Temat 2
Wyznaczenie błędu indeksu
Spis treści
Sprawozdanie techniczne
Dzienniki pomiaru
Obliczenia i algorytmy
Ocena dokładności
Zestawienie wyników i ich błędów
Poniższe tabelki ułatwiają obliczenie błędu indeksu i kątów wolnych od błędu indeksu.
Tab. 1.
Nr |
ZI [g] |
ZII [g] |
Σ [g] |
2 ε |
ZI - ε [g] |
ZII - ε [g] |
Σ [g] |
|
|
|
|
ε |
|
|
|
1 |
69,9236 |
330,0738 |
399,9974 |
-0,0026 |
69,9249 |
330,0751 |
400,0000 |
|
|
|
|
-0,0013 |
|
|
|
2 |
71,2442 |
328,7607 |
400,0049 |
0,0049 |
71,2418 |
328,7582 |
400,0000 |
|
|
|
|
0,00245 |
|
|
|
3 |
75,7677 |
324,2264 |
399,9941 |
-0,0059 |
75,7706 |
324,2294 |
400,0000 |
|
|
|
|
-0,00295 |
|
|
|
4 |
77,2075 |
322,7916 |
399,9991 |
-0,0009 |
77,2080 |
322,7920 |
400,0000 |
|
|
|
|
-0,00045 |
|
|
|
5 |
81,9244 |
318,0776 |
400,0020 |
0,0020 |
81,9234 |
318,0766 |
40,00000 |
|
|
|
|
0,0010 |
|
|
|
6 |
83,2895 |
316,7087 |
399,9982 |
-0,0018 |
83,2904 |
316,7096 |
400,0000 |
|
|
|
|
-0,0009 |
|
|
|
gdzie: ZI+ ZII= 400g+2ε
Tab. 2.
Nr |
ZI [g] |
ZII [g] |
Σ [g] |
2 ε |
ZI - ε [g] |
ZII - ε [g] |
Σ [g] |
|
|
|
|
ε |
|
|
|
1 |
69,9238 |
330,0785 |
400,0023 |
|
69,9226
|
330,0774
|
400,0000 |
|
|
|
|
0,00115 |
|
|
|
2 |
71,2398 |
328,7578 |
399,9976 |
|
71,241 |
328,7590 |
400,0000 |
|
|
|
|
-0,0012 |
|
|
|
3 |
75,7718 |
324,2233 |
399,9951 |
-0,0049 |
75,7742
|
324,2258
|
400,0000 |
|
|
|
|
-0,00245 |
|
|
|
4 |
77,2053 |
322,7964 |
400,0017 |
|
77,2044 |
322,7956 |
400,0000 |
|
|
|
|
-0,00085 |
|
|
|
5 |
81,9256 |
318,0724 |
399,9980 |
|
81,9266 |
318,0734 |
400,0000 |
|
|
|
|
-0,0010 |
|
|
|
6 |
83,2894 |
316,7148 |
399,0042 |
|
83,2873 |
316,7127 |
400,0000 |
|
|
|
|
-0,0021 |
|
|
|
Tab. 3.
Nr |
βI [g] |
βII [g] |
βŚr [g] |
βI popr. [g] |
βIIpopr. [g] |
1 |
30,0764 |
30,0738 |
30,0751 |
30,0751 |
30,0751 |
2 |
28,7558 |
28,7607 |
28,7582 |
28,7582 |
28,7582 |
3 |
24,2323 |
24,2264 |
24,2294 |
24,2294 |
24,2294 |
4 |
22,7925 |
22,7916 |
22,7920 |
22,7920 |
22,7920 |
5 |
18,0756 |
18,0776 |
18,0766 |
18,0766 |
18,0766 |
6 |
16,7105 |
16,7087 |
16,7096 |
16,7096 |
16,7096 |
gdzie: βI = 100g - ZI βII = ZII - 300g
βI popr. = 100g - ( ZI - Ɛ) βIIpopr. = ( ZII - Ɛ) - 300g
Tab. 4.
Nr |
βI [g] |
βII [g] |
βŚr [g] |
βI popr. [g] |
βIIpopr. [g] |
1 |
30,0762 |
30,0785 |
30,0774 |
30,0774 |
30,0774 |
2 |
28,7602 |
28,7578 |
28,7590 |
28,7590 |
28,7590 |
3 |
24,2282 |
24,2233 |
24,2258 |
24,2258 |
24,2258 |
4 |
22,7947 |
22,7964 |
22,7956 |
22,7956 |
22,7956 |
5 |
18,0744 |
18,0724 |
18,0734 |
18,0734 |
18,0734 |
6 |
16,7106 |
16,7148 |
16,7127 |
16,7127 |
16,7127 |
Wyznaczenie błędu kąta pionowego z teorii par spostrzeżeń
Nr |
β1s [g] |
β2s [g] |
di = β1s - β2s [cc] |
di2 [cc2] |
||
1 |
30,0751 |
30,0774 |
-23 |
529 |
||
2 |
28,7582 |
28,759 |
-8 |
64 |
||
3 |
24,2294 |
24,2258 |
36 |
1296 |
||
4 |
22,792 |
22,7956 |
-36 |
1296 |
||
5 |
18,0766 |
18,0734 |
32 |
1024 |
||
6 |
16,7096 |
16,7127 |
-31 |
961 |
||
Σ = 5170 |
Tab. 5.
mβ = ±
mβ = ±14,7 cc
Wyznaczenie błędu indeksu z teorii par spostrzeżeń
Tab. 6.
Nr |
ε1s [g] |
ε2s [g] |
di = ε1s - ε2s [cc] |
di2 [cc2] |
1 |
-0,0013 |
0,0012 |
-2,5 |
6,25 |
2 |
0,00245 |
-0,0012 |
3,65 |
13,32 |
3 |
-0,00295 |
-0,0024 |
-0,55 |
0,30 |
4 |
-0,00045 |
0,0008 |
-1,25 |
1,56 |
5 |
0,0010 |
-0,0010 |
2 |
4,00 |
6 |
-0,0009 |
0,0021 |
-3 |
9,00 |
Σ = 39,43 |
mε = ±
mε = ±1,2 cc
Obliczenie błędu wyznaczenia błędu indeksu ze średniej arytmetycznej
Tab. 7.
Nr |
εi [cc] |
vi = εi - εśr [cc] |
vi*vi [cc2] |
|
1 |
-13,0 |
-10,8 |
116,64 |
|
2 |
24,5 |
24,5 |
600,25 |
|
3 |
-29,5 |
-29,5 |
870,25 |
|
4 |
-4,5 |
-4,5 |
20,25 |
|
5 |
10,0 |
10,0 |
100,00 |
|
6 |
-9,0 |
-9,0 |
81,00 |
|
7 |
12,0 |
12,0 |
144,00 |
|
8 |
-12,0 |
-12,0 |
144,00 |
|
9 |
-24,0 |
-24,0 |
576,00 |
|
10 |
8,0 |
8,0 |
64,00 |
|
11 |
-10,0 |
-10,0 |
100,00 |
|
12 |
21,0 |
21,0 |
441,00 |
|
εśr.=-2,2 |
|
Σ = 3257,39 |
mεśr. =
mεśr. = ± 5,0 cc
Zestawienie wyników
mβ = ±14,7 cc
εśr.=-2,2 cc
mεśr. = ± 5,0 cc