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TRNG I HC LC HNG KHOA K THUT CNG TRNH

Bi ging mn: Trc a i cng PGS.TS. o Xun Lc

Bi 4

DUNG CU VA PHNG PHAP O DAI, O DIN TCH

5.1. KHAI NIEM CHUNG

Khoang cach hay o dai la mot trong nhng yeu to e xac nh v tr khong gian cua cac iem tren mat at t nhien.

o dai cua mot oan thang c hieu la hnh chieu cua no tren mat phang nam ngang. Do o, khi o o dai gia hai iem tren mat at, ngoai khoang cach ta con phai o o nghieng gia hai iem o. Neu goi AB la khoang cach o tren mat at, V la goc nghieng gia hai iem AB th khoang cach ngang ab se la:

ab = ABcosV (5.1) o dai bao gom o trc tiep va o gian tiep. o dai bang thc day vai, o dai

bang thc thep, thc day inva la o dai trc tiep. o dai quang hoc, o dai quang ien, o mot so yeu to goc va canh trong tam giac e tnh chieu dai cua mot canh la o dai gian tiep.

e ap ng o chnh xac o dai khac nhau ta s dung phng phap o khac nhau, ieu nay c the hien bang 5.1.

Bang 5.1

STT o chnh xac o dai Phng phap o dai

1 2

3

4



Thc thep c lam bang thep mong 0,4 mm, rong 15-25 mm vi cac o dai 20 m, 24 m, 30 m, 50 m. Thc c chia vach nho nhat la dm, cm hoac mm t au en cuoi. Co loai ch chia vach mm oan thc au, cac oan thc con lai chia en cm. Thc c cuon trong vong sat tron hay hop kn. Hai au thc co khoen hoac tay cam e keo cang thc. Can lu y xac nh v tr iem 0 cua au thc v v tr iem 0 co the nam au thc nhng cung co khi nam khoen cam. V lam bang thep cng nen thc rat de b gay hay b mop lam thay oi chieu dai nen khi s dung thc phai het sc can than, nhat la khi o ng pho co nhieu xe co qua lai, khi di chuyen thc va khi cuon thc vao hop.

Hnh 5.1

b- Dung cu bo tr

Dung cu bo tr o dai thc thep gom co sao tieu (jalon) va bo pht sat (H.5.2). Sao tieu c lam bang thep tron rong 10-15 mm dai 1,5 m, nhon au di, sn

oan trang oan o, moi oan dai 20cm. Tieu c dung e dong hng ng thang khi o dai va lam tieu ngam khi o goc.

Bo pht sat gom 11 cay c lam bang thep ac 5-6 mm, dai 30 cm, nhon au di, uon tron au tren e xau vao mot vong sat. Pht sat cung c sn oan trang, oan o. Ngoai tac dung anh dau hai au thc va tnh so lan at thc, pht sat con c dung e dng cay tieu (ba pht), lam tieu ngam o goc khi hng ngam ngan.



Hnh 5.3 Hnh 5.2 2. nh hng thang

Tuyen o dai gia hai iem AB la giao tuyen gia mat phang thang ng qua hai iem AB va mat at t nhien. Tuyen o se la ng thang neu a hnh bang phang, la ng cong neu a hnh phc tap (H.5.3). Trng hp tuyen o la ng thang dai khoang 100-150 m, e lam can c keo thc ung tren tuyen o ta ch can dng hai sao tieu hai au. Neu tuyen o kha dai hoac la ng cong th phai bo tr them mot so iem dng sao tieu gia. Viec bo tr mot so iem dng sao tieu nam tren tuyen o dai gia hai iem AB, goi la nh hng thang. Khoang cach gia cac iem dng sao tieu gia la 70-100 m neu tuyen o dai la ng thang va 20-50 m neu la ng cong. Tuy theo o chnh xac yeu cau co the nh hng thang bang mat, bang ong nhom hoac may kinh v.

a- nh hng thang khi A nhn thay B

Dng co nh hai sao tieu A va B, ngi th nhat ng cach sao A khoang 2 m ngam ve sao B sao cho sao A che lap sao B, ong thi ieu khien ngi th hai cam sao tieu di chuyen vao tuyen o cho ti khi sao A che lap sao at tai iem 1, roi ong coc anh dau. Bang cach tng t ieu khien dng sao va ong coc anh dau tai iem 2

Khi A nhn thay B viec nh hng thang bang may kinh v thng ket hp vi qua trnh at thc o dai. Khi o mot ngi at may kinh v tai A ngam chuan ve sao tieu at tai B, co nh ban o ngang, chuc ong knh xuong ieu khien e ngi cam au thc pha trc at pht sat va ung iem cuoi thc o va nam tren tuyen o dai.



