Drawing scale (مقياس الرسم)

Definition

The scale of a drawing, map or plan is the ratio:

• scale = length on the drawing : the corresponding real length, both in the same units.
• A scale of 1 : 50,000 means 1 cm on the map represents 50,000 cm = 500 m = 0.5 km on the ground.
• A scale of 1 : 100 means 1 cm on the plan = 100 cm = 1 m in reality.
• An enlarging scale (a machine part, a bacterium) is written the other way, e.g. 20 : 1 — drawing : real.

The three conversions

1. Real length = drawing length × the second term (for a 1 : n scale). A field measures 4 cm × 6 cm on a plan of scale 1 : 2,000 ⟹ real sides 80 m and 120 m.
2. Drawing length = real length ÷ n. A road 3.6 km long = 360,000 cm appears on a 1 : 20,000 map as 360,000 ÷ 20,000 = 18 cm.
3. Scale = drawing ÷ real after converting the real length to the same unit.

Area and volume on a scaled drawing

• Lengths are multiplied by n, so areas by n² and volumes by n³.
• A plot drawn as 4 cm × 6 cm at scale 1 : 2,000 has real area 80 × 120 = 9,600 m², and the drawing area is 24 cm² = 9,600 m² ÷ (2,000)² × 10,000 — check: 24 cm² × 2000² = 96,000,000 cm² = 9,600 m².
• So: real area = area on plan × n², and 1 feddan = 4,200 m², 1 km² = 100 hectares = 238 feddans approximately.

Worked map example

Two cities are 7 cm apart on a map of scale 1 : 250,000. The real distance = 7 × 250,000 = 1,750,000 cm = 17.5 km. A train covering it in 15 minutes travels 17.5 ÷ 0.25 = 70 km/h.