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Surveying Omitted Measurement

1) The document discusses different cases of omitted measurements in surveying, including when the length and bearing of one side are unknown or when the lengths or bearings of two adjoining sides are unknown. 2) It provides an example where the length of one side (DE) and the bearing of an adjoining side (EA) are unknown, and calculates the total length of the closing line to determine these values. 3) By calculating latitudes, departures, and the closing error, the unknown length and bearing are able to be solved for.

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79 views10 pages

Surveying Omitted Measurement

1) The document discusses different cases of omitted measurements in surveying, including when the length and bearing of one side are unknown or when the lengths or bearings of two adjoining sides are unknown. 2) It provides an example where the length of one side (DE) and the bearing of an adjoining side (EA) are unknown, and calculates the total length of the closing line to determine these values. 3) By calculating latitudes, departures, and the closing error, the unknown length and bearing are able to be solved for.

Uploaded by

p8jpcffmyz
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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OMITTED

MEASUREMENTS

COMMON TYPES OF OMITTED MEASUREMENTS:

1. Omitted Measurements Are in One Side


Case: Length and Bearing of One Side Unknown
2. Omitted Measurements Involving Two Adjoining Sides
1st Case: Length of One Side and Bearing of Another Side Unknown
2nd Case: Lengths of Two Sides Unknown
3rd Case: Bearings of Two Sides Unknown
3. Omitted Measurements Involving Two Non-Adjoining Sides
1st Case: Length of One Side and Bearing of Another Side Unknown
2nd Case: Lengths of Two Sides Unknown
3rd Case: Bearings of Two Sides Unknown

1
OMITTED
MEASUREMENTS
ARE IN ONE SIDE
LENGTH AND BEARING OF ONE SIDE
U N K N OW N

Omitted Measurements Are in One Side


Length and Bearing of One Side Unknown

C LINE LENGTH BEARING


(m)
D AB 733.75 N 76°18’ E
F BC 598.23 N 23° 20’ W
CD 415.05 S 61° 35’ W
DE 511.38 N 57° 00’ W
B EF 395.06 S 32° 45’ W
FA Unknown Unknown
Unknown Length
and Bearing
A

2
Omitted Measurements Are in One Side
Length and Bearing of One Side Unknown
LINE LENGTH BEARING LATITUDES DEPARTURES
(m) +N -S +E -W
AB 733.75 N 76° 18’ E 173.78 712.87
BC 598.23 N 23° 20’ W 549.30 236.95
CD 415.05 S 61° 35’ W 197.51 365.04
DE 511.38 N 57° 00’ W 278.52 428.88
EF 395.06 S 32° 45’ W 332.26 213.72
FA Unknown Unknown
+1001.60 -529.77 +712.87 -1244.59
+,! +(+./0.23) 5./0.23
𝑪𝑳 = # 𝑁𝐿 + # 𝑆𝐿 𝑪𝑫 = # 𝐸𝐷 + # 𝑊𝐷 tan 𝛂𝐹𝐴 = = =
+," +(5620.7/) +620.7/
CL = +1001.60m + (-529.77m) CD = +712.87m + (-1244.59m) 𝛂𝐹𝐴 = 48° 25’
CL = +471.83 m CD = -531.72 m
LFA= (𝐶𝐿)!+(𝐶𝐷)! = (+471.83)!+(−531.72)! BearingFA = S 48° 25’ E
LFA= 𝟕𝟏𝟎. 𝟖𝟖 𝐦

3
OMITTED
MEASUREMENTS
I N V O LV I N G T W O
ADJOINING SIDES
1 ST C A S E :
LENGTH OF ONE SIDE AND BEARING
O F A N OT H E R S I D E U N K N OW N

Given the following sketch and tabulated data for a closed traverse in which the
length of DE and the bearing of EA have not been observed in the field. Determine
Omitted Measurements Involving Two Adjoining Sides

these unknown quantities.

A
LINE LENGTH BEARING
Length of One Side and Bearing of Another Side Unknown

Unknown Bearing B
(m)
E
AB 1084.32 S 75°48’ E
BC 1590.51 S 15° 18’ W
2
e
ng Lin

1 CD 1294.74 S 68° 06’ W


DE Unknown N 28° 39’ W
Closi

EA 1738.96 Unknown

Unknown Length
C

4
Solution:
Determining Length and Bearing of the Closing Line

LATITUDES DEPARTURES
Omitted Measurements Involving Two Adjoining Sides

LINE LENGTH (m) BEARING


+N -S +E -W
AB 1084.32 S 75°48’ E 265.99 1051.19
BC 1590.51 S 15° 18’ W 1534.14 419.69
Length of One Side and Bearing of Another Side Unknown

CD 1294.74 S 68° 06’ W 482.92 1201.31


DE Unknown N 28° 39’ W - - - -
EA 1738.96 Unknown - - - -
+0.00 -2283.05 +1051.19 -1621.00

