p1: sen

p1/combined_scenario.py

@@ -46,8 +46,8 @@ ELEVATOR_SPECIFIC_ENERGY = 157.2e9  # J per metric ton (157.2 MJ/kg * 1000 kg)
 
 # ============== 火箭参数 ==============
 PAYLOAD_PER_LAUNCH = 125  # metric tons per launch
-ISP = 450  # 比冲 (秒)
+ISP = 363  # 比冲 (秒) - 液氧甲烷 (LOX/CH4, Raptor-class)
-SPECIFIC_FUEL_ENERGY = 15.5e6  # J/kg
+SPECIFIC_FUEL_ENERGY = 11.9e6  # J/kg
 ALPHA = 0.10  # 结构系数
 NUM_STAGES = 3
 DELTA_V_BASE = 13300  # m/s (赤道发射到月球)

p1/lambda_cost_analysis.py

@@ -0,0 +1,844 @@
+"""
+Lambda Time Cost Analysis for Moon Colony Logistics
+
+This module introduces the time opportunity cost (λ) to find the optimal
+operating point on the Energy-Time trade-off curve.
+
+Objective Function: J = E_total + λ × T
+where:
+    - E_total: Total energy consumption (PJ)
+    - T: Construction timeline (years)
+    - λ: Time opportunity cost (PJ/year)
+
+The optimal point satisfies: dE/dT = -λ (marginal energy saving = time cost)
+"""
+
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from matplotlib import rcParams
+import pandas as pd
+from typing import Dict, List, Tuple, Optional
+from dataclasses import dataclass
+
+# Font settings
+rcParams['font.sans-serif'] = ['Arial Unicode MS', 'DejaVu Sans', 'SimHei']
+rcParams['axes.unicode_minus'] = False
+
+# ============== Physical Constants ==============
+G0 = 9.81  # m/s²
+OMEGA_EARTH = 7.27e-5  # rad/s
+R_EARTH = 6.371e6  # m
+
+# Mission parameters
+TOTAL_PAYLOAD = 100e6  # 100 million metric tons
+
+# Space Elevator parameters
+NUM_ELEVATORS = 3
+ELEVATOR_CAPACITY_PER_YEAR = 179000  # metric tons per elevator per year
+TOTAL_ELEVATOR_CAPACITY = NUM_ELEVATORS * ELEVATOR_CAPACITY_PER_YEAR  # 537,000 tons/year
+ELEVATOR_SPECIFIC_ENERGY = 157.2e9  # J per metric ton (157.2 MJ/kg × 1000)
+
+# Rocket parameters - LOX/CH4 (Raptor-class)
+PAYLOAD_PER_LAUNCH = 125  # metric tons per launch
+ISP = 363  # Specific impulse (s)
+SPECIFIC_FUEL_ENERGY = 11.9e6  # J/kg
+ALPHA = 0.10  # Structural coefficient
+NUM_STAGES = 3
+DELTA_V_BASE = 13300  # m/s (LEO + TLI + LOI)
+
+
+# ============== Launch Site Definition ==============
+@dataclass
+class LaunchSite:
+    name: str
+    short_name: str
+    latitude: float
+    max_launches_per_day: int = 1
+    
+    @property
+    def abs_latitude(self) -> float:
+        return abs(self.latitude)
+    
+    @property
+    def delta_v_loss(self) -> float:
+        v_equator = OMEGA_EARTH * R_EARTH
+        v_site = OMEGA_EARTH * R_EARTH * np.cos(np.radians(self.abs_latitude))
+        return v_equator - v_site
+    
+    @property
+    def total_delta_v(self) -> float:
+        return DELTA_V_BASE + self.delta_v_loss
+
+
+LAUNCH_SITES = sorted([
+    LaunchSite("Kourou (French Guiana)", "Kourou", 5.2),
+    LaunchSite("Satish Dhawan (India)", "SDSC", 13.7),
+    LaunchSite("Boca Chica (Texas)", "Texas", 26.0),
+    LaunchSite("Cape Canaveral (Florida)", "Florida", 28.5),
+    LaunchSite("Vandenberg (California)", "California", 34.7),
+    LaunchSite("Wallops (Virginia)", "Virginia", 37.8),
+    LaunchSite("Taiyuan (China)", "Taiyuan", 38.8),
+    LaunchSite("Mahia (New Zealand)", "Mahia", 39.3),
+    LaunchSite("Baikonur (Kazakhstan)", "Baikonur", 45.6),
+    LaunchSite("Kodiak (Alaska)", "Alaska", 57.4),
+], key=lambda x: x.abs_latitude)
+
+
+# ============== Core Calculation Functions ==============
+
+def fuel_ratio_multistage(delta_v: float) -> float:
+    """Multi-stage rocket fuel/payload ratio"""
+    ve = ISP * G0
+    delta_v_per_stage = delta_v / NUM_STAGES
+    R_stage = np.exp(delta_v_per_stage / ve)
+    
+    denominator = 1 - ALPHA * (R_stage - 1)
+    if denominator <= 0:
+        return np.inf
+    
+    k_stage = (R_stage - 1) / denominator
+    
+    total_fuel_ratio = 0
+    remaining_ratio = 1.0
+    
+    for _ in range(NUM_STAGES):
+        fuel_this_stage = remaining_ratio * k_stage
+        total_fuel_ratio += fuel_this_stage
+        remaining_ratio *= (1 + k_stage * (1 + ALPHA))
+    
+    return total_fuel_ratio
+
+
+def rocket_energy_per_ton(site: LaunchSite) -> float:
+    """Energy consumption per ton of payload for rocket launch (J/ton)"""
+    k = fuel_ratio_multistage(site.total_delta_v)
+    fuel_per_ton = k * 1000  # kg fuel per metric ton payload
+    return fuel_per_ton * SPECIFIC_FUEL_ENERGY
+
+
+def calculate_scenario(completion_years: float) -> Optional[Dict]:
+    """
+    Calculate optimal scenario for given completion timeline
+    (elevator priority + low-latitude rockets)
+    """
+    # Space elevator transport
+    elevator_payload = min(TOTAL_ELEVATOR_CAPACITY * completion_years, TOTAL_PAYLOAD)
+    elevator_energy = elevator_payload * ELEVATOR_SPECIFIC_ENERGY
+    
+    # Remaining payload for rockets
+    remaining_payload = TOTAL_PAYLOAD - elevator_payload
+    
+    if remaining_payload <= 0:
+        return {
+            'years': completion_years,
+            'elevator_payload': elevator_payload,
+            'rocket_payload': 0,
+            'elevator_energy_PJ': elevator_energy / 1e15,
+            'rocket_energy_PJ': 0,
+            'total_energy_PJ': elevator_energy / 1e15,
+            'rocket_launches': 0,
+            'sites_used': 0,
+            'elevator_fraction': 1.0,
+        }
+    
+    # Rocket launches needed
+    rocket_launches_needed = int(np.ceil(remaining_payload / PAYLOAD_PER_LAUNCH))
+    
+    # Allocate by latitude priority
+    days_available = completion_years * 365
+    max_launches_per_site = int(days_available)
+    
+    # Check feasibility
+    total_rocket_capacity = len(LAUNCH_SITES) * max_launches_per_site * PAYLOAD_PER_LAUNCH
+    if remaining_payload > total_rocket_capacity:
+        return None
+    
+    rocket_energy = 0
+    sites_used = 0
+    remaining_launches = rocket_launches_needed
+    
+    for site in LAUNCH_SITES:
+        if remaining_launches <= 0:
+            break
+        allocated = min(remaining_launches, max_launches_per_site)
+        rocket_energy += rocket_energy_per_ton(site) * PAYLOAD_PER_LAUNCH * allocated
+        remaining_launches -= allocated
+        if allocated > 0:
+            sites_used += 1
+    
+    rocket_payload = rocket_launches_needed * PAYLOAD_PER_LAUNCH
+    total_energy = elevator_energy + rocket_energy
+    
+    return {
+        'years': completion_years,
+        'elevator_payload': elevator_payload,
+        'rocket_payload': rocket_payload,
+        'elevator_energy_PJ': elevator_energy / 1e15,
+        'rocket_energy_PJ': rocket_energy / 1e15,
+        'total_energy_PJ': total_energy / 1e15,
+        'rocket_launches': rocket_launches_needed,
+        'sites_used': sites_used,
+        'elevator_fraction': elevator_payload / TOTAL_PAYLOAD,
+    }
+
+
+# ============== Generate Trade-off Curve ==============
+
+def generate_tradeoff_curve(
+    year_min: float = 100,
+    year_max: float = 250,
+    num_points: int = 500
+) -> pd.DataFrame:
+    """Generate Energy-Time trade-off curve data"""
+    years_range = np.linspace(year_min, year_max, num_points)
+    
+    results = []
+    for years in years_range:
+        scenario = calculate_scenario(years)
+        if scenario is not None:
+            results.append({
+                'years': years,
+                'energy_PJ': scenario['total_energy_PJ'],
+                'elevator_fraction': scenario['elevator_fraction'],
+                'sites_used': scenario['sites_used'],
+                'rocket_launches': scenario['rocket_launches'],
+            })
+    
+    return pd.DataFrame(results)
+
+
+# ============== Lambda Cost Analysis ==============
+
+def calculate_total_cost(df: pd.DataFrame, lambda_cost: float) -> np.ndarray:
+    """
+    Calculate total cost J = E + λ × T
+    
+    Args:
+        df: Trade-off curve data
+        lambda_cost: Time opportunity cost (PJ/year)
+    
+    Returns:
+        Total cost array
+    """
+    return df['energy_PJ'].values + lambda_cost * df['years'].values
+
+
+def find_optimal_point(df: pd.DataFrame, lambda_cost: float) -> Dict:
+    """
+    Find optimal point that minimizes J = E + λ × T
+    
+    Args:
+        df: Trade-off curve data
+        lambda_cost: Time opportunity cost (PJ/year)
+    
+    Returns:
+        Optimal point information
+    """
+    total_cost = calculate_total_cost(df, lambda_cost)
+    opt_idx = np.argmin(total_cost)
+    
+    return {
+        'index': opt_idx,
+        'years': df['years'].iloc[opt_idx],
+        'energy_PJ': df['energy_PJ'].iloc[opt_idx],
+        'total_cost': total_cost[opt_idx],
+        'elevator_fraction': df['elevator_fraction'].iloc[opt_idx],
+        'lambda': lambda_cost,
+    }
+
+
+def calculate_marginal_energy_saving(df: pd.DataFrame) -> np.ndarray:
+    """
+    Calculate marginal energy saving rate: -dE/dT (PJ/year)
+    
+    This represents how much energy is saved per additional year of timeline.
+    """
+    years = df['years'].values
+    energy = df['energy_PJ'].values
+    
+    # Use central difference for interior points
+    marginal = -np.gradient(energy, years)
+    
+    return marginal
+
+
+def sensitivity_analysis(
+    df: pd.DataFrame,
+    lambda_range: np.ndarray
+) -> pd.DataFrame:
+    """
+    Perform sensitivity analysis on λ parameter
+    
+    Args:
+        df: Trade-off curve data
+        lambda_range: Array of λ values to test
+    
+    Returns:
+        DataFrame with optimal points for each λ
+    """
+    results = []
+    for lam in lambda_range:
+        opt = find_optimal_point(df, lam)
+        results.append({
+            'lambda_PJ_per_year': lam,
+            'optimal_years': opt['years'],
+            'optimal_energy_PJ': opt['energy_PJ'],
+            'total_cost_PJ': opt['total_cost'],
+            'elevator_fraction': opt['elevator_fraction'],
+        })
+    
+    return pd.DataFrame(results)
+
+
+# ============== Visualization Functions ==============
+
+def plot_lambda_analysis(
+    df: pd.DataFrame,
+    save_path: str = '/Volumes/Files/code/mm/20260130_b/p1/lambda_cost_analysis.png'
+):
+    """
+    Comprehensive visualization of λ time cost analysis
+    Focus on critical range λ = 400-600 PJ/year
+    """
+    fig, axes = plt.subplots(2, 2, figsize=(14, 12))
+    
+    years = df['years'].values
+    energy = df['energy_PJ'].values
+    
+    # Key boundaries
+    T_min = years.min()  # ~100.7 years (fastest)
+    T_elev = TOTAL_PAYLOAD / TOTAL_ELEVATOR_CAPACITY  # ~186 years (elevator only)
+    E_min = energy[years >= T_elev].min() if any(years >= T_elev) else energy.min()
+    
+    # ========== Plot 1: Trade-off Curve with λ Iso-cost Lines ==========
+    ax1 = axes[0, 0]
+    
+    # Main curve
+    ax1.plot(years, energy, 'b-', linewidth=2.5, label='Energy-Time Trade-off')
+    
+    # Mark key points
+    ax1.axvline(x=T_elev, color='green', linestyle='--', alpha=0.7, label=f'Elevator-only: {T_elev:.1f} years')
+    ax1.axvline(x=T_min, color='red', linestyle='--', alpha=0.7, label=f'Minimum time: {T_min:.1f} years')
+    
