Giáo trình Trắc địa
Bꢀ GIÁO DꢁC VÀ ðÀO TꢂO
TRƯꢃNG ðꢂI HꢄC NÔNG NGHIꢅP I
TS. ðÀM XUÂN HOÀN
TRꢆC ðꢇA
(Giáo trình cho ngành ðꢈa chính & Quꢉn lý Ðꢊt ñai)
Hà nội – 2007
4ꢀ
ꢀ
Ch−¬ngꢀ1ꢀ
Nh÷ngꢀkiÕnꢀthøcꢀchungꢀvÒꢀꢀtr¾cꢀ®Þaꢀ
1.1.ꢀ§èiꢀt−îngꢀvꢁꢀnhiÖmꢀvôꢀcñaꢀtr¾cꢀ®Þaꢀ
Tr¾cꢀ®Þaꢀlꢁꢀmétꢀkhoaꢀhäcꢀnghiªnꢀcøuꢀh×nhꢀd¹ng,ꢀkÝchꢀth−ícꢀtr¸iꢀ®ÊtꢀvꢁꢀbiÓuꢀdiÔnꢀbÒꢀmÆtꢀ
ꢀ
tr¸iꢀ®Êtꢀd−íiꢀd¹ngꢀb×nhꢀ®åꢀhoÆcꢀb¶nꢀ®å.ꢀNgoꢁiꢀraꢀtr¾cꢀ®Þaꢀcßnꢀgi¶iꢀquyÕtꢀhꢁngꢀlo¹tꢀc¸cꢀvÊnꢀ®Òꢀ
trongꢀ®oꢀ®¹cꢀc¸cꢀc«ngꢀtr×nhꢀnh−ꢀchuyÓnꢀb¶nꢀthiÕtꢀkÕꢀraꢀthùcꢀ®Þa,ꢀquanꢀs¸tꢀ®éꢀlón,ꢀbiÕnꢀd¹ngꢀc¸cꢀ
c«ngꢀtr×nh:ꢀthñyꢀ®iÖn,ꢀthñyꢀlîi,ꢀx©yꢀdùng...ꢀv×ꢀ®èiꢀt−îngꢀnghiªnꢀcøuꢀcñaꢀtr¾cꢀ®ÞaꢀrÊtꢀréngꢀng−êiꢀ
taꢀchiaꢀtr¾cꢀ®ÞaꢀraꢀnhiÒuꢀchuyªnꢀngꢁnhꢀkh¸cꢀnhauꢀnh−:ꢀ
ꢀ
Tr¾cꢀ®ÞaꢀcaoꢀcÊp:ꢀNghiªnꢀcøuꢀh×nhꢀd¹ng,ꢀkÝchꢀth−ícꢀtr¸iꢀ®Êt,ꢀnghiªnꢀcøuꢀviÖcꢀx©yꢀ
dùngꢀl−íiꢀtr¾cꢀ®Þaꢀquècꢀgia,ꢀnghiªnꢀcøuꢀhiÖnꢀt−îngꢀ®Þaꢀ®éngꢀhäc,ꢀgi¶iꢀc¸cꢀbꢁiꢀto¸nꢀtr¾cꢀ®Þaꢀtrªnꢀ
bÒꢀmÆtꢀtr¸iꢀ®Êtꢀvꢁꢀtrongꢀvòꢀtrô.ꢀ
ꢀ
Tr¾cꢀ®Þaꢀc«ngꢀtr×nh:ꢀNghiªnꢀcøuꢀviÖcꢀkh¶oꢀs¸t,ꢀthamꢀgiaꢀthiÕtꢀkÕ,ꢀthiꢀc«ngꢀc¸cꢀc«ngꢀ
tr×nh,ꢀquanꢀs¸tꢀ®éꢀlón,ꢀbiÕnꢀd¹ngꢀcñaꢀc¸cꢀc«ngꢀtr×nh....ꢀ
Tr¾cꢀ®Þaꢀ¶nh:ꢀnghiªnꢀcøuꢀviÖcꢀx©yꢀdùngꢀb¶nꢀ®åꢀb»ngꢀ¶nhꢀm¸yꢀbay,ꢀ¶nhꢀmÆtꢀ®Êt,ꢀ¶nhꢀ
ꢀ
vÖꢀtinh,ꢀdïngꢀ¶nhꢀthayꢀthÕꢀchoꢀc¸cꢀph−¬ngꢀph¸pꢀtruyÒnꢀthèngꢀ®Óꢀquanꢀs¸tꢀ®éꢀlónꢀvꢁꢀbiÕnꢀd¹ngꢀ
cñaꢀc¸cꢀc«ngꢀtr×nhꢀx©yꢀdùng.ꢀꢀ
ꢀ
Ngꢁyꢀ nayꢀ xuꢀ h−íngꢀ chungꢀ ng−êiꢀ taꢀ gäiꢀ c¸cꢀ ngꢁnh:ꢀ tr¾cꢀ ®Þa,ꢀ b¶nꢀ ®å,ꢀ viÔnꢀ th¸mꢀ lꢁꢀ
Geometics.ꢀNg−êiꢀtaꢀcoiꢀGeometicsꢀgåmꢀkiÕnꢀthøcꢀcñaꢀc¸cꢀm«nꢀtr¾cꢀ®ÞaꢀcaoꢀcÊp,ꢀtr¾cꢀ®Þaꢀc«ngꢀ
tr×nh,ꢀtr¾cꢀ®Þaꢀ¶nhꢀviÔnꢀth¸m,ꢀbiªnꢀtËpꢀb¶nꢀ®å,ꢀhÖꢀthèngꢀth«ngꢀtinꢀ®Êt,ꢀtinꢀhäc.ꢀ
ꢀ
Trongꢀch−¬ngꢀtr×nhꢀm«nꢀhäcꢀnꢁyꢀchóngꢀtaꢀnghiªnꢀcøuꢀnh÷ngꢀkiÕnꢀthøcꢀc¬ꢀb¶nꢀcñaꢀm«nꢀ
tr¾cꢀ®Þaꢀphæꢀth«ng.ꢀPh¹mꢀviꢀnghiªnꢀcøuꢀlꢁꢀ®oꢀ®¹cꢀtrªnꢀph¹mꢀviꢀnháꢀcñaꢀbÒꢀmÆtꢀtr¸iꢀ®Êt.ꢀC¸cꢀsèꢀ
liÖuꢀ®oꢀ®¹cꢀ(chiÒuꢀdꢁi,ꢀgãc...)ꢀ®−îcꢀtiÕnꢀhꢁnhꢀtrªnꢀmÆtꢀph¼ngꢀvꢁꢀbiÓuꢀdiÔnꢀchóngꢀlªnꢀmÆtꢀph¼ngꢀ
(kh«ngꢀtÝnhꢀ®Õnꢀ¶nhꢀh−ëngꢀ®éꢀcongꢀcñaꢀbÒꢀmÆtꢀtr¸iꢀ®Êt).ꢀV×ꢀvËyꢀnhiÖmꢀvôꢀc¬ꢀb¶nꢀcñaꢀm«nꢀhäcꢀ
nꢁyꢀlꢁꢀtrangꢀbÞꢀchoꢀsinhꢀviªnꢀnh÷ngꢀkiÕnꢀthøcꢀc¬ꢀb¶nꢀvÒꢀtr¾cꢀ®ÞaꢀtrªnꢀmÆtꢀph¼ng,ꢀbiÕtꢀc¸chꢀx©yꢀ
dùngꢀ b×nhꢀ ®å,ꢀ b¶nꢀ ®åꢀ ®Óꢀ tõꢀ ®ãꢀ giópꢀ sinhꢀ viªnꢀ vËnꢀ dôngꢀ kiÕnꢀ thøcꢀ cñaꢀ m×nhꢀ vꢁoꢀ lÜnhꢀ vùcꢀ
chuyªnꢀm«nꢀtrongꢀngꢁnhꢀqu¶nꢀlýꢀvꢁꢀquyꢀho¹chꢀ®Êtꢀ®ai.ꢀ
1.2ꢀC¸cꢀ®¬nꢀvÞꢀth−êngꢀdïngꢀtrongꢀtr¾cꢀ®Þaꢀ
ꢀ
Trongꢀtr¾cꢀ®Þaꢀth−êngꢀph¶iꢀ®oꢀc¸cꢀ®¹iꢀl−îngꢀh×nhꢀhäcꢀnh−ꢀchiÒuꢀdꢁi,ꢀgãcꢀb»ng,ꢀgãcꢀ
®øng...ꢀvꢁꢀc¸cꢀ®¹iꢀl−îngꢀvËtꢀlýꢀnh−:ꢀnhiÖtꢀ®é,ꢀ¸pꢀxuÊt....ꢀ
1.2.1ꢀꢀ§¬nꢀvÞꢀ®oꢀchiÒuꢀdꢁiꢀ
ꢀ
N¨mꢀ1791ꢀtæꢀchøcꢀ®oꢀl−êngꢀquècꢀtÕꢀlÊyꢀ®¬nꢀvÞꢀ®oꢀchiÒuꢀdꢁiꢀtrongꢀhÖꢀthèngꢀSIꢀlꢁꢀmÐtꢀ
víiꢀquyꢀ®Þnh:ꢀ"MétꢀmÐtꢀlꢁꢀchiÒuꢀdꢁiꢀøngꢀvíiꢀ4.10ꢂ7ꢀchiÒuꢀdꢁiꢀcñaꢀkinhꢀtuyÕnꢀ®iꢀquaꢀParis"ꢀvꢁꢀ®ꢃꢀ
chÕꢀt¹oꢀraꢀmétꢀth−ícꢀchuÈnꢀcãꢀ®éꢀdꢁiꢀ1mꢀb»ngꢀthÐpꢀkh«ngꢀgØ,ꢀcãꢀ®éꢀgiꢃnꢀnëꢀrÊtꢀnháꢀ®Ætꢀt¹iꢀ
ViÖnꢀ®oꢀl−êngꢀParis.ꢀ
ꢀ
TõꢀsauꢀthÕꢀkûꢀ19,ꢀ®éꢀchÝnhꢀx¸cꢀcñaꢀth−ícꢀchuÈnꢀkh«ngꢀcßnꢀ®¸pꢀøngꢀ®−îcꢀyªuꢀcÇuꢀ®oꢀ
l−êngꢀc¸cꢀph©nꢀtöꢀv«ꢀcïngꢀnhá.ꢀV×ꢀthÕꢀn¨mꢀ1960ꢀquyꢀ®Þnhꢀ®¬nꢀvÞꢀ®oꢀchiÒuꢀdꢁiꢀlꢁ:ꢀ"MétꢀmÐtꢀlꢁꢀ
chiÒuꢀdꢁiꢀb»ngꢀ1.650.763,73ꢀchiÒuꢀdꢁiꢀcñaꢀb−ícꢀsãngꢀbøcꢀx¹ꢀtrongꢀch©nꢀkh«ngꢀcñaꢀnguyªnꢀtöꢀ
Kriptonꢀꢂꢀ86,ꢀt−¬ngꢀ®−¬ngꢀvíiꢀquüꢀ®¹oꢀchuyÓnꢀrêiꢀcñaꢀ®iÖnꢀtöꢀgi÷aꢀ2ꢀmøcꢀn¨ngꢀl−îngꢀ2P10ꢀꢀvꢁꢀ
5ꢀ
ꢀ
5d5".ꢀ1ꢀmÐtꢀ(m)ꢀ=ꢀ10ꢀdecimÐtꢀ(dm)ꢀ=ꢀ102ꢀcentimetꢀ(cm)ꢀ=ꢀ103ꢀmilimetꢀ(m.m)ꢀ=ꢀ106ꢀmicrometꢀ
(µm)ꢀ=ꢀ109ꢀnanomÐtꢀ(Nm).ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
§¬nꢀvÞꢀ®oꢀdiÖnꢀtÝchꢀth−êngꢀdïngꢀlꢁꢀmÐtꢀvu«ngꢀ(m2),ꢀkilomÐtꢀvu«ngꢀ(km2)ꢀvꢁꢀhectaꢀ(ha).ꢀ
1ꢀkm2ꢀ=ꢀ106ꢀm2ꢀ=ꢀ100ꢀha,ꢀ1ꢀhaꢀ=ꢀ104m2ꢀ
Ngoꢁiꢀraꢀmétꢀsèꢀn−ícꢀcßnꢀdïngꢀ®¬nꢀvÞꢀ®oꢀchiÒuꢀdꢁiꢀcñaꢀAnhꢀlꢁ:ꢀ
1footꢀ=ꢀ0,3048m,ꢀ1inchꢀ=ꢀ25,3ꢀmmꢀ
ꢀ
ꢀ
1.2.2.ꢀ§¬nꢀvÞꢀ®oꢀgãcꢀ
ꢀ
ꢀ
Trongꢀtr¾cꢀ®Þaꢀth−êngꢀdïngꢀ3ꢀ®¬nꢀvÞꢀ®oꢀgãcꢀlꢁ:ꢀRadian,ꢀ®é,ꢀGrad.ꢀ
1ꢂꢀRadian:ꢀKýꢀhiÖuꢀlꢁꢀRadꢀlꢁꢀ1ꢀgãcꢀph¼ngꢀcãꢀ®Ønhꢀtrïngꢀvíiꢀt©mꢀcñaꢀ1ꢀvßngꢀtrßnꢀvꢁꢀ
ch¾nꢀ1ꢀcungꢀtrªnꢀ®−êngꢀtrßnꢀvíiꢀchiÒuꢀdꢁiꢀcungꢀtrßnꢀ®óngꢀb»ngꢀb¸nꢀkÝnhꢀcñaꢀ®−êngꢀtrßnꢀ®ã.ꢀ
ꢀ
§éꢀlínꢀcñaꢀgãcꢀbÊtꢀkúꢀsÏꢀb»ngꢀtûꢀsèꢀgi÷aꢀ®éꢀdꢁiꢀcungꢀch¾nꢀbëiꢀgãcꢀvꢁꢀb¸nꢀkÝnhꢀvßngꢀ
trßn.ꢀ
ꢀ
Gãcꢀtrßnꢀlꢁꢀgãcꢀëꢀtrªnꢀ®−êngꢀtrßnꢀch¾nꢀcungꢀtrßnꢀcãꢀchiÒuꢀdꢁiꢀb»ngꢀchuꢀviꢀh×nhꢀtrßn.ꢀ
Chuꢀviꢀh×nhꢀtrßnꢀcãꢀchiÒuꢀdꢁiꢀlꢁ:ꢀ2πRꢀnªnꢀgãcꢀtrßnꢀcãꢀ®éꢀlínꢀlꢁ:ꢀ2πRad.ꢀRadianꢀlꢁꢀ®¬nꢀvÞꢀ®oꢀ
gãcꢀ®−îcꢀdïngꢀtrongꢀtÝnhꢀto¸n,ꢀ®ÆcꢀbiÖtꢀlꢁꢀkhiꢀsöꢀdôngꢀc¸cꢀph−¬ngꢀph¸pꢀnéiꢀsuyꢀc¸cꢀgi¸ꢀtrÞꢀ
hꢁmꢀl−îngꢀgi¸c.ꢀ
ꢀ
2.ꢀ§é:ꢀkýꢀhiÖuꢀlꢁꢀ(o)ꢀlꢁꢀgãcꢀëꢀt©mꢀ®−êngꢀtrßnꢀch¾nꢀ1ꢀcungꢀtrßnꢀcãꢀchiÒuꢀdꢁiꢀb»ngꢀ1/360ꢀ
chuꢀviꢀh×nhꢀtrßn.ꢀ1®éꢀchiaꢀthꢁnhꢀ60ꢀphót,ꢀ1ꢀphótꢀchiaꢀthꢁnhꢀ60ꢀgi©y,ꢀkýꢀhiÖuꢀlꢁ:ꢀꢀ0ꢀ'ꢀ"ꢀ
ꢀ
ꢀ
ꢀ
VÝꢀdô:ꢀgãcꢀ®−îcꢀviÕtꢀAꢀ=ꢀ120025'42''ꢀ
Tuyꢀnhiªnꢀgãcꢀ®ãꢀcãꢀthÓꢀviÕtꢀb»ngꢀ®é,ꢀphótꢀvꢁꢀphÇnꢀm−êiꢀphót.ꢀGãcꢀtrªnꢀcãꢀthÓꢀviÕtꢀlꢁ:ꢀ
Aꢀ=ꢀ120o25'7ꢀ
ꢀ
3.ꢀGrad:ꢀkýꢀhiÖuꢀlꢁꢀGrꢀlꢁꢀgãcꢀëꢀt©mꢀch¾nꢀcungꢀtrßnꢀcãꢀ®éꢀdꢁiꢀb»ngꢀ1/400ꢀchuꢀviꢀ®−êngꢀ
trßn.ꢀ 1ꢀ Gradꢀ chiaꢀ thꢁnhꢀ 100ꢀ phótꢀ Gradꢀ (miligrad),ꢀ 1ꢀ phótꢀ Gradꢀ chiaꢀ thꢁnhꢀ 100ꢀ gi©yꢀ Gradꢀ
(decimiligrad),ꢀkýꢀhiÖuꢀt−¬ngꢀøngꢀlꢁ:ꢀc,ꢀccꢀ
ꢀ
ꢀ
ꢀ
ꢀ
VÝꢀdô:ꢀGãcꢀBꢀꢀ=ꢀ172grꢀ12cꢀ27ccꢀ
4.ꢀQuanꢀhÖꢀgi÷aꢀc¸cꢀ®¬nꢀvÞ:ꢀ
Tõꢀ®ÞnhꢀnghÜaꢀbaꢀlo¹iꢀ®¬nꢀvÞꢀ®oꢀgãc,ꢀtaꢀcãꢀquanꢀhÖ:ꢀ
1ꢀgãcꢀtrßnꢀ=ꢀ2πRadꢀ=ꢀ360oꢀ=ꢀ400ꢀgrꢀ
Tõꢀ®ãꢀsuyꢀraꢀc¸cꢀquanꢀhÖꢀ®ÓꢀchuyÓnꢀ®æiꢀc¸cꢀ®¬nꢀvÞꢀ®oꢀgãc.ꢀKhiꢀtÝnhꢀto¸nꢀ
π
180
Rad
o
ꢀ
ꢀ
2πꢀRadꢀ=ꢀ360oꢀsuyꢀra:ꢀα ꢀ=ꢀα
ꢀ
180
Rad
o
α ꢀ=ꢀα ꢀ
ꢀ
π
§Ætꢀc¸cꢀhÖꢀsè:ꢀ
1800
o
ꢀ
ꢀ
ρ ꢀ=ꢀ
=ꢀ57o17'44''8ꢀ
π
6ꢀ
ꢀ
180x60
ꢀ
ꢀ
ꢀ
ρ
'ꢀ=ꢀ
''ꢀ=ꢀ
=ꢀ3438'ꢀ
π
180x60x60
ꢀ
ꢀ
ρ
=ꢀ206265''ꢀ
π
T−¬ngꢀøngꢀvíiꢀc«ngꢀthøcꢀtrªnꢀtaꢀcãꢀc«ngꢀthøcꢀchuyÓnꢀ®æiꢀgi÷aꢀ®éꢀvꢁꢀRadian:ꢀ
Radꢀ
ꢀ
ꢀ
α
α
α
oꢀ=ꢀ
ρ
o.ꢀ
α
ꢀ
ꢀ
Radꢀ
'ꢀ=ꢀ
''ꢀ=ꢀ
ρ
'.ꢀ
''.ꢀ
α
ꢀ
ꢀ
ꢀ
ρ
α
Radꢀ
Trongꢀc¸cꢀbꢁiꢀto¸nꢀküꢀthuËtꢀkhiꢀtÝnhꢀto¸nꢀgi¸ꢀtrÞꢀc¸cꢀhꢁmꢀsèꢀl−îngꢀgi¸cꢀcñaꢀc¸cꢀgãcꢀnháꢀ
cãꢀthÓꢀdïngꢀquanꢀhÖꢀt−¬ngꢀ®−¬ng,ꢀnghÜaꢀlꢁꢀchØꢀlÊyꢀsèꢀh¹ngꢀbËcꢀnhÊtꢀtrongꢀc«ngꢀthøcꢀkhaiꢀtriÓnꢀ
hꢁmꢀl−îngꢀgi¸cꢀthꢁnhꢀchuçiꢀsè.ꢀ
3
5
ε
ε
3! 5!
