Handbook of Civil Engineering Calculations

TfME OF CULMINATION OFA STAR

Determine the Eastern Standard Time (75th meridian time) of the upper culmination of
Polaris at a site having a longitude 810 W of Greenwich. Reference to an almanac shows
that the Greenwich Civil Time (GCT) of upper culmination for the date of observation is
3
h
20
m
Q5
s

Calculation Procedure:

1. Convert the longitudes to the hour-minute-second system
   The rotation of the earth causes a star to appear to describe a circle on the celestial sphere
   centered at the celestial axis. The star is said to be at culmination or transit when it ap-
   pears to cross the observer's meridian.
   In Fig. 12, P and M represent the po-
   sition of Polaris and the mean sun, re-
   spectively, when Polaris is at the Green-
   wich meridian, and P' and M' represent
   the position of these bodies when Polaris
   is at the observer's meridian. The dis-
   tances h and h' represent, respectively,
   the time of culmination of Polaris at
   Greenwich and at the observer's site,
   measured from local noon. Since the ap-
   parent velocity of the mean sun is less
   than that of the stars, h' is less than h, the
   difference being approximately 10 s/h of

FIGURE 12. Culmination of Polaris. longitude.
By converting the longitudes, 360°
corresponds to 24 h; therefore, 15° corre-
sponds to 1 h. Longitude of site = 81° =
54/, = 5^4"W; standard longitude =
75° = 5 h.

2. Calculate the time of upper culmination at the site
   Correct this result to Eastern Standard Time. Since the standard meridian is east of the ob-
   server's meridian, the standard time is greater. Thus

GCT of upper culmination at Greenwich 3 h2Qm 05 s

Correction for longitude, 5.4 x 10 s 54*

Local civil time of upper culmination at site 3* 19 W 115

Correction to standard meridian 24"^1 OO^5

EST of upper culmination at site 3*43m 1 Pa.m.

PLOTTING A CIRCULAR CURVE

A horizontal circular curve having an intersection angle of 28° is to have a radius of 1200

ft (365.7 m). The point of curve is at station 82 + 30. (a) Determine the tangent distance,

Apporent

motion

Longitude of site

StandardmeridianObserver'smeridian Greenwichmeridian