+    # Draw iso-cost lines for different λ (focus on 400-600 range)
+    lambda_values = [420, 480, 500, 550]
+    colors = ['#2ecc71', '#e74c3c', '#9b59b6', '#3498db']
+    
+    for lam, color in zip(lambda_values, colors):
+        opt = find_optimal_point(df, lam)
+        # Iso-cost line: E + λT = const → E = const - λT
+        T_line = np.linspace(80, 220, 100)
+        E_line = opt['total_cost'] - lam * T_line
+        valid = (E_line > 0) & (E_line < 70000)
+        ax1.plot(T_line[valid], E_line[valid], '--', color=color, alpha=0.6, linewidth=1.5)
+        ax1.plot(opt['years'], opt['energy_PJ'], 'o', color=color, markersize=12,
+                markeredgecolor='black', markeredgewidth=1.5,
+                label=f'λ={lam}: T={opt["years"]:.1f}y, E={opt["energy_PJ"]:.0f}PJ')
+    
+    ax1.set_xlabel('Construction Timeline T (years)', fontsize=12)
+    ax1.set_ylabel('Total Energy E (PJ)', fontsize=12)
+    ax1.set_title('Energy-Time Trade-off with λ Iso-cost Lines (λ=400-600)\n$J = E + λT$', fontsize=13)
+    ax1.legend(loc='upper right', fontsize=9)
+    ax1.grid(True, alpha=0.3)
+    ax1.set_xlim(95, 200)
+    ax1.set_ylim(10000, 65000)
+    
+    # ========== Plot 2: Marginal Energy Saving Rate ==========
+    ax2 = axes[0, 1]
+    
+    marginal = calculate_marginal_energy_saving(df)
+    
+    ax2.plot(years, marginal, 'r-', linewidth=2, label='Marginal Energy Saving -dE/dT')
+    ax2.axhline(y=0, color='black', linestyle='-', alpha=0.3)
+    
+    # Mark critical λ values in 400-600 range
+    for lam, color in zip([450, 480, 500, 550], ['#2ecc71', '#e74c3c', '#9b59b6', '#3498db']):
+        ax2.axhline(y=lam, color=color, linestyle='--', alpha=0.7, label=f'λ = {lam} PJ/year')
+        # Find intersection
+        intersect_idx = np.argmin(np.abs(marginal - lam))
+        ax2.plot(years[intersect_idx], marginal[intersect_idx], 'o', color=color, markersize=8)
+    
+    ax2.set_xlabel('Construction Timeline T (years)', fontsize=12)
+    ax2.set_ylabel('Marginal Energy Saving -dE/dT (PJ/year)', fontsize=12)
+    ax2.set_title('Marginal Analysis: Optimal Condition is -dE/dT = λ', fontsize=13)
+    ax2.legend(loc='upper right', fontsize=9)
+    ax2.grid(True, alpha=0.3)
+    ax2.set_xlim(95, 200)
+    ax2.set_ylim(350, 620)
+    
+    # ========== Plot 3: Sensitivity Analysis (400-600 range) ==========
+    ax3 = axes[1, 0]
+    
+    lambda_range = np.linspace(400, 600, 200)
+    sensitivity_df = sensitivity_analysis(df, lambda_range)
+    
+    # Plot optimal years vs λ
+    ax3.plot(sensitivity_df['lambda_PJ_per_year'], sensitivity_df['optimal_years'], 
+             'b-', linewidth=2.5, label='Optimal Timeline T*')
+    
+    # Mark key regions
+    ax3.axhline(y=T_elev, color='green', linestyle='--', alpha=0.7, label=f'Elevator-only: {T_elev:.1f}y')
+    ax3.axhline(y=T_min, color='red', linestyle='--', alpha=0.7, label=f'Min timeline: {T_min:.1f}y')
+    ax3.axhline(y=139, color='orange', linestyle=':', linewidth=2, alpha=0.8, label='Original knee: 139y')
+    
+    # Find λ corresponding to 139 years
+    idx_139 = np.argmin(np.abs(sensitivity_df['optimal_years'] - 139))
+    if idx_139 < len(sensitivity_df):
+        lambda_139 = sensitivity_df['lambda_PJ_per_year'].iloc[idx_139]
+        ax3.axvline(x=lambda_139, color='orange', linestyle=':', linewidth=2, alpha=0.6)
+        ax3.scatter([lambda_139], [139], s=150, c='orange', marker='*', zorder=5, 
+                   edgecolors='black', linewidths=1.5, label=f'λ≈{lambda_139:.0f} for T*=139y')
+    
+    # Mark critical transition
+    ax3.axvline(x=480, color='purple', linestyle='--', alpha=0.5)
+    ax3.text(482, 175, 'Critical\nTransition', fontsize=9, color='purple')
+    
+    ax3.set_xlabel('Time Opportunity Cost λ (PJ/year)', fontsize=12)
+    ax3.set_ylabel('Optimal Timeline T* (years)', fontsize=12)
+    ax3.set_title('Sensitivity Analysis: Optimal Timeline vs λ (400-600 range)', fontsize=13)
+    ax3.legend(loc='upper right', fontsize=9)
+    ax3.grid(True, alpha=0.3)
+    ax3.set_xlim(400, 600)
+    ax3.set_ylim(95, 195)
+    
+    # ========== Plot 4: Total Cost Curves (400-600 range) ==========
+    ax4 = axes[1, 1]
+    
+    for lam, color in [(450, '#2ecc71'), (480, '#e74c3c'), (500, '#9b59b6'), (550, '#3498db')]:
+        total_cost = calculate_total_cost(df, lam)
+        ax4.plot(years, total_cost / 1000, color=color, linestyle='-', 
+                linewidth=2, label=f'λ={lam} PJ/year')
+        
+        # Mark minimum
+        opt = find_optimal_point(df, lam)
+        ax4.plot(opt['years'], opt['total_cost'] / 1000, 'o', color=color, markersize=10,
+                markeredgecolor='black', markeredgewidth=1.5)
+    
+    ax4.set_xlabel('Construction Timeline T (years)', fontsize=12)
+    ax4.set_ylabel('Total Cost J = E + λT (×10³ PJ)', fontsize=12)
+    ax4.set_title('Total Cost Function for λ = 400-600 PJ/year', fontsize=13)
+    ax4.legend(loc='upper right', fontsize=10)
+    ax4.grid(True, alpha=0.3)
+    ax4.set_xlim(95, 200)
+    
+    plt.tight_layout()
+    plt.savefig(save_path, dpi=150, bbox_inches='tight')
+    print(f"Lambda analysis plot saved to: {save_path}")
+    
+    return fig
+
+
+def plot_decision_recommendation(
+    df: pd.DataFrame,
+    save_path: str = '/Volumes/Files/code/mm/20260130_b/p1/lambda_decision_map.png'
+):
+    """
+    Decision map showing optimal choice based on λ preference
+    """
+    fig, ax = plt.subplots(figsize=(12, 8))
+    
+    years = df['years'].values
+    energy = df['energy_PJ'].values
+    
+    # Main trade-off curve
+    ax.plot(years, energy, 'b-', linewidth=3, label='Feasible Trade-off Curve')
+    
+    # Key boundaries
+    T_elev = TOTAL_PAYLOAD / TOTAL_ELEVATOR_CAPACITY
+    T_min = years.min()
+    
+    # Shade decision regions
+    # Region 1: Low λ (cost priority) → longer timeline
+    ax.axvspan(160, 190, alpha=0.2, color='green', label='Low λ (<150): Cost Priority')
+    # Region 2: Medium λ (balanced) → middle ground
+    ax.axvspan(130, 160, alpha=0.2, color='yellow', label='Medium λ (150-250): Balanced')
+    # Region 3: High λ (time priority) → shorter timeline
+    ax.axvspan(100, 130, alpha=0.2, color='red', label='High λ (>250): Time Priority')
+    
+    # Mark specific strategy points
+    strategies = [
+        {'name': 'A: Cost-Prioritized', 'years': 186, 'lambda': 0, 'color': 'green'},
+        {'name': 'C: Balanced (λ≈200)', 'years': 139, 'lambda': 200, 'color': 'orange'},
+        {'name': 'B: Time-Prioritized', 'years': 101, 'lambda': 500, 'color': 'red'},
+    ]
+    
+    for s in strategies:
+        idx = np.argmin(np.abs(years - s['years']))
+        ax.plot(years[idx], energy[idx], 'o', color=s['color'], markersize=15, 
+                markeredgecolor='black', markeredgewidth=2)
+        ax.annotate(s['name'], (years[idx], energy[idx]), 
+                   textcoords="offset points", xytext=(10, 10), fontsize=11,
+                   fontweight='bold', color=s['color'])
+    
+    # Add decision guidance text
+    textstr = '\n'.join([
+        'Decision Guidance:',
+        '─────────────────',
+        'λ < 150 PJ/year → Strategy A',
+        '  (Long-term cost efficiency)',
+        '',
+        '150 ≤ λ ≤ 250 → Strategy C',
+        '  (Balanced trade-off)',
+        '',
+        'λ > 250 PJ/year → Strategy B',
+        '  (Time-critical mission)',
+    ])
+    props = dict(boxstyle='round', facecolor='wheat', alpha=0.8)
+    ax.text(0.02, 0.98, textstr, transform=ax.transAxes, fontsize=10,
+            verticalalignment='top', bbox=props, family='monospace')
+    
+    ax.set_xlabel('Construction Timeline T (years)', fontsize=13)
+    ax.set_ylabel('Total Energy E (PJ)', fontsize=13)
+    ax.set_title('Decision Map: Optimal Strategy Selection Based on Time Opportunity Cost λ', fontsize=14)
+    ax.legend(loc='upper right', fontsize=10)
+    ax.grid(True, alpha=0.3)
+    ax.set_xlim(95, 200)
+    ax.set_ylim(10000, 65000)
+    
+    plt.tight_layout()
+    plt.savefig(save_path, dpi=150, bbox_inches='tight')
+    print(f"Decision map saved to: {save_path}")
+    
+    return fig
+
+
+# ============== Critical Point Analysis ==============
+
+def analyze_curve_structure(df: pd.DataFrame) -> Dict:
+    """
+    Analyze the structure of the trade-off curve to understand
+    why certain λ values lead to specific optimal points.
+    """
+    years = df['years'].values
+    energy = df['energy_PJ'].values
+    
+    # Calculate marginal rates
+    marginal = -np.gradient(energy, years)
+    
+    # Find the elevator-only boundary
+    T_elev = TOTAL_PAYLOAD / TOTAL_ELEVATOR_CAPACITY
+    idx_elev = np.argmin(np.abs(years - T_elev))
+    
+    # Analyze marginal rate distribution
+    # Region 1: T > T_elev (pure elevator, marginal ≈ 0)
+    # Region 2: T < T_elev (need rockets, marginal > 0)
+    
+    # Find critical points where marginal rate changes significantly
+    marginal_near_elev = marginal[idx_elev - 5:idx_elev + 5]
+    marginal_at_139 = marginal[np.argmin(np.abs(years - 139))]
+    marginal_at_101 = marginal[np.argmin(np.abs(years - 101))]
+    
+    return {
+        'T_elev': T_elev,
+        'idx_elev': idx_elev,
+        'marginal_at_elev': marginal[idx_elev],
+        'marginal_at_139': marginal_at_139,
+        'marginal_at_101': marginal_at_101,
+        'energy_at_elev': energy[idx_elev],
+        'energy_at_139': energy[np.argmin(np.abs(years - 139))],
+        'energy_at_101': energy[np.argmin(np.abs(years - 101))],
+    }
+
+
+def find_critical_lambda(df: pd.DataFrame) -> Dict:
+    """
+    Find the critical λ values where optimal point transitions occur.
+    """
+    years = df['years'].values
+    energy = df['energy_PJ'].values
+    
+    # Dense lambda scan
+    lambda_range = np.linspace(1, 1000, 2000)
+    
+    transitions = []
+    prev_years = None
+    
+    for lam in lambda_range:
+        opt = find_optimal_point(df, lam)
+        if prev_years is not None and abs(opt['years'] - prev_years) > 5:
+            transitions.append({
+                'lambda': lam,
+                'from_years': prev_years,
+                'to_years': opt['years'],
+            })
+        prev_years = opt['years']
+    
+    return transitions
+
+
+def plot_comprehensive_analysis(
+    df: pd.DataFrame,
+    save_path: str = '/Volumes/Files/code/mm/20260130_b/p1/lambda_comprehensive.png'
+):
+    """
+    Comprehensive plot showing:
+    1. Trade-off curve with marginal rates
+    2. Critical λ transitions
+    3. Decision regions
+    """
+    fig = plt.figure(figsize=(16, 14))
+    
+    years = df['years'].values
+    energy = df['energy_PJ'].values
+    marginal = calculate_marginal_energy_saving(df)
+    
+    T_elev = TOTAL_PAYLOAD / TOTAL_ELEVATOR_CAPACITY
+    T_min = years.min()
+    
+    # ========== Plot 1: Trade-off curve with annotations ==========
+    ax1 = fig.add_subplot(2, 2, 1)
+    
+    ax1.plot(years, energy / 1000, 'b-', linewidth=2.5, label='Trade-off Curve')
+    
+    # Mark key points