ꢀ
sinꢀ
εꢀ=ꢀ
εꢀ+ꢀ
+
+...... ≈ ε.
ꢀ
3
5
ε
ε
3! 5!
ꢀ
ꢀ
ꢀ
tgꢀ
ε
ꢀ=ꢀ
ε
ꢀ+ꢀ
+
+...... ≈ ε.
ꢀ
NghÜaꢀlꢁꢀgi¸ꢀtrÞꢀgãcꢀnháꢀtÝnhꢀb»ngꢀgi©yꢀ®−îcꢀlÊyꢀb»ngꢀgi¸ꢀtrÞꢀgãcꢀtÝnhꢀb»ngꢀRadian.ꢀ
1''Rad
1''ꢀ
≈
ꢀsinꢀ1''ꢀ
≈ꢀ
ꢀ=ꢀ0,00000ꢀ4848ꢀRadꢀ
206265''
ꢀ VÝꢀdô:ꢀCãꢀ1ꢀgãcꢀnháꢀαꢀ=ꢀ15''ꢀch¾nꢀ1ꢀcungꢀtrßnꢀcãꢀb¸nꢀkÝnhꢀRꢀ=ꢀ1000m.ꢀTaꢀcãꢀthÓꢀsuyꢀ
raꢀchiÒuꢀdꢁiꢀcungꢀtrßnꢀch¾nꢀbëiꢀcungꢀ®ãꢀlꢁ:ꢀ
α''
ρ
15''
ꢀ
C=ꢀR.
ꢀ=ꢀ1000000ꢀmmꢀ
=ꢀ72,7mmꢀ
206265''
1.3.ꢀKh¸iꢀniÖmꢀvÒꢀc¸cꢀmÆtꢀ®Æcꢀtr−ngꢀchoꢀh×nhꢀd¹ngꢀcñaꢀTr¸iꢀ®Êtꢀ
ꢀ
Khiꢀnghiªnꢀcøuꢀh×nhꢀd¹ngꢀtr¸iꢀ®Êtꢀng−êiꢀtaꢀthÊyꢀr»ngꢀtr¸iꢀ®Êtꢀcãꢀd¹ngꢀelÝpꢀquay,ꢀdÑtꢀëꢀ2ꢀ
cùc,ꢀbÒꢀmÆtꢀtùꢀnhiªnꢀcñaꢀtr¸iꢀ®ÊtꢀrÊtꢀphøcꢀt¹p.ꢀDiÖnꢀtÝchꢀbÒꢀmÆtꢀtr¸iꢀ®Êtꢀlꢁ:ꢀ510575.103ꢀkm2ꢀ
trongꢀ®ãꢀ®¹iꢀd−¬ngꢀchiÕmꢀ71,8%,ꢀlôcꢀ®ÞaꢀchiÕmꢀ28,2%.ꢀ§éꢀcaoꢀtrungꢀb×nhꢀcñaꢀlôcꢀ®Þaꢀsoꢀvíiꢀ
mùcꢀn−ícꢀ®¹iꢀd−¬ngꢀkho¶ngꢀgÇnꢀ900m.ꢀNh−ꢀvËyꢀꢀbÒꢀmÆtꢀh×nhꢀhäcꢀtr¸iꢀ®Êtꢀkh«ngꢀthÓꢀbiÓuꢀdiÔnꢀ
b»ngꢀmétꢀph−¬ngꢀtr×nhꢀto¸nꢀhäcꢀnꢁoꢀ®−îc.ꢀTuyꢀnhiªnꢀtrongꢀmétꢀsèꢀtr−êngꢀhîpꢀtÝnhꢀto¸nꢀgÇnꢀ
®óngꢀng−êiꢀtaꢀcoiꢀtr¸iꢀ®Êtꢀcãꢀd¹ngꢀh×nhꢀcÇu,ꢀb¸nꢀkÝnhꢀlꢁ:ꢀ6371ꢀkm.ꢀ
ꢀ
Trongꢀ®oꢀvÏꢀb¶nꢀ®åꢀc¸cꢀsèꢀliÖuꢀ®oꢀ®¹cꢀ®−îcꢀtiÕnꢀhꢁnhꢀtrªnꢀmÆtꢀcong,ꢀkhiꢀbiÓuꢀdiÔnꢀ
chóngꢀl¹iꢀthùcꢀhiÖnꢀtrªnꢀmÆtꢀph¼ng.ꢀ§Óꢀxöꢀlýꢀc¸cꢀsèꢀliÖuꢀ®oꢀ®¹cꢀng−êiꢀtaꢀ®−aꢀraꢀc¸cꢀlo¹iꢀmÆtꢀ
dïngꢀtrongꢀtr¾cꢀ®Þaꢀnh−ꢀsau:ꢀ
1.3.1.ꢀMÆtꢀGeoidꢀvꢁꢀKvazigeoid.ꢀ
ꢀ
ꢀ
1.ꢀMÆtꢀGeoidꢀ
MÆtꢀGeoidꢀlꢁꢀbÒꢀmÆtꢀtr¸iꢀ®Êtꢀgiíiꢀh¹nꢀbëiꢀmÆtꢀ®¼ngꢀthÕꢀ®iꢀquaꢀ®iÓmꢀtÝnhꢀ®éꢀcao.ꢀViÖcꢀ
7ꢀ
ꢀ
ꢀx¸cꢀ®ÞnhꢀmÆtꢀGeoidꢀ®−îcꢀx¸cꢀ®ÞnhꢀgÇnꢀvíiꢀmùcꢀn−ícꢀbiÓnꢀtrungꢀb×nh.ꢀThÕꢀträngꢀtr−êngꢀt¹iꢀ
Geoidꢀ®−îcꢀviÕtꢀlꢁ:ꢀWo.ꢀꢀ
ꢀ
ꢀ
2.ꢀMÆtꢀKvazigeoidꢀ
V×ꢀnh÷ngꢀbiÕnꢀ®æiꢀphøcꢀt¹pꢀcñaꢀgi¸ꢀtrÞꢀträngꢀtr−êng,ꢀ®Óꢀx¸cꢀ®ÞnhꢀchÝnhꢀx¸cꢀGeoidꢀngoꢁiꢀ
c¸cꢀtrÞꢀ®oꢀtr¾cꢀ®ÞaꢀtrªnꢀbÒꢀmÆtꢀtr¸iꢀ®ÊtꢀcßnꢀcÇnꢀcãꢀhiÓuꢀbiÕtꢀ®Çyꢀ®ñꢀvÒꢀcÊuꢀt¹oꢀcñaꢀtr¸iꢀ®Êt,ꢀ®©yꢀ
lꢁꢀ®iÓmꢀkh«ngꢀdÔꢀlꢁmꢀ®−îc.ꢀViÖnꢀsÜꢀNgaꢀMolodenxkiꢀ®−aꢀraꢀlýꢀthuyÕtꢀx¸cꢀ®ÞnhꢀmÆtꢀgÇnꢀvíiꢀ
mÆtꢀGeoid,ꢀëꢀ®ångꢀb»ngꢀchØꢀchªnhꢀlÖchꢀsoꢀvíiꢀGeoidꢀtõꢀ2ꢀ®Õnꢀ4ꢀcm,ꢀvïngꢀnóiꢀchªnhꢀkh«ngꢀqu¸ꢀ
2mꢀvꢁꢀ®−îcꢀgäiꢀlꢁꢀmÆtꢀKvazigeoid.ꢀNhiÒuꢀn−ícꢀtrªnꢀthÕꢀgiíiꢀtrongꢀ®ãꢀcãꢀViÖtꢀNamꢀdïngꢀmÆtꢀ
KvazigeoidꢀlꢁmꢀmÆtꢀc¬ꢀsëꢀ®Óꢀx¸cꢀ®Þnhꢀ®éꢀcaoꢀquècꢀgiaꢀgäiꢀlꢁꢀ®éꢀcaoꢀth−êng(1).ꢀ
1.3.2.ꢀꢀMÆtꢀEllipsoidꢀtr¸iꢀ®ÊtꢀvꢁꢀmÆtꢀEllipsoidꢀquyꢀchiÕuꢀ
ꢀ
1.ꢀMÆtꢀEllipsoidꢀtr¸iꢀ®Êtꢀ
ꢀ
Nh−ꢀtaꢀ®ꢃꢀbiÕtꢀmÆtꢀGeoidꢀhoÆcꢀKvazigeoidꢀlꢁꢀkhèiꢀ®¹iꢀdiÖnꢀchoꢀtÝnhꢀchÊtꢀvËtꢀlýꢀcñaꢀ
Tr¸iꢀ®Êt.ꢀNãꢀcãꢀliªnꢀquanꢀchÆtꢀchÏꢀ®ÕnꢀtrÞꢀ®oꢀtr¾cꢀ®Þaꢀnh−ngꢀkh«ngꢀthÓꢀdïngꢀlꢁmꢀc¬ꢀsëꢀ®Óꢀxöꢀlýꢀ
to¸nꢀhäcꢀc¸cꢀtrÞꢀ®oꢀtr¾cꢀ®Þaꢀv×ꢀkh«ngꢀthÓꢀdïngꢀph−¬ngꢀtr×nhꢀto¸nꢀhäcꢀnꢁoꢀ®ÓꢀbiÓuꢀthÞꢀmÆtꢀ®ãꢀ
®−îcꢀ(mÆtꢀkh«ngꢀcãꢀph−¬ngꢀtr×nhꢀto¸nꢀhäc).ꢀ
ꢀ
TõꢀlýꢀthuyÕtꢀvÒꢀkhèiꢀchÊtꢀlángꢀquayꢀquanhꢀtrôc,ꢀng−êiꢀtaꢀnghÜꢀ®ÕnꢀviÖcꢀbiÓuꢀdiÔnꢀto¸nꢀ
häcꢀcñaꢀTr¸iꢀ®Êtꢀph¶iꢀlꢁꢀ1ꢀkhèiꢀEllipꢀquay,ꢀdÑtꢀëꢀ2ꢀcùcꢀgäiꢀlꢁꢀEllipsoidꢀtr¸iꢀ®Êt.ꢀBëiꢀv×ꢀmÆtꢀ
EllipsoidꢀlꢁꢀmÆtꢀto¸nꢀhäc,ꢀnªnꢀ®ÓꢀthùcꢀhiÖnꢀc¸cꢀtÝnhꢀto¸nꢀtrªnꢀmÆtꢀnꢁyꢀtrongꢀTr¾cꢀ®ÞaꢀcaoꢀcÊpꢀ
®ꢃꢀx©yꢀdùngꢀc¸cꢀc«ngꢀthøcꢀquyꢀchiÕuꢀc¸cꢀtrÞꢀ®oꢀ(gãc,ꢀchiÒuꢀdꢁi...)ꢀlªnꢀmÆtꢀnꢁy.ꢀ
ꢀ
KhèiꢀEllipꢀcãꢀträngꢀt©mꢀvꢁꢀxÝchꢀ®¹oꢀtrïngꢀvíiꢀträngꢀt©mꢀvꢁꢀxÝchꢀ®¹oꢀcñaꢀtr¸iꢀ®Êt,ꢀcãꢀ
khèiꢀl−îngꢀb»ngꢀkhèiꢀl−îngꢀtr¸iꢀ®Êtꢀquayꢀquanhꢀtrôcꢀt¹oꢀraꢀbÒꢀmÆtꢀgÇnꢀvíiꢀmÆtꢀGeoidꢀtrªnꢀ
ph¹mꢀviꢀtoꢁnꢀcÇuꢀgäiꢀlꢁꢀEllipsoidꢀchungꢀhayꢀEllipsoidꢀtr¸iꢀ®Êt.ꢀKÝchꢀth−ícꢀcñaꢀEllipsoidꢀtr¸iꢀ
®Êtꢀ®−îcꢀ®Æcꢀtr−ngꢀbëiꢀb¸nꢀtrôcꢀlínꢀa,ꢀb¸nꢀtrôcꢀnháꢀb,ꢀ®éꢀdÑtꢀf.ꢀꢀ
a − b
a
ꢀ
ꢀf=ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
b
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
aꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
H×nhꢀ1.1ꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
1ꢀ*ꢀNgoꢁiꢀ®éꢀcaoꢀth−êngꢀcßnꢀcãꢀ®éꢀcaoꢀchÝnh,ꢀ®éꢀcaoꢀ®éngꢀlùcꢀ
8ꢀ
ꢀ
ꢀ
ꢀ
CãꢀnhiÒuꢀnhꢁꢀkhoaꢀhäcꢀtrªnꢀthÕꢀgiíiꢀx¸cꢀ®ÞnhꢀkÝchꢀth−ícꢀEllipsoidꢀ(b¶ngꢀ1.1).ꢀ
B¶ngꢀ1.1ꢀ
§éꢀdÑtꢀfꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
TªnꢀEllipꢀsoidꢀ
Everestꢀ
N¨mꢀx¸cꢀ®Þnhꢀ
1830ꢀ
B¸nꢀtrôcꢀlínꢀaꢀ(m)ꢀ
6.377.276ꢀ
1:300,80ꢀ
1:ꢀ297,00ꢀ
1:ꢀ298,3ꢀ
Hayfordꢀ
1909ꢀ
6.378.286ꢀ
Karaxovskiꢀ
Referenceꢀ
W.G.Sꢂ84ꢀ
1940ꢀ
6.378.245ꢀ
1967ꢀ
6.378.100ꢀ
1:ꢀ298,25ꢀ
1:ꢀ298,257ꢀ
1984ꢀ
6.378.137ꢀ
ꢀ
ꢀ
2.ꢀMÆtꢀEllipsoidꢀquyꢀchiÕuꢀ
Tr−ícꢀ khiꢀcãꢀ Ellipsoidꢀchungꢀ doꢀ yªuꢀcÇuꢀ xöꢀ lýꢀ to¸nꢀ häcꢀcñaꢀ mçiꢀ quècꢀ giaꢀ tÝnhꢀ raꢀ
Ellipsoidꢀ choꢀ phïꢀ hîpꢀ víiꢀ lꢃnhꢀ thæꢀ cñaꢀ n−ícꢀ m×nh,ꢀcãꢀ thÓꢀ dïngꢀ Ellipꢀ soidꢀ cñaꢀ n−ícꢀ kh¸cꢀ
nh−ngꢀc¶ꢀ2ꢀtr−êngꢀhîpꢀ®−îcꢀ®ÞnhꢀvÞꢀchoꢀphïꢀhîpꢀnhÊtꢀvíiꢀGeoidꢀcñaꢀlꢃnhꢀthæꢀn−ícꢀm×nh.ꢀEllipꢀ
soidꢀ®−îcꢀsöꢀdôngꢀriªngꢀcñaꢀtõngꢀn−ícꢀgäiꢀlꢁꢀEllipꢀsoidꢀquyꢀchiÕu.ꢀTrongꢀhÖꢀtoaꢀ®éꢀHNꢂ72ꢀ
ViÖtꢀNamꢀlÊyꢀEllipsoidꢀKraxovskiꢀ(1940)ꢀlꢁmꢀEllipꢀsoidꢀquyꢀchiÕu.ꢀHiÖnꢀnayꢀViÖtꢀNamꢀcãꢀhÖꢀ
täaꢀ®éꢀmíiꢀVNꢂ2000ꢀlÊyꢀEllipꢀsoidꢀW.G.Sꢂ84ꢀlꢁmꢀEllipꢀsoidꢀquyꢀchiÕu.ꢀGècꢀtäaꢀ®éꢀ®Ætꢀt¹iꢀ
khu«nꢀviªnꢀViÖnꢀnghiªnꢀcøuꢀ§ÞaꢀchÝnhꢀtrªnꢀ®−êngꢀHoꢁngꢀQuècꢀViÖtꢀꢂꢀHꢁꢀNéi.ꢀ
1.4.ꢀ§éꢀcaoꢀtuyÖtꢀ®èi,ꢀt−¬ngꢀ®èi,ꢀchªnhꢀcaoꢀ
ꢀ
§ÓꢀnghiªnꢀcøuꢀbÒꢀmÆtꢀgåꢀghÒꢀcñaꢀtr¸iꢀ®ÊtꢀphôcꢀvôꢀchoꢀviÖcꢀx©yꢀdùngꢀc¸cꢀc«ngꢀtr×nh:ꢀ
thñyꢀlîi,ꢀthñyꢀ®iÖn,ꢀgiaoꢀth«ng,ꢀx©yꢀdùng....ꢀvꢁꢀnghiªnꢀcøuꢀbÒꢀmÆtꢀtr¸iꢀ®Êtꢀng−êiꢀtaꢀ®−aꢀraꢀc¸cꢀ
®ÞnhꢀnghÜaꢀvÒꢀ®éꢀcao.ꢀꢀ
1.4.1.ꢀ§ÞnhꢀnghÜaꢀ
ꢀ
ꢀ
§éꢀcaoꢀcñaꢀmétꢀ®iÓmꢀlꢁꢀkho¶ngꢀc¸chꢀth¼ngꢀ®øngꢀtõꢀ®iÓmꢀ®ãꢀ®ÕnꢀmÆtꢀthñyꢀchuÈn.ꢀ
MÆtꢀthñyꢀchuÈn:ꢀmÆtꢀthñyꢀchuÈnꢀlꢁꢀmÆtꢀcãꢀph−¬ngꢀvu«ngꢀgãcꢀvíiꢀ®−êngꢀd©yꢀdäiꢀt¹iꢀ
mäiꢀ®iÓm.ꢀ
ꢀ
Nh−ꢀvËy,ꢀvÒꢀ®ÞnhꢀnghÜaꢀtrªnꢀbÒꢀmÆtꢀtr¸iꢀ®Êtꢀcãꢀv«ꢀsèꢀmÆtꢀthñyꢀchuÈn.ꢀCøꢀquaꢀ1ꢀ®iÓmꢀ
