Effect of hills on calculated miles

Assumptions:

• 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”.
• 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.
• For calculation purposes, we will assume the hill is 1 mile long, with an consistent grade.

Definitions:

• 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:

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

Conclusions:

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