1009 lines
35 KiB
Python
1009 lines
35 KiB
Python
"""
|
||
地面发射 vs 太空电梯发射：比能量计算与对比
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||
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可配置参数进行不同场景的能量分析
|
||
"""
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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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from dataclasses import dataclass
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||
from typing import Optional
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||
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# 设置中文字体支持
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rcParams['font.sans-serif'] = ['Arial Unicode MS', 'SimHei', 'DejaVu Sans']
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rcParams['axes.unicode_minus'] = False
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||
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# ============== 物理常数 ==============
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@dataclass
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class PhysicalConstants:
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"""物理常数"""
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G: float = 6.674e-11 # 万有引力常数 (m³/kg/s²)
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M_earth: float = 5.972e24 # 地球质量 (kg)
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M_moon: float = 7.342e22 # 月球质量 (kg)
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R_earth: float = 6.371e6 # 地球半径 (m)
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R_moon: float = 1.737e6 # 月球半径 (m)
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g0: float = 9.81 # 地表重力加速度 (m/s²)
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d_earth_moon: float = 3.844e8 # 地月平均距离 (m)
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omega_earth: float = 7.27e-5 # 地球自转角速度 (rad/s)
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@property
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def GM_earth(self) -> float:
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"""地球引力参数"""
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return self.G * self.M_earth
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@property
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def GM_moon(self) -> float:
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"""月球引力参数"""
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return self.G * self.M_moon
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# ============== 发动机参数 ==============
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@dataclass
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class EngineParams:
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"""发动机/推进系统参数"""
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name: str = "液氧液氢"
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isp: float = 450 # 比冲 (秒)
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specific_energy: float = 15.5e6 # 燃料比能量 (J/kg)
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@property
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def exhaust_velocity(self) -> float:
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"""排气速度 (m/s)"""
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return self.isp * 9.81
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# ============== 发射场参数 ==============
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@dataclass
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class LaunchSite:
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"""发射场参数"""
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name: str = "赤道发射场"
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latitude: float = 0.0 # 纬度 (度)
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# 常见发射场纬度参考:
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# 赤道: 0°
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# 文昌 (中国): 19.6°
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# 卡纳维拉尔角 (美国): 28.5°
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# 拜科努尔 (哈萨克斯坦): 45.6°
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# 酒泉 (中国): 40.9°
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# 普列谢茨克 (俄罗斯): 62.9°
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@property
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def latitude_rad(self) -> float:
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"""纬度 (弧度)"""
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return np.radians(self.latitude)
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# 预定义的发射场
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LAUNCH_SITES = {
