Obliczanie poprawek
redukcyjnych do długości
Tematem zadania było obliczenie poprawek redukcyjnych K K K dla zadanych odległości.
2. 3, E
Obliczenia zostały zrobione w programie Microsoft Exel do których sporządzono wykresy
zależności poprawek od długości (od 0 do 80 km, z częstotliwością co kilometr). Dodatkowo na
wykresach zaznaczono funkcję odpowiadającą ustalonej wielkości poprawek, kolejno: -1mm, -
0,1 mm, -1mm.
We wszystkich obliczeniach wartość K wynosiła 0,13.
1. Według wzoru:
obliczono wartość D = 16,268km dla K = -1 mm.
1 2
Punkt przecięcia się krzywych to punkt o współrzędnych (65,614; -65,614).
20
K2[mm]
0
D1 [km]
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79
-20
-40
k2 od d1
-60
ppm
-80
-100
-120
-140
2. Według wzoru:
obliczono wartość D = 17,928km dla K =-0,1 mm.
2 3
Punkt przecięcia się krzywych to punkt o współrzędnych (75,910; 7,591).
[mm]
0
D2 [km]
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79
-1
-2
-3
-4
K3
-5
ppm
-6
-7
-8
-9
-10
3. Według wzoru:
obliczono wartość D = 9,912km dla K = -1 mm.
0 E
Punkt przecięcia wykresów to punkt o współrzędnych (31,205; 31,206).
[mm] 600
500
400
300
Ke od D0
ppm
200
100
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79
D0 [km]
D0 [km] Ke [km] Ke [mm]
0,999999999750 0,0000000010268568241 0,001027
2,000000000888 0,0000000082148545930 0,008215
2,999999993260 0,0000000277251342513 0,027725
3,999999984024 0,0000000657188367437 0,065719
4,999999968796 0,0000001283571030151 0,128357
5,999999946080 0,0000002218010740101 0,221801
6,999999914377 0,0000003522118906734 0,352212
7,999999872190 0,0000005257506939498 0,525751
8,999999818021 0,0000007485786247841 0,748579
9,999999750371 0,0000010268568241208 1,026857
10,999999667744 0,0000013667464329048 1,366746
11,999999568641 0,0000017744085920807 1,774409
12,999999451565 0,0000022560044425934 2,256004
13,999999315018 0,0000028176951253874 2,817695
14,999999157503 0,0000034656417814077 3,465642
15,999998977520 0,0000042060055515987 4,206006
16,999998773573 0,0000050449475769054 5,044948
17,999998544164 0,0000059886289982724 5,988629
18,999998287795 0,0000070432109566445 7,043211
19,999998002969 0,0000082148545929663 8,214855
20,999997688187 0,0000095097210481826 9,509721
21,999997341952 0,0000109339714632381 10,93397
22,999996962765 0,0000124937669790776 12,49377
23,999996549130 0,0000141952687366457 14,19527
24,999996099549 0,0000160446378768873 16,04464
25,999995612523 0,0000180480355407469 18,04804
26,999995086555 0,0000202116228691694 20,21162
27,999994520147 0,0000225415610030995 22,54156
28,999993911801 0,0000250440110834818 25,04401
29,999993260020 0,0000277251342512612 27,72513
30,999992563306 0,0000305910916473823 30,59109
31,999991820161 0,0000336480444127899 33,64804
32,999991029087 0,0000369021536884286 36,90215
33,999990188587 0,0000403595806152433 40,35958
34,999989297162 0,0000440264863341786 44,02649
35,999988353315 0,0000479090319861793 47,90903
36,999987355549 0,0000520133787121901 52,01338
37,999986302364 0,0000563456876531557 56,34569
38,999985192265 0,0000609121199500208 60,91212
39,999984023752 0,0000657188367437302 65,71884
40,999982795328 0,0000707719991752286 70,772
41,999981505496 0,0000760777683854607 76,07777
42,999980152757 0,0000816423055153712 81,64231
D0 [km] Ke [km] Ke [mm]
43,999978735614 0,0000874717717059049 87,47177
44,999977252569 0,0000935723280980065 93,57233
45,999975702125 0,0000999501358326207 99,95014
46,999974082782 0,0001066113560506920 106,6114
47,999972393044 0,0001135621498931660 113,5621
48,999970631414 0,0001208086785009860 120,8087
49,999968796392 0,0001283571030150980 128,3571
50,999966886482 0,0001362135845764460 136,2136
51,999964900185 0,0001443842843259750 144,3843
52,999962836004 0,0001528753634046300 152,8754
53,999960692441 0,0001616929829533550 161,693
54,999958467999 0,0001708433041130960 170,8433
55,999956161179 0,0001803324880247960 180,3325
56,999953770484 0,0001901666958294000 190,1667
57,999951294415 0,0002003520886678550 200,3521
