: the health system is overwhelmed by an incident. Conclude with the margin to monitor and the operational decision.
Answer — Exercise 10: Science, production and priorities
- Case data
- The exercise is about “Science, production and priorities” and uses the relationship “Growth = (N_end - N_start) / duration.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: the health system is overwhelmed by an incident.
- Relationship
- Growth = (N_end - N_start) / duration — the control relationship used for this exercise.
- Reasoning
- The reasoning must start from the quantities actually available for “Growth = (N_end - N_start) / duration.” Once the units are harmonized, carry out the calculation or the symbolic check, then verify the result by an independent estimate. The scenario “the health system is overwhelmed by an incident” is then used to test the robustness of the conclusion.
- Result
- The expected result is a checked conclusion, not an invented value. For “Science, production and priorities,” the calculation based on “Growth = (N_end - N_start) / duration” must come with its unit and the useful margin. The scenario “the health system is overwhelmed by an incident” must lead to changing the decision if this margin becomes insufficient or if a piece of data ceases to be credible.
Exercise 11: Dependence on Earth and progressive autonomy
In “Dependence on Earth and progressive autonomy,” start from the relationship “Load_pp = Total_load / N” and show how it serves as a check. Clearly distinguish data, assumptions and result, then replay the reasoning with this degraded scenario: an electrical extension reduces the reserve margin. State whether the initial decision remains defensible.
Answer — Exercise 11: Dependence on Earth and progressive autonomy
- Case data
- The exercise is about “Dependence on Earth and progressive autonomy” and uses the relationship “Load_pp = Total_load / N.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: an electrical extension reduces the reserve margin.
- Relationship
- Load_pp = Total_load / N — the control relationship used for this exercise.
- Reasoning
- Use “Load_pp = Total_load / N” as a chain of control: input data, units, operation, result, then interpretation. Do not mix a measured value with an assumption. The degraded case “an electrical extension reduces the reserve margin” must be handled separately to determine whether it reduces the margin or invalidates a piece of data.
- Result
- The right answer links the result of “Load_pp = Total_load / N” to an operational decision. Without imposed numerical data, the result must be kept in symbolic form or explicitly stated values must be used as assumptions. The case “an electrical extension reduces the reserve margin” serves to decide whether the conclusion remains robust.
Exercise 12: Cautious growth versus accelerated growth
Solve the case “Cautious growth versus accelerated growth” with the relationship “Dependence = Imported_mass / Total_mass_consumed.” The goal is not only to obtain a number: check the units, plausibility and margin, then explain the course of action in this situation: population growth outpaces housing.
Answer — Exercise 12: Cautious growth versus accelerated growth
- Case data
- The exercise is about “Cautious growth versus accelerated growth” and uses the relationship “Dependence = Imported_mass / Total_mass_consumed.” The quantities must be defined before calculating and their units made compatible. The robustness scenario to test is the following: population growth outpaces housing.
- Relationship
- Dependence = Imported_mass / Total_mass_consumed — the control relationship used for this exercise.
- Reasoning
- Start by explaining what each term of “Dependence = Imported_mass / Total_mass_consumed” represents. Check the units before any substitution, then interpret the result in the context of “Cautious growth versus accelerated growth.” Finally, revisit the decision when the scenario “population growth outpaces housing” is imposed.
- Result
- Precision that is absent from the problem statement must not be manufactured. A valid answer presents the data chosen, the application of “Dependence = Imported_mass / Total_mass_consumed,” the unit and the margin, then explains what changes under “population growth outpaces housing.” If the degraded case breaks the main assumption, the conclusion must be put on hold or recalculated.
Numerical reference points kept. 40%.
Reference solution file: growth from 30 to 100 people over 1,000 sols
For each sector of the 100-person settlement, compare the expected function, the nominal capacity, the available capacity, the degraded mode and the criteria for returning to nominal. This grid is used to check the settlement’s real resilience, not just the inventory of its equipment.
1. Starting point at 30 residents
The initial architecture is treated as an existing system with its limits and its maintenance debt. Growth therefore starts with an audit of residual capacity, not with an automatic multiplication by 100/30. The first pass consists of mapping the interfaces: which resource comes in, which goes out, which command acts, which data confirm the state and which other subsystem depends on the result. The mapping in “Starting point at 30 residents” serves to reveal dependencies and failure propagation paths.
