""" 地面发射 vs 太空电梯发射:比能量计算与对比 可配置参数进行不同场景的能量分析 """ import numpy as np import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt from matplotlib import rcParams from dataclasses import dataclass from typing import Optional # 设置中文字体支持 rcParams['font.sans-serif'] = ['Arial Unicode MS', 'SimHei', 'DejaVu Sans'] rcParams['axes.unicode_minus'] = False # ============== 物理常数 ============== @dataclass class PhysicalConstants: """物理常数""" G: float = 6.674e-11 # 万有引力常数 (m³/kg/s²) M_earth: float = 5.972e24 # 地球质量 (kg) M_moon: float = 7.342e22 # 月球质量 (kg) R_earth: float = 6.371e6 # 地球半径 (m) R_moon: float = 1.737e6 # 月球半径 (m) g0: float = 9.81 # 地表重力加速度 (m/s²) d_earth_moon: float = 3.844e8 # 地月平均距离 (m) omega_earth: float = 7.27e-5 # 地球自转角速度 (rad/s) @property def GM_earth(self) -> float: """地球引力参数""" return self.G * self.M_earth @property def GM_moon(self) -> float: """月球引力参数""" return self.G * self.M_moon # ============== 发动机参数 ============== @dataclass class EngineParams: """发动机/推进系统参数""" 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: """排气速度 (m/s)""" return self.isp * 9.81 # ============== 发射场参数 ============== @dataclass class LaunchSite: """发射场参数""" name: str = "赤道发射场" latitude: float = 0.0 # 纬度 (度) # 常见发射场纬度参考: # 赤道: 0° # 文昌 (中国): 19.6° # 卡纳维拉尔角 (美国): 28.5° # 拜科努尔 (哈萨克斯坦): 45.6° # 酒泉 (中国): 40.9° # 普列谢茨克 (俄罗斯): 62.9° @property def latitude_rad(self) -> float: """纬度 (弧度)""" return np.radians(self.latitude) # 预定义的发射场 LAUNCH_SITES = { # 赤道参考 '赤道': LaunchSite("Equator", 0.0), # 法属圭亚那 (接近赤道) 'Kourou': LaunchSite("French Guiana", 5.2), # 印度 'SDSC': LaunchSite("Satish Dhawan", 13.7), # 美国 'Texas': LaunchSite("Texas", 26.0), 'Florida': LaunchSite("Florida", 28.5), 'California': LaunchSite("California", 34.7), 'Virginia': LaunchSite("Virginia", 37.8), 'Alaska': LaunchSite("Alaska", 57.4), # 中国 'Taiyuan': LaunchSite("Taiyuan", 38.8), # 新西兰 'Mahia': LaunchSite("Mahia", -39.3), # 南半球 # 哈萨克斯坦 'Baikonur': LaunchSite("Kazakhstan", 45.6), } # ============== 任务参数 ============== @dataclass class MissionParams: """任务参数""" # 结构系数 alpha: float = 0.10 # 目标轨道 (环月轨道高度) lunar_orbit_altitude: float = 100e3 # 100 km # 地面发射参数 (赤道发射基准值) leo_altitude: float = 400e3 # LEO高度 400 km delta_v_ground_to_leo_base: float = 9400 # 赤道发射到LEO的基准ΔV (m/s) delta_v_tli: float = 3100 # 地月转移注入 (m/s) delta_v_loi: float = 800 # 月球轨道捕获 (m/s) # 目标轨道倾角 (度), 0 = 赤道轨道 target_inclination: float = 0.0 # 太空电梯参数 elevator_length: float = 1.0e8 # 电梯长度 (m), 默认10万km @property def total_delta_v_ground(self) -> float: """地面发射总ΔV (赤道发射基准)""" return self.delta_v_ground_to_leo_base + self.delta_v_tli + self.delta_v_loi # ============== 纬度相关计算函数 ============== def earth_rotation_velocity(latitude: float, constants: PhysicalConstants = PhysicalConstants()) -> float: """ 计算地球表面某纬度的自转线速度 参数: latitude: 纬度 (度) constants: 物理常数 返回: 自转线速度 (m/s) """ lat_rad = np.radians(latitude) return constants.omega_earth * constants.R_earth * np.cos(lat_rad) def delta_v_rotation_loss(latitude: float, constants: PhysicalConstants = PhysicalConstants()) -> float: """ 计算相对赤道发射损失的自转速度贡献 参数: latitude: 发射场纬度 (度) constants: 物理常数 返回: 损失的ΔV (m/s) """ v_equator = earth_rotation_velocity(0, constants) # 赤道速度 ~465 m/s v_latitude = earth_rotation_velocity(latitude, constants) return v_equator - v_latitude def delta_v_inclination_change( launch_latitude: float, target_inclination: float, orbital_velocity: float = 7800 # LEO轨道速度 (m/s) ) -> float: """ 计算轨道倾角改变所需的ΔV 从发射场纬度的轨道转到目标倾角轨道 注意: 最小轨道倾角 = 发射场纬度 参数: launch_latitude: 发射场纬度 (度) target_inclination: 目标轨道倾角 (度) orbital_velocity: 轨道速度 (m/s) 返回: 倾角改变ΔV (m/s) """ # 发射场纬度决定最小可达倾角 min_inclination = abs(launch_latitude) if target_inclination < min_inclination: # 需要进行纯倾角改变机动 (非常昂贵!) # ΔV = 2 * v * sin(Δi/2) delta_i = np.radians(min_inclination - target_inclination) return 2 * orbital_velocity * np.sin(delta_i / 2) else: # 可以通过发射方位角直接进入目标倾角,无额外ΔV return 0 def total_delta_v_with_latitude( launch_site: LaunchSite, mission: MissionParams, constants: PhysicalConstants = PhysicalConstants() ) -> dict: """ 计算考虑纬度因素的总ΔV 参数: launch_site: 发射场 mission: 任务参数 constants: 物理常数 返回: 包含各项ΔV的字典 """ # 1. 自转速度损失 dv_rotation_loss = delta_v_rotation_loss(launch_site.latitude, constants) # 2. 