2. Calculations you must be able to do <ul><li>Map code </li></ul><ul><li>Distance </li></ul><ul><li>Gradient </li></ul><ul><li>Area </li></ul><ul><li>Speed/distance/time </li></ul><ul><li>Co-ordinates / grid reference </li></ul><ul><li>Bearing & direction </li></ul><ul><li>Magnetic bearing and magnetic declination </li></ul><ul><li>Vertical exaggeration & cross section </li></ul><ul><li>Word scale conversion </li></ul><ul><li>General </li></ul>
3. 1) Map code <ul><li>The map code indicates the position of a map on a grid of longitude and latitude </li></ul><ul><li>South Africa is divided into a series of grid blocks by using lines of latitudes and longitudes (like when playing ‘Battle ship’) </li></ul><ul><li>E.g. 2634CB </li></ul><ul><li>26 = latitude </li></ul><ul><li>34 = longitude </li></ul><ul><li>C = Big block </li></ul><ul><li>B = Small block in the big block </li></ul>
6. Each grid block can be divided into lines of 60 seconds latitudes and longitudes Divide the grid block in two half's (30’ latitude and 30’ longitude) Each quarter now become a ‘Big block’ numbered A to D 24˚ 25˚ 34˚ 35˚ Divide each big block in half’s (15’ and 45’ latitude and longitude) Number each ‘small block’ in the big block A to D Finally find now big block C and small block B 30’ 30’ 15’ 15’ 45’ 45’ A B C D A B C D A B C D A B C D A B C D
7. 2) Distance <ul><li>Always measure the map distance in millimeters!!!!! </li></ul><ul><li>NOW you can convert the map distance into the real distance by using the following formula </li></ul>Distance = Map distance x scale 1000( m) OR 1 000 000( km )
8. 124mm 1: 50 000
9. Distance = map distance x scale 1000 000 What is the real distance in km ? = 124mm x 50 000 1000 000 = 6,2km Remember, if you had to give the answer in meters you must divide by a 1000 !!!
10. 3) Gradient <ul><li>Gradient is the steepness of a slope </li></ul><ul><li>You can easily see on a topographic map whether the slope is steep or gentle </li></ul><ul><li>When the contour lines </li></ul><ul><li>are close together the slope is </li></ul><ul><li>steep and when contour lines </li></ul><ul><li>are far apart the slope is gentle </li></ul>
11. <ul><li>Gradient is shown in a fraction format e.g. 1:8 </li></ul><ul><li>1 represents the vertical distance (1m change in height) </li></ul><ul><li>8 represents the horizontal distance (8m change with distance) </li></ul>1m 8m
12. Gradient = Height difference (m) . Distance (m) Calculate the gradient between X and Y.
13. 72mm X Y
14. <ul><li>Height difference between X and Y </li></ul><ul><li>X = 2140m </li></ul><ul><li>Y = 2320m </li></ul><ul><li>DH = 2320m </li></ul><ul><li> - 2140m </li></ul><ul><li>180m </li></ul>To calculate the distance in meters use the normal formula for distance (D) D = map distance x scale 1000 = 72mm x 50 000 1000 = 3600m
16. 4) Area <ul><li>To calculate the area of a given place you need to do TWO distance calculations!!! </li></ul><ul><li>Convert each side in to meters or kilometers before you apply it to the area formula </li></ul>Calculate the map area in km² Click here for topographic map
17. Area = Length x Breadth Length Breadth L = 155mm x 50 000 1000 000 = 7,75km B = 155mm x 50 000 1000 000 = 7,75km Area = L ength x B readth = 7.75km x 7.75km = 60.063km²
18. 5) Speed / distance / time Distance Speed Time
19. <ul><li>If you walk from V to W at an average speed of 5km/h. How long will it take to cover the distance? </li></ul><ul><li>Fist, calculate the distance in km between the tow points </li></ul><ul><li>Secondly, apply it to the formula </li></ul>D = 93mm x 50 000 1000 000 = 4,65km Time = Distance Speed = 0.93 x 60 = 0,93h = 4,65km 5km/h = 55 minutes 48seconds Click here for topographic map
20. 6) Co-ordinates (Grid reference) <ul><li>Always give the latitude first followed by the longitude </li></ul><ul><li>Co-ordinates are given in degrees, minutes and seconds </li></ul><ul><li>E.g. 23˚38’41”S and 31˚16’52”E </li></ul>
21. <ul><li>Remember, between each degree (°) it is divided into 60 minutes and between each minute (‘) it is divided into 60 seconds (“) </li></ul><ul><li>Always start with the latitude and then the longitude </li></ul><ul><li>Write down the latitude degrees, minutes and seconds South </li></ul><ul><li>Then write down the longitude degrees, minutes and seconds East </li></ul><ul><li>E.g. 29°17’33” South & 24°35’22” East </li></ul>
22. 29°S 24°E 30’ 45’ 15’ 30’ 45’ 15’
23. 29°26' 24°38' Latitude: Measure (mm) from 29°26’ to the point (A) Measure (mm) the distance from 29°26’ to the next latitude (B) Divide A by B x 60 Longitude: Measure (mm) from 24°38’ to the point (C) Measure (mm) the distance from 24°38’ to the next latitude (D) Divide C by D x 60 C D B A
24. 7) Bearing & Direction <ul><li>Bearing refers to the degrease between two points. </li></ul><ul><li>0˚ is always at the ‘top’ or true north </li></ul><ul><li>Always measure the degrease in a clockwise direction from 0˚ </li></ul><ul><li>Direction refers to the compass direction </li></ul>
25. A B Bearing: 240˚ Direction: SW
26. Magnetic declination <ul><li>The difference between true north and magnetic north </li></ul><ul><li>Magnetic declination changes from year to year </li></ul><ul><li>Change can be to the east (angle becomes smaller) or to the west (angle becomes greater </li></ul><ul><li>Change to east you subtract </li></ul><ul><li>Change to west you add </li></ul>
27.
