Name: crosswind vector navigation in 2d
Uploaded: 2026-06-08T09:38:47.183Z
Duration: 1 min 29 s
Channel: JoVE

一架飞机以每小时180公里的恒定空速向正北方向飞行。30分钟后，发现其位置距离起点80公里，但偏北偏东5度。这表明风改变了飞机的预定航迹。目标是求出风速以及飞机为保持预定航向应飞行的方向。飞机的对地速度由其预期速度与风速合成，形成一个矢量三角形。该飞机在30分钟内飞行了80公里，由此可得其地速的大小。由于该速度方向为北偏东5度，因此可分解为两个分量：向北分量和向东分量。目标速度为正北方向，每小时180公里。从地速中减去该速度可得到风速。其大小通过勾股定理求得。最后，为了保持航向，飞行员必须略微向西偏北方向飞行，以抵消风的影响。通过将调整后的速度分解为分量，并使向西的分量与风的向东推力相平衡，可得出该调整值。结果表明，飞机必须向北偏西约 4.4 度方向飞行，才能保持预定航向。

二维矢量：问题求解

Vectors in 2D: Problem Solving

一架在静止空气中以每小时180公里的速度向正北飞行的飞机，30分钟后被发现偏离预定航线约80公里，偏移方向为北偏东约5度。这种偏离表明侧风影响了飞机的预定航迹。实际的地面路径呈对角线，说明由于风的影响，飞机相对于地面的有效速度降低至每小时160公里，并略微偏向东方。通过分析偏离预定路径的位移，推断出风所导致的速度分量。风引入了一个明显的向东方向分量，导致飞机偏离其预定的向北航线。该风致运动的大小估计约为 24.9 km/h，在整个观测期间持续作用。为了抵消这种偏离并确保飞向预定目的地的直线航径，需要进行航向修正。这要求将飞机的航向略微调整至北偏西方向。此类调整引入了一个向西的运动分量，从而有效抵消风力带来的向东影响。将航向调整至北偏西约 4.4 度即可实现所需的平衡，使最终飞行轨迹与期望的正北航向一致。该技术体现了矢量原理在航空导航中的实际应用。

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Education

教育

JoVE Core

Calculus

微积分

Unit

单元

Vectors in Space

空间向量

KEY TERMS AND CONCEPTS

关键术语与概念

二维向量：问题解决

crosswind vector navigation in 2d

Crosswind vector navigation in 2D shows how wind changes an airplane’s path. A plane flew due north at 180 km/h in still air, but after 30 minutes it was 80 km off course. Its track was about 5 degrees east of north, which shows that a crosswind pushed it away from the intended route.

The plane’s ground path was diagonal, not straight north. That means its effective ground speed was reduced to 160 km/h and shifted slightly east. By studying the displacement from the planned path, the wind’s velocity can be found as a vector. In this case, the wind added an eastward component and acted in the same way throughout the flight interval.

The wind speed was estimated at about 24.9 km/h. To return to the correct route, the plane would need a correction in heading. A tilt of about 4.4 degrees west of north creates a westward component that cancels the wind’s eastward effect. This vector balance lets the aircraft travel north as intended.

Crosswind Vector Navigation in 2D

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Crosswind vector navigation in 2D shows how wind changes an airplane’s path. A plane flew due north at 180 km/h in still air, but after 30 minutes it was 80 km off course. Its track was about 5 degrees east of north, which shows that a crosswind pushed it away from the intended route. The plane’s ground path was diagonal, not straight north. That means its effective ground speed was reduced to 160 km/h and shifted slightly east. By studying the displacement from the planned path, the wind’s...

vectors in space: problem solving

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key terms and concepts

Learn how 2D vectors explain a plane’s crosswind drift, ground speed, and heading correction using a real navigation problem for high school science.

Crosswind Vector Navigation in 2D | JoVE K12

The JoVE Core Calculus collection provides a comprehensive visual guide to the entire calculus sequence, seamlessly connecting mathematical theory to real-world applications in physics and economics. Through dynamic animated lessons, the course transitions smoothly from foundational single-variable concepts to advanced multivariable topics. Students will explore everything from standard differentiation and integration to spatial vectors, multi-dimensional derivatives, and complex vector fields. By breaking down abstract coordinate systems, infinite series, and spatial motion, this structured approach builds the robust analytical skills and advanced mastery essential for STEM success.

calculus

Crosswind Vector Navigation in 2D

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