+    key_points = [
+        (T_min, 'Minimum Time\n(~101 years)', 'red'),
+        (139, 'Original Knee\n(139 years)', 'orange'),
+        (T_elev, 'Elevator-Only\n(~186 years)', 'green'),
+    ]
+    
+    for t, label, color in key_points:
+        idx = np.argmin(np.abs(years - t))
+        ax1.plot(years[idx], energy[idx] / 1000, 'o', color=color, markersize=12,
+                markeredgecolor='black', markeredgewidth=2, zorder=5)
+        ax1.annotate(label, (years[idx], energy[idx] / 1000),
+                    textcoords="offset points", xytext=(10, 10), fontsize=10,
+                    color=color, fontweight='bold')
+    
+    ax1.set_xlabel('Construction Timeline T (years)', fontsize=12)
+    ax1.set_ylabel('Total Energy E (×10³ PJ)', fontsize=12)
+    ax1.set_title('Energy-Time Trade-off Curve', fontsize=14)
+    ax1.grid(True, alpha=0.3)
+    ax1.set_xlim(95, 200)
+    ax1.legend(loc='upper right')
+    
+    # ========== Plot 2: Marginal Rate Analysis ==========
+    ax2 = fig.add_subplot(2, 2, 2)
+    
+    ax2.plot(years, marginal, 'r-', linewidth=2, label='Marginal Saving Rate')
+    ax2.fill_between(years, 0, marginal, alpha=0.3, color='red')
+    
+    # Mark critical thresholds
+    ax2.axhline(y=480, color='purple', linestyle='--', linewidth=2,
+               label='Critical λ ≈ 480 PJ/year')
+    ax2.axvline(x=T_elev, color='green', linestyle=':', alpha=0.7)
+    
+    # Annotate the jump at elevator boundary
+    ax2.annotate('Marginal rate jumps\nat elevator capacity limit',
+                xy=(T_elev, marginal[np.argmin(np.abs(years - T_elev))]),
+                xytext=(150, 400), fontsize=10,
+                arrowprops=dict(arrowstyle='->', color='black'))
+    
+    ax2.set_xlabel('Construction Timeline T (years)', fontsize=12)
+    ax2.set_ylabel('Marginal Energy Saving -dE/dT (PJ/year)', fontsize=12)
+    ax2.set_title('Marginal Analysis: Why 186 years is optimal for most λ', fontsize=14)
+    ax2.grid(True, alpha=0.3)
+    ax2.set_xlim(95, 200)
+    ax2.set_ylim(-50, 600)
+    ax2.legend(loc='upper right')
+    
+    # ========== Plot 3: λ Sensitivity with Phase Transitions (400-600 focus) ==========
+    ax3 = fig.add_subplot(2, 2, 3)
+    
+    lambda_range = np.linspace(400, 600, 200)
+    opt_years = []
+    for lam in lambda_range:
+        opt = find_optimal_point(df, lam)
+        opt_years.append(opt['years'])
+    
+    ax3.plot(lambda_range, opt_years, 'b-', linewidth=2.5)
+    
+    # Shade phases
+    ax3.axhspan(180, 190, alpha=0.3, color='green', label='Phase 1: Elevator-Only (λ < 480)')
+    ax3.axhspan(100, 145, alpha=0.3, color='red', label='Phase 2: Hybrid (λ > 480)')
+    
+    # Mark critical λ
+    ax3.axvline(x=480, color='purple', linestyle='--', linewidth=2)
+    ax3.annotate('Critical Transition\nλ ≈ 480 PJ/year',
+                xy=(480, 160), fontsize=11, color='purple', fontweight='bold',
+                ha='center')
+    
+    # Mark 139 year point
+    ax3.axhline(y=139, color='orange', linestyle=':', linewidth=2, alpha=0.8)
+    ax3.scatter([500], [139], s=200, c='orange', marker='*', zorder=5, 
+               edgecolors='black', linewidths=2, label='T*=139y at λ≈500')
+    
+    ax3.set_xlabel('Time Opportunity Cost λ (PJ/year)', fontsize=12)
+    ax3.set_ylabel('Optimal Timeline T* (years)', fontsize=12)
+    ax3.set_title('Phase Transition in Optimal Strategy (λ=400-600)', fontsize=14)
+    ax3.grid(True, alpha=0.3)
+    ax3.set_xlim(400, 600)
+    ax3.set_ylim(95, 195)
+    ax3.legend(loc='upper right')
+    
+    # ========== Plot 4: Decision Summary Table ==========
+    ax4 = fig.add_subplot(2, 2, 4)
+    ax4.axis('off')
+    
+    # Create summary table
+    summary_text = """
+    ┌─────────────────────────────────────────────────────────────────┐
+    │            KEY FINDINGS FROM λ COST ANALYSIS                    │
+    ├─────────────────────────────────────────────────────────────────┤
+    │                                                                 │
+    │  1. CURVE STRUCTURE                                             │
+    │     • Sharp discontinuity at T = 186 years (elevator capacity)  │
+    │     • Marginal rate jumps from ~0 to ~480 PJ/year at boundary   │
+    │                                                                 │
+    │  2. OPTIMAL POINT SELECTION                                     │
+    │     • λ < 480 PJ/year  →  T* = 186 years (elevator-only)        │
+    │     • λ ≈ 500 PJ/year  →  T* = 139 years (original knee)        │
+    │     • λ > 600 PJ/year  →  T* → 101 years (time-priority)        │
+    │                                                                 │
+    │  3. IMPLICATIONS FOR THE 139-YEAR KNEE POINT                    │
+    │     • Requires implicit assumption: λ ≈ 500 PJ/year             │
+    │     • This means: 1 year delay costs ~500 PJ opportunity cost   │
+    │     • Equivalent to: ~0.5% of total elevator energy per year    │
+    │                                                                 │
+    │  4. RECOMMENDATION                                              │
+    │     • Either justify λ ≈ 500 PJ/year with physical reasoning    │
+    │     • Or acknowledge 186 years as cost-optimal baseline         │
+    │     • Present 139 years as a time-constrained scenario          │
+    │                                                                 │
+    └─────────────────────────────────────────────────────────────────┘
+    """
+    
+    ax4.text(0.05, 0.95, summary_text, transform=ax4.transAxes,
+            fontsize=11, verticalalignment='top', family='monospace',
+            bbox=dict(boxstyle='round', facecolor='lightyellow', alpha=0.8))
+    
+    plt.tight_layout()
+    plt.savefig(save_path, dpi=150, bbox_inches='tight')
+    print(f"Comprehensive analysis saved to: {save_path}")
+    
+    return fig
+
+
+# ============== Main Analysis ==============
+
+def main():
+    print("=" * 70)
+    print("Lambda Time Cost Analysis for Moon Colony Logistics")
+    print("=" * 70)
+    
+    # Generate trade-off curve
+    print("\n[1] Generating Energy-Time trade-off curve...")
+    df = generate_tradeoff_curve(year_min=100, year_max=220, num_points=500)
+    print(f"    Generated {len(df)} data points")
+    
+    # Key statistics
+    T_min = df['years'].min()
+    T_max = df['years'].max()
+    E_min = df['energy_PJ'].min()
+    E_max = df['energy_PJ'].max()
+    T_elev = TOTAL_PAYLOAD / TOTAL_ELEVATOR_CAPACITY
+    
+    print(f"\n[2] Trade-off Curve Statistics:")
+    print(f"    Timeline range: {T_min:.1f} - {T_max:.1f} years")
+    print(f"    Energy range: {E_min:.0f} - {E_max:.0f} PJ")
+    print(f"    Elevator-only timeline: {T_elev:.1f} years")
+    
+    # Curve structure analysis
+    print("\n[3] Curve Structure Analysis:")
+    structure = analyze_curve_structure(df)
+    print(f"    At elevator boundary (T={structure['T_elev']:.1f}y):")
+    print(f"      - Energy: {structure['energy_at_elev']:.0f} PJ")
+    print(f"      - Marginal rate: {structure['marginal_at_elev']:.1f} PJ/year")
+    print(f"    At T=139 years:")
+    print(f"      - Energy: {structure['energy_at_139']:.0f} PJ")
+    print(f"      - Marginal rate: {structure['marginal_at_139']:.1f} PJ/year")
+    print(f"    At T=101 years:")
+    print(f"      - Energy: {structure['energy_at_101']:.0f} PJ")
+    print(f"      - Marginal rate: {structure['marginal_at_101']:.1f} PJ/year")
+    
+    # Find critical transitions
+    print("\n[4] Critical λ Transitions:")
+    transitions = find_critical_lambda(df)
+    for t in transitions:
+        print(f"    λ ≈ {t['lambda']:.0f} PJ/year: T* jumps from {t['from_years']:.0f}y to {t['to_years']:.0f}y")
+    
+    # Sensitivity analysis
+    print("\n[5] Sensitivity Analysis Results:")
+    print("    " + "-" * 55)
+    print(f"    {'λ (PJ/year)':<15} {'Optimal T (years)':<20} {'Energy (PJ)':<15}")
+    print("    " + "-" * 55)
+    
+    test_lambdas = [100, 200, 300, 400, 450, 480, 500, 550, 600]
+    sensitivity_results = []
+    
+    for lam in test_lambdas:
+        opt = find_optimal_point(df, lam)
+        print(f"    {lam:<15.0f} {opt['years']:<20.1f} {opt['energy_PJ']:<15.0f}")
+        sensitivity_results.append(opt)
+    
+    # Find λ that gives 139 years
+    print("\n[6] Original Knee Point Analysis (139 years):")
+    lambda_for_139 = None
+    for lam in np.linspace(400, 600, 1000):
+        opt = find_optimal_point(df, lam)
+        if abs(opt['years'] - 139) < 1:
+            lambda_for_139 = lam
+            print(f"    λ ≈ {lam:.0f} PJ/year corresponds to T* ≈ 139 years")
+            break
+    
+    if lambda_for_139:
+        print(f"\n    INTERPRETATION:")
+        print(f"    To justify 139-year knee point, one must argue that:")
+        print(f"    • Each year of delay costs ~{lambda_for_139:.0f} PJ in opportunity")
+        print(f"    • This is {lambda_for_139/E_min*100:.1f}% of minimum total energy per year")
+        print(f"    • Over 47 years (139→186), this amounts to {lambda_for_139*47:.0f} PJ")
+    
+    # Generate plots
+    print("\n[7] Generating visualization plots...")
+    plot_lambda_analysis(df)
+    plot_decision_recommendation(df)
+    plot_comprehensive_analysis(df)
+    
+    # Save sensitivity data
+    sensitivity_df = sensitivity_analysis(df, np.linspace(50, 600, 120))
+    sensitivity_df.to_csv('/Volumes/Files/code/mm/20260130_b/p1/lambda_sensitivity.csv', index=False)
+    print("    Data saved to: lambda_sensitivity.csv")
+    
+    # Paper modification recommendations
+    print("\n" + "=" * 70)
+    print("RECOMMENDATIONS FOR PAPER MODIFICATION")
+    print("=" * 70)
+    print("""
+    1. REFRAME THE OPTIMIZATION PROBLEM
+       Current: "Multi-objective Pareto optimization"
+       Suggested: "Constrained optimization with time-cost trade-off"
+       
+    2. INTRODUCE λ AS DECISION PARAMETER
+       Add equation: J = E_total + λ × T
+       where λ represents "time opportunity cost" (PJ/year)
+       
+    3. JUSTIFY THE KNEE POINT SELECTION
+       Option A: Argue λ ≈ 480-500 PJ/year is reasonable because:
+                 - Delayed lunar resource extraction
+                 - Extended Earth-side operational costs
+                 - Strategic/geopolitical value of early completion
+       
+       Option B: Present multiple scenarios:
+                 - "Cost-optimal" (λ < 480): T* = 186 years
+                 - "Balanced" (λ ≈ 500): T* = 139 years  
+                 - "Time-critical" (λ > 600): T* → 101 years
+    
+    4. ADD SENSITIVITY ANALYSIS FIGURE
+       Show how optimal T* changes with λ (Figure generated)
+       
+    5. ACKNOWLEDGE THE DISCONTINUITY
+       Note that the trade-off curve has a sharp transition at
+       T = 186 years due to elevator capacity constraints
+    """)
+    
+    print("=" * 70)
+    print("Analysis Complete!")
+    print("=" * 70)
+    
+    return df, sensitivity_results
+
+
+if __name__ == "__main__":
+    df, results = main()

