### 4. Metric Character

A contour map drawn to a horizontal scale and with a uniform contour interval is a metric map. Measurements can be made with which computations can be performed. A hydrologist can use a contour map to determine rainfall runoff direction for planning stormwater management. A transportation engineer can compute grades and elevations of alternate road layouts. A land developer can determine site grading volumes.

Although the following examples are in terms of paper maps, digital versions can be used similarly albeit with different measurement tools.

#### a. Distance Example

Figure D-23 is another part of the Platteville area topoquad.

Figure D-23 Platteville Area Topoquad |

Determine the average slope for the drainage channel from the road intersection at point A to the river floodplain at point B.

Measure the channel length in segments, Figure D-24.

Figure D-24 Channel Length Measurement |

Figure D-25(a) shows the channel segments; Figure D-25(b) is the segments aligned.

(a) As measured |

(b) Aligned |

Figure D-25 Channel Segments |

Using the graphic scale on the topoquad, Figure D-26, the length is ~4200 ft.

Figure D-26 Topoquad Graphic Scale |

Considering the measurement errors in each segment, rounding the distance to the smallest graphic division (200 ft) is reasonable.

Elevations can be interpolated to one-half the contour interval; this map's interval is 10 ft.

The elevation at point A is 920 ft, at point B 735 ft.

Slope, in percent, is (elevation difference) / (horizontal distance) x 100

Slope = (920 ft - 735 ft) / (4200 ft ) x 100 = -4.4%

#### b. Volume Example

Map measurements can support more complex calculations. For example, if an earthen dam with a top elevation of 800 ft were to be constructed perpendicular to the channel at the location shown in Figure D-27, what volume of water would be impounded before it spills over?

Figure D-27 Dam Location |

Because its top elevation is 800 ft, the dam would intersect the 800 ft contour line on both sides of the channel, Figure D-28.

Figure D-28 Dam Width |

When full, the water elevation will be at 800 ft and its surface area defined by the dam and 800 ft contour line, Figure D-29.

Figure D-29 Full Impoundment |

The surface area, A_{800}, is measured on the map with a digital or mechanical planimeter, Figure D-30, tracing out the area bounded by the 800 ft contour and dam.

Figure D-30 |

The next lower contour is 790 ft. The surface area bounded by the dam and 790 ft contour, A_{790}, is measured, Figure D-31.

Figure D-31 Surface Area at 790 Ft Elevation |

The volume of water between the two elevations is the average surface area multiplied by the contour interval:

Vol_{1} = (A_{800} + A_{790}) / 2 x 10 ft

Each volume between adjacent contours is computed to the lowest impounded elevation and summed to determine the total volume, Figure D-32.

Figure D-32 Reservoir Volume |

#### c. Measurement Accuracy

Measurement accuracy is affected by

- Contour interval
- Contour smoothness
- Horizontal scale
- Measuring device (instrumental and personal errors)
- Map purpose
- Data collection density and accuracy

In both examples, measurements and computations are only accurate enough for initial design alternative considerations; neither support detailed final design. Larger scale and higher resolution data is needed for design, important considerations for collecting data and new map compilation.