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@@ -42,7 +42,7 @@
\setlength{\cftbeforesecskip}{6pt}
\renewcommand{\contentsname}{\hspace*{\fill}\Large\bfseries Contents \hspace*{\fill}}
\title{Resilience, Efficiency, and Ecology: Optimizing Hybrid Interplanetary Transport for the 2050 Moon Colony}
\title{Energy as Currency: Optimizing Hybrid Transport for the 2050 Lunar Frontier}
% \author{\small \href{http://www.latexstudio.net/}
% {\includegraphics[width=7cm]{mcmthesis-logo}}}
\date{\today}
@@ -52,23 +52,25 @@
\begin{abstract}
To address the logistical requirements for establishing a 100,000-person Moon Colony by 2050, this study develops a comprehensive evaluation system spanning interplanetary transport decision-making, stochastic risk management, and multi-objective ecological balancing.
To address the logistical challenge of transporting 100 million metric tons of material to establish a 100,000-person Moon colony by 2050, we develop a Universal Energy-Equivalent and Temporal Co-ordination Model and a Life-Support Logistics and Stochastic Water Balance Model. These models evaluate the trade-offs between the Space Elevator System and traditional rocket launches across energy, time, and environmental dimensions.
We first construct the \textbf{Universal Energy-Equivalent and Temporal Coordination Model (UETCM)}. By establishing \textbf{Universal Energy-Equivalent} measured in Joules as the primary cost proxy, the model bypasses the volatility of monetary valuations and enables a standardized comparison between chemical rockets and space elevator technologies. Grounded in the Tsiolkovsky equation and gravitational mechanics, the model delineates a linear mapping between energy expenditure and payload mass. To resolve the energy-time trade-off, we formulate a system burden function based on the \textbf{time opportunity cost}, which is calibrated at 504 PJ per year through weight equilibrium and geometric centroid methods. Simulation results demonstrate that hybrid transport can complete the 100-million-metric-ton mission in 100.7 years, significantly outperforming standalone elevator and rocket-only scenarios. Under the calibrated cost parameters, a balanced 139-year strategy is identified as the global deterministic optimum.
Firstly, we establish a \textbf{Universal Energy-Equivalent (UEE)} metric to facilitate a thermodynamically consistent comparison between chemical rockets and electric space elevators. We introduce a \textbf{Time-Opportunity Parameter ($\lambda$)} to transform the energy-time trade-off into a single optimization objective. To ensure robustness, we incorporate \textbf{CVaR-style risk adjustments} and \textbf{Monte Carlo simulations} to account for system failures, tether swaying, and operational downtime.
To manage real-world uncertainties, we extend the UETCM into a \textbf{Stochastic Risk and Robustness Framework} utilizing Conditional Value-at-Risk and 10,000 Monte Carlo iterations. This analysis identifies significant long-tail risks stemming from mechanical oscillations and system failures. To achieve a 95 percent completion confidence level, we recommend extending the operational timeline to a range of 155 to 160 years, adjusting the space elevator share to between 65 and 70 percent, and maintaining a 10 percent capacity reserve as a strategic buffer.
For task 1, we compare three delivery scenarios. We find that while a \textbf{Rocket-Only} approach offers the shortest initial timeline, it is energetically prohibitive. The \textbf{Elevator-Only} scenario requires 186 years but consumes the least energy. The \textbf{Balanced Hybrid} scenario (139 years) emerges as a strategic compromise, balancing construction velocity with resource efficiency.
For the subsequent operational phase, we establish the \textbf{Life-Support Logistics and Stochastic Water Balance Model (LSL-SWBM)}. This model integrates multi-tier domestic demand with stochastic medical emergency needs approximated via normal distributions. Our findings indicate that annual water demand at the Luxury Standard is more than 35 times that of the Survival Standard. For the Comfort Standard, we recommend a hybrid scheme utilizing both the elevator and low-latitude rocket sites, which completes the initial filling in 4.57 days with a balanced energy footprint.
For task 2, we evaluate system reliability under non-ideal conditions. Our results indicate that the space elevator's throughput is highly sensitive to tether stability. However, even with a \textbf{15\% downtime margin}, the elevator remains the superior long-term infrastructure compared to the high failure-cost risks of mass rocket launches.
Furthermore, environmental footprints are integrated into a \textbf{tri-objective optimization framework}. While rocket-only delivery incurs massive carbon dioxide and stratospheric water vapor emissions, the space elevator remains nearly carbon-neutral. Consequently, the 186-year standalone elevator scenario is proposed as the ultimate sustainable strategy, emitting only 846 million metric tons of carbon dioxide, which represents less than 6.5 percent of the rocket baseline.
For task 3, we develop a \textbf{Tiered Water Logistics Model} based on three comfort levels. Using sensitivity analysis, we identify \textbf{recycling efficiency ($\eta$)} as the dominant lever; a 1\% drop in $\eta$ increases annual supply needs by 9.6\%. We conclude that the space elevator can comfortably support a Luxury tier, occupying 69.68\% of its annual capacity.
Finally, we provide the Moon Colony Management Agency with actionable strategic recommendations. By proposing a phased hybrid transport plan with rebalancing triggers based on key performance indicators, this study offers a resilient pathway to lunar colonization that ensures logistical reliability while upholding ecological preservation.
For task 4, we extend the model into an \textbf{Environmental Single-Objective Framework}. By quantifying CO$_2$ emissions and stratospheric H$_2$O injection, we find the \textbf{Elevator-Only} plan reduces carbon footprints by 93.5\% compared to rockets. By synthesizing temporal efficiency, energy consumption, and environmental externalities, the model identifies the optimal transport strategy for lunar colonization that prioritizes the preservation of Earth’s ecological integrity.
