LOGO DETERMINING HEIGHT TOPIC 1.xxx

LOGO Introduction  For many jobs it is important to be able to determine the height of features. For example:  Trees  Buildings  Etc.  The best equipment and method to use is determined by the desired accuracy and precision of the data.  The equipment and methods used can be divided into two categories:  Estimates  Measurements.

LOGO Estimate Methods  Shadow  Line of sight  Fixed angle

LOGO Estimating Height- Shadow Method  The shadow length of all objects is proportional to their height.  The height of an object can be determined by measuring the shadow length of an object with a known height and comparing it to the length of the shadow for the unknown height.

LOGO Shadow Method-Example Determine the height of the tree m 4.5 m 6.0 m

LOGO Shadow Method Advantages 1.No surveying equipment 2.Easy math Disadvantages 1.Requires sunny day 2.Must have clear space to see shadows. 3.Low precision

LOGO Height- Line of Sight Method  The line of sight method is base on the principles of right triangles.  The ratio of the lengths of the sides of a right triangle are the same as long as the angle is the same. If two lengths of a small triangle and one side of the large triangle are known the length of the other side of the large triangle can be calculated using a ratio.

LOGO Height- Line of Sight--cont. 1.Select a stick of known height. 2.Move away from tree some distance and place stick in ground.  Insure it is plumb 3.Lay on ground and sight across top of stick to the top of the object. 4.Move towards or away from the stick until the sight line is aligned with the top of the stick and the top of the object. 5.Measure the distance from the stick to your eye position. 6.Measure the distance from your eye position to the base of the tree.

LOGO Line of Sight Method--Example  Determine the height of the tower.  The stake and sight position form one triangle, the tower and sight position form a second triangle.  Both triangles have the same angle.  Therefore:

LOGO Line of Sight Method--cont. Advantages: 1.Low tech 2.Doesn’t require sunny day 3.Adaptable to many different objects 4.Easy math Disadvantages: 1.Difficulty establishing line of sight accurately. 2.Low precision 3.Precision is reduced if stake is not at same elevation as base of the object.

LOGO Height- Fixed Angle Method  The fixed angle method uses a principle of triangles--the legs of a 45 degree triangle are the same length.  Easy way to get a 45 angle is to fold a piece of paper.  The height is determined by sighting along the hypotenuse of the triangle until the line of sight aligns with the top of the the object.  The height of the object is the distance from the object plus the eye height. The paper must held horizontal for acceptable results.

LOGO Fixed Angle Method-Example Determine the height of the tree m 5.8 m 16.4 m

LOGO Measuring Methods  Transit or theodolite  Others  With a theodolite the vertical angle to the top of the object can be measured using the tangent trig. function.  Knowing the angle, the height of the instrument and the distance from the transit to the object, the height can be calculated.

LOGO Height Measuring-Theodolite

LOGO Hgt. Measuring- Theodolite Example 165m 5.9m

LOGO

TOPIC 4: ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING ERT247/4 GEOMATICS ENGINEERING

LOGO Introduction  An angle is defined as the difference in direction between two convergent lines.

LOGO Types of Angles  Vertical angles  Zenith angles  Nadir angles

LOGO Definition  A vertical angle is formed by two intersecting lines in a vertical plane, one of these lines horizontal.  A zenith angle is the complementary angle to the vertical angle and is directly above the obeserver  A Nadir angle is below the observer

LOGO Three Reference Directions - Angles

LOGO Meridians  A line on the mean surface of the earth joining north and south poles is called meridian. Note: Geographic meridians are fixed, magnetic meridians vary with time and location. Relationship between “true” meridian and grid meridians Figure 4.2

LOGO Geographic and Grid Meridians

LOGO Horizontal Angles  A horizontal angle is formed by the directions to two objects in a horizontal plane.  Interior angles  Exterior angles  Deflection angles

LOGO Definitions:  Interior angles are measured clockwise or counter-clockwise between two adjacent lines on the inside of a closed polygon figure.  Exterior angles are measured clockwise or counter-clockwise between two adjacent lines on the outside of a closed polygon figure.  Deflection angles, right or left, are measured from an extension of the preceding course and the ahead line. It must be noted when the deflection is right (R) or left (L).

LOGO Closed Traverse Interior Angles Closed traverse showing the interior angles.