𝑪𝑳 = # 𝑁𝐿 + # 𝑆𝐿 𝑪𝑫 = # 𝐸𝐷 + # 𝑊𝐷

CL = +0.00m + (-2283.05m) CD = +1051.19m + (-1621.00m)


+,! +(+.89.70) 5.89.70
CL = -2283.05 m CD = -569.81m tan 𝛂𝐷𝐴 = = =
+," +(+337/.:.) 5337/.:.
LDA= (𝐶𝐿)!+(𝐶𝐷)! = (−2283.05)!+(−569.81)!
𝛂𝐷𝐴 = 14° 01’
LDA= 𝟐𝟑𝟓𝟑. 𝟎𝟖 𝐦
BearingDA = N 14° 01’ E

Solution:
Determining Bearing of Line EA and Length of Line DE

A
Omitted Measurements Involving Two Adjoining Sides

By Sine Law: ϴ= 180° - ∢E - 28°39’


6
1738.9 𝐷𝐴 𝐸𝐴
ϴ= ? = ϴ= 180° - 66°30’ - 28°39’
E 14°01’ 𝑆𝑖𝑛 𝐸 𝑆𝑖𝑛 𝐷
%& '() % ϴ= 84°51’
Sin E=
Length of One Side and Bearing of Another Side Unknown

*&
28°39’ 2 !+,+../ 012 3!°3.’
Sin E= Bearing EA= N 84°51’ E
. 08

67+/.89
2353

∢E = 66°30’

By Sine Law:
𝐷𝐸 𝐸𝐴 ∢A = 180° - ∢E - ∢D
=
14°01’ 𝑆𝑖𝑛 𝐴 𝑆𝑖𝑛 𝐷 ∢A = 180° - 66°30’ - 42°40’
28°39’
𝐸𝐴 sin 𝐴 ∢A = 70°50’
𝐷𝐸 =
D sin 𝐷
1738.96 sin 70°50′
∢D = 28°39’+14°01’ = 42°40’ 𝐷𝐸 = DE = 2423.62m
sin 42°40′

5
OMITTED
MEASUREMENTS
I N V O LV I N G T W O
ADJOINING SIDES
2ND C ASE:
L E N G T H S O F T W O S I D E S U N K N OW N

Given the following sketch and tabulated data for a closed traverse in which the
lengths of BC and CD have not been measured in the field. Determine these
unknown quantities.
Omitted Measurements Involving Two Adjoining Sides

C
Unknown Length LINE LENGTH BEARING
Unknown Length
2 (m)
B AB 639.32 N 09°30’ W
Closing Line
D
BC Unknown N 56° 55’ W
CD Unknown S 56° 13’ W
DE 570.53 S 02° 02’ E
1
Lengths of Two Sides Unknown

EA 1082.71 S 89° 31’ E

E A

6
Solution:
Determining Length and Bearing of the Closing Line

LATITUDES DEPARTURES
Omitted Measurements Involving Two Adjoining Sides

LINE LENGTH (m) BEARING


+N -S +E -W
AB 639.32 N 09°30’ W 630.55 105.52
BC Unknown N 56° 55’ W - - - -
CD Unknown S 56° 13’ W - - - -
DE 570.53 S 02° 02’ E 570.17 20.24
EA 1082.71 S 89° 31’ E 9.13 1082.67
+630.55 -579.30 +1102.91 -105.52
Lengths of Two Sides Unknown

𝑪𝑳 = # 𝑁𝐿 + # 𝑆𝐿 𝑪𝑫 = # 𝐸𝐷 + # 𝑊𝐷

CL = +630.55m + (-579.30m) CD = +1102.91m + (-105.52m)


+,! +(5992./9) +992./9
CL = +51.25 m CD = +997.39m tan 𝛂𝐵𝐷 = = =
+," +(5.0.3.) +.0.3.
LBD= (𝐶𝐿)!+(𝐶𝐷)! = (+51.25)!+(+997.39)!
𝛂𝐵𝐷 = 87° 04’
LBD= 𝟗𝟗𝟖. 𝟕𝟏 𝐦
BearingBD = S 87° 04’ W

Solution:
Determining Length of Lines BC and CD

C
Omitted Measurements Involving Two Adjoining Sides

By Sine Law:
56°13’ 56°55’
𝐵𝐶 𝐶𝐷 𝐵𝐷
= =
87° 04’ 56°55’ 𝑆𝑖𝑛 𝐷 𝑆𝑖𝑛 𝐵 𝑆𝑖𝑛 𝐶
2
56°13’ B 𝐵𝐶 𝐶𝐷 𝐵𝐷
998.71
87° 04’ = =
D 𝑆𝑖𝑛 30°51’ 𝑆𝑖𝑛 36°01’ 𝑆𝑖𝑛 113°08’

##$.&' ()* +,°.'’


