p1: sen
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@@ -46,8 +46,8 @@ ELEVATOR_SPECIFIC_ENERGY = 157.2e9 # J per metric ton (157.2 MJ/kg * 1000 kg)
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# ============== 火箭参数 ==============
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PAYLOAD_PER_LAUNCH = 125 # metric tons per launch
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ISP = 450 # 比冲 (秒)
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SPECIFIC_FUEL_ENERGY = 15.5e6 # J/kg
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ISP = 363 # 比冲 (秒) - 液氧甲烷 (LOX/CH4, Raptor-class)
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SPECIFIC_FUEL_ENERGY = 11.9e6 # J/kg
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ALPHA = 0.10 # 结构系数
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NUM_STAGES = 3
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DELTA_V_BASE = 13300 # m/s (赤道发射到月球)
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p1/lambda_cost_analysis.py
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p1/lambda_cost_analysis.py
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"""
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Lambda Time Cost Analysis for Moon Colony Logistics
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This module introduces the time opportunity cost (λ) to find the optimal
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operating point on the Energy-Time trade-off curve.
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Objective Function: J = E_total + λ × T
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where:
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- E_total: Total energy consumption (PJ)
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- T: Construction timeline (years)
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- λ: Time opportunity cost (PJ/year)
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The optimal point satisfies: dE/dT = -λ (marginal energy saving = time cost)
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"""
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import numpy as np
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import matplotlib
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matplotlib.use('Agg')
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import matplotlib.pyplot as plt
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from matplotlib import rcParams
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import pandas as pd
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from typing import Dict, List, Tuple, Optional
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from dataclasses import dataclass
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# Font settings
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rcParams['font.sans-serif'] = ['Arial Unicode MS', 'DejaVu Sans', 'SimHei']
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rcParams['axes.unicode_minus'] = False
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# ============== Physical Constants ==============
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G0 = 9.81 # m/s²
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OMEGA_EARTH = 7.27e-5 # rad/s
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R_EARTH = 6.371e6 # m
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# Mission parameters
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TOTAL_PAYLOAD = 100e6 # 100 million metric tons
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# Space Elevator parameters
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NUM_ELEVATORS = 3
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ELEVATOR_CAPACITY_PER_YEAR = 179000 # metric tons per elevator per year
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TOTAL_ELEVATOR_CAPACITY = NUM_ELEVATORS * ELEVATOR_CAPACITY_PER_YEAR # 537,000 tons/year
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ELEVATOR_SPECIFIC_ENERGY = 157.2e9 # J per metric ton (157.2 MJ/kg × 1000)
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# Rocket parameters - LOX/CH4 (Raptor-class)
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PAYLOAD_PER_LAUNCH = 125 # metric tons per launch
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ISP = 363 # Specific impulse (s)
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SPECIFIC_FUEL_ENERGY = 11.9e6 # J/kg
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ALPHA = 0.10 # Structural coefficient
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NUM_STAGES = 3
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DELTA_V_BASE = 13300 # m/s (LEO + TLI + LOI)
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# ============== Launch Site Definition ==============
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@dataclass
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class LaunchSite:
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name: str
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short_name: str
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latitude: float
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max_launches_per_day: int = 1
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@property
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def abs_latitude(self) -> float:
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return abs(self.latitude)
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@property
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def delta_v_loss(self) -> float:
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v_equator = OMEGA_EARTH * R_EARTH
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v_site = OMEGA_EARTH * R_EARTH * np.cos(np.radians(self.abs_latitude))
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return v_equator - v_site
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@property
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def total_delta_v(self) -> float:
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return DELTA_V_BASE + self.delta_v_loss
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LAUNCH_SITES = sorted([
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LaunchSite("Kourou (French Guiana)", "Kourou", 5.2),
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LaunchSite("Satish Dhawan (India)", "SDSC", 13.7),
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LaunchSite("Boca Chica (Texas)", "Texas", 26.0),
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LaunchSite("Cape Canaveral (Florida)", "Florida", 28.5),
