Instytut Geodezji Gospodarczej
Politechnika Warszawska
Ćwiczenie 1
Badanie pionowości krawędzi ściany
Wykonali:
Patrycja Ojczyk
Judyta Nakoneczna
Maciej Paśnikowski
Krystian Pruszyński
Wojciech Straszewski
Grupa 4
Rok akademicki: 2008/2009
Spis treści:
Sprawozdanie
Szkic pomiarowy
Dziennik obserwacji z obliczeniami
Wykresy
Sprawozdanie
Celem ćwiczenia był pomiar pionowości elementów konstrukcyjnych krawędzi budynku GG Politechniki Warszawskiej. Pomiar wykonano z dwóch stanowisk teodolitu. Stanowiska były dobrane w taki sposób, aby kąt między celowymi był w przybliżeniu kątem prostym., co przedstawia szkic pomiarowy. Do ćwiczenia użyto 2óch instrumentów Theo 010 i łaty. W celu wyeliminowania wpływu błędów instrumentalnych , obserwacje wykonywane były w 2óch położeniach lunety. Pomiar wykonany był dwiema metodami:
-trygonometryczną
-bezpośredniego rzutowania
Zestawienie obliczeń:
P1
Odległość instrumentu od ściany-14.97m Błąd pomiaru kąta-0,0010grad Błąd pomiaru odległości-0,01m Błąd odczytu z łaty-0,001m |
I seria |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
Łata |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
||||||
|
|
|
|
|
|
||||||
P |
203.71 |
54 |
53 |
|
|
|
203.7154 |
|
|
||
|
3.80 |
2 |
2 |
|
|
|
3.8002 |
19.3876 |
19.3876 |
|
|
0 |
184.32 |
81 |
74 |
297.6823 |
26.30 |
26.40 |
184.3278 |
19.3876 |
|
|
|
|
384.41 |
21 |
31 |
102.3178 |
26.50 |
|
384.4126 |
-0.0085 |
-0.0095 |
2.6752 |
2.6754 |
1 |
184.33 |
55 |
70 |
300.3575 |
26.65 |
26.68 |
184.3363 |
-0.0104 |
|
2.6755 |
|
|
384.42 |
30 |
30 |
99.6423 |
26.70 |
|
384.4230 |
-0.0419 |
-0.0406 |
5.1785 |
5.1805 |
2 |
184.37 |
80 |
84 |
305.5360 |
27.70 |
27.70 |
184.3782 |
-0.0393 |
|
5.1825 |
|
|
384.46 |
23 |
24 |
94.4598 |
27.70 |
|
384.4624 |
0.0041 |
0.0058 |
3.9669 |
3.9656 |
3 |
184.37 |
48 |
33 |
309.5029 |
27.55 |
27.55 |
184.3741 |
0.0075 |
|
3.9642 |
|
|
384.45 |
54 |
42 |
90.4956 |
27.55 |
|
384.4548 |
-0.1072 |
-0.0583 |
7.2623 |
7.2635 |
4 |
184.48 |
14 |
11 |
316.7652 |
27.95 |
27.85 |
184.4813 |
-0.0093 |
|
7.2647 |
|
|
384.46 |
49 |
34 |
83.2309 |
27.75 |
|
384.4642 |
0.0281 |
0.0317 |
11.1338 |
11.1325 |
5 |
184.45 |
30 |
34 |
72.0998 |
27.20 |
27.05 |
184.4532 |
0.0354 |
|
11.1311 |
|
|
384.42 |
90 |
84 |
327.8990 |
26.90 |
|
384.4287 |
19.3474 |
19.3599 |
|
30.2174 |
P |
3.80 |
1 |
20 |
|
|
3.8011 |
19.3724 |
|
|
||
|
203.80 |
10 |
2 |
|
|
203.8006 |
|
|
|||
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|
|
|
|
|
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II seria |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
Łata |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
||||||
|
|
|
|
|
|
||||||
P |
203.80 |
26 |
30 |
|
|
203.8028 |
|
|
|||
|
3.80 |
8 |
2 |
|
|
3.8005 |
19.3813 |
