測(cè)量學(xué)課后習(xí)題及答案

測(cè)量學(xué)課后習(xí)題及答案(Measurementofhomeworkproblemsand

answers)

Problemsets1

Whatisgeoidlevel?Whatareitsfeaturesandfunctions?

2.Whatarethebesttermsforelevation,relativeelevation

andheight?

3.Whatisthedifferencebetweentheplanerectangular

coordinatesystemandtheplanerectangularcoordinatesystem

inmathematics?

4.Whatisagaussianprojection?Howisthegaussplane

rectangularcoordinatesystemestablished?

5.Knowntosomepointinthegaussprojectionwith6°no.

20,ifthatpointintheprojectionwithgaussplanerectangular

coordinatesystemoftheabscissa=306579.210m,writethis

pointdoesnotcontainnegativenumberandcontaintheabscissa

andcentralmeridianlongitudeofthebelt.

6.Whatisthestraightline?Whatarethestandarddirections?

WhatistheazimuthAngle?

Theanswer:

1.Throughalevel,theaverageseasurfacecalledgeoid,its

characteristicislevelanypointonthesurfaceofplumbline

perpendiculartothesurfaceofthepoint,isasurfacegravity,

itseffectismeasurementdatum.

2.Theverticaldistancefromgroundpointtoearthlevelis

calledabsoluteelevationofthispoint.Theverticaldistance

fromthegroundpointtotheassumedleveliscalledthe

relativeelevationofthepoint.Thedifferencebetweenthetwo

pointsiscalledtheheightdifference.

3.ThemeasurementcoordinatesystemXaxisisthenorth-south

direction,towardthenorth,theXaxisdirectionY,Yaxis

towardtheeast,theotherfourquadrantofmeasuring

coordinatesystemaccordingtoclockwisechoreography,thisis

justthereverseofmathematicscoordinatesystem.

4,supposedtoahorizontalellipticalcylinderissetoutside

theellipsoid,makethehorizontalellipticcylinderaxis

throughthecenterofellipsoid,andcentralmeridianandthe

ellipsoidaprojectionwiththetangent,nearthecentral

meridian(thatis,thingsedgemeridianrange)onthesurface

oftheellipsoidpointprojectiononahorizontalelliptical

cylinder,thenfollowtheellipticcylindricalpolarbuswill

unfoldastheplane,theplaneiscalledgaussprojectionplane.

Sothisprojectionisaconformalprojection.Onthegaussian

projectionplane,thecentralmeridianprojectionistheX-axis,

theequatorialprojectionistheY-axis,andtheintersection

pointofthetwoaxesistheoriginofcoordinates,whichforms

theindependentgaussianplanerectangularcoordinatesystem

ofthedivision.

5.Y=20x(306579.210m+500000m)=20193420.790.

6.Determinetherelationshipbetweenthelineandthestandard

direction(describedbytheazimuth)asastraightline

orientation.Thestandarddirectionhasatruemeridian

direction,amagneticmeridiandirection,andacoordinateaxis

(Xaxis)direction.Thedirectionoftheverticalaxisofthe

coordinateaxis(Xaxis),clockwisetotheAngleoftheline,

iscalledtheazimuthAngleofthe1ine

Problemset2

2.Whatistheleveltubeaxis?Whatisthecircularlevelaxis?

Whatisalevelingvalue?

3.Whatisvisualaxis?Whatistherelationshipbetweenthe

collimationaxisandthelineofsight?

4.Whatisparallax?Whatisthecauseofparallax?Howshould

parallaxbeeliminated?

5.Whyisthefrontandrearvisibilityequalinleveling?

6.Whatistheroleofsettingtherotationpointinleveling

measurement?WhyshouldIputafootpadwhenIturnapoint?

Whycan，tyouputafootcushion?

WhatarethemainaxesoftheS3type?Whatgeometricconditions

shouldtheymeet?Whyisthat?Whichisthemaincondition?

8.Howtorecordandcalculatethecheckandverificationof

theresultsoftheschoolandtheforeignindustry?

