2026_mcm_b/p4/knee_point_report.txt

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MULTI-OBJECTIVE PARETO KNEE POINT ANALYSIS
Time - Energy - Environment Optimization
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1. PARETO DATA RANGE
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  Completion Time: 101 - 200 years
  Energy: 15720 - 65177 PJ
  CO2: 846 - 6393 Mt
  Elevator Fraction: 54.2% - 100.0%

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2. KNEE POINT DETECTION RESULTS
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  Max Distance (3D):
    Completion Time: 101 years
    Energy: 65177 PJ
    CO2 Emissions: 6393 Mt
    Elevator Fraction: 54.2%
    Rocket Sites Used: 10
    Annual CO2: 63.3 Mt/yr

  Kneedle (Time-CO2):
    Completion Time: 186 years
    Energy: 15842 PJ
    CO2 Emissions: 859 Mt
    Elevator Fraction: 99.9%
    Rocket Sites Used: 1
    Annual CO2: 4.6 Mt/yr

  Kneedle (Time-Energy):
    Completion Time: 186 years
    Energy: 15842 PJ
    CO2 Emissions: 859 Mt
    Elevator Fraction: 99.9%
    Rocket Sites Used: 1
    Annual CO2: 4.6 Mt/yr

  Second Derivative:
    Completion Time: 186 years
    Energy: 15842 PJ
    CO2 Emissions: 859 Mt
    Elevator Fraction: 99.9%
    Rocket Sites Used: 1
    Annual CO2: 4.6 Mt/yr

  Marginal Benefit:
    Completion Time: 189 years
    Energy: 15720 PJ
    CO2 Emissions: 846 Mt
    Elevator Fraction: 100.0%
    Rocket Sites Used: 0
    Annual CO2: 4.5 Mt/yr

  Weighted (Time Priority):
    Completion Time: 186 years
    Energy: 15842 PJ
    CO2 Emissions: 859 Mt
    Elevator Fraction: 99.9%
    Rocket Sites Used: 1
    Annual CO2: 4.6 Mt/yr

  Consensus (Median):
    Completion Time: 186 years
    Energy: 15842 PJ
    CO2 Emissions: 859 Mt
    Elevator Fraction: 99.9%
    Rocket Sites Used: 1
    Annual CO2: 4.6 Mt/yr

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3. RECOMMENDED SOLUTION
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  Based on consensus of multiple knee detection methods:
  
  RECOMMENDED CONFIGURATION:
  ├── Completion Time: 186 years
  ├── Total Energy: 15842 PJ
  ├── Total CO2: 859 Mt
  ├── Elevator Fraction: 99.9%
  ├── Rocket Sites: 1 (low-latitude priority)
  ├── Total Fuel: 80.0 Mt
  ├── Stratospheric H2O: 2.2 Mt
  └── Annual CO2: 4.6 Mt/yr
  
  TRADE-OFF ANALYSIS:
  ├── vs Min Time (101yr): 
  │   +85 years, 
  │   -5534 Mt CO2
  │
  └── vs Min CO2 (200yr):
      -14 years,
      +14 Mt CO2


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4. INTERPRETATION
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  The recommended knee point at 186 years represents the optimal
  trade-off between:
  
  - TIME: Not the fastest, but 85 years longer gives significant benefits
  - ENERGY: 15842 PJ (moderate consumption)
  - ENVIRONMENT: 859 Mt CO2 (substantial reduction from max)
  
  Key insight: Beyond ~186 years, the marginal environmental 
  benefit of extending timeline decreases significantly. This is the 
  "diminishing returns" point.
  
  Recommendation: Target 186-year completion with 100% 
  elevator transport and 1 low-latitude rocket sites.

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