Bearings and Scale Drawings | 方位角与比例尺绘图

📚 Bearings and Scale Drawings | 方位角与比例尺绘图

Bearings and scale drawings are essential tools for describing direction and representing real-world distances on paper. They are widely used in navigation, map reading, construction and engineering. This topic will help you read and draw accurate diagrams, convert between map and actual sizes, and use three-figure bearings to specify direction.

方位角与比例尺绘图是描述方向、在纸面上表示现实距离的基本工具，广泛应用于导航、地图阅读、建筑和工程中。本专题将帮助你学会阅读和绘制精确的图示，进行地图尺寸与实际尺寸的转换，并运用三位数方位角来表示方向。

1. What Are Bearings? | 什么是方位角？

A bearing is a way of describing direction. It is measured in degrees (°) from North, always moving clockwise. Bearings are always written as three figures, such as 045° or 235°. The angle is measured from the North line at the starting point.

方位角是一种表示方向的方法。它以正北为起点，按顺时针方向测量角度，单位为度（°）。方位角总是写成三位数的形式，例如 045° 或 235°。这个角度是从起点处的正北线开始度量的。

2. Three-Figure Bearings Rule | 三位数方位角规则

Always give bearings using three digits. For angles less than 100°, put a zero in front, for example 005° means 5° clockwise from North. Angles between 100° and 360° are already three-figure. Remember that 000° represents North, 090° East, 180° South and 270° West.

方位角必须使用三位数字。对于小于 100° 的角度，要在前面加零，例如 005° 表示从正北顺时针方向 5°。100° 到 360° 之间的角度本身就是三位数。请记住 000° 代表正北，090° 代表正东，180° 代表正南，270° 代表正西。

3. Measuring a Bearing | 测量方位角

To measure the bearing of B from A, place the centre of the protractor on point A, with 0° along the North line. Read the angle clockwise from North to the line joining A to B. Always measure from the North line at the starting point.

要测量从 A 到 B 的方位角，把量角器的中心放在点 A，使 0° 沿着正北线。按顺时针方向读出从正北线到 AB 连线的角度。始终从起点处的正北线开始测量。

4. Drawing a Bearing | 绘制方位角

Start by drawing a clear North line at the given point. Place the protractor with its centre at the point and 0° towards North. Mark the required angle clockwise, then draw a straight line through the point and your mark. Label the line with the bearing.

先从给定点画出一条清晰的正北线。将量角器的中心放在该点，0° 指向正北。按顺时针方向标记出所需的角度，然后通过该点和标记画一条直线。在这条线上标出方位角。

5. Introduction to Scale Drawings | 比例尺绘图简介

A scale drawing is a representation of something too large or too small to be drawn at its actual size. It uses a scale factor, such as 1 : 100 or 1 cm to 1 km, to reduce or enlarge all lengths in proportion.

比例尺绘图是一种用缩小的或放大的方式表示过大或过小实体物体的方法。它利用比例因子（例如 1 : 100 或 1 厘米代表 1 公里）按比例缩小或放大所有长度。

6. Common Types of Scales | 常见比例尺类型

Scales can be written as ratios (1 : 500), as statements (1 cm represents 5 m) or as scale bars. A ratio scale is unit-free, while a statement scale links specific units. A scale bar gives a visual representation of real distances on the drawing.

比例尺可以写成比的形式（1 : 500），也可以用文字陈述（1 cm 代表 5 m），或者使用比例尺条。比的形式没有单位限制，而文字陈述比例尺则联系具体单位。比例尺条可以直观地表示图上距离与实际距离的关系。

Type	Example	Meaning
Ratio scale	1 : 10 000	1 unit on the map = 10 000 units on the ground
Statement scale	1 cm : 2 km	1 cm represents 2 km in real life
Scale bar	\|—-\| = 1 km	Visual measure of distance

Understanding these formats helps you move easily between map measurements and real-world distances.