For starting point at 30 residents, the answer requires a table separating need, capacity, margin and unit. For “Starting point at 30 residents,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Starting point at 30 residents,” a number without a unit or a time horizon is incomplete. For “Starting point at 30 residents,” a one-significant-figure estimate comes before the precise calculation.
The “Starting point at 30 residents” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. A single telemetry reading is not sufficient evidence when a common bias is possible. For “Starting point at 30 residents,” look for independent confirmation or physical consistency with another quantity. The “Starting point at 30 residents” answer states what would be observed if the assumed state were real.
For “Starting point at 30 residents,” remove a useful capacity and recalculate the decision horizon. In “Starting point at 30 residents,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Starting point at 30 residents” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy.
For “Starting point at 30 residents,” reject a local optimization whose effects on the other functions have not been quantified. In “Starting point at 30 residents,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The answer therefore calls for an assessment of cross-effects before accepting an optimization.
2. Population trajectory
Arrivals are grouped into waves. Each wave must be preceded by a capacity milestone on habitat, energy, water, food, care and human time. A free bed in a dormitory does not prove that the settlement can absorb one more resident. For “Population trajectory,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Population trajectory” serves to reveal dependencies and failure propagation paths.
For population trajectory, the answer requires a table separating need, capacity, margin and unit. For “Population trajectory,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Population trajectory,” a number without a unit or a time horizon is incomplete. For “Population trajectory,” a one-significant-figure estimate comes before the precise calculation.
The “Population trajectory” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Population trajectory,” a single telemetry reading is not enough if a common bias is plausible. For “Population trajectory,” look for independent confirmation or physical consistency with another quantity. The “Population trajectory” answer states what would be observed if the assumed state were real.
For “Population trajectory,” remove a useful capacity and recalculate the decision horizon. In “Population trajectory,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Population trajectory” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy.
For “Population trajectory,” reject a local optimization whose effects on the other functions have not been quantified. In “Population trajectory,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Population trajectory” answer therefore calls for an assessment of cross-effects before accepting an optimization.
3. Energy at the 100 scale
The grid becomes multi-source and multi-use. Industrial peaks, vital loads and storage are managed by priority. The file measures the reserve after the loss of the largest credible source. For “Energy at the 100 scale,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Energy at the 100 scale” serves to reveal dependencies and failure propagation paths.
For energy at the 100 scale, the answer requires a table separating need, capacity, margin and unit. For “Energy at the 100 scale,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Energy at the 100 scale,” a number without a unit or a time horizon is incomplete. For “Energy at the 100 scale,” a one-significant-figure estimate comes before the precise calculation.
The “Energy at the 100 scale” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Energy at the 100 scale,” a single telemetry reading is not enough if a common bias is plausible. For “Energy at the 100 scale,” look for independent confirmation or physical consistency with another quantity. The “Energy at the 100 scale” answer states what would be observed if the assumed state were real.
For “Energy at the 100 scale,” remove a useful capacity and recalculate the decision horizon. In “Energy at the 100 scale,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Energy at the 100 scale” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy.
For “Energy at the 100 scale,” reject a local optimization whose effects on the other functions have not been quantified. In “Energy at the 100 scale,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Energy at the 100 scale” answer therefore calls for an assessment of cross-effects before accepting an optimization.
4. Heat as a limit to growth
More energy used means more heat to reject. Radiators, loops and heat exchangers become infrastructure in their own right. An extension may be delayed because thermal capacity is insufficient even if electricity production seems abundant. For “Heat as a limit to growth,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Heat as a limit to growth” serves to reveal dependencies and failure propagation paths.
For heat as a limit to growth, the answer requires a table separating need, capacity, margin and unit. For “Heat as a limit to growth,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Heat as a limit to growth,” a number without a unit or a time horizon is incomplete. For “Heat as a limit to growth,” a one-significant-figure estimate comes before the precise calculation.
The “Heat as a limit to growth” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Heat as a limit to growth,” a single telemetry reading is not enough if a common bias is plausible. For “Heat as a limit to growth,” look for independent confirmation or physical consistency with another quantity. The “Heat as a limit to growth” answer states what would be observed if the assumed state were real.