trªnꢀbÒꢀmÆtꢀTr¸iꢀ®Êtꢀcãꢀ1ꢀmÆtꢀthñyꢀchuÈnꢀ®iꢀqua.ꢀ§Óꢀph©nꢀbiÖtꢀc¸cꢀmÆtꢀthñyꢀchuÈnꢀng−êiꢀtaꢀ
ph©nꢀchóngꢀthꢁnhꢀ2ꢀlo¹i:ꢀ
ꢀ
ꢀ
MÆtꢀthñyꢀchuÈnꢀ®¹iꢀ®Þa:ꢀ
MÆtꢀthñyꢀchuÈnꢀ®¹iꢀ®ÞaꢀlꢁꢀmÆtꢀn−ícꢀbiÓn,ꢀ®¹iꢀd−¬ngꢀëꢀtr¹ngꢀth¸iꢀtrungꢀb×nh,ꢀyªnꢀtÜnh.ꢀ
§ãꢀcòngꢀchÝnhꢀlꢁꢀmÆtꢀKvazigeoid.ꢀ
ꢀ
ꢀ
MÆtꢀthñyꢀchuÈnꢀgi¶ꢀ®Þnh:ꢀ
MÆtꢀthñyꢀchuÈnꢀgi¶ꢀ®ÞnhꢀlꢁꢀmÆtꢀthñyꢀchuÈnꢀ®iꢀquaꢀmétꢀ®iÓmꢀbÊtꢀkú.ꢀ§iÓmꢀnꢁyꢀ®−îcꢀgi¶ꢀ
®Þnhꢀꢀ®éꢀcaoꢀgäiꢀlꢁꢀ®éꢀcaoꢀgi¶ꢀ®Þnh.ꢀ
9ꢀ
ꢀ
1.4.2.ꢀ§éꢀcaoꢀtuyÖtꢀ®èiꢀ
ꢀ
§éꢀcaoꢀ tuyÖtꢀ®èiꢀ cñaꢀ1ꢀ®iÓmꢀlꢁꢀ kho¶ngꢀc¸chꢀth¼ngꢀ ®øngꢀtõꢀ ®iÓmꢀ ®ãꢀ®ÕnꢀmÆtꢀ thñyꢀ
chuÈnꢀ®¹iꢀ®Þa.ꢀ§éꢀcaoꢀnꢁyꢀ®−îcꢀgäiꢀlꢁꢀ®éꢀcaoꢀth−êng.ꢀ§iÓmꢀgècꢀ®éꢀcaoꢀcãꢀ®éꢀcaoꢀlꢁꢀ0m.ꢀViÖtꢀ
NamꢀlÊyꢀmùcꢀn−ícꢀbiÓnꢀtrungꢀb×nhꢀt¹iꢀTr¹mꢀnghiÖmꢀtriÒuꢀHßnꢀDÊuꢀꢂꢀ§åꢀS¬nꢀꢂꢀH¶iꢀPhßngꢀlꢁmꢀ
®iÓmꢀ®éꢀcaoꢀgèc.ꢀ§éꢀcaoꢀ®−îcꢀghiꢀtrªnꢀb¶nꢀ®åꢀlꢁꢀ®éꢀcaoꢀtuyÖtꢀ®èi.ꢀꢀ
1.4.3.ꢀ§éꢀcaoꢀt−¬ngꢀ®èiꢀ
ꢀ
§éꢀcaoꢀt−¬ngꢀ®èiꢀcñaꢀmétꢀ®iÓmꢀlꢁꢀkho¶ngꢀc¸chꢀth¼ngꢀ®øngꢀtõꢀ®iÓmꢀ®ãꢀ®ÕnꢀmÆtꢀthñyꢀ
chuÈnꢀgi¶ꢀ®Þnhꢀgäiꢀlꢁꢀ®éꢀcaoꢀgi¶ꢀ®Þnh.ꢀ
§ÓꢀphôcꢀvôꢀviÖcꢀnghiªnꢀcøuꢀbÒꢀmÆtꢀtr¸iꢀ®Êt,ꢀphucꢀvôꢀviÖcꢀx©yꢀdùngꢀc¸cꢀc«ngꢀtr×nhꢀthñyꢀ
ꢀ
lîi,ꢀthñyꢀ®iÖn,ꢀgiaoꢀth«ng...ꢀtrongꢀph¹mꢀviꢀlꢃnhꢀthæꢀcñaꢀmétꢀn−ícꢀng−êiꢀtaꢀ®ꢃꢀx©yꢀdùngꢀl−íiꢀ®éꢀ
caoꢀgåmꢀnhiÒuꢀcÊp,ꢀgäiꢀlꢁꢀl−íiꢀ®éꢀcaoꢀNhꢁꢀn−íc.ꢀ
ꢀ
Tuyꢀnhiªnꢀc¸cꢀ®iÓmꢀ®éꢀcaoꢀNhꢁꢀn−ícꢀvÉnꢀrÊtꢀth−aꢀthítꢀkh«ngꢀ®¸pꢀøngꢀ®−îcꢀchoꢀtÊtꢀc¶ꢀ
c¸cꢀc«ngꢀtr×nh.ꢀV×ꢀvËyꢀtrªnꢀkhuꢀvùcꢀnháꢀkhiꢀx©yꢀdùngꢀc¸cꢀc«ngꢀtr×nhꢀng−êiꢀtaꢀcãꢀthÓꢀtÝnhꢀto¸nꢀ
theoꢀ®¬nꢀvÞꢀ®éꢀcaoꢀt−¬ngꢀ®èiꢀ(®éꢀcaoꢀgi¶ꢀ®Þnh).ꢀ
ꢀ
KhiꢀmuènꢀchuyÓnꢀ®éꢀcaoꢀt−¬ngꢀ®èiꢀvÒꢀ®éꢀcaoꢀtuyÖtꢀ®èiꢀng−êiꢀtaꢀph¶iꢀ®oꢀnèiꢀ®éꢀcaoꢀ
(®−îcꢀtr×nhꢀꢀbꢁyꢀtrongꢀch−¬ngꢀ2ꢀcñaꢀgi¸oꢀtr×nhꢀnꢁy).ꢀ
1.4.4.ꢀChªnhꢀcaoꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀChªnhꢀcaoꢀlꢁꢀhiÖuꢀ®éꢀcaoꢀcñaꢀ2ꢀ®iÓm.ꢀ ꢀ
Gi¶ꢀsöꢀ®iÓmꢀAꢀcãꢀ®éꢀcaoꢀlꢁꢀHA,ꢀ®iÓmꢀBꢀcãꢀ
®éꢀ caoꢀ lꢁꢀ HBꢀ (h×nhꢀ 1.2).ꢀ Chªnhꢀ caoꢀ cñaꢀ 2ꢀ
®iÓmꢀAꢀvꢁꢀBꢀlꢁ:ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀhABꢀ=ꢀHBꢀꢂꢀHAꢀ
ꢀ
H×nhꢀ1.2ꢀ
ꢀ
NÕuꢀ®éꢀcaoꢀ®iÓmꢀBꢀlínꢀh¬nꢀ®éꢀcaoꢀcñaꢀ®iÓmꢀAꢀth×ꢀhABꢀ>ꢀ0ꢀ
ꢀ
ꢀ
ꢀ
NÕuꢀ®éꢀcaoꢀcñaꢀ®iÓmꢀBꢀnháꢀh¬nꢀ®éꢀcaoꢀcñaꢀ®iÓmꢀAꢀth×ꢀhABꢀ<ꢀ0ꢀ
Nh−ꢀvËyꢀchªnhꢀcaoꢀcãꢀdÊu.ꢀ
KhiꢀbiÕtꢀ®éꢀcaoꢀcñaꢀ®iÓmꢀAꢀlꢁꢀHA,ꢀbiÕtꢀchªnhꢀcaoꢀhABꢀtaꢀcãꢀthÓꢀtÝnhꢀ®−îcꢀ®éꢀcaoꢀcñaꢀ
®iÓmꢀBꢀlꢁ:ꢀ
ꢀ
ꢀ
ꢀ
HBꢀ=ꢀHAꢀ+ꢀhABꢀ
ChªnhꢀcaoꢀhABꢀ®−îcꢀx¸cꢀ®Þnhꢀꢀb»ngꢀnhiÒuꢀph−¬ngꢀph¸pꢀkh¸cꢀnhau:ꢀph−¬ngꢀph¸pꢀ®oꢀcaoꢀ
h×nhꢀ häc,ꢀph−¬ngꢀ ph¸pꢀ®oꢀ caoꢀl−îngꢀgi¸c,ꢀph−¬ngꢀ ph¸pꢀ ®oꢀcaoꢀb»ngꢀ thiÕtꢀ bÞꢀ GPSꢀ(Globalꢀ
PositioningꢀSystem)...ꢀ(®−îcꢀtr×nhꢀbꢁyꢀëꢀch−¬ngꢀ2).ꢀ
1.5.ꢀB×nhꢀ®é,ꢀb¶nꢀ®åꢀvꢁꢀmÆtꢀc¾tꢀ
1.5.1.ꢀB×nhꢀ®åꢀ
ꢀ
B×nhꢀ®åꢀlꢁꢀh×nhꢀchiÕuꢀthuꢀnháꢀcñaꢀ1ꢀphÇnꢀnháꢀbÒꢀmÆtꢀtr¸iꢀ®ÊtꢀlªnꢀgiÊyꢀtheoꢀmétꢀtûꢀlÖꢀ
nhÊtꢀ®Þnhꢀ(kh«ngꢀtÝnhꢀ®Õnꢀ¶nhꢀh−ëngꢀ®éꢀcongꢀcñaꢀꢀbÒꢀmÆtꢀtr¸iꢀ®Êt).ꢀ
10ꢀ
ꢀ
ꢀ
Nh−ꢀtaꢀ®ꢃꢀbiÕtꢀ®Óꢀphôcꢀvôꢀc¸cꢀmôcꢀ®Ýchꢀkh¸cꢀnhau.ꢀVÝꢀdôꢀkhiꢀcÇnꢀkh¶oꢀs¸t,ꢀthiÕtꢀkÕꢀ
métꢀkhuꢀvùcꢀnháꢀng−êiꢀtaꢀcÇnꢀbiÓuꢀdiÔnꢀc¸cꢀyÕuꢀtèꢀ(nh−ꢀ®Þaꢀh×nh,ꢀ®ÞaꢀvËt)ꢀlªnꢀtrªnꢀgiÊyꢀtheoꢀ
métꢀtûꢀlÖꢀnhÊtꢀ®Þnh.ꢀKhiꢀ®ãꢀng−êiꢀtaꢀcoiꢀbÒꢀmÆtꢀtr¸iꢀ®Êtꢀtrongꢀkhuꢀvùcꢀ®oꢀvÏꢀlꢁꢀph¼ng.ꢀC¸cꢀyÕuꢀ
tèꢀ®oꢀ®¹cꢀ(chiÒuꢀdꢁi,ꢀgãc...)ꢀ®−îcꢀx¸cꢀ®Þnhꢀcoiꢀnh−ꢀx¸cꢀ®ÞnhꢀtrªnꢀmÆtꢀph¼ngꢀvꢁꢀkhiꢀbiÓuꢀdiÔnꢀ
chóngꢀcòngꢀ®−îcꢀtiÕnꢀhꢁnhꢀtrªnꢀmÆtꢀph¼ng,ꢀv×ꢀvËyꢀkh«ngꢀcãꢀsùꢀbiÕnꢀd¹ng.ꢀC¸cꢀyÕuꢀtèꢀ®−îcꢀ
biÓuꢀthÞꢀtheoꢀmétꢀtûꢀlÖꢀnhÊtꢀ®ÞnhꢀgäiꢀlꢁꢀtûꢀlÖꢀb×nhꢀ®å.ꢀTûꢀlÖꢀb×nhꢀ®åꢀth−êngꢀlín:ꢀtûꢀlÖꢀ1:500,ꢀ
1:1000,ꢀ1:2000.ꢀB×nhꢀ®åꢀth−êngꢀbiÓuꢀdiÔnꢀ1ꢀkhuꢀvùcꢀnhá,ꢀëꢀ®ãꢀth−êngꢀkh«ngꢀcãꢀ®iÓmꢀtäaꢀ®é,ꢀ
®éꢀcaoꢀNhꢁꢀn−íc.ꢀTäaꢀ®éꢀvꢁꢀ®éꢀcaoꢀtrªnꢀb×nhꢀ®åꢀth−êngꢀlꢁꢀgi¶ꢀ®Þnh.ꢀThùcꢀtÕꢀchoꢀthÊyꢀmétꢀkhuꢀ
vùcꢀcãꢀdiÖnꢀtÝchꢀkho¶ngꢀ20km2ꢀng−êiꢀtaꢀcãꢀthÓꢀbiÓuꢀdiÔnꢀnãꢀd−íiꢀd¹ngꢀb×nhꢀ®å,ꢀngoꢁiꢀph¹mꢀviꢀ
®ãꢀph¶iꢀbiÓuꢀdiÔnꢀd−íiꢀd¹ngꢀb¶nꢀ®å.ꢀ
1.5.2.ꢀB¶nꢀ®åꢀ
ꢀ
B¶nꢀ®åꢀlꢁꢀh×nhꢀchiÕuꢀthuꢀnháꢀcñaꢀmétꢀphÇnꢀhayꢀtoꢁnꢀbéꢀtr¸iꢀ®ÊtꢀlªnꢀgiÊyꢀtheoꢀmétꢀtûꢀlÖꢀ
nhÊtꢀ®Þnhꢀ(cãꢀtÝnhꢀ®Õnꢀ¶nhꢀh−ëngꢀ®éꢀcongꢀcñaꢀbÒꢀmÆtꢀtr¸iꢀ®Êt).ꢀ
V×ꢀvËyꢀ®iÓmꢀkh¸cꢀnhauꢀc¬ꢀb¶nꢀgi÷aꢀb×nhꢀ®åꢀvꢁꢀb¶nꢀ®åꢀlꢁꢀëꢀchçꢀc¸cꢀyÕuꢀtèꢀ®oꢀ®¹cꢀtrªnꢀ
ꢀ
b×nhꢀ®åꢀ®−îcꢀcoiꢀnh−ꢀ®oꢀtrªnꢀmÆtꢀph¼ngꢀvꢁꢀviÖcꢀꢀbiÓuꢀdiÔnꢀnãꢀcòngꢀ®−îcꢀtiÕnꢀhꢁnhꢀtrªnꢀmÆtꢀ
ph¼ng,ꢀcoiꢀnh−ꢀkh«ngꢀcãꢀsùꢀbiÕnꢀd¹ng.ꢀCßnꢀtrongꢀb¶nꢀ®åꢀc¸cꢀyÕuꢀtèꢀ®oꢀ®¹cꢀ®−îcꢀthùcꢀhiÖnꢀtrªnꢀ
mÆtꢀcong,ꢀkhiꢀbiÓuꢀdiÔnꢀchóngꢀl¹iꢀtiÕnꢀhꢁnhꢀtrªnꢀmÆtꢀph¼ngꢀv×ꢀvËyꢀkh«ngꢀthÓꢀtr¸nhꢀ®−îcꢀsùꢀꢀ
biÕnꢀd¹ng.ꢀDoꢀ®ãꢀng−êiꢀtaꢀph¶iꢀtÝnhꢀto¸nꢀsùꢀbiÕnꢀd¹ngꢀ®ãꢀb»ngꢀc¸chꢀchiÕuꢀc¸cꢀyÕuꢀtèꢀ®oꢀ(khiꢀ
x©yꢀdùngꢀl−íiꢀtäaꢀ®é,ꢀ®éꢀcaoꢀNhꢁꢀn−íc)ꢀlªnꢀmÆtꢀEllipsoidꢀquyꢀchiÕu,ꢀtõꢀmÆtꢀEllipsoidꢀquyꢀ
chiÕuꢀ®−îcꢀchiÕuꢀlªnꢀmÆtꢀph¼ngꢀtrungꢀgianꢀ(mÆtꢀnãnꢀhoÆcꢀmÆtꢀtrô).ꢀTõꢀmÆtꢀtrungꢀgianꢀ®ãꢀtr¶iꢀ
raꢀmÆtꢀph¼ng.ꢀQuaꢀqu¸ꢀtr×nhꢀthùcꢀhiÖnꢀphÐpꢀchiÕuꢀng−êiꢀtaꢀtÝnhꢀto¸nꢀsèꢀhiÖuꢀchØnhꢀvÒꢀgãcꢀvꢁꢀ
chiÒuꢀdꢁi.ꢀHÖꢀthèngꢀtäaꢀ®é,ꢀ®éꢀcaoꢀtrongꢀ®oꢀvÏꢀb¶nꢀ®åꢀ®−îcꢀthèngꢀnhÊtꢀtrongꢀtõngꢀquècꢀgia.ꢀ
B¶nꢀ®åꢀViÖtꢀNamꢀtr−ícꢀ®©yꢀ®−îcꢀthèngꢀnhÊtꢀtrongꢀ1ꢀhÖꢀtäaꢀ®éꢀHNꢂ72,ꢀEllipꢀsoidꢀquyꢀchiÕuꢀlꢁꢀ
EllipsoidꢀKraxovski.ꢀHiÖnꢀnayꢀViÖtꢀNamꢀ®angꢀsöꢀdôngꢀhÖꢀtäaꢀ®éꢀVNꢂ2000,ꢀEllipꢀsoidꢀquyꢀ
chiÕuꢀlꢁꢀEllipꢀsoidꢀW.G.Sꢂ84.ꢀꢀ
ꢀ
B¶nꢀ®åꢀ®−îcꢀchiaꢀlꢁmꢀ2ꢀlo¹iꢀ®ãꢀlꢁꢀb¶nꢀ®åꢀ®Þaꢀlýꢀchungꢀvꢁꢀb¶nꢀ®åꢀchuyªnꢀ®Ò.ꢀTûꢀlÖꢀb¶nꢀ
®åꢀtheoꢀmôcꢀ®Ýchꢀsöꢀdông,ꢀb¶nꢀ®åꢀcãꢀtûꢀlÖꢀ1/200,ꢀ1/500,ꢀ1/1.000,ꢀ1/1.000.000...ꢀ
1.5.3.ꢀMÆtꢀc¾tꢀ®Þaꢀh×nhꢀ
ꢀ
Khiꢀkh¶oꢀs¸tꢀc¸cꢀtuyÕnꢀ®−êngꢀm−¬ngꢀm¸ngꢀngoꢁiꢀb×nhꢀ®åꢀhoÆcꢀb¶nꢀ®åꢀcßnꢀph¶iꢀlËpꢀ
mÆtꢀc¾tꢀdäcꢀvꢁꢀngangꢀtuyÕn.ꢀMÆtꢀc¾tꢀphôcꢀvôꢀchoꢀviÖcꢀthiÕtꢀkÕ,ꢀtÝnhꢀto¸nꢀkhèiꢀl−îngꢀ®ꢁoꢀ®¾p...ꢀ
kh¸cꢀvíiꢀb×nhꢀ®å,ꢀb¶nꢀ®åꢀbiÓuꢀdiÔnꢀmÆtꢀ®ÊtꢀtrªnꢀmÆtꢀph¼ngꢀngang,ꢀcßnꢀmÆtꢀc¾tꢀ®Þaꢀh×nhꢀlꢁꢀh×nhꢀ