Finally, we recommend a \textbf{Tiered Strategy}: beginning with Survival-tier logistics to secure the colony, then transitioning to a Comfort-tier elevator-based operation to achieve long-term sustainability.
\end{abstract}
\begin{keywords}
Universal Energy-Equivalent; Stochastic Risk Analysis ; Multi-objective Optimization
Energy-based cost proxy; Stochastic Risk Analysis ; Multi-objective Optimization: Earth–Moon logistics: Space Elevator
\end{keywords}
\maketitle
@@ -82,15 +84,7 @@ Universal Energy-Equivalent; Stochastic Risk Analysis ; Multi-objective Optimiza
\section{Introduction}
\subsection{Background}
As human space exploration shifts from short-term landings to permanent settlement, Earth’s finite resources and fragile ecosystems motivate the development of scalable off-world habitats. Yet traditional chemical-propulsion rockets face persistent bottlenecks—limited payload ratios, high marginal launch costs, and non-negligible environmental impacts—making it difficult to sustain the mass logistics required for constructing and operating a 100,000-person Moon Colony. In this context, the Space Elevator System has been proposed as a transformative infrastructure \cite{penoyre2019spacelinepracticalspaceelevator} that can provide routine, energy-efficient access to space when paired with lunar transfer, but it also introduces new reliability and operational uncertainties. Therefore, the central challenge is to quantify and compare the energy (as a cost proxy), timeline, robustness under failures, and environmental footprint of rockets, elevators, and hybrid portfolios to support an actionable construction and sustainment strategy.
\begin{figure}[H]
\centering
\includegraphics[width=12cm]{background.png}
\caption{background}
\label{background}
\end{figure}
As human space exploration shifts from short-term landings to permanent settlement, Earth’s finite resources and fragile ecosystems motivate the development of scalable off-world habitats. Yet traditional chemical-propulsion rockets face persistent bottlenecks—limited payload ratios, high marginal launch costs, and non-negligible environmental impacts—making it difficult to sustain the mass logistics required for constructing and operating a 100,000-person Moon Colony. In this context, the Space Elevator System has been proposed as a transformative infrastructure \cite{penoyre2019spacelinepracticalspaceelevator} that can provide routine, energy-efficient access to space when paired with lunar transfer, but it also introduces new reliability and operational uncertainties.
@@ -114,7 +108,7 @@ We develop a quantitative model to estimate the cost proxy (energy) and timeline
\begin{figure}[H]
\centering
\includegraphics[width=12cm]{Our Work.png}
\includegraphics[width=11cm]{Our Work.png}
\caption{Our Work}
\end{figure}
@@ -166,12 +160,11 @@ $W$ & Total water replenishment demand for the colony & metric
\section{Model I: Universal Energy-Equivalent and Temporal Coordination Model}
\subsection{Model Overview}
To evaluate Earth--Moon logistics, we propose the Universal Energy-Equivalent and Temporal Coordination Model (UETCM). We use Universal Energy-Equivalent (UEE, J) as a physics-based cost proxy to compare chemical rockets and the space elevator on a common basis.
To evaluate Moon Colony logistics, we develop the Universal Energy-Equivalent and Temporal Coordination Model (UETCM). The model adopts Universal Energy-Equivalent (UEE), measured in Joules, as the primary metric to bypass volatile monetary valuations, facilitating a standardized thermodynamic comparison between the momentum transfer of chemical rockets and the gravitational potential gains of the Space Elevator System.
UETCM maps payload mass to energy using the Tsiolkovsky equation and gravitational mechanics, and reconciles the energy--time trade-off by introducing a time opportunity cost parameter $\lambda$ to form a single objective $J$.
The modeling process begins with establishing a linear mapping between payload mass and energy consumption via the Tsiolkovsky equation and gravitational gradients, integrated with physio-geographical constraints to identify the feasibility gap within the delivery window. To integrate the competing dimensions of timeline and cost, we define a Time Opportunity Cost parameter $\lambda$—derived through a consensus of four independent analytical methodologies—to scalarize the initial multi-dimensional problem into a unified objective function. This allows for the identification of a globally optimal operating point that minimizes the total system burden ($J$).
Finally, UETCM is extended into a stochastic model incorporating Risk-Adjusted Optimization and Conditional Value-at-Risk (CVaR). Through 10,000 Monte Carlo simulations, we quantify not only the performance impact of perturbations such as tether swaying and system failures but also derive modified strategies with robust safety margins, providing a comprehensive framework that spans from physical mechanisms to resilient strategic decision-making.
We further incorporate non-ideal operations via a stochastic extension with Monte Carlo simulation and Conditional Value-at-Risk (CVaR), yielding risk-aware strategies with explicit robustness margins.
\begin{figure}[H]
\centering
@@ -191,31 +184,30 @@ where $x$ is the number of reuse cycles. As reuse increases in a mature post-205
\subsubsection{Empirical Industry Validation}
Evidence from mature terrestrial transport supports this modeling choice: in commercial aviation, fuel remains a persistent and material share (15--25\%) of operating expenses, indicating that energy is a primary driver once hardware is amortized and operations are standardized.