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# 赤道参考
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'赤道': LaunchSite("Equator (参考)", 0.0),
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# 法属圭亚那 (接近赤道)
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'Kourou': LaunchSite("Kourou (French Guiana)", 5.2),
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# 印度
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'SDSC': LaunchSite("Satish Dhawan (India)", 13.7),
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# 美国
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'Texas': LaunchSite("Boca Chica (Texas)", 26.0),
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'Florida': LaunchSite("Cape Canaveral (Florida)", 28.5),
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'California': LaunchSite("Vandenberg (California)", 34.7),
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'Virginia': LaunchSite("Wallops (Virginia)", 37.8),
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'Alaska': LaunchSite("Kodiak (Alaska)", 57.4),
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# 中国
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'Taiyuan': LaunchSite("Taiyuan (China)", 38.8),
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# 新西兰
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'Mahia': LaunchSite("Mahia (New Zealand)", -39.3), # 南半球
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# 哈萨克斯坦
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'Baikonur': LaunchSite("Baikonur (Kazakhstan)", 45.6),
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}
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# ============== 任务参数 ==============
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@dataclass
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class MissionParams:
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"""任务参数"""
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# 结构系数
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alpha: float = 0.10
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# 目标轨道 (环月轨道高度)
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lunar_orbit_altitude: float = 100e3 # 100 km
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# 地面发射参数 (赤道发射基准值)
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leo_altitude: float = 400e3 # LEO高度 400 km
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delta_v_ground_to_leo_base: float = 9400 # 赤道发射到LEO的基准ΔV (m/s)
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delta_v_tli: float = 3100 # 地月转移注入 (m/s)
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delta_v_loi: float = 800 # 月球轨道捕获 (m/s)
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# 目标轨道倾角 (度), 0 = 赤道轨道
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target_inclination: float = 0.0
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# 太空电梯参数
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elevator_length: float = 1.0e8 # 电梯长度 (m), 默认10万km
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||
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@property
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def total_delta_v_ground(self) -> float:
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"""地面发射总ΔV (赤道发射基准)"""
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return self.delta_v_ground_to_leo_base + self.delta_v_tli + self.delta_v_loi
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# ============== 纬度相关计算函数 ==============
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def earth_rotation_velocity(latitude: float, constants: PhysicalConstants = PhysicalConstants()) -> float:
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"""
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计算地球表面某纬度的自转线速度
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||
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参数:
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latitude: 纬度 (度)
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constants: 物理常数
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返回:
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自转线速度 (m/s)
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"""
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lat_rad = np.radians(latitude)
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return constants.omega_earth * constants.R_earth * np.cos(lat_rad)
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def delta_v_rotation_loss(latitude: float, constants: PhysicalConstants = PhysicalConstants()) -> float:
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"""