chiÕuꢀcñaꢀmÆtꢀc¾tꢀdäcꢀhoÆcꢀngangꢀcñaꢀmétꢀtuyÕnꢀ®Þaꢀh×nhꢀlªnꢀmÆtꢀph¼ngꢀth¼ngꢀ®øngꢀꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
a)ꢀ§Þaꢀh×nhꢀ
b)ꢀMÆtꢀc¾tꢀdäcꢀtuyÕnꢀ
H×nhꢀ1.3ꢀ
11ꢀ
ꢀ
ꢀ
§ÓꢀbiÓuꢀdiÔnꢀ®Þaꢀh×nhꢀb»ngꢀmÆtꢀc¾tꢀdäc,ꢀtaꢀraꢀthùcꢀ®Þaꢀ®ãngꢀc¸cꢀcäcꢀtheoꢀsùꢀthayꢀ®æiꢀ
cñaꢀ®Þaꢀh×nhꢀ(cäcꢀ1,ꢀ2,ꢀ3,ꢀ4,ꢀ5ꢀꢂꢀh×nhꢀ1.3a).ꢀSauꢀ®ãꢀtiÕnꢀhꢁnhꢀ®oꢀ®éꢀcaoꢀvꢁꢀkho¶ngꢀc¸chꢀgi÷aꢀc¸cꢀ
cäc.ꢀTrªnꢀgiÊyꢀkÎꢀliꢀlÊyꢀtrôcꢀth¼ngꢀ®øngꢀlꢁmꢀtrôcꢀ®éꢀcaoꢀ(H),ꢀtrôcꢀn»mꢀlꢁmꢀtrôcꢀkho¶ngꢀc¸chꢀ
ngangꢀtheoꢀtûꢀlÖꢀ®øngꢀvꢁꢀtûꢀlÖꢀngangꢀbiÓuꢀthÞꢀc¸cꢀ®iÓmꢀ1,ꢀ2,ꢀ3,ꢀ4,ꢀ5ꢀ(h×nhꢀ1.3b).ꢀTïyꢀthuécꢀvꢁoꢀ
®éꢀdècꢀ®Þaꢀh×nhꢀchänꢀtûꢀlÖꢀ®øngꢀvꢁꢀngangꢀchoꢀphïꢀhîp.ꢀTh−êngꢀtûꢀlÖꢀ®øngꢀlínꢀh¬nꢀtûꢀlÖꢀngang.ꢀ
VÝꢀdôꢀtûꢀlÖꢀ®øngꢀlꢁꢀ1/500,ꢀtûꢀlÖꢀngangꢀlꢁꢀ1/1000.ꢀ
1.6.ꢀTûꢀlÖꢀb¶nꢀ®å,ꢀ®éꢀchÝnhꢀx¸cꢀcñaꢀtûꢀlÖꢀb¶nꢀ®åꢀ
1.6.1.ꢀTûꢀlÖꢀb¶nꢀ®åꢀ
ꢀ
KhiꢀthꢁnhꢀlËpꢀb¶nꢀ®åꢀ(hoÆcꢀb×nhꢀ®å)ꢀkÕtꢀqu¶ꢀ®oꢀ®¹cꢀ®−îcꢀthuꢀnháꢀl¹iꢀ100,ꢀ1000ꢀlÇnꢀ®Óꢀ
biÓuꢀthÞꢀtrªnꢀgiÊy.ꢀMøcꢀ®éꢀthuꢀnháꢀphôꢀthuécꢀvꢁoꢀdiÖnꢀtÝchꢀkhuꢀvùc,ꢀyªuꢀcÇuꢀmøcꢀ®éꢀchiꢀtiÕtꢀ
cñaꢀ®èiꢀt−îngꢀbiÓuꢀthÞ,ꢀmôcꢀ®Ýchꢀsöꢀdôngꢀb¶nꢀ®å.ꢀMøcꢀ®éꢀthuꢀnháꢀgäiꢀlꢁꢀtûꢀlÖꢀb¶nꢀ®å.ꢀ
ꢀ
TûꢀlÖꢀb¶nꢀ®åꢀlꢁꢀtûꢀsèꢀgi÷aꢀ®o¹nꢀabꢀtrªnꢀb¶nꢀ®åꢀvꢁꢀ®o¹nꢀth¼ngꢀABꢀt−¬ngꢀøngꢀngoꢁiꢀthùcꢀ
®Þa,ꢀkýꢀhiÖuꢀtûꢀlÖꢀb¶nꢀ®åꢀlꢁꢀ1/M.ꢀ
1
ab
ꢀ
ꢀ
ꢀ
ꢀ
=
ꢀ
M
AB
TûꢀlÖꢀb¶nꢀ®åꢀ®−îcꢀbiÓuꢀthÞꢀb»ngꢀph©nꢀsèꢀcãꢀtöꢀsèꢀb»ngꢀ1.ꢀ
1
1
1
1
ꢀ
ꢀ
VÝꢀdô:ꢀB¶nꢀ®åꢀtûꢀlÖꢀ
=
,
=
....ꢀ
M
500
M
1000
Nh−ꢀvËyꢀkhiꢀbiÕtꢀ®−îcꢀchiÒuꢀdꢁiꢀ®o¹nꢀabꢀtrªnꢀb¶nꢀ®å,ꢀchiÒuꢀdꢁiꢀt−¬ngꢀøngꢀABꢀngoꢁiꢀ
thùcꢀ®ÞaꢀtaꢀcãꢀthÓꢀtÝnhꢀ®−îcꢀtûꢀlÖꢀb¶nꢀ®å.ꢀVÝꢀdôꢀ®oꢀtrªnꢀb¶nꢀ®åꢀ®−îcꢀ®o¹nꢀth¼ngꢀabꢀ=ꢀ5cm,ꢀ
chiÒuꢀdꢁiꢀABꢀt−¬ngꢀøngꢀngoꢁiꢀthùcꢀ®ÞaꢀlꢁꢀABꢀ=ꢀ100m.ꢀVËyꢀtûꢀlÖꢀb¶nꢀ®åꢀlꢁ:ꢀ
1
ab 5cm
5cm
M AB 100m 10000cm 2000
TrongꢀthùcꢀtÕꢀkhiꢀbiÕtꢀtûꢀlÖꢀb¶nꢀ®åꢀ1/M,ꢀbiÕtꢀchiÒuꢀdꢁiꢀꢀ®o¹nꢀth¼ngꢀabꢀtrªnꢀb¶nꢀ®åꢀtaꢀcãꢀ
1
ꢀ
ꢀ
=
=
=
=
ꢀ
ꢀ
thÓꢀtÝnhꢀ®−îcꢀchiÒuꢀdꢁiꢀ®o¹nꢀABꢀngoꢁiꢀthùcꢀ®Þaꢀvꢁꢀng−îcꢀl¹i.ꢀ
VÝꢀdôꢀ1:ꢀBiÕtꢀtûꢀlÖꢀb¶nꢀ®åꢀ1/10000ꢀchiÒuꢀdꢁiꢀ®o¹nꢀabꢀlꢁꢀ2cm,ꢀtÝnhꢀchiÒuꢀdꢁiꢀABꢀngoꢁiꢀ
thùcꢀ®Þa.ꢀ
ꢀ
1
ab
ꢀ
Theoꢀ®ÞnhꢀnghÜa:ꢀ
=
ꢀsuyꢀra:ꢀABꢀ=ꢀab.Mꢀꢀ
M
AB
ꢀ
ꢀ
ꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀ=ꢀ2cm.10000ꢀ=ꢀ20000ꢀcmꢀ=ꢀ200m.ꢀ
VÝꢀdôꢀ2:ꢀBiÕtꢀtûꢀlÖꢀb¶nꢀ®åꢀlꢁꢀ1/2000,ꢀ®o¹nꢀABꢀ=ꢀ100m.ꢀHꢃyꢀbiÓuꢀdiÔnꢀ®o¹nꢀABꢀlªnꢀtrªnꢀ
b¶nꢀ®å.ꢀTõꢀ®ÞnhꢀnghÜaꢀtaꢀcã:ꢀ
1
ab
AB 100m 10000cm
=
ꢀ
ꢀ
ꢀ
=
ꢀsuyꢀra;ꢀabꢀ=ꢀ
=
=
5cm
ꢀ
M
AB
M
2000
2000
Nh−ꢀvËyꢀbiÓuꢀdiÔnꢀ®o¹nꢀABꢀngoꢁiꢀthùcꢀ®Þaꢀlªnꢀb¶nꢀ®åꢀtûꢀlÖꢀ1/2000ꢀlꢁꢀ®o¹nꢀabꢀ=ꢀ5cm.ꢀ
12ꢀ
ꢀ
1.6.2.ꢀ§éꢀchÝnhꢀx¸cꢀcñaꢀtûꢀlÖꢀb¶nꢀ®åꢀ
B»ngꢀthùcꢀnghiÖmꢀng−êiꢀtaꢀthÊyꢀr»ngꢀ®èiꢀvíiꢀm¾tꢀng−êiꢀb×nhꢀth−êngꢀ®Óꢀph©nꢀbiÖtꢀ®−îcꢀ
ꢀ
2ꢀ®iÓmꢀëꢀkho¶ngꢀc¸chꢀnh×nꢀlꢁꢀ20cm,ꢀth×ꢀkho¶ngꢀc¸chꢀnháꢀnhÊtꢀgi÷aꢀ2ꢀ®iÓmꢀlꢁꢀ0,1mm.ꢀTõꢀ®ãꢀ
ng−êiꢀtaꢀ®−aꢀraꢀ®ÞnhꢀnghÜaꢀvÒꢀ®éꢀchÝnhꢀx¸cꢀcñaꢀtûꢀlÖꢀb¶nꢀ®å.ꢀ
ꢀ
§éꢀchÝnhꢀx¸cꢀcñaꢀtûꢀlÖꢀb¶nꢀ®åꢀlꢁꢀkho¶ngꢀc¸chꢀngoꢁiꢀthùcꢀ®Þaꢀt−¬ngꢀøngꢀvíiꢀ0,1mmꢀ
theoꢀtûꢀlÖꢀb¶nꢀ®å.ꢀꢀ
ꢀ
ꢀ
VÝꢀdô:ꢀb¶nꢀ®åꢀtûꢀlÖꢀ1:10000ꢀ®éꢀchÝnhꢀx¸cꢀcñaꢀnãꢀlꢁ:ꢀ0,1mmꢀxꢀ10000ꢀ=ꢀ1000mmꢀ=ꢀ1m.ꢀ
VËyꢀ®éꢀchÝnhꢀx¸cꢀcñaꢀb¶nꢀ®åꢀtûꢀlÖꢀ1/10000ꢀlꢁꢀ1m,ꢀt−¬ngꢀtùꢀ®éꢀchÝnhꢀx¸cꢀcñaꢀb¶nꢀ®åꢀtûꢀ
lÖꢀ1/500ꢀlꢁꢀ0,1mmꢀxꢀ500ꢀ=ꢀ50mmꢀ=ꢀ5ꢀcm.ꢀ
Nh−ꢀvËyꢀb¶nꢀ®åꢀcãꢀtûꢀlÖꢀcꢁngꢀlínꢀ®éꢀchÝnhꢀx¸cꢀcꢁngꢀcaoꢀvꢁꢀng−îcꢀl¹i.ꢀNgoꢁiꢀraꢀb¶nꢀ®åꢀ
ꢀ
cãꢀtûꢀlÖꢀcꢁngꢀlínꢀmøcꢀ®éꢀchiꢀtiÕtꢀcꢁngꢀcao,ꢀbiÓuꢀthÞꢀ®−îcꢀvËtꢀcãꢀdiÖnꢀtÝchꢀvïngꢀnhá.ꢀB¶nꢀ®åꢀcãꢀ
tûꢀlÖꢀcꢁngꢀnháꢀtÝnhꢀkh¸iꢀqu¸tꢀvÒꢀ®Þaꢀh×nhꢀvꢁꢀ®ÞaꢀvËtꢀcꢁngꢀcao.ꢀTïyꢀtheoꢀmôcꢀ®Ýchꢀsöꢀdôngꢀmꢁꢀ
ng−êiꢀtaꢀsöꢀdôngꢀb¶nꢀ®åꢀcãꢀtûꢀlÖꢀthÝchꢀhîp.ꢀ
1.7.ꢀTh−ícꢀtûꢀlÖꢀ
ꢀ
§ÓꢀthuËnꢀtiÖnꢀchoꢀviÖcꢀsöꢀdôngꢀb¶nꢀ®åꢀd−íiꢀmçiꢀtêꢀb¶nꢀ®åꢀng−êiꢀtaꢀth−êngꢀdùngꢀth−ícꢀ
tûꢀlÖ.ꢀCãꢀ2ꢀlo¹iꢀth−ícꢀtûꢀlÖꢀlꢁꢀth−ícꢀtûꢀlÖꢀth¼ngꢀvꢁꢀth−ícꢀtûꢀlÖꢀxiªn.ꢀ
1.7.1.ꢀTh−ícꢀtûꢀlÖꢀth¼ngꢀ
ꢀ
ꢀ
Gi¶ꢀsöꢀdùngꢀth−ícꢀtûꢀlÖꢀth¼ngꢀchoꢀb¶nꢀ®åꢀtûꢀlÖꢀ1:5000ꢀ
Trªnꢀ®o¹nꢀth¼ngꢀc¬ꢀb¶nꢀABꢀ=ꢀ2cmꢀt−¬ngꢀøngꢀvíiꢀtûꢀlÖꢀb¶nꢀ®åꢀlꢁꢀ100mꢀngoꢁiꢀthùcꢀ®Þaꢀ
(h×nhꢀ1.4).ꢀTaꢀ®Ætꢀc¸cꢀ®o¹nꢀliªnꢀtiÕpꢀcãꢀ®éꢀdꢁiꢀ2cm,ꢀ4cm,ꢀ6cmꢀtÝnhꢀtõꢀ®iÓmꢀgècꢀ0,ꢀt−¬ngꢀøngꢀ
víiꢀchóngꢀlꢁ:ꢀ100m,ꢀ200mꢀngoꢁiꢀthùcꢀ®Þa.ꢀTrªnꢀ®o¹nꢀc¬ꢀb¶nꢀABꢀtaꢀchiaꢀlꢁmꢀ10ꢀphÇnꢀnháꢀb»ngꢀ
nhau.ꢀNh−ꢀvËyꢀmçiꢀ®o¹nꢀnháꢀcãꢀ®o¹nꢀdꢁiꢀ2mmꢀt−¬ngꢀøngꢀvíiꢀ10mꢀngoꢁiꢀthùcꢀ®Þaꢀ(h×nhꢀ1.4).ꢀ
ꢀ
ꢀ
ꢀ
H×nh1.4ꢀ
ꢀ
ꢀ
C¸chꢀsöꢀdôngꢀth−ícꢀtûꢀlÖꢀth¼ng:ꢀ
Dïngꢀcompaꢀ®oꢀchiÒuꢀdꢁiꢀ®o¹nꢀth¼ngꢀabꢀtrªnꢀb¶nꢀ®åꢀtûꢀlÖꢀ1/5000.ꢀGi÷ꢀnguyªnꢀkhÈuꢀ®éꢀ
compaꢀ−ímꢀvꢁoꢀth−ícꢀ®äcꢀ®−îcꢀgi¸ꢀtrÞꢀthùcꢀ®Þaꢀcñaꢀ®o¹nꢀth¼ngꢀABꢀ=ꢀ240m.ꢀ
1.7.2.ꢀTh−ícꢀtûꢀlÖꢀxiªnꢀ
ꢀ
§Óꢀn©ngꢀcaoꢀ®éꢀchÝnhꢀx¸cꢀx¸cꢀ®ÞnhꢀchiÒuꢀdꢁiꢀtrªnꢀb¶nꢀ®å,ꢀëꢀb¶nꢀ®åꢀtûꢀlÖꢀlínꢀng−êiꢀtaꢀ
th−êngꢀdïngꢀth−ícꢀtûꢀlÖꢀxiªn.ꢀ
ꢀ
1.ꢀC¸chꢀdùngꢀth−ícꢀtûꢀlÖꢀxiªnꢀꢀ
ꢀ
Gi¶ꢀsöꢀcÇnꢀdùngꢀth−ícꢀtûꢀlÖꢀxiªnꢀchoꢀb¶nꢀ®åꢀtûꢀlÖꢀ1/2000.ꢀTrªnꢀnöaꢀ®o¹nꢀth¼ngꢀtaꢀlÊyꢀ
®o¹nꢀc¬ꢀb¶nꢀlꢁꢀABꢀ=ꢀ2cmꢀøngꢀvíiꢀchiÒuꢀdꢁiꢀ40mꢀngoꢁiꢀthùcꢀ®Þa.ꢀB¾tꢀ®Çuꢀtõꢀ0ꢀ®Ætꢀc¸cꢀ®o¹nꢀliªnꢀ
tiÕpꢀcãꢀchiÒuꢀdꢁiꢀlꢁ:ꢀ2cm,ꢀ4cm,ꢀ6cm,ꢀ8cmꢀt−¬ngꢀøngꢀvíiꢀgi¸ꢀtrÞꢀthùcꢀ®Þalꢁꢀ40m,ꢀ80m,ꢀ120m,ꢀ
160mꢀ(h×nhꢀ1.5).ꢀ
13ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
C
ꢀ
Dꢀ
H×nhꢀ1.5ꢀ
Dùngꢀc¸cꢀ«ꢀvu«ngꢀt−¬ngꢀøngꢀcãꢀkÝchꢀth−ícꢀ2ꢀxꢀ2cm,ꢀëꢀ«ꢀvu«ngꢀthøꢀnhÊtꢀchiaꢀc¸cꢀc¹nhꢀ
ꢀ
«ꢀvu«ngꢀthꢁnhꢀc¸cꢀphÇnꢀb»ngꢀnhauꢀ(nꢀ=ꢀ10,ꢀmꢀ=ꢀ10).ꢀTheoꢀchiÒuꢀngangꢀkÎꢀc¸cꢀ®−êngꢀsongꢀ
songꢀvꢁꢀ®Òuꢀnhau.ꢀ
ꢀ
TheoꢀchiÒuꢀ®øngꢀkÎꢀc¸cꢀd−êngꢀxiªnꢀsongꢀsongꢀvꢁꢀ®Òuꢀnhau.ꢀVíiꢀc¸chꢀdùngꢀnh−ꢀtrªnꢀtaꢀ
cãꢀ
∆
IKBꢀ®ångꢀd¹ngꢀvíiꢀ
∆
NOB.ꢀTaꢀcãꢀtûꢀsè.ꢀ
IK BK
=
BK.NO
ꢀ
→ IK =
ꢀ ꢀ
(1.1)ꢀ
(1.2)ꢀ
NO BO
BO
AB
BK
1
mꢁꢀ
=
, NO =
ꢀ
ꢀ
BO
Thayꢀ(1.2)ꢀvꢁoꢀ(1.1)ꢀtaꢀ®−îc:ꢀ
AB 40
n
m
ꢀ
ꢀ
IKꢀ=ꢀ
=
ꢀ=ꢀ0,4mꢀ
m.n 10.10
vꢁꢀc¸cꢀ®o¹nꢀtiÕpꢀtheoꢀcãꢀchiÒuꢀdꢁiꢀt−¬ngꢀøngꢀngoꢁiꢀthùcꢀ®Þaꢀlꢁ:ꢀ0,8m,ꢀ1,2m,ꢀ1,6m,ꢀ2,0m...ꢀ