Evidence from mature terrestrial transport supports this modeling choice: in commercial aviation, fuel remains a persistent and material share (15--25\%) of operating expenses, indicating that energy is a primary driver once hardware is amortized and operations are standardized \cite{xan3011_airline_2019}.
\begin{figure}[H]
\centering
\includegraphics[width=10cm]{fuel_share_trend.png}
\caption{Trend of fuel cost as a percentage of total operating expenses}
\caption{Trend of Fuel Cost as a Percentage of Total Operating Expenses}
\label{fig:fuel_share_trend}
\end{figure}
In summary, we adopt Universal Energy-Equivalent as the primary metric to avoid long-horizon monetary ambiguity and to compare transport architectures on a common thermodynamic baseline (i.e., overcoming gravitational wells and imparting the required kinetic energy).
\subsection{Ideal Energy Cost Modeling}
\subsubsection{Rocket Momentum Dynamics}
\textbf{Rocket Momentum Dynamics:}
For traditional rocket transport, energy demand is dominated by propellant required to deliver a payload to the Earth--Moon transfer trajectory. Neglecting air resistance, the Tsiolkovsky rocket equation gives the mass ratio $R$:
\[ R = \frac{m_0}{m_f} = e^{\Delta V / v_e} \]
where $v_e$ is the effective exhaust velocity and $\Delta V$ (e.g., for Trans-Lunar Injection) is treated as a mission constant. Accounting for structural mass via a structural coefficient $\alpha$ (structure-to-fuel ratio), the fuel mass scales linearly with payload:
\[ m_{fuel} = \underbrace{\frac{R-1}{1-\alpha(R-1)}}_{k} \cdot m_p \]
which defines the proportional coefficient $k$. Using the idealized chemical energy release proxy, the rocket energy is:
\[ E_{rocket} = \frac{1}{2} m_{fuel} \cdot v_e^2 = \frac{1}{2} k \cdot v_e^2 \cdot m_p \]
Therefore, under fixed mission and vehicle parameters, rocket energy scales linearly with payload mass. For completeness, we also express the total energy requirement as the sum of gravitational and transition terms:
which defines the proportional coefficient $k$. Using the idealized chemical energy release proxy and under fixed vehicle parameters,rocket energy scales linearly with payload mass. For completeness, we also express the total energy requirement as the sum of gravitational and transition terms:
\[ \Delta E_{total} = m_p \cdot \left[ \left( \frac{G M_E}{R_E} - \frac{G M_E}{d_{EM}} \right) - \frac{G M_M}{2 r_M} \right] \]
which is likewise proportional to $m_p$.
\subsubsection{Space Elevator Mechanics}
\textbf{Space Elevator Mechanics:}
Compared with direct rockets, the Space Elevator System adds an Earth-surface-to-apex segment along the tether before the lunar-transfer rocket leg (already covered above). We model only the elevator segment energy change.
@@ -235,19 +227,21 @@ where $r_0$ is the distance from the Apex Anchor to Earth's center and $\omega$
After resolving the physical energy efficiency, the model determines the construction timeline. The complexity arises from the fact that 100 million metric tons of material cannot be delivered instantaneously; the progress is constrained by the geographical distribution of launch sites, frequency limits, and the inherent capacities of the space elevator and rocket systems.
\subsubsection{Transport Progress Formulas}
\textbf{1. Transport Progress Formulas:}
To quantify the construction timeline, the model defines $M_{total} = 10^8$ metric tons as the total demand. Based on the three scenarios provided, the completion time $t$ depends on the annual cumulative capacity $C$:
\begin{itemize}
\item Space elevator only (Scenario a): $t_{a} = \frac{M_{total}}{C_{e}}$
\item Rockets only (Scenario b): $t_{b} = \frac{M_{total}}{C_{r}}$
\item Hybrid transport (Scenario c): $t_{c} = \frac{M_{total}}{\lambda C_{e} + \mu C_{r}}$
\item Hybrid transport (Scenario c): $t_{c} = \frac{M_{total}}{ w_e C_e + (1-w_e) C_r}$
\end{itemize}
We interpret the problem-stated throughput of 179,000 t/yr as the annual capacity of a single Galactic Harbour; therefore, the three-harbour Space Elevator System has a combined capacity of
$$
C_e = 3 \times 179,000 \text{ t/yr}
$$. And $C_r$ is the integrated annual capacity of the rocket system. Shortening the timeline requires increasing annual capacity. By adjusting the hybrid weights $\lambda$ and $\mu$, we seek a dynamic balance between construction speed and energy cost.
where $C_e$ is the annual throughput of the space elevator system and $C_r$ is the integrated annual capacity of the rocket system. Shortening the timeline requires increasing annual capacity. By adjusting the hybrid weights $\lambda$ and $\mu$, we seek a dynamic balance between construction speed and energy cost.
\subsubsection{Spatial and Geographical Optimization}
\textbf{2. Spatial and Geographical Optimization}
The primary obstacles to construction progress are geographical constraints and frequency limits, which define the upper bound of $C_r$.
\begin{itemize}
@@ -296,7 +290,7 @@ Here $\lambda$ (PJ/year) is an energy-equivalent penalty per additional year, ca
\begin{figure}[H]
\centering
\includegraphics[width=0.7\textwidth]{total_cost_curves.png}
\includegraphics[width=0.6\textwidth]{total_cost_curves.png}
\caption{Sensitivity analysis of optimal timeline $T^*$ versus time opportunity cost $\lambda$}
\label{fig:lambda_sensitivity}
\end{figure}
@@ -309,7 +303,7 @@ Rather than choosing $\lambda$ subjectively, we cross-check it using four indepe
Through numerical simulation of the 100 million metric ton material transport mission, this study elucidates the intrinsic correlation between construction progress and resource consumption under diverse technical constraints. The findings demonstrate that the optimal transport strategy is not a simple superposition of individual methods but a dynamic equilibrium based on the trade-off between physical energy efficiency and temporal costs.