b- nh hng thang trong trng hp A khong nhn thay B

Khi gia hai iem A, B hai ben ngon oi khong nhn thay nhau, ta nh hng thang theo phng phap nhch dan nh sau:

Dng hai tieu co nh tai A va B (H.5.4). Ngi cam tieu th nhat dng tai iem b1 nam gan hng AB nhn thay A. Ngi cam tieu th hai dng tai iem a1 nam tren hng Ab1 nhn thay B. Ngi th nhat di chuyen en iem b2 nam tren hng Ba1 nhn thay A. Ngi th hai di chuyen en a2 tren hng Ab2 nhn thay B. C tiep tuc cho en khi ngi th nhat nhn thay ba tieu at tai a, b, A trung nhau va ngi th hai cung nhn thay cac tieu at tai b, a, B trung nhau th dng lai.

Khi s dung may kinh v, ta at may tai M1 nam kha gan tuyen AB (H.5.5). o goc 1 gia hai hng M1A va M1B.

- Neu 1



A. Ngi trc cam au thc co vach 20m va 10 pht. Ngi nay cang thc o that nam ngang va at thc ung tuyen AB theo s ieu khien cua ngi sau, sau o cam mot pht tai vach 20. Tiep theo ngi sau nho pht tai A, ngi trc e lai cay pht va cam, ca hai cung tien ve pha B (trong khi di chuyen khong nen e thc b keo le di at). Khi ngi sau en v tr cay pht do ngi trc e lai th ra hieu cho ngi trc dng. Cac ong tac c lap lai nh oan o th nhat cho ti khi o xong oan cuoi cung.

So pht nam trong tay ngi sau bang chnh so lan at thc. Khi so pht trong tay ngi trc a het, co ngha la oan a o dai bang 10 lan at thc. e o tiep, ngi sau phai a lai toan bo pht (ch co 10 pht, mot pht con cam di at cho ngi sau) cho ngi trc va ghi mot lan trao pht vao so.

oan cuoi thng ngan hn o dai mot oan thc nen ngi trc phai can c vao tam nh coc B e oc so tren thc.

V du: sau khi o, so lan trao pht la 1, so pht trong tay ngi sau la 4, so oc oan cuoi la 13,26 m, chieu dai canh AB se la:

SAB = 20.10 + 20.4 + 13,26 = 293,26 m e kiem tra ket qua o va tang cng o chnh xac, thng phai o hai lan i, ve

tren mot canh. Chenh lech ket qua gia hai lan o i, o ve khong c ln hn 1:2000 chieu dai canh o. Khi ieu kien nay thoa man th lay tr trung bnh cua hai lan o lam ket qua cuoi cung. Can lu y ieu kien tren ay neu len ch nham anh gia mc can than cua ngi o e at o chnh xac cua phng phap ch khong phai o chnh xac a at c.

b- Trng hp mat at doc

Neu mat at gia hai iem can o co o doc th dung phng phap nac thang e o o dai. Khi o, ngoai cac dung cu a dung trng hp trc, can co them thuy bnh cam tay va day doi.

at mot au thc sat mat at, au kia dung day doi e anh dau iem di at (H.5.7). Thc c at nam ngang nh thuy bnh cam tay.

Hnh 5.7 Hnh 5.8

Neu mat at gia hai iem can o tng oi phang va doc eu th o khoang cach D tren mat doc va goc nghieng V, roi tnh o dai nghieng SAB theo cong thc:

SAB = DcosV (5.3) Trng hp biet hieu o cao h gia hai iem A va B, o dai ngang tnh theo cong

thc:



2 2ABS D h (5.4)

e o goc ng V ta at may kinh v tai A. Sau khi nh tam can bang may, o chieu cao may i. Quay ong knh ngam ch gia vao mia dng B tai v tr co so oc ung bang chieu cao may i roi oc so tren ban o ng.

4. o chnh xac o dai bang thc thep Khi o dai bang thc thep trc tiep tren mat at thng pham phai nhng sai so

chu yeu sau ay: Sai so do chieu dai thc cua thc khac vi chieu dai danh ngha (sai so kiem

nghiem thc). V du chieu dai thc la 20,000 m nhng chieu dai danh ngha la 20,001 m.

1- Sai so do thc b dan n theo nhiet o. Neu nhiet o luc o cao hn nhiet o luc xac nh chieu dai danh ngha th thc se b dai ra.

2- Sai so do at thc khong trung vi hng gia hai iem au canh o lam cho ket qua o dai ln hn o dai thc cua canh o.

3- Sai so do cang thc khac vi lc cang chuan khi xac nh chieu dai danh ngha cua thc trong phong th nghiem, sai so nay mang tnh chat ngau nhien ...