LOGO Open Traverse (a)Open traverse showing the interior angles. oo (b) Same traverse showing angle right (202 o 18’) and angle left (157 o 42’)

LOGO Types of Measured Angles

LOGO Angle Units  Several different units can be used to measure angles.  This class uses two.  Decimal Degrees (DD)  Degrees Minutes Seconds (DMS)

LOGO Angle Units-DD  DD expresses any part of an angle less than a whole degree as a decimal.  o  Electronic instruments such as total stations and GPS can output angles in DD.  Angles in DD is the system of choice today because it is the easiest form to use with calculators and computer software.

LOGO Angle Units-DMS  DMS is the angle measuring method used on most mechanical instruments.  108 o 23’ 40”  In the DMS system there are 60 minutes in each degree and 60 seconds in each minute.  Because both systems are still used, it is useful to know how to convert from one to the other.

LOGO DMS to DD  Many calculators have a DMS to DD and DD to DMS conversion key.  It will save a lot of time and reduce mistakes if you learn how to do these conversions on a calculator.  If you cannot do it on a calculator, then you must learn how to do it manually. To convert from a DMS angle to a DD angle the minutes and seconds must be converted to a fraction. The fractions are reduced to decimal equivalents and then the parts are added.

LOGO DMS to DD-cont. Example: Convert 120 o 34’ 45” to DD

LOGO DD to DMS  The manual method from DD to DMS follows the same math principles.  The decimal part of the angle must be converted to minutes and seconds. Example: convert the angle o to DMS

LOGO Adding & Subtracting Angles in DMS  Occasionally when using mechanical instruments it is necessary to add and subtract angles using DMS.  The addition and subtraction principles are the same, except units of 60 are carried or subtracted instead of units of 10.

LOGO Adding Angles in DMS Example: Add the angles 20 o 45’ 27” and 30 o 24’ 35” In is not proper to leave an angle measurement with more that 60 minutes or seconds. The answer must be reduced.

LOGO Subtracting Angles In DMS Subtraction follows the same principles. Example: Subtract 40 o 18’ 50” from 120 o 15’ 45” and would result in negative numbers. 120 o 15’ 45” must be converted to: The answer is:

LOGO Directions  Azimuth  An Azimuth is the direction of a line as given by an angle measured clockwise (usually) from the north.  Azimuth range in magnitude from 0° to 360°.  Bearing  Bearing is the direction of a line as given by the acute angle between the line and a meridian.  The bearing angle is always accompanied by letters that locate the quadrant in which line falls (NE, NW, SE or SW).  Range 0° to 90°.

LOGO Bearings and Azimuths

LOGO Azimuths

LOGO Azimuths

LOGO Bearing

LOGO Bearing

LOGO Bearings

LOGO Relationships Between Bearings and Azimuths To convert from azimuths to bearing,  a = azimuths  b = bearing QuadrantAnglesConversion NE 0 o  90 o a = b SE 90 o  180 o a = 180 o – b SW180 o  270 o a = b +180 o NW270 o  360 o a = 360 o – b

LOGO Reverse Direction  In figure 4.8, the line  AB has a bearing of N 62 o 30’ E  BA has a bearing of S 62 o 30’ W To reverse bearing: reverse the direction Figure 4.7 Reverse Directions Figure 4.8 Reverse Bearings LineBearing ABN 62 o 30’ E BAS 62 o 30’ W

LOGO

Reverse Direction  CD has an azimuths of 128 o 20’  DC has an azimuths of 308 o 20’ To reverse azimuths: add 180 o Figure 4.8 Reverse Bearings LineAzimuths CD128 o 20’ DC308 o 20’

LOGO Counterclockwise Direction (1) Start Given

LOGO Counterclockwise Direction (2)

LOGO Counterclockwise Direction (3)

LOGO Counterclockwise Direction (4)

LOGO Counterclockwise Direction (5) Finish Check

LOGO Sketch for Azimuth Computation

LOGO Clockwise Direction (1) Start Given

LOGO Clockwise Direction (2)

LOGO Clockwise Direction (3)

LOGO Clockwise Direction (4)

LOGO Clockwise Direction (5) Finish Check

LOGO Start Given Finish Check

LOGO Azimuth Computation  When computations are to proceed around the traverse in a clockwise direction,subtract the interior angle from the back azimuth of the previous course.  When computations are to proceed around the traverse in a counter-clockwise direction, add the interior angle to the back azimuth of the previous course.