58,999948731476 0,0002108948276811030 210,8948
59,999946080168 0,0002218010740100890 221,8011
60,999943338994 0,0002330769887957600 233,077
61,999940506456 0,0002447287331790580 244,7287
62,999937581056 0,0002567624683009300 256,7625
63,999934561296 0,0002691843553023190 269,1844
64,999931445679 0,0002820005553241700 282,0006
65,999928232707 0,0002952172295074290 295,2172
66,999924920881 0,0003088405389930400 308,8405
67,999921508705 0,0003228766449219470 322,8766
68,999917994681 0,0003373317084350950 337,3317
69,999914377310 0,0003522118906734290 352,2119
70,999910655095 0,0003675233527778940 367,5234
71,999906826538 0,0003832722558894350 383,2723
72,999902890142 0,0003994647611489950 399,4648
73,999898844408 0,0004161070296975210 416,107
74,999894687839 0,0004332052226759560 433,2052
75,999890418937 0,0004507655012252460 450,7655
76,999886036205 0,0004687940264863340 468,794
77,999881538144 0,0004872969596001670 487,297
78,999876923257 0,0005062804617076880 506,2805
79,999872190046 0,0005257506939498420 525,7507
D1
[km] K2 [km] K2 [mm]
1 -0,00000000023227501 -0,000232275
2 0,00000000102685682 0,001026857
3 -0,00000000627142537 -0,006271425
4 -0,00000001486560087 -0,014865601
5 -0,00000002903437670 -0,029034377
6 -0,00000005017140294 -0,050171403
7 -0,00000007967032967 -0,07967033
8 -0,00000011892480697 -0,118924807
9 -0,00000016932848493 -0,169328485
10 -0,00000023227501362 -0,232275014
11 -0,00000030915804312 -0,309158043
12 -0,00000040137122353 -0,401371224
13 -0,00000051030820491 -0,510308205
14 -0,00000063736263736 -0,637362637
15 -0,00000078392817095 -0,783928171
16 -0,00000095139845577 -0,951398456
17 -0,00000114116714190 -1,141167142
18 -0,00000135462787941 -1,354627879
19 -0,00000159317431839 -1,593174318
20 -0,00000185820010893 -1,858200109
21 -0,00000215109890110 -2,151098901
22 -0,00000247326434498 -2,473264345
23 -0,00000282609009067 -2,826090091
24 -0,00000321096978823 -3,210969788
25 -0,00000362929708775 -3,629297088
26 -0,00000408246563932 -4,082465639
27 -0,00000457186909301 -4,571869093
28 -0,00000509890109890 -5,098901099
29 -0,00000566495530708 -5,664955307
30 -0,00000627142536764 -6,271425368
31 -0,00000691970493064 -6,919704931
32 -0,00000761118764617 -7,611187646
33 -0,00000834726716432 -8,347267164
34 -0,00000912933713517 -9,129337135
35 -0,00000995879120879 -9,958791209
36 -0,00001083702303527 -10,83702304
37 -0,00001176542626470 -11,76542626
38 -0,00001274539454714 -12,74539455
39 -0,00001377832153269 -13,77832153
40 -0,00001486560087143 -14,86560087
41 -0,00001600862621344 -16,00862621
42 -0,00001720879120879 -17,20879121
43 -0,00001846748950758 -18,46748951
D1
[km] K2 [km] K2 [mm]
44 -0,00001978611475988 -19,78611476
45 -0,00002116606061577 -21,16606062
46 -0,00002260872072534 -22,60872073
47 -0,00002411548873867 -24,11548874
48 -0,00002568775830583 -25,68775831
49 -0,00002732692307692 -27,32692308
50 -0,00002903437670202 -29,0343767
51 -0,00003081151283119 -30,81151283
52 -0,00003265972511454 -32,65972511
53 -0,00003458040720213 -34,5804072
54 -0,00003657495274405 -36,57495274
55 -0,00003864475539038 -38,64475539
56 -0,00004079120879121 -40,79120879
57 -0,00004301570659661 -43,0157066
58 -0,00004531964245667 -45,31964246
59 -0,00004770441002147 -47,70441002
60 -0,00005017140294108 -50,17140294
61 -0,00005272201486560 -52,72201487
62 -0,00005535763944510 -55,35763945
63 -0,00005807967032967 -58,07967033
64 -0,00006088950116938 -60,88950117
65 -0,00006378852561433 -63,78852561
66 -0,00006677813731458 -66,77813731
67 -0,00006985972992023 -69,85972992
68 -0,00007303469708134 -73,03469708
69 -0,00007630443244802 -76,30443245
70 -0,00007967032967033 -79,67032967
71 -0,00008313378239836 -83,1337824
72 -0,00008669618428219 -86,69618428
73 -0,00009035892897190 -90,35892897
74 -0,00009412341011758 -94,12341012
75 -0,00009799102136930 -97,99102137
76 -0,00010196315637715 -101,9631564
77 -0,00010604120879121 -106,0412088
78 -0,00011022657226156 -110,2265723
79 -0,00011452064043828 -114,5206404