4- Sai so do o dai tren mat at nghieng tren 2o nhng khong tnh so hieu chnh. 5- Sai so do thc b cong ngang (do gio hay b vng co) cong len hoac vong xuong

(do mat at khong bang phang) lam cho ket qua o luon ln hn o dai thc cua canh o.

6- Sai so do khong ong thi lam trung vach khac hai au thc vi hai tam moc cua oan o, do pht sat anh dau oan o b nghieng hoac dch chuyen

Do anh hng tong hp cua cac nguon sai so noi tren ma phng phap o dai bang thc thep tren mat at ch at:

1:3000 khi o a hnh bang phang thuan li, 1:2000 khi o vung co a hnh trung bnh, 1:1000 khi o vung co a hnh phc tap, b chia cat, doc, co nhieu bui ram Can lu y o chnh xac cua phng phap o dai bang thc thep c ac trng

bang sai so trung phng tng oi tnh t sai so thc hoac sai so xac suat nhat cua cac ket qua o nhieu lan mot ai lng a biet hoac cha biet rut ra t cac thc nghiem (xem muc 3.4, 3.5 chng 3).

e kiem tra mc o can than cua viec o nham at c o chnh xac noi tren cua phng phap, ngi ta thng tnh t so gia chenh lech ket qua hai lan o i, o ve vi tr trung bnh cua chung. T so nay khong vt qua 1:2000 khi o vung thuan li va 1:1000 vung kho khan.

Trong thc te o ac, nhieu khi t so /S S tnh c bang 1:20000, 1:50000, tham ch 1:100000. ieu o khong co ngha la o chnh xac o dai bang thc thep at c la 1:20000, 1:50000 hay 1:100000, ma thc ra cung ch at 1:2000 hoac 1:3000. Nhng t so kha cao noi tren chng to mc o can than gia hai lan o i, o ve gan nh nhau.

e nang cao o chnh xac o dai thc thep len 1:5000 tr len phai kiem nghiem



thc e xac nh chieu dai thc, o dai tren au coc ong xuong at, cang thc bang lc ke 5-10 kg, o nhiet o va tnh so hieu chnh do anh hng cua nhiet o, o chenh cao gia hai au thc va tnh so hieu chnh, ieu khien at thc tren tuyen o bang may kinh v

5.3. NGUYEN LY O DAI BANG CH LNG C

Nh a biet, trong he ch ch thap (H.4.4) co hai ch tren va ch di dung e o o dai c goi la ch lng c. Khi o o dai, at may kinh v tai A ngam ve mia at tai B, em so vach centimet tren mia nam gia hai ch lng c e suy ra o dai AB. V du, so vach centimet gia hai ch lng c la 54,6 co ngha la khoang cach gia hai iem AB la 54,6 m. e giai thch ieu nay ta da vao nguyen ly o dai bang ch lng c. Nguyen ly o dai bang ch lng c trong ong knh co bo phan ieu quang ngoai kha n gian, nhng trong hau het cac may quang hoc hien nay ch cau tao bo phan ieu quang trong nen trong tiet nay se e cap en ca hai.

1. oi vi may co ong knh ieu quang ngoai Khi o dai bang ch lng c, du s dung ong knh ieu quang ngoai hay ong knh

ieu quang trong eu gap phai hai trng hp. a- Trng hp tia ngam nam ngang

Khi o dai vung bang phang th tia ngam t may ti mia se nam ngang. Cong thc tnh o dai trong trng hp nay se c dan giai nh sau: Gia s at may kinh v tai A va dng mia tai B.

Theo H.5.9 ta co: S = E + f + (5.5)

trong o: S - o dai ngang t truc chnh may kinh v ti mia (o dai oan AB) E - o dai ngang t tieu iem vat knh ti mia f - tieu c cua vat knh - o dai ngang t vat knh ti truc chnh cua may

T hai tam giac ong dang MFN va mFn ta co: E fP

l

Suy ra: fEP

l (5.6)

Trong o: P - khoang cach cua hai ch lng c l - khoang cach chan tren mia gia hai ch lng c

MN - oan mia

LL1 - Truc chnh cua may

mn - Man day ch thap

Hnh 5.9



at: f KP la he so o dai

Va: f + = C la hang so o dai Ta co cong thc tnh o dai lng c khi tia ngam nam ngang:

S K C l (5.7)

b- Trng hp tia ngam nam nghieng

Khi o dai vung at doc, hoac khi tia ngam ngang b che lap, can phai at ong knh nghieng e o khoang cach. Muon co o dai nam ngang phai o goc ng v e tnh so hieu chnh vao chieu dai nghieng. Mat khac khi o dai ngi i mia thng dng mia theo phng day doi ma le ra phai dng vuong goc vi tia ngam, lam cho khoang chan l tren mia gia hai ch lng c dai ra va do o chieu dai tnh c se dai hn chieu dai thc te. V vay, cong thc tnh chieu dai lng c khi tia ngam nghieng phai e cap en

hai kha canh: g Anh hng do mia khong vuong goc vi tia ngam

Hnh 5.10 Neu k hieu l la khoang chan tren mia gia hai ch lng c khi at mia vuong goc

vi tia ngam va l - khi at mia theo phng day doi th theo tam giac vuong IMM (co the coi goc tai M la goc vuong) ta co:

cos v2 2

l' l

Hay: cos vl' l (5.8)

Thay l tnh theo (5.8) vao (5.7) ta c cong thc tnh chieu dai nghieng: cosD K v C l (5.9)

g Anh hng do tia ngam b nghieng mot goc v so vi ng nam ngang

e tnh chieu dai ngang ta nhan chieu dai nghieng D vi cosv vDS cos hay: cos cos2S k v c v l (5.10)

ay la cong thc tong quat tnh chieu dai o bang ch lng c. vung bang 0v (5.10) se tr ve dang (5.7).

may kinh v co ong knh ieu quang ngoai, hang so C = 0,3 va he so K = 100. T o (5.7) va (5.10) co dang:



,S 100 0 3 l (5.11)

cos , cos2S 100 v 0 3 v l (5.12)



2. oi vi may co ong knh ieu quang trong

Hnh 5.11 Ong knh ieu quang trong co mot thau knh phan ky 2L co tac dung thay oi tieu

c knh vat lam cho anh hien ro tren mang day ch thap. Theo H.5.11, tia sang ti t vo cc en knh vat 1L tai A se hoi tu ve tieu iem 1F nhng trong khoang 1 1O F co thau knh phan ky 2L nen tia 1AF khi gap 2L tai B se khuc xa theo BF a anh len mat phang cha mang day ch thap. Keo dai ng FB ngc ve pha 1L cat tia sang ti tai C. Neu tng tng tai C at thau knh hoi tu tdL co tieu c tdf OF th thau knh nay c coi la tng ng vi he thong hai thau knh 1L va 2L . Tieu c cua thau knh tng ng tdf c tnh theo cong thc:

1 2td

1 2

f fff f

(5.13)

trong o: 1f - tieu c cua vat knh 2f - tieu c cua thau knh phan ky 2L (thau knh ieu quang) - khoang cach gia vat knh 1L va knh ieu quang 2L

Khi xem he thong thau knh L1, L2 trong ong knh ieu quang la vat knh tng ng th ta co the dung (5.7) va (5.10) e tnh o dai, trong o:

tdfKP

(5.14)

va: tdC f

Trong ong knh ieu quang trong, ngi ta cau tao may cho K = 100 va C = 0 nen (5.7) va (5.10) se co dang n gian hn:

S 100 l (5.15)

cos2S 100 v l (5.16)

3. o chnh xac o dai bang ch lng c e anh gia o chnh xac o dai bang ch lng c ta s dung (5.7):

D K C l (5.17)

vi: K = 100; C = 0 th: D = 100 l Theo (3.22) ta co sai so o dai bang ch lng c:

Dm 100m l (5.18)



Neu goi m la sai so trung phng oc so tren mia theo mot ch lng c, th sai so trung phng oc so theo hai ch lng c la m 2 . Neu coi m m 2l th sai so trung

phng Dm se la:

Dm 100 2m (5.19)

Sai so m phu thuoc vao sai so ngam qua ong knh ngm va khoang cach sai so D.

Sai so ngam bang mat thng c nhan bang 1. Khi ngam qua ong knh co o phong ai Vx th sai so nay se giam va ' / xngm 1 V , khi o:

'.' x

D 1m3438 V

em thay vao (5.19) ta c sai so trung phng tng oi o dai bang ch lng c:

,D

x xm 100 2 1D 3438V 24 31V

(5.20)

Cac loai may kinh v hien nay thng co o phong ai cua ong ngam t 20 en 25 lan, neu lay Vx = 20x th:

Dm 1D 486

(5.21)

Tren ay, chung ta mi e cap en anh hng cua sai so oc so tren mia. Thc ra, sai so xac nh khoang chan tren mia gia hai ch lng c ml con phu thuoc rat nhieu

nguon sai so khac: sai so do anh hng cua hien tng chiet quang ng va hien tng oi lu khong kh, sai so do anh hng cua viec dng mia nghieng, sai so do he so K 100, hang so C 0, sai so do anh hng cua goc nghieng tia ngam ...