LOGO Azimuths Computation  Counterclockwise direction: add the interior angle to the back azimuth of the previous course CourseAzimuthsBearing BC270 o 28’N 89 o 32’ W CD209 o 05’S 29 o 05’ W DE134 o 27’S 45 o 33’ E EA 62 o 55’N 62 o 55’ E AB330 o 00’N 30 o 00’ W

LOGO Azimuths Computation  Clockwise direction: subtract the interior angle from the back azimuth of the previous course CourseAzimuthsBearing AE242 o 55’S 62 o 55’ W ED314 o 27’N 45 o 33’ W DC 29 o 25’N 29 o 05’ E CB90 o 28’S 89 o 32’ E BA150 o 00’S 30 o 00’ E

LOGO Bearing Computation  Prepare a sketch showing the two traverse lines involved, with the meridian drawn through the angle station.  On the sketch, show the interior angle, the bearing angle and the required angle.

LOGO Bearing Computation  Computation can proceed in a Clockwise or counterclockwise Figure 4.11 Sketch for Bearings Computations

LOGO Sketch for bearing Computation

LOGO Comments on Bearing and Azimuths  Advantage of computing bearings directly from the given data in a closed traverse, is that the final computation provides a check on all the problem, ensuring the correctness of all the computed bearings

LOGO Measuring Angles  There are two methods for measuring existing or laying out new angles.  Indirect  Direct  Indirect methods measure and lay out angles by utilizing equipment that can not measure angles directly.  Direct measurement and lay out of angles is accomplished by instruments with angle scales.

LOGO Angle Measuring - Indirect  Tapes (or other distance measurement)  Using triangle principles  Using trigonometry based on slope angles

LOGO Determining Angles – Taping Need to: measure 90° angle at point X dd Lay off distance d either side of X X ll Swing equal lengths (l) Connect point of intersection and X

LOGO Determining Angles – Taping  A B C Need to: measure angle  at point A Measure distance AB Measure distance AC Measure distance BC Compute angle 

LOGO Determining Angles – Taping  A B C Need to: measure angle  at point A Q Lay off distance AP Establish QP  AP Measure distance QP Compute angle  P

LOGO Determining Angles – Taping  A B C Need to: measure angle  at point A D Lay off distance AD Lay off distance AE = AD Measure distance DE Compute angle  E

LOGO Angle Measuring Equipment - Direct  Direct methods of measuring angles involves the use of surveying equipment with angle scales.  The operator must understand how to use each type of instrument.  Examples of Instruments:  Sextants  Compass  Digital theodolites and;  Total stations

LOGO Angle Measuring Equipment

LOGO Theodolites  General Background:  Theodolites are surveying instruments designed to precisely measure horizontal and vertical angles.  They are used to establish straight and curved lines.  To establish or measure distance (Stadia)  To establish Elevation when used as a level. (When we set the vertical angle to 90°).

LOGO Theodolites They have:  3 screw level base  Glass horizontal and vertical circles, read directly or through micrometer.  Right angle prism (optical plummet)  High precision

LOGO Theodolites

LOGO Theodolites  Electronic read out 1” eliminate mistakes and reading the angles.  Precision varies from 0.5” – 20”  Zero is set by a button.  Repeated angle averaging.  Replacing optical theodolites (It is less expensive to purchase and maintain).

LOGO Total Stations  Combined measurements  Digital display

LOGO Measures and Records: Horizontal Angles Vertical Angles and Slope Distances Calculates: Horizontal Distance Vertical Distance Azimuths of Lines X,Y,Z Coordinates Layout Etc.

LOGO Measuring Angles  Instrument handling and setup  Discussed in lab  Procedure with repeating instrument

LOGO Angles  All angles have three parts  Backsight: The baseline or point used as zero angle.  Vertex: Point where the two lines meet.  Foresight: The second line or point

LOGO Errors in Angle Measurement  Gross – reading, pointing, setting up over the wrong point, booking  Random – settling of tripod, wind, temperature, refraction  Systematic/instrumental  Horizontal axis not perpendicular to the vertical axis  Axis of sight not perpendicular to the horizontal axis  Axis of the plate bubble not perpendicular to the vertical axis.  Vertical index error

LOGO