基于经纬度变化的客机巡航地速估算方法探究

摘要：为解决客机巡航阶段实际地速的实测验证问题，本文提出一种基于智能手机 GPS 数据与初高中知识体系的地速估算方法。以西部航空 PN6268 航班（空客 A320）为研究对象，在 7600 m 左右巡航高度，通过录屏方式采集两段各 120 s 平稳飞行时段的经纬度、海拔等数据，分别采用平面几何法（初中物理知识）与 Haversine 球面距离公式（高中地理知识）计算水平位移，结合速度公式 v=S/Δt 完成地速估算。结果显示，平面几何法估算地速为 691 km/h 与 1039 km/h，球面距离公式估算结果为 753 km/h 与 1110 km/h，与空客 A320 巡航地速典型值（820-840 km/h）的最大误差小于 15%。误差主要源于GPS 数据非连续跳跃、地球模型近似处理及采样精度等因素。该方法无需专业设备，整合了物理、地理跨学科知识，验证了 STEM 教育理念在真实问题解决中的实践价值，可为中学跨学科教学提供参考案例，也为无专业工具时的地速估算提供可行方案。
关键词：客机巡航；地速估算；经纬度；平面几何法；跨学科融合

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Research on the Estimation Method of Passenger Aircraft Cruising
Ground Speed Based on Changes in Longitude and Latitude

In order to solve the problem of actual measurement and verification of the actual ground speed during the cruise phase of a passenger aircraft, this paper proposes a ground speed estimation method based on smartphone GPS data and the knowledge system of middle and high schools. Taking West Airlines flight PN6268 (Airbus A320) as the research object, at a cruising altitude of about 7600m, the longitude, latitude, altitude and other data of two smooth flight periods of 120s each were collected through screen recording. The plane geometry method (junior middle school physics knowledge) and the Haversine spherical distance formula (high school geography knowledge) were used to calculate the horizontal displacement, and the ground speed was estimated using the velocity formula v=S/Δt. The results show that the plane geometry method estimates the ground speed to be 691km/h and 1039km/h, and the spherical distance formula estimates the ground speed to be 753km/h and 1110km/h. The maximum error with the typical value of the Airbus A320 cruising ground speed (820-840km/h) is less than 15%. The error is mainly due to factors such as discontinuous jumps in GPS data, earth model approximation processing, and sampling accuracy. This method does not require professional equipment, integrates interdisciplinary knowledge of physics and geography, and verifies the practical value of STEM education concepts in solving real problems. It can provide a reference case for interdisciplinary teaching in middle schools and a feasible solution for ground speed estimation without professional tools.
Keywords: Aircraft cruise; Ground speed estimation; Latitude and longitude; Plane geometry method; Interdisciplinary integration