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计算相对赤道发射损失的自转速度贡献
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||
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参数:
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latitude: 发射场纬度 (度)
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constants: 物理常数
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返回:
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损失的ΔV (m/s)
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"""
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v_equator = earth_rotation_velocity(0, constants) # 赤道速度 ~465 m/s
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v_latitude = earth_rotation_velocity(latitude, constants)
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return v_equator - v_latitude
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||
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def delta_v_inclination_change(
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launch_latitude: float,
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target_inclination: float,
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orbital_velocity: float = 7800 # LEO轨道速度 (m/s)
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) -> float:
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"""
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计算轨道倾角改变所需的ΔV
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||
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从发射场纬度的轨道转到目标倾角轨道
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注意: 最小轨道倾角 = 发射场纬度
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||
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参数:
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launch_latitude: 发射场纬度 (度)
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target_inclination: 目标轨道倾角 (度)
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orbital_velocity: 轨道速度 (m/s)
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返回:
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倾角改变ΔV (m/s)
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"""
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# 发射场纬度决定最小可达倾角
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min_inclination = abs(launch_latitude)
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if target_inclination < min_inclination:
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# 需要进行纯倾角改变机动 (非常昂贵!)
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# ΔV = 2 * v * sin(Δi/2)
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delta_i = np.radians(min_inclination - target_inclination)
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return 2 * orbital_velocity * np.sin(delta_i / 2)
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else:
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# 可以通过发射方位角直接进入目标倾角，无额外ΔV
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return 0
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def total_delta_v_with_latitude(
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launch_site: LaunchSite,
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mission: MissionParams,
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constants: PhysicalConstants = PhysicalConstants()
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) -> dict:
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"""
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计算考虑纬度因素的总ΔV
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参数:
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launch_site: 发射场
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mission: 任务参数
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constants: 物理常数
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返回:
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包含各项ΔV的字典
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"""
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# 1. 自转速度损失
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dv_rotation_loss = delta_v_rotation_loss(launch_site.latitude, constants)
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# 2. 倾角改变损失 (如果目标是低倾角轨道)
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dv_inclination = delta_v_inclination_change(
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launch_site.latitude,
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mission.target_inclination,
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orbital_velocity=7800
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)
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# 3. 总地面到LEO的ΔV