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LaunchSite("Vandenberg (California)", "California", 34.7),
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LaunchSite("Wallops (Virginia)", "Virginia", 37.8),
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LaunchSite("Taiyuan (China)", "Taiyuan", 38.8),
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LaunchSite("Mahia (New Zealand)", "Mahia", 39.3),
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LaunchSite("Baikonur (Kazakhstan)", "Baikonur", 45.6),
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LaunchSite("Kodiak (Alaska)", "Alaska", 57.4),
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], key=lambda x: x.abs_latitude)
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# ============== Core Calculation Functions ==============
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def fuel_ratio_multistage(delta_v: float) -> float:
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"""Multi-stage rocket fuel/payload ratio"""
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ve = ISP * G0
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delta_v_per_stage = delta_v / NUM_STAGES
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R_stage = np.exp(delta_v_per_stage / ve)
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denominator = 1 - ALPHA * (R_stage - 1)
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if denominator <= 0:
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return np.inf
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k_stage = (R_stage - 1) / denominator
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total_fuel_ratio = 0
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remaining_ratio = 1.0
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for _ in range(NUM_STAGES):
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fuel_this_stage = remaining_ratio * k_stage
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total_fuel_ratio += fuel_this_stage
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remaining_ratio *= (1 + k_stage * (1 + ALPHA))
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return total_fuel_ratio
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def rocket_energy_per_ton(site: LaunchSite) -> float:
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"""Energy consumption per ton of payload for rocket launch (J/ton)"""
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k = fuel_ratio_multistage(site.total_delta_v)
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fuel_per_ton = k * 1000 # kg fuel per metric ton payload
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return fuel_per_ton * SPECIFIC_FUEL_ENERGY
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def calculate_scenario(completion_years: float) -> Optional[Dict]:
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"""
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Calculate optimal scenario for given completion timeline
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(elevator priority + low-latitude rockets)
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"""
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# Space elevator transport
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elevator_payload = min(TOTAL_ELEVATOR_CAPACITY * completion_years, TOTAL_PAYLOAD)
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elevator_energy = elevator_payload * ELEVATOR_SPECIFIC_ENERGY
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# Remaining payload for rockets
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remaining_payload = TOTAL_PAYLOAD - elevator_payload
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if remaining_payload <= 0:
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return {
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'years': completion_years,
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'elevator_payload': elevator_payload,
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'rocket_payload': 0,
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'elevator_energy_PJ': elevator_energy / 1e15,
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'rocket_energy_PJ': 0,
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'total_energy_PJ': elevator_energy / 1e15,
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'rocket_launches': 0,
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'sites_used': 0,
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'elevator_fraction': 1.0,
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}
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# Rocket launches needed
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rocket_launches_needed = int(np.ceil(remaining_payload / PAYLOAD_PER_LAUNCH))
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# Allocate by latitude priority
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days_available = completion_years * 365
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max_launches_per_site = int(days_available)
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# Check feasibility
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total_rocket_capacity = len(LAUNCH_SITES) * max_launches_per_site * PAYLOAD_PER_LAUNCH
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if remaining_payload > total_rocket_capacity:
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return None
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rocket_energy = 0
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sites_used = 0
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remaining_launches = rocket_launches_needed
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for site in LAUNCH_SITES:
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if remaining_launches <= 0:
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break
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allocated = min(remaining_launches, max_launches_per_site)
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rocket_energy += rocket_energy_per_ton(site) * PAYLOAD_PER_LAUNCH * allocated
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remaining_launches -= allocated
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if allocated > 0:
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sites_used += 1
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rocket_payload = rocket_launches_needed * PAYLOAD_PER_LAUNCH
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total_energy = elevator_energy + rocket_energy