\subsubsection{Comparison of Baseline Scenarios}
\textbf{1. Comparison of Baseline Scenarios}
Based on the model outputs, Table \ref{tab:comparison} summarizes the core indicators for the three baseline scenarios.
\begin{table}[H]
@@ -332,7 +326,8 @@ Integrating Table \ref{tab:comparison} and Figure \ref{Three Transport Scenarios
\caption{Three Transport Scenarios Feasibility Comparison}
\label{Three Transport Scenarios Feasibility Comparison}
\end{figure}
\subsubsection{Optimal Strategy Selection and Allocation}
\textbf{2. Optimal Strategy Selection and Allocation}
To determine the optimal operating point, we analyze the behavior of the total cost function $J(T) = E(T) + \lambda T$. Based on the consensus value of $\lambda = 504$ PJ/year, three strategic configurations are evaluated within the feasible optimization space (100.7--186 years), as detailed in Table \ref{tab:strategies}.
\begin{table}[H]
@@ -358,7 +353,7 @@ These strategies represent key operational configurations: Strategy A minimizes
\end{enumerate}
\subsubsection{Sensitivity and Parameter Stability}
\textbf{3. Sensitivity and Parameter Stability}
To assess the robustness of our model, we perform sensitivity analysis
on five key parameters. Figure \ref{fig:sensitivity} summarizes the results.
@@ -366,7 +361,7 @@ on five key parameters. Figure \ref{fig:sensitivity} summarizes the results.
\begin{figure}[H]
\centering
\includegraphics[width=8cm]{tornado_chart.png}
\caption{Sensitivity Analysis}
\caption{Sensitivity Analysis of Key Parameters for UETCM}
\label{fig:sensitivity}
\end{figure}
@@ -399,7 +394,7 @@ but practical considerations favor the latter.
Parameter & Range & $\Delta T^*$ & $\Delta E^*$ \\
\midrule
Payload Capacity & 100--150 t & $-7$ y ($-5.0\%$) & $+3246$ PJ ($+8.4\%$) \\
Elevator Capacity & $\pm 20\%$ & $+42$ y ($+30.2\%$) & $-47902$ PJ ($-123.5\%$) \\
Elevator Capacity & $\pm 20\%$ & $+42$ y ($+30.2\%$) & $-47902$ PJ ($-61.7\%$) \\
Launch Frequency & 0.5--2/day & $-43$ y ($-30.9\%$) & $+20867$ PJ ($+53.8\%$) \\
Structural Coef. $\alpha$ & 0.06--0.14 & $+85$ y ($+61.4\%$) & $-28149$ PJ ($-72.6\%$) \\
\bottomrule
@@ -408,7 +403,8 @@ Structural Coef. $\alpha$ & 0.06--0.14 & $+85$ y ($+61.4\%$) & $-28149$ PJ ($-72
\subsection{Stochastic Risk and Robustness Analysis}
Task 2 asks a fundamentally different question from Task 1: not merely how much performance degrades, but how our recommended strategy should change in response to system uncertainties. We achieve this through a three-stage methodology: quantifying perturbation impacts, identifying risk-adjusted decision boundaries, and finally deriving modified optimal strategies with robust safety margins.
\subsubsection{Stochastic Perturbation Modeling}
\textbf{(1) Stochastic Perturbation Modeling}
Given the unprecedented nature of the Space Elevator System, we acknowledge significant epistemic uncertainty in failure parameters. We adopt a conservative approach by establishing parameter ranges rather than point estimates:
\begin{table}[H]
@@ -429,7 +425,7 @@ Weather cancellation & 10\% & [5\%, 20\%] & Site-specific meteorological data \\
\end{table}
\subsubsection{Risk-Adjusted Optimization}
\textbf{(2) Risk-Adjusted Optimization}
Under uncertainty, the deterministic objective function must be extended to incorporate risk preferences. We reformulate the optimization as:
\begin{equation}
@@ -439,7 +435,7 @@ Under uncertainty, the deterministic objective function must be extended to inco
where $\text{CVaR}_{\alpha}(T)$ denotes the Conditional Value-at-Risk at confidence level $\alpha$ (typically 95\%), representing the expected completion time in the worst $1-\alpha$ scenarios \cite{chatgpt}. The risk aversion coefficient $\gamma$ (PJ/year) quantifies the MCM Agency's willingness to pay for reduced schedule uncertainty.
\subsubsection{Monte Carlo Lifecycle Assessment}
\textbf{(3) Monte Carlo Lifecycle Assessment}
Due to the highly non-linear interactions between these stochastic variables, we utilized a Monte Carlo algorithm to execute 10,000 simulations of the construction cycle.
@@ -460,7 +456,7 @@ Due to the highly non-linear interactions between these stochastic variables, we
Idealized models define the theoretical limits, but stochastic variables such as tether swaying, equipment failure, and weather interference cause performance to deviate. We evaluate system performance under disturbance based on 10,000 Monte Carlo iterations.
\subsubsection{Assessment of Performance Degradation}
\textbf{1. Assessment of Performance Degradation}
Table \ref{tab:stochastic_comparison} compares the deterministic solutions with stochastic means, quantifying the costs of system perturbations.
\begin{table}[H]
@@ -494,7 +490,7 @@ Table \ref{tab:stochastic_comparison} compares the deterministic solutions with
\end{tabular}
}
\end{table}
\subsubsection{Resilient Strategic Adjustments}
\textbf{2. Resilient Strategic Adjustments}
The Monte Carlo results reveal that perturbations do not merely shift performance metrics---they fundamentally alter the risk-return profile of each strategy:
@@ -522,7 +518,7 @@ We recommend maintaining a 10\% reserve margin in annual transport capacity:
\end{equation}
This reserve can absorb localized disruptions without triggering cascading delays.