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dv_to_leo = mission.delta_v_ground_to_leo_base + dv_rotation_loss
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# 4. 总ΔV
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dv_total = dv_to_leo + dv_inclination + mission.delta_v_tli + mission.delta_v_loi
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return {
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'launch_site': launch_site.name,
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'latitude': launch_site.latitude,
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'rotation_velocity': earth_rotation_velocity(launch_site.latitude, constants),
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'dv_rotation_loss': dv_rotation_loss,
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'dv_inclination_change': dv_inclination,
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'dv_to_leo': dv_to_leo,
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'dv_tli': mission.delta_v_tli,
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'dv_loi': mission.delta_v_loi,
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'dv_total': dv_total
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}
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||
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# ============== 核心计算函数 ==============
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||
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def mass_ratio(delta_v: float, engine: EngineParams) -> float:
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||
"""
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计算质量比 R = m0/mf
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参数:
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delta_v: 速度增量 (m/s)
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engine: 发动机参数
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返回:
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质量比 R
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"""
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return np.exp(delta_v / engine.exhaust_velocity)
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||
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def fuel_to_payload_ratio(delta_v: float, engine: EngineParams, alpha: float = 0.1) -> float:
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"""
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计算燃料与载荷的质量比（单级火箭）
|
||
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参数:
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delta_v: 速度增量 (m/s)
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engine: 发动机参数
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alpha: 结构系数
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返回:
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m_fuel / m_payload
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"""
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R = mass_ratio(delta_v, engine)
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denominator = 1 - alpha * (R - 1)
|
||
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||
if denominator <= 0:
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return np.inf
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||
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return (R - 1) / denominator
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||
|
||
|
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def fuel_to_payload_ratio_multistage(
|
||
delta_v: float,
|
||
engine: EngineParams,
|
||
alpha: float = 0.1,
|
||
num_stages: int = 3
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||
) -> float:
|
||
"""
|
||
计算燃料与载荷的质量比（多级火箭）
|
||
|
||
假设各级均分ΔV，使用相同发动机和结构系数
|
||
|
||
参数:
|
||
delta_v: 总速度增量 (m/s)
|
||
engine: 发动机参数
|
||
alpha: 结构系数
|
||
num_stages: 级数
|
||
返回:
|
||
m_fuel_total / m_payload
|
||
"""
|
||
# 每级分配的ΔV
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||
delta_v_per_stage = delta_v / num_stages
|
||
|
||
# 每级的质量比
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||
R_stage = mass_ratio(delta_v_per_stage, engine)
|
||
|
||
# 每级的燃料比 (相对于该级有效载荷)
|
||
denominator = 1 - alpha * (R_stage - 1)
|
||
if denominator <= 0:
|
||
return np.inf
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||
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||
k_stage = (R_stage - 1) / denominator
|
||
|
||
# 结构质量比 (相对于燃料)
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||
# 每级末质量 = 载荷 + 结构 = 载荷 + alpha * 燃料
|
||
# 每级初质量 = 载荷 + 结构 + 燃料 = 载荷 * (1 + k_stage * (1 + alpha))
|
||
|
||
# 对于多级火箭，总质量比是各级质量比的乘积
|
||
# 第i级的"载荷"是第i+1级及以上所有质量
|
||
|
||
# 简化计算：假设各级结构系数相同
|
||
