Earth Science Laboratory
EAS 100-51 : Lab 7
Answers to practice problems for
Complete the questions which follow:

1.(a)    Express the verbal scale "1 inch = 1 mile" as an R.F.

To convert to an R.F., the map and land scales must use the same units.  It is best to convert to the smaller unit, so the land unit (1 mile) must be converted into an equivalent number of inches.

1 mile = ? inches

1 mile  X   (5,280 feet/mile)   X   (12 inches/foot)  = 63,360 inches

Now that the land unit has been converted from 1 mile into 63,360 inches, the verbal scale may be re-written as:

1 inch = 63,360 inches

Since both the map unit (1 inch) has the same unit as land (63,360 inches), the units may be deleted.

1 : 63,360

For more details on how to perform the above calculation, see the handout, Map Scales & Units

1.(b)    Express the verbal scale "1 foot = 2,000 yards" as an R.F.

Convert everything into feet (the smaller unit).  The unit which needs conversion is the land unit (2,000 yards).

2,000 yards = ? feet

2,000 yards X  (3 feet/yard) = 6,000 feet

Rewrite the original verbal scale by substituting 6,000 feet for 2,000 yards:

1 foot = 6,000 feet

1 : 6000

1.(c).    Express the R.F. "1 : 250,000" as a verbal scale.

You may choose any SINGLE unit and apply them to both map and land.  You CANNOT use 2 different units - if you do, the ratio cannot remain 1 : 250,000.   Any of the following are correct conversions to a verbal scale:

1 inch = 250,000 inches
1 cm = 250,000 cm

1.(d)    An area has been mapped at an R.F. of 1:50,000.  A new map of the same area is drawn at an R.F. of 1:25,000.  What area of paper, in relation to the first map, will be needed for the new map?

This problem may be solved by comparing the R.F. scales of both maps, which are exact multiples of each other.  Map A (1:50,000) fits more land into the same size sheet than Map B (1:25,000), but exactly how much more?  If you measure distances on both maps, you will find that Map A can fit 2 times as much distance on the same sized map as Map B; this is called the Scale Factor.  However, when you calculate area, you must multiply Length X Width.  It is obvious that both North-South distances ("length") as well as East-West distances ("width") are doubled on Map A, so the Map A has 4 times as much area as Map B.  So, the Area Factor is the square of the Scale Factor:

Area Factor = (Scale Factor)2

Since Map A covers 4 times the area of Map B, using Map B's R.F. scale of 1:25,000, you will need 4 sheets of paper to provide the same area coverage as Map A. This should be clear by analyzing the diagram below:

Map A
The entire area of
Map B is only
1/4 the area of
Map A

To provide the same
area coverage as Map A, you would need 4 sheets of paper

 Map B

WestY (East)
2. The diagram at the left is a contoured map.

(a) Mark the positions of North, South, East, and West with appropriate letters.   (Shown at left)

(b) Is the X boundary latitude or longitude?  Latitude

(c) In which geographic direction does the stream flow?  How do you know?   The stream flows towards the southwest, because the contour lines in a stream valley must bend upstream.

(d) The gradient is defined as the vertical change in elevation (in feet) per horizontal (map) distance (in miles).  Calculate the stream's gradient on this map, if the stream is 2 miles long, and the contour interval is 10 feet.

There are 4 known contours on the map, and 30 feet of elevation change between the highest and lowest contours .  However, the NE and SW ends of the stream extend beyond these known contours - the best estimate of these elevation changes is to use HALF the contour interval.  Therefore, the elevation change of the stream is

30 + 5 + 5 = 40 feet

gradient = elevation change / distance
40 feet / 2 miles = 20 feet/mile

3. (a) What is the contour interval (C.I.) of the map at the left?

The contour interval may be calculated by noting the spacing of the labeled contours 250 and 300 feet.  The contour interval is 10 feet.

3(b)  What is a approximate different in the elevation between the highest and lowest points on this map? 

To solve this problem, it is necessary to estimate the elevation at the SE and NW corners.  The nearest known contours are 240 feet and 310 feet, but it should be obvious that the NW corner is lower than 240 feet, and the SE corner is higher than 310 feet.  The best estimate (interpolation) is to use HALF of the contour interval - therefore, the NW corner has an approximate elevation of 235 feet, while the SE corner has an approximate elevation of 315 feet.  (NOTE: You CANNOT ASSUME that the elevation of NW corner is 230 feet or that the SE corner is 320 feet because those contour lines should then be visible on the map, and they are not!)

3(c) If you were standing at point "A" and wanted to walk downhill along the maximum gradient or slope (or if you spilled a bucket of water from point A), in which geographic direction is this?

Water should flow at right angles to the contour lines, so it should flow downhill from point A towards the NW corner.

3(d) The graphic scale of this map (for 1 mile) is shown below the map at the left.  Calculate the distance from the northeast to the southwest corner.

Take a sheet of blank paper, and mark off the distance between the NE and SW corners and make 2 marks on your paper.  Then, place the edge of the paper against the graphic scale in the diagram at the left to see how many multiples of the graphic scale you have.  You should have slightly more than 6 miles, or about 6 1/3 miles.

4. (a) In which geographic direction does the stream flow?  How do you know this?

The stream flows towards the SOUTH.   The Rule of V's require that in a stream valley, contours bend upstream (opposite the flow direction), and the top of any map indicates North.

4. (b) If you were standing at "X," would it be easier to walk due East or due West?   Justify your answer.

Walking due East is easier because the wider spacing of contours indicates a less steep surface than walking due West, where the contours are more crowded together (indicating a more rapid elevation change).

4. (c) If the distance "AX" is 2 miles, and the distance "BX" is 8 miles, which is higher above X, A or B?

The answer is NEITHER!  If you look carefully at the diagram, you should note that both points A and B are located on the SAME contour, meaning they are at the same elevation.

Copyright  © 1999 by William K. Tong