Coordinates and Bearings BE1S204 David Harper

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

Co-ordinate systems and distances

Angles and Bearings

Casio scientific calculator – single line display

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

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”.

Calculate the co-ordinates of Point B? Bearings (cont.) B 58.612 m 195o07’36” A C 1010.223 E 1999.789 N 1210.477 E 1909.505 N Calculate the co-ordinates of Point B?

Method Calculate WCB A → C N.B. Target co-ordinates – Base co-ordinates = ∆ E Target co-ordinates – Base co-ordinates = ∆ N C = 1210.477 E 1909.505 N Ddt A = 1010.223 E 1999.789 N 200.254 ∆ E - 90.284 ∆ N Casio scientific calculator: - Pol(∆ N, ∆ E) = distance = WCB Pol(-90.284, 200.254) r = distance = 219.66534 m Ѳ = WCB = 114.2681099 = 114O16’5”

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

Method (cont.) 3) Calculate co-ordinates of point B (cont.) Rec(58.612, 309o23’41”) X = ∆ N = 37.199 Add to base point Y = ∆ E = -45.295 A = 1010.233 E 1999.789 N + ∆ = - 45.295 ∆ E 37.199 ∆ N B = 964.938 E 2036.988 N

Examples of surveying calculations

Hints for using your calculator

Solutions

Solutions (cont.)

Surveying calculations

Surveying calculations - solutions N.B. Target co-ordinates – Base co-ordinates = ∆ E Target co-ordinates – Base co-ordinates = ∆ N B → A 519.262 mE 819.714 mN Ddt 386.119 mE 692.583 mN 133.143 ∆E 127.131 ∆N B → C 701.114 mE 488.149 mN Ddt 386.119 mE 692.583 mN 314.995 ∆E -204.434 ∆N N.B. Pol(ΔN, ΔE) = Polar coordinates B → A Pol(127.131, 133.143) = dist. = 184.091 m Ѳ = 46.32322469 = 46o 19’ 23.61”

Surveying calculations – solutions (cont.) B → C Pol(-204.434, 314.995) = dist. = 375.520 m Ѳ = 122.9838582 = 122o 59’ 1.89” N.B. Rec(Distance, WCB) = ∆ N = ∆ E C → D Rec(227.114, 23o 14’ 27”) = X = ∆ N = 208.685 m = Y = ∆ E = 89.618 m C 701.114 mE 488.149 mN Add 89.618 ∆E 208.685 ∆N D 790.732 mE 696.834 mN

Surveying calculations – solutions (cont.) B → D 790.732 mE 696.834 mN Ddt 386.119 mE 692.583 mN 404.613 ∆E 4.251 ∆N N.B. Pol(ΔN, ΔE) = Polar coordinates B → D Pol(4.251, 404.613) = dist. = 404.635 m Ѳ = 89.39805345 = 89o 23’ 52.99”

Calculating angles 72 45 46 72 45 47 72 45 46.5 72 45 40 72 45 38 72 45 39 72 45 43 P6 307 15 02 127 14 30 P8 200 00 44 200 00 16 72 45 42 72 45 46 72 45 44

Calculating angles (another example this time try yourselves)

Surveying calculations (try for yourselves)

Solutions

Solutions – (cont.)

Some more surveying calculations – try for yourselves

Solutions

Some more surveying calculations for you – try yourselves B3

Solutions

Solutions (cont.)

Final set of surveying calculations for you – try yourselves

Solutions

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