For “Heat as a limit to growth,” remove a useful capacity and recalculate the decision horizon. In “Heat as a limit to growth,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Heat as a limit to growth” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy.
For “Heat as a limit to growth,” reject a local optimization whose effects on the other functions have not been quantified. In “Heat as a limit to growth,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Heat as a limit to growth” answer therefore calls for an assessment of cross-effects before accepting an optimization.
5. Urban water and sanitation
The loops are no longer just those of a habitat but of a small network. Zones, storage, treatment lines and isolation capacities are separated. A local contamination must not doom the whole reserve. For “Urban water and sanitation,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Urban water and sanitation” serves to reveal dependencies and failure propagation paths.
For urban water and sanitation, the answer requires a table separating need, capacity, margin and unit. For “Urban water and sanitation,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Urban water and sanitation,” a number without a unit or a time horizon is incomplete. For “Urban water and sanitation,” a one-significant-figure estimate comes before the precise calculation.
The “Urban water and sanitation” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Urban water and sanitation,” a single telemetry reading is not enough if a common bias is plausible. For “Urban water and sanitation,” look for independent confirmation or physical consistency with another quantity. The “Urban water and sanitation” answer states what would be observed if the assumed state were real. In module 58, this point must be reread from the section “5 — Urban water and sanitation”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Urban water and sanitation,” remove a useful capacity and recalculate the decision horizon. In “Urban water and sanitation,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Urban water and sanitation” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy. In module 58, this point must be reread from the section “5 — Urban water and sanitation”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Urban water and sanitation,” reject a local optimization whose effects on the other functions have not been quantified. In “Urban water and sanitation,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Urban water and sanitation” answer therefore calls for an assessment of cross-effects before accepting an optimization. In module 58, this point must be reread from the section “5 — Urban water and sanitation”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
6. Food and stocks
Local production reduces some imports but adds energy, water, nutrients, labor and biological risk. The plan tracks calories, diversity, losses, safety stocks and cooking and storage capacity. For “Food and stocks,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Food and stocks” serves to reveal dependencies and failure propagation paths.
For food and stocks, the answer requires a table separating need, capacity, margin and unit. For “Food and stocks,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Food and stocks,” a number without a unit or a time horizon is incomplete. For “Food and stocks,” a one-significant-figure estimate comes before the precise calculation.
The “Food and stocks” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Food and stocks,” a single telemetry reading is not enough if a common bias is plausible. For “Food and stocks,” look for independent confirmation or physical consistency with another quantity. The “Food and stocks” answer states what would be observed if the assumed state were real. In module 58, this point must be reread from the section “6 — Food and stocks”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Food and stocks,” remove a useful capacity and recalculate the decision horizon. In “Food and stocks,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Food and stocks” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy. In module 58, this point must be reread from the section “6 — Food and stocks”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Food and stocks,” reject a local optimization whose effects on the other functions have not been quantified. In “Food and stocks,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Food and stocks” answer therefore calls for an assessment of cross-effects before accepting an optimization. In module 58, this point must be reread from the section “6 — Food and stocks”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
7. Habitat, urban planning and refuge
Zoning separates living, industry, hazardous storage, science, mobility and refuges. Distances start to cost time and energy. The growth plan reserves corridors and interfaces before the ground is saturated. For “Habitat, urban planning and refuge,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Habitat, urban planning and refuge” serves to reveal dependencies and failure propagation paths.
For habitat, urban planning and refuge, the answer requires a table separating need, capacity, margin and unit. For “Habitat, urban planning and refuge,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Habitat, urban planning and refuge,” a number without a unit or a time horizon is incomplete. For “Habitat, urban planning and refuge,” a one-significant-figure estimate comes before the precise calculation.