10.Intable2-5,theresultsoftheattachedlevelmeasurement

arearranged,andthenumberofhighdifferencecorrectionis

calculatedandtheheightdifferenceandelevationare

corrected.

Table2-5tableofmeasurementresultsoftheattachedlevel

line

LinelengthL(km)observationofhighdifferencehi(m)high

difference(m)

Correctedhighdifference(m)

ElevationH(m)remarks

BM.A1.5+4.3627.967isknown

1

0.6+2.413

2

0.8to3.121

3

1.0+1.263

4

1.2+2.716

5

1.6to3.715

BM.B11.819isknown

￡

Fh=sigmahmeasurement-(hb-ha)=fhcapacity=plusorminus

40=

Sigma=answer:

1.HAB=+0.344m,hB=13.002m

2.Thetangentofthezeropointoftheleveltubeisknownas

theleveltubeaxis.Thenormal1ineofthezeropointofthe

circleiscalledthecircularlevelaxis.Levelpipearcbetween

twoadjacentpointsmarking(2mm)ofthecentralAngle,

referredtoasastandardpipescaleunit.

3.TheconnectionCC,throughtheintersectionofobjectiveand

crosswires,iscalledtelescopicvisualaxis,andthe

extensionoftheaxisisthelineofsight,whichisthebasis

ofthetarget.

4.Duetoimperfectionofobjectivelensfocus,therelative

movementphenomenonoftargetrealimageandtheincomplete

overlapofthecross-wireplaneiscalledparallax.Thereason

isthatobjectiveimageisnotperfect,sothatthetargetimage

isnotcompletelyimaginginthecrossplane.Asmallamount

ofmovementintheeyeoftheeyepieceobserver,suchasthe

relativemovementofthetarget,indicatesthatthereisa

parallax;Carefullyfocusontheobjectivelensuntiltheimage

isstableandclear.

5.Inordertoeliminatetheerrorofparallelandhorizontal

axisofthecollimationaxis,theeffectoftheearthcurvature

andatmosphericrefractionontheheightdifferenceis

eliminatedorreduced

6.Itisconvenienttopasstheelevation,soastocorrectly

passtheelevation,maketheverticalpointstableandaccurate,

andthelevelingpoint(knownelevationpoint)cannotbeplaced

ontherulerpad.

7.Theaxisoftheleveloftheleveloftheinstrumentismainly:

thecollimationaxis,thehorizontalaxis,thecircularlevel

axis,theinstrumentverticalaxis.Geometryoflevelaxis

shouldsatisfyareasfollows:1)roundlevelshouldbeparallel

totheaxisinstrumentverticalaxis(〃);2)thewireshould

beperpendiculartotheverticalaxisoftheinstrument(i.e.

3)levelpipeshallbeparalleltotheaxiscollimationaxis

(//).

8.Stationrecordsiscalculated:-=,fieldresultschecking:

aclosed,alongwithlevelline,oralevelline,calculation

ofclosure,whenmeetspecifiedelevationdifferenceclosure

permissiblevalue(thatis),thoughtfieldobservationresults

qualified,shouldfindoutthereasonforreworkheavier,until

meettherequirements.

10.

LinelengthL(km)observationofhighdifferencehi(m)high

difference(m)

Correctedhighdifference(m)

ElevationH(m)remarks

BM.A1.5+4.362-0.015+4.3477.967isknown

1,12.314

0.62.413+0.6+2.407

2,14.721

0.8-3.121-3.121-3.121

311.592

1.01.263+1.0+1.253

412.845

1.22.716+1.2+2.704

515.549

1.6-3.715-3.715-3.715

BM.B11.819isknown

S6.7

Fh=sigmahmeasurement-(hb-ha)=+66mmfhcapacity=plus

orminus40=plusorminus104mm

-9.

85mm/km=S-66-mm

Problemset3

Settlethetheodolite

(1)putthefootframeontheteststation,sothatthehead

ofthefootisroughlyhorizontal,andtheheadcenterofthe

footisroughlyalignedtothestationcenter;Fixedthe

instrumentontherackandmovedthelegsofthefeettomake

thegroundstationmarkcenterroughlycoincidewiththecenter

ofthecenter.