80 -0,00011892480697145 -118,924807
D2 [km] K3 [km] K3 [mm]
0,9999999998 -0,00000000001735 -0,00001735388
2,0000000010 -0,00000000013883 -0,00013883104
2,9999999937 -0,00000000046855 -0,00046855477
3,9999999851 -0,00000000111065 -0,00111064833
4,9999999710 -0,00000000216924 -0,00216923500
5,9999999498 -0,00000000374844 -0,00374843806
6,9999999203 -0,00000000595238 -0,00595238075
7,9999998811 -0,00000000888519 -0,00888518633
8,9999998307 -0,00000001265098 -0,01265097804
9,9999997677 -0,00000001735388 -0,01735387912
10,9999996908 -0,00000002309801 -0,02309801277
11,9999995986 -0,00000002998750 -0,02998750220
12,9999994897 -0,00000003812647 -0,03812647059
13,9999993626 -0,00000004761904 -0,04761904112
14,9999992161 -0,00000005856934 -0,05856933692
15,9999990486 -0,00000007108148 -0,07108148114
16,9999988588 -0,00000008525960 -0,08525959688
17,9999986454 -0,00000010120781 -0,10120780722
18,9999984068 -0,00000011903024 -0,11903023522
19,9999981418 -0,00000013883100 -0,13883100392
20,9999978489 -0,00000016071424 -0,16071423633
21,9999975267 -0,00000018478406 -0,18478405541
22,9999971739 -0,00000021114458 -0,21114458411
23,9999967890 -0,00000023989995 -0,23989994536
24,9999963707 -0,00000027115426 -0,27115426203
25,9999959175 -0,00000030501166 -0,30501165696
26,9999954281 -0,00000034157625 -0,34157625297
27,9999949011 -0,00000038095217 -0,38095217283
28,9999943350 -0,00000042324354 -0,42324353928
29,9999937286 -0,00000046855447 -0,46855447500
30,9999930803 -0,00000051698910 -0,51698910264
31,9999923888 -0,00000056865154 -0,56865154482
32,9999916527 -0,00000062364592 -0,62364592409
33,9999908707 -0,00000068207636 -0,68207636296
34,9999900412 -0,00000074404698 -0,74404698392
35,9999891630 -0,00000080966191 -0,80966190937
36,9999882346 -0,00000087902526 -0,87902526169
37,9999872546 -0,00000095224116 -0,95224116318
38,9999862217 -0,00000102941374 -1,02941373611
39,9999851344 -0,00000111064710 -1,11064710269
40,9999839914 -0,00000119604539 -1,19604538506
41,9999827912 -0,00000128571271 -1,28571270532
42,9999815325 -0,00000137975319 -1,37975318549
D2 [km] K3 [km] K3 [mm]
43,9999802139 -0,00000147827095 -1,47827094756
44,9999788339 -0,00000158137011 -1,58137011343
45,9999773913 -0,00000168915480 -1,68915480494
46,9999758845 -0,00000180172914 -1,80172914388
47,9999743122 -0,00000191919725 -1,91919725195
48,9999726731 -0,00000204166325 -2,04166325080
49,9999709656 -0,00000216923126 -2,16923126201
50,9999691885 -0,00000230200541 -2,30200540709
51,9999673403 -0,00000244008981 -2,44008980745
52,9999654196 -0,00000258358858 -2,58358858446
53,9999634250 -0,00000273260586 -2,73260585941
54,9999613552 -0,00000288724575 -2,88724575349
55,9999592088 -0,00000304761239 -3,04761238783
56,9999569843 -0,00000321380988 -3,21380988349
57,9999546804 -0,00000338594236 -3,38594236142
58,9999522956 -0,00000356411394 -3,56411394251
59,9999498286 -0,00000374842875 -3,74842874756
60,9999472780 -0,00000393899090 -3,93899089728
61,9999446424 -0,00000413590451 -4,13590451229
62,9999419203 -0,00000433927371 -4,33927371314
63,9999391105 -0,00000454920262 -4,54920262027
64,9999362115 -0,00000476579535 -4,76579535404
65,9999332219 -0,00000498915603 -4,98915603471
66,9999301403 -0,00000521938878 -5,21938878245
67,9999269653 -0,00000545659772 -5,45659771734
68,9999236956 -0,00000570088696 -5,70088695934
69,9999203297 -0,00000595236063 -5,95236062834
70,9999168662 -0,00000621112284 -6,21112284411
71,9999133038 -0,00000647727773 -6,47727772634
72,9999096411 -0,00000675092939 -6,75092939459
73,9999058766 -0,00000703218197 -7,03218196832
74,9999020090 -0,00000732113957 -7,32113956691
75,9998980368 -0,00000761790631 -7,61790630961
76,9998939588 -0,00000792258632 -7,92258631556
77,9998897734 -0,00000823528370 -8,23528370379
78,9998854794 -0,00000855610259 -8,55610259325
79,9998810752 -0,00000888514710 -8,88514710272
Zadanie 2. Z jaką dokładnością należy mierzyć czas, aby pomiar odcinka150 m miał błąd nie
większy niż 3 mm?
Odp. Z dokładnością .