2.ꢀSöꢀdôngꢀth−ícꢀtûꢀlÖꢀxiªnꢀ
ꢀ
§oꢀtrªnꢀb¶nꢀ®åꢀ®o¹nꢀabꢀb»ngꢀcompa.ꢀGi÷ꢀnguyªnꢀkhÈuꢀ®éꢀcompaꢀ®ãꢀ−ímꢀvꢁoꢀth−ícꢀ
®äcꢀ®−îcꢀchiÒuꢀdꢁiꢀCDꢀngoꢁiꢀthùcꢀ®Þaꢀlꢁ:ꢀꢀ
CDꢀ=ꢀ80mꢀ+ꢀ8mꢀ+ꢀ1,6mꢀ=ꢀ89,6mꢀ
1.8.ꢀPh−¬ngꢀph¸pꢀbiÓuꢀdiÔnꢀ®Þaꢀh×nhꢀb»ngꢀ®−êngꢀ®ångꢀmøcꢀ
Trªnꢀb¶nꢀ®åꢀ®Þaꢀh×nhꢀth−êngꢀthÓꢀhiÖnꢀ2ꢀyÕuꢀtèꢀ®ãꢀlꢁꢀ®Þaꢀh×nhꢀvꢁꢀ®ÞaꢀvËt.ꢀViÖcꢀbiÓuꢀdiÔnꢀ
ꢀ
ꢀ
ꢀ
®Þaꢀh×nhꢀcãꢀthÓꢀ®−îcꢀthùcꢀhiÖnꢀb»ngꢀc¸cꢀph−¬ngꢀph¸p:ꢀph−¬ngꢀph¸pꢀt«ꢀmꢁu,ꢀph−¬ngꢀph¸pꢀkÎꢀ
v©n...ꢀNh−ngꢀth«ngꢀdôngꢀvꢁꢀchÝnhꢀx¸cꢀnhÊtꢀlꢁꢀph−¬ngꢀph¸pꢀbiÓuꢀdiÔnꢀ®Þaꢀh×nhꢀb»ngꢀ®−êngꢀ
®ångꢀmøcꢀ(®−êngꢀb×nhꢀ®é,ꢀ®−êngꢀ®¼ngꢀcao).ꢀ
ꢀ
Gi¶ꢀsöꢀcãꢀ®Þaꢀh×nhꢀ(métꢀqu¶ꢀ®åi).ꢀTaꢀt−ëngꢀt−îngꢀdïngꢀc¸cꢀmÆtꢀph¼ngꢀE1,ꢀE2,ꢀE3ꢀ(c¸cꢀ
mÆtꢀph¼ngꢀnꢁyꢀsongꢀsongꢀvíiꢀmÆtꢀthñyꢀchuÈn)ꢀc¾tꢀqu¶ꢀ®åiꢀtheoꢀc¸cꢀmÆtꢀph¼ngꢀngangꢀ®ã.ꢀC¸cꢀ
mÆtꢀph¼ngꢀnꢁyꢀc¸chꢀ®Òuꢀnhauꢀmétꢀkho¶ngꢀlꢁꢀhꢀ(h×nhꢀ1.6).ꢀC¸cꢀvÕtꢀc¾tꢀnhËnꢀ®−îcꢀ®−îcꢀchiÕuꢀ
th¼ngꢀ®øngꢀxuèngꢀmÆtꢀph¼ngꢀngangꢀE.ꢀH×nhꢀchiÒuꢀcñaꢀchóngꢀlꢁꢀc¸cꢀ®−êngꢀcongꢀkhÐpꢀkÝnꢀ
®−îcꢀgäiꢀlꢁꢀ®−êngꢀ®ångꢀmøcꢀ(®−êngꢀb×nhꢀ®é)ꢀhꢀ®−îcꢀgäiꢀlꢁꢀkho¶ngꢀcaoꢀ®Òuꢀcñaꢀ®−êngꢀ®ångꢀ
møc.ꢀCãꢀ3ꢀlo¹iꢀ®−êngꢀ®ångꢀmøc:ꢀ
ꢀ
ꢀ
§−êngꢀ®ångꢀmøcꢀcon,ꢀ®−êngꢀ®ångꢀꢀmøcꢀc¸iꢀvꢁꢀ®−êngꢀ®ångꢀmøcꢀphô.ꢀ
ꢀ
14ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
H×nhꢀ1.6ꢀ
ꢀ
§−êngꢀ ®ångꢀ møcꢀ con:ꢀ ꢀ Lꢁꢀ ®−êngꢀ ®ångꢀ møcꢀ biÓuꢀ thÞꢀ b»ngꢀ nÐtꢀ nháꢀ vꢁꢀ trªnꢀ ®ãꢀ
kh«ngꢀghiꢀ®éꢀcao.ꢀ
§−êngꢀ®ångꢀmøcꢀc¸i:ꢀLꢁꢀ®−êngꢀ®ångꢀmøcꢀbiÓuꢀ thÞꢀ b»ngꢀnÐtꢀlínꢀh¬nꢀ®−êngꢀ®ångꢀ
møcꢀconꢀvꢁꢀtrªnꢀnãꢀcãꢀghiꢀ®éꢀcao.ꢀ
§−êngꢀ®ångꢀmøcꢀphô:ꢀëꢀvïngꢀ®ångꢀb»ngꢀ®Þaꢀh×nhꢀb»ngꢀph¼ngꢀv×ꢀvËyꢀkho¶ngꢀc¸chꢀ
ꢀ
ꢀ
ꢀ
gi÷aꢀc¸cꢀ®−êngꢀ®ångꢀmøcꢀlín,ꢀ®Óꢀnéiꢀsuyꢀc¸cꢀ®iÓmꢀ®éꢀcaoꢀtrªnꢀb¶nꢀ®åꢀ®−îcꢀdÔꢀdꢁngꢀgi÷aꢀ2ꢀ
®−êngꢀ®ångꢀmøcꢀconꢀngoꢁiꢀraꢀkÎꢀthªmꢀmétꢀ®−êngꢀ®ångꢀmøcꢀphô,ꢀ®−êngꢀ®ångꢀmøcꢀphôꢀ®−îcꢀ
thÓꢀhiÖnꢀb»ngꢀnÐtꢀ®øtꢀtrªnꢀ®ãꢀkh«ngꢀghiꢀ®éꢀcao.ꢀ
1.ꢀC¸cꢀtÝnhꢀchÊtꢀcñaꢀ®−êngꢀ®ångꢀmøc:ꢀ
ꢀ
ꢀ
ꢀ
ꢂꢀC¸cꢀ®iÓmꢀn»mꢀtrªnꢀcïngꢀmétꢀ®−êngꢀ®ångꢀmøcꢀcãꢀcïngꢀ®éꢀcaoꢀngoꢁiꢀthùcꢀ®Þa.ꢀ
ꢂꢀC¸cꢀ®−êngꢀ®ångꢀmøcꢀlꢁꢀc¸cꢀ®−êngꢀcongꢀtr¬nꢀtru,ꢀliªnꢀtôcꢀkhÐpꢀkÝn.ꢀ
ꢂꢀN¬iꢀnꢁoꢀcãꢀ®−êngꢀ®ångꢀmøcꢀcꢁngꢀth−aꢀth×ꢀ®Þaꢀh×nhꢀcꢁngꢀtho¶iꢀvꢁꢀng−îcꢀl¹iꢀ®−êngꢀ
®ångꢀmøcꢀcꢁngꢀmauꢀ®Þaꢀh×nhꢀcꢁngꢀdèc.ꢀNÕuꢀchóngꢀtrïngꢀnhauꢀth×ꢀëꢀ®ãꢀcãꢀv¸chꢀ®øng.ꢀ
ꢀ
ꢀ
ꢂꢀC¸cꢀ®−êngꢀ®ångꢀmøcꢀkh«ngꢀbaoꢀgiêꢀc¾tꢀnhauꢀ(trõꢀtr−êngꢀhîpꢀ®Þaꢀh×nhꢀhꢁmꢀÕch).ꢀ
Nh÷ngꢀyÕuꢀtèꢀ®Þaꢀh×nhꢀkh«ngꢀbiÓuꢀthÞꢀ®−îcꢀb»ngꢀc¸cꢀ®−êngꢀ®ångꢀmøcꢀnh−ꢀv¸chꢀnói,ꢀ
bêꢀm−¬ngꢀ®−îcꢀdïngꢀkýꢀhiÖuꢀkh¸cꢀ®ÓꢀbiÓuꢀthÞꢀ.ꢀ§Óꢀph©nꢀbiÖtꢀgi÷aꢀnóiꢀvꢁꢀhåꢀng−êiꢀtaꢀth−êngꢀ
dïngꢀkýꢀhiÖuꢀnÐtꢀchØꢀh−íngꢀdècꢀhoÆcꢀghiꢀchóꢀ®éꢀcaoꢀ®Þaꢀh×nh.ꢀ
ꢀ
ꢂꢀKho¶ngꢀc¸chꢀng¾nꢀnhÊtꢀgi÷aꢀ2ꢀ®−êngꢀ®ångꢀmøcꢀlꢁꢀ®o¹nꢀvu«ngꢀgãcꢀt¹iꢀchçꢀdècꢀnhÊt.ꢀ
15ꢀ
ꢀ
2.ꢀNguyªnꢀt¾cꢀchänꢀkho¶ngꢀcaoꢀ®Òuꢀcu¶ꢀ®−êngꢀ®ångꢀmøcꢀ
Chªnhꢀꢀcaoꢀgi÷aꢀ2ꢀ®−êngꢀ®ångꢀmøcꢀkÒꢀnhauꢀgäiꢀlꢁꢀkho¶ngꢀcaoꢀ®Òu,ꢀkýꢀhiÖuꢀlꢁꢀh.ꢀViÖcꢀ
ꢀ
chänꢀhꢀph¶iꢀ®¶mꢀb¶oꢀtÝnhꢀkinhꢀtÕ,ꢀküꢀthuËt.ꢀTrÞꢀsèꢀhꢀcꢁngꢀnháꢀth×ꢀmøcꢀ®éꢀbiÓuꢀthÞꢀ®Þaꢀh×nhꢀtrªnꢀ
b¶nꢀ®åꢀcꢁngꢀchÝnhꢀx¸c.ꢀTuyꢀnhiªnꢀ®ßiꢀháiꢀkhèiꢀl−îngꢀ®oꢀ®¹cꢀngoꢁiꢀthùcꢀ®ÞaꢀcꢁngꢀnhiÒuꢀvꢁꢀgi¸ꢀ
thꢁnhꢀcꢁngꢀcao.ꢀNgoꢁiꢀraꢀtrÞꢀsèꢀhꢀcßnꢀphôꢀthuécꢀvꢁoꢀ®éꢀdècꢀ®Þaꢀh×nhꢀkhiꢀ®o.ꢀTûꢀlÖꢀb¶nꢀ®åꢀnháꢀ
®éꢀdècꢀ®Þaꢀh×nhꢀlínꢀth×ꢀkh«ngꢀthÓꢀbiÓnꢀthÞꢀc¸cꢀ®−êngꢀ®ångꢀmøcꢀvíiꢀkho¶ngꢀcaoꢀ®Òuꢀnháꢀ®−îcꢀ
v×ꢀkhiꢀ®ãꢀc¸cꢀ®−êngꢀ®ångꢀmøcꢀsÏꢀchångꢀlªnꢀnhau.ꢀChoꢀnªnꢀviÖcꢀtÝnhꢀto¸nꢀkho¶ngꢀcaoꢀ®Òuꢀcñaꢀ
®−êngꢀ®ångꢀmøcꢀph¶iꢀdùaꢀvꢁoꢀ2ꢀyÕuꢀtèꢀ®ãꢀlꢁ:ꢀ®éꢀdècꢀ®Þaꢀh×nhꢀvꢁꢀtûꢀlÖꢀb¶nꢀ®å.ꢀTrongꢀthùcꢀtÕꢀ
kho¶ngꢀcaoꢀ®Òuꢀcñaꢀ®−êngꢀ®ångꢀmøcꢀ®−îcꢀquyꢀ®ÞnhꢀcôꢀthÓꢀtrongꢀquyꢀph¹mꢀ®oꢀvÏꢀb¶nꢀ®åꢀ®Þaꢀ
h×nhꢀ(b¶ngꢀ2.2).ꢀ
B¶ngꢀ2.2ꢀ
Kho¶ngꢀcaoꢀ®Õnꢀhꢀ(m)ꢀ
§Þaꢀh×nhꢀ
1:500ꢀ
1:2000ꢀ
1:ꢀ10000ꢀ
2,0ꢀ
Vïngꢀb»ngꢀph¼ngꢀ(®éꢀdècꢀvꢀ<ꢀ20)ꢀ
Vïngꢀ®åiꢀ(2o<V<ꢀ6o)ꢀ
0,5ꢀ
1,0ꢀ
1,0ꢀ
2,5ꢀ
5,0ꢀ
Vïngꢀnóiꢀ(Vꢀ>ꢀ150)ꢀ
1,0ꢀ
5,0ꢀ
5,0ꢀ
1.9.ꢀKýꢀhiÖuꢀquyꢀ−ícꢀcñaꢀb¶nꢀ®åꢀ
ꢀ
Trªnꢀb¶nꢀ®åꢀ®Þaꢀh×nhꢀ(hoÆcꢀ®ÞaꢀchÝnh)ꢀth−êngꢀbiÓuꢀthÞꢀ2ꢀyÕuꢀtèꢀ®ãꢀlꢁ:ꢀ®Þaꢀh×nhꢀvꢁꢀ®Þaꢀ
vËt.ꢀ§Þaꢀh×nhꢀ®−îcꢀbiÓuꢀthÞꢀb»ngꢀ®éꢀcaoꢀ®iÓmꢀhoÆcꢀb»ngꢀ®−êngꢀ®ångꢀmøc.ꢀ
C¸cꢀyÕuꢀtèꢀ®ÞaꢀvËtꢀ®−îcꢀbiÓuꢀthÞꢀtrªnꢀb¶nꢀ®åꢀb»ngꢀc¸cꢀph−¬ngꢀph¸pꢀkh¸cꢀnhauꢀ®èiꢀvíiꢀ
ꢀ
®ÞaꢀvËtꢀcãꢀkÝchꢀth−ícꢀlínꢀnh−ꢀs«ng,ꢀhå,ꢀ®−êngꢀquècꢀlé,ꢀkhuꢀc«ngꢀnghiÖp...ꢀth×ꢀph¶iꢀbiÓuꢀthÞꢀ
®óngꢀvÞꢀtrÝ,ꢀkÝchꢀth−ícꢀcñaꢀnãꢀtheoꢀtûꢀlÖꢀb¶nꢀ®å.ꢀTøcꢀlꢁꢀchóngꢀ®−îcꢀbiÓuꢀthÞꢀtheoꢀtäaꢀ®éꢀph¼ngꢀ
(x,ꢀy)ꢀhoÆcꢀtheoꢀtäaꢀ®éꢀcùcꢀ(B,ꢀS).ꢀKhiꢀx¸cꢀ®Þnhꢀnãꢀtrªnꢀb¶nꢀ®åꢀtheoꢀtûꢀlÖꢀtaꢀcãꢀthÓꢀtÝnhꢀ®−îcꢀ
kÝchꢀth−íc,ꢀdiÖnꢀtÝchꢀcñaꢀchóngꢀngoꢁiꢀthùcꢀ®Þaꢀvꢁꢀc¸chꢀbiÓuꢀthÞꢀnh−ꢀvËyꢀ®−îcꢀgäiꢀlꢁꢀbiÓuꢀdiÔnꢀ
®ÞaꢀvËtꢀtheoꢀtûꢀlÖ.ꢀ
ꢀ
§èiꢀvíiꢀvËtꢀcãꢀkÝchꢀth−ícꢀnháꢀmꢁꢀkh«ngꢀthÓꢀbiÓuꢀdiÔnꢀnãꢀtheoꢀtûꢀlÖꢀ®−îcꢀng−êiꢀtaꢀbiÓuꢀ
thÞꢀphiꢀtûꢀlÖ.ꢀVÝꢀdô:ꢀgiÕngꢀn−íc,ꢀcétꢀ®iÖn,ꢀ®−êngꢀmßn,ꢀ®Þaꢀgiíi....ꢀkhiꢀ®ãꢀng−êiꢀtaꢀx¸cꢀ®Þnhꢀ
chÝnhꢀx¸cꢀt©mꢀcñaꢀnãꢀvꢁꢀdïngꢀkýꢀhiÖuꢀquyꢀ−ícꢀ®ÓꢀbiÓuꢀthÞ.ꢀC¸cꢀkýꢀhiÖuꢀquyꢀ−ícꢀ®−îcꢀtr×nhꢀbꢁyꢀ
râꢀtrongꢀcuènꢀ"KýꢀhiÖuꢀb¶nꢀ®åꢀ®Þaꢀh×nh"ꢀhoÆcꢀcuènꢀ"kýꢀhiÖuꢀb¶nꢀ®åꢀ®ÞaꢀchÝnh".ꢀC¸cꢀkýꢀhiÖuꢀ
quyꢀ−ícꢀnꢁyꢀ®−îcꢀx©yꢀdùngꢀtrªnꢀc¬ꢀsëꢀkhoaꢀhäc.ꢀTøcꢀlꢁꢀkhiꢀnh×nꢀvꢁoꢀkýꢀhiÖuꢀng−êiꢀtaꢀliªnꢀ
t−ëngꢀ®Õnꢀ®ÞaꢀvËtꢀcãꢀh×nhꢀd¹ngꢀt−¬ngꢀtù.ꢀ§iÒuꢀ®ãꢀgiópꢀchoꢀng−êiꢀdïngꢀdÔꢀnhí,ꢀdÔꢀsöꢀdông.ꢀ
ꢀ
Ngoꢁiꢀraꢀ®ÓꢀthÓꢀhiÖnꢀnéiꢀdungꢀcñaꢀ®ÞaꢀvËtꢀcßnꢀph¶iꢀghiꢀchóꢀb»ngꢀch÷ꢀhoÆcꢀb»ngꢀsèꢀnh−ꢀ
®Þaꢀdanhꢀlꢁng,ꢀxꢃ,ꢀtªnꢀs«ngꢀnói,ꢀ®éꢀs©uꢀlßngꢀhå,ꢀh−íngꢀdßngꢀch¶y...ꢀTuyꢀnhiªnꢀc¸cꢀghiꢀchóꢀ
còngꢀcÇnꢀtu©nꢀtheoꢀc¸cꢀquyꢀ®Þnhꢀsau:ꢀ
ꢀ
Ch÷ꢀghiꢀchóꢀtrªnꢀb×nhꢀ®å,ꢀb¶nꢀ®åꢀph¶iꢀviÕtꢀsongꢀsongꢀvíiꢀc¹nhꢀkhungꢀtrªnꢀhoÆcꢀd−íi.ꢀ
Tªnꢀgäiꢀcñaꢀs«ng,ꢀsuèi,ꢀmámꢀnóiꢀcÇnꢀviÕtꢀdäcꢀtheoꢀh−ãngꢀcñaꢀchóng,ꢀ®éꢀcaoꢀcñaꢀ®−êngꢀ®ångꢀ