The “Habitat, urban planning and refuge” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Habitat, urban planning and refuge,” a single telemetry reading is not enough if a common bias is plausible. For “Habitat, urban planning and refuge,” look for independent confirmation or physical consistency with another quantity. The “Habitat, urban planning and refuge” answer states what would be observed if the assumed state were real. In module 58, this point must be reread from the section “7 — Habitat, urban planning and refuge”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Habitat, urban planning and refuge,” remove a useful capacity and recalculate the decision horizon. In “Habitat, urban planning and refuge,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Habitat, urban planning and refuge” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy. In module 58, this point must be reread from the section “7 — Habitat, urban planning and refuge”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Habitat, urban planning and refuge,” reject a local optimization whose effects on the other functions have not been quantified. In “Habitat, urban planning and refuge,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Habitat, urban planning and refuge” answer therefore calls for an assessment of cross-effects before accepting an optimization. In module 58, this point must be reread from the section “7 — Habitat, urban planning and refuge”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
8. Industry and qualification
At 100 residents, the question is no longer just making things but guaranteeing repeatability, metrology, material, procedure and traceability. An unqualified local part may be useful for a piece of furniture and unacceptable for a vital function. For “Industry and qualification,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Industry and qualification” serves to reveal dependencies and failure propagation paths.
For industry and qualification, the answer requires a table separating need, capacity, margin and unit. For “Industry and qualification,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Industry and qualification,” a number without a unit or a time horizon is incomplete. For “Industry and qualification,” a one-significant-figure estimate comes before the precise calculation.
The “Industry and qualification” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Industry and qualification,” a single telemetry reading is not enough if a common bias is plausible. For “Industry and qualification,” look for independent confirmation or physical consistency with another quantity. The “Industry and qualification” answer states what would be observed if the assumed state were real. In module 58, this point must be reread from the section “8 — Industry and qualification”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Industry and qualification,” remove a useful capacity and recalculate the decision horizon. In “Industry and qualification,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Industry and qualification” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy. In module 58, this point must be reread from the section “8 — Industry and qualification”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Industry and qualification,” reject a local optimization whose effects on the other functions have not been quantified. In “Industry and qualification,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Industry and qualification” answer therefore calls for an assessment of cross-effects before accepting an optimization. In module 58, this point must be reread from the section “8 — Industry and qualification”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
9. Health and specialization
The number of roles increases, but the settlement remains vulnerable where skills are rare. The file defines skill redundancy, cross-training, diagnostic capacity and on-call load without assuming a complete terrestrial hospital. For “Health and specialization,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Health and specialization” serves to reveal dependencies and failure propagation paths.
For health and specialization, the answer requires a table separating need, capacity, margin and unit. For “Health and specialization,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Health and specialization,” a number without a unit or a time horizon is incomplete. For “Health and specialization,” a one-significant-figure estimate comes before the precise calculation.
The “Health and specialization” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Health and specialization,” a single telemetry reading is not enough if a common bias is plausible. For “Health and specialization,” look for independent confirmation or physical consistency with another quantity. The “Health and specialization” answer states what would be observed if the assumed state were real. In module 58, this point must be reread from the section “9 — Health and specialization”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Health and specialization,” remove a useful capacity and recalculate the decision horizon. In “Health and specialization,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Health and specialization” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy. In module 58, this point must be reread from the section “9 — Health and specialization”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Health and specialization,” reject a local optimization whose effects on the other functions have not been quantified. In “Health and specialization,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Health and specialization” answer therefore calls for an assessment of cross-effects before accepting an optimization. In module 58, this point must be reread from the section “9 — Health and specialization”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
10. Governance and institutions
Growth creates resource conflicts, more rules and the need to delegate. Emergency, appeal, logging and review processes are sized for a community that can no longer decide everything in a permanent assembly. For “Governance and institutions,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Governance and institutions” serves to reveal dependencies and failure propagation paths.
For governance and institutions, the answer requires a table separating need, capacity, margin and unit. For “Governance and institutions,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Governance and institutions,” a number without a unit or a time horizon is incomplete. For “Governance and institutions,” a one-significant-figure estimate comes before the precise calculation.
The “Governance and institutions” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Governance and institutions,” a single telemetry reading is not enough if a common bias is plausible. For “Governance and institutions,” look for independent confirmation or physical consistency with another quantity. The “Governance and institutions” answer states what would be observed if the assumed state were real. In module 58, this point must be reread from the section “10 — Governance and institutions”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Governance and institutions,” remove a useful capacity and recalculate the decision horizon. In “Governance and institutions,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Governance and institutions” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy. In module 58, this point must be reread from the section “10 — Governance and institutions”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Governance and institutions,” reject a local optimization whose effects on the other functions have not been quantified. In “Governance and institutions,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Governance and institutions” answer therefore calls for an assessment of cross-effects before accepting an optimization. In module 58, this point must be reread from the section “10 — Governance and institutions”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
11. Dependence on Earth
Autonomy is measured by function, not by slogan. The settlement can produce its water and remain dependent on an electronic component or a medicine. The dependency matrix distinguishes imported mass from imported criticality. For “Dependence on Earth,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Dependence on Earth” serves to reveal dependencies and failure propagation paths.
