Post on 04-Nov-2015
description
175
8 PROBLEME REZOLVATE - DRUMUIREA PLANIMETRIC
8.1 Drumuirea planimetric sprijinit la capete pe puncte de
coordonate cunoscute i orientri
Se dau:
1.Coordonatele planimetrice ale punctelelor de sprijin:
Nr. Pct. X(m) Y(m)
A 160,380 195,498
B 222,156 134,429
C 140,580 550,804
D 112,860 667,546
2.Distanele ntre laturile de drumuire msurate cu panglica:
662.111
264.134
882.84
837.119
316.81
4
34
23
12
1
=
=
=
=
=
C
A
L
L
L
L
L
3.Unghiurile orizontale interiore
2575.283
0967.77
0238.293
0302.101
5747.286
4817.123
4
3
2
1
=
=
=
=
=
=
C
A
4.Unghiurile zenitale
176
42.100
85.99
65.100
37.99
45.99
4
34
23
12
1
=
=
=
=
=
C
A
z
z
z
z
z
Se cere s se calculeze coordonatele punctelor noi de drumuire 1, 2,
3, 4
Figura 8.1 Drumuirea planimetric sprijinit la capete pe puncte de
coordonate cunoscute
Rezolvare
1. Calculul orientrilor punctelor de sprijin
8415.114
3664.350
=
=
=
=
CD
CD
CD
AB
AB
AB
XX
YY
arctg
XX
YY
arctg
177
2. Calculul orientrilor provizorii ntre punctele de drumuire
8310.1148310.5142575.283535.231
5735.315735.4310967.774768.354
4768.1544768.5540238.2934530.261
4530.614530.4610302.1014228.360
4228.1604228.5605747.2868481.273
8481.738481.4734817.1233664.350
`
4
`
4
`
43
`
4
3
`
32
`
34
2
`
21
`
23
1
`
1
`
12
`
1
==+=+=
==+=+=
==+=+=
==+=+=
==+=+=
==+=+=
ccCD
C
A
AABA
3. Calculul erorii orientrii de drumuire
cc
cc
cc
cc
CDCD
n
c
k
ec
e
0017.0
6
105
105
1058415.1148310.114
`
===
==
===
Unde n este numrul de staii de drumuire
4. Calculul orientrilor definitive ale punctelor de drumuire
8415.1140105.08310.1146
5820.310085.05735.315
4836.1540068.04768.1544
4581.610051.04530.613
4262.1600034.04228.1602
8498.730017.08481.73
`
`
44
`
3434
`
2323
1
1212
`
!1
=+=+=
=+=+=
=+=+=
=+=+=
=+=+=
=+=+=
k
k
k
k
k
k
CDCD
CC
AA
5. Calculul distanelor reduse la orizont
178
mzLD
mzLD
mzLD
mzLD
mzLD
CC
AA
659.11142.100sin662.111sin
263.13485.99sin264.134sin
877.8465.100sin882.84sin
831.11937.99sin837.119sin
313.8145.99sin316.81sin
44
3434
2323
1212
11
===
===
===
===
===
6. Calculul coordonatelor relative provizorii
mDX
mDX
mDX
mDX
mDX
CCC
AAA
198.98cos
384.101cos
304.48cos
415.97cos
469.32cos
44
`
4
3434
`
34
2323
`
23
1212
`
12
11
`
1
==
==
==
==
==
mDY
mDY
mDY
mDY
mDY
CCC
AAA
148.53sin
022.88sin
791.69sin
784.69sin
549.74sin
44
`
4
3434
`
34
2323
`
23
1212
`
12
11
`
1
==
==
==
==
==
7. Calculul erorii i coreciei coordonatelor relative
00005263.0
943.531
028.0
028.0
028.0)800.19(828.19)(
==
=
==
===
D
c
k
mec
mXXXe
x
x
xx
ACx
179
000022558.0
943.531
012.0
012.0
012.0306.355294.355)(
==
=
==
===
D
c
k
mec
mYYYe
y
y
yy
ACy
8. Calculul coordonatelor relative compensate
mDkXX
mDkXX
mDkXX
mDkXX
mDkXX
CxCC
x
x
x
AxAA
204.98006.0198.98
376.101008.0384.101
308.48004.0304.48
409.97006.0415.97
473.32004.0469.32
4
`
44
34
`
3434
23
`
2323
12
`
1212
1
`
11
=+=+=
=+=+=
=+=+=
=+=+=
=+=+=
mDkYY
mDkYY
mDkYY
mDkYY
mDkYY
CyCC
y
y
y
AyAA
150.53002.0148.53
025.88003.0022.88
793.69002.0791.69
787.69003.0784.69
551.74002.0549.74
4
`
44
34
`
3434
23
`
2323
12
`
1212
1
`
!1
=+=+=
=+=+=
=+=+=
=+=+=
=+=+=
Verificare
AC
AC
YYY
XXX
=
=
9. Calculul coordonatelor absolute ale punctelor de drumuire
180
mXXX
mXXX
mXXX
mXXX
mXXX
CC
AA
580.140204.98376.42
376.42376.101752.143
752.143308.48444.95
444.95409.97853.192
853.192473.32380.160
44
3434
2323
1212
11
=+=+=
==+=
=+=+=
==+=
=+=+=
mYYY
mYYY
mYYY
mYYY
mYYY
CC
AA
804.550150.53654.497
654.497025.88629.409
629.409793.69836.339
836.339787.69049.270
049.270551.74498.195
44
3434
2323
1212
11
=+=+=
=+=+=
=+=+=
=+=+=
=+=+=
8.2 Drumuirea planimetric n circuit nchis
Se dau coordonatele punctelor de sprijin A, B, distanele reduse la
orizont ale laturilor de drumuire i direciile unghiulare orizontale