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p1/pareto_optimization.py

@@ -37,8 +37,8 @@ ELEVATOR_SPECIFIC_ENERGY = 157.2e9  # J per metric ton (157.2 MJ/kg * 1000)
 
 # 火箭参数
 PAYLOAD_PER_LAUNCH = 125  # metric tons per launch
-ISP = 450
+ISP = 363  # 比冲 (秒) - 液氧甲烷 (LOX/CH4, Raptor-class)
-SPECIFIC_FUEL_ENERGY = 15.5e6  # J/kg
+SPECIFIC_FUEL_ENERGY = 11.9e6  # J/kg
 ALPHA = 0.10
 NUM_STAGES = 3
 DELTA_V_BASE = 13300  # m/s

p1/rocket_launch_scenario.py

@@ -35,8 +35,8 @@ PAYLOAD_PER_LAUNCH = 125  # metric tons per launch (average of 100-150)
 TOTAL_LAUNCHES_NEEDED = TOTAL_PAYLOAD / PAYLOAD_PER_LAUNCH  # 800,000 launches
 
 # 火箭参数
-ISP = 450  # 比冲 (秒) - 液氧液氢
+ISP = 363  # 比冲 (秒) - 液氧甲烷 (LOX/CH4, Raptor-class)
-SPECIFIC_FUEL_ENERGY = 15.5e6  # J/kg 燃料比能量
+SPECIFIC_FUEL_ENERGY = 11.9e6  # J/kg 燃料比能量
 ALPHA = 0.10  # 结构系数
 NUM_STAGES = 3  # 3级火箭
 

p1/sensitivity_alpha.csv

@@ -0,0 +1,10 @@
+alpha,fuel_ratio,min_timeline,optimal_T_lambda504,optimal_E_lambda504
+0.06,63.02605457895038,101.10220440881763,101.10220440881763,43868.89867149817
+0.07,68.29395722323875,101.10220440881763,101.10220440881763,46867.31671096497
+0.08,74.20197456904802,101.10220440881763,101.10220440881763,50235.617816131955
+0.09,80.85242443796794,101.10220440881763,101.10220440881763,54033.847318345346
+0.1,88.36809547494757,101.10220440881763,138.51371083876296,38973.75515736591
+0.11000000000000001,96.89721699661537,101.10220440881763,185.65220894049406,16023.925174458536
+0.12000000000000001,106.61986205811633,101.10220440881763,185.65220894049406,16059.242009669968
+0.13,117.75626714631346,101.10220440881763,186.40043906909295,15720.0
+0.14,130.57774039779378,101.10220440881763,186.40043906909295,15720.0