For dependence on earth, the answer requires a table separating need, capacity, margin and unit. For “Dependence on Earth,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Dependence on Earth,” a number without a unit or a time horizon is incomplete. For “Dependence on Earth,” a one-significant-figure estimate comes before the precise calculation.
The “Dependence on Earth” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Dependence on Earth,” a single telemetry reading is not enough if a common bias is plausible. For “Dependence on Earth,” look for independent confirmation or physical consistency with another quantity. The “Dependence on Earth” answer states what would be observed if the assumed state were real. In module 58, this point must be reread from the section “11 — Dependence on Earth”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Dependence on Earth,” remove a useful capacity and recalculate the decision horizon. In “Dependence on Earth,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Dependence on Earth” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy. In module 58, this point must be reread from the section “11 — Dependence on Earth”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Dependence on Earth,” reject a local optimization whose effects on the other functions have not been quantified. In “Dependence on Earth,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Dependence on Earth” answer therefore calls for an assessment of cross-effects before accepting an optimization. In module 58, this point must be reread from the section “11 — Dependence on Earth”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
12. Two growth trajectories
The cautious variant builds the margins before the arrivals; the accelerated variant accepts more capacity debt. The answer compares not only growth speed but also reversibility, stock, human workload and sensitivity to logistics delays. For “Two growth trajectories,” first map the interfaces: resources, commands, data and dependencies. The mapping in “Two growth trajectories” serves to reveal dependencies and failure propagation paths.
For two growth trajectories, the answer requires a table separating need, capacity, margin and unit. For “Two growth trajectories,” subtract unavailability, reserves and simultaneity constraints from the nominal capacity. In “Two growth trajectories,” a number without a unit or a time horizon is incomplete. For “Two growth trajectories,” a one-significant-figure estimate comes before the precise calculation.
The “Two growth trajectories” milestone requires stated evidence: measurement, test, inventory, inspection or demonstration. For “Two growth trajectories,” a single telemetry reading is not enough if a common bias is plausible. For “Two growth trajectories,” look for independent confirmation or physical consistency with another quantity. The “Two growth trajectories” answer states what would be observed if the assumed state were real. In module 58, this point must be reread from the section “12 — Two growth trajectories”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Two growth trajectories,” remove a useful capacity and recalculate the decision horizon. In “Two growth trajectories,” preserve vital functions and reversible options rather than the initial plan at all costs. The degraded mode of “Two growth trajectories” quantifies shed loads, stocks, duration, repair and the threshold for changing strategy. In module 58, this point must be reread from the section “12 — Two growth trajectories”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
For “Two growth trajectories,” reject a local optimization whose effects on the other functions have not been quantified. In “Two growth trajectories,” a mass saving must be weighed against its maintenance, emergency, energy and thermal costs. The “Two growth trajectories” answer therefore calls for an assessment of cross-effects before accepting an optimization. In module 58, this point must be reread from the section “12 — Two growth trajectories”: the evidence required must remain consistent with the goal “Capstone project: growing a Mars settlement from 30 to 100 people” and with the margins actually available in this scenario.