msurate pe teren
181
Figura 8.2 Drumuirea planimetric n circuit nchis
Nr. Pct. X(m) Y(m)
A 1010 2012
B 1090 1835
PS PV Direcii
unghiulare
orizontale
Distane reduse
la orizont (m)
B 125.4318 A
1 200.6548 85.058
A 399.9950 1
2 223.4300 104.390
1 225.0350 2
3 157.4550 111.310
2 350.4950 3
4 172.3550 90.443
4 3 370.7500
182
5 286.9050 82.153
4 90.1050 5
B 291.7800 58.034
5 295.6050 A
B 124.8520
Se cere s se calculeze coordonatele punctelor noi de drumuire 1, 2,
3, 4, 5
Rezolvare
1.Calculul unghiurilor orizontale exterioare msurate n punctele de
staie
2230.754318.1256548.200
`
==
A
4350.2239950.3994300.6239950.3994300.223
1
===
4200.3320350.2254550.5570350.2254550.157
2
===
8600.2214950.3503550.5724950.3503550.172
3
===
1550.3167500.3709050.6867500.3709050.286
4
===
6750.2011050.907800.291
5
==
2470.2296050.2958250.5246050.2958520.124
``
===
A
2.Calculul orientrii laturii de sprijin AB
0243.3279757.72400
9757.722125.2
80
177
==
+
=
+
=
+
=
AB
AB
arctgarctg
3.Transmiterea orientrilor
2473.22473.4022230.750243.327
1
==+=+=
AABA
6823.256823.4254350.2232473.202
1112
==+=+=
A
183
1023.1581023.5584200.3326823.225
22123
==+=+=
9623.1799623.5798600.2211023.358
33234
==+=+=
1173.2961173.6961550.3169623.379
44345
==+=+=
7923.2976750.2011173.96
5545
=+=+=
A
0393.3272470.2297923.97
5
=+=+=
AAAB
4. Calculul erorii i coreciilor
cc
cc
cc
k
c
21
7
150
150
=
=
=
5.Calculul orientrilor compensate
2453.2212473.2
1
==
cc
A
6781.25426823.25
12
==
cc
0960.158631023.158
23
==
cc
9539.179849623.179
34
==
cc
1068.2961051173.296
45
==
cc
7787.2971367923.297
5
==
cc
A
0243.3271500393.327 ==
cc
AB
6.Calculul coordonatelor relative provizorii
mX
A
005.852453.2cos058.85
1
==
mX 013.916781.25cos390.104
12
==
mX 055.880960.158cos310.111
23
==
mX 996.859539.179cos443.90
34
==
mX 021.51068.296cos153.82
45
==
cc
ABAB
e 1500150.00243.3270393.327 ====
184
mX
A
024.27787.297cos034.58
5
==
mY
A
999.22453.2sin058.85
1
==
mY 973.406781.25sin390.104
12
==
mY 090.680960.158sin310.111
23
==
mY 011.289539.179sin443.90
34
==
mY 999.811068.296sin153.82
45
==
mY
A
999.577787.297sin034.58
5
==
7.Calculul erorii i coreciilor coordonatelor
=
mX 078.0
0001411398.0
388.531
075.0
075.0
075.0
=
=
=
=
y
y
y
k
mc
me
8.Calculul coordonatelor relative compensate
mX
A
017.85012.0005.85
1
=+=
mX 028.96015.0013.96
12
=+=
mX 039.88016.0055.88
23
=+=
00014678.0
388.531
078.0
388.531
078.0
078.0
==
=
=
=
x
x
x
k
mD
mc
me
=
mY 075.0
185
mX 982.85014.0996.85
34
=+=
mX 009.5012.0021.5
45
=+=
mX
A
015.2009.0024.2
5
=+=
Verificare 0=
X
mY
A
987.2012.0999.2
1
==
mY 958.40015.0973.40
12
==
mY 998.27013.0011.28
34
==
mY 011.82012.0999.81
45
==
mY
A
007.58008.0999.57
5
==
Verificare 0=
Y
9.Calculul coordonatelor absolute
X
1
= X
A
+
X
A1
= 1010 + 85.017 = 1095.017m
X
2
= X
1
+ X
12
= 1095.017 + 96.028 = 1191.045m
X
3
= X
2
+ X
23
= 1191.045 88.055 = 1103.006m
X
4
= X
3
+ X
34
= 1103.006 85.982 = 1017.024m
X
5
= X
4
+ X
45
= 1017.024 5.009 = 1012.015m
Verificare X
A
= X
5
+ X
5A
= 1012.015 - 2.015 = 1010m
Y
1
= Y
A
+ Y
A1
= 2012 + 2.987 = 2014.987m
Y
2
= Y
1
+ Y
12
= 2014.987 + 40.958 = 2055.945m
Y
3
= Y
2
+ Y
23
= 2055.945 + 68.075 = 2124.020m
Y
4
= Y
3
+ Y
34
= 2124.020 + 27.998 = 2152.018m
Y
5
= Y
4
+ Y
45
= 2152.018 - 82.011 = 2070.007m
Verificare Y
A
= Y
5
+ Y
5A
= 2070.007 58.007 = 2012m
mY 075.68015.0090.68
23
==
186
8.3 Drumuirea planimetric cu punct nodal
Se dau punctelor vechi de sprijin, unghiurile orizontale i distanele
reduse la orizont msurate ntr-o drumuire cu punct nodal.
Figura 8.3 Drumuire planimetric cu punct nodal
Nr.pct. X (m) Y (m)
A 6020.454 7734.262
B 4389.447 7498.874
C 6388.565 8390.504
D 8324.414 7824.731
E 6258.181 7704.289
F 7604.883 6272.923