(2)throughliftingthebrackettomakethecirclelevelbubble

center,loosentheinstrumentconnectionscrew,movethe

instrument,makethegroundstationmarkcenterandthecenter

preciseoverlap,tightentheconnectionscrew.

(3)withtheinstrumentfoothelixpreciselevelinginstrument:

first,thelongleveltubeandthetwolegsspiralparallel,

andadjustthetwofeettomakethebubblecenter;Tomakethe

longhorizontalpipeperpendiculartothelineofthetwofoot

screws,adjustthethirdleghelixandcenterthebubble.

Theabovepairsmayberepeatedoverandoveragainuntilthe

precisioniscorrect,andtherotatingdirectionisinall

directions,withalonghorizontalpipebubblecentered.There

isno(1)and(2)stepinforcingtheinstrumenttobeplaced

ontheobservationpier.

Settingthelevelofthewaterlevel

Levelintheplacedoesnotneedto,otherskillsandbasicsteps

andtheodoliteweresimilar,butthelevelintheprocessof

coarse-afterfineflatwiththeodoliteisdifferent:level

ofpureflatisinlinewiththelevelinsidetheinstrument,

fineprocessofflattolookthroughtheeyepiece;The

theodoliteisrefinedbytwolevelingtubes.Ofcourse,ifuse

theautomaticanpinglevelisnotrequired,theinstrument's

owncompensationdeviceitselfcanberefined,onlyneedthe

roundleveldevicebubblecentered

1.WhatisthehorizontalAngle?WhatistheverticalAngle?

Whatistherangeofvalues?

WhatarethecomponentsoftheDJ6opticaltheodolite?

3.Whatarethetwocontentsofthetheodolite?How?The

purpose?

4.Testtheoperationprocedure,recordingcalculationandthe

limitationofthemeasurement?

5.Howtoconfiguretheinitialorientationofthetheodolite

tobe0?00?00?Right?

6.WhenmeasuringtheverticalAngle,whyshouldthevertical

platelevelpipebubblebecenteredbeforethereadingofthe

verticalscalebeforereading?

7.WhenmeasuringthehorizontalAngle,whyshouldweusethe

rightandleftofthedisktoobserve?

8.Whatareverticaldiskindicators?Howtoeliminatevertical

diskindexdifference?

Whatarethemainaxesoftheodolite?Whatconditionsshould

theymeet?

10.Usingthetheodolitetoaimattwopointsatdifferent

heightsinthesameverticalplane,willthereadingsonthe

horizontaldiskbethesame?Isthedifferencebetweenthetwo

readingsontheverticaldialtheverticalAngle?Whyisthat?

14.Whatarethemethodsofmeasuringdistance?Whatisthe

principleofrangingfromtheelectro-opticalrangefinder?

16.Whatistotalstation?Whatpartsdoesithave?Whatare

thegeneralmeasurementfunctions?

Theanswer:

1.TheAngleoftheverticalprojectionofleadvertical

projectionontothehorizontalsurfaceofacertainpointon

thegroundisknownasthehorizontalAngle.Thevalueof0°

~360°.Inthesameleadface,theAnglebetweenonedirection

andthehorizontallineofsightiscalledtheverticalAngle.

TheverticalAnglevalueis00~+90°.

2.DJ6opticaltheodoliteconsistsofthreeparts:thebase,

thecameraandthedial.

3.Thetheodoliteinstallationinvolvesneutralizingand

leveling.Thepurposeofthisistomakethecenterofthe

instrumentatthesameverticallineasthesite(signcenter).

Thewholeflatpurposeistomaketheverticalaxisofthe

instrument,sothatthehorizontaldiskisinthehorizontal

position.Themediumcanbeoperatedwithaverticaloroptical

alignment.Usingthebasepinspiral,thelevellinglinewill

behorizontaltothedirectionofthespirallineofanytwo

legs,andbothofthetwofeetwillberotatedwithbothhands,

whichwillcenterthelevellingpipebubble.Andthenyourotate

itby90,right?Turnthethirdfootscrewtocenterthelevel

pipebubble.Repeattheprocedureuntiltheinstrumentisin

anyposition,andthegasbubbleisalwayscentered.

