Surveying Angles Measurement Faculty of Applied Engineering and Urban Planning Civil Engineering Department Surveying First Semester 2010/2011 Angles Measurement Lecture 18 - Week 11

Content Type of Angles Reference Direction Reduced Bearing of Line Azimuth or Whole Circle Bearing Back Reduced Bearing and Back Azimuth

Horizontal Angles A C Ground surface A’ C’ B Horizontal plane B’ A horizontal angles is the angle between two interacting lines lay in horizontal plane ( the value of the angle is between 0º to 360º )

Vertical Angles A vertical angles is measured in a vertical plane in two ways depending on the reference from which the angle is measured: 1- Elevation or depression angle: using the horizontal plane as a reference ( the value of the angle is between -90º to 90º ) a- when the point being sighted on is above the horizontal plane, the angle is called an angle of elevation with positive value. b- when the point being sighted on is below the horizontal plane, the angle is called an angle of depression with negative value.

Zenith Angles Zenith angle : using the overhead extension of the plumb line as a reference line, its value ranges from 0º to 180º.

Reference Direction In the horizontal plane, direction of all lines of a survey are referenced to the meridian ( the true or geographic north – the magnetic north – the assumed north ). True meridian (at any point): the direction of the line that connects this point to the north pole of the earth. This line usually coincides with the great circle that passes through that point and the (true) geographic north and south poles of the earth.

Reference Direction Magnetic meridian: a direction that the magnetic needle takes when allowed to come to rest in the earth’s magnetic needle , and this meridian usually does not coincide with the true meridian .They make a small angle with each other called the magnetic declination . Declination: The angle between the magnetic and true meridian is called the magnetic declination and expressed as the angular distance east or west of the true meridian , and its value is about 3º. Assumed meridian: if neither the geographic north, nor the magnetic north is known in a certain local area for which the surveyor is performing measurements, a line can be arbitrarily chosen and assumed to be in the direction the north .

Reduced Bearing of Line There two ways to determine the direction in surveying: Azimuth and Bearing. 1- Bearing : is the acute angle that the line makes with the reference meridian ( true or magnetic ). It expressed as North (or South) so many degrees to the East (or West). and its value ranges from 0º to 90º. and called true bearing if the true meridian is used and magnetic bearing if the magnetic meridian is used

Reduced Bearing of Line The magnetic reduced bearing of lines OE, OF, OG, and OH are: N 40º E S 63º E S 81º W N 47º W The magnetic meridian is 3º east of the true meridian. The true reduced bearing of lines OE, OF, OG, and OH are: N 43º E S 60º E S 84º W N 44º W

Azimuth or Whole Circle Bearing 2- Azimuth : is the clockwise horizontal angle that the line makes with the north end of the reference meridian, and its value ranges from 0º to 360º. And called true azimuth if the true meridian is used as the reference and called magnetic azimuth if the magnetic meridian is used The azimuths of lines OA, OB, OC, and OD are: 70º 135º 265º 36’ 20’’ 328º Respectively relative to the true north .

Back Reduced Bearing and Back Azimuth: Back Reduced Bearing and Back Azimuth: Back bearing or Back azimuth of a line going from A to B is the azimuth or Bearing of the same line going from B to A. N Reference meridian N A 60º 60º O

Questions?!