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return {
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'years': completion_years,
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'elevator_payload': elevator_payload,
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'rocket_payload': rocket_payload,
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'elevator_energy_PJ': elevator_energy / 1e15,
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'rocket_energy_PJ': rocket_energy / 1e15,
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'total_energy_PJ': total_energy / 1e15,
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'rocket_launches': rocket_launches_needed,
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'sites_used': sites_used,
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'elevator_fraction': elevator_payload / TOTAL_PAYLOAD,
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}
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# ============== Generate Trade-off Curve ==============
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def generate_tradeoff_curve(
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year_min: float = 100,
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year_max: float = 250,
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num_points: int = 500
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) -> pd.DataFrame:
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"""Generate Energy-Time trade-off curve data"""
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years_range = np.linspace(year_min, year_max, num_points)
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results = []
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for years in years_range:
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scenario = calculate_scenario(years)
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if scenario is not None:
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results.append({
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'years': years,
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'energy_PJ': scenario['total_energy_PJ'],
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'elevator_fraction': scenario['elevator_fraction'],
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'sites_used': scenario['sites_used'],
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'rocket_launches': scenario['rocket_launches'],
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})
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return pd.DataFrame(results)
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# ============== Lambda Cost Analysis ==============
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def calculate_total_cost(df: pd.DataFrame, lambda_cost: float) -> np.ndarray:
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"""
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Calculate total cost J = E + λ × T
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Args:
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df: Trade-off curve data
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lambda_cost: Time opportunity cost (PJ/year)
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Returns:
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Total cost array
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"""
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return df['energy_PJ'].values + lambda_cost * df['years'].values
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def find_optimal_point(df: pd.DataFrame, lambda_cost: float) -> Dict:
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"""
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Find optimal point that minimizes J = E + λ × T
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Args:
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df: Trade-off curve data
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lambda_cost: Time opportunity cost (PJ/year)
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Returns:
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Optimal point information
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"""
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total_cost = calculate_total_cost(df, lambda_cost)
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opt_idx = np.argmin(total_cost)
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return {
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'index': opt_idx,
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'years': df['years'].iloc[opt_idx],
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'energy_PJ': df['energy_PJ'].iloc[opt_idx],
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'total_cost': total_cost[opt_idx],
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'elevator_fraction': df['elevator_fraction'].iloc[opt_idx],
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'lambda': lambda_cost,
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}
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def calculate_marginal_energy_saving(df: pd.DataFrame) -> np.ndarray:
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"""
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Calculate marginal energy saving rate: -dE/dT (PJ/year)
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This represents how much energy is saved per additional year of timeline.
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"""
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years = df['years'].values
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energy = df['energy_PJ'].values
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# Use central difference for interior points
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marginal = -np.gradient(energy, years)
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return marginal
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def sensitivity_analysis(
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df: pd.DataFrame,
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lambda_range: np.ndarray
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) -> pd.DataFrame:
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"""
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Perform sensitivity analysis on λ parameter
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Args:
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df: Trade-off curve data