4.ThemeasurementmethodisthebasicmethodoftheAngle

measurement,whichisusedtoobservethehorizontalAngle

betweenthetwotargetdirections.Thespecificstepsareas

follows:

(1)theplacementinstrumentislocatedatthestationpoint,

andthetargetmark(suchastheverticaldrillorflowerrod)

issetinthemiddleandthelevellingattwopoints.

(2)theverticalplateisintheleftpositionofthetelescope

dish,aimleftfirst,andthehorizontalcirclereadingfor

recordtorecordthecorrespondingcolumn,thenloosenthe

sightinglevelbrakescrew,clockwisesightingaimright,

horizontalcircleforreadings,recordtorecordthe

correspondingcolumn.

Theaboveisreferredtoastheupperhalf,andtheleftcorner

valueofthediskis:

(3)invertthetelescopesothattheverticaldiskislocated

intherightpositionofthetelescopedisk,aimingattheright

targetfirst,andthehorizontaldiskreadingisrecordedin

thecorrespondingcolumnoftherecordsheet;Thenloosenthe

horizontalbrakespiral,rotatethenormal,andaimattheleft

target,andthehorizontaldiskreadingisrecordedinthe

correspondingcolumnoftherecordsheet.Theaboveiscalled

thebottomhalf,andtherightcornervalueis:.Theupperhalf

andthebottomaremeasuredback.

(4)if-?40orless?ThemeanvalueoftheAngleoftheupper

andlowerhalfoftheobservationisconsideredastheAngle

ofthemeasurement

WhentheprecisionoftheAngleofmeasurementishigh,itcan

beobservedwiththemeanoftheaverageAngle.Inorderto

reducetheinhomogeneityerrorofthedial,weshouldusethe

instrumenthorizontaldisktochangethehandwheel

configurationdial.Eachobservationaccordingtothe180°

/n(back)fortestAnglechangebetweenhorizontalcircle

position.TheAngleofeachmeasurementshallbecontrolledin

plusorminus24.

5.Usethetheodolitetotransformthehandwheel,openthe

protectivecover,andturnthehandwheel.Thehorizontaldisk

willrotatewithit.Togotozero?00?00?Whenposition,loosen

thehand,closethedialchangehandwheelprotectioncover,the

horizontaldialis0?00?00.

6.Inordertoputtheverticalindicatorinthecorrect

position,theverticaldiskreadingiscorrect.

7.Inordertoeliminatetheerroroftheinstrumentandthe

horizontalaxiserror,improvetheaccuracyandpreventthe

coarsedeviation.

8.Whentheeyelevelandverticalplatelevelbubblescentered

onthetubeofverticalplatewithverticaldiskindicatoras

itshouldbethecorrectreading(i.e.,amultipleof90°)

isasmallpointofdifference,knownastheverticalplate

index,namelyverticalplateindexdifferencecausedby

deviatingfromthecorrectposition.UsingtheverticalAngle

oftherightandleftsideoftheplate,theinfluenceofthe

differenceoftheverticalplateindexiseliminated.

9.Themainaxesofthetheodoliteare:verticalaxis,

horizontalaxis,telescopicvisualaxisandthehorizontalaxis

ofthestandard.

AccordingtotheAnglemeasurementprincipleandtheaccuracy

oftheAngleofassurance,thefollowingconditionsshouldbe

metbetweenthemainaxesofthetheodolite:

(1)thehorizontalaxisofthestandardshouldbeverticalto

theverticalaxis;

(2)thecrosswiresshouldbeverticaltothehorizontalaxis;

(3)thecollimationaxisshouldbeverticalaxis;

(4)thehorizontalaxisshouldbeverticaltotheverticalaxis;

(5)theindexdifferenceshouldbezero.