Anh hng cua tat ca cac nguon sai so noi tren lam cho o chnh xac o dai lng c ch at khoang 1:300 1:400.

5.4. O DAI IEN QUANG

1. Khai niem chung

Theo xu hng t ong hoa trong khau thu nhap so lieu trac a ngoai hien trng, ben canh may kinh v ien t, ngi ta che tao ra may o dai ien t hay con goi la may o dai ien quang. May o dai ien quang co the la may rieng le, co the la bo phan lap vao may kinh v quang hoc hoac may kinh v ien t, co the cau tao chung vi may kinh v ien t tao thanh may toan ac ien t (total station).

o dai ien quang la loai o dai gian tiep s dung song ien t (song vo tuyen cc ngan) hoac song anh sang (hong ngoai va t ngoai).

May o dai bang song ien t co the o khoang cach hang chuc, co khi ti hang tram km, c s dung nhieu trong hang hai. May o dai bang song anh sang co the o khoang cach t 50 m en 10 km vi o chnh xac cao hn may o dai bang song ien t, nen c s dung rong rai trong o ac a hnh va cong trnh.



2. Nguyen ly o dai bang song anh sang

e o khoang cach S gia hai iem A, B, tai A at may o dai co chc nang phat thu tn hieu, tai B at gng phan xa. Song anh sang c phat i t bo ieu bien cua may (H.5.12) en gng phan xa doi tr ve may c thu lai bo thu tn hieu. Nh vay, song anh sang a i c mot quang ng bang hai lan khoang cach can o. T o, khoang cach can o c tnh theo cong thc:

.V tS2

(5.22)

trong o: V - toc o truyen song trong kh quyen t - thi gian song i ve tren quang ng AB Toc o truyen song trong kh quyen c tnh theo cong thc:

cVn

(5.23)

trong o: c - toc o truyen song anh sang trong chan khong, bang: 299792,2 km/S n - he so khuc xa cua kh quyen, phu thuoc vao chieu dai bc song ,

ap suat, nhiet o, ham lng bui Thi gian song i ve tren tuyen o c xac nh theo mot trong hai phng phap

sau ay: g Phng phap o xung: o trc tiep khoang thi gian truyen xung anh sang tren

khoang cach can o gia thi iem phat i va thi iem thu ve sau khi gng phan xa lai. Phng phap nay co o chnh xac thap nen t c s dung.

g Phng phap o pha: o gian tiep khoang thi gian truyen song anh sang, da tren c s o goc lech pha gia song thu c vi song phat ra. May thu phat phat ra mot loai song mang la song anh sang c mo un hoa theo bc song nao o, song nay i ti gng phan chieu roi quay tr lai. Qua trnh o goc lech pha trong may gia song thu c va song phat ra, chnh la qua trnh o phan le cua buc song. e xac nh so nguyen N bc song can phai o tren mot so tan so f co nh.

Khoang cach khong tnh theo (5.22) ma tnh theo cong thc:

( )S N2

(5.24)

trong o: N - so nguyen bc song; - o dai bc song mo un - goc lech pha o c

Hnh 5.12



Phng phap o pha c ng dung trong cac loai may o dai bang song anh sang tren khoang cach < 10 km. S d khoang cach trong o dai bang song anh sang b han che v song anh sang de b yeu khi gap cac lp sng mu, khoi, bui va oi hoi phai co tam nhn thong suot gia hai au canh o.

Nguon sang trong cac may o dai ien quang hien nay thng la Laser ban dan. Cac may toan ac ien t (ket hp o goc va o dai ien t) c t ong hoa cao. Cac ket qua o goc va o dai hien so tren man hnh va c ghi lai trong bo nh cua may hoac trong so o ien t e sau o a vao may tnh x ly theo cac chng trnh kem theo. Thao tac o kha n gian, thi gian o mot goc hoac mot canh ch trong vai giay. May toan ac ien t c s dung e lap li khong che toa o, o ve ban o va bo tr cong trnh.

ac trng ky thuat cua mot so may toan ac ien t va may o dai ien quang thong dung c neu trong bang 5.1.



