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Zorluk: Çok zorSlope and Gradient Calculation

A topographic map with an original scale of 1:50,0001 : 50,000 is reduced to half its linear size. On the reduced map, the measured distance between Point X (elevation 750 m750\text{ m}) and Point Y along a slope is 5.0 cm5.0\text{ cm}. If Point Y lies 88 contour intervals below Point X on a map with a contour interval of 25 m25\text{ m}, what is the gradient between Point X and Point Y expressed as a ratio?

  1. A
    1 in 6.251 \text{ in } 6.25
  2. 1 in 251 \text{ in } 25Cevap
  3. C
    1 in 401 \text{ in } 40
  4. D
    1 in 201 \text{ in } 20

Cevap

The gradient between Point X and Point Y is 1 in 251 \text{ in } 25.
The gradient expressed as 1 in 251 \text{ in } 25 is correct because reducing a 1:50,0001 : 50,000 map to half its linear size yields a scale of 1:100,0001 : 100,000. At this scale, 5.0 cm5.0\text{ cm} corresponds to a Horizontal Equivalent (HE) of 5,000 m5,000\text{ m}. With 88 contour intervals at 25 m25\text{ m} each, the Vertical Interval (VI) is 200 m200\text{ m}. Dividing VI by HE gives 2005,000=125\frac{200}{5,000} = \frac{1}{25}.

Adım Adım Çözüm

1
Determine the new map scale after linear reduction
New Scale = 1:100,0001 : 100,000
Reducing a map to half its linear size doubles the scale denominator (50,000×2=100,00050,000 \times 2 = 100,000).
2
Calculate the Horizontal Equivalent (HE) ground distance
HE=5.0 cm×100,000=500,000 cm=5,000 m\text{HE} = 5.0\text{ cm} \times 100,000 = 500,000\text{ cm} = 5,000\text{ m}
Multiply map distance by the new scale factor and convert centimeters to meters.
3
Calculate the Vertical Interval (VI) between Point X and Point Y
VI=8×25 m=200 m\text{VI} = 8 \times 25\text{ m} = 200\text{ m}
Multiply the number of contour intervals by the contour interval value.
4
Compute the gradient ratio
Gradient=VIHE=200 m5,000 m=125\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{200\text{ m}}{5,000\text{ m}} = \frac{1}{25} or 1 in 251 \text{ in } 25
Divide Vertical Interval by Horizontal Equivalent in identical units to find the simple ratio.

Anahtar Kavram

Topographic Gradient and Map Scale Reduction
Tahmini Süre:3m 0s
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Konular

Slope and Gradient Calculation

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