# 级比 = (1 + k_stage * (1 + alpha))
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||
stage_ratio = 1 + k_stage * (1 + alpha)
|
||
|
||
# 总初始质量/最终载荷 = stage_ratio ^ num_stages
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total_ratio = stage_ratio ** num_stages
|
||
|
||
# 总燃料 = 总初始质量 - 载荷 - 总结构
|
||
# 近似：总燃料/载荷 ≈ total_ratio - 1 (忽略结构细节)
|
||
|
||
# 更精确的计算
|
||
total_fuel_ratio = 0
|
||
remaining_ratio = 1.0
|
||
|
||
for _ in range(num_stages):
|
||
# 当前级燃料相对于最终载荷
|
||
fuel_this_stage = remaining_ratio * k_stage
|
||
total_fuel_ratio += fuel_this_stage
|
||
# 下一级的质量（相对于最终载荷）
|
||
remaining_ratio *= (1 + k_stage * (1 + alpha))
|
||
|
||
return total_fuel_ratio
|
||
|
||
|
||
# ============== 地面发射比能量计算 ==============
|
||
|
||
def ground_launch_specific_energy(
|
||
engine: EngineParams,
|
||
mission: MissionParams,
|
||
constants: PhysicalConstants = PhysicalConstants(),
|
||
num_stages: int = 3
|
||
) -> dict:
|
||
"""
|
||
计算地面发射的比能量（使用多级火箭）
|
||
|
||
参数:
|
||
engine: 发动机参数
|
||
mission: 任务参数
|
||
constants: 物理常数
|
||
num_stages: 火箭级数 (默认3级)
|
||
|
||
返回:
|
||
包含各项比能量的字典 (单位: J/kg 载荷)
|
||
"""
|
||
# 总ΔV
|
||
delta_v_total = mission.total_delta_v_ground
|
||
|
||
# 燃料/载荷比 (使用多级火箭模型)
|
||
k = fuel_to_payload_ratio_multistage(delta_v_total, engine, mission.alpha, num_stages)
|
||
|
||
# 推进剂化学能 (J/kg 载荷)
|
||
propellant_energy = k * engine.specific_energy
|
||
|
||
# 载荷轨道能量增益
|
||
r_moon_orbit = constants.R_moon + mission.lunar_orbit_altitude
|
||
|
||
# 从地面静止到月球轨道的比能量变化
|
||
E_initial = -constants.GM_earth / constants.R_earth
|
||
E_final = -constants.GM_moon / (2 * r_moon_orbit) - constants.GM_earth / constants.d_earth_moon
|
||
payload_orbital_energy = E_final - E_initial
|
||
|
||
# 效率
|
||
efficiency = payload_orbital_energy / propellant_energy if propellant_energy > 0 and not np.isinf(propellant_energy) else 0
|
||
|
||
return {
|
||
'delta_v': delta_v_total,
|
||
'fuel_ratio': k,
|
||
'num_stages': num_stages,
|
||
'propellant_energy': propellant_energy,
|
||
'payload_orbital_energy': payload_orbital_energy,
|
||
'total_energy': propellant_energy, # 地面发射全靠推进剂
|
||
'efficiency': efficiency,
|
||
'method': f'地面发射({num_stages}级)'
|
||
}
|
||
|
||
|
||
def ground_launch_specific_energy_with_latitude(
|
||
engine: EngineParams,
|
||
mission: MissionParams,
|
||
launch_site: LaunchSite,
|
||
constants: PhysicalConstants = PhysicalConstants(),
|
||
num_stages: int = 3
|
||
) -> dict:
|
||
"""
|
||
计算考虑发射场纬度的地面发射比能量
|
||
|
||
参数:
|
||
engine: 发动机参数
|
||
mission: 任务参数
|
||
launch_site: 发射场
|
||
constants: 物理常数
|
||
num_stages: 火箭级数 (默认3级)
|
||
|
||
返回:
|
||
包含各项比能量的字典 (单位: J/kg 载荷)
|
||
"""
|
||
# 计算纬度相关的ΔV
|
||
dv_info = total_delta_v_with_latitude(launch_site, mission, constants)
|
||
delta_v_total = dv_info['dv_total']
|
||
|
||
# 燃料/载荷比 (使用多级火箭模型)
|
||
k = fuel_to_payload_ratio_multistage(delta_v_total, engine, mission.alpha, num_stages)
|
||
|
||
# 推进剂化学能 (J/kg 载荷)
|
||
propellant_energy = k * engine.specific_energy
|
||
|
||
# 载荷轨道能量增益
|
||
r_moon_orbit = constants.R_moon + mission.lunar_orbit_altitude
|
||
E_initial = -constants.GM_earth / constants.R_earth
|
||
E_final = -constants.GM_moon / (2 * r_moon_orbit) - constants.GM_earth / constants.d_earth_moon
|
||
payload_orbital_energy = E_final - E_initial
|
||
|
||
# 效率
|
||
efficiency = payload_orbital_energy / propellant_energy if propellant_energy > 0 and not np.isinf(propellant_energy) else 0
|
||
|
||
return {
|
||
'launch_site': launch_site.name,
|
||
'latitude': launch_site.latitude,
|
||
'rotation_velocity': dv_info['rotation_velocity'],
|
||
'dv_rotation_loss': dv_info['dv_rotation_loss'],
|
||
'dv_inclination_change': dv_info['dv_inclination_change'],
|
||
'delta_v': delta_v_total,
|
||
'fuel_ratio': k,
|
||
'num_stages': num_stages,
|
||
'propellant_energy': propellant_energy,
|
||
'payload_orbital_energy': payload_orbital_energy,
|
||
'total_energy': propellant_energy,
|
||
'efficiency': efficiency,
|
||
'method': f'地面发射({launch_site.name}, {num_stages}级)'
|
||
}
|
||
|
||
|
||
def compare_launch_sites(
|
||
engine: EngineParams = EngineParams(),
|
||
mission: MissionParams = MissionParams(),
|
||
constants: PhysicalConstants = PhysicalConstants(),
|
||
num_stages: int = 3
|
||
) -> list:
|
||
"""
|
||
比较不同发射场的燃料和能量需求
|
||
|
||
返回:
|
||
各发射场的分析结果列表 (按纬度绝对值排序)
|
||
"""
|
||
results = []
|
||
for name, site in LAUNCH_SITES.items():
|
||
# 使用纬度绝对值进行计算（南北半球对称）
|
||
abs_lat = abs(site.latitude)
|
||
site_normalized = LaunchSite(site.name, abs_lat)
|
||
result = ground_launch_specific_energy_with_latitude(
|
||
engine, mission, site_normalized, constants, num_stages
|
||
)
|
||
result['original_latitude'] = site.latitude
|
||
result['abs_latitude'] = abs_lat
|
||
results.append(result)