\subsubsection{Evolution of Key Indicators}
\textbf{3. Evolution of Key Indicators}
Stochastic disturbances transform deterministic values into probability distributions, but the strategic ranking remains robust.
@@ -549,12 +545,12 @@ As the Moon Colony transitions from the construction phase to the operational ph
\begin{figure}[H]
\centering
\includegraphics[width=11cm]{Flow Chart of Model II.png}
\caption{Flow Chart of Model II}
\label{Flow Chart of Model II}
\end{figure}
% \begin{figure}[H]
% \centering
% \includegraphics[width=11cm]{Flow Chart of Model II.png}
% \caption{Flow Chart of Model II}
% \label{Flow Chart of Model II}
% \end{figure}
@@ -566,9 +562,9 @@ In an isolated lunar ecosystem, water consumption is primarily sustained by a re
Within the colony, domestic water consists of survival and hygiene components. The daily demand is formulated as:
\begin{equation}
W_{r} = N \times (w_{s} + 0.4\alpha)
W_{r} = N \times (w_{s} + 0.4\kappa)
\end{equation}
where $N$ is the population, $w_{s}$ represents the survival baseline, and $\alpha$ is the comfort factor. The following table summarizes the water standards across different demand tiers \cite{francisco2025nasa}\cite{whitmore2012nasa}:
where $N$ is the population, $w_{s}$ represents the survival baseline, and $\kappa$ is the comfort factor. The following table summarizes the water standards across different demand tiers \cite{francisco2025nasa}\cite{whitmore2012nasa}:
\begin{table}[H]
\small
@@ -576,7 +572,7 @@ where $N$ is the population, $w_{s}$ represents the survival baseline, and $\alp
\caption{Water Demand Standards Across Different Comfort Tiers}
\begin{tabular}{lccl}
\toprule
\textbf{Demand Tier} & \textbf{$\alpha$ Value} & \textbf{Daily Use per Capita} & \textbf{Description} \\ \midrule
\textbf{Demand Tier} & \textbf{$\kappa$ Value} & \textbf{Daily Use per Capita} & \textbf{Description} \\ \midrule
Survival Standard & 1 & 2.9 L & Minimum survival threshold \\
Comfort Standard & 50 & 22.5 L & Moderate domestic comfort \\
Luxury Standard & 250 & 102.5 L & Equivalent to Earth-like usage \\ \bottomrule
@@ -615,7 +611,7 @@ This model precisely offsets recycling losses and daily medical consumption to m
To evaluate the operational sustainability of the Moon Colony, we perform a quantitative decomposition of the water replenishment mission across temporal and energetic dimensions. By assuming ideal conditions and excluding the perturbations analyzed in Task 2, this approach isolates the specific influence of varying living standards to facilitate a definitive baseline comparison.
\subsubsection{Demand Scaling Across Comfort Tiers}
Minute variations in the comfort factor $\alpha$ trigger significant shifts in logistical scale. The water demand metrics for the three simulated tiers are summarized in Table \ref{tab:water_demand_stats}.
Minute variations in the comfort factor $\kappa$ trigger significant shifts in logistical scale. The water demand metrics for the three simulated tiers are summarized in Table \ref{tab:water_demand_stats}.
\begin{table}[H]
\small
@@ -624,7 +620,7 @@ Minute variations in the comfort factor $\alpha$ trigger significant shifts in l
\label{tab:water_demand_stats}
\begin{tabular}{lccccc}
\toprule
\textbf{Demand Tier} & \textbf{$\alpha$} & \makecell{\textbf{Water Inventory} \\ \textbf{(metric tons)}} & \makecell{\textbf{Daily Rep.} \\ \textbf{(metric tons)}} & \makecell{\textbf{Initial Trans.} \\ \textbf{(metric tons)}} & \makecell{\textbf{Annual Total} \\ \textbf{(metric tons)}} \\
\textbf{Demand Tier} & \textbf{$\kappa$} & \makecell{\textbf{Water Inventory} \\ \textbf{(metric tons)}} & \makecell{\textbf{Daily Rep.} \\ \textbf{(metric tons)}} & \makecell{\textbf{Initial Trans.} \\ \textbf{(metric tons)}} & \makecell{\textbf{Annual Total} \\ \textbf{(metric tons)}} \\
\midrule
Survival Standard & 1 & 290 & 29.1 & 1,163 & 10,622 \\
Comfort Standard & 50 & 2,250 & 225.1 & 9,003 & 82,162 \\
@@ -656,7 +652,7 @@ To satisfy these requirements, we mapped the demand indicators onto the transpor
\end{tabular}
\end{table}
By consolidating the simulation outputs for all scenarios, Table \ref{tab:consolidated_performance} presents a comprehensive comparison of scheme performance across $\alpha$ tiers.
