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