|
||
|
||
return sorted(results, key=lambda x: x['abs_latitude'])
|
||
|
||
|
||
def print_latitude_comparison(results: list):
|
||
"""打印不同纬度发射场的对比"""
|
||
print("=" * 110)
|
||
print("Launch Site Latitude Effects on Fuel and Energy")
|
||
print("=" * 110)
|
||
|
||
print(f"\n{'Launch Site':<30} {'Lat':>6} {'V_rot':>8} {'ΔV_loss':>8} {'ΔV_total':>9} {'Fuel/PL':>9} {'Energy':>10}")
|
||
print(f"{'':30} {'(°)':>6} {'(m/s)':>8} {'(m/s)':>8} {'(km/s)':>9} {'Ratio':>9} {'(MJ/kg)':>10}")
|
||
print("-" * 110)
|
||
|
||
for r in results:
|
||
lat = r.get('abs_latitude', abs(r['latitude']))
|
||
print(f"{r['launch_site']:<30} {lat:>6.1f} {r['rotation_velocity']:>8.0f} {r['dv_rotation_loss']:>8.0f} {r['delta_v']/1000:>9.2f} {r['fuel_ratio']:>9.1f} {r['total_energy']/1e6:>10.1f}")
|
||
|
||
print("-" * 110)
|
||
|
||
# 计算相对赤道的损失
|
||
equator_result = next((r for r in results if abs(r['latitude']) < 0.1), results[0])
|
||
print(f"\nExtra consumption relative to Equator launch:")
|
||
for r in results:
|
||
lat = r.get('abs_latitude', abs(r['latitude']))
|
||
if lat > 0.1:
|
||
fuel_increase = (r['fuel_ratio'] / equator_result['fuel_ratio'] - 1) * 100
|
||
energy_increase = (r['total_energy'] / equator_result['total_energy'] - 1) * 100
|
||
print(f" {r['launch_site']:<30}: Fuel +{fuel_increase:>5.1f}%, Energy +{energy_increase:>5.1f}%")
|
||
|
||
print("=" * 110)
|
||
|
||
|
||
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',
|
||
lunar_mission: bool = True
|
||
):
|
||
"""
|
||
绘制纬度影响图表
|
||
|
||
参数:
|
||
lunar_mission: 如果True，使用月球任务场景（不需要轨道平面改变）
|
||
"""
|
||
|
||
# 月球任务场景：设置高目标倾角，避免轨道平面改变惩罚
|
||
if lunar_mission:
|
||
mission_plot = MissionParams(
|
||
alpha=mission.alpha,
|
||
lunar_orbit_altitude=mission.lunar_orbit_altitude,
|
||
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
|
||
elevator_length=mission.elevator_length
|
||
)
|
||
title_suffix = "\n(Lunar Mission - 无轨道平面改变)"
|
||
else:
|
||
mission_plot = mission
|
||
title_suffix = "\n(目标: 赤道轨道)"
|
||
|
||
fig, axes = plt.subplots(2, 2, figsize=(16, 14))
|
||
|
||
# 连续纬度范围
|
||
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]
|
||
|
||
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')
|
||
|
||
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)
|
||
label = site.name.split('(')[0].strip()
|
||
ax3.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')
|
||
|
||
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}")
|
||
|
||
return fig
|
||
|
||
|
||
# ============== 电梯发射比能量计算 ==============
|
||
|
||
def elevator_launch_specific_energy(
|
||
engine: EngineParams,
|
||
mission: MissionParams,
|
||
constants: PhysicalConstants = PhysicalConstants(),
|
||
release_height: Optional[float] = None
|
||
) -> dict:
|
||
"""
|
||
计算太空电梯发射的比能量
|
||
|
||
参数:
|
||
engine: 发动机参数
|
||
mission: 任务参数
|
||
constants: 物理常数
|
||
release_height: 释放高度 (m)，None则使用电梯顶端
|
||
|
||
返回:
|
||
包含各项比能量的字典 (单位: J/kg 载荷)
|
||
"""
|
||
# 释放点参数
|
||
if release_height is None:
|
||
release_height = mission.elevator_length
|
||
|
||
r_release = constants.R_earth + release_height
|
||
|
||
# 释放点速度 (随地球自转)
|
||
v_release = constants.omega_earth * r_release
|
||
|
||
# 释放点的逃逸速度
|
||
v_escape = np.sqrt(2 * constants.GM_earth / r_release)
|
||
|
||
# 释放点的圆轨道速度
|
||
v_circular = np.sqrt(constants.GM_earth / r_release)
|
||
|
||
# 计算C3 (特征能量)
|
||
C3 = v_release**2 - v_escape**2
|
||
|
||
# 电梯提升能量 (从地面到释放点)
|
||
# 包括势能变化和动能获得
|
||
lift_energy = (
|
||
constants.GM_earth / constants.R_earth
|
||
- constants.GM_earth / r_release
|
||
+ 0.5 * v_release**2
|
||
)
|
||
|
||
# 计算所需ΔV
|
||
if C3 > 0:
|
||
# 已超过逃逸速度，需要减速
|
||
# 目标：进入地月转移轨道 (C3 ≈ -2 km²/s²)
|
||
C3_target = -2e6 # -2 km²/s² 转换为 m²/s²
|
||
v_needed = np.sqrt(max(0, v_escape**2 + C3_target))
|
||
delta_v_adjust = abs(v_release - v_needed)
|
||
maneuver_type = "减速"
|
||
else:
|
||
# 未达逃逸速度，需要加速
|
||
# 计算到达月球轨道所需的额外速度
|
||
v_needed = np.sqrt(v_escape**2 - 2e6) # 地月转移
|
||
delta_v_adjust = v_needed - v_release
|
||
maneuver_type = "加速"
|
||
|
||
# 加上月球轨道捕获
|
||
delta_v_total = abs(delta_v_adjust) + mission.delta_v_loi
|
||
|
||
# 燃料/载荷比
|
||
k = fuel_to_payload_ratio(delta_v_total, engine, mission.alpha)
|
||
|
||
# 推进剂化学能
|
||
propellant_energy = k * engine.specific_energy
|
||
|
||
# 载荷轨道能量增益 (与地面发射相同)
|
||
r_moon_orbit = constants.R_moon + mission.lunar_orbit_altitude
|
||
E_initial = -constants.GM_earth / constants.R_earth
|
||
E_final = -constants.GM_moon / (2 * r_moon_orbit) - constants.GM_earth / constants.d_earth_moon
|
||
payload_orbital_energy = E_final - E_initial
|
||
|
||
# 总能量 = 电梯提升 + 推进剂
|
||
total_energy = lift_energy + propellant_energy
|
||
|
||
# 效率
|
||
efficiency = payload_orbital_energy / total_energy if total_energy > 0 else 0
