Article Index

3. Grade

a. Definition

Grade is the slope of a straight line and is computed from:

eqn 01      Equation A-1
elev diff: elevation difference
horiz dist: horizontal distance

 

If the elev diff and horiz dist are both in feet (or meters) Equation A-1 results in grade as a dimensionless ratio; multiplying it by 100 converts it to a percentage (%).

If elev diff is feet and hori dist is stations, Equation A-1 returns grade as a percentage.

Grade is positive (+) going uphill in the direction of stationing, negative (-) going downhill, Figure A-7.

gen 07
Figure A-7
Grade

 

b. Examples

(1) The elevation at sta 10+25.00 is 1214.80 ft; at sta 12+75.00 it is 1193.50 ft.

What is the grade of the line between the two stations?

First, draw a sketch:

gr ex1

Using Equation A-1:

gr ex1b

(2) At sta 16+50.00 the elevation is 867.50 ft. If the grade through 16+50.00 is +3.00%, what is the elevation at sta 19+00.00?

Sketch:

gr ex2

We need to rearrange Equation A-1 to solve for the elevation difference between the two stations:

 grade07

 The horizontal distance is  gr ex2c
 and elevation difference is   gr ex2d
 and elevation at 19+00.00   gr ex2e

 

According to the sketch, 19+00 is higher than 16+50 so the computed elevation looks correct

(3) Using the data in example (2), what is the elevation at station 14+00?

Sketch:

gr ex3

The horizontal distance is:

gr ex3 dist

Since we're going backwards along the alignment, the distance is negative.

The elevation is:

gr ex3 elev

From the sketch we see that 14+00 is lower than 16+50, so the computed elevation looks correct.

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