14.Methodsofdistancemeasurementare:directmeasurement

(steelmeasurementdistance),opticaldistancemeasurement

(distancemeasurement)andphysicalmethod(photoelectric

ranging).Electro-opticalrangingisthedistancebetweentwo

pointsofelectromagneticwaveoropticalwave.Inorderto

improvetheaccuracyofelectro-opticaldistancemeasurement,

indirectmeasurementshouldbeadoptedwhenthemethod-----

phasemeasurementmethod,

16.Thetotalstationmeansthatonceobservedonthestation,

theangulardistance,verticalAngle,horizontalAngleandso

onareautomaticallydisplayed,andthecoordinatesof

horizontaldistance,highdifferenceandpointareimmediately

obtained.Thetotalstationiscomposedofelectronic

theodolite,electro-opticaldistancemeteranddatarecording

device.HorizontalAnglemeasurement,verticalAngle

measurement,distancemeasurement,coordinatemeasurement;

Theapplicationsoftwarecanalsocarryoutfunctionssuchas

forwardintersection,resection,crosssectionmeasurement,

suspensionheightmeasurementandpointloftingaccordingto

designcoordinates.

Problemsets4

L.Howtodistinguisherrorandcoarseerrorinmeasurement

work?

2.Whatisthedifferencebetweenaccidentalandsystematic

errors?Whatarethecharacteristicsofaccidentalerror?

3.Whyisthearithmeticmeanofobservedvaluesthemost

reliable?

4.Inwhatcircumstancesaretheaccuracyofmeasurement

measuredbymediumerror?Underwhatcircumstancesisthe

relativeerror?

5.Alinesegmentwasmeasured4times.Theresultswere:98.427

m,98.415m,98.430m,98.426m.UsingtheCASIOfx-3950P

calculator,thearithmeticmean,theerrorintheobserved

valueandtheerrorandrelativeerrorinarithmeticmeanare

calculatedinthesingle-variablestatisticalmode.

6.SetupfiveofthehorizontalAngleobservationandits

perspectiveis:63°26'12〃，63°26'09”,18〃63°26

',15'63°26\63°26'06”.Themedianerrorofthe

arithmeticmean,themedianerroroftheobservedvalueandthe

meanofarithmeticmeanarecalculated.

Theanswer:

1.Theerrorinmeasurementisunavoidable,soaslongasthe

requirementsoftheprescribederroraremet,measurescanbe

takentoreduceordealwithit.

Thegenerationofgrosserrorismainlyduetothecarelessness

orimproperobservationmethodinthework,containingthe

grosserrorobservationresultsisnotqualified,proper

methodsandmeasuresmustbetakentoeliminategrosserroror

observations.

2.Thesetwokindsoferror,mainlyonthemeaningandsystem

erroriscumulative,hadagreatinfluenceonthemeasured

results,butthiskindofinfluencehascertainregularity,can

throughtheproperwaytodetermineitssizeandsymbols,using

thecalculationformu1aoferrorcorrectionsystem'sinfluence

ontheobservedvalue,orproperobservationmethods,improve

theaccuracyofmeasuringinstrumentstoeliminateorweaken

them.Accidentalerrorisinevitable,andcannoteliminate,but

observationtakeitsaverageformanytimes,canoffsetsome

accidentalerror,soaccidentalerrorisoffsetting,multiple

observationsthantheaverageofameasuredvalueismoreclose

tothetruevalue,inaddition,improvetheaccuracyof

measuringinstruments,andthechoiceofgoodoutside

observationconditions,improveobservationprocedures,

adoptingreasonabledataprocessingmethodssuchasleast

squaremethodandothermeasurestoreducetheaccidentalerror

influenceonmeasuringresults.

Thecharacteristicsofaccidentalerroraresummarizedas:

1.Undercertainobservationconditions,

Thefrequencywithwhichtheabsolutevalueexceedsacertain

limitiszero;

2.Thefrequencyoftheerrorwithasmallabsolutevalueis

large,andtheerroroftheabsolutevalueissmall;

3.Thepositiveandnegativeerrorsthatareequalinabsolute

valueareapproximatelyequal.

