Angles and Direction Lecture Notes (FRM 61, 2024-2025)

**Angles and Direction (lecture 3)** FRM 61 Forest Surveying and Engineering 1^st^ sem SY 2024-2025 **ANGLES** the difference in direction between two convergent lines Three types: **1. Horizontal** angle is formed by the directions to two objects in a horizontal plane **2. Vertical** angle...

**Angles and Direction (lecture 3)** FRM 61 Forest Surveying and Engineering 1^st^ sem SY 2024-2025 **ANGLES** the difference in direction between two convergent lines Three types: **1. Horizontal** angle is formed by the directions to two objects in a horizontal plane **2. Vertical** angle is formed by two intersecting lines in a vertical plane, one of these lines is horizontal **3. Zenith** angle is the complementary angle to the vertical angle and is formed by two intersecting lines in a vertical plane, one of these lines directed toward the zenith **DIRECTION** defined by the horizontal angle it makes with a fixed reference line known as the **meridian** Types of meridian: 1\. TRUE \- also known as geographic or astronomic \- adapted in surveying practice \- lines passes through the geographic north and south poles of the earth \- fixed, not parallel to each other  2\. MAGNETIC \- lines parallel with the magnetic force of the earth \- vary with time and location \- not parallel with the true meridian 3\. GRID \- parallel to the central meridian of a system of plane rectangular coordinates \- one central meridian coincides with the true meridian \- applicable to plane surveys 4\. ASSUMED \- arbitrarily chosen fixed line of reference which is taken for convenience Kinds of Horizontal Angles 1\. Interior Angles -- the angles between adjacent lines in a closed polygon 2\. Deflection Angles -- the angle between a line and the prolongation of the preceding line. It may be turned clockwise or counterclockwise 3\. Angles to the Right -- angles to the right are measured clockwise from the preceding line to the succeeding line. These angles are also referred to as azimuths from back line. Units of Angular Measurement 1\. The Degree -- sexagesimal system; circumference of a circle is divided into 360 parts or degrees - Each degree is further subdivided into 60 minutes and per minute is subdivided again into 60 seconds 2\. The Grad - centesimal system; circumference of a circle is divided into 400 parts called grads - The grad is subdivided into 100 centesimal minutes and a centesimal minute is further subdivided into 100 centesimal seconds 3\. The Mil -- the circumference is divided into 6400 parts called mils, or 1600 mils is equal to 90^o^ - commonly used in military operations 4\. The Radian -- one radian is defined as the angle subtended at the center of a circle by an arc length exactly equal to the radius of the circle - One radian equals 180/π or approximately 57.2958^o^ and 1^o^ equals π/180 or approximately 0.0174533 radians Bearing The **acute** horizontal angle between the reference meridian and the line. Either the letters N or S precedes the bearing angle and the letters E or W follows the indicated value of the angle. *It is never done the other way around*. Forward and Back Bearings Using the quadrantal system: o**forward bearing -** observed in the direction in which the survey progresses o **back bearing -** the same line but as observed in an opposite direction How to obtain back bearing from the forward bearing: -- Change first letter from N to S or from S to N and the second letter from E to W or from W to E. Azimuth The horizontal angle measured from the meridian to the line Usually measured in a clockwise direction with respect to either the north meridian or the south meridian. Forward and Back Azimuths To determine the back azimuth when the forward azimuth is known, the following rules are used: RULE 1: if the forward azimuth of the line is greater than 180 degrees, subtract 180 degrees to obtain the back azimuth. RULE 2: when the forward azimuth of the line is less than 180 degrees, add 180 degrees to determine the back azimuth. 0^o^ -- 90^o^ BEARING & AZIMUTH 0^o^ -- 360^o^ Requires 2 letters & a numerical value Clockwise & counterclockwise Measured from north or south Requires only a numerical value Clockwise (only?) Measured either from north or south *Relationships Between Bearings and Azimuths* **N** B = 360^o^- A A = 360^o^- B B = A **W E** B = A - 180^o^ A = 180^o^ + B B = 180^o^- A A = 180^o^- B **S** Seatwork +-----------------------------------+-----------------------------------+ | **Bearing** | **Azimuth** | | | | | N 66^o^ 30' W | | +===================================+===================================+ | | 0^o^ | +-----------------------------------+-----------------------------------+ | | 135^o^ | +-----------------------------------+-----------------------------------+ | S 50^o^ 10' 25" E | | +-----------------------------------+-----------------------------------+ | | 270^o^ 1' | +-----------------------------------+-----------------------------------+ The Compass A hand-held angular instrument for determining the horizontal direction of a line with reference to the magnetic meridian Types of Compasses: 1\. **Brunton** compass -- most versatile and widely used \- with clinometer; can be mounted on tripod or Jacob staff or just held on hand 2\. Lensatic - its name is derived from the magnifying lens which is mounted in the eyepiece; \- designed for military use whose north point on its magnetic needle is luminous as well as the cardinal points on the begel crystal \- Mils as well as degrees are shown on the dial 3\. Surveyor's compass -- popular on plane surveying; - for forest survey and geological exploration - can also be mounted on Jacob staff 4\. Plain pocket -- same with surveyor's except that it has no sight vanes; \- small and handy 5\. Prismatic -- sometimes called liquid compasses because it is filled with liquid to minimize frictional effects of the needle; \- widely used by sailors for navigation at sea 6\. Forester's compass -- very similar to  surveyor's compass Local Attraction Local influences that attracts magnetic needle from its normal pointing towards magnetic north Examples are steel, iron, magnetic ores and direct electric current Local attraction is present if the forward and back bearings differ substantially The Magnetic Declination The horizontal angle and direction by which the needle of a compass deflects from the true meridian at any particular locality Deflection may be eastward or westward of the true meridian Magnetic poles are not points but oval areas located about 2000 km from geographic poles Sample Problem Determine the true bearings and azimuth reckoned from north of a line whose magnetic bearing is S 60^o^ 5' E. The magnetic declination is known to be 12^o^, W.