∢B = 180° - 87°04’ - 56°55’ = 36°01’ BC =
∢C = 56°13’ + 56°55’ = 113°08’ ()* ''+°,$’
∢D = 87°04’ - 56°13’ = 30°51’
SUM= 180°00’ (checks) BC = 556.91m
Lengths of Two Sides Unknown

##$.&' ()* +0°,'’


CD =
()* ''+°,$’

CD = 638.61 m

7
OMITTED
MEASUREMENTS
I N V O LV I N G T W O
ADJOINING SIDES
3 RD C A S E :
B E A R I N G S O F T W O S I D E S U N K N OW N

Given the following sketch and tabulated data for a closed traverse in which the
bearings of DE and EA have not been measured in the field. Determine these
unknown directions.
Omitted Measurements Involving Two Adjoining Sides

A
Unknown Bearing LINE LENGTH BEARING
B
(m)
E
AB 1081.35 S 73°47’ E
BC 1589.50 S 15° 14’ W
2
e
ng Lin

1 CD 1293.72 S 67° 07’ W


DE 2506.94 Unknown
Closi
Bearings of Two Sides Unknown

EA 1737.98 Unknown

Unknown Bearing
C

8
Solution:
Determining Length and Bearing of the Closing Line

LATITUDES DEPARTURES
Omitted Measurements Involving Two Adjoining Sides

LINE LENGTH (m) BEARING


+N -S +E -W
AB 1081.35 S 73°47’ E 301.99 1038.33
BC 1589.50 S 15° 14’ W 1533.65 417.64
CD 1293.72 S 67° 07’ W 503.07 1191.90
DE 2506.94 Unknown - - - -
EA 1737.98 Unknown - - - -
+0.00 -2338.71 +1038.33 -1609.54
Bearings of Two Sides Unknown

𝑪𝑳 = # 𝑁𝐿 + # 𝑆𝐿 𝑪𝑫 = # 𝐸𝐷 + # 𝑊𝐷

CL = +0.00m + (-2338.71m) CD = +1038.33m + (-1609.54m)


+,! +(+.20.30) 5.20.30
CL = -2338.71 m CD = -571.21m tan 𝛂𝐷𝐴 = = =
+," +(+3//7.20) 53//7.20
LDA= (𝐶𝐿)!+(𝐶𝐷)! = (−2338.71)!+(−571.21)!
𝛂𝐷𝐴 = 13° 44’
LDA= 𝟐𝟒𝟎𝟕. 𝟒𝟔 𝐦
BearingDA = N 13° 44’ E

Solution:
Determining Bearings of Lines DE and EA
By Cosine Law:
A 𝑎! + 𝑏 ! − 𝑐 !
c2 = a2 + b2 – 2abCosC
Omitted Measurements Involving Two Adjoining Sides

𝐶𝑜𝑠 𝐶 =
2𝑎𝑏
.98 𝐸𝐴! + 𝐷𝐸 ! − 𝐷𝐴!
β 1737 𝐶𝑜𝑠 𝐸 =
13°44’ 2(𝐸𝐴)(𝐷𝐸)
E
(1737.98)!+(2506.94)!−(2407.46)!
𝐶𝑜𝑠 𝐸 =
2(1737.98)(2506.94)
ϴ
2
∢E = 66°15’
. 46
2407
25
06

By Sine Law: ϴ = ∢D - 13°44’ = 41°22’ - 13°44’


.94

𝐸𝐴 𝐷𝐸 𝐷𝐴
= = ϴ = 27°38’
𝑆𝑖𝑛 𝐷 𝑆𝑖𝑛 𝐴 𝑆𝑖𝑛 𝐸
Bearings of Two Sides Unknown

1737.98 2506.94 2407.46 Bearing DE= N 27°38’ W


13°44’ = =
ϴ 𝑆𝑖𝑛 𝐷 𝑆𝑖𝑛 𝐴 𝑆𝑖𝑛 66°15’

D β = 180° - ∢E - ϴ = 180° - 66°15’- 27°38’


∢D = 41°22’
Solution check: β = 86°07’
∢A+ ∢D+ ∢E = 180° ∢A = 72°23’
72°23’+ 41°22’+ 66°15’ = 180° Bearing EA= N 86°07’ E
180° = 180° ✓

9
OMITTED
MEASUREMENTS
I N V O LV I N G T W O N O N -
ADJOINING SIDES
1 ST C A S E : L E N G T H O F O N E S I D E A N D B E A R I N G
O F A N OT H E R S I D E U N K N O W N
ND
2 C A S E : L E N G T H S O F T WO S I D E S U N K N OW N
3 RD C A S E : B E A R I N G S O F T W O S I D E S U N K N OW N

A A
1 1
5 5
B B
C
E E
3

B D
2

4 4
2

D D C

10

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