19.3835 |
|
||
0 |
184.42 |
20 |
10 |
297.6828 |
26.50 |
26.55 |
184.4215 |
19.3857 |
|
|
|
|
384.41 |
49 |
47 |
102.3181 |
26.60 |
|
384.4148 |
-0.0059 |
-0.0062 |
2.6746 |
2.6758 |
1 |
184.42 |
61 |
87 |
300.3574 |
26.70 |
26.73 |
184.4274 |
-0.0065 |
|
2.6769 |
|
|
384.42 |
9 |
16 |
99.6412 |
26.75 |
|
384.4213 |
-0.0463 |
-0.0430 |
5.1828 |
5.1828 |
2 |
184.47 |
62 |
12 |
305.5402 |
27.70 |
27.75 |
184.4737 |
-0.0396 |
|
5.1828 |
|
|
384.00 |
4630 |
4588 |
94.4584 |
27.80 |
|
384.4609 |
0.0134 |
0.0097 |
3.9627 |
3.9634 |
3 |
184.00 |
4608 |
4598 |
309.5029 |
27.55 |
27.55 |
184.4603 |
0.0059 |
|
3.9642 |
|
|
384.45 |
36 |
63 |
90.4942 |
27.55 |
|
384.4550 |
-0.0108 |
-0.0098 |
7.2709 |
7.2684 |
4 |
184.00 |
4688 |
4733 |
316.7738 |
27.75 |
27.80 |
184.4711 |
-0.0089 |
|
7.2659 |
|
|
384.46 |
34 |
44 |
83.2283 |
27.85 |
|
384.4639 |
0.0320 |
0.0345 |
11.1169 |
11.1249 |
5 |
184.43 |
93 |
88 |
327.8907 |
26.90 |
26.93 |
184.4391 |
0.0370 |
|
11.1329 |
|
|
384.42 |
69 |
68 |
72.0954 |
26.95 |
|
384.4269 |
19.3641 |
19.3690 |
|
30.2153 |
P |
203.80 |
32 |
31 |
|
|
203.8032 |
19.3739 |
|
|
||
|
3.80 |
8 |
6 |
|
|
3.8007 |
|
|
|||
III seria |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
Łata |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
||||||
|
|
|
|
|
|
||||||
P |
3.80 |
8 |
2 |
|
|
3.8005 |
|
|
|||
|
203.80 |
22 |
35 |
|
|
203.8029 |
19.3841 |
19.3835 |
|
||
0 |
184.41 |
95 |
81 |
297.6827 |
26.55 |
26.58 |
184.4188 |
19.3830 |
|
|
|
|
384.41 |
79 |
72 |
102.3252 |
26.60 |
|
384.4176 |
-0.0073 |
-0.0069 |
2.6739 |
2.6781 |
1 |
184.42 |
58 |
65 |
300.3566 |
26.75 |
26.75 |
184.4262 |
-0.0065 |
|
2.6823 |
|
|
384.42 |
38 |
42 |
99.6429 |
26.75 |
|
384.4240 |
-0.0435 |
-0.0410 |
5.1799 |
5.1800 |
2 |
184.00 |
4690 |
4702 |
305.5365 |
27.75 |
27.75 |
184.4696 |
-0.0385 |
|
5.1801 |
|
|
384.46 |
23 |
27 |
94.4628 |
27.75 |
|
384.4625 |
0.0395 |
0.0235 |
4.1784 |
4.0722 |
3 |
184.00 |
4305 |
4298 |
309.7149 |
27.80 |
27.70 |
184.4302 |
0.0075 |
|
3.9659 |
|
|
384.45 |
51 |
50 |
90.4969 |
27.60 |
|
384.4551 |
-0.0414 |
-0.0258 |
7.0548 |
7.1616 |
4 |
184.47 |
14 |
18 |
316.7697 |
27.75 |
27.78 |
184.4716 |
-0.0101 |
|
7.2684 |
|
|
384.46 |
59 |
44 |
83.2285 |
27.80 |
|
384.4652 |
0.0353 |
0.0355 |
11.0338 |
11.0836 |
5 |
184.43 |
80 |
46 |
327.8035 |
26.90 |
26.95 |
184.4363 |
0.0357 |
|
11.1334 |
|
|
384.42 |
93 |
95 |
72.0951 |
27.00 |
|
384.4294 |
19.3666 |
19.3695 |
|
30.1755 |
P |
203.80 |
22 |
35 |
|
|
203.8029 |
19.3725 |
|
|
||
|
3.80 |
20 |
18 |
|
|
3.8019 |
|
|
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P2
Odległość instrumentu od ściany-13.78m Błąd pomiaru kąta-0,0010grad Błąd pomiaru odległości-0,01m Błąd odczytu z łaty-0,001m |
I seria |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
