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UNIVERSITY OF NAIROBIDEPARTMENT OF CIVIL AND CONSTRUCTION

ENGINEERINGFCE 351: ENGINEERING SURVEYING II

OUTLINE ANSWERS CAT - 6thNov!"# $%13_____________________________________________________________________

&UESTION 1

(a)The main sources of error in vertical sta tacheometry may beidentied as: -

(i) Errors in the reading of the sta.(ii) Non-verticality of the sta.

(iii) Errors in the measurement of the vertical angle.

(b)o! the scale on a cadastral "lan may be determined# if the "ortion on!hich the scale is !ritten has been torn o. $ number of o"tions areavailable: -

%se a scale and the grid-line values on the "lan to !or& out the scale. %se a scale'ruler and the given distances of "lot boundary lines to !or&

out the scale. %se the coordinates of any t!o "oints: !or& out the distance bet!een

them using a oin com"utation and the use a scale'ruler to !or& out thescale of the "lan

(c)The ray traceis not as suitable as the closed traversefor "rovision ofcontrol

losed traverse: *"ening and closing stations are &no!n. as o"eningand closing orientations. $dustment can be carried out.+ay trace traverse: Traverse !hose end "oints are &no!n but o"eningand'or closing orientations missing. The ray trace does not oer a !ay ofsu,ciently detecting errors in the observations during traversing.asic assum"tions !hen the ray trace is used: That the end-"oints are correctly identied.

End "oints have not moved since they !ere coordinated. There are no gross errors in the eld observations for the ray trace.

(d)odulating !aves and carrier !aves in E/ instruments:odulating !aves are measuring !aves in E/ instruments (fre0uencyrange 1223 - 4.135 6 2.7m to 82m) - es"ecially in "hasecom"arison techni0ues. These !aves have di,culty in transmissionthrough the atmos"here due to fading# re9ection# scatter# interferenceetc. They are su"erim"osed on carrier !aves electronically (modulation)to assist in transmission. arrier !aves have higher fre0uency than

modulating !aves.

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arrier !aves are mainly of t!o ty"es: isible and near infrared (E*/).

;hort and medium range (6 2.81 to < = # ; and ?). 6 @ =

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&UESTION $

a) The gradient bet!een and :;lo"e distance 6 L ksCos= ori3ontal distance 6 6 2ksCos

ertical distance# 6 12 2ksSin

$6

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m: A.4Bm

(b)alculate the side !idths and area of the cross-section on Jigure

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!' # #! 2% #% #! !% - 2&* # #! 1%

,raverse co-utation.

!" + !% !"/ 12 #"'.#% 2" .2$

1!1 2$ #& + 1&".%2 11%.%$1$&.&!&- (+&.&2) (&.&2)

!% + #& !%/ 12 !"1."" 2" 2.2# & 2& 1" 1&$.%" 1".$'1&.&%"- (+&.&1) (&.&1)

#& + !$ #&/ 12 #".#% 2" 21%.%2 &$ &1 "" 1!2.! 1#.!!."$- (+&.&2) (&.&2)

12 "%1.!& 2" 2!!.% &.&& &.&&

!$/ 12 "%1.!& 2" 2!!.%

0 (-) By atu-/ 1!!.1 1#%.'2By traverse/ 1!!.$ 1#%.$'Misclosure/ + &.&" &.&"

3ength o4 traverse/ #&1.$%!-Accuracy/ 15"'&& (aro6.)

&UESTION 5

(a)olumes

(i) M2/ A#2 Mtho': olume 6A

Ln

351 379 396 412 428 455 478

120 10007

x x+ + + + + +

6 .671.$,!3

8 .671.3!3

(ii) The End $reas ethod

olume 6 DA A

A An

n

1

2 1

2

++ + +;T g

.... !here 6 B2m

Vo*(! 8 .6%%%%!3

(iii) olume using the Mrismoidal Jormula

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olume !ill be determined by the Mrismoidal formula but the volumebet!een the last "air of areas !ill be determined using the end-areasmethod.

olume 6D

X E O EALastprismoid3

4 2+ + +b g !here 6 B2m

Vo*(! 8 .7.%%%%!3

(b)eights !ere ta&en for t!elve grid intersections at a building site toenable the contractor to estimate the volume of material to bee=cavated. Ff the formation level of the building is to be 448.22m#calculate the volume of material to be e=cavated# if the site is dividedu" into triangles# as sho!n on Figure 2

Figure 2

A 82.2m B 82.2m C7educed levels at grid corners

(-)B1.2m $ 6 44@.B1 E 6

44@.B4 G 6 4@B.84 J 6 4@