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Task 1 Sensitivity Analysis for Moon Colony Logistics

This module performs comprehensive sensitivity analysis on key model parameters:
1. Rocket payload capacity (100-150 tons, as specified in problem)
2. Elevator capacity (±20%)
3. Launch frequency (0.5-2 launches/day)
4. Engine technology (Isp variations)
5. Structural coefficient α

Author: MCM 2026 Team
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X#U4$)NzF======================================================================z5Task 1 Sensitivity Analysis for Moon Colony LogisticszG
======================================================================zSENSITIVITY ANALYSIS RESULTSz:
[1] Rocket Payload Capacity (Problem range: 100-150 tons)F)
<01>indexu
[2] Elevator Capacity (±20%)z
[3] Launch Frequencyz
[4] Engine Technologyu
[5] Structural Coefficient αzGenerating Visualization...z</Volumes/Files/code/mm/20260130_b/p1/sensitivity_payload.csvz=/Volumes/Files/code/mm/20260130_b/p1/sensitivity_elevator.csvz>/Volumes/Files/code/mm/20260130_b/p1/sensitivity_frequency.csvz;/Volumes/Files/code/mm/20260130_b/p1/sensitivity_engine.csvz:/Volumes/Files/code/mm/20260130_b/p1/sensitivity_alpha.csvz
Data saved to CSV files.zKEY FINDINGSu

    1. ROCKET PAYLOAD CAPACITY (100-150 tons):
       - Higher capacity reduces minimum timeline significantly
       - Limited impact on energy when elevator dominates
       - Baseline 125 tons is a reasonable middle estimate
    
    2. ELEVATOR CAPACITY (±20%):
       - Most sensitive parameter for timeline
       - ±20% capacity changes elevator-only timeline by ~37 years
       - Critical for long-term planning
    
    3. LAUNCH FREQUENCY:
       - Doubling frequency halves minimum rocket-only timeline
       - Essential for time-constrained scenarios
       - Less impact when elevator provides majority of transport
    
    4. ENGINE TECHNOLOGY:
       - Primarily affects energy, not timeline
       - LOX/Hydrogen saves ~30% energy vs LOX/Methane
       - But LOX/Methane has practical advantages (storage, cost)
    
    5. STRUCTURAL COEFFICIENT α:
       - Lower α (better technology) improves fuel efficiency
       - Moderate impact on total energy
       - Progress from 0.10 to 0.08 saves ~8% energy
    zAnalysis Complete!)
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