Lecture 7: Mapwork Calculations PDF

LECTURE 7: MAPWORK CALCULATIONS Distance, Scale, Area DISTANCE  Map = drawing of a part of the earth  Maps are drawn so that a certain distance on the map represents a much larger distance on earth, i.e. Scale  Scale – makes it possible to show the whole earth on a piece of piece  All...

LECTURE 7: MAPWORK CALCULATIONS Distance, Scale, Area DISTANCE  Map = drawing of a part of the earth  Maps are drawn so that a certain distance on the map represents a much larger distance on earth, i.e. Scale  Scale – makes it possible to show the whole earth on a piece of piece  All maps have a scale – tells you what distance on earth is represented by a certain distance on the map LINE/LINEAR SCALE  horizontal line drawn on the map, which is divided into a number of equal parts  line scale is accurate and no calculations are used  divided into two parts:  right of zero – each division of the scale represents a distance of 1km  left of zero – The distance represents 1km (1 000m). This is subdivided into ten equal parts, each representing a distance of 100m. RATIO SCALE  Text based scale, no units shown  simple ratio of map to ground measurement with a colon between the two measurements  numerical way of showing how greatly ground distances have been reduced  Topo maps – 1 unit on the map represents 50 000 units on the ground  Ortho maps – 1 unit on the map represents 10 000 units on the ground WORD SCALE  indicates scale by means of a verbal statement such as 1cm on the map represents 500m on the ground  scale is given in words  statement mentions two distances: The smaller distance refers to the map and the larger distance refers to the ground – a distance of 1cm on the map represents a distance of 500m on the ground. LARGE VS SMALL SCALE  Maps – described as either large scale or small scale  Large scale maps  show a smaller amount of area with a greater amount of detail  geographic extent shown on a large scale map is small.  large scaled map – smaller number to the right of the colon, eg: 1 : 1 000  used to show neighbourhoods, a localize area, small towns, etc.  Small scale maps  show a larger geographic area with few details on them  small scale map – larger number to the right of the colon, eg: 1 : 1 000 000  used to show the extent of an entire country, region, or continent  A B C MATCH THE SCALE TO THE MAP 1:25 000 1:100 000 1:250 000 USEFUL SCALE CONVERSIONS Scale – 1:50 Scale – 1:10 000 000 CALCULATING DISTANCE  Distance on the map is calculated between two points, e.g. between a school and the museum  Learners are required to convert map distance into actual distances on the ground  Measuring straight line distance (as the crow flies):  Use a ruler and measure the distance between two points in centimetres  Convert the centimetre reading to kilometres by multiplying by 0,5km if the map scale is (1:50 000) to obtain the kilometres on the ground  Measuring a curved line distance:  Find a straight edge of a paper  Using a pencil, mark off the straight sections of the distance to be measured  To measure the distance between two points, place the paper at the start and mark off the point on the sheet of paper. Slowly move the paper along the line, marking off the straight sections until the end point is reached  Transfer the marked paper on to the linear scale. Read off the distance  Easier method – use a piece of string to trace the curved distance, then convert to ground distance DISTANCE EXERCISE  Calculate distance in km from spot height 1268 to spot height 1282  Actual Distance = Map distance x Scale (1:50 000)  Answer: 3,8cm x 0,5 = 1. On a 1:10 000 scale map, a road 3. The distance between two towns is represented as 4 centimeters. on a 1:50,000 scale map is 12 What is the actual length of the centimeters. What is the actual road on the ground in m? ground distance in km? a) 0.4 m a) 60 km b) 40 m b) 120 km c) 400 m c) 300 km d) 4 m d) 6 km 2. If a gorge on a 1:50 000 map is 4. A railway track on a 1:25 000 map 6 centimeters wide, what is the measures 8 centimeters. What is the actual width of the gorge on the actual length of the track on the ground in m? ground in km? a) 600 m a) 0.8 km b) 3 000 m b) 2 km c) 300 m c) 4 km d) 6 000 m