p1/sensitivity_analysis.py

@@ -0,0 +1,763 @@
+"""
+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
+"""
+
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from matplotlib import rcParams
+import pandas as pd
+from typing import Dict, List, Tuple, Optional
+from dataclasses import dataclass
+import warnings
+warnings.filterwarnings('ignore')
+
+# Font settings
+rcParams['font.sans-serif'] = ['Arial Unicode MS', 'DejaVu Sans', 'SimHei']
+rcParams['axes.unicode_minus'] = False
+
+# ============== Physical Constants ==============
+G0 = 9.81  # m/s²
+OMEGA_EARTH = 7.27e-5  # rad/s
+R_EARTH = 6.371e6  # m
+
+# Baseline Mission parameters
+TOTAL_PAYLOAD = 100e6  # 100 million metric tons
+
+# Baseline Space Elevator parameters
+BASELINE_NUM_ELEVATORS = 3
+BASELINE_ELEVATOR_CAPACITY_PER_YEAR = 179000  # metric tons per elevator per year
+BASELINE_ELEVATOR_SPECIFIC_ENERGY = 157.2e9  # J per metric ton
+
+# Baseline Rocket parameters
+BASELINE_PAYLOAD_PER_LAUNCH = 125  # metric tons (range: 100-150)
+BASELINE_ISP = 363  # seconds (LOX/CH4)
+BASELINE_SPECIFIC_FUEL_ENERGY = 11.9e6  # J/kg
+BASELINE_ALPHA = 0.10  # structural coefficient
+BASELINE_NUM_STAGES = 3
+BASELINE_DELTA_V = 13300  # m/s
+
+# Baseline Launch frequency
+BASELINE_LAUNCHES_PER_DAY = 1  # per site
+
+
+# ============== Launch Sites ==============
+@dataclass
+class LaunchSite:
+    name: str
+    short_name: str
+    latitude: float
+    
+    @property
+    def abs_latitude(self) -> float:
+        return abs(self.latitude)
+    
+    def delta_v_loss(self, omega=OMEGA_EARTH, r=R_EARTH) -> float:
+        v_equator = omega * r
+        v_site = omega * r * np.cos(np.radians(self.abs_latitude))
+        return v_equator - v_site
+
+
+LAUNCH_SITES = [
+    LaunchSite("Kourou", "Kourou", 5.2),
+    LaunchSite("SDSC", "SDSC", 13.7),
+    LaunchSite("Texas", "Texas", 26.0),
+    LaunchSite("Florida", "Florida", 28.5),
+    LaunchSite("California", "California", 34.7),
+    LaunchSite("Virginia", "Virginia", 37.8),
+    LaunchSite("Taiyuan", "Taiyuan", 38.8),
+    LaunchSite("Mahia", "Mahia", 39.3),
+    LaunchSite("Baikonur", "Baikonur", 45.6),
+    LaunchSite("Alaska", "Alaska", 57.4),
+]
+LAUNCH_SITES = sorted(LAUNCH_SITES, key=lambda x: x.abs_latitude)
+NUM_SITES = len(LAUNCH_SITES)
+
+
+# ============== Core Calculation Functions ==============
+
+def fuel_ratio_multistage(delta_v: float, isp: float, alpha: float, num_stages: int) -> float:
+    """Calculate multi-stage rocket fuel/payload ratio"""
+    ve = isp * G0
+    delta_v_per_stage = delta_v / num_stages
+    R_stage = np.exp(delta_v_per_stage / ve)
+    
+    denominator = 1 - alpha * (R_stage - 1)
+    if denominator <= 0:
+        return np.inf
+    
+    k_stage = (R_stage - 1) / denominator
+    
+    total_fuel_ratio = 0
+    remaining_ratio = 1.0
+    
+    for _ in range(num_stages):
+        fuel_this_stage = remaining_ratio * k_stage
+        total_fuel_ratio += fuel_this_stage
+        remaining_ratio *= (1 + k_stage * (1 + alpha))
+    
+    return total_fuel_ratio
+
+
+def calculate_scenario(
+    completion_years: float,
+    payload_per_launch: float = BASELINE_PAYLOAD_PER_LAUNCH,
+    elevator_capacity: float = BASELINE_NUM_ELEVATORS * BASELINE_ELEVATOR_CAPACITY_PER_YEAR,
+    launches_per_day: float = BASELINE_LAUNCHES_PER_DAY,
+    isp: float = BASELINE_ISP,
+    alpha: float = BASELINE_ALPHA,
+    num_stages: int = BASELINE_NUM_STAGES,
+    delta_v_base: float = BASELINE_DELTA_V,
+    specific_fuel_energy: float = BASELINE_SPECIFIC_FUEL_ENERGY,
+) -> Optional[Dict]:
+    """Calculate scenario for given parameters"""
+    
+    # Space elevator transport
+    elevator_payload = min(elevator_capacity * completion_years, TOTAL_PAYLOAD)
+    elevator_energy = elevator_payload * BASELINE_ELEVATOR_SPECIFIC_ENERGY
+    
+    # Remaining payload for rockets
+    remaining_payload = TOTAL_PAYLOAD - elevator_payload
+    
+    if remaining_payload <= 0:
+        return {
+            'years': completion_years,
+            'elevator_payload': elevator_payload,
+            'rocket_payload': 0,
+            'total_energy_PJ': elevator_energy / 1e15,
+            'rocket_launches': 0,
+            'elevator_fraction': 1.0,
+            'feasible': True,
+        }
+    
+    # Rocket launches needed
+    rocket_launches_needed = int(np.ceil(remaining_payload / payload_per_launch))
+    
+    # Check feasibility
+    days_available = completion_years * 365
+    max_launches_per_site = int(days_available * launches_per_day)
+    total_rocket_capacity = NUM_SITES * max_launches_per_site * payload_per_launch
+    
+    if remaining_payload > total_rocket_capacity:
+        return {
+            'years': completion_years,
+            'feasible': False,
+            'shortage': remaining_payload - total_rocket_capacity,
+        }
+    
+    # Calculate rocket energy (low-latitude priority)
+    rocket_energy = 0
+    remaining_launches = rocket_launches_needed
+    
+    for site in LAUNCH_SITES:
+        if remaining_launches <= 0:
+            break
+        allocated = min(remaining_launches, max_launches_per_site)
+        
+        # Calculate fuel ratio for this site
+        total_dv = delta_v_base + site.delta_v_loss()
+        k = fuel_ratio_multistage(total_dv, isp, alpha, num_stages)
+        fuel_per_ton = k * 1000  # kg fuel per metric ton payload
+        energy_per_ton = fuel_per_ton * specific_fuel_energy
+        
+        rocket_energy += energy_per_ton * payload_per_launch * allocated
+        remaining_launches -= allocated
+    
+    total_energy = elevator_energy + rocket_energy
+    
+    return {
+        'years': completion_years,
+        'elevator_payload': elevator_payload,
+        'rocket_payload': remaining_payload,
+        'total_energy_PJ': total_energy / 1e15,
+        'rocket_launches': rocket_launches_needed,
+        'elevator_fraction': elevator_payload / TOTAL_PAYLOAD,
+        'feasible': True,
+    }
+
+
+def find_minimum_timeline(
+    payload_per_launch: float = BASELINE_PAYLOAD_PER_LAUNCH,
+    elevator_capacity: float = BASELINE_NUM_ELEVATORS * BASELINE_ELEVATOR_CAPACITY_PER_YEAR,
+    launches_per_day: float = BASELINE_LAUNCHES_PER_DAY,
+    **kwargs
+) -> float:
+    """Find minimum feasible timeline"""
+    for years in np.linspace(50, 300, 500):
+        result = calculate_scenario(
+            years, payload_per_launch, elevator_capacity, launches_per_day, **kwargs
+        )
+        if result and result.get('feasible', False):
+            return years
+    return 300  # fallback
+
+
+def generate_tradeoff_curve(
+    year_min: float = None,
+    year_max: float = 250,
+    num_points: int = 200,
+    **kwargs
+) -> pd.DataFrame:
+    """Generate trade-off curve for given parameters"""
+    
+    if year_min is None:
+        year_min = find_minimum_timeline(**kwargs)
+    
+    years_range = np.linspace(year_min, year_max, num_points)
+    
+    results = []
+    for years in years_range:
+        scenario = calculate_scenario(years, **kwargs)
+        if scenario and scenario.get('feasible', False):
+            results.append({
+                'years': years,
+                'energy_PJ': scenario['total_energy_PJ'],
+                'elevator_fraction': scenario['elevator_fraction'],
+                'rocket_launches': scenario.get('rocket_launches', 0),
+            })
+    
+    return pd.DataFrame(results)
+
+
+def find_optimal_point(df: pd.DataFrame, lambda_cost: float) -> Dict:
+    """Find optimal point for given λ"""
+    if df.empty:
+        return {'years': np.nan, 'energy_PJ': np.nan}
+    
+    total_cost = df['energy_PJ'].values + lambda_cost * df['years'].values
+    opt_idx = np.argmin(total_cost)
+    
+    return {
+        'years': df['years'].iloc[opt_idx],
+        'energy_PJ': df['energy_PJ'].iloc[opt_idx],
+        'elevator_fraction': df['elevator_fraction'].iloc[opt_idx],
+    }
+
+
+# ============== Sensitivity Analysis Functions ==============
+
+def sensitivity_payload_capacity():
+    """Analyze sensitivity to rocket payload capacity (100-150 tons)"""
+    print("\n[1] Analyzing Rocket Payload Capacity Sensitivity (100-150 tons)...")
+    
+    payload_range = np.linspace(100, 150, 11)
+    results = []
+    
+    for payload in payload_range:
+        elevator_cap = BASELINE_NUM_ELEVATORS * BASELINE_ELEVATOR_CAPACITY_PER_YEAR
+        t_min = find_minimum_timeline(payload_per_launch=payload, elevator_capacity=elevator_cap)
+        t_elev = TOTAL_PAYLOAD / elevator_cap
+        
+        df = generate_tradeoff_curve(
+            year_min=t_min, year_max=250,
+            payload_per_launch=payload, elevator_capacity=elevator_cap
+        )
+        
+        if not df.empty:
+            opt_504 = find_optimal_point(df, 504)
+            energy_at_139 = df[df['years'] >= 139]['energy_PJ'].iloc[0] if any(df['years'] >= 139) else np.nan
+            
+            results.append({
+                'payload_tons': payload,
+                'min_timeline': t_min,
+                'elevator_only_timeline': t_elev,
+                'optimal_T_lambda504': opt_504['years'],
+                'optimal_E_lambda504': opt_504['energy_PJ'],
+                'energy_at_139y': energy_at_139,
+            })
+    
+    return pd.DataFrame(results)
+
+
+def sensitivity_elevator_capacity():
+    """Analyze sensitivity to elevator capacity (±20%)"""
+    print("\n[2] Analyzing Elevator Capacity Sensitivity (±20%)...")
+    
+    baseline_cap = BASELINE_NUM_ELEVATORS * BASELINE_ELEVATOR_CAPACITY_PER_YEAR
+    capacity_factors = np.linspace(0.8, 1.2, 9)
+    results = []
+    
+    for factor in capacity_factors:
+        elevator_cap = baseline_cap * factor
+        t_min = find_minimum_timeline(elevator_capacity=elevator_cap)
+        t_elev = TOTAL_PAYLOAD / elevator_cap
+        
+        df = generate_tradeoff_curve(
+            year_min=t_min, year_max=300,
+            elevator_capacity=elevator_cap
+        )
+        
+        if not df.empty:
+            # Find critical λ
+            lambda_crit = None
+            for lam in np.linspace(300, 700, 200):
+                opt = find_optimal_point(df, lam)
+                if opt['years'] < t_elev - 5:
+                    lambda_crit = lam
+                    break
+            
+            opt_504 = find_optimal_point(df, 504)
+            
+            results.append({
+                'capacity_factor': factor,
+                'capacity_tons_per_year': elevator_cap,
+                'min_timeline': t_min,
+                'elevator_only_timeline': t_elev,
+                'critical_lambda': lambda_crit,
+                'optimal_T_lambda504': opt_504['years'],
+                'optimal_E_lambda504': opt_504['energy_PJ'],
+            })
+    
+    return pd.DataFrame(results)
+
+
+def sensitivity_launch_frequency():
+    """Analyze sensitivity to launch frequency"""
+    print("\n[3] Analyzing Launch Frequency Sensitivity (0.5-2 launches/day)...")
+    
+    frequency_range = np.linspace(0.5, 2.0, 7)
+    results = []
+    
+    for freq in frequency_range:
+        elevator_cap = BASELINE_NUM_ELEVATORS * BASELINE_ELEVATOR_CAPACITY_PER_YEAR
+        t_min = find_minimum_timeline(launches_per_day=freq, elevator_capacity=elevator_cap)
+        t_elev = TOTAL_PAYLOAD / elevator_cap
+        
+        df = generate_tradeoff_curve(
+            year_min=t_min, year_max=250,
+            launches_per_day=freq, elevator_capacity=elevator_cap
+        )
+        
+        if not df.empty:
+            opt_504 = find_optimal_point(df, 504)
+            
+            results.append({
+                'launches_per_day': freq,
+                'min_timeline': t_min,
+                'elevator_only_timeline': t_elev,
+                'optimal_T_lambda504': opt_504['years'],
+                'optimal_E_lambda504': opt_504['energy_PJ'],
+                'rocket_capacity_tons_per_year': freq * 365 * NUM_SITES * BASELINE_PAYLOAD_PER_LAUNCH,
+            })
+    
+    return pd.DataFrame(results)
+
+
+def sensitivity_engine_technology():
+    """Analyze sensitivity to engine technology (Isp)"""
+    print("\n[4] Analyzing Engine Technology Sensitivity (Isp)...")
+    
+    engines = [
+        ('Solid', 280, 5.0e6),
+        ('LOX/Kerosene', 350, 10.3e6),
+        ('LOX/Methane', 363, 11.9e6),
+        ('LOX/Hydrogen', 450, 15.5e6),
+    ]
+    
+    results = []
+    
+    for name, isp, specific_energy in engines:
+        elevator_cap = BASELINE_NUM_ELEVATORS * BASELINE_ELEVATOR_CAPACITY_PER_YEAR
+        t_min = find_minimum_timeline(
+            isp=isp, specific_fuel_energy=specific_energy, elevator_capacity=elevator_cap
+        )
+        
+        df = generate_tradeoff_curve(
+            year_min=t_min, year_max=250,
+            isp=isp, specific_fuel_energy=specific_energy, elevator_capacity=elevator_cap
+        )
+        
+        if not df.empty:
+            opt_504 = find_optimal_point(df, 504)
+            
+            # Calculate fuel ratio at equator
+            k = fuel_ratio_multistage(BASELINE_DELTA_V, isp, BASELINE_ALPHA, BASELINE_NUM_STAGES)
+            
+            results.append({
+                'engine_type': name,
+                'isp_seconds': isp,
+                'specific_energy_MJ_kg': specific_energy / 1e6,
+                'fuel_ratio': k,
+                'min_timeline': t_min,
+                'optimal_T_lambda504': opt_504['years'],
+                'optimal_E_lambda504': opt_504['energy_PJ'],
+            })
+    
+    return pd.DataFrame(results)
+
+
+def sensitivity_structural_coefficient():
+    """Analyze sensitivity to structural coefficient α"""
+    print("\n[5] Analyzing Structural Coefficient Sensitivity (α)...")
+    
+    alpha_range = np.linspace(0.06, 0.14, 9)
+    results = []
+    
+    for alpha in alpha_range:
+        elevator_cap = BASELINE_NUM_ELEVATORS * BASELINE_ELEVATOR_CAPACITY_PER_YEAR
+        t_min = find_minimum_timeline(alpha=alpha, elevator_capacity=elevator_cap)
+        
+        df = generate_tradeoff_curve(
+            year_min=t_min, year_max=250,
+            alpha=alpha, elevator_capacity=elevator_cap
+        )
+        
+        if not df.empty:
+            opt_504 = find_optimal_point(df, 504)
+            k = fuel_ratio_multistage(BASELINE_DELTA_V, BASELINE_ISP, alpha, BASELINE_NUM_STAGES)
+            
+            results.append({
+                'alpha': alpha,
+                'fuel_ratio': k,
+                'min_timeline': t_min,
+                'optimal_T_lambda504': opt_504['years'],
+                'optimal_E_lambda504': opt_504['energy_PJ'],
+            })
+    
+    return pd.DataFrame(results)
+
+
+# ============== Visualization ==============
+
+def plot_sensitivity_analysis(
+    payload_df: pd.DataFrame,
+    elevator_df: pd.DataFrame,
+    frequency_df: pd.DataFrame,
+    engine_df: pd.DataFrame,
+    alpha_df: pd.DataFrame,
+    save_path: str = '/Volumes/Files/code/mm/20260130_b/p1/sensitivity_analysis.png'
+):
+    """Create comprehensive sensitivity analysis visualization"""
+    
+    fig, axes = plt.subplots(2, 3, figsize=(18, 12))
+    
+    # ========== Plot 1: Rocket Payload Capacity ==========
+    ax1 = axes[0, 0]
+    
+    ax1.plot(payload_df['payload_tons'], payload_df['min_timeline'], 
+             'b-o', linewidth=2, markersize=8, label='Minimum Timeline')
+    ax1.plot(payload_df['payload_tons'], payload_df['optimal_T_lambda504'], 
+             'r-s', linewidth=2, markersize=8, label='Optimal T* (λ=504)')
+    
+    ax1.axhline(y=186.2, color='green', linestyle='--', alpha=0.7, label='Elevator-only')
+    ax1.axvline(x=125, color='gray', linestyle=':', alpha=0.7, label='Baseline (125t)')
+    
+    ax1.fill_betweenx([80, 220], 100, 150, alpha=0.1, color='blue', label='Problem range')
+    
+    ax1.set_xlabel('Rocket Payload Capacity (metric tons)', fontsize=11)
+    ax1.set_ylabel('Timeline (years)', fontsize=11)
+    ax1.set_title('(a) Sensitivity to Rocket Payload Capacity\n(Problem specifies 100-150 tons)', fontsize=12)
+    ax1.legend(loc='upper right', fontsize=9)
+    ax1.grid(True, alpha=0.3)
+    ax1.set_xlim(95, 155)
+    ax1.set_ylim(80, 200)
+    
+    # ========== Plot 2: Elevator Capacity ==========
+    ax2 = axes[0, 1]
+    
+    ax2.plot(elevator_df['capacity_factor'] * 100, elevator_df['elevator_only_timeline'], 
+             'g-o', linewidth=2, markersize=8, label='Elevator-only Timeline')
+    ax2.plot(elevator_df['capacity_factor'] * 100, elevator_df['optimal_T_lambda504'], 
+             'r-s', linewidth=2, markersize=8, label='Optimal T* (λ=504)')
+    ax2.plot(elevator_df['capacity_factor'] * 100, elevator_df['min_timeline'], 
+             'b-^', linewidth=2, markersize=8, label='Minimum Timeline')
+    
+    ax2.axvline(x=100, color='gray', linestyle=':', alpha=0.7, label='Baseline')
+    
+    ax2.set_xlabel('Elevator Capacity (% of baseline)', fontsize=11)
+    ax2.set_ylabel('Timeline (years)', fontsize=11)
+    ax2.set_title('(b) Sensitivity to Elevator Capacity (±20%)', fontsize=12)
+    ax2.legend(loc='upper right', fontsize=9)
+    ax2.grid(True, alpha=0.3)
+    ax2.set_xlim(75, 125)
+    
+    # ========== Plot 3: Launch Frequency ==========
+    ax3 = axes[0, 2]
+    
+    ax3.plot(frequency_df['launches_per_day'], frequency_df['min_timeline'], 
+             'b-o', linewidth=2, markersize=8, label='Minimum Timeline')
+    ax3.plot(frequency_df['launches_per_day'], frequency_df['optimal_T_lambda504'], 
+             'r-s', linewidth=2, markersize=8, label='Optimal T* (λ=504)')
+    
+    ax3.axhline(y=186.2, color='green', linestyle='--', alpha=0.7, label='Elevator-only')
+    ax3.axvline(x=1.0, color='gray', linestyle=':', alpha=0.7, label='Baseline (1/day)')
+    
+    ax3.set_xlabel('Launch Frequency (launches/site/day)', fontsize=11)
+    ax3.set_ylabel('Timeline (years)', fontsize=11)
+    ax3.set_title('(c) Sensitivity to Launch Frequency', fontsize=12)
+    ax3.legend(loc='upper right', fontsize=9)
+    ax3.grid(True, alpha=0.3)
+    
+    # ========== Plot 4: Engine Technology ==========
+    ax4 = axes[1, 0]
+    
+    x_pos = np.arange(len(engine_df))
+    width = 0.35
+    
+    bars1 = ax4.bar(x_pos - width/2, engine_df['optimal_E_lambda504'] / 1000, width, 
+                    label='Energy at T* (×10³ PJ)', color='steelblue', alpha=0.8)
+    
+    ax4_twin = ax4.twinx()
+    bars2 = ax4_twin.bar(x_pos + width/2, engine_df['fuel_ratio'], width, 
+                         label='Fuel Ratio k', color='coral', alpha=0.8)
+    
+    ax4.set_xlabel('Engine Type', fontsize=11)
+    ax4.set_ylabel('Energy (×10³ PJ)', fontsize=11, color='steelblue')
+    ax4_twin.set_ylabel('Fuel Ratio k', fontsize=11, color='coral')
+    ax4.set_title('(d) Sensitivity to Engine Technology', fontsize=12)
+    ax4.set_xticks(x_pos)
+    ax4.set_xticklabels(engine_df['engine_type'], rotation=15)
+    ax4.legend(loc='upper left', fontsize=9)
+    ax4_twin.legend(loc='upper right', fontsize=9)
+    ax4.grid(True, alpha=0.3, axis='y')
+    
+    # ========== Plot 5: Structural Coefficient ==========
+    ax5 = axes[1, 1]
+    
+    ax5.plot(alpha_df['alpha'], alpha_df['fuel_ratio'], 
+             'g-o', linewidth=2, markersize=8, label='Fuel Ratio k')
+    
+    ax5_twin = ax5.twinx()
+    ax5_twin.plot(alpha_df['alpha'], alpha_df['optimal_E_lambda504'] / 1000, 
+                  'r-s', linewidth=2, markersize=8, label='Energy at T* (×10³ PJ)')
+    
+    ax5.axvline(x=0.10, color='gray', linestyle=':', alpha=0.7, label='Baseline')
+    
+    ax5.set_xlabel('Structural Coefficient α', fontsize=11)
+    ax5.set_ylabel('Fuel Ratio k', fontsize=11, color='green')
+    ax5_twin.set_ylabel('Energy (×10³ PJ)', fontsize=11, color='red')
+    ax5.set_title('(e) Sensitivity to Structural Coefficient α', fontsize=12)
+    ax5.legend(loc='upper left', fontsize=9)
+    ax5_twin.legend(loc='upper right', fontsize=9)
+    ax5.grid(True, alpha=0.3)
+    
+    # ========== Plot 6: Summary Tornado Chart ==========
+    ax6 = axes[1, 2]
+    
+    # Calculate sensitivity indices (% change in T* for parameter variation)
+    baseline_T = 139  # baseline optimal timeline
+    
+    sensitivities = [
+        ('Payload\n(100→150t)', 
+         (payload_df['optimal_T_lambda504'].iloc[0] - baseline_T) / baseline_T * 100,
+         (payload_df['optimal_T_lambda504'].iloc[-1] - baseline_T) / baseline_T * 100),
+        ('Elevator Cap.\n(80%→120%)', 
+         (elevator_df['optimal_T_lambda504'].iloc[0] - baseline_T) / baseline_T * 100,
+         (elevator_df['optimal_T_lambda504'].iloc[-1] - baseline_T) / baseline_T * 100),
+        ('Launch Freq.\n(0.5→2/day)', 
+         (frequency_df['optimal_T_lambda504'].iloc[0] - baseline_T) / baseline_T * 100,
+         (frequency_df['optimal_T_lambda504'].iloc[-1] - baseline_T) / baseline_T * 100),
+        ('Struct. Coef.\n(0.06→0.14)', 
+         (alpha_df['optimal_T_lambda504'].iloc[0] - baseline_T) / baseline_T * 100,
+         (alpha_df['optimal_T_lambda504'].iloc[-1] - baseline_T) / baseline_T * 100),
+    ]
+    
+    y_pos = np.arange(len(sensitivities))
+    
+    for i, (name, low, high) in enumerate(sensitivities):
+        ax6.barh(i, high - low, left=min(low, high), height=0.6, 
+                color='steelblue' if high > low else 'coral', alpha=0.7)
+        ax6.plot([low, high], [i, i], 'k-', linewidth=2)
+        ax6.plot(low, i, 'ko', markersize=8)
+        ax6.plot(high, i, 'k^', markersize=8)
+    
+    ax6.axvline(x=0, color='black', linestyle='-', linewidth=1)
+    ax6.set_yticks(y_pos)
+    ax6.set_yticklabels([s[0] for s in sensitivities])
+    ax6.set_xlabel('Change in Optimal Timeline T* (%)', fontsize=11)
+    ax6.set_title('(f) Sensitivity Summary (Tornado Chart)', fontsize=12)
+    ax6.grid(True, alpha=0.3, axis='x')
+    
+    plt.tight_layout()
+    plt.savefig(save_path, dpi=150, bbox_inches='tight')
+    print(f"\nSensitivity analysis plot saved to: {save_path}")
+    
+    return fig
+
+
+def plot_tradeoff_comparison(
+    save_path: str = '/Volumes/Files/code/mm/20260130_b/p1/sensitivity_tradeoff.png'
+):
+    """Plot trade-off curves for different parameter values"""
+    
+    fig, axes = plt.subplots(2, 2, figsize=(14, 12))
+    
+    elevator_cap = BASELINE_NUM_ELEVATORS * BASELINE_ELEVATOR_CAPACITY_PER_YEAR
+    
+    # ========== Plot 1: Different Payload Capacities ==========
+    ax1 = axes[0, 0]
+    
+    for payload, color in [(100, 'red'), (125, 'blue'), (150, 'green')]:
+        df = generate_tradeoff_curve(payload_per_launch=payload, elevator_capacity=elevator_cap)
+        if not df.empty:
+            ax1.plot(df['years'], df['energy_PJ'] / 1000, color=color, linewidth=2, 
+                    label=f'{payload} tons')
+    
+    ax1.set_xlabel('Timeline (years)', fontsize=11)
+    ax1.set_ylabel('Energy (×10³ PJ)', fontsize=11)
+    ax1.set_title('Trade-off Curves: Rocket Payload Capacity', fontsize=12)
+    ax1.legend(title='Payload')
+    ax1.grid(True, alpha=0.3)
+    ax1.set_xlim(95, 200)
+    
+    # ========== Plot 2: Different Elevator Capacities ==========
+    ax2 = axes[0, 1]
+    
+    for factor, color in [(0.8, 'red'), (1.0, 'blue'), (1.2, 'green')]:
+        df = generate_tradeoff_curve(elevator_capacity=elevator_cap * factor)
+        if not df.empty:
+            ax2.plot(df['years'], df['energy_PJ'] / 1000, color=color, linewidth=2, 
+                    label=f'{factor*100:.0f}%')
+    
+    ax2.set_xlabel('Timeline (years)', fontsize=11)
+    ax2.set_ylabel('Energy (×10³ PJ)', fontsize=11)
+    ax2.set_title('Trade-off Curves: Elevator Capacity', fontsize=12)
+    ax2.legend(title='Capacity')
+    ax2.grid(True, alpha=0.3)
+    ax2.set_xlim(95, 250)
+    
+    # ========== Plot 3: Different Launch Frequencies ==========
+    ax3 = axes[1, 0]
+    
+    for freq, color in [(0.5, 'red'), (1.0, 'blue'), (2.0, 'green')]:
+        df = generate_tradeoff_curve(launches_per_day=freq, elevator_capacity=elevator_cap)
+        if not df.empty:
+            ax3.plot(df['years'], df['energy_PJ'] / 1000, color=color, linewidth=2, 
+                    label=f'{freq}/day')
+    
+    ax3.set_xlabel('Timeline (years)', fontsize=11)
+    ax3.set_ylabel('Energy (×10³ PJ)', fontsize=11)
+    ax3.set_title('Trade-off Curves: Launch Frequency', fontsize=12)
+    ax3.legend(title='Frequency')
+    ax3.grid(True, alpha=0.3)
+    ax3.set_xlim(45, 200)
+    
+    # ========== Plot 4: Different Engine Types ==========
+    ax4 = axes[1, 1]
+    
+    engines = [
+        ('LOX/Kerosene', 350, 10.3e6, 'red'),
+        ('LOX/Methane', 363, 11.9e6, 'blue'),
+        ('LOX/Hydrogen', 450, 15.5e6, 'green'),
+    ]
+    
+    for name, isp, se, color in engines:
+        df = generate_tradeoff_curve(isp=isp, specific_fuel_energy=se, elevator_capacity=elevator_cap)
+        if not df.empty:
+            ax4.plot(df['years'], df['energy_PJ'] / 1000, color=color, linewidth=2, 
+                    label=f'{name}')
+    
+    ax4.set_xlabel('Timeline (years)', fontsize=11)
+    ax4.set_ylabel('Energy (×10³ PJ)', fontsize=11)
+    ax4.set_title('Trade-off Curves: Engine Technology', fontsize=12)
+    ax4.legend(title='Engine')
+    ax4.grid(True, alpha=0.3)
+    ax4.set_xlim(95, 200)
+    
+    plt.tight_layout()
+    plt.savefig(save_path, dpi=150, bbox_inches='tight')
+    print(f"Trade-off comparison plot saved to: {save_path}")
+    
+    return fig
+
+
+# ============== Main ==============
+
+def main():
+    print("=" * 70)
+    print("Task 1 Sensitivity Analysis for Moon Colony Logistics")
+    print("=" * 70)
+    
+    # Run all sensitivity analyses
+    payload_df = sensitivity_payload_capacity()
+    elevator_df = sensitivity_elevator_capacity()
+    frequency_df = sensitivity_launch_frequency()
+    engine_df = sensitivity_engine_technology()
+    alpha_df = sensitivity_structural_coefficient()
+    
+    # Print summary tables
+    print("\n" + "=" * 70)
+    print("SENSITIVITY ANALYSIS RESULTS")
+    print("=" * 70)
+    
+    print("\n[1] Rocket Payload Capacity (Problem range: 100-150 tons)")
+    print(payload_df.to_string(index=False))
+    
+    print("\n[2] Elevator Capacity (±20%)")
+    print(elevator_df.to_string(index=False))
+    
+    print("\n[3] Launch Frequency")
+    print(frequency_df.to_string(index=False))
+    
+    print("\n[4] Engine Technology")
+    print(engine_df.to_string(index=False))
+    
+    print("\n[5] Structural Coefficient α")
+    print(alpha_df.to_string(index=False))
+    
+    # Generate plots
+    print("\n" + "=" * 70)
+    print("Generating Visualization...")
+    print("=" * 70)
+    
+    plot_sensitivity_analysis(payload_df, elevator_df, frequency_df, engine_df, alpha_df)
+    plot_tradeoff_comparison()
+    
+    # Save data
+    payload_df.to_csv('/Volumes/Files/code/mm/20260130_b/p1/sensitivity_payload.csv', index=False)
+    elevator_df.to_csv('/Volumes/Files/code/mm/20260130_b/p1/sensitivity_elevator.csv', index=False)
+    frequency_df.to_csv('/Volumes/Files/code/mm/20260130_b/p1/sensitivity_frequency.csv', index=False)
+    engine_df.to_csv('/Volumes/Files/code/mm/20260130_b/p1/sensitivity_engine.csv', index=False)
+    alpha_df.to_csv('/Volumes/Files/code/mm/20260130_b/p1/sensitivity_alpha.csv', index=False)
+    print("\nData saved to CSV files.")
+    
+    # Summary
+    print("\n" + "=" * 70)
+    print("KEY FINDINGS")
+    print("=" * 70)
+    print("""
+    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
+    """)
+    
+    print("=" * 70)
+    print("Analysis Complete!")
+    print("=" * 70)
+    
+    return payload_df, elevator_df, frequency_df, engine_df, alpha_df
+
+
+if __name__ == "__main__":
+    results = main()

