1. Coordinates and Bearings
BE1S204
David Harper

2. Introduction to today’s lecture
Co-ordinate systems and distances
Angles and bearings
Functions for Casio Scientific calculator
Bearing and co-ordinate calculations
Surveying calculations including calculating angles

3. Co-ordinate systems and distances

4. Angles and Bearings

5. Casio scientific calculator – single line display

6. Casio scientific calculator – double line display
Rec(distance, WCB) =
Pol(ΔN, ΔE) =

7. Bearings Angle – always between two lines e.g. 83o Grid North
Whole Circle Bearing e.g. 105o 57’23”.
000o → 360o clockwise from grid North.
WCB
WCB
Difference in WCB’s = 180o 00’00”.

8. Calculate the co-ordinates of Point B?
Bearings (cont.) B m
195o07’36” A C E N E N
Calculate the co-ordinates of Point B?

9. Method Calculate WCB A → C N.B.
Target co-ordinates – Base co-ordinates = ∆ E
Target co-ordinates – Base co-ordinates = ∆ N
C = E N
Ddt A = E N
∆ E ∆ N
Casio scientific calculator: - Pol(∆ N, ∆ E)
= distance
= WCB
Pol( , )
r = distance = m
Ѳ = WCB =
= 114O16’5”

10. Method (cont.)
2) Calculate WCB A → B WCB A → C = 114O16’5” + angle C A B = 195o07’36” WCB A → B = 309o23’41” 3) Calculate co-ordinates of point B Rec(Distance, WCB) = ∆ N = ∆ E

11. Method (cont.)
3) Calculate co-ordinates of point B (cont.) Rec(58.612, 309o23’41”) X = ∆ N = Add to base point Y = ∆ E = A = E N + ∆ = ∆ E ∆ N B = E N

12. Examples of surveying calculations

13. Hints for using your calculator

14. Solutions

15. Solutions (cont.)

16. Surveying calculations

17. Surveying calculations - solutions
N.B. Target co-ordinates – Base co-ordinates = ∆ E Target co-ordinates – Base co-ordinates = ∆ N B → A mE mN Ddt mE mN ∆E ∆N B → C mE mN Ddt mE mN ∆E ∆N N.B. Pol(ΔN, ΔE) = Polar coordinates B → A Pol( , ) = dist. = m Ѳ = = 46o 19’ 23.61”

18. Surveying calculations – solutions (cont.)
B → C Pol( , ) = dist. = m Ѳ = = 122o 59’ 1.89” N.B. Rec(Distance, WCB) = ∆ N = ∆ E C → D Rec( , 23o 14’ 27”) = X = ∆ N = m = Y = ∆ E = m C mE mN Add ∆E ∆N D mE mN

19. Surveying calculations – solutions (cont.)
B → D mE mN Ddt mE mN ∆E ∆N N.B. Pol(ΔN, ΔE) = Polar coordinates B → D Pol(4.251, ) = dist. = m Ѳ = = 89o 23’ 52.99”

20. Calculating angles P6 P8

21. Calculating angles (another example this time try yourselves)

22. Surveying calculations (try for yourselves)

23. Solutions

24. Solutions – (cont.)

25. Some more surveying calculations – try for yourselves

26. Solutions

27. Some more surveying calculations for you – try yourselvesB3

28. Solutions

29. Solutions (cont.)

30. Final set of surveying calculations for you – try yourselves

31. Solutions

32. Summary of today’s lecture
Co-ordinate systems and distances
Angles and bearings
Functions for Casio Scientific calculator
Bearing and co-ordinate calculations
Surveying calculations including calculating angles