Lecture+ 5 Earth_s coordinates and measurement from a map.pptx

Geography

1. Lecture 5: Making measurements on a map By G.A.B. Yiran

2. objectives By the end of this lecture, you should be able to: Be able to make measurements of coordinates To understand why we make these measurements or to understand the uses of the measurements

3. Coordinate Systems They are map Reference Systems or MODELS used to determine the location of features in the real world or on a map A geographic coordinate system attempts to model the shape of the earth as accurately as possible based on varying models of the shape of the earth No system is completely accurate (therefore the need to be familiar with their properties)   3

4. The Shape of the Earth 4

5. Figure ..Graticules showing Major lines of Longitude and Latitude Source: Compiled from the web . Prime Meridian (North – South lines: Longitude ) Equator (East - West lines: Latitude ) 5

6. Geographical or Spherical Projected Plane Cartesian Comparison of globe (spheroid) & a flat map of the world . 6

7. Geographic Coordinate Systems Reference system for identifying locations and measuring features on the curved surface of the earth. It consists of a network of intersecting lines called a graticule or grid The graticule is made up of vertical lines, called lines of longitude ( meridians e.g. “Prime Meridian” or Greenwich Meridian) , and horizontal lines, called lines of latitude ( parallels ) e.g. Equator 7

8. Projected/Plane/Cartesian Coordinate Systems Used to locate objects on a flat surface (either a paper map or a digital map) Projected coordinate systems are based on Cartesian coordinates (remember the graphs in maths) It is a two-dimensional, planar (plane) coordinate system based on a grid in which x (measures horizontal distance) and y (measures vertical distance) from an origin This same type of spatial reference system is used in making graphs. The x, y coordinate defines each point in the graticule or grid. Points can then be located with respect to the origin and the axes in the graticule. 8

9. Determination/measurement of Location or Position on a map Mathematical location With the Rectangular coordinate system, a False Origin is chosen such the entire earth or the portion of the earth that is mapped appears on the first quadrant. In such as case, we have only North and East, no South and West. Thus, all coordinates are in East and North A False origin is an arbitrary zero point to the south and west of a grid zone which is assigned to avoid negative coordinate values. The false origin for Ghana is 900,000ft (274,320m, approx. 300,000m) E, 0ft (0m) N At the global level (i.e. UTM), the False origin for the Northern hemisphere is 500,000m E, 0m N and the southern hemisphere is 500,000m E, 10,000,000m N False Origin True Origin

10. Determination of Location or Position Geographic and Rectangular coordinates on a topomap Geographic coordinate mark Rectangular coordinate mark

11. Determination of Location or Position Geographic and Rectangular coordinates on a topomap

12. Determination of Location or Position Steps to determine Mathematical or accurate location on a map To measure or determine the coordinates, first determine the point which you will use to represent the feature. If it is a point feature, then you have no problem, but if it is an areal feature, you will have to determine an appropriate point. This could be the town centre, junction, chief’s palace, etc. usually where the town started. Next, you locate the grid lines within which the feature falls. Draw lines connecting these grids if they are not already on the map. However, be careful with drawing these lines and clean them afterwards. Draw a vertical and horizontal lines through the centre of the point to cut the grid lines that you just drew. N.B: Care must be taken in drawing the lines. If the map is a topo map, then don’t draw lines on it as your line will obstruct other features. Instead make marks at the border of the map. Please use set squares to aid in marking.