By consolidating the simulation outputs for all scenarios, Table \ref{tab:consolidated_performance} presents a comprehensive comparison of scheme performance across $\kappa$ tiers.
\begin{table}[H]
\small
@@ -667,19 +663,19 @@ By consolidating the simulation outputs for all scenarios, Table \ref{tab:consol
\toprule
\textbf{Scenario} & \textbf{Scheme} & \textbf{Initial Days} & \textbf{Initial En. (TJ)} & \textbf{Monthly Days} & \textbf{Annual En. (PJ)} \\
\midrule
\multirow{4}{*}{Survival ($\alpha=1$)}
\multirow{4}{*}{Survival ($\kappa=1$)}
& Scheme 1 & 0.79 & 182.8 & 0.59 & 1.67 \\
& Scheme 2 & 0.93 & 588.6 & 0.69 & 5.38 \\
& Scheme 3 & 0.43 & 369.2 & 0.32 & 3.37 \\
& Scheme 4 & 0.59 & 283.1 & 0.44 & 2.59 \\
\midrule
\rowcolor{recommendColor} \multirow{4}{*}{Comfort ($\alpha=50$)}
\rowcolor{recommendColor} \multirow{4}{*}{Comfort ($\kappa=50$)}
& Scheme 1 & 6.12 & 1,415.3 & 4.59 & 12.92 \\
& Scheme 2 & 7.20 & 4,556.3 & 5.40 & 41.58 \\
& Scheme 3 & 3.31 & 2,858.1 & 2.48 & 26.08 \\
& Scheme 4 & 4.57 & 2,191.9 & 3.43 & 20.00 \\
\midrule
\multirow{4}{*}{Luxury ($\alpha=250$)}
\multirow{4}{*}{Luxury ($\kappa=250$)}
& Scheme 1 & 27.87 & 6,445.7 & 20.90 & 58.82 \\
& Scheme 2 & 32.80 & 20,751.2 & 24.60 & 189.36 \\
& Scheme 3 & 15.07 & 13,016.9 & 11.30 & 118.78 \\
@@ -687,15 +683,15 @@ By consolidating the simulation outputs for all scenarios, Table \ref{tab:consol
\bottomrule
\end{tabular}
\end{table}
While water transport is highly feasible for survival, the Comfort Scenario ($\alpha=50$) serves as the planning representative where efficiency-timeline trade-offs intensify. In this tier, Scheme 1 defines the efficiency baseline, Scheme 3 maximizes throughput to minimize delivery time, and Scheme 4 offers the optimal operational balance. Under the Luxury Scenario ($\alpha=250$), energy demand for rocket transport peaks at 189.36 PJ. Crucially, even this extreme demand represents only 0.37 percent of the total construction energy, confirming that post-2050 logistical constraints stem from capacity allocation rather than aggregate energy availability.
While water transport is highly feasible for survival, the Comfort Scenario ($\kappa=50$) serves as the planning representative where efficiency-timeline trade-offs intensify. In this tier, Scheme 1 defines the efficiency baseline, Scheme 3 maximizes throughput to minimize delivery time, and Scheme 4 offers the optimal operational balance. Under the Luxury Scenario ($\kappa=250$), energy demand for rocket transport peaks at 189.36 PJ. Crucially, even this extreme demand represents only 0.37 percent of the total construction energy, confirming that post-2050 logistical constraints stem from capacity allocation rather than aggregate energy availability.
\subsection{Sensitivity Analysis for Water Supply Model}
To assess the robustness of Model II and identify the dominant levers in water logistics, we conduct a sensitivity analysis over five variables: recycling efficiency ($\eta$), comfort factor ($\alpha$), population ($N$), medical demand parameters, and buffer duration.
To assess the robustness of Model II and identify the dominant levers in water logistics, we conduct a sensitivity analysis over five variables: recycling efficiency ($\eta$), comfort factor ($\kappa$), population ($N$), medical demand parameters, and buffer duration.
\subsubsection{Parameter Sensitivity Ranking via Tornado Analysis}
\textbf{1. Parameter Sensitivity Ranking via Tornado Analysis}
We systematically varied each parameter within its feasible range while holding others at baseline values ($\alpha=50$, $\eta=90\%$, $N=100,000$, sickness rate $p=2\%$, buffer $=30$ days). The resulting impacts on annual water supply are visualized through a tornado diagram (Figure \ref{fig:tornado}).
We systematically varied each parameter within its feasible range while holding others at baseline values ($\kappa=50$, $\eta=90\%$, $N=100,000$, sickness rate $p=2\%$, buffer $=30$ days). The resulting impacts on annual water supply are visualized through a tornado diagram (Figure \ref{fig:tornado}).
\begin{figure}[h]
\centering
@@ -705,10 +701,10 @@ We systematically varied each parameter within its feasible range while holding
\end{figure}
\begin{enumerate}
\item \textbf{Recycling efficiency ($\eta$)} dominates: modest degradations cause large increases in annual resupply because losses scale with $(1-\eta)$.
\item \textbf{Secondary drivers}: comfort ($\alpha$) is the next lever (tightening provides headroom), population ($N$) is near-linear, while medical/buffer settings have limited effect on annual totals but affect initial fill and resilience.
\item \textbf{Secondary drivers}: comfort ($\kappa$) is the next lever (tightening provides headroom), population ($N$) is near-linear, while medical/buffer settings have limited effect on annual totals but affect initial fill and resilience.
\end{enumerate}
\subsubsection{Quantitative Sensitivity Coefficients}
\textbf{2. Quantitative Sensitivity Coefficients}
Table \ref{tab:sensitivity_coefficients} presents the normalized sensitivity coefficients, defined as the percentage change in output per percentage change in input parameter:
@@ -722,21 +718,17 @@ Table \ref{tab:sensitivity_coefficients} presents the normalized sensitivity coe
\textbf{Parameter} & \textbf{Baseline} & \textbf{Range} & \textbf{$\Delta$ Annual Supply} & \textbf{Sensitivity} & \textbf{Rank} \\
\midrule
Recycling Rate ($\eta$) & 90\% & 80\%--95\% & $-$52\% to +96\% & $-$9.6 & 1 \\
Comfort Factor ($\alpha$) & 50 & 25--100 & $-$71\% to +17\% & +0.88 & 2 \\
Comfort Factor ($\kappa$) & 50 & 25--100 & $-$71\% to +17\% & +0.88 & 2 \\
Population ($N$) & 100k & 80k--120k & $\pm$20\% & +1.0 & 3 \\
Sickness Rate ($p$) & 2\% & 1\%--4\% & $-$0.3\% to +0.6\% & +0.30 & 4 \\
Sickness Rate ($p_{ill}$) & 2\% & 1\%--4\% & $-$0.3\% to +0.6\% & +0.30 & 4 \\
Buffer Days & 30 & 15--45 & $\pm$0\%$^*$ & 0 & 5 \\
\bottomrule
\end{tabular}
\begin{tablenotes}
\small
\item $^*$ Buffer days affect only initial transport, not annual replenishment.