|
||
|
||
return {
|
||
'release_height': release_height,
|
||
'release_velocity': v_release,
|
||
'escape_velocity': v_escape,
|
||
'C3': C3,
|
||
'maneuver_type': maneuver_type,
|
||
'delta_v': delta_v_total,
|
||
'fuel_ratio': k,
|
||
'lift_energy': lift_energy,
|
||
'propellant_energy': propellant_energy,
|
||
'payload_orbital_energy': payload_orbital_energy,
|
||
'total_energy': total_energy,
|
||
'efficiency': efficiency,
|
||
'method': '电梯发射'
|
||
}
|
||
|
||
|
||
# ============== 对比分析函数 ==============
|
||
|
||
def compare_launch_methods(
|
||
engine: EngineParams = EngineParams(),
|
||
mission: MissionParams = MissionParams(),
|
||
constants: PhysicalConstants = PhysicalConstants()
|
||
) -> dict:
|
||
"""
|
||
对比两种发射方式
|
||
|
||
返回:
|
||
对比结果字典
|
||
"""
|
||
ground = ground_launch_specific_energy(engine, mission, constants)
|
||
elevator = elevator_launch_specific_energy(engine, mission, constants)
|
||
|
||
return {
|
||
'ground': ground,
|
||
'elevator': elevator,
|
||
'fuel_saving': 1 - elevator['fuel_ratio'] / ground['fuel_ratio'],
|
||
'energy_saving': 1 - elevator['total_energy'] / ground['total_energy'],
|
||
'delta_v_saving': 1 - elevator['delta_v'] / ground['delta_v']
|
||
}
|
||
|
||
|
||
def print_comparison(comparison: dict):
|
||
"""打印对比结果"""
|
||
ground = comparison['ground']
|
||
elevator = comparison['elevator']
|
||
|
||
ground_label = ground['method']
|
||
elevator_label = elevator['method']
|
||
|
||
print("=" * 70)
|
||
print("地面发射 vs 太空电梯发射：比能量对比")
|
||
print("=" * 70)
|
||
|
||
print(f"\n{'参数':<25} {ground_label:>18} {elevator_label:>18}")
|
||
print("-" * 70)
|
||
|
||
print(f"{'ΔV (km/s)':<25} {ground['delta_v']/1000:>18.2f} {elevator['delta_v']/1000:>18.2f}")
|
||
print(f"{'燃料/载荷比':<25} {ground['fuel_ratio']:>18.2f} {elevator['fuel_ratio']:>18.2f}")
|
||
print(f"{'电梯提升能量 (MJ/kg)':<25} {'0':>18} {elevator['lift_energy']/1e6:>18.1f}")
|
||
print(f"{'推进剂能量 (MJ/kg)':<25} {ground['propellant_energy']/1e6:>18.1f} {elevator['propellant_energy']/1e6:>18.1f}")
|
||
print(f"{'总能量 (MJ/kg)':<25} {ground['total_energy']/1e6:>18.1f} {elevator['total_energy']/1e6:>18.1f}")
|
||
print(f"{'载荷能量增益 (MJ/kg)':<25} {ground['payload_orbital_energy']/1e6:>18.1f} {elevator['payload_orbital_energy']/1e6:>18.1f}")
|
||
print(f"{'系统效率':<25} {ground['efficiency']*100:>17.1f}% {elevator['efficiency']*100:>17.1f}%")
|
||
|
||
print("\n" + "-" * 70)
|
||
print(f"{'ΔV 节省':<25} {comparison['delta_v_saving']*100:>18.1f}%")
|
||
print(f"{'燃料节省':<25} {comparison['fuel_saving']*100:>18.1f}%")
|
||
print(f"{'总能量节省':<25} {comparison['energy_saving']*100:>18.1f}%")
|
||
print("=" * 70)
|
||
|
||
|
||
def plot_comparison(
|
||
engine: EngineParams = EngineParams(),
|
||
mission: MissionParams = MissionParams(),
|
||
constants: PhysicalConstants = PhysicalConstants(),
|
||
save_path: str = '/Volumes/Files/code/mm/20260130_b/specific_energy_comparison.png'
|
||
):
|
||
"""绘制对比图表"""
|
||
|
||
fig, axes = plt.subplots(2, 2, figsize=(14, 12))
|
||
|
||
# ========== 图1: 不同电梯高度的ΔV需求 ==========
|
||
ax1 = axes[0, 0]
|
||
heights = np.linspace(3.6e7, 1.5e8, 100) # 36,000 km 到 150,000 km
|
||
|
||
delta_vs = []
|
||
for h in heights:
|
||
mission_temp = MissionParams(elevator_length=h)
|
||
result = elevator_launch_specific_energy(engine, mission_temp, constants, h)
|
||
delta_vs.append(result['delta_v'] / 1000)
|
||
|
||
ax1.plot(heights/1e6, delta_vs, 'b-', linewidth=2, label='电梯发射')
|
||
ax1.axhline(y=mission.total_delta_v_ground/1000, color='r', linestyle='--',
|
||
linewidth=2, label='地面发射')
|
||
ax1.axvline(x=35.786, color='g', linestyle=':', label='GEO高度')
|
||
|
||
ax1.set_xlabel('电梯释放高度 (千km)', fontsize=12)
|
||
ax1.set_ylabel('ΔV 需求 (km/s)', fontsize=12)
|
||
ax1.set_title('释放高度 vs ΔV需求', fontsize=14)
|
||
ax1.legend()
|
||
ax1.grid(True, alpha=0.3)
|
||
|
||
# ========== 图2: 燃料/载荷比对比 ==========
|
||
ax2 = axes[0, 1]
|
||
|
||
fuel_ratios_elevator = []
|
||
for h in heights:
|
||
mission_temp = MissionParams(elevator_length=h)
|
||
result = elevator_launch_specific_energy(engine, mission_temp, constants, h)
|
||
fuel_ratios_elevator.append(result['fuel_ratio'])
|
||
|
||
ground_result = ground_launch_specific_energy(engine, mission, constants, num_stages=3)
|
||
|
||
ax2.plot(heights/1e6, fuel_ratios_elevator, 'b-', linewidth=2, label='电梯发射')
|
||
ax2.axhline(y=ground_result['fuel_ratio'], color='r', linestyle='--',
|
||
linewidth=2, label='地面发射(3级)')
|
||
|
||
ax2.set_xlabel('电梯释放高度 (千km)', fontsize=12)
|
||
ax2.set_ylabel('燃料/载荷 质量比', fontsize=12)
|
||
ax2.set_title('释放高度 vs 燃料效率', fontsize=14)
|
||
ax2.legend()
|
||
ax2.grid(True, alpha=0.3)
|
||
ax2.set_ylim(0, 30)
|
||
|
||