理解这些比例尺格式有助于你在图上测量值和现实距离之间进行自如转换。

7. Converting Map Distances to Real Distances | 将图上距离转换为实际距离

To find the actual distance, measure the length on the drawing and multiply by the scale factor. If the scale is 1 : 200, a line of 5 cm on the map represents 5 × 200 = 1000 cm = 10 m in reality. Always convert to appropriate units.

要计算实际距离，先测量图中的长度，再乘以比例因子。如果比例尺为 1 : 200，图上 5 cm 长的线段代表实际距离 5 × 200 = 1000 cm = 10 m。注意要换算成合适的单位。

Real distance = Map distance × Scale factor

实际距离 = 图上距离 × 比例因子

8. Converting Real Distances to Map Distances | 将实际距离转换为图上距离

When designing a scale drawing, divide the real length by the scale factor to obtain the drawing measurement. For example, if a room is 6 m long and the scale is 1 : 50, the length on the plan should be 600 ÷ 50 = 12 cm.

在设计比例尺绘图时，将实际长度除以比例因子就能得到图上长度。例如，如果一间房间实际长 6 m，比例尺为 1 : 50，那么平面图上的长度应为 600 ÷ 50 = 12 cm。

Map distance = Real distance ÷ Scale factor

图上距离 = 实际距离 ÷ 比例因子

9. Using Bearings and Scales Together | 组合使用方位角与比例尺

Many problems require you to plot a course using bearings and measure distances using a scale. For instance, a ship sails on a bearing of 070° for 15 km, then changes to 160° for 20 km. You can draw the path to scale and measure the final bearing and distance from the starting point.

许多问题要求你根据方位角画出航线，并利用比例尺测量距离。例如，一艘船沿着 070° 的方位角航行 15 km，随后转向 160° 继续航行 20 km。你可以按比例尺画出路径，并测量最终相对于起点的方位角和距离。

10. Scale Drawings of Maps and Plans | 地图与平面图中的比例尺绘图

When working with maps, the scale is often given as a statement (e.g., 1 cm to 5 km). Measure carefully between points, and convert using the scale. Always include a North arrow on your map to show direction. Use a sharp pencil and ruler to achieve precision.

处理地图时，比例尺常用文字表述（例如 1 cm 代表 5 km）。仔细测量两点之间的图距，然后按比例尺换算。地图上一定要画上指北箭头以表明方向。用削尖的铅笔和直尺来保证精确度。

11. Scales and Area | 比例尺与面积

Lengths scale linearly, but areas scale by the square of the scale factor. If the linear scale is 1 : k, then the area ratio is 1 : k². For example, a map at 1 : 1000 has an area scale of 1 : 1 000 000. This is important when estimating real-world areas from a plan.

长度按线性比例缩放，但面积要按比例因子的平方缩放。如果长度比例为 1 : k，那么面积比例就是 1 : k²。例如，一张 1 : 1000 的地图，其面积比例是 1 : 1 000 000。当从平面图上估算实际面积时，这一点很重要。

Area scale factor = (Linear scale factor)²

面积比例因子 = （长度比例因子）²

12. Common Mistakes and Tips | 常见错误与技巧

Never forget to write bearings as three digits. An angle of 50° must be recorded as 050°.

绝不要忘记把方位角写成三位数字。50° 的角必须记为 050°。
Always check that your protractor is aligned with North, and that you measure the angle clockwise.

务必检查量角器是否与正北线对齐，并且是按顺时针方向测量的角度。
When using scales, include units in your working and label your final answer with the correct unit.

使用比例尺运算时，在计算过程中带上单位，并确保最终答案带有正确的单位。
For scale drawings, draw lightly first and check measurements before finalising the lines.

绘制比例尺图形时，先轻轻画出草图，检查测量结果无误后再定稿。

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Bearings and Scale Drawings | 方位角与比例尺绘图