diff --git a/p1/combined_decision.png b/p1/combined_decision.png index 67197a1..01813f0 100644 Binary files a/p1/combined_decision.png and b/p1/combined_decision.png differ diff --git a/p1/combined_scenario.py b/p1/combined_scenario.py index 9b2952c..6f8ac3f 100644 --- a/p1/combined_scenario.py +++ b/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) -SPECIFIC_FUEL_ENERGY = 15.5e6 # J/kg +ISP = 363 # 比冲 (秒) - 液氧甲烷 (LOX/CH4, Raptor-class) +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) diff --git a/p1/decision_recommendation.png b/p1/decision_recommendation.png index 0dd6828..dce445a 100644 Binary files a/p1/decision_recommendation.png and b/p1/decision_recommendation.png differ diff --git a/p1/lambda_comprehensive.png b/p1/lambda_comprehensive.png new file mode 100644 index 0000000..c7b020d Binary files /dev/null and b/p1/lambda_comprehensive.png differ diff --git a/p1/lambda_cost_analysis.png b/p1/lambda_cost_analysis.png new file mode 100644 index 0000000..f22ebd9 Binary files /dev/null and b/p1/lambda_cost_analysis.png differ diff --git a/p1/lambda_cost_analysis.py b/p1/lambda_cost_analysis.py new file mode 100644 index 0000000..9233ca0 --- /dev/null +++ b/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() diff --git a/p1/lambda_decision_map.png b/p1/lambda_decision_map.png new file mode 100644 index 0000000..47adde6 Binary files /dev/null and b/p1/lambda_decision_map.png differ diff --git a/p1/lambda_sensitivity.csv b/p1/lambda_sensitivity.csv new file mode 100644 index 0000000..a149daf --- /dev/null +++ b/p1/lambda_sensitivity.csv @@ -0,0 +1,121 @@ +lambda_PJ_per_year,optimal_years,optimal_energy_PJ,total_cost_PJ,elevator_fraction +50.0,186.3326653306613,15720.0,25036.633266533066,1.0 +54.621848739495796,186.3326653306613,15720.0,25897.834660918474,1.0 +59.24369747899159,186.3326653306613,15720.0,26759.036055303884,1.0 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b/p1/pareto_knee_analysis.png index 364785d..a039748 100644 Binary files a/p1/pareto_knee_analysis.png and b/p1/pareto_knee_analysis.png differ diff --git a/p1/pareto_optimization.py b/p1/pareto_optimization.py index 787d90c..579c28a 100644 --- a/p1/pareto_optimization.py +++ b/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 -SPECIFIC_FUEL_ENERGY = 15.5e6 # J/kg +ISP = 363 # 比冲 (秒) - 液氧甲烷 (LOX/CH4, Raptor-class) +SPECIFIC_FUEL_ENERGY = 11.9e6 # J/kg ALPHA = 0.10 NUM_STAGES = 3 DELTA_V_BASE = 13300 # m/s diff --git a/p1/rocket_launch_scenario.py b/p1/rocket_launch_scenario.py index 4e9ff3f..baba2fb 100644 --- a/p1/rocket_launch_scenario.py +++ b/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 -SPECIFIC_FUEL_ENERGY = 15.5e6 # J/kg 燃料比能量 +ISP = 363 # 比冲 (秒) - 液氧甲烷 (LOX/CH4, Raptor-class) +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 diff --git a/p1/sensitivity_alpha.csv b/p1/sensitivity_alpha.csv new file mode 100644 index 0000000..201b52d --- /dev/null +++ b/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 diff --git a/p1/sensitivity_analysis.png b/p1/sensitivity_analysis.png new file mode 100644 index 0000000..cea9356 Binary files /dev/null and b/p1/sensitivity_analysis.png differ diff --git a/p1/sensitivity_analysis.py b/p1/sensitivity_analysis.py new file mode 100644 index 0000000..f4d4938 --- /dev/null +++ b/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() diff --git a/p1/sensitivity_elevator.csv b/p1/sensitivity_elevator.csv new file mode 100644 index 0000000..12339a9 --- /dev/null +++ b/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 diff --git a/p1/sensitivity_engine.csv b/p1/sensitivity_engine.csv new file mode 100644 index 0000000..3bbbfcf --- /dev/null +++ b/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 diff --git a/p1/sensitivity_frequency.csv b/p1/sensitivity_frequency.csv new file mode 100644 index 0000000..a84a4dd --- /dev/null +++ b/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 diff --git a/p1/sensitivity_payload.csv b/p1/sensitivity_payload.csv new file mode 100644 index 0000000..54a5a18 --- /dev/null +++ b/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 diff --git a/p1/sensitivity_tradeoff.png b/p1/sensitivity_tradeoff.png new file mode 100644 index 0000000..60cb34b Binary files /dev/null and b/p1/sensitivity_tradeoff.png differ diff --git a/p1/specific_energy_comparison.py b/p1/specific_energy_comparison.py index 43e8823..b73e384 100644 --- a/p1/specific_energy_comparison.py +++ b/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" - isp: float = 450 # 比冲 (秒) - specific_energy: float = 15.5e6 # 燃料比能量 (J/kg) + name: str = "液氧甲烷" + isp: float = 363 # 比冲 (秒) - LOX/CH4 (Raptor-class) + 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: - lunar_mission: 如果True，使用月球任务场景（不需要轨道平面改变） + Args: + 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 ========== - 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] - + # Calculate fuel ratio for each latitude 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) - ax3.set_ylabel('Fuel / Payload Mass Ratio', fontsize=12) - ax3.set_title(f'Fuel Requirement vs Launch Latitude{title_suffix}', fontsize=13) - ax3.grid(True, alpha=0.3) - ax3.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') + ax.set_xlabel('Latitude |φ| (°)', fontsize=12) + ax.set_ylabel('Fuel / Payload Mass Ratio', fontsize=12) + ax.set_title(f'Fuel Requirement vs Launch Latitude{title_suffix}', fontsize=13) + ax.grid(True, alpha=0.3) + ax.set_xlim(0, 65) 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", - isp=450, # 比冲 (秒) - specific_energy=15.5e6 # 燃料比能量 (J/kg) + name="液氧甲烷", + isp=363, # 比冲 (秒) + specific_energy=11.9e6 # 燃料比能量 (J/kg) ) # 任务参数