BUDOWNICTWO ROK AK. 2013/1014

SPRAWOZDANIE 2

Temat: Pomiary geodezyjne.

Monika Łaszczak

Grupa III

Punkty:

Lp.	X	y
1.	24,25	30,38
2.	120,38	30,95
3.	135,29	66,29
4.	111,95	100,29
5.	31,31	97,23
6.	05,05	70,29

Skala 1:500

1. X₁ = 24, 25 ÷ 5 = 4,85 [cm]

Y₁ = 30,38 ÷ 5 = 6,08 [cm]

1. X₂ = 120,38 ÷ 5 = 24,078 [cm]

Y₂ = 30,95 ÷ 5 = 6,19 [cm]

1. X₃ = 135,29 ÷ 5 = 27,06 [cm]

Y₃ = 66,29 ÷ 5 = 13,26 [cm]

1. X₄ = 111,95 ÷ 5 = 22,39 [cm]

Y₄ = 100,29 ÷ 5 = 20,06 [cm]

1. X₅ =31,31 ÷ 5 = 6,26 [cm]

Y₅ = 97,23 ÷ 5 =19,45 [cm]

1. X₆ = 05,05 ÷ 5 = 1,01 [cm]

Y₆ = 70,29 ÷ 5 = 14,06 [cm]

1. Obliczam delty:

• ∆x_1-2 = 96,13 [m]

∆y_1-2 = 0,57 [m]

• ∆x_2-3 = 35,34 [m]

∆y_2-3 = 14,91 [m]

• ∆x_3-4 = -23,34 [m]

∆y_3-4 = 34 [m]

• ∆x_4-5 = -80,64 [m]

∆y_4-5 = -3,06 [m]

• ∆x_5-6 = -26,26 [m]

∆y_5-6 = -3,06 [m]

• ∆x_6-1 = -19,2 [m]

∆y_6-1 = 39,91 [m]

1. Obliczam odległości według wzoru $\sqrt{}\lbrack\left( x \right)^{2} + \left( y \right)^{2}\rbrack$

• D₁ = 96,13 [m]

• D₂ = 38,36 [m]

• D₃ = 41,24 [m]

• D₄ = 80,70 [m]

• D₅ = 37,62 [m]

• D₆ = 44,29 [m]

1. Obliczam azymuty:

• A_1-2 = arctg(∆y₁/∆x₁) = 0,77477^g

• A_2-3 = arctg(∆y₂/∆x₂) = 74,583383^g

• A_3-4 = arctg(∆y₃/∆x₃) + 200^g = 138,298281^g

• A_4-5 = arctg(∆y₄/∆x₄) + 200^g = 202,414586^g

• A_5-6 = arctg(∆y₅/∆x₅) + 200^g = 250,813680^g

• A_6-1 = arctg(∆y₆/∆x₆) + 400^g = 328.545989^g

1. Obliczam kąty wewnętrzne:

• α₁= A_6-1 - A_1-2 - 200 ^g = 128,168512 ^g

• α₂= A_1-2 - A_2-3 + 200 ^g = 125,794094 ^g

• α₃= A_2-3- A_3-4 + 200 ^g = 136,285102 ^g

• α₄= A_3-4 - A_4-5 + 200 ^g = 135,883695 ^g

• α₅= A_4-5 - A_5-6 + 200 ^g = 151,600906 ^g

• α₆= A_5-6- A_6-1 +200 ^g = 122,267691 ^g

Sprawdzenie: ∑ α₁ + α₂ + α₃ + α₄ + α₅ + α₆ = 800,00000 ^g

1. Obliczam azymuty odwrotne :

• A_2-1 = A_1-2 + 200 ^g = 200,77477 ^g

• A_3-2 = A_2-3 + 200 ^g = 274,583383 ^g

• A_4-3 = A_3-4 + 200 ^g = 338,298281 ^g

• A_5-4 = A_4-5 - 200 ^g = 2,414586 ^g

• A_6-5 = A_5-6 - 200 ^g = 50,813680 ^g

• A_1-6 = A_6-1 - 200 ^g = 128,545989 ^g

1. Wyliczam powierzchnię figury:

1. Ze wzoru:

2P = $\sum_{i = 1}^{6}{x_{1}(}y_{2} - y_{6}) + x_{2}\left( y_{3} - \ y_{1} \right) + \ x_{3}\left( y_{4} - \ y_{2} \right) + \ x_{4}\left( y_{5} - \ y_{3} \right) + \ x_{5}\left( y_{6} - \ y_{4} \right) + x_{6}(y_{1} - \ y_{5\ })$

2P = 14936,7 |/2

P = 7468,35 [m²]

Sprawdzenie:

-2P = $\sum_{i = 1}^{6}{y_{1}(}x_{2} - x_{6}) + y_{2}\left( x_{3} - \ x_{1} \right) + \ y_{3}\left( x_{4} - \ x_{2} \right) + \ y_{4}\left( x_{5} - \ x_{3} \right) + \ y_{5}\left( x_{6} - \ x_{4} \right) + y_{6}(x_{1} - \ x_{5\ })$

-2P = -14936,7 |/(-2)

P = 7468,35 [m²]

1. Z mapy :

• P_G1 = $\sum_{}^{}{P_{t} = P_{t1} + \ P_{t2} + \ P_{t3} + \ P_{t4} = \ \frac{1}{2}*69,85}*19,08 + \ \frac{1}{2}*111,03*50,59 + \ \frac{1}{2}*111,03*57,85 + \frac{1}{2}*67,20*23,29 = 666,369 + 2808,50 + 3211,54 + 782,544 = 7468,953$ [m²]

• P_G2 = $\sum_{}^{}{P_{t} = P_{t1} + \ P_{t2} + \ P_{t3} + \ P_{t4} = \frac{1}{2}*116,71}*29,03 + \ \frac{1}{2}*130,31*39,29 + \ \frac{1}{2}*130,31*33,28 + \frac{1}{2}*111,03*18,83 = 1694,05 + 2559,94 + 2168,36 + 1045,35 = 7467,7$ [m²]

P_G = $\frac{PG1 + PG2}{2} = 7468,33$ [m²]

Błąd obliczeń wynosi: $\frac{P - \ P_{G}}{P}*100\% = \ \frac{0,02}{7468,35}*100\% = 0,00028\ \%$