Master table of budgets and evidence
| Budget | Question to close | Evidence expected | Degraded mode to study |
|---|---|---|---|
| Population | What population need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the population capacity. | Recalculate population after removing a capacity and state the time before the threshold is crossed. |
| Habitat | What habitat need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the habitat capacity. | Recalculate habitat after removing a capacity and state the time before the threshold is crossed. |
| Energy | What energy need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the energy capacity. | Recalculate energy after removing a capacity and state the time before the threshold is crossed. |
| Thermal | What thermal need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the thermal capacity. | Recalculate thermal after removing a capacity and state the time before the threshold is crossed. |
| Water | What water need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the water capacity. | Recalculate water after removing a capacity and state the time before the threshold is crossed. |
| Sanitation | What sanitation need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the sanitation capacity. | Recalculate sanitation after removing a capacity and state the time before the threshold is crossed. |
| Food | What food need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the food capacity. | Recalculate food after removing a capacity and state the time before the threshold is crossed. |
| Industry | What industry need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the industry capacity. | Recalculate industry after removing a capacity and state the time before the threshold is crossed. |
| Mobility | What mobility need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the mobility capacity. | Recalculate mobility after removing a capacity and state the time before the threshold is crossed. |
| Medical | What medical need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the medical capacity. | Recalculate medical after removing a capacity and state the time before the threshold is crossed. |
| Human time | What human-time need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the human-time capacity. | Recalculate human time after removing a capacity and state the time before the threshold is crossed. |
| Dependence on Earth | What dependence-on-Earth need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the dependence-on-Earth capacity. | Recalculate dependence on Earth after removing a capacity and state the time before the threshold is crossed. |
| Strategic stocks | What strategic-stock need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the strategic-stock capacity. | Recalculate strategic stocks after removing a capacity and state the time before the threshold is crossed. |
| Governance | What governance need coincides with the unfavorable scenario, and what margin remains after unavailability? | Table of assumptions, unit, measurement or test that confirms the governance capacity. | Recalculate governance after removing a capacity and state the time before the threshold is crossed. |
Timeline of six injected events
T0: the anomaly is detected and logged. T+1: characterize “logistics delay” with at least two clues that do not share the same source of error. T+2: redistribute loads or tasks to prevent the incident from spreading. T+3: update the module 58 resource table with the capacity actually remaining. T+4: compare this new state with the safety threshold and the time needed to reach a stable solution. T+5: the nominal configuration is restored only after the function has been demonstrated and the lessons learned have been recorded.
Event 2: partial loss of electricity production. T0: the anomaly is detected and logged. T+1: confirm “partial loss of electricity production” with independent data before changing the configuration. T+2: isolate the function affected by “partial loss of electricity production” and preserve vital functions as a priority. T+3: recalculate the autonomy available in the state created by “partial loss of electricity production.” T+4: compare this autonomy with the decision threshold defined in the capstone project: growing a Mars settlement from 30 to 100 people. T+5: return to nominal is authorized only after a test showing that the cause of “partial loss of electricity production” is under control.
Event 3: drift of a vital-function sensor. T0: the anomaly is detected and logged. T+1: for “drift of a vital-function sensor,” first look for a second measurement that does not depend on the same sensor or the same chain. T+2: switch to the backup resource or procedure relevant to module 58. T+3: draw up the new balance of time, stock and capacity after this switch. T+4: decide on the basis of the remaining margin, not of the wish to continue the initial plan. T+5: document the recovery test of “drift of a vital-function sensor” before re-arming the function.
Event 4: a mobility asset immobilized. T0: the anomaly is detected and logged. T+1: characterize “a mobility asset immobilized” by separating symptom, measurement and presumed cause. T+2: immediately reduce the activities that would worsen this anomaly in the capstone project: growing a Mars settlement from 30 to 100 people. T+3: check which redundancies really remain available after the incident. T+4: apply the abort-or-continue criterion associated with the resource that has become limiting. T+5: reinstate the function only when the cross-check no longer reproduces “a mobility asset immobilized.”
Event 5: temporary unavailability of a key skill. T0: the anomaly is detected and logged. T+1: open an anomaly report for “temporary unavailability of a key skill” and confirm the deviation with a separate observation. T+2: put the crew and equipment in the safe configuration planned for this type of deviation. T+3: quantify the consequence of the incident on the duration, power, consumables or mobility concerned. T+4: if the calculated margin crosses the module 58 threshold, trigger the degraded scenario without waiting. T+5: close the anomaly only after a test, a stable reading and cross-validation.
Event 6: loss of a communication or coordination capability. T0: the anomaly is detected and logged. T+1: faced with “loss of a communication or coordination capability,” stop the intuitive interpretation and look for evidence that could contradict it. T+2: secure the hardest-to-replace function in the capstone project: growing a Mars settlement from 30 to 100 people. T+3: project the degraded state up to the next point where a resource, a deadline or a capacity becomes critical. T+4: choose the action that preserves this critical margin, even if it sacrifices a secondary goal. T+5: before resuming, repeat the measurement that had revealed “loss of a communication or coordination capability” and compare it with a healthy reference.