Łata |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
||||||
|
|
|
|
|
|
||||||
P |
188.88 |
26 |
26 |
|
23.5 |
188.8826 |
|
|
|||
|
388.88 |
59 |
59 |
|
|
388.8859 |
12.7551 |
12.7541 |
|
||
0 |
176.12 |
72 |
78 |
102.1855 |
51.36 |
51.36 |
176.1275 |
12.7532 |
|
|
|
|
376.13 |
30 |
25 |
297.8146 |
51.35 |
|
376.1328 |
-0.0006 |
-0.0093 |
2.4851 |
2.4842 |
1 |
176.12 |
74 |
87 |
99.7004 |
51.36 |
51.36 |
176.1281 |
-0.0180 |
|
2.4832 |
|
|
376.15 |
5 |
10 |
300.2978 |
51.36 |
|
376.1508 |
-0.1054 |
-0.0955 |
4.8132 |
4.8182 |
2 |
176.23 |
42 |
28 |
94.8872 |
51.07 |
51.07 |
176.2335 |
-0.0856 |
|
4.8231 |
|
|
376.23 |
66 |
60 |
305.1209 |
51.06 |
|
376.2363 |
-0.0081 |
-0.0066 |
3.6892 |
3.6892 |
3 |
176.24 |
17 |
15 |
91.1980 |
51.05 |
51.05 |
176.2416 |
-2.0050 |
|
3.6891 |
|
|
376.24 |
20 |
6 |
308.8100 |
51.05 |
|
378.2413 |
-0.0281 |
0.9705 |
6.8100 |
6.8064 |
4 |
176.26 |
92 |
102 |
84.3880 |
50.97 |
50.97 |
176.2697 |
1.9691 |
|
6.8028 |
|
|
376.27 |
17 |
27 |
315.6128 |
50.97 |
|
376.2722 |
-0.0002 |
0.0093 |
10.4176 |
10.4210 |
5 |
176.26 |
86 |
112 |
73.9704 |
51.03 |
51.03 |
176.2699 |
0.0187 |
|
10.4243 |
|
|
376.25 |
34 |
36 |
326.0371 |
51.02 |
|
376.2535 |
12.6150 |
12.6224 |
|
28.2188 |
P |
188.88 |
32 |
32 |
|
|
188.8832 |
12.6297 |
|
|
||
|
388.88 |
49 |
49 |
|
|
388.8849 |
|
|
|||
II seria |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
Łata |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
||||||
|
|
|
|
|
|
||||||
P |
188.88 |
42 |
42 |
|
|
188.8842 |
|
|
|||
|
388.88 |
54 |
54 |
|
|
388.8854 |
12.7524 |
12.7523 |
|
||
0 |
176.13 |
15 |
22 |
102.1901 |
51.35 |
51.35 |
176.1319 |
12.7523 |
|
|
|
|
376.13 |
32 |
30 |
297.8163 |
51.34 |
|
376.1331 |
0.0003 |
0.0023 |
2.4838 |
2.4854 |
1 |
176.13 |
15 |
15 |
99.7063 |
51.36 |
51.36 |
176.1315 |
0.0043 |
|
2.4869 |
|
|
376.12 |
90 |
86 |
300.3032 |
51.36 |
|
376.1288 |
-0.1035 |
-0.1061 |
4.8127 |
4.8125 |
2 |
176.23 |
41 |
59 |
94.8936 |
51.07 |
51.07 |
176.2350 |
-0.1087 |
|
4.8124 |
|
|
376.23 |
82 |
68 |
305.1156 |
51.07 |
|
376.2375 |
-0.0053 |
-0.0053 |
3.6966 |
3.6964 |
3 |
176.24 |
2 |
4 |
91.1970 |
51.05 |
51.05 |
176.2403 |
-0.0052 |
|
3.6962 |
|
|
376.24 |
38 |
16 |
308.8118 |
51.05 |
|
376.2427 |
-0.0308 |
-0.0298 |
6.8070 |
6.8057 |
4 |
176.27 |
6 |
16 |
84.3900 |
50.97 |
50.97 |
176.2711 |
-0.0289 |
|
6.8044 |
|
|
376.27 |
7 |
25 |
315.6162 |
50.97 |
|
376.2716 |
0.0205 |
0.0192 |
10.4219 |
10.4213 |
5 |
176.25 |
4 |
9 |
73.9681 |
51.02 |
51.02 |
176.2507 |
0.0180 |
|
10.4206 |
|
|
376.25 |
30 |
42 |
326.0368 |
51.01 |
|
376.2536 |
12.6343 |
12.6331 |
|
28.2213 |
P |
188.88 |
49 |
49 |
|
|
188.8849 |
12.6320 |
|
|
||
|
388.88 |
56 |
56 |
|
|
388.8856 |
|
|
|||
