To calculate the run (horizontal distance) of a road with a given grade and rise, you can use the formula for the slope of a right triangle. The grade percentage represents the ratio of the rise (vertical change) to the run (horizontal change).
First, let’s understand the relationship between the grade, rise, and run.
The formula for grade is:
Grade (%) = (Rise / Run) * 100
In this case, you know the grade is 4% and the rise is 200 feet. You need to rearrange the formula to find the run:
Run = Rise / (Grade / 100)
Substituting in your values:
Run = 200 / (4 / 100)
Now, calculate:
Run = 200 / 0.04 = 5000 feet
Thus, the run (horizontal distance) of the road with a 4% grade and a 200 feet rise is 5000 feet.
This means that for every 5000 feet you travel horizontally, the road will rise 200 feet, forming a gentle incline.