Assessment grid for the file
- Assumptions: 15 points.
- Budgets and units: 20 points.
- Interfaces: 15 points.
- Degraded modes: 15 points.
- Evidence and verification: 10 points.
- Timeline and operations: 10 points.
- Sensitivity analysis: 10 points.
- Clarity and traceability: 5 points.
The settlement matures: from technical capability to a lasting organization
At one hundred residents, the difficulty is no longer only sizing machines. The settlement must be able to detect when a rule, a skill or a supply chain is becoming a bottleneck. The reference file therefore adds a maturity register for each function: dependence on a single person, dependence on an imported part, local measurement capability, ability to train a replacement and time needed to restore the function after an incident. Credible autonomy is not the absence of imports; it is precise knowledge of what is still imported, of how long one can hold out and of the options available if that import is delayed.
Growth must also preserve reversibility. A rapid extension can use up the whole electrical reserve, occupy the last refuge volume or saturate the workshop. The answer therefore requires a milestone before each wave of arrivals: check the reserve after the loss of the largest credible source, water/food autonomy, care capacity, human maintenance time and the ability to make a new quarter safe. If an indicator is red, the next arrival is postponed, even if the physical places exist. This principle turns demography into an engineering decision and prevents confusing desired population with sustainable population.
Finally, the hundred-person settlement must learn to correct itself. Each incident feeds a design review: which assumptions were wrong, which warning sign was not read, which barrier actually limited the spread, which stock was consumed and which change reduces the risk of recurrence? The result is built into the maintenance plan, the training and the next cargo budget. The success of the capstone is therefore not a perfect Martian city on paper; it is a system able to measure its deviations, keep margins, slow its growth when necessary and improve its own understanding after each campaign.
Integrated mini-project and reference file
Compare two trajectories over 1,000 sols: cautious and accelerated growth. Close energy, water, food, habitat, industry, health, mobility, governance, maintenance and dependence on Earth, then inject events and explain why one trajectory remains reversible or becomes fragile.
“Exercise 12: Cautious growth versus accelerated growth” — assumptions, budget, margins.
“Exercise 12: Cautious growth versus accelerated growth” — interfaces and common causes.
“Exercise 12: Cautious growth versus accelerated growth” — calculations, limits, criteria.
Mastery check for module 58
- “Exercise 12: Cautious growth versus accelerated growth” — units and order of magnitude.
- “Exercise 12: Cautious growth versus accelerated growth” — degraded case.
- “Exercise 12: Cautious growth versus accelerated growth” — decision margin.
- “Exercise 12: Cautious growth versus accelerated growth” — control measurement.
Key points of the passage: state
Key points of the passage: availability · substitution
Key points of the passage: order of magnitude · validation
Key points of the passage: Degraded mode
Key points of the passage: robustness
Key points of the passage: flow
Key points of the passage: autonomy
Key points of the passage: zoning
Key points of the passage: subsystem
Key points of the passage: telemetry
Key points of the passage: optimization
Key points of the passage: velocity

The 100-person project: changing topology, not mechanically multiplying a small base
At one hundred residents, districts, backbone networks, specialized teams, public health, shifts, internal logistics, more formal governance and maintenance debt all appear. Some functions gain economies of scale; others become more vulnerable because the same trunk or shared service affects more people.
Population capacity must be checked resource by resource
The population that can be authorized is limited by the resource or function whose verified capacity per person is the lowest. An average across water, energy, refuges and health has no physical meaning.
Distribution networks become first-rank systems
Water, power, data, heat and logistics must make it possible to isolate a district without stopping the whole settlement. Interconnections offer alternative paths but can also spread a fault; their reconfiguration must be measured and controlled.
Specialization creates new human dependencies
A larger population allows deep skills but can turn a single expert into a point of failure. Each critical discipline needs a primary capability, a backup, procedures and qualification tracking.
Public health appears before the hospital
Respiratory and digestive surveillance, water and food quality, isolation, ventilation and continuity of work become population variables. The medical architecture therefore extends from individual clinical care to a collective health function.
Local industry must close the loops that pay off most in autonomy
Making everything locally can cost more energy, tooling and skills than importing. Production is prioritized by criticality, logistics mass, storage life, feasibility and the consequence of a shortage.