13. Determination of Location or Position Steps to determine Mathematical or accurate location on a map Measure the distance between the latitude and the longitude marks in the map with a rule. Measure the distance from the smaller grid value to the point where the line through the town cuts the gridlines. So you measure from these points to the horizontal and vertical lines through the town respectively. Note that the lines passing through the point are the latitude and longitude of the point. Find the difference between the latitude grids and the longitude grids Use proportions to calculate the latitude difference and the longitude difference. Use the formula: Latitude or longitude difference = (Distance measured from lower grid to horizontal line)/(Distance measured between grid lines) x Difference between gird values Add the answer to the smaller grid value to obtain the latitude of the town. Repeat for the longitude

14. Determination of Location or Position Place one of the sets square on the line you want to draw. If you want to draw a horizontal line, place it on the line so that the side follows the line. Fix the other set square firmly to it. Look at the direction your point and slide the sets squares against each other till you are on the point (note: when sliding one, the other is firmly fixed. If it moves, then you have to start all over. Do same for the other line

15. Determination of Location or Position Example: determine the location of Dormaa Ahenkro on the map For Latitude: Distance between latitudes (A) = 4.4cm Distance between the lower latitude and latitude passing through the point (C) = 0.4cm Difference between grid latitudes ( Ld ) = 7°30’- 7°15’ = 0°15’ Difference between lower latitude and latitude passing through point = (C/A) xLd = (0.4/4.4)x0°15’ = 0.0909 x 0° 15’ = 0° 1.35’ = 0°01’21” B D A C

16. Determination of Location or Position Latitude of Dorma Ahenkro = 7°15’00” + 0°01’21” = 7°16’21”N For longitude: Distance between longitudes (B) = 5.8cm Distance between the lower longitude and longitude passing through the point (D) = 3.6cm Difference between grid longitudes ( Lc ) = 3°00’- 2°40’ = 0°20’ Difference between lower long. and long. passing through point = (D/B) xLc = (3.6/5.8)x0°20’ = 0.6207 x 0° 20’ = 0°12.414’ = 0°12’25” Longitude of Dorma Ahenkro = 2°40’00” + 2°12’25” = 2°52’25”W The coordinates of Dorma Ahenkro is latitude 7°16’21”N and longitude 2°52’25”W

17. Plotting a Point on the Map Plotting a point is the reverse operation of measuring coordinates on a map However some of the steps outlined above are reversed while some remain the same. So the steps that are reversed are outlined below The same formula as above is used We know the latitude and longitude of the points but we have to determine the distances between them and grids so we can measure and plot. First the determine the grids within which the point will lie Measure the distance between the grids (lower and upper grids) and distance between the lower grid and point Determine the latitude difference from the latitude of the point and the lower grid latitude Substitute the values you have in the formula and calculate the unknown which is the distance between the lower grid lat. Lat. Diff = difference between point and lower grid/diff between grids)x distance between grids

18. Plotting a Point on the Map Measure the distances you just determined from the lower grids on both sides on the map and connect them. Repeat the steps above for the longitude difference The intersection of the lines representing the lat. and long should be the location of the point Example: locate a point with lat. 7° 22’ 10”N , and long. 2° 39’ 41”W This point falls between latitudes 7° 30’ N and 7° 15’ N and longitudes 2° 20’ W and 2° 40’ W . lat. difference of grids = 7° 30’ - 7° 15’ = 0° 15’ = 0.25° lat. difference of lower grid and point = 7 ° 22’ 10” - 7 ° 15’ 0” = 0 ° 7’ 10” = 0.1194° Distance between lat. grids = 4.4cm Distance between lower lat. and lat. of point = (0.1194/.25)x4.4cm = 2.1cm Do same for the longitude difference long. difference of grids = 2° 40’ - 2° 20’ = 0° 20’ = 0.33333° long. difference of grids = 2° 39’ 41” - 2 ° 20’ 0” = 0 ° 19’ 41” = 0.3281° Distance between long. grids = 5.8cm Distance between lower long. and long. of point = (0.3281/.3333)x5.8cm = 5.7cm

19. Plotting a Point on the Map 5.7cm 5.7cm 2.1cm 2.1cm Measure these distance on both grids and join them Their intersection represents the location of the point.

20. Uses of Measurements Coordinates To locate features on the ground (i.e., features or objects can be traced using their coordinates) To site projects To determine area of settlements For navigation purposes