倾角改变损失 (如果目标是低倾角轨道) dv_inclination = delta_v_inclination_change( launch_site.latitude, mission.target_inclination, orbital_velocity=7800 ) # 3. 总地面到LEO的ΔV dv_to_leo = mission.delta_v_ground_to_leo_base + dv_rotation_loss # 4. 总ΔV dv_total = dv_to_leo + dv_inclination + mission.delta_v_tli + mission.delta_v_loi return { 'launch_site': launch_site.name, 'latitude': launch_site.latitude, 'rotation_velocity': earth_rotation_velocity(launch_site.latitude, constants), 'dv_rotation_loss': dv_rotation_loss, 'dv_inclination_change': dv_inclination, 'dv_to_leo': dv_to_leo, 'dv_tli': mission.delta_v_tli, 'dv_loi': mission.delta_v_loi, 'dv_total': dv_total } # ============== 核心计算函数 ============== def mass_ratio(delta_v: float, engine: EngineParams) -> float: """ 计算质量比 R = m0/mf 参数: delta_v: 速度增量 (m/s) engine: 发动机参数 返回: 质量比 R """ return np.exp(delta_v / engine.exhaust_velocity) def fuel_to_payload_ratio(delta_v: float, engine: EngineParams, alpha: float = 0.1) -> float: """ 计算燃料与载荷的质量比(单级火箭) 参数: delta_v: 速度增量 (m/s) engine: 发动机参数 alpha: 结构系数 返回: m_fuel / m_payload """ R = mass_ratio(delta_v, engine) denominator = 1 - alpha * (R - 1) if denominator <= 0: return np.inf return (R - 1) / denominator def fuel_to_payload_ratio_multistage( delta_v: float, engine: EngineParams, alpha: float = 0.1, num_stages: int = 3 ) -> 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 delta_v_per_stage = delta_v / num_stages # 每级的质量比 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 k_stage = (R_stage - 1) / denominator # 结构质量比 (相对于燃料) # 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)) stage_ratio = 1 + k_stage * (1 + alpha) # 总初始质量/最终载荷 = stage_ratio ^ num_stages 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/p1/latitude_effects.png', lunar_mission: bool = True ): """ Plot fuel ratio vs launch latitude. 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) """ # Lunar mission scenario: set high target inclination to avoid plane change penalty 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, # Allow any inclination elevator_length=mission.elevator_length ) title_suffix = " (Lunar Mission)" else: mission_plot = mission title_suffix = " (Target: Equatorial Orbit)" # Golden ratio aspect: 缩小尺寸使字体相对更大 fig, ax = plt.subplots(figsize=(8, 8 * 0.618)) # 中低饱和度配色 color_curve = '#52796F' # 暗绿色 - 曲线 color_point = '#8E7B9A' # 灰紫色 - 数据点 # Continuous latitude range latitudes = np.linspace(0, 65, 100) # 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']) # Plot continuous curve ax.plot(latitudes, fuel_ratios, color=color_curve, linewidth=2, label='Fuel Ratio vs Latitude') # Mark launch sites with custom offsets to avoid overlap with curve # Offsets: (x, y) in points - positive y moves text up, positive x moves right # 纬度参考: Equator(0), French Guiana(5.2), Satish Dhawan(13.7), Texas(26), # Florida(28.5), California(34.7), Virginia(37.8), Taiyuan(38.8), # Mahia(39.3), Kazakhstan(45.6), Alaska(57.4) label_offsets = { '赤道': (5, -15), # Below curve 'Kourou': (-75, 15), # Left above (French Guiana) 'SDSC': (8, -15), # Below right (Satish Dhawan) 'Texas': (-38, -15), # Left below 'Florida': (8, -15), # Right below 'California': (8, -15), # Right below 'Virginia': (8, 12), # Right above 'Taiyuan': (-52, 12), # Left above (避开California) 'Mahia': (8, -18), # Right below 'Alaska': (8, 8), # Right above 'Baikonur': (8, 8), # Right above (Kazakhstan) } 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) ax.plot(abs_lat, result['fuel_ratio'], 'o', color=color_point, markersize=8) # Simplified label label = site.name.split('(')[0].strip() # Get custom offset for this site, default to (5, 8) offset = label_offsets.get(name, (5, 8)) ax.annotate(label, (abs_lat, result['fuel_ratio']), textcoords="offset points", xytext=offset, fontsize=11) 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(-2, 65) plt.tight_layout() plt.savefig(save_path, dpi=150, bbox_inches='tight') print(f"Latitude effects plot saved to: {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="液氧甲烷", isp=363, specific_energy=11.9e6), 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 - 液氧甲烷 (LOX/CH4, Raptor-class) engine = EngineParams( 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 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 """)