møcꢀ®−îcꢀghiꢀëꢀchçꢀng¾tꢀquꢃngꢀvꢁꢀ®Çuꢀch÷ꢀ®−îcꢀquayꢀlªnꢀphÝaꢀcao.ꢀKhiꢀthꢁnhꢀlËpꢀb×nhꢀ®åꢀhoÆcꢀ
b¶nꢀ®åꢀcÇnꢀtu©nꢀtheoꢀc¸cꢀquyꢀ®Þnhꢀtïyꢀtheoꢀlo¹iꢀb¶nꢀ®åꢀ(b¶nꢀ®åꢀ®ÞaꢀchÝnhꢀhoÆcꢀb¶nꢀ®åꢀ®Þaꢀh×nh).ꢀ
16ꢀ
ꢀ
1.10.ꢀC¸cꢀhÖꢀtäaꢀ®éꢀth−êngꢀdïngꢀtrongꢀtr¾cꢀ®Þaꢀ
§Óꢀx¸cꢀ®ÞnhꢀvÞꢀtrÝꢀmétꢀ®iÓmꢀtrªnꢀmÆtꢀ®Êtꢀtrongꢀtr¾cꢀ®Þaꢀng−êiꢀtaꢀth−êngꢀdïngꢀnhiÒuꢀhÖꢀ
ꢀ
täaꢀ®éꢀkh¸cꢀnhau.ꢀHÖꢀtäaꢀ®éꢀ®Þaꢀlý,ꢀhÖꢀtäaꢀ®éꢀtr¾cꢀ®Þa,ꢀhÖꢀtäaꢀ®éꢀvu«ngꢀgãcꢀph¼ngꢀGaussꢀꢂꢀ
Kruger,ꢀhÖꢀtäaꢀ®éꢀUTM.ꢀ
ꢀ
Trongꢀgi¸oꢀtr×nhꢀnꢁy,ꢀchóngꢀtaꢀxÐtꢀhÖꢀtäaꢀ®éꢀth−êngꢀdïngꢀtrongꢀtr¾cꢀ®Þaꢀthùcꢀhꢁnh.ꢀ
1.10.1.ꢀHÖꢀtäaꢀ®éꢀ®Þaꢀlýꢀ
ꢀ
ꢀ
HÖꢀtäaꢀ®éꢀ®Þaꢀlýꢀcßnꢀ®−îcꢀgäiꢀlꢁꢀhÖꢀtäaꢀ®éꢀthiªnꢀv¨n.ꢀ
Täaꢀ®éꢀ®Þaꢀlýꢀcñaꢀmétꢀ®iÓmꢀtrªnꢀmÆtꢀ®Êtꢀ®−îcꢀx¸cꢀ®ÞnhꢀbëiꢀkinhꢀvꢁꢀvÜꢀ®éꢀ®Þaꢀlýꢀvꢁꢀ®−îcꢀ
®ÞnhꢀnghÜa:ꢀ
ꢀ
VÜꢀ®éꢀ®Þaꢀlý:ꢀvÜꢀ®éꢀ®Þaꢀlýꢀcñaꢀmétꢀ®iÓmꢀ
λ
ꢀ
lꢁꢀgãcꢀhîpꢀbëiꢀ®−êngꢀd©yꢀdäiꢀ®iꢀquaꢀ®iÓmꢀ®ãꢀ
vꢁꢀmÆtꢀph¼ngꢀxÝchꢀ®¹o.ꢀVÜꢀ®éꢀ®Þaꢀlýꢀ®−îcꢀkýꢀ
hiÖuꢀlꢁꢀ
ϕ
.ꢀꢀ
ϕ
vꢁꢀNamꢀtÝnhꢀtõꢀxÝchꢀ®¹oꢀ(h×nhꢀ1.7).ꢀꢀ
ꢀbiÕnꢀ®æiꢀtõꢀꢀOꢀ
ꢀ90oꢀvÒꢀ2ꢀphÝaꢀB¾cꢀ
÷
ϕ
ꢀ
ꢀ
ꢀ
Kinhꢀ®éꢀ®Þaꢀlý:ꢀ
Kinhꢀ®éꢀ®Þaꢀlýꢀcñaꢀmétꢀ®iÓmꢀlꢁꢀgãcꢀnhÞꢀ
diÖnꢀhîpꢀbëiꢀmÆtꢀph¼ngꢀkinhꢀtuyÕnꢀgècꢀvꢁꢀmÆtꢀ
ph¼ngꢀkinhꢀtuyÕnꢀ®iꢀquaꢀ®iÓmꢀ®ã,ꢀkinhꢀ®éꢀ®Þaꢀ
lýꢀ®−îcꢀkýꢀhiÖuꢀlꢁꢀ
2ꢀphÝaꢀ§«ngꢀvꢁꢀT©yꢀtÝnhꢀtõꢀkinhꢀtuyÕnꢀgèc(2*).ꢀ
NÕuꢀ®iÓmꢀ®ãꢀn»mꢀphÝaꢀ§«ngꢀkinhꢀtuyÕnꢀgècꢀth×ꢀ®iÓmꢀ®ãꢀcãꢀkinhꢀ®éꢀ§«ng.ꢀNÕuꢀ®iÓmꢀ
λ.ꢀꢀ
λꢀbiÕnꢀ®æiꢀtõꢀ0ꢀ
÷
ꢀ180oꢀvÒꢀ
H×nhꢀ1.7ꢀ
ꢀ
®ãꢀn»mꢀëꢀphÝaꢀT©yꢀkinhꢀtuyÕnꢀgècꢀth×ꢀ®iÓmꢀcãꢀkinhꢀ®éꢀT©y.ꢀTäaꢀ®éꢀ®Þaꢀlýꢀcñaꢀ1ꢀ®iÓmꢀcãꢀthÓꢀ®oꢀ
trªnꢀb¶nꢀ®åꢀhoÆcꢀx¸cꢀ®ÞnhꢀtrùcꢀtiÕpꢀngoꢁiꢀthùcꢀ®Þaꢀb»ngꢀviÖcꢀ"®oꢀthiªnꢀv¨n".ꢀ
ꢀ
ViÖtꢀNamꢀhoꢁnꢀtoꢁnꢀn»mꢀëꢀphÝaꢀB¾cꢀb¸nꢀcÇuꢀvꢁꢀphÝaꢀ§«ngꢀkinhꢀtuyÕnꢀGreenwichꢀchoꢀ
nªnꢀtoꢁnꢀbéꢀlꢃnhꢀthæꢀViÖtꢀNamꢀ®ÒuꢀcãꢀvÜꢀ®éꢀB¾cꢀvꢁꢀkinhꢀ®éꢀ§«ng.ꢀ
ꢀ
ꢀ
ꢀ
VÝꢀdô:ꢀCétꢀcêꢀHꢁꢀNéiꢀcãꢀtäaꢀ®éꢀ®Þaꢀlýꢀlꢁ:ꢀ
ꢀ=ꢀ21002'B,ꢀ =ꢀ105o50'§ꢀ
Trªnꢀc¸cꢀtêꢀb¶nꢀ®åꢀ®Þaꢀh×nhꢀth−êngꢀbiÓuꢀthÞꢀl−íiꢀkinhꢀvÜꢀtuyÕnꢀvꢁꢀtäaꢀ®éꢀ®Þaꢀlýꢀcñaꢀc¸cꢀ
ꢀ
ϕ
λ
gãcꢀkhungꢀcñaꢀtêꢀb¶nꢀ®å.ꢀChªnhꢀlÖchꢀvÜꢀ®éꢀvꢁꢀkinhꢀ®éꢀcñaꢀgãcꢀkhungꢀlꢁ:ꢀ
ꢀ
ꢀ
∆ϕꢀ=ꢀ
ϕ
Nꢀꢂꢀ
ϕ
M,ꢀꢀꢀ
∆
λꢀ=ꢀ
λ
Nꢀꢂꢀ
λ
Mꢀ
TõꢀsùꢀchªnhꢀlÖchꢀ®ãꢀvꢁꢀtäaꢀ®éꢀcñaꢀc¸cꢀgãcꢀkhungꢀb¶nꢀ®åꢀtaꢀcãꢀthÓꢀx¸cꢀ®Þnhꢀ®−îcꢀtäaꢀ®éꢀ
®ÞaꢀlýꢀcñaꢀbÊtꢀkúꢀ®iÓmꢀnꢁoꢀtrªnꢀb¶nꢀ®å.ꢀ
1.10.2.ꢀHÖꢀtäaꢀ®éꢀvu«ngꢀgãcꢀGaussꢀꢂꢀKrugerꢀ
ꢀ
TõꢀthÕꢀkûꢀ19ꢀnhꢁꢀto¸nꢀhäcꢀK.F.ꢀGaussꢀ®ꢃꢀ®−aꢀraꢀphÐpꢀchiÕuꢀh×nhꢀb¶nꢀ®åꢀvꢁꢀsauꢀ®ãꢀ®−îcꢀ
KrugerꢀhoꢁnꢀthiÖn.ꢀV×ꢀvËyꢀgäiꢀlꢁꢀphÐpꢀchiÕuꢀGaussꢀꢂꢀKruger.ꢀPhÐpꢀchiÕuꢀ®−îcꢀm«ꢀt¶ꢀnh−ꢀsau:ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
2ꢀKinhꢀtuyÕnꢀgècꢀlꢁꢀkinhꢀtuyÕnꢀ®iꢀquaꢀ®Çuꢀthiªnꢀv¨nꢀGreenwichꢀꢂꢀLu©nꢀ§«nꢀ
17ꢀ
ꢀ
ꢀ
Ng−êiꢀtaꢀchiaꢀqu¶ꢀ®Êtꢀthꢁnhꢀ60ꢀmói,ꢀhoÆcꢀ120ꢀmói,ꢀmçiꢀmóiꢀlꢁꢀ6oꢀhoÆcꢀ3oꢀ®¸nhꢀ®Êuꢀ
theoꢀthøꢀtùꢀtõꢀT©yꢀsangꢀ§«ngꢀtÝnhꢀtõꢀkinhꢀtuyÕnꢀgèc.ꢀMçiꢀmóiꢀ®−îcꢀchiaꢀthꢁnhꢀ2ꢀphÇnꢀ®Òuꢀ
nhauꢀbëiꢀkinhꢀtuyÕnꢀgi÷aꢀmóiꢀgäiꢀlꢁꢀkinhꢀtuyÕnꢀtrôc.ꢀTõꢀt©mꢀOꢀcñaꢀqu¶ꢀ®ÊtꢀchiÕuꢀlªnꢀmÆtꢀtrôꢀ
sauꢀ®ãꢀc¾tꢀmÆtꢀtrôꢀtheoꢀ®−êngꢀsinhꢀvꢁꢀtr¶iꢀraꢀmÆtꢀph¼ng.ꢀMÆtꢀph¼ngꢀnꢁyꢀgäiꢀlꢁꢀmÆtꢀph¼ngꢀchiÕuꢀ
h×nhꢀGauss.ꢀ
ꢀ
HÖꢀtäaꢀ®éꢀ®−îcꢀx©yꢀdùngꢀtrªnꢀmÆtꢀph¼ngꢀcñaꢀmóiꢀchiÕuꢀ6oꢀtrongꢀmÆtꢀph¼ngꢀchiÕuꢀh×nhꢀ
Gaussꢀ®−îcꢀgäiꢀlꢁꢀhÖꢀtäaꢀ®éꢀGaussꢂꢀKruger.ꢀTrongꢀ®ãꢀnhËnꢀh×nhꢀchiÕuꢀcñaꢀkinhꢀtuyÕnꢀtrôcꢀlꢁmꢀ
trôcꢀX,ꢀcñaꢀxÝchꢀ®¹oꢀlꢁmꢀtrôcꢀY.ꢀNh−ꢀvËyꢀnÕuꢀtÝnhꢀtõꢀgècꢀvÒꢀphÝaꢀB¾cꢀxꢀlu«nꢀlu«nꢀmangꢀdÊuꢀ
d−¬ng,ꢀvÒꢀphÝaꢀNamꢀmangꢀdÊuꢀ©m.ꢀCßnꢀtrÞꢀsèꢀyꢀvÒꢀphÝaꢀ§«ngꢀmangꢀdÊuꢀd−¬ng,ꢀvÒꢀphÝaꢀT©yꢀ
mangꢀdÊuꢀ©m.ꢀB¸nꢀcÇuꢀB¾cꢀcãꢀxꢀ>ꢀ0,ꢀyꢀcãꢀthÓꢀ©mꢀcãꢀthÓꢀd−¬ng.ꢀ§ÓꢀkhiꢀtÝnhꢀto¸nꢀtr¸nhꢀyꢀ©mꢀtaꢀ
quyꢀ−ícꢀ®iÓmꢀgècꢀOꢀcñaꢀtäaꢀ®éꢀxoꢀ=ꢀ0,ꢀyoꢀ=ꢀ500ꢀkm,ꢀnghÜaꢀlꢁꢀtÞnhꢀtiÕnꢀꢀkinhꢀtuyÕnꢀtrôcꢀvÒꢀphÝaꢀ
T©yꢀ500ꢀkmꢀ(h×nhꢀ1.8)ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀ§ÓꢀtiÖnꢀviÖcꢀsöꢀdôngꢀtrªnꢀb¶nꢀ®åꢀ®Þaꢀh×nhꢀng−êiꢀtaꢀ ꢀ
kÎꢀs½nꢀl−íiꢀtäaꢀ®éꢀvu«ngꢀgãcꢀGaussꢀb»ngꢀnh÷ngꢀ®−êngꢀ
songꢀsongꢀvíiꢀtrôcꢀOXꢀvꢁꢀOYꢀt¹oꢀthꢁnhꢀl−íiꢀkm.ꢀChiÒuꢀ
dꢁiꢀc¹nhꢀcñaꢀl−íiꢀ«ꢀvu«ngꢀcãꢀthÓꢀtÝnhꢀ®Õnꢀ¶nhꢀh−ëngꢀ
cñaꢀbiÕnꢀd¹ngꢀt−¬ngꢀøngꢀvíiꢀtûꢀlÖꢀb¶nꢀ®å.ꢀVÝꢀdôꢀvíiꢀ
b¶nꢀ®åꢀtûꢀlÖꢀ1:10000ꢀchänꢀ«ꢀvu«ngꢀ10ꢀcmꢀxꢀ10cm,ꢀb¶nꢀ
®åꢀtûꢀlÖꢀ1:25000ꢀꢀchänꢀ«ꢀvu«ngꢀ4ꢀcmꢀxꢀ4cm,ꢀb¶nꢀ®åꢀtûꢀ
lÖꢀ1:50.000ꢀchänꢀ«ꢀvu«ngꢀ2cmꢀxꢀ2cm.ꢀ
H×nhꢀ1.8ꢀ
PhÝaꢀngoꢁiꢀkhungꢀb¶nꢀ®åꢀcãꢀghiꢀtrÞꢀsèꢀXꢀvꢁꢀYꢀcñaꢀc¸cꢀ®−êngꢀsongꢀsong.ꢀ§Óꢀph©nꢀbiÖtꢀngayꢀ
®−îcꢀtäaꢀ®éꢀcñaꢀ®iÓmꢀn»mꢀëꢀmóiꢀchiÕuꢀthøꢀmÊyꢀvꢁꢀc¸chꢀ®iÓmꢀgècꢀOꢀbaoꢀnhiªuꢀng−êiꢀtaꢀquyꢀ
®Þnhꢀc¸chꢀviÕtꢀhoꢁnhꢀ®éꢀyꢀvꢁꢀghiꢀkÌmꢀtheoꢀthøꢀtùꢀmóiꢀchiÕu.ꢀ
ꢀ
VÝꢀdô:ꢀtäaꢀ®éꢀ®iÓmꢀL¸ngꢀTrungꢀ(HꢁꢀNéi)ꢀlꢁ:ꢀ2325464,246;ꢀ48.505973,362ꢀcãꢀnghÜaꢀlꢁꢀ
®iÓmꢀc¸chꢀxÝchꢀ®¹oꢀëꢀphÝaꢀB¾c:ꢀ2325464,246ꢀmꢀvꢁꢀëꢀmóiꢀthøꢀ48ꢀvÒꢀphÝaꢀ®«ngꢀkinhꢀtuyÕnꢀgi÷aꢀ
105o§.ꢀ
ꢀ
(505973,362ꢀꢂꢀ500000,000ꢀ=ꢀ5973,362m)ꢀ
®ÓꢀtÝnhꢀtrÞꢀsèꢀkinhꢀ®éꢀcñaꢀkinhꢀtuyÕnꢀgi÷aꢀmóiꢀthøꢀnꢀ(*)ꢀnꢁoꢀ®ãꢀtaꢀdïngꢀc«ngꢀthøcꢀ
ꢀ
ꢀ
λ
Nꢀ=ꢀ6o.nꢀꢂꢀ3ꢀ
§¶oꢀHoꢁngꢀSaꢀn»mꢀëꢀmóiꢀthøꢀ49ꢀkinhꢀtuyÕnꢀgi÷aꢀcñaꢀmóiꢀnꢁyꢀcãꢀkinhꢀ®éꢀ®éꢀlꢁ:ꢀꢀ
λꢀ=ꢀ
6o.19ꢀꢂꢀ3=ꢀ111o§ꢀ
L−íiꢀkhèngꢀchÕꢀtr¾cꢀ®ÞaꢀmÆtꢀph¼ngꢀXYꢀëꢀViÖtꢀNamꢀtrongꢀhÖꢀtäaꢀ®éꢀHNꢂ72ꢀ®−îcꢀx©yꢀ
dùngꢀtheoꢀhÖꢀtäaꢀ®éꢀvu«ngꢀgãcꢀGaussꢀꢂꢀKruger.ꢀꢀ
ꢀ
ꢀ
Trongꢀ®ãꢀEllipꢀsoidꢀquyꢀchiÕuꢀlꢁꢀEllipꢀsoidꢀKraxovski.ꢀ
ꢀ
ꢀ
ꢀ
(*)ꢀ§èiꢀꢀꢀvíiꢀmóiꢀn»mꢀëꢀphÝaꢀ§«ngꢀth×ꢀnꢀph¶iꢀhiÓuꢀlꢁꢀsèꢀmóiꢀtrõꢀ®iꢀ30.ꢀVÝꢀdô:ꢀn=ꢀ49,ꢀth×ꢀhiÓuꢀlꢁꢀn=ꢀ49ꢀ–ꢀ30ꢀ=ꢀ19
18ꢀ
ꢀ
1.10.3.ꢀHÖꢀtäaꢀ®éꢀvu«ngꢀgãcꢀUTMꢀ(N.E)ꢀ
PhÐpꢀchiÕuꢀUTMꢀ(UniversalꢀTranserseꢀMercator)ꢀkh¸cꢀvíiꢀphÐpꢀchiÕuꢀGaussꢀlꢁꢀëꢀchçꢀ
ꢀ
EllipꢀsoidꢀquyꢀchiÕuꢀc¾tꢀmÆtꢀtrôꢀchøꢀkh«ngꢀtiÕpꢀxócꢀvíiꢀmÆtꢀtrôꢀt¹iꢀkinhꢀtuyÕnꢀgi÷¨ꢀ(kinhꢀtuyÕnꢀ
trôc).ꢀ§iÒuꢀ®ãꢀlꢁmꢀh¹nꢀchÕꢀsùꢀbiÕnꢀd¹ngꢀëꢀ2ꢀkinhꢀtuyÕnꢀbiªn.ꢀDùaꢀtrªnꢀc¬ꢀsëꢀcñaꢀphÐpꢀchiÕuꢀ
