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Difficulty: MediumSlope and Gradient Calculation

A field surveyor analyzing a topographical map with a scale of 1:50,0001 : 50,000 measures a straight line distance of 4 cm4\text{ cm} along a road connecting Hilltop Village at an elevation of 350 m350\text{ m} and Valley Junction at an elevation of 150 m150\text{ m}. What is the gradient of the road between these two settlements?

  1. 1 in 101 \text{ in } 10Answer
  2. B
    1 in 1,0001 \text{ in } 1,000
  3. C
    1 in 81 \text{ in } 8
  4. D
    1 in 11 \text{ in } 1

Answer

The gradient of the road is 1 in 101 \text{ in } 10.
The gradient is determined by dividing Vertical Interval (VI) by Horizontal Equivalent (HE). With a VI of 200 m200\text{ m} (350 m−150 m350\text{ m} - 150\text{ m}) and a ground distance HE of 2,000 m2,000\text{ m} (4 cm×50,000=200,000 cm=2,000 m4\text{ cm} \times 50,000 = 200,000\text{ cm} = 2,000\text{ m}), the ratio 2002,000\frac{200}{2,000} simplifies to 110\frac{1}{10} or 1 in 101 \text{ in } 10.

Step-by-Step Solution

1
Calculate the Vertical Interval (VI)
VI=350 m−150 m=200 m\text{VI} = 350\text{ m} - 150\text{ m} = 200\text{ m}
Vertical Interval is the difference in elevation between the two points.
2
Calculate the Horizontal Equivalent (HE) in meters
HE=4 cm×50,000=200,000 cm=2,000 m\text{HE} = 4\text{ cm} \times 50,000 = 200,000\text{ cm} = 2,000\text{ m}
Horizontal Equivalent is the actual ground distance converted to the same unit as VI.
3
Compute the slope gradient ratio
Gradient=VIHE=200 m2,000 m=110\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{200\text{ m}}{2,000\text{ m}} = \frac{1}{10} or 1 in 101 \text{ in } 10
Gradient is defined as the ratio of Vertical Interval to Horizontal Equivalent.

Key Concept

Topographic Slope and Gradient Calculation
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Topics

Slope and Gradient Calculation

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