Bang 5.1

Khoang cach (m)

TT Ten may Hang san xuat

o chnh

xac o

goc

o chnh xac o

canh Mot gng Ba gng

A. MAY O DAI IEN QUANG

1 RED2L Sokkia (Nhat) 5mm+3mm/1km 4600 5200m

2 GEOD220 Geotronics (Thu ien) 5mm+5mm/1km 2300 4000

3 DL1001 WiLD(Thuy s) 5mm+5mm/1km 800 1100

4 DI1600 WiLD 3mm+2mm/1km 25000 3500

5 DI2002 WiLD 1mm+1mm/1km 2500 3500

6 DI3000S WiLD 3mm+1mm/1km 9000 11000

B. MAY TOAN AC IEN T

(Total station)

1 SET2000 Sokkisha (Nhat) 2 2mm+2mm/1km 2400 3100

2 SET3000 Sokkisha 3 2mm+2mm/1km 2200 2900

3 SET2B,2C Sokkisha 2 3mm+2mm/1km 3500

4 SET4B,4C Sokkisha 5 5mm+3mm/1km 2100

5 GTS701 Topcon (Nhat) 2 2mm+2mm/1km 2400 3100

6 GTS702 Topcon 3 2mm+2mm/1km 2200 2900

7 TC400 WiLD (Thuy s) 10 5mm+5mm/1km 800 1300

8 TC600 WiLD 5 3mm+3mm/1km 1300 2000

9 TC1010 WiLD 3 2mm+2mm/1km 3500 5000

10 TC2002 WiLD 0,5 1mm+1mm/1km 2000 2800

11 DTM550 Nikon (Nhat) 1 2mm+2mm/1km 2400 310

12 DTM530 Nikon 2 2mm+2mm/1km 2200 2900

13 DTM520 Nikon 3 2mm+2mm/1km 1600 2300



Bai 4 (tiep)

DUNG CU VA PHNG PHAP O DIEN TCH

7.1. KHAI NIEM CHUNG

Trong cong tac quan ly qui hoach s dung at, trong tnh toan dung tch ho cha nc phuc vu thiet ke nha may thuy ien, tnh toan khoi lng ap ng, ao mng, tnh toan khoi lng san lap mat bang va lap qui hoach xay dng khu cong nghiep hoac khu dan c eu can phai xac nh dien tch.

e xac nh dien tch co the da theo ket qua o trc tiep ngoai thc a hoac theo so lieu o tren ban o a hnh hoac a chanh. Thng o chnh xac xac nh dien tch theo so lng o ngoai thc a cao gap 3-5 lan theo so lieu o tren ban o.

7.2. XAC NH DIEN TCH THEO SO LIEU O TRC TIEP NGOAI THC A

e xac nh dien tch theo so lieu o trc tiep ngoai thc a co the s dung mot trong cac phng phap chnh sau ay:

1. Theo ket qua o canh Trong tam giac ABC (H.7.1a), neu o ba canh a, b, c co the tnh dien tch tam giac

ABC theo cong thc: ( )( )( )P p a p b p c (7.1)

trong o: , ( )p 0 5 a b c - la na chu vi tam giac.

e xac nh dien tch cua mot khu at hoac mot tha ruong co dang t giac bat ky ABCD, ngoai bon canh S1, S2, S3, S4 con phai o them ng cheo S5.

Dien tch cua t giac ABCD (H.7.1b) bang tong dien tch hai tam giac ABD va BCD:

ABCD ABD BCDP P P

trong o: ABDP va BCDP tnh theo (7.1).



Hnh 7.1 oi vi khu at co ranh gii la ng gay khuc khep kn, e tnh dien tch ta chia

ra thanh nhieu tam giac, o tat ca cac canh, tnh dien tch cac tam giac theo (7.1) roi cong lai.

Phng phap nay thch hp khi trong tay ngi o dien tch ch co thc day vai hoac thc thep cuon.

2. Theo ket qua o canh va o goc Trong tam giac ABC (H.7.2a) neu o hai canh S1, S2 va goc nam gia hai canh

nay co the tnh dien tch tam giac ABC theo cong thc: sin1 2P S S (7.2)

Hnh 7.2 a- Trng hp at may kinh v tai m ot hoac nhieu iem nam

tren ranh khu at

e xac nh dien tch khu at co dang t giac bat ky ABCD ta chia no thanh hai tam giac roi at may toan ac quang hoc hoac toan ac ien t tai mot tram (H.7.2b) hoac tai hai tram (H7.2c) e o cac goc va cac canh bang ch lng c hoac bang ien quang. Trong mot so trng hp co the o canh bang thc thep.

