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Transportation routing, scheduling and monitoring

Effect of hills on calculated miles


Assumption:

  1. The map data does not accurately reflect the distance of a road based on the “steepness” of a hill. Map data only reflects “Horizontal Distance”.
  2. The steepness of a “typical” hill is an 8% grade. Road steepness is regulated by local townships. Roads greater than 8% grade are usually permitted but for short distances.
  3. For calculation purposes, we will assume the hill is 1 mile long, with an consistent grade.

Definitions:

  1. Road Grade is stated in the percent of elevation change over horizontal change in distance. For example, 100 feet in horizontal change and 8 feet in elevation change would result in an 8% grade.

Calculations:

  1. For 1 mile in horizontal distance, the elevation distance would be 0.08 miles.
  2. Convert to feet. 5280 feet of horizontal distance would result in 422.4 feet of elevation distance.
  3. The actual distance of the road can be calculated using the Pythagorean theorem.
  4. (Actual Distance)2 = (Horizontal Distance)2 + (Elevation Distance)2
  5. (Actual Distance)2 = (5280 * 5280) + (422.4 * 422.4)
  6. (Actual Distance)2 = 27878400 + 178421.8
  7. Take the square root of both sides... Actual Distance = 5297 feet.
  8. The difference in distance is 17 feet over the course of 1 mile.

Conclusions:

  1. Inaccuracies in map data effect reported miles
  2. Over the length of 1 mile of an 8% grade hill, the map inaccuracy amounts to 17 feet.
  3. After traveling 310 miles, map inaccuracies will accumulate to a reported 1-mile difference.
  4. Steeper hills have a greater effect on the inaccuracy, while level roads have no inaccuracies.

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