# ========== 图3: 能量构成对比 (柱状图) ==========
|
||
ax3 = axes[1, 0]
|
||
|
||
comparison = compare_launch_methods(engine, mission, constants)
|
||
|
||
categories = ['地面发射', '电梯发射']
|
||
lift_energy = [0, comparison['elevator']['lift_energy']/1e6]
|
||
prop_energy = [comparison['ground']['propellant_energy']/1e6,
|
||
comparison['elevator']['propellant_energy']/1e6]
|
||
|
||
x = np.arange(len(categories))
|
||
width = 0.35
|
||
|
||
bars1 = ax3.bar(x, lift_energy, width, label='电梯提升能量', color='green')
|
||
bars2 = ax3.bar(x, prop_energy, width, bottom=lift_energy, label='推进剂能量', color='orange')
|
||
|
||
ax3.set_ylabel('比能量 (MJ/kg)', fontsize=12)
|
||
ax3.set_title('能量构成对比', fontsize=14)
|
||
ax3.set_xticks(x)
|
||
ax3.set_xticklabels(categories)
|
||
ax3.legend()
|
||
ax3.grid(True, alpha=0.3, axis='y')
|
||
|
||
# 添加数值标签
|
||
for i, (l, p) in enumerate(zip(lift_energy, prop_energy)):
|
||
total = l + p
|
||
ax3.text(i, total + 5, f'{total:.0f}', ha='center', fontsize=11, fontweight='bold')
|
||
|
||
# ========== 图4: 不同发动机对比 ==========
|
||
ax4 = axes[1, 1]
|
||
|
||
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="液氧液氢", isp=450, specific_energy=15.5e6),
|
||
]
|
||
|
||
x_pos = np.arange(len(engines))
|
||
ground_ratios = []
|
||
elevator_ratios = []
|
||
|
||
for eng in engines:
|
||
g = ground_launch_specific_energy(eng, mission, constants, num_stages=3)
|
||
e = elevator_launch_specific_energy(eng, mission, constants)
|
||
ground_ratios.append(min(g['fuel_ratio'], 100)) # 限制显示范围
|
||
elevator_ratios.append(e['fuel_ratio'])
|
||
|
||
width = 0.35
|
||
ax4.bar(x_pos - width/2, ground_ratios, width, label='地面发射(3级)', color='red', alpha=0.7)
|
||
ax4.bar(x_pos + width/2, elevator_ratios, width, label='电梯发射', color='blue', alpha=0.7)
|
||
|
||
ax4.set_ylabel('燃料/载荷 质量比', fontsize=12)
|
||
ax4.set_title('不同发动机的燃料效率对比', fontsize=14)
|
||
ax4.set_xticks(x_pos)
|
||
ax4.set_xticklabels([e.name for e in engines])
|
||
ax4.legend()
|
||
ax4.grid(True, alpha=0.3, axis='y')
|
||
|
||
plt.tight_layout()
|
||
plt.savefig(save_path, dpi=150, bbox_inches='tight')
|
||
print(f"图表已保存至: {save_path}")
|
||
|
||
return fig
|
||
|
||
|
||
# ============== 主程序 ==============
|
||
|
||
if __name__ == "__main__":
|
||
# 可以在这里修改参数
|
||
|
||
# 发动机参数
|
||
engine = EngineParams(
|
||
name="液氧液氢",
|
||
isp=450, # 比冲 (秒)
|
||
specific_energy=15.5e6 # 燃料比能量 (J/kg)
|
||
)
|
||
|
||
# 任务参数
|
||
mission = MissionParams(
|
||
alpha=0.10, # 结构系数
|
||
lunar_orbit_altitude=100e3, # 环月轨道高度 (m)
|
||
delta_v_ground_to_leo_base=9400, # 赤道发射到LEO的基准ΔV (m/s)
|
||
delta_v_tli=3100, # 地月转移注入 (m/s)
|
||
delta_v_loi=800, # 月球轨道捕获 (m/s)
|
||
target_inclination=0.0, # 目标轨道倾角 (度)
|
||
elevator_length=1.0e8 # 电梯长度 10万km (m)
|
||
)
|
||
|
||
# 物理常数 (通常不需要修改)
|
||
constants = PhysicalConstants()
|
||
|
||
# ========== 1. 地面发射 vs 电梯发射对比 ==========
|
||
comparison = compare_launch_methods(engine, mission, constants)
|
||
print_comparison(comparison)
|
||
|
||
# 绘制对比图表
|
||
print("\n正在生成对比图表...")
|
||
plot_comparison(engine, mission, constants)
|
||
|
||
# 电梯发射详细信息
|
||
print("\n" + "=" * 70)
|
||
print("电梯发射详细参数:")
|
||
print("=" * 70)
|
||
elevator = comparison['elevator']
|
||
print(f" 释放高度: {elevator['release_height']/1e6:.1f} 千km")
|
||
print(f" 释放点速度: {elevator['release_velocity']/1000:.2f} km/s")
|
||
print(f" 当地逃逸速度: {elevator['escape_velocity']/1000:.2f} km/s")
|
||
print(f" 特征能量 C3: {elevator['C3']/1e6:.1f} km²/s²")
|
||
print(f" 机动类型: {elevator['maneuver_type']}")
|
||
|
||
# ========== 2. 发射场纬度影响分析 (月球任务) ==========
|
||
print("\n")
|
||
print("=" * 110)
|
||
print("LUNAR MISSION: Launch Site Comparison")
|
||
print("(No orbital plane change required - only rotation velocity loss)")
|
||
print("=" * 110)
|
||
|
||
# 月球任务配置（允许倾角与发射场纬度匹配）
|
||
mission_lunar = MissionParams(
|
||
alpha=mission.alpha,
|
||
lunar_orbit_altitude=mission.lunar_orbit_altitude,
|
||
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
|
||
elevator_length=mission.elevator_length
|
||
)
|
||
|
||
latitude_results = compare_launch_sites(engine, mission_lunar, constants)
|
||
print_latitude_comparison(latitude_results)
|
||
|
||
# 绘制纬度影响图表 (月球任务模式)
|
||
print("\n正在生成纬度影响图表 (Lunar Mission)...")
|
||
plot_latitude_effects(engine, mission_lunar, constants, lunar_mission=True)
|
||
|
||
# ========== 3. 公式总结 ==========
|
||
print("\n" + "=" * 70)
|
||
print("数学关系总结:")
|
||
print("=" * 70)
|
||
print("""
|
||
地球自转速度:
|
||
v(φ) = ω × R_E × cos(φ)
|
||
|
||
自转速度损失:
|
||
Δv_loss = v(0°) - v(φ) = 465 × (1 - cos(φ)) m/s
|
||
|
||
纬度对燃料的影响:
|
||
由于 ΔV 增加 → R = exp(ΔV/ve) 指数增长 → 燃料比指数增长
|
||
|
||
关键结论:
|
||
- 赤道发射: 自转贡献 465 m/s, 燃料最省
|
||
- 高纬度发射: 损失自转贡献, 且可能需要额外倾角机动
|
||
- 每损失 100 m/s 自转速度 ≈ 增加 ~3% 燃料需求
|
||
""")
|