Dien tch t giac ABCD H.7.2b va H.7.2c tnh theo cong thc: P = S1S2sin1 + S2S3 sin2 (7.3)

va: P = S1S2sin1 + S3S4 sin2 (7.4) Co the s dung phng phap nay cho trng hp khu at chia c thanh nhieu

tam giac. b- Trng hp at may kinh v ngoai khu at - tnh dien tch theo toa o cc

at may kinh v tai iem kinh v A, ngam chuan ve iem B, quay may theo chieu kim ong ho ngam cac iem 1, 2, 3, 4 oc so c cac goc 1, 2, 3, 4. Da vao goc nh hng canh khi au AB va cac goc 1, 2, 3, 4 tnh cac goc nh hng 1, 2, 3, 4 cua canh A-1, A-2, A-3, A-4. T H.7.3 ta co cong Hnh 7.3



thc tnh dien tch cua khu at khep kn 1234. P = PA12 + PA23 + PA34 PA14

2P = S1S2sin(2 1) + S2S3sin(3 2) + S3S4sin(4 3) + S4S1sin(1 4) (7.5) Trong (7.5) trc so hang th 4 ben ve trai mang dau (+) v theo cong thc lng

giac sin(x) = sinx nen: sin(1 - 4) = sin(4 1)

t (7.5) suy ra cong thc tong quat:

P = sin( )n

i i 1 i 1 i1

1 S S2

(7.6)

neu tnh t so o toan ac ta co cong thc:

P = sin( )n

i i 1 i 1 i1

1 S S2

(7.7)

Lu y: - anh so th t cac iem goc at t 1

en n theo chieu kim ong ho. - Thay ch so i t 1 4 vao (7.6) e kiem

tra (7.5) khi i = 4 th i +1 chnh la iem 1.

3. Xac nh dien tch theo toa o vuong goc

Toa o vuong goc cua cac iem 1, 2, 3, 4 thuoc t giac bat ky 1234 co the nhan c bang cach chuyen t cac so lieu toa o cc o trc tiep bang may toan ac quang hoc hay toan ac ien t, co the nhan c t ban o so hoac o trc tiep tren ban o giay.

Dien tch khu at 1234 se bang tong ai so dien tch cac hnh thang. P1234 = P1122 + P2233 P1144 P4433 (7.8)

hoac: P1234 = P2233 + P3344 P2211 P1144 (7.9) T (7.8) va cac so lieu tren H.7.4 ta co:

( )( ) ( )( ) ( )( ) ( )( )1 2 2 1 2 3 3 2 3 4 3 4 4 1 4 12P x x y y x x y y x x y y x x y y ( )( ) ( )( ) ( )( ) ( )( )1 2 2 1 2 3 3 2 3 4 4 3 4 1 1 42P x x y y x x y y x x y y x x y y

( ) ( ) ( ) ( )1 2 1 2 2 1 2 3 2 3 3 22P x y y x y y x y y x y y ( ) ( )3 4 3 4 4 3x y y x y y ( ) ( )4 1 4 1 1 4x y y x y y

( ) ( ) ( ) ( )1 2 4 2 3 1 3 4 2 4 1 32P x y y x y y x y y x y y (7.10)

T (7.10) va lu y khi i = n th i+1 se la iem au tien (iem 1), ta co cong thc tong quat:

( ) ( )n n

i i 1 i 1 i i 1 i 11 1

1 1P x y y y x x2 2

(7.11)

7.3. XAC NH DIEN TCH THEO SO LIEU O TREN BAN O GIAY

e xac nh dien tch theo so lieu o tren ban o giay ta co the s dung mot trong ba phng phap sau ay:

Hnh 7.4



1. Tnh dien tch theo cach chia hnh tam giac

oi vi khu at tng oi ln (khoang 10-15cm2 tren ban o) co ng bien gay khuc khep kn, e tnh dien tch ta chia no thanh nhieu tam giac roi tien hanh o canh ay va chieu cao cua moi tam giac bang thc t le hoac phim ke li o vuong 1 1 mm hay 2 2 mm hoac 5 5 mm.

Tnh dien tch cua tng tam giac theo (7.2) roi cong tat ca lai:

1P ah2

(7.12)

Trng hp hai tam giac ke nhau co chung canh ay, v du tam giac 135 va 345, ta s dung cong thc:

( )b c1P b h h2

(7.13)

e kiem tra va nang cao o chnh xac ta chia khu at thanh nhieu tam giac theo kieu khac roi tnh dien tch lan th hai. V du chia theo H.7.5 thanh ba tam giac 234, 124, va 145. Chenh lech dien tch gia hai lan o khong c vt qua tr so:

,0 04mp p100

(7.14)

trong o: m - mau so t le ban o; P - dien tch hnh can o tnh en m2 Dien tch cuoi cung cua khu at la tr trung bnh cua hai ket qua tnh c. Khi

chia can lu y e chieu cao cua cac tam giac co o dai gan bang canh ay.

2. o dien tch bang phm ke o vuong e o dien tch khu at nho co ng bien la ng

cong khep kn, ta dung phim ke li o vuong 1 1mm, 2 2mm hoac 5 5mm at len hnh can o (H.7.6).

au tien em so o nguyen, sau o c lng cac o le (bang 0,10,9 o nguyen) nam sat ng bien.

