### 3. Grade

#### a. Definition

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

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.

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:

Using Equation A-1:

(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:

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

The horizontal distance is | |

and elevation difference is | |

and elevation at 19+00.00 |

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:

The horizontal distance is:

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

The elevation is:

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