\end{tablenotes}
\end{table}
The sensitivity coefficient for $\eta$ reaches $-9.6$: a 1\% decrease in recycling efficiency increases annual resupply by about 9.6\%, making recycling integrity the primary control variable.
\subsubsection{Worst-Case Stress Testing}
\textbf{3. Worst-Case Stress Testing}
Beyond univariate analysis, we evaluate system performance under compound adverse conditions through Monte Carlo-informed scenario construction. Table \ref{tab:worst_case} summarizes nine representative scenarios spanning from optimal to catastrophic conditions:
@@ -748,7 +740,7 @@ Beyond univariate analysis, we evaluate system performance under compound advers
\resizebox{\textwidth}{!}{
\begin{tabular}{lcccccccc}
\toprule
\textbf{Scenario} & \textbf{$\alpha$} & \textbf{$\eta$} & \textbf{$N$ (k)} & \textbf{$p$} & \textbf{Buffer} & \textbf{Annual (kt)} & \textbf{Capacity (\%)} & \textbf{Feasible} \\
\textbf{Scenario} & \textbf{$\kappa$} & \textbf{$\eta$} & \textbf{$N$ (k)} & \textbf{$p_{ill}$} & \textbf{Buffer} & \textbf{Annual (kt)} & \textbf{Capacity (\%)} & \textbf{Feasible} \\
\midrule
Survival Mode & 1 & 90\% & 100 & 2\% & 30 & 14.2 & 2.7\% & \checkmark \\
\rowcolor{recommendColor}
@@ -765,7 +757,7 @@ Beyond univariate analysis, we evaluate system performance under compound advers
}
\end{table}
The stress test shows that feasibility is controlled mainly by the joint condition \textbf{$\eta<82\%$ with $\alpha>200$}, under which annual water demand can exceed elevator capacity (worst case: \textbf{171.3\%}), whereas moderate stress remains well within capacity (49.2\%).
The stress test shows that feasibility is controlled mainly by the joint condition \textbf{$\eta<82\%$ with $\kappa>200$}, under which annual water demand can exceed elevator capacity (worst case: \textbf{171.3\%}), whereas moderate stress remains well within capacity (49.2\%).
\subsection{Conclusion and Strategic Insights}
@@ -849,12 +841,18 @@ Accident Risk & Hydrocarbon spills & No leakage risk & Negligible \\
\end{table}
The analogy confirms that the Earth Port's environmental footprint is significantly lower than that of existing oil platforms. Compared to the widespread atmospheric damage caused by rockets, the localized impacts of the space elevator are nearly negligible, reinforcing its ecological superiority.
\subsection{Tri-objective Decision Framework}
We expand the bi-objective optimization to a tri-objective framework ($J_{total}$) by integrating environmental externalities as primary constraints:
\subsection{Environmental Priority Optimization Framework}
To prioritize Earth's ecological integrity, we redefine the optimization logic by transitioning from a multi-objective trade-off to an Environmental Single-Objective framework. In this model, environmental impact is the primary objective to be minimized, while construction time and energy consumption are treated as boundary constraints:
\begin{equation}
\min J_{total} = \alpha \cdot \text{Time} + \beta \cdot \text{Energy} + \gamma \cdot \text{Emission}_{\text{CO}_2} + \delta \cdot \text{Emission}_{\text{H}_2\text{O, strat}}
\begin{aligned}
\min \quad & J_{env} = \gamma \cdot \text{Emission}_{\text{CO}_2} + \delta \cdot \text{Emission}_{\text{H}_2\text{O, strat}} \\
\end{aligned}
\end{equation}
Simulation analysis reveals that by setting $J_{env}$ as the sole optimization target, the system naturally eliminates chemical propulsion dependencies. The 186-year mark represents the absolute floor of ecological externalities—the point where stratospheric pollution is zeroed and carbon emissions reach their global minimum. Beyond this threshold, further extending the timeline yields no additional environmental gain, confirming the Elevator-Only scenario as the most sustainable strategy.
\begin{figure}[H]
\centering
\includegraphics[width=0.6\textwidth]{marginal_benefit.png}
@@ -862,8 +860,6 @@ We expand the bi-objective optimization to a tri-objective framework ($J_{total}
\label{fig:reduction_analysis}
\end{figure}
Simulation analysis reveals a significant coupling between environmental benefits and energy efficiency. Notably, the system reaches its peak marginal environmental benefit at approximately the 186-year mark, representing an "Efficiency Cliff". Beyond this threshold, any further extension of the construction timeline yields diminishing returns in environmental preservation.
\subsection{Result of Task 4}
@@ -890,23 +886,16 @@ Conclusively, the 186-year standalone space elevator scenario is proposed as the
\item \textbf{Comparable cost proxy across technologies.}
Using Universal Energy-Equivalent (UEE, Joules) avoids long-horizon monetary uncertainty and enables a thermodynamically consistent comparison between chemical rockets and space-elevator lifting.