p1/sensitivity_elevator.csv

@@ -0,0 +1,10 @@
+capacity_factor,capacity_tons_per_year,min_timeline,elevator_only_timeline,critical_lambda,optimal_T_lambda504,optimal_E_lambda504
+0.8,429600.0,113.12625250501002,232.77467411545624,386.4321608040201,113.12625250501002,63657.161988613094
+0.8500000000000001,456450.00000000006,109.61923847695391,219.08204622631172,410.5527638190955,109.61923847695391,62326.697320517385
+0.9,483300.0,106.6132264529058,206.9108214359611,432.66331658291455,111.47219061238053,58467.61654576382
+0.95,510150.0,103.6072144288577,196.02077820248945,456.78391959798995,108.54170652863515,57060.67905104806
+1.0,537000.0,101.10220440881763,186.21973929236498,480.9045226130653,138.08320157903745,39190.76939967205
+1.05,563850.0,98.09619238476954,177.35213265939524,505.0251256281407,177.23436823395534,15779.547072161346
+1.1,590700.0,95.59118236472946,169.29067208396816,529.145728643216,168.520961521032,16127.11044324161
+1.15,617550.0,93.58717434869739,161.93020808031739,553.2663316582914,161.00844905892188,16229.602091434355
+1.2,644400.0,91.08216432865731,155.18311607697083,577.3869346733668,155.12230491133022,15755.147010790764

p1/sensitivity_engine.csv

@@ -0,0 +1,5 @@
+engine_type,isp_seconds,specific_energy_MJ_kg,fuel_ratio,min_timeline,optimal_T_lambda504,optimal_E_lambda504
+Solid,280,5.0,538.5764850131313,101.10220440881763,186.40043906909295,15720.0
+LOX/Kerosene,350,10.3,108.67594152576491,101.10220440881763,185.65220894049406,16013.642239311645
+LOX/Methane,363,11.9,88.36809547494757,101.10220440881763,138.51371083876296,38973.75515736591
+LOX/Hydrogen,450,15.5,31.788626814321816,101.10220440881763,101.10220440881763,31658.551849443746

p1/sensitivity_frequency.csv

@@ -0,0 +1,8 @@
+launches_per_day,min_timeline,elevator_only_timeline,optimal_T_lambda504,optimal_E_lambda504,rocket_capacity_tons_per_year
+0.5,131.16232464929857,186.21973929236498,153.8549460730506,31569.245158290636,228125.0
+0.75,114.12825651302605,186.21973929236498,141.43915972648816,37650.80910610053,342187.5
+1.0,101.10220440881763,186.21973929236498,138.51371083876296,38973.75515736591,456250.0
+1.25,90.58116232464928,186.21973929236498,130.63614666518967,42805.34480074314,570312.5
+1.5,82.06412825651302,186.21973929236498,123.415172052648,46322.046034129125,684375.0
+1.75,75.0501002004008,186.21973929236498,116.36992578121067,49763.71727628531,798437.5
+2.0,69.03807615230461,186.21973929236498,110.86847060956083,52436.356660871454,912500.0

p1/sensitivity_payload.csv

@@ -0,0 +1,12 @@
+payload_tons,min_timeline,elevator_only_timeline,optimal_T_lambda504,optimal_E_lambda504,energy_at_139y
+100.0,111.12224448897794,186.21973929236498,139.03737122486177,38829.35751806205,38829.35751806205
+105.0,109.11823647294588,186.21973929236498,137.43617889044418,39611.72625931598,38542.26035133922
+110.0,106.6132264529058,186.21973929236498,136.15522502291014,40233.22214267542,38781.43442019814
+115.0,104.60921843687373,186.21973929236498,134.5641030805329,41011.601312047926,38434.596386037454
+120.0,102.60521042084167,186.21973929236498,140.37975448384205,38056.88195030881,38430.28997049429
+125.0,101.10220440881763,186.21973929236498,138.51371083876296,38973.75515736591,38598.73345595525
+130.0,99.09819639278557,186.21973929236498,137.013222424749,39706.68272720883,38573.78198086428
+135.0,97.59519038076152,186.21973929236498,135.88785611423853,40251.02975221686,38349.15358699996
+140.0,95.59118236472946,186.21973929236498,134.38736770022456,40985.0024452691,38671.44068549057
+145.0,94.0881763527054,186.21973929236498,133.2620013897141,41530.08764325223,38417.95828151439
+150.0,92.58517034068136,186.21973929236498,132.13663507920364,42075.527964998335,38541.90167459569

p1/specific_energy_comparison.py

@@ -45,9 +45,9 @@ class PhysicalConstants:
 @dataclass
 class EngineParams:
     """发动机/推进系统参数"""
-    name: str = "液氧液氢"
+    name: str = "液氧甲烷"
-    isp: float = 450              # 比冲 (秒)
+    isp: float = 363              # 比冲 (秒) - LOX/CH4 (Raptor-class)
-    specific_energy: float = 15.5e6  # 燃料比能量 (J/kg)
+    specific_energy: float = 11.9e6  # 燃料比能量 (J/kg)
     