28. 138° Step 1: Calculate the difference in years 2010 – 2002 = 8 years Step 2: Calculate the magnetic change 8years x 7’ W = 56’W Step 3: Determine the total change 24°34’W + 56’W = 25°30’W Step 4: Calculate the magnetic bearing True bearing + magnetic declination 138° + 25°30’ = 163°30’
29. CROSS SECTION <ul><li>A cross section is a side view of a feature on the land surface </li></ul>Vertical scale: 1cm represents 20m Horizontal scale 1: 50 000
30. trig beacon 7 . Draw a cross section from the settlement TO 1362,1 1340m 1320m 1300m 1280m 7 1360m Always make sure that your starting point is on the LEFT hand side!! Otherwise you will draw a mirror image. 1360m
31. 1280 1362,1 1360 1340 1320 1300 1280 Place a piece of paper on the line joining the settlement and the trig beacon Mark the settlement , trig beacon and every contour line that touches your paper Find the height of each contour line and write it down below the appropriate marking. Don’t forget the heights of the settlement and trig beacon 1362,1 1340m 1320m 1300m 1280m 7
32. Now you are going to draw the cross section Draw the horizontal axis (slightly longer than the line between the settlement and the trig beacon) Transfer the markings from the piece of paper onto the horizontal axis On the vertical axis make a mark every 20cm’s Indicate the heights on the vertical axis, starting with the lowest altitude (1280m) from horizontal axis next to the first marking Each marking’s height increase by 20m upwards till you get to the highest altitude from the horizontal axis 1280m 1300m 1320m 1340m 1360m 1360m 1380m Indicate each intersection point between the vertical and horizontal axis Finally, connect each point
33. 1362,1 1340m 1320m 1300m 1280m 7
34. A cross section from the settlement to trig beacon 7 Horizontal scale 1: 50 000 Vertical scale 1cm r.p. 20m Footpath Trig beacon 7 Settlement
35. Vertical exaggeration <ul><li>Tells you by how much the vertical axis (height) has been stretched out (distorted) </li></ul><ul><li>The ‘bigger’ the vertical scale, the more stretched your cross section </li></ul><ul><li>E.g. 1cm rp 20cm will be more stretched as 5mm rp 20cm </li></ul>If you stretch this object out (upwards) will it still show the real shape?
36. <ul><li>Lets see the difference </li></ul>VS = 1:2000 and HS 1:50 000 VE = VS HS = 1/2000 1/50000 = 1 . X 50 000 2000 1 = 25 times Everything on this cross section appears 25 times higher. Poor representation! VS = 1:4000 and HS 1:50 000 VE = VS HS = 1/4000 1/50000 = 1 . X 50 000 4000 1 = 12,5 times Everything on this cross section appears 12,5 times higher. Better representation! 1cm represents 20m = 1:2000 5mm represents 20m = 1:4000
37. 10) Converting a word scale into a fraction scale <ul><li>When will you use this? </li></ul><ul><li>A cross section can have a scale for the vertical axis </li></ul><ul><li>E.g. A vertical scale of 1cm represents 20m </li></ul><ul><li>You need to make sure that all the units are the same. </li></ul><ul><li>Convert the ‘larger’ unit into the smaller unit </li></ul><ul><li>Therefore, 20m will be converted into cm’s </li></ul>
38. 1cm represents 20m 1cm represents 20m x 100 1cm represents 2000cm 1:2000 5mm represents 20m 5mm represents 20m x 1000 5mm represents 20000mm 5 5 1mm represents 4000mm 1:4000 Units must be the same Nee to be 1 There is 1000mm in 1m There is 100cm in 1 meter
39. Convex and concave slopes Convex slope Concave slope
40. Landforms due to inclined strata Cuesta???? Homoclinal ridge???? Hogsback???? CUESTA WHY?? Dip slope scarp slope <25˚