ng−êiꢀtaꢀx¸cꢀ®ÞnhꢀhÖꢀtäaꢀ®éꢀgäiꢀlꢁꢀhÖꢀtäaꢀ®éꢀUTM.ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀTrongꢀphÐpꢀchiÕuꢀUTMꢀh×nhꢀchiÕuꢀcñaꢀ ꢀ
kinhꢀ tuyÕnꢀ gi÷aꢀ vꢁꢀ xÝchꢀ ®¹oꢀ lꢁꢀ 2ꢀ ®−êngꢀ
ꢀ
th¼ngꢀ vu«ngꢀ gãcꢀ víiꢀ nhauꢀ ®−îcꢀ chänꢀ lꢁmꢀ
ꢀ
γꢀ
trôcꢀtäaꢀ®éꢀ(h×nhꢀ1.9).ꢀTrongꢀ®ãꢀMꢀlꢁꢀ®iÓmꢀ
cÇnꢀ x¸cꢀ ®Þnhꢀ täaꢀ ®é.ꢀ O'ꢀ lꢁꢀ giaoꢀ ®iÓmꢀ h×nhꢀ
ꢀ
chiÕuꢀkinhꢀtuyÕnꢀtrôcꢀO'ZꢀvꢁꢀxÝchꢀ®¹oꢀO'E.ꢀ ꢀ
§iÓmꢀFꢀlꢁꢀh×nhꢀchiÕuꢀcñaꢀMꢀlªnꢀkinhꢀtuyÕnꢀ
ꢀ
trôc.ꢀ Cungꢀ LMꢀ lꢁꢀ h×nhꢀ chiÕuꢀ cñaꢀ vÜꢀ tuyÕnꢀ
ꢀ
quaꢀ M.ꢀ Cungꢀ ZMꢀ lꢁꢀ h×nhꢀ chiÕuꢀ cñaꢀ kinhꢀ
tuyÕnꢀquaꢀM.ꢀγꢀlꢁꢀꢀ®éꢀlÖchꢀkinhꢀtuyÕnꢀ(®éꢀ
gÇnꢀkinhꢀtuyÕn).ꢀTäaꢀ®éꢀUTMꢀꢀcñaꢀ®iÓmꢀMꢀ
®−îcꢀx¸cꢀ®Þnhꢀbëiꢀtungꢀ
H×nhꢀ1.9ꢀ
®éꢀNMꢀ(North)ꢀvꢁꢀhoꢁnhꢀ®éꢀ(EM)ꢀ(East)ꢀgièngꢀnh−ꢀquyꢀ®ÞnhꢀtrongꢀphÐpꢀchiÕuꢀGaussꢀng−êiꢀtaꢀ
rêiꢀ0'ꢀ®Õnꢀ0,ꢀ00'ꢀ=ꢀ500ꢀkmꢀtøcꢀlꢁꢀgècꢀtäaꢀ®éꢀlꢁꢀ0ꢀv×ꢀvËyꢀtäaꢀ®é:ꢀ
ꢀ
ꢀ
ꢀ
EMꢀ=ꢀE'ꢀ+ꢀ500ꢀkm.ꢀ
Tr−ícꢀn¨mꢀ1975ꢀqu©nꢀ®éiꢀMüꢀsöꢀdôngꢀhÖꢀtäaꢀ®éꢀUTMꢀvíiꢀEllipꢀsoidꢀquyꢀchiÕuꢀlꢁꢀEllipꢀ
soidꢀEverestꢀ®ÓꢀthꢁnhꢀlËpꢀb¶nꢀ®åꢀ®Þaꢀh×nhꢀmiÒnꢀNamꢀViÖtꢀNam.ꢀDoꢀ®ãꢀkhiꢀsöꢀdôngꢀb¶nꢀ®åꢀnꢁyꢀ
choꢀthèngꢀnhÊtꢀtaꢀph¶iꢀchuyÓnꢀhÖꢀtäaꢀ®éꢀUTMꢀ(XUTMꢀvꢁꢀYUTM)ꢀsangꢀhÖꢀtäaꢀ®éꢀGaussꢀꢂꢀKurgerꢀ
(XG,ꢀYG).ꢀ
ꢀ
TrongꢀhÖꢀtäaꢀ®éꢀVNꢂ2000ꢀtaꢀcòngꢀdïngꢀphÐpꢀchiÕuꢀUTMꢀnh−ngꢀEllipꢀsoidꢀquyꢀchiÕuꢀlꢁꢀ
EllipꢀsoidꢀW.G.Sꢂ84.ꢀGècꢀtäaꢀ®éꢀn»mꢀt¹iꢀkhu«nꢀviªnꢀViÖnꢀNghiªnꢀcøuꢀ®ÞaꢀchÝnhꢀꢂꢀHꢁꢀNéi.ꢀꢀ
1.10.4.ꢀHÖꢀtäaꢀ®éꢀgi¶ꢀ®Þnhꢀ
Khiꢀ ®oꢀ vÏꢀ b×nhꢀ ®åꢀ ëꢀ khuꢀ vùcꢀ nhá,ꢀ ëꢀ ®ãꢀ ꢀ
kh«ngꢀcãꢀhÖꢀtäaꢀ®éꢀNhꢁꢀn−ícꢀtaꢀcãꢀthÓꢀgi¶ꢀ
ꢀ
®ÞnhꢀmétꢀhÖꢀtäaꢀ®éꢀvu«ngꢀgãc.ꢀTrongꢀ®ãꢀgècꢀ
ꢀ
täaꢀ®éꢀ0ꢀlꢁꢀtïyꢀý.ꢀTaꢀcãꢀthÓꢀgi¶ꢀthiÕtꢀtäaꢀ®éꢀ
ꢀ
®iÓmꢀgècꢀ0ꢀlꢁꢀxoyoꢀ(h×nhꢀ.1.10).ꢀTrôcꢀxꢀtrïngꢀ
víiꢀkinhꢀtuyÕnꢀtõ.ꢀTrôcꢀnꢁyꢀcãꢀthÓꢀx¸cꢀ®Þnhꢀ
®−îcꢀb»ngꢀc¸chꢀ®Ætꢀm¸yꢀkinhꢀvÜꢀt¹iꢀ0ꢀ®Óꢀx¸cꢀ
®ÞnhꢀkinhꢀtuyÕnꢀtõꢀt¹iꢀ®ã.ꢀTrôcꢀyꢀvu«ngꢀgãcꢀ
víiꢀtrôcꢀx.ꢀ§Óꢀxꢀ>ꢀ0,ꢀyꢀ>ꢀ0ꢀtaꢀchänꢀgècꢀtäaꢀ
®éꢀn»mꢀëꢀvÞꢀtrÝꢀthÝchꢀhîp.ꢀKhiꢀ®ãꢀtäaꢀ®éꢀc¸cꢀ
®iÓmꢀtrongꢀkhuꢀ®oꢀthuécꢀhÖꢀtäaꢀ®éꢀgi¶ꢀ®Þnhꢀ
xoyoꢀ®ꢃꢀlùaꢀchän.ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
H×nhꢀ1.10ꢀ
19ꢀ
ꢀ
1.10.5.ꢀHÖꢀtäaꢀ®éꢀcùcꢀ
ꢀ
ꢀ
Trongꢀ®oꢀvÏꢀ®iÓmꢀchiꢀtiÕtꢀb»ngꢀph−¬ngꢀph¸pꢀtoꢁnꢀ®¹cꢀth−êngꢀdïngꢀhÖꢀtäaꢀ®éꢀnꢁy.ꢀꢀ
Gi¶ꢀ söꢀ trªnꢀ mÆtꢀ ph¼ngꢀ chänꢀ ®iÓmꢀ Aꢀ lꢁꢀ
®iÓmꢀ cùc,ꢀ vꢁꢀ 1ꢀ hꢀ −íngꢀ ABꢀ lꢁmꢀ trôcꢀ cùc.ꢀ VÞꢀ trÝꢀ
®iÓmꢀ1ꢀ®−îcꢀx¸cꢀ®Þnhꢀbëiꢀgãcꢀ 1ꢀc¹nhꢀcùcꢀS1ꢀ(h×nhꢀ
1.11)ꢀgãcꢀcùcꢀ 1ꢀlꢁꢀgãcꢀtÝnhꢀtõꢀh−íngꢀtrôcꢀcùcꢀABꢀ
β
β
1ꢀ
theoꢀchiÒuꢀkimꢀ®ångꢀhåꢀ®Õnꢀh−íngꢀc¹nhꢀcùcꢀS1,ꢀ
cßnꢀc¹nhꢀcùcꢀS1ꢀ lꢁꢀchiÒuꢀdꢁiꢀngangꢀtÝnhꢀtõꢀ®iÓmꢀ
gècꢀAꢀ®Õnꢀ®iÓmꢀ1.ꢀT−¬ngꢀtùꢀnh−ꢀvËyꢀ®Óꢀx¸cꢀ®Þnhꢀꢀ
2ꢀ
β1ꢀ
β2ꢀ
H×nhꢀ1.11ꢀ
Trongꢀ®oꢀvÏꢀ®iÓmꢀchiꢀtiÕtꢀ®iÓmꢀAꢀlꢁꢀ®iÓmꢀ®Ætꢀm¸yꢀkinhꢀvÜ,ꢀcßnꢀ®iÓmꢀBꢀlꢁꢀ®iÓmꢀ®Þnhꢀꢀh−íng.ꢀ
§Óꢀx¸cꢀ®Þnhꢀ®iÓmꢀchiꢀtiÕtꢀiꢀnꢁoꢀ®ãꢀcÇnꢀph¶iꢀx¸cꢀ®Þnhꢀgãcꢀcùcꢀꢀ iꢀvꢁꢀchiÒuꢀdꢁiꢀc¹nhꢀcùcꢀ
®iÓmꢀ2ꢀcÇnꢀbiÕtꢀgãcꢀcùcꢀ 2ꢀvꢁꢀc¹nhꢀcùcꢀS2...ꢀꢀ
β
ꢀ
β
Siꢀt−¬ngꢀøng.ꢀ
1.11.1.ꢀ§Þnhꢀh−íngꢀ®−êngꢀth¼ngꢀ
ꢀ
KhiꢀbiÓuꢀthÞꢀmétꢀ®o¹nꢀth¼ngꢀlªnꢀtrªnꢀb×nhꢀ®åꢀꢀhoÆcꢀb¶nꢀ®åꢀkh«ngꢀnh÷ngꢀbiÕtꢀchiÒuꢀdꢁiꢀ
®o¹nꢀth¼ngꢀmꢁꢀcßnꢀph¶iꢀbiÕtꢀph−¬ngꢀh−íngꢀcñaꢀnã.ꢀViÖcꢀx¸cꢀ®Þnhꢀh−íngꢀcñaꢀ1ꢀ®−êngꢀth¼ngꢀsoꢀ
víiꢀh−íngꢀgècꢀgäiꢀlꢁꢀ®Þnhꢀh−íngꢀ®−êngꢀth¼ng.ꢀH−íngꢀgècꢀ(h−íngꢀchuÈn)ꢀcãꢀthÓꢀlꢁꢀh−íngꢀcñaꢀ
kinhꢀtuyÕnꢀthùcꢀhoÆcꢀkinhꢀtuyÕnꢀtõꢀhoÆcꢀkinhꢀtuyÕnꢀtrôc.ꢀTïyꢀtheoꢀh−íngꢀcñaꢀkinhꢀtuyÕnꢀgècꢀ
mꢁꢀcãꢀc¸cꢀlo¹iꢀgãcꢀkh¸cꢀnhau.ꢀ
1.ꢀGãcꢀph−¬ngꢀvÞꢀ
ꢀ
Gãcꢀph−¬ngꢀvÞꢀcñaꢀmétꢀ®−êngꢀth¼ngꢀlꢁꢀgãcꢀngangꢀhîpꢀbëiꢀh−íngꢀb¾cꢀcñaꢀkinhꢀtuyÕnꢀvíiꢀh−íngꢀ
cñaꢀ®−êngꢀth¼ng.ꢀGãcꢀph−¬ngꢀvÞꢀ®−îcꢀtÝnhꢀtheoꢀchiÒuꢀkimꢀ®ångꢀhå,ꢀbiÕnꢀ®æiꢀtõꢀ00ꢀ ꢀ360o.ꢀ
NÕuꢀkinhꢀtuyÕnꢀ®ãꢀlꢁꢀkinhꢀtuyÕnꢀthùcꢀgãcꢀph−¬ngꢀvÞꢀ®ãꢀgäiꢀlꢁꢀgãcꢀph−¬ngꢀvÞꢀthùcꢀkýꢀ
hiÖuꢀlꢁꢀAꢀthùcꢀ(AꢀthùcꢀbiÕnꢀ®æiꢀꢀ0ꢀ
ꢀ3600)ꢀ
NÕuꢀkinhꢀtuyÕnꢀ®ãꢀlꢁꢀkinhꢀtuyÕnꢀtõꢀth×ꢀgãcꢀph−¬ngꢀvÞꢀ®ãꢀgäiꢀlꢁꢀgãcꢀph−¬ngꢀvÞꢀtõ,ꢀkýꢀ
hiÖuꢀlꢁꢀAꢀtõꢀ(AꢀtõꢀbiÕnꢀ®æiꢀtõꢀ0oꢀ ꢀ360o).ꢀ
KinhꢀtuyÕnꢀthùc:ꢀKinhꢀtuyÕnꢀthùcꢀlꢁꢀ®−êngꢀgiaoꢀcñaꢀmÆtꢀph¼ngꢀquaꢀtrôcꢀtr¸iꢀ®ÊtꢀvꢁꢀbÒꢀ
mÆtꢀtr¸iꢀ®Êt.ꢀ
KinhꢀtuyÕnꢀtõ:ꢀꢀKinhꢀtuyÕnꢀtõꢀlꢁꢀ®−êngꢀgiaoꢀcñaꢀmÆtꢀph¼ngꢀquaꢀtrôcꢀcñaꢀkimꢀnamꢀ
÷
ꢀ
÷
ꢀ
÷
ꢀ
ꢀ
ch©mꢀvꢁꢀbÒꢀmÆtꢀtr¸iꢀ®Êt.ꢀT¹iꢀmétꢀ®iÓmꢀtrªnꢀbÒꢀmÆtꢀtr¸iꢀ®Êtꢀh−íngꢀcñaꢀkinhꢀtuyÕnꢀthùcꢀvꢁꢀkinhꢀ
tuyÕnꢀtõꢀkh«ngꢀtrïngꢀnhau.ꢀGãcꢀhîpꢀbëiꢀkinhꢀtuyÕnꢀthùcꢀvꢁꢀkinhꢀtuyÕnꢀtõꢀgäiꢀlꢁꢀ®éꢀtõꢀthiªnꢀcñaꢀ
kimꢀnamꢀch©m,ꢀkýꢀhiÖuꢀlꢁꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀNÕuꢀkimꢀnamꢀch©mꢀlÖchꢀvÒꢀphÝaꢀ§«ngꢀ ꢀ
kinhꢀtuyÕnꢀthùcꢀth×ꢀ ꢀmangꢀdÊuꢀ+,ꢀnÕuꢀkimꢀ
namꢀch©mꢀlÖchꢀvÒꢀphÝaꢀT©yꢀkinhꢀtuyÕnꢀthùcꢀ
th×ꢀ ꢀmangꢀdÊuꢀꢂ.ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀQuanꢀ hÖꢀ gi÷aꢀ gãcꢀ ph−¬ngꢀ vÞꢀ thùcꢀ vꢁꢀ
ph−¬ngꢀvÞꢀtõꢀlꢁ:ꢀꢀAꢀthùcꢀ=ꢀAtõꢀ ꢀ
δ
ꢀ.ꢀꢀ
δ
δ+ꢀ
δꢂꢀ
δ
δꢀ
ꢀ
H×nhꢀ1.12ꢀ
20ꢀ
ꢀ
2.ꢀGãcꢀ®Þnhꢀꢀh−íngꢀ ꢀ
ꢀ
Gãcꢀ®Þnhꢀh−íngꢀcñaꢀmétꢀ®−êngꢀth¼ngꢀlꢁꢀgãcꢀngangꢀhîpꢀbëiꢀh−íngꢀb¾cꢀcñaꢀkinhꢀtuyÕnꢀ
trôcꢀhoÆcꢀ®−êngꢀsongꢀsongꢀvíiꢀkinhꢀtuyÕnꢀtrôcꢀvíiꢀh−íngꢀcñaꢀ®−êngꢀth¼ng.ꢀGãcꢀ®Þnhꢀh−íngꢀ
ꢀ360oꢀtheoꢀchiÒuꢀkimꢀ®ångꢀhå,ꢀgãcꢀ®Þnhꢀh−íngꢀkýꢀhiÖulꢁꢀ
biÕnꢀ®æiꢀꢀtõꢀ0ꢀ
÷
α.ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀKinhꢀ tuyÕnꢀ trôc:ꢀ Trongꢀ phÐpꢀ chiÕuꢀ
b¶nꢀ®åꢀng−êiꢀtaꢀchiaꢀtr¸iꢀ®ÊtꢀlꢁmꢀnhiÒuꢀmóiꢀ
6oꢀhoÆcꢀ3o,ꢀmétꢀmóiꢀ®−îcꢀgiíiꢀh¹nꢀbëiꢀ2ꢀkinhꢀ
tuyÕnꢀlꢁꢀ2ꢀkinhꢀtuyÕnꢀbiªn.ꢀKinhꢀtuyÕnꢀn»mꢀ
ëꢀgi÷aꢀmóiꢀgäiꢀlꢁꢀkinhꢀtuyÕnꢀtrôcꢀ(h×nhꢀ1.13)ꢀꢀ
γ+ꢀ
γꢂꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀ§éꢀ gÇnꢀ kinhꢀ tuyÕn:ꢀ §éꢀ gÇnꢀ kinhꢀ
tuyÕnꢀcñaꢀ1ꢀ®iÓmꢀlꢁꢀgãcꢀhîpꢀbëiꢀkinhꢀtuyÕnꢀ
trôcꢀ hoÆcꢀ ®−êngꢀ songꢀ songꢀ víiꢀ kinhꢀ tuyÕnꢀ
