Working with Scale

All topographic maps provide information on the scale of the map, usually at the bottom of the map sheet. The scale is the ratio of distances on the map to distances on the ground. For example, if the scale of the map is 1 : 24,000, this means that one unit of distance on the map represents 24,000 units of distance on the ground. The units could be any units of distance--one inch on the map represents 24,000 inches on the ground, one centimeter on the map is 24,000 cm on the ground, one foot on the map = 24,000 feet on the ground, etc. Note that this DOES NOT work for areas (that is, one square inch on the map does not represent 24,000 square inches on the ground, it represents 24,0000 or 576,000,000 square inches).

**Solving scale
problems**

Follow these steps to solve most basic map scale problems:

(1) First, identify
the given information and the required answer.

(2) Determine the conversions that can be used to manipulate the given information.

(3) Set up an equation to solve the problem, cancelling units that appear both
on the top and bottom of fractions.

Three miles on the ground are shown by how many inches on the map? (1) Given
information: 3 miles on the ground (2) Conversions needed: miles to feet feet to inches inches on ground to inches on map (3) Equation: (3 miles on the ground) x (5280 ft./1 mi.) x (12 in./1 ft.) x (1 in map / 24,000 in ground) = 7.92 inches on the map |
Three inches on the map indicate how many miles on the ground? (1) Given
information: 3 inches on the map (2) Conversions
needed: inches on map to inches on ground (3) Equation: (3 inches on the map) x (24,000 in ground/1 in map) x (1 ft./12 in.) x (1 mi./5280 ft.) = 1.14 miles on the ground |

**Working with
areas**

Rather than altering the scale that represents distance to one that works with areas, it is often easier to break down area problems so that they can be solved as distance problems. For example, if you need to know how much area is represented by four square inches on the map, follow this procedure:

(1) Four square
inches can be easily represented as a square that is 2 inches on a side

(2 in. X 2 in. = 4 in.2).

(2) Calculate the ground distance represented by one side of the square, or 2 inches on the map.

(2 inches on the map) x (24,000 in ground/1 in map) x (1 ft./12 in.) x (1 mi./5280 ft.)

= 0.76 miles on the ground

(3) Square your answer to calculate the area of a square that is 0.76 miles on a side, the same area represented by the square on the map that is 2 inches on a side or 4 in.2 total.

(0.76 miles)2 = 0.58 square miles

*Example
#3*

Nine square miles on the ground is shown as how many square inches on a 1 :
24,000 map?

(1) Nine square miles can be easily represented as a square that is 3 miles on a side.

(2) Calculate the map distance represented by one side of the square, or 3 miles on the ground (See Example 1 above).

= 7.92 inches on the map

(3) Square your answer to calculate the area of a square that is 7.92 inches on a side, the same area as the 9 mi2 on the ground.

62.7 square inches on the map.

**For your reference:**

Unit conversion tables

Distance Area

1 km = 1000 m 1 sq. mi = 640 acres

1 m = 100 cm 1 sq. mi = 52802 ft2 = 27878400 ft2 = 2.590 km2

1 cm - 10 mm 1 sq. km = 100 ha

1 mi = 1.609 km 1 sq. km = 10002 m2 = 1000000 m2

1 km = 0.6214 mi 1 ha = 2.471 ac = 0.00386 mi2

1 mi = 5280 ft

1 ft = 12 in

1 in = 25.4 mm

1 m = 3.2808 ft

Pairs of topographic maps and landscape photographs are provided for you to become more familiar with how to interpret the landscape as it appears on topographic maps. Look at the map, especially studying the contour lines that represent the form of the landscape. Then, examine the paired photo to see what a similar landscape looks like. You may wish to resize and move the windows on your computer desktop to easily view the map and photo side-by-side. Note: Many photos show a similar landscape to that on the map, but not exactly the same area.

Voltaire, North Dakota- Pecatonica River, southwestern WI

Leavenworth, Kansas- Mississippi River, Iowa-Wisconsin

Ayer, Massachusetts and Campti, Louisiana - Kansas oxbow lake photo

Mt. Rainier, Washington- Mt Rainer, Washington

Chief Mountain, Montana- Mt. Rosalie, Colorado

Holy Cross, Colorado - Mt. Rosalie, Colorado

Ennis, Montana - Matterhorn, Switzerland

Jackson, Missouri - Kettle Moraine State Park, Wisconsin

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