1. The line of sight of a theodolite is out of adjustment by 12". 10

Size: px

Start display at page:

Download "1. The line of sight of a theodolite is out of adjustment by 12". 10"

Angela Hines
5 years ago
Views:

1 ASSOCIATION OF CANADA LANDS SURVEYORS - BOARD OF EXAMINERS WESTERN CANADIAN BOARD OF EXAMINERS FOR LAND SURVEYORS ATLANTIC PROVINCES BOARD OF EXAMINERS FOR LAND SURVEYORS SCHEDULE I / ITEM 3 Advancd Survying (including Survy Astronomy) Fbruary 000 (1990 Rgulations) (Closd Book) Tim: 3 hours Marks Not: This xamination consists of 8 qustions on 3 pags. Astronomical tabls and formula shts ar attachd. All numrical answrs must b supportd with calculations. 1. Th lin of sight of a thodolit is out of adjustmnt by 1". 10 (a) In prolonging a lin by plunging th tlscop btwn backsight and forsight, but not doubl cntring, what angular rror is introducd? (b) What off-lin linar rror rsults on a forsight of 500 m? (c) Dscrib th procss of doubl cntring. (d) Many lctronic thodolits / total stations allow saving crtain instrumntally rrors intrnally so that thy may b automatically applid to obsrvd angls. What is th nam of this thodolit rror? How should it b dtrmind in th fild? Is doubl-cntring ncssary with an lctronic thodolit if this rror is corrctly dtrmind, savd intrnally, and applid to obsrvd angls?. Thodolit rrors can b minimizd by appropriat obsrving procdurs. 15 (a) Dscrib th procdurs usd to masur prcis horizontal angls with a dirctional thodolit such as a Wild T or Krn E. (b) Indicat th thodolit rrors that ar minimizd by ach obsrving procdur. Pag 1 of 7

2 3. Stations A, B and C ar on a straight lin. Th following distancs ar masurd with 5 an EDM: Distanc AB m Distanc AC m Distanc BC m (a) Dtrmin th EDM systm masurmnt constant (b) Dtrmin th lngth of ach sgmnt corrctd for th EDM systm masurmnt constant. 4. Th NAD83(CSRS) position of th Algonquin Activ Control Point (ACP) is 15 latitud N longitud W llipsoidal hight m goidal hight m orthomtric hight m Th rfrnc llipsoid has a m and 1/f Th stability of th Algonquin ACP is confirmd by masuring to svral rfrnc stations. Th northing and asting of th Algonquin ACP and rfrnc station A, in th Univrsal Transvrs Mrcator projction, ar as follows: Station Northing (m) Easting (m) Algonquin ACP Rfrnc Station A (a) What is th grid distanc from th Algonquin ACP to Rfrnc Station A? (b) What is th distanc on th rfrnc llipsoid? (c) What is th combind scal factor? (d) What should th masurd horizontal distanc b? () What is th UTM zon numbr? 5. Discuss th diffrncs among godtic azimuths drivd from GPS obsrvations, 10 astronomic azimuth drivd from obsrvations to Polaris and a grid azimuth drivd from UTM coordinats. Pag of 7

3 6. Discuss th diffrncs among llipsoidal hights drivd from GPS, hights drivd 10 dirctly from lvlling, publishd CGVD8 orthomtric hights and gopotntial hight diffrncs. 7. Th following data was obtaind from obsrvations on Polaris: 5 Dat: 9:00 pm PST, January 3, 000 Latitud: N Longitud: W Point Sightd D/R HCR Univrsal Tim RO D Polaris D h 38 m 39 s Polaris R h 41 m 4 s RO R (a) Dtrmin th astronomic azimuth of th Rfrnc Objct (RO). (b) Illustrat, on a Clstial sphr, for ths obsrvations: th Grnwich Hour Angl (GHA), Local Hour Angl (LHA) and dclination (δ) of Polaris at th tim of obsrvation; th Azimuth of Polaris (Az ); Local Mridian of th obsrvr, Grnwich mridian, Longitud of local mridian, Clstial quator, North Clstial Pol (NCP), Horizon, Znith, North point and East point. 8. Th latitud and longitud of a point is: 10 Latitud: Longitud: N W (a) Comput th tim th sun crosss th local mridian on January 3, 000. (b) Comput th maximum altitud of th sun on January 3, 000. Hint: At Culmination, th sun crosss th local mridian and attains its maximum altitud. Total marks: 100 Pag 3 of 7

4 Formulas Horizontal Collimation Error Error in Circl rading C C i whr cos β C : rror in circl rading i C : inclination of collimation axis wrt horizontal axis β : angl of lvation of obsrvd targt Horizontal axis rror Error in circl rading t i t tan β whr t : rror in circl rading i t : inclination of horizontal axis wrt vrtical axis β : angl of lvation of obsrvd targt Influnc of tilt of vrtical axis on (a) Vrtical angls τ cosα (b) Horizontal angl τ sin α tan β τv τ H whr τ: angl vrtical axis inclind wrt dirction of gravity α: angl btwn plan of tiltd axis and dirction of tlscop Group rfractiv indx of Light and NIR wavs at standard conditions (Dry air, 0 C K, 760 mmhg mb) Ng ( ng 1) x λ λ whr λ : carrir wavlngth in µm Group rfractiv indx of Light and NIR wavs at ambint tmpratur N P Ng T Ng Ng w 760 T whr Ng w λ λ : carrir wavlngth in µm P : Prssur in mb T : thrmodynamic tmpratur T t C : watr vapour prssur (ambint) in mmhg Pag 4 of 7

5 Rfractiv indx for Microwavs N M nm ( 1) x10 ( P ) T T T whr P : Prssur in mb T : thrmodynamic tmpratur T t C : watr vapour prssur (ambint) in mmhg Partial Watr vapour Prssur ( t t ) p( t t ) E W p E ICE from frozn wt bulb wick t [ ( 3.46x10 p) ]* 6.111xp E W t 6.45t E ICE ( 4.18x10 p) *6.1115xp t [ ] whr : partial watr vapour prssur in mb p : atmosphric prssur in mb t : dry bulb tmpratur in C t : wt bulb tmpratur E W : saturation watr vapour prssur ovr watr E ICE : saturation watr vapour prssur ovr watr Azimuth from Astronomic Triangl sin t tan Az whr Az : Azimuth cosϕ tanδ sin ϕ cost t : LHA or 360 -LHA ϕ : latitud of obsrvr s position δ : dclination Pag 5 of 7

6 Univrsal Transvrs Mrcator Projction Smi-major axis a Smi-minor axis b Flattning a b f a Eccntricity a b a a( 1 ) Radius of curvatur in mridian ρ 3 ( 1 sin ϕ ) Radius of curvatur in prim vrtical ν a 1 ( 1 sin ϕ ) Gomtric man radius R M ρν Scal factor Elvation factor Combind scal factor X K K o 1 + RM whr K o X (E )/ RM M RM + h whr h : man hight abov rfrnc llipsoid M K * M C Scal Map (Grid) Distanc / Ground Distanc Pag 6 of 7

7 POLARIS DATA FOR 0 HOURS UT JANUARY 000 Dat Right Ascnsion G. App. Sid. Tim GHA Dclination h m s h m s ' " ' " 000 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan SOLAR EPHEMERIS FOR 0 HOURS UT JANUARY 000 Dat Right Ascnsion G. App. Sid. Tim GHA Dclination Distanc Equation of Tim h m s h m s ' " ' " AU m s 000 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Pag 7 of 7

Sundials and Linear Algebra

Sundials and Linear Algebra Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.