trôcꢀvꢁꢀkinhꢀtuyÕnꢀ®iꢀquaꢀ®iÓmꢀ®ã,ꢀkýꢀhiÖuꢀ
lꢁꢀ
ꢀꢀꢀꢀꢀꢀꢀNh÷ngꢀ ®iÓmꢀ n»mꢀ ëꢀ phÝaꢀ §«ngꢀ kinhꢀ
tuyÕnꢀtrôcꢀ ꢀmangꢀdÊuꢀ+,ꢀnh÷ngꢀ®iÓmꢀn»mꢀëꢀ
γ
.ꢀꢀ
ꢀ
γ
H×nhꢀ1.13ꢀ
phÝaꢀT©yꢀkinhꢀtuyÕnꢀtrôcꢀ
γ
ꢀmangꢀdÊuꢀꢂ.ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀT¹iꢀ kinhꢀ tuyÕnꢀ trôcꢀ vꢁꢀ xÝchꢀ ®¹oꢀ γꢀ =ꢀ 0ꢀ
trongꢀ phÐpꢀ chiÕuꢀ b¶nꢀ ®åꢀ ng−êiꢀ taꢀ chiÕuꢀ c¸cꢀ
yÕuꢀtèꢀgãc,ꢀchiÒuꢀdꢁiꢀlªnꢀmÆtꢀEllipꢀsoidꢀquyꢀ
chiÕu,ꢀsauꢀ®ãꢀchiÕuꢀlªnꢀmÆtꢀtrungꢀgianꢀ(mÆtꢀ
nãnꢀhoÆcꢀmÆtꢀtrô)ꢀvꢁꢀtr¶iꢀraꢀmÆtꢀph¼ng,ꢀkhiꢀ®ãꢀ
c¸cꢀc¹nhꢀlꢁꢀ®−êngꢀcongꢀchuyÓnꢀthꢁnhꢀ®−êngꢀ
th¼ngꢀvꢁꢀkhiꢀ®ãꢀcãꢀthªmꢀsèꢀc¶iꢀchÝnhꢀh−íngꢀlꢁꢀ
γ
ꢀ
α
ꢀ
Aꢀ
δ.ꢀ Gãcꢀ ph−¬ngꢀ vÞꢀ tr¾cꢀ ®Þaꢀ Aꢀ vꢁꢀ gãcꢀ ®Þnhꢀ
h−íngꢀ
α
ꢀcãꢀquanꢀhÖꢀ(h×nhꢀ1.14)ꢀ
ꢀ=ꢀAꢀꢂꢀ ꢀꢂꢀ
δꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
α
γ
δꢀ
H×nhꢀ1.14ꢀ
ꢀ
Trongꢀ®ãꢀ
γꢀlꢁꢀ®éꢀgÇnꢀkinhꢀtuyÕnꢀ
Nh−ꢀvËy,ꢀcãꢀthÓꢀdïngꢀgãcꢀph−¬ngꢀvÞꢀthùc,ꢀph−¬ngꢀvÞꢀtõꢀhoÆcꢀgãcꢀ®Þnhꢀh−íngꢀ®Óꢀ®Þnhꢀ
h−íngꢀ®−êngꢀth¼ng.ꢀThùcꢀtÕꢀtrongꢀ®oꢀvÏꢀb×nhꢀ®åꢀth−êngꢀdïngꢀgãcꢀph−¬ngꢀvÞꢀtõꢀ®Óꢀ®Þnhꢀh−íngꢀ
b×nhꢀ®åꢀv×ꢀviÖcꢀx¸cꢀ®Þnhꢀnãꢀ®¬nꢀgi¶n.ꢀTrongꢀ®oꢀvÏꢀb¶nꢀ®åꢀth−êngꢀdïngꢀgãcꢀ®Þnhꢀh−íngꢀ®Óꢀ®Þnhꢀ
h−íngꢀb¶nꢀ®å.ꢀMétꢀ®Æcꢀ®iÓmꢀc¬ꢀb¶nꢀcñaꢀgãcꢀ®Þnhꢀh−íngꢀlꢁ:ꢀT¹iꢀc¸cꢀ®iÓmꢀkh¸cꢀnhauꢀtrªnꢀmétꢀ
®−êngꢀth¼ng,ꢀgãcꢀ®Þnhꢀh−íngꢀ®Òuꢀb»ngꢀnhau.ꢀV×ꢀvËy,ꢀgi÷aꢀgãcꢀ®Þnhꢀh−íngꢀthuËn,ꢀnghÞchꢀcãꢀ
mèiꢀquanꢀhÖꢀlꢁ:ꢀꢀ
α
thuËnꢀ=ꢀαnghÞchꢀ ꢀꢀ1800ꢀ
VÝꢀdô:ꢀGãcꢀ®Þnhꢀh−íngꢀcñaꢀ®−êngꢀth¼ngꢀABꢀlꢁꢀ thuËnꢀgãcꢀ®Þnhꢀh−íngꢀcñaꢀ®−êngꢀth¼ngꢀ
ꢀ
α
21ꢀ
ꢀ
BAꢀlꢁꢀ
αnghÞchꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀTaꢀcã:ꢀ
1800.ꢀTuyꢀnhiªn,ꢀcãꢀtr−êngꢀhîpꢀph¶iꢀ+ꢀ1800.ꢀ
V×ꢀvËyꢀtængꢀqu¸tꢀhãaꢀlꢁꢀ ꢀ1800.ꢀ
α
BAꢀ=ꢀ
α
ABꢀ+ꢀ1800ꢀꢂ>ꢀ
α
ABꢀ=ꢀαBAꢀꢂꢀ
ꢀ
ꢀ
ꢀ
ꢀ
α
Nꢀ
3)ꢀGãcꢀ2ꢀph−¬ngꢀ
αTꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀV×ꢀgãcꢀph−¬ngꢀvÞ,ꢀgãcꢀ®Þnhꢀh−íngꢀbiÕnꢀ
®æiꢀ tõꢀ 00ꢀ
ꢀ
÷
thuËnꢀlîi.ꢀV×ꢀvËyꢀng−êiꢀtaꢀdïngꢀgãcꢀ2ꢀph−¬ng.ꢀ
ꢀ 3600ꢀ qu¸ꢀ tr×nhꢀ tÝnhꢀ to¸nꢀ kh«ngꢀ
ꢀ
H×nhꢀ1.15ꢀ
ꢀ
Gãcꢀ2ꢀph−¬ngꢀcñaꢀmétꢀ®−ꢀêngꢀth¼ngꢀlꢁꢀgãcꢀngangꢀhîpꢀbëiꢀh−íngꢀB¾cꢀꢂꢀꢀNamꢀgÇnꢀnhÊtꢀ
ꢀ900ꢀ
cñaꢀkinhꢀtuyÕnꢀvíiꢀh−íngꢀcñaꢀ®−êngꢀth¼ng.ꢀKýꢀhiÖuꢀlꢁꢀR,ꢀgãcꢀ2ꢀph−¬ngꢀbiÕnꢀ®æiꢀtõꢀꢀ00ꢀ
÷
cãꢀkÌmꢀtheoꢀtªnꢀcñaꢀgãcꢀphÇnꢀt−ꢀ(h×nhꢀ1.16).ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀT−¬ngꢀøngꢀ víiꢀgãcꢀph−¬ngꢀvÞꢀthùcꢀcãꢀ ꢀ
gãcꢀ2ꢀph−¬ngꢀthùcꢀkýꢀhiÖuꢀlꢁꢀR'ꢀꢀthùc.ꢀT−¬ngꢀ
ꢀ
øngꢀvíiꢀgãcꢀph−¬ngꢀvÞꢀtõꢀcãꢀgãcꢀ2ꢀph−¬ngꢀtõ,ꢀ
kýꢀ hiÖuꢀ lꢁꢀ R'ꢀ tõ.ꢀ T−¬ngꢀ øngꢀ víiꢀ gãcꢀ ®Þnhꢀ
ꢀ
α
4ꢀ
α
1ꢀ
ꢀ
h−íngꢀcãꢀgãcꢀ2ꢀph−¬ngꢀkýꢀhiÖuꢀlꢁꢀR:ꢀQuanꢀhÖꢀ
gi÷aꢀ gãcꢀ ®Þnhꢀ h−íngꢀ vꢁꢀ gãcꢀ 2ꢀ ph−¬ngꢀ ®−îcꢀ
chØꢀraꢀëꢀb¶ngꢀ1.3.ꢀ
α
2ꢀ
ꢀ
α
3ꢀ
ꢀ
ꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀC¨nꢀcøꢀvꢁoꢀb¶ngꢀ1.3ꢀtaꢀcãꢀthÓꢀchuyÓnꢀtõꢀ
gãcꢀ®Þnhꢀh−íngꢀsangꢀgãcꢀ2ꢀph−¬ngꢀvꢁꢀng−îcꢀ
l¹i.ꢀThùcꢀtÕꢀkhiꢀtÝnhꢀto¸nꢀb»ngꢀc¸cꢀthiÕtꢀbÞꢀth«ꢀ
s¬ꢀtaꢀcãꢀthÓꢀꢀtÝnhꢀchuyÓnꢀtõꢀgãcꢀ®Þnhꢀh−íngꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀH×nhꢀ1.6ꢀ
B¶ngꢀ1.3.ꢀ
Xꢀ , Yꢀ
sangꢀ gãcꢀ 2ꢀ ph−¬ngꢀ ®Óꢀ xÐtꢀ dÊuꢀ cñaꢀ
hoÆcꢀx,yꢀtheoꢀc¸cꢀgãcꢀphÇnꢀt−.ꢀ
∆
∆
GãcꢀphÇnꢀt−ꢀ Gãcꢀ®Þnhꢀh−íngꢀvꢁꢀ2ꢀph−¬ngꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀVÝꢀ dô:ꢀ Trongꢀ hÖꢀ täaꢀ ®éꢀ gi¶ꢀ ®Þnhꢀ (h×nhꢀ
1.7)ꢀdÊuꢀcñaꢀgiaꢀsèꢀtäaꢀ®éꢀ®−îcꢀthÓꢀhiÖnꢀtrongꢀ
b¶ngꢀ1.4.ꢀ
Iꢀ
RBDꢀ=ꢀα1ꢀ
RNDꢀ=ꢀ1800ꢀꢂꢀα2
ꢀ
IIꢀ
3ꢀꢂꢀ1800ꢀ
IIIꢀ
RNTꢀ=ꢀ
α
IVꢀ
RBTꢀ=ꢀ3600ꢀꢂꢀ
α4ꢀ
ꢀ
∆xꢀ
αꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀB¶ngꢀ1.4.ꢀ
GãcꢀphÇnꢀ
t−
Gãcꢀ
Giaꢀsèꢀtäaꢀ®éꢀ
∆yꢀ
ꢀ
2ꢀph−¬ngꢀ
∆Xꢀ
+ꢀ
ꢂꢀ
∆Yꢀ
+ꢀ
+ꢀ
ꢂꢀ
Iꢀ
RBDꢀ
ꢀ
RND
IIꢀ
IIIꢀ
RNTꢀ
ꢂꢀ
IV
ꢀ
RBT
ꢀ
+ꢀ
ꢂꢀ
H×nhꢀ1.7ꢀ
ꢀ
22ꢀ
ꢀ
ꢀ
ꢀThùcꢀtÕꢀchoꢀthÊy,ꢀkhiꢀbiÕtꢀgãcꢀph−¬ngꢀꢀ
vÞꢀtõꢀcñaꢀmétꢀ®−êngꢀth¼ng,ꢀbiÕtꢀ®éꢀtõꢀthiªnꢀ ꢀvꢁꢀ
®éꢀgÇnꢀkinhꢀtuyÕnꢀ ꢀtaꢀcãꢀthÓꢀtÝnhꢀ®−îcꢀgãcꢀ
®Þnhꢀh−íngꢀcñaꢀ®−êngꢀth¼ngꢀ®ã.ꢀ
VÝꢀdô:ꢀTÝnhꢀgãcꢀ®Þnhꢀh−íngꢀcñaꢀ®−êngꢀ
th¼ngꢀABꢀbiÕtꢀgãcꢀph−¬ngꢀvÞꢀtõꢀcñaꢀnãꢀlꢁꢀAtõꢀ=ꢀ
300ꢀ15',ꢀ®éꢀtõꢀthiªnꢀ ꢀ=ꢀ5',ꢀ®éꢀgÇnꢀkinhꢀtuyÕnꢀꢀꢀꢀ
ꢀ=ꢀꢂꢀ3'ꢀ.ꢀVÏꢀh×nhꢀbiÓuꢀdiÔnꢀnã?ꢀꢀ
δ
γ
δꢀ
γ
ꢀ
ꢀ
αꢀ
δ
γ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀDùaꢀ vꢁoꢀ ®Þnhꢀ nghÜaꢀ taꢀ vÏꢀ ®−îcꢀ c¸cꢀ
kinhꢀ tuyÕnꢀ vꢁꢀ gãcꢀ ph−¬ngꢀ vÞꢀ tõꢀ cñaꢀ ®−êngꢀ
th¼ngꢀAB.ꢀ(h×nhꢀ1.8).ꢀꢀ
//ꢀKTꢀtrôcꢀ
KTꢀtrôcꢀ
H×nhꢀ1.8ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀTõꢀh×nhꢀvÏꢀtaꢀcã:ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
Athùc=ꢀAtõꢀ+ꢀꢀ
ꢀ=ꢀAthùcꢀ+ꢀ
ꢀ=ꢀ30020'ꢀ+ꢀ3'ꢀ=ꢀ30023'ꢀ
ꢀ<ꢀ900.ꢀ§−êngꢀth¼ngꢀn»mꢀëꢀgãcꢀphÇnꢀt−ꢀthøꢀnhÊtꢀ ꢀ=ꢀRB§ꢀ=ꢀ30023'ꢀ
δ
ꢀ=ꢀ30015'ꢀ+5'ꢀꢀ=ꢀ30020'ꢀ
α
γ
ꢀ
V×ꢀ
α
α
1.12.ꢀBꢁiꢀto¸nꢀx¸cꢀ®Þnhꢀtäaꢀ®éꢀvu«ngꢀgãcꢀph¼ngꢀ
Trongꢀtr¾cꢀ®Þaꢀth−êngꢀph¶iꢀgi¶iꢀ2ꢀbꢁiꢀto¸nꢀc¬ꢀb¶nꢀtrongꢀhÖꢀtäaꢀ®éꢀvu«ngꢀgãcꢀph¼ngꢀ®ãꢀlꢁ:ꢀ
1ꢂꢀBꢁiꢀto¸nꢀtr¾cꢀ®ÞaꢀthuËn:ꢀ
ꢀ
ꢀꢀ
ꢀ
Néiꢀdungꢀbꢁiꢀto¸nꢀtr¾cꢀ®ÞaꢀthuËnꢀlꢁ:ꢀꢀ
Trongꢀ hÖꢀ täaꢀ ꢀ ®éꢀ vu«ngꢀ gãcꢀ ph¼ngꢀ
(h×nhꢀ1.19).ꢀBiÕtꢀtäaꢀ®éꢀ®iÓmꢀAꢀlꢁꢀxA,ꢀyA,ꢀchiÒuꢀ
dꢁiꢀ®o¹nꢀABꢀlꢁꢀSAB.ꢀGãcꢀ®Þnhꢀh−íngꢀc¹nhꢀABꢀ
∆x αꢀ
ꢀ
lꢁꢀ
α
ABꢀ (hoÆcꢀ gãcꢀ 2ꢀ ph−¬ngꢀ c¹nhꢀ ABꢀ lꢁꢀ RB§).ꢀ
∆yꢀ
TÝnhꢀtäaꢀꢀ®éꢀ®iÓmꢀB.ꢀ
ꢀ
ꢀ
Nh×nꢀvꢁoꢀh×nhꢀvÏꢀ1.9ꢀtaꢀcãꢀ:ꢀ
ꢀ
∆
∆
xABꢀ=ꢀSABꢀ.ꢀCos
yABꢀ=ꢀSABꢀ.ꢀSin
αABꢀ=ꢀSAB.CosRB§
αABꢀꢀ=ꢀSAB.SinRB§ꢀ
ꢀ
ꢀ
ꢀ
Täaꢀ®éꢀ®iÓmꢀBꢀlꢁ:ꢀ
ꢀ
ꢀ
ꢀ
xBꢀ=xAꢀ+ꢀ
∆
xAB.ꢀ
yAB.ꢀꢀ
ꢀꢀ
yBꢀ=ꢀyAꢀ+ꢀ
∆
ꢀ
H×nhꢀ1.9ꢀ
2ꢂꢀBꢁiꢀto¸nꢀtr¾cꢀ®Þaꢀng−îcꢀ
BiÕtꢀtäaꢀ®éꢀ®iÓmꢀAꢀlꢁꢀxAyA,ꢀtäaꢀ®éꢀ®iÓmꢀBꢀlꢁꢀxByB,ꢀtÝnhꢀchiÒuꢀdꢁiꢀ®o¹nꢀth¼ngꢀAB;ꢀgãcꢀ
®Þnhꢀh−íngꢀc¹nhꢀAB.ꢀꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
Trªnꢀh×nhꢀ1.9ꢀtaꢀcã:ꢀ
∆
∆
xABꢀ=xBꢀꢂꢀxAꢀ.ꢀ
yABꢀ=ꢀyBꢀ–yAꢀ.ꢀ
∆xA2B + ∆yA2B
SABꢀ=ꢀ
23ꢀ
ꢀ
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