4.Thearithmeticmeanofincidentalerrortendstozerowhen

theobservedfrequencyincreases.

3.Accordingtothecharactersofaccidentalerrorfourth

(offsetting),becauseofthearithmeticmeanismanytimesthe

averageoftheobservedvalue,whenthenumberofobservations

increases,thearithmeticmeanvalueapproachthetruevalue,

itisthemostreliablevalue.

4.WhenmeasuringAngleorleveling,theaccuracyismeasured

bymeansofmediumerror.Indistancemeasurement,theaccuracy

ismeasuredbymeansofrelativemediumerror.

5.X=98.4245m,m=plusorminus0.0066m,mx=plusorminus

0.0033m,1/30,000

6.12〃X=63°26',m=+/-4.7",mx=+/-2.1

Problemset5

Whatisthecontrolpoint?Whatiscontrolmeasurement?

2.Whatisthebrokenpoint?Whatisthedivisionmeasure?

3.Whatproblemsshouldbepaidattentiontoinchoosingthe

mappingcontrolpoints(conductorpoints)?

4.Calculatethecoordinatevaluesofeachpointofaclosed

traverseaccordingtotable5-16.,known.

Table5-16closedtraversecoordinatecalculation

PointAngleobservationvalue(rightAngle)

Coordinateazimuth0

0’"sidelength(m)coordinates

X(m)y(m)

1,2000.002000.00

6945at103.85

21390500

114.57

3941554

162.46

4883636

133.54

5,122and30

123.68

1,95,23to30

5.Alongwithwire,,,,,forseniorpointknown=48°48'48

"=1438.38m,4973.66m==24〃331°25',=1660.84m,5296.85

m=;MeasuredwireleftAngleof<=271°36'36<1=94°

18'18",<2=10106'6<3=267°24'24",<C=88°

12'12Measuringtraverselength:=118.14m,=172.36m,

=142.74m,=185.69m.Calculatethecoordinatesof1,2,and

3.,known.

6.Height=182.232m,knownpointsinverticalAngle

observationpointsto18036'48”,amounttohighpoint

instrumentsfor1.452m,thehighpointofprism1.673m.In

verticalAngleobservationpointsfor1834'42”,highpoint

instrumentsfor1.466m,thehighpointofaprismfor1.6

15m,known=486.75Im,andtry.

7.Abriefdescriptionofthedifferencesinthecalculation

oftheannexedwireandtheclosedconductor.

8.Measurementofobservationdataoffourlevelsinthewhole

table5-19.

Table5-19,4,etc

Thedirectionofthewireundertherulerofthemeasuring

station

and

RulerreadingK+black

Reductionof

Heightofthered

Numberinthereferenceappendix

Theuppersilkwillbeseenbefore

Thereardistanceisredface

Parallaxdifferencedsigmad

119790738,171864050KI=4.687

K2=4,787

Priorto04765265-2

52.252.4-front+1.242+1.140+21.2410

-0.2-0.2

2,27390965,24617247

2183040106835370

Afterbefore一

3.1918,16046291

12901226115486336

Afterbefore-

07425528after2388

20486736before1708

Afterbefore一

9.WhatistheprincipleofadjustmentofAngleclosureinwire

calculation?Whatistheadjustmentprincipleofthechangeof

coordinateincrement?

10.Whydoyouhavetoobservethetrigelevationmeasurements?

11.HowmanypartsofGPSglobalpositioningsystem?Whatare

theadvantages?

Theanswer:

1.Anetworkwithcontrolglobalfunctioniscalledcontrol

point,andmeasurementofplanepositionandelevationof

controlpointiscalledcontrolmeasurement.

2.Thepointsdirectlyusedforthetopographicpointsorthe

constructionloftingpointsarereferredtoasthebreaking

points.Theplanepositionandelevationofthepointofthe

brokenpartaremeasuredbythecontrolpoint.

3.Whenselectingthelocationofthetraversepoints,the

followingpointsshouldbenoted:

(1)theadjacentpointsaregood,