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lambda_range: Array of λ values to test
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Returns:
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DataFrame with optimal points for each λ
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"""
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results = []
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for lam in lambda_range:
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opt = find_optimal_point(df, lam)
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results.append({
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'lambda_PJ_per_year': lam,
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'optimal_years': opt['years'],
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'optimal_energy_PJ': opt['energy_PJ'],
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'total_cost_PJ': opt['total_cost'],
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'elevator_fraction': opt['elevator_fraction'],
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})
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return pd.DataFrame(results)
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# ============== Visualization Functions ==============
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def plot_lambda_analysis(
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df: pd.DataFrame,
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save_path: str = '/Volumes/Files/code/mm/20260130_b/p1/lambda_cost_analysis.png'
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):
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"""
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Comprehensive visualization of λ time cost analysis
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Focus on critical range λ = 400-600 PJ/year
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"""
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fig, axes = plt.subplots(2, 2, figsize=(14, 12))
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years = df['years'].values
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energy = df['energy_PJ'].values
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# Key boundaries
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T_min = years.min() # ~100.7 years (fastest)
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T_elev = TOTAL_PAYLOAD / TOTAL_ELEVATOR_CAPACITY # ~186 years (elevator only)
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E_min = energy[years >= T_elev].min() if any(years >= T_elev) else energy.min()
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# ========== Plot 1: Trade-off Curve with λ Iso-cost Lines ==========
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ax1 = axes[0, 0]
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# Main curve
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ax1.plot(years, energy, 'b-', linewidth=2.5, label='Energy-Time Trade-off')
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# Mark key points
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ax1.axvline(x=T_elev, color='green', linestyle='--', alpha=0.7, label=f'Elevator-only: {T_elev:.1f} years')
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ax1.axvline(x=T_min, color='red', linestyle='--', alpha=0.7, label=f'Minimum time: {T_min:.1f} years')
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# Draw iso-cost lines for different λ (focus on 400-600 range)
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lambda_values = [420, 480, 500, 550]
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colors = ['#2ecc71', '#e74c3c', '#9b59b6', '#3498db']
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for lam, color in zip(lambda_values, colors):
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opt = find_optimal_point(df, lam)
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# Iso-cost line: E + λT = const → E = const - λT
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T_line = np.linspace(80, 220, 100)
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E_line = opt['total_cost'] - lam * T_line
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valid = (E_line > 0) & (E_line < 70000)
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ax1.plot(T_line[valid], E_line[valid], '--', color=color, alpha=0.6, linewidth=1.5)
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ax1.plot(opt['years'], opt['energy_PJ'], 'o', color=color, markersize=12,
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markeredgecolor='black', markeredgewidth=1.5,
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label=f'λ={lam}: T={opt["years"]:.1f}y, E={opt["energy_PJ"]:.0f}PJ')
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ax1.set_xlabel('Construction Timeline T (years)', fontsize=12)
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ax1.set_ylabel('Total Energy E (PJ)', fontsize=12)
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ax1.set_title('Energy-Time Trade-off with λ Iso-cost Lines (λ=400-600)\n$J = E + λT$', fontsize=13)
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ax1.legend(loc='upper right', fontsize=9)
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ax1.grid(True, alpha=0.3)
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ax1.set_xlim(95, 200)
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ax1.set_ylim(10000, 65000)
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# ========== Plot 2: Marginal Energy Saving Rate ==========
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ax2 = axes[0, 1]
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marginal = calculate_marginal_energy_saving(df)
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ax2.plot(years, marginal, 'r-', linewidth=2, label='Marginal Energy Saving -dE/dT')
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ax2.axhline(y=0, color='black', linestyle='-', alpha=0.3)
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# Mark critical λ values in 400-600 range
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for lam, color in zip([450, 480, 500, 550], ['#2ecc71', '#e74c3c', '#9b59b6', '#3498db']):
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ax2.axhline(y=lam, color=color, linestyle='--', alpha=0.7, label=f'λ = {lam} PJ/year')
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# Find intersection
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intersect_idx = np.argmin(np.abs(marginal - lam))