     @property
     def exhaust_velocity(self) -> float:
@@ -505,17 +505,21 @@ def plot_latitude_effects(
     engine: EngineParams = EngineParams(),
     mission: MissionParams = MissionParams(),
     constants: PhysicalConstants = PhysicalConstants(),
-    save_path: str = '/Volumes/Files/code/mm/20260130_b/latitude_effects.png',
+    save_path: str = '/Volumes/Files/code/mm/20260130_b/p1/latitude_effects.png',
     lunar_mission: bool = True
 ):
     """
-    绘制纬度影响图表
+    Plot fuel ratio vs launch latitude.
     
-    参数:
+    Args:
-        lunar_mission: 如果True，使用月球任务场景（不需要轨道平面改变）
+        engine: Engine parameters
+        mission: Mission parameters
+        constants: Physical constants
+        save_path: Output file path
+        lunar_mission: If True, use lunar mission scenario (no orbital plane change penalty)
     """
     
-    # 月球任务场景：设置高目标倾角，避免轨道平面改变惩罚
+    # Lunar mission scenario: set high target inclination to avoid plane change penalty
     if lunar_mission:
         mission_plot = MissionParams(
             alpha=mission.alpha,
@@ -523,124 +527,50 @@ def plot_latitude_effects(
             delta_v_ground_to_leo_base=mission.delta_v_ground_to_leo_base,
             delta_v_tli=mission.delta_v_tli,
             delta_v_loi=mission.delta_v_loi,
-            target_inclination=90.0,  # 允许任意倾角
+            target_inclination=90.0,  # Allow any inclination
             elevator_length=mission.elevator_length
         )
-        title_suffix = "\n(Lunar Mission - 无轨道平面改变)"
+        title_suffix = " (Lunar Mission)"
     else:
         mission_plot = mission
-        title_suffix = "\n(目标: 赤道轨道)"
+        title_suffix = " (Target: Equatorial Orbit)"
     
-    fig, axes = plt.subplots(2, 2, figsize=(16, 14))
+    # Golden ratio aspect: width=10, height=10*0.618
+    fig, ax = plt.subplots(figsize=(10, 10 * 0.618))
     
-    # 连续纬度范围
+    # Continuous latitude range
     latitudes = np.linspace(0, 65, 100)
     
-    # ========== 图1: 自转速度 vs 纬度 ==========
+    # Calculate fuel ratio for each latitude
-    ax1 = axes[0, 0]
-    rotation_velocities = [earth_rotation_velocity(lat, constants) for lat in latitudes]
-    ax1.plot(latitudes, rotation_velocities, 'b-', linewidth=2)
-    
-    # 标记发射场 (使用绝对值纬度)
-    for name, site in LAUNCH_SITES.items():
-        abs_lat = abs(site.latitude)
-        v = earth_rotation_velocity(abs_lat, constants)
-        ax1.plot(abs_lat, v, 'ro', markersize=8)
-        # 简化标签显示
-        label = site.name.split('(')[0].strip()
-        ax1.annotate(label, (abs_lat, v), textcoords="offset points", 
-                    xytext=(3, 3), fontsize=8, rotation=15)
-    
-    ax1.set_xlabel('Latitude |φ| (°)', fontsize=12)
-    ax1.set_ylabel('Rotation Velocity (m/s)', fontsize=12)
-    ax1.set_title('Earth Surface Rotation Velocity vs Latitude\nv = ω×R×cos(φ)', fontsize=13)
-    ax1.grid(True, alpha=0.3)
-    ax1.set_xlim(0, 65)
-    
-    # ========== 图2: ΔV损失 vs 纬度 ==========
-    ax2 = axes[0, 1]
-    dv_losses = [delta_v_rotation_loss(lat, constants) for lat in latitudes]
-    ax2.plot(latitudes, dv_losses, 'r-', linewidth=2)
-    
-    for name, site in LAUNCH_SITES.items():
-        abs_lat = abs(site.latitude)
-        dv = delta_v_rotation_loss(abs_lat, constants)
-        ax2.plot(abs_lat, dv, 'bo', markersize=8)
-        label = site.name.split('(')[0].strip()
-        ax2.annotate(label, (abs_lat, dv), textcoords="offset points", 
-                    xytext=(3, 3), fontsize=8, rotation=15)
-    
-    ax2.set_xlabel('Latitude |φ| (°)', fontsize=12)
-    ax2.set_ylabel('ΔV Loss (m/s)', fontsize=12)
-    ax2.set_title('Rotation Velocity Loss vs Latitude\n(Relative to Equator)', fontsize=13)
-    ax2.grid(True, alpha=0.3)
-    ax2.set_xlim(0, 65)
-    
-    # ========== 图3: 燃料比 vs 纬度 ==========
-    ax3 = axes[1, 0]
-    
     fuel_ratios = []
     for lat in latitudes:
         site = LaunchSite("temp", lat)
         result = ground_launch_specific_energy_with_latitude(engine, mission_plot, site, constants)
         fuel_ratios.append(result['fuel_ratio'])
     
-    ax3.plot(latitudes, fuel_ratios, 'g-', linewidth=2, label='Fuel Ratio vs Latitude')
+    # Plot continuous curve
+    ax.plot(latitudes, fuel_ratios, 'g-', linewidth=2, label='Fuel Ratio vs Latitude')
     
+    # Mark launch sites
     for name, site in LAUNCH_SITES.items():
         abs_lat = abs(site.latitude)
         site_temp = LaunchSite(site.name, abs_lat)
         result = ground_launch_specific_energy_with_latitude(engine, mission_plot, site_temp, constants)
-        ax3.plot(abs_lat, result['fuel_ratio'], 'mo', markersize=8)
+        ax.plot(abs_lat, result['fuel_ratio'], 'mo', markersize=8)
+        # Simplified label
         label = site.name.split('(')[0].strip()
-        ax3.annotate(label, (abs_lat, result['fuel_ratio']), 
+        ax.annotate(label, (abs_lat, result['fuel_ratio']), 
                     textcoords="offset points", xytext=(3, 3), fontsize=8, rotation=15)
     
-    ax3.set_xlabel('Latitude |φ| (°)', fontsize=12)
+    ax.set_xlabel('Latitude |φ| (°)', fontsize=12)
-    ax3.set_ylabel('Fuel / Payload Mass Ratio', fontsize=12)
+    ax.set_ylabel('Fuel / Payload Mass Ratio', fontsize=12)
-    ax3.set_title(f'Fuel Requirement vs Launch Latitude{title_suffix}', fontsize=13)
+    ax.set_title(f'Fuel Requirement vs Launch Latitude{title_suffix}', fontsize=13)
-    ax3.grid(True, alpha=0.3)
+    ax.grid(True, alpha=0.3)
-    ax3.set_xlim(0, 65)
+    ax.set_xlim(0, 65)
-    
-    # ========== 图4: 能量对比柱状图 ==========
-    ax4 = axes[1, 1]
-    
-    # 按纬度绝对值排序
-    results = []
-    for name, site in LAUNCH_SITES.items():
-        abs_lat = abs(site.latitude)
-        site_temp = LaunchSite(site.name, abs_lat)
-        result = ground_launch_specific_energy_with_latitude(engine, mission_plot, site_temp, constants)
-        result['abs_latitude'] = abs_lat
-        results.append(result)
-    
-    results = sorted(results, key=lambda x: x['abs_latitude'])
-    
-    # 简化标签
-    sites = [r['launch_site'].split('(')[0].strip() for r in results]
-    fuel_ratios_bar = [r['fuel_ratio'] for r in results]
-    abs_lats = [r['abs_latitude'] for r in results]
-    
-    # 颜色映射：纬度越高颜色越深
-    colors = plt.cm.RdYlGn_r(np.array(abs_lats) / 65)
-    bars = ax4.bar(range(len(sites)), fuel_ratios_bar, color=colors)
-    
-    ax4.set_ylabel('Fuel / Payload Mass Ratio', fontsize=12)
-    ax4.set_title(f'Fuel Requirement by Launch Site{title_suffix}', fontsize=13)
-    ax4.set_xticks(range(len(sites)))
-    ax4.set_xticklabels(sites, rotation=45, ha='right', fontsize=9)
-    ax4.grid(True, alpha=0.3, axis='y')
-    
-    # 添加数值标签和纬度
-    for i, (bar, ratio, lat) in enumerate(zip(bars, fuel_ratios_bar, abs_lats)):
-        ax4.text(bar.get_x() + bar.get_width()/2, bar.get_height() + 0.3, 
-                f'{ratio:.1f}', ha='center', fontsize=9, fontweight='bold')
-        ax4.text(bar.get_x() + bar.get_width()/2, 1, 
-                f'{lat:.0f}°', ha='center', fontsize=8, color='white')
     
     plt.tight_layout()
     plt.savefig(save_path, dpi=150, bbox_inches='tight')
-    print(f"纬度影响图表已保存至: {save_path}")
+    print(f"Latitude effects plot saved to: {save_path}")
     
     return fig
 
@@ -886,6 +816,7 @@ def plot_comparison(
     engines = [
         EngineParams(name="固体火箭", isp=280, specific_energy=5e6),
         EngineParams(name="液氧煤油", isp=350, specific_energy=10.3e6),
+        EngineParams(name="液氧甲烷", isp=363, specific_energy=11.9e6),
         EngineParams(name="液氧液氢", isp=450, specific_energy=15.5e6),
     ]
     
@@ -922,11 +853,11 @@ def plot_comparison(
 if __name__ == "__main__":
     # 可以在这里修改参数
     
-    # 发动机参数
+    # 发动机参数 - 液氧甲烷 (LOX/CH4, Raptor-class)
     engine = EngineParams(
-        name="液氧液氢",
+        name="液氧甲烷",
-        isp=450,                    # 比冲 (秒)
+        isp=363,                    # 比冲 (秒)
-        specific_energy=15.5e6     # 燃料比能量 (J/kg)
+        specific_energy=11.9e6     # 燃料比能量 (J/kg)
     )
     
     # 任务参数