III seria |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
Łata |
Kąt poziomy [Hz] |
Kąt pionowy [v] |
||||||
|
|
|
|
|
|
||||||
P |
188.88 |
26 |
26 |
|
|
188.8826 |
|
|
|||
|
388.88 |
51 |
51 |
|
|
388.8851 |
212.7526 |
12.7520 |
|
||
0 |
176.13 |
30 |
20 |
102.1889 |
51.35 |
51.35 |
176.1325 |
212.7514 |
|
|
|
|
376.13 |
10 |
15 |
297.8168 |
51.35 |
|
376.1313 |
0.0025 |
0.0029 |
2.4824 |
2.4844 |
1 |
176.12 |
92 |
108 |
99.7065 |
51.35 |
51.36 |
176.1300 |
0.0033 |
|
2.4864 |
|
|
376.12 |
72 |
87 |
300.3032 |
51.36 |
|
376.1280 |
-0.1038 |
-0.1052 |
4.8145 |
4.8125 |
2 |
176.23 |
40 |
36 |
94.8920 |
51.08 |
51.08 |
176.2338 |
-0.1066 |
|
4.8105 |
|
|
376.23 |
38 |
52 |
305.1137 |
51.07 |
|
376.2345 |
-0.0056 |
-0.0059 |
3.6990 |
3.6972 |
3 |
176.23 |
87 |
102 |
91.1930 |
51.05 |
51.05 |
176.2395 |
-0.0062 |
|
3.6955 |
|
|
376.24 |
7 |
8 |
308.8092 |
51.05 |
|
376.2408 |
-0.0310 |
-0.0315 |
6.8041 |
6.8051 |
4 |
176.27 |
6 |
2 |
84.3889 |
50.97 |
50.97 |
176.2704 |
-0.0320 |
|
6.8060 |
|
|
376.27 |
33 |
22 |
315.6152 |
50.97 |
|
376.2728 |
0.0207 |
0.0195 |
10.4215 |
10.4215 |
5 |
176.24 |
98 |
97 |
73.9675 |
51.02 |
51.02 |
176.2498 |
0.0184 |
|
10.4214 |
|
|
376.25 |
49 |
38 |
326.0367 |
51.01 |
|
376.2544 |
12.6339 |
12.6319 |
|
28.2207 |
P |
188.88 |
36 |
36 |
|
|
188.8836 |
12.6299 |
|
|
||
|
388.88 |
42 |
42 |
|
|
388.8842 |
|
|
|||
METODA BEZPOŚREDNIEGO RZUTOWANIA
Dzienniki z tej metody załączyliśmy na końcu sprawozdania.
ZESTAWIENIE WYNIKÓW
Współrzędne punktów |
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Wyniki - pomiar kątów poziomych [m] |
|
|
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|
x |
y |
|
|
Stanowiska |
P1 |
13.799 |
0.000 |
|
|
|
P2 |
0.000 |
14.977 |
|
|
Krawędź |
0 |
0.000 |
0.000 |
|
|
|
1 |
-0.002 |
0.001 |
|
|
|
2 |
-0.011 |
-0.024 |
|
|
|
3 |
-0.009 |
-0.026 |
|
|
|
4 |
-0.013 |
-0.033 |
|
|
|
5 |
-0.009 |
-0.028 |
|
|
Wychylenia |
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|
|
pomiar kątów poziomych [m] |
odczyty z łaty [m] |
||
|
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|
|
podłużne |
poprzeczne |
podłużne |
poprzeczne |
|
0 |
0.00 |
0.00 |
0.00 |
0.00 |
|
1 |
-0.16 |
0.06 |
-0.21 |
0.01 |
|
2 |
-1.06 |
-2.42 |
-1.23 |
-0.28 |
|
3 |
-0.89 |
-2.56 |
-1.09 |
-0.30 |
|
4 |
-1.28 |
-3.28 |
-1.30 |
-0.38 |
|
5 |
-0.86 |
-2.83 |
-0.47 |
-0.33 |
|
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|
Wysokości poziomów: |
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|
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|
|
st. P1 |
St. P2 |
średnia |
|
|
0 |
0.000 |
0.000 |
0.000 |
|
|
1 |
0.580 |
0.585 |
0.583 |
|
|
2 |
1.712 |
1.725 |
1.718 |
|
|
3 |
2.592 |
2.612 |
2.602 |
|
|
4 |
4.266 |
4.300 |
4.283 |
|
|
5 |
7.090 |
7.111 |
7.101 |
|