d) 80 km QUESTION 1 QUESTION 3 1 cm on the map = 10 000cm on 1 cm on the map = 50 000cm on the the ground ground 1 cm on the map = (10 000/100) = 1 cm on the map = (50 000/100 000) 100m on the ground = 0,5km on the ground Therefore: 4 cm on the map = (4 x Therefore: 12 cm on the map = (12 x 100) = 400m on the ground (C) 0,5) = 6m on the ground (D) QUESTION 2 QUESTION 4 1 cm on the map = 50 000cm on 1 cm on the map = 25 000cm on the the ground ground 1 cm on the map = (50 000/100) = 1 cm on the map = (25 000/100 000) 500m on the ground = 0,25km on the ground Therefore: 6 cm on the map = (6 x Therefore: 8 cm on the map = (8 x 500) = 3 000m on the ground (B) 0,25) = 2km on the ground (B) AREA  Calculated to determine the actual size on the ground of a feature/region/demarcated area  Learners generally required to calculate area of rectangular shapes (lower grades)  How would you calculate the area of the block in the picture? ANSWER Formula - Area = (Length x scale) x (Breadth x Scale) 1. Using a ruler measure the Length and multiply by the scale of the map and convert to kilometres i.e.:  Length - 9.8cm x 50 000 cm = 490 000cm OR 9,8 x 0,5  Converted to km (divide by 100 000) = 4.9 Km 2. Using a ruler measure the Breadth and multiply by the scale of the map and convert to kilometres i.e.:  Breadth = 7.4cm x 50 000 cm. = 370 000 cm OR 7,4 x 0,5  Converted to = 3.7 Km 3. Multiply the length and breadth (final answer must be in km²): 4.9km x 3.7 Km = 18.13 Km² 1. On a 1:10 000 scale map, a 2. On a map with a scale of 1:50 000, rectangular park is represented as 8 a forest is represented as a rectangle cm in length and 5 cm in breadth. measuring 16 cm by 10 cm. What is What is the actual area of the park the actual area of the forest on the on the ground in square meters? ground in square kilometers? a) 400m2 a) 400km2 b) 4000m2 b) 8000km2 c) 40 000m2 c) 40km2 d) 400 000m2 d) 80km2 3. On a 1:25 000 scale map, a farm is depicted as a rectangle with dimensions of 10 cm by 6 cm. What is the actual area of the farm on the ground in square kilometers? a) 60km2 b) 3,75km2 c) 60 000km2 d) 300km2 QUESTION 1 1 cm on the map = 10 000cm on the ground 1 cm on the map = (10 000/100) = 100m on the ground Length: 4 cm on the map = (8 x 100) = 800m on the ground Breadth: 5 cm on the map = (5 x 100) = 500m on the ground Area: length x breadth = 800m x 500m = 400 000m2 (D) QUESTION 2 1 cm on the map = 50 000cm on the ground 1 cm on the map = (50 000/100 000) = 0,5Km on the ground Length: 16 cm on the map = (16 x 0,5) = 8km on the ground Breadth: 10 cm on the map = (10 x 0,5) = 500m on the ground Area: length x breadth = 8km x 5km = 40km2 (C) QUESTION 3 1 cm on the map = 25 000cm on the ground 1 cm on the map = (25 000/100) = 0,25Km on the ground Length: 10 cm on the map = (10 x 0,25) = 2,5km on the ground Breadth: 6 cm on the map = (6 x 0,25) = 1,5km on the ground Area: length x breadth = 2,5km x 1,5km = 3,75km2 (B) AREA OF REGULAR VS IRREGULAR SHAPES  Shapes of surfaces on a map can either be regular or irregular  To calculate the area of regular shapes (rectangles, squares or right angled triangles) – apply the formula used in mathematics  Scale should be used in working out the length and breadth/width before they are multiplied. Answer is given in square kilometres  Most areas of surfaces are irregular in shape – area can only be estimated AREA OF IRREGULAR SHAPE  Use a piece of graph paper or divide the map into grids or squares of 1 cm by 1 cm – each square on the map represents 0,25 km2 on land (Scale – 1:50 000, so area of square = 0,5km x 0,5km = 0,25km2)  Count all the full squares covered by the shape  Count all the partly covered squares, however small, as half squares. Add all of them up and multiply the figure by half  Add up all the full squares and the figure obtained from the part squares to get the final area Calculate the ground area of the shape in the above picture. Assume that the scale of the map is 1:50 000 and that each block is 1cm x 1cm. Your answer should be in km2. Answer? ANSWER  Area of 1 square is: (1x0,5km) x (1x0,5km) = 0,25km2  Number of squares:  12 full squares  6 half squares (6 x 0,5 = 3 full squares)  15 squares in total  Area: 15 squares x 0,25km2 = 3,75km2