Dien tch cua khu at bang tong so o nhan vi dien tch cua mot o ngoai thc a. Dien tch moi o ngoai thc a bang bnh phng cua canh o tren ban o nhan vi mau so t le. V du canh li o vuong dai 1 mm, mau so t le ban o la 5000 th dien tch cua moi o vuong la: (1mm 5000)2 = (5 m)2 = 25 m2

e kiem tra va tang cng o chnh xac ta xoay phim ke o vuong theo hng khac, lai em so o nguyen va c lng o le roi tnh dien tch lan th hai. Neu chenh lech dien tch gia hai lan o khong qua tr so tnh theo (7.14) th lay tr trung bnh lam dien tch cuoi cung cua khu at.

3. o dien tch bang may

May o dien tch la dung cu c hoc dung e o dien tch cac hnh tren ban o theo nguyen ly tch phan. May co ba phan chnh: tay on cc (1), tay on quay (2) va bo

Hnh 7.5

Hnh 7.6

Hnh 7.7



phan oc so (3) (H.7.7).



Tay on cc la mot thanh kim loai, mot au moc vao qua nang la cc cua may, au kia moc vao bo phan oc so. Tay on quay la mot thanh vuong dai co khac vach ghi so. Mot au co kim o (5), au kia lap vao bo phan oc so. Tay on quay co the thay oi chieu dai.

Bo phan oc so (H.7.8) gom co vong oc (6), banh xe oc so (7) va du xch (8). Khi cho kim o di ong theo chu vi khu o tren ban o, banh xe oc so se lan tren mat giay lam cho vong oc so quay theo.

Vong oc so chia thanh 10 phan. Banh xe oc so chia thanh 100 vach. Banh xe oc so quay het mot vong 100 vach th vong oc so quay het mot vong 10 phan. 10 vach cua du xch co gia tr bang mot vach tren banh xe oc so.

Tr so oc tren may co 4 so. So th nhat la hang ngan oc tren vong oc so. So th 2 va 3 la hang tram va hang chuc oc tren banh xe oc so. So th 4 la hang chuc oc tren du xch. V du so oc tren H.7.8 la m = 3583 vach.

e o dien tch mot hnh tren ban o, ta trai t ban o len ban, at may len mat giay. Neu hnh nho ta at cc p ngoai khu o, neu hnh ln ta at cc p trong khu o (H.7.9)

Hnh 7.9

Hnh 7.8



Co nh cc (qua nang) tren ban o, anh dau iem A tren ng bien hnh cau o. at kim o trung vi iem A oc c so m1. Di chuyen kim o theo chieu kim ong ho tren ng bien hnh can o. Khi kim o vong ve en iem A th oc so m2.

Neu cc may nam ngoai khu o th tnh dien tch theo (7.15), neu nam trong khu o tnh theo (7.16).

P = C(m2 m1) (7.15) P = C(m2 m1) + q (7.16)

trong o: m2 m1 = n - la so vach chia o c C - gia tr vach chia cua may; q - hang so may Gia tr vach chia C va hang so q co the xac nh bang cach o ng bien cua mot

khu vc a biet dien tch. V du: e xac nh tr so C ta at cc may ngoai, o dien tch hai o toa o kch thc 10 20 cm tren ban o t le 1:2000. S dung (7.15) ta co:

2 1

PCm m

(7.17)

trong o: P = (0,1 m 2000) (0,2 m 2000) = 80000 m2 m2 m1 - so vach chia o c

e xac nh hang so P ta at trong o 9 o toa o kch thc 30 30 cm tren ban o t le 1:2000. T (7.16) ta co:

q = P C(m2 m1) (7.18) trong o: C - gia tr vach chia a xac nh theo (7.17)

P - dien tch khu o bang (0,3 m 2000)2 = 360.000 m2 m2 m1 - so vach chia o c Tr so C va q thng c xac nh 2-3 lan roi lay tr trung bnh. Ngay nay, tren th trng xuat hien nhieu loai may o dien tch ien t, trong o

co may o dien tch ien t X-plan. Ngoai chc nang chnh la o dien tch, may X-plan con c s dung e o dai, o goc, xac nh toa o trc tiep tren ban o. Neu s dung phan mem LT/X-plan i kem co the s dung may e so hoa ban o [28].



TAI LIEU THAM KHAO

1. .Nguyn tn Lc.Trc a i cng .nh xb i hc Quc gia tp. HCM 2002 (tr79-tr92;110-116)

2. Phm vn Chuyn. o c ; Nh XB xy dng; H ni 2001. (tr38-tr41;tr82-tr88) .

3. ao Duy Liem (chu bien), Trac a, Nha Xuat ban Giao duc, Ha Noi, 1992

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