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ax2.plot(years[intersect_idx], marginal[intersect_idx], 'o', color=color, markersize=8)
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ax2.set_xlabel('Construction Timeline T (years)', fontsize=12)
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ax2.set_ylabel('Marginal Energy Saving -dE/dT (PJ/year)', fontsize=12)
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ax2.set_title('Marginal Analysis: Optimal Condition is -dE/dT = λ', fontsize=13)
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ax2.legend(loc='upper right', fontsize=9)
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ax2.grid(True, alpha=0.3)
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ax2.set_xlim(95, 200)
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ax2.set_ylim(350, 620)
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# ========== Plot 3: Sensitivity Analysis (400-600 range) ==========
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ax3 = axes[1, 0]
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lambda_range = np.linspace(400, 600, 200)
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sensitivity_df = sensitivity_analysis(df, lambda_range)
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# Plot optimal years vs λ
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ax3.plot(sensitivity_df['lambda_PJ_per_year'], sensitivity_df['optimal_years'],
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'b-', linewidth=2.5, label='Optimal Timeline T*')
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# Mark key regions
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ax3.axhline(y=T_elev, color='green', linestyle='--', alpha=0.7, label=f'Elevator-only: {T_elev:.1f}y')
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ax3.axhline(y=T_min, color='red', linestyle='--', alpha=0.7, label=f'Min timeline: {T_min:.1f}y')
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ax3.axhline(y=139, color='orange', linestyle=':', linewidth=2, alpha=0.8, label='Original knee: 139y')
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# Find λ corresponding to 139 years
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idx_139 = np.argmin(np.abs(sensitivity_df['optimal_years'] - 139))
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if idx_139 < len(sensitivity_df):
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lambda_139 = sensitivity_df['lambda_PJ_per_year'].iloc[idx_139]
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ax3.axvline(x=lambda_139, color='orange', linestyle=':', linewidth=2, alpha=0.6)
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ax3.scatter([lambda_139], [139], s=150, c='orange', marker='*', zorder=5,
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edgecolors='black', linewidths=1.5, label=f'λ≈{lambda_139:.0f} for T*=139y')
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# Mark critical transition
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ax3.axvline(x=480, color='purple', linestyle='--', alpha=0.5)
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ax3.text(482, 175, 'Critical\nTransition', fontsize=9, color='purple')
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ax3.set_xlabel('Time Opportunity Cost λ (PJ/year)', fontsize=12)
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ax3.set_ylabel('Optimal Timeline T* (years)', fontsize=12)
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ax3.set_title('Sensitivity Analysis: Optimal Timeline vs λ (400-600 range)', fontsize=13)
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ax3.legend(loc='upper right', fontsize=9)
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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()
|
||||
BIN
p1/lambda_decision_map.png
Normal file
BIN
p1/lambda_decision_map.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 148 KiB |
121
p1/lambda_sensitivity.csv
Normal file
121
p1/lambda_sensitivity.csv
Normal file
@@ -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
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
595.3781512605042,100.72144288577154,58547.47792525526,118514.82438287638,0.5408741482965931
|
||||
600.0,100.72144288577154,58547.47792525526,118980.34365671818,0.5408741482965931
|
||||
|
Binary file not shown.
|
Before Width: | Height: | Size: 298 KiB After Width: | Height: | Size: 80 KiB |
@@ -1,301 +1,301 @@
|
||||
years,energy_PJ,elevator_fraction,sites_used,rocket_launches
|
||||
101.0,31679.76095710881,0.54237,10,366104
|
||||
101.28501585047614,31620.609850415538,0.5439005351170569,10,364880
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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||||
184.96993987975952,16320.927840970344,0.9932885771543087,1,5370
|
||||
185.37074148296594,16128.230433532259,0.9954408817635271,1,3648
|
||||
185.77154308617236,15935.533026094176,0.9975931863727456,1,1926
|
||||
186.17234468937875,15742.835618656089,0.9997454909819639,1,204
|
||||
186.5731462925852,15720.0,1.0,0,0
|
||||
186.97394789579158,15720.0,1.0,0,0
|
||||
187.374749498998,15720.0,1.0,0,0
|
||||
|
||||
|
Binary file not shown.
|
Before Width: | Height: | Size: 276 KiB After Width: | Height: | Size: 279 KiB |
@@ -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
|
||||
|
||||
@@ -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
|
||||
|
||||
|
||||
10
p1/sensitivity_alpha.csv
Normal file
10
p1/sensitivity_alpha.csv
Normal file
@@ -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
|
||||
|
BIN
p1/sensitivity_analysis.png
Normal file
BIN
p1/sensitivity_analysis.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 338 KiB |
763
p1/sensitivity_analysis.py
Normal file
763
p1/sensitivity_analysis.py
Normal file
@@ -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()
|
||||
10
p1/sensitivity_elevator.csv
Normal file
10
p1/sensitivity_elevator.csv
Normal file
@@ -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
|
||||
|
5
p1/sensitivity_engine.csv
Normal file
5
p1/sensitivity_engine.csv
Normal file
@@ -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
|
||||
|
8
p1/sensitivity_frequency.csv
Normal file
8
p1/sensitivity_frequency.csv
Normal file
@@ -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
|
||||
|
12
p1/sensitivity_payload.csv
Normal file
12
p1/sensitivity_payload.csv
Normal file
@@ -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
|
||||
|
BIN
p1/sensitivity_tradeoff.png
Normal file
BIN
p1/sensitivity_tradeoff.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 238 KiB |
@@ -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
|
||||
|
||||
Reference in New Issue
Block a user