\item \textbf{Interpretable multi-objective decision logic.}
The time-opportunity parameter $\lambda$ converts the energy--time trade-off into a single objective with a clear optimality condition ($dE/dT=-\lambda$), making stakeholder preferences explicit and auditable.
\item \textbf{Risk-aware recommendation.}
CVaR-style risk adjustment and Monte Carlo simulations translate uncertainties (failures, downtime, weather) into a confidence-bounded schedule and actionable operational policies (strategy band, reserve margin, trigger actions).
\item \textbf{Actionable sensitivity insights.}
Sensitivity analysis identifies dominant levers (e.g., elevator capacity and recycling efficiency), directly informing engineering priorities and governance constraints.
The time-opportunity parameter $\lambda$ converts the energy--time trade-off into a single objective with a clear optimality condition, making stakeholder preferences explicit and auditable.
\end{itemize}
\subsection{Weaknesses and Possible Improvement}
\begin{itemize}
\item \textbf{Parameter uncertainty and long-horizon extrapolation.}
Key inputs (elevator throughput, failure/downtime rates, future launch cadence) are necessarily assumed or extrapolated.
\textit{Improvement:} expand scenario sets and report threshold/robust regions where the recommendation remains unchanged.
Key inputs are necessarily assumed or extrapolated.
\item \textbf{UEE is not a complete economic cost.}
Energy captures a physical lower bound but does not fully represent CAPEX, labor, insurance, and supply-chain constraints.
\textit{Improvement:} add a parallel monetary sensitivity layer (order-of-magnitude CAPEX/OPEX ranges) to validate ranking stability.
\end{itemize}
@@ -929,27 +918,23 @@ Conclusively, the 186-year standalone space elevator scenario is proposed as the
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\section*{Report on Use of AI}
\begin{enumerate}
\item OpenAI ChatGPT (accessed 2026--02--01)
\begin{description}[leftmargin=!,labelwidth=2.6cm]
\begin{description}[leftmargin=!,labelwidth=2.6cm,itemindent=0pt]
\item[Purpose:] We used a generative AI assistant only for (i) outlining and language polishing, (ii) checking for clarity/consistency of model descriptions, and (iii) LaTeX presentation suggestions (tables/figures). We did \textbf{not} use AI to generate final numerical results, figures, or citations; all computations and plots were produced by the team using our own scripts and datasets, and all claims were verified by the team before inclusion.
\item[Where AI was potentially useful in the paper:] background framing (Introduction), simplifying and explaining assumptions (Assumptions), verifying the expression/units of key equations (Model I \& II), drafting/condensing the robustness narrative (stochastic/CVaR), and improving readability of the recommendation/strengths-weaknesses sections.
\item[Query 1:] ``Rewrite the following paragraph in concise academic English, keep the meaning, do not add new claims: \emph{Monetary costs are ill-conditioned for an Earth--Moon logistics program spanning many decades due to inflation, technology shocks, and geopolitical uncertainty. We therefore use energy consumption as a stable proxy for marginal cost, enabling a consistent comparison between rockets and the Space Elevator System.}''
\item[Query 1:] ``Rewrite the following paragraph in concise academic English, keep the meaning, do not add new claims: \emph{Monetary costs are ill-conditioned for an Earth--Moon logistics program spanning many decades due to inflation, technology shocks, and geopolitical uncertainty. We therefore use energy consumption as a stable proxy for marginal cost, enabling a consistent comparison between rockets and the Space Elevator System.}''
\item[Output 1:] ``Because monetary costs over multi-decade programs are highly uncertain (inflation, technology shocks, and geopolitics), we adopt energy consumption as a physics-grounded proxy for marginal cost, enabling consistent comparison between rockets and the Space Elevator System.''
\item[Query 2:] ``Give a short, publication-style definition of CVaR at confidence level \( \alpha \) and one sentence on how it is used in schedule-risk planning.''
\item[Query 2:] ``Give a short, publication-style definition of CVaR at confidence level \( \alpha \) and one sentence on how it is used in schedule-risk planning.''
\item[Output 2:] ``Conditional Value-at-Risk (CVaR\(_\alpha\)) is the expected value of a random variable conditional on outcomes in the worst \(1-\alpha\) tail of its distribution. In schedule-risk planning, CVaR\(_\alpha\) summarizes ``expected worst-case'' delays beyond the \( \alpha \)-quantile and can be penalized to obtain risk-averse plans.''
\item[Query 3:] ``Provide a minimal LaTeX example (xcolor + booktabs) to highlight one recommended row in light blue and keep the rest plain, suitable for an MCM paper table.''
\item[Query 3:] ``Provide a minimal LaTeX example (xcolor + booktabs) to highlight one recommended row in light blue and keep the rest plain, suitable for an MCM paper table.''
\item[Output 3:] ``Use \verb|\usepackage[table]{xcolor}| and define a color, then apply \verb|\rowcolor{...}| to the recommended row. Example:
\begin{verbatim}
\definecolor{recommendColor}{RGB}{217,234,249}
@@ -963,9 +948,10 @@ Baseline & ... \\
\end{tabular}
\end{verbatim}''
\end{description}
\newpage
\thispagestyle{empty}
\item Cursor IDE Autocomplete (Free plan, accessed 2026--02--01)
\begin{description}[leftmargin=!,labelwidth=2.6cm]
\begin{description}[leftmargin=!,labelwidth=2.6cm,itemindent=0pt]
\item[Purpose:] Auto-completions for code used in preparing our models.
\end{description}
\end{enumerate}