Population supported by the weakest constraint
- Two levels of capacity to distinguish
- N_capacity is the equivalent continuous capacity imposed by the most limiting function; N_admissible is the maximum whole number of people, obtained by rounding N_capacity down to the nearest integer.
- Concrete question
- When several critical functions have different capacities, what maximum population can the actually verified system support?
- Intuition without symbols
- Each function imposes its own population ceiling. The whole settlement is limited by the smallest of these ceilings, because a surplus of water does not make up for a shortfall of oxygen or sanitation.
- Reading aloud
- “Population capacity equals the minimum, over all functions j, of the verified capacity divided by the need per person; admissible population equals the integer part of this capacity.”
- Symbols, pronunciation and meaning
- C_j,verified: demonstrated capacity of function j; q_j,person: design need per person for this function; min_j: the smallest ratio is chosen; floor: rounding down to the nearest integer.
- Units
- Water example: L/day divided by L/person/day gives people. The same reasoning applies separately to each function with consistent units.
- Origin and status of values
- The capacities come from commissioning/verified operation; the needs per person come from the mission assumptions and measured behavior.
- Why these operations
- Each ratio gives a population ceiling for one function. The minimum selects the bottleneck; floor avoids counting a fraction of a person.
- Worked example
- Oxygen: 118 equivalent people; water: 126; food logistics: 104.7; sanitation: 112.
- Substitution and calculation
- N_capacity = min(118; 126; 104.7; 112) = 104.7 equivalent people. N_admissible = floor(104.7) = 104 people.
- Mental estimate
- 104.7 is the smallest continuous capacity: food logistics controls the result. Rounding down then gives 104 admissible people.
- Independent check
- At 104 people, check that each of the other functions still has a capacity ≥ its demand calculated with the same assumptions.
- Interpretation
- For a target of 100 residents, only four people of margin remain on the limiting function in this example.
- Sensitivity
- If food capacity rises from 104 to 120, sanitation at 112 becomes the new bottleneck: improving one function often shifts the constraint.
- Assumptions and domain of validity
- Each C_j,verified and q_j,person must refer to the same function, the same period and a consistent boundary; q_j,person > 0. The continuous minimum represents an equivalent capacity, and floor applies only afterward, to the whole number of admissible people.
- Limits of the model
- Each capacity is treated as a scalar: peaks, storage, degraded modes, distribution topology and crew skills are not represented.
- What the result does not prove
- Nominally supporting 100 people does not prove that they will survive a major failure or a long resupply delay.
- Classic mistake
- Averaging population capacities, or replacing a capacity that has not been commissioned with its nominal installed value.
- Degraded case
- If a critical function has not been verified, its capacity must not be assumed to be available; the growth gate stays closed.
- Mission decision
- Authorize the population increase only when the limiting function keeps a demonstrated margin compatible with the degraded modes adopted.
Final exercise — refusing growth that the averages nevertheless support
An 85-person settlement wants to grow to 105. The averages for water, power and food allow it, but one district has only one water trunk, the second medical team lacks an advanced operator and a critical part has no local spare. Decide.
Reasoned solution. Expected solution: delay or phase the growth until the specific bottlenecks are closed. Hosting capacity is constrained by the most critical verified weakness, not by the average of resources.
To link this workshop to the references already used in the module, see NASA — Moon to Mars Architecture Components and NASA — Environmental Control and Life Support Systems.
Additional mastery exercises
Mastery exercise — continuous capacity and admissible population
Situation. The verified critical functions give the following equivalent capacities: oxygen 112.8 people, water 119.4, food 106.6 and sanitation 110.2.
Task. 1) Calculate N_capacity = min_j(C_j/q_j). 2) Calculate N_admissible = floor(N_capacity). 3) Explain why 107 people cannot be authorized. 4) A 104-person settlement wants to take in 2 new arrivals: say whether this nominal capacity check alone authorizes it and what else must be checked.
Reasoned answer
N_capacity = min(112.8; 119.4; 106.6; 110.2) = 106.6 equivalent people. N_admissible = floor(106.6) = 106 people. 107 people cannot be authorized because the limiting function covers only 106.6 unit needs. Going from 104 to 106 remains compatible with this nominal calculation alone, but the real decision also requires degraded modes, redundancy, critical stocks, maintenance, skills and safety reserves.
