LESSON NOTE ON HORIZON : Introduction

The horizon is the line that separates the Earth from the sky. Some of the best places to see the unobstructed horizon are beaches, where the ocean meets the sky in an uninterrupted line. Here, Venus and the Moon rise together over the Atlantic Ocean horizon on the coast of Jacksonville, Florida.

The Horizon Line is the place where the ground and the sky appear to meet.It is also your eye level.

The horizon is the line that separates the Earth from thesky. 

There two main types of horizons—Earth-sky horizons and celestial horizons. Both Earth-sky and celestial horizons have different sub-types of horizons.

The local horizon, geographic horizon, and sea-level horizonare all Earth-sky horizons. The astronomical horizon and true horizon are celestial horizons. 

Earth-Sky Horizons

The local horizon, also called the geometrical horizon, is the visible boundary between the Earth and sky. The localhorizon may include trees, buildings, and mountains.

The geographic horizon is the apparent boundary between the Earth and sky. Mountains, trees, and other elevated features are not considered part of the geographic horizon.

The sea-level horizon is the geographic horizon at sea level. One of the best places to see the sea-level horizon is abeach. The ocean and the sky provide a clean, flat line where the Earth seems to meet the sky. If you're standing on the beach looking out at the sea, the part of the sea that "touches" the horizon is called the offing.

Celestial Horizons

Celestial horizons are used by astronomers. They aremeasurements of the position of the Earth relative to the rest of the sky.

The astronomical horizon is the imaginary horizontal planealways at a 90-degree angle from the observer's zenith (the point directly above the observer). Astronomical horizons are great circles that surround the observer.

The true horizon is the imaginary plane that passes through the center of the Earth, perpendicular to its radius. From orbit, the true horizon is spherical, following the shape of the Earth.

LESSON NOTE ON TYPES OF HORIZON LINE

THREE TYPES OF HORIZON LINE

1.     ASTRONOMICAL HORIZON : In astronomy the horizon is the horizontal plane through (the eyes of) the observer. It is the fundamental plane of the horizontal coordinate system, the locus of points that have an altitude of zero degrees.

2.     VISIBLE HORIZON: Horizon, in astronomy, boundary where the sky seems to meet the ground or sea. (In astronomy it is defined as the intersection on the celestial sphere of a plane perpendicular to a plumb line.) The higher the observer, the lower and more distant is his visible horizon.

3.     TRUE HORIZON : 1. The boundary of a horizontal plane passing through a point of vision.
2. In photogrammetry, the boundary of a horizontal plane passing through the perspective center of a lens system.

4.     The 'EVENT HORIZON' is the boundary defining the region of space around a black hole from which nothing (not even light) can escape. In other words, the escape velocity for an object within the event horizon exceeds the speed of light.

If the Earth is assumed to be a sphere with no atmosphere, then the distance to the horizon can easily be calculated. (Note: The Earth's radius of curvature actually varies by 1% between the Equator and the Poles, so this formula isn't absolutely exact even assuming no refraction.^[

LESSON NOTE ON Importance of the Horizon Line

Importance of the Horizon

The concept of the horizon is important to different types of work, including aviation, navigation, and art. 

Pilots use the horizon to keep aircraft level while in the air. Using a method called "attitude flying," they can control their aircraft by determining the relationship between the aircraft's nose, or front end, and the horizon. Pilots can change their altitude or flight pattern by changing thehorizon to be composed of mostly sky (increasing their altitude) or mostly ground (lowering their altitude).

Before the introduction of modern tools such as global positioning system (GPS) devices, sailors depended on a clear view of the horizon to navigate the ocean. The sun's position to the horizon told sailors what time of day it was and what direction they were sailing. 

At night, sailors could use celestial navigation, or the appearance of certain stars or planets relative to thehorizon. As the Earth turns, stars and constellations rise and set on the horizon, just like the sun. Different constellations appear at different times of the year, or are only visible from certain places. The rising of the constellation of the Southern Cross, for instance, signaled that sailors were in the Southern Hemisphere.

Artists use the concept of the horizon to create perspectivein paintings and drawings. When depicted with shapes getting smaller and less detailed closer to it, a horizon can create the illusion of depth on a flat canvas. 

The horizon was also important for early methods ofcommunication. Before the radio and telegraph were invented, people couldn't communicate with anyone farther away than the local horizon.

DIFFERENCE BETWEEN SURVEYING AND LEVELLING:

LECTURE NOTES : WHAT IS SURVEYING?

☞

Surveying is the branch of applied mathematics which deals with measuring

and recording of the size and shape of any portion of the earth’s surface, and

the delineation of the same in a map or plan.

☞

It deals with the setting out of works such as roads, railways, waterworks,

drainage schemes etc and the calculation of areas and volumes.

☞

It may be taken to include levelling i.e. determination of the relative heights

of different points on the earth surface.

TYPES OF SURVEYING

1. Trigonometrical surveying : - This is for the preparation of maps of large

extents of territory

2. Land surveying: - this is ranging from the land division system and extensive

topographical surveys and work for boundary commission to small ones such

as farms and estates.

3. Hydrographical surveying: - ranging from coast surveys to plans for harbour works.

4. Engineering location surveying: - For the construction of highways, railways

and various public works.

5. Preliminary or parliamentary surveys: - This is in connection with a projected

scheme such as the construction of a railway or a waterworks.

6. Exploratory surveying: - This is for geological, engineering and mining

enterprises including archaeological expeditions.

7. Environmental survey: - his is survey carried out for forest and water

parameters.

DIFFERENCE BETWEEN SURVEYING AND LEVELLING:

Surveying consists in making measurements in the horizontal plane while

Levelling is making measurements in the vertical plane.

In surveying, the measurements consist in fixing position of points in the

horizontal plane; 2 points fix a straight line while 3 or more straight lines

determine the plan of a plane figure.

WHAT IS VISUAL SURVEY?

This is also called reconnaissance survey.

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It is the preliminary inspection of an area to be surveyed.

⇒

It is a see-for-yourself walk-over of the ground to be used for a fish pond or a

fish farm. It is first done with a view to visualise the work to be done.

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It is the venture taken to note and identify all the parameters to be measured

or surveyed.

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It is a rough sketch of the field or fields in which all positions and stations

are made in the field book.

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It is preliminary work done whereby the routes of the main chain lines are

noted.

WHAT DO YOU DO DURING VISUAL SURVEY?

(i)

The purposes of the survey should be noted.

This includes (a) is it for pond construction?

(b) Is it for damming? (c) Is it for irrigation purposes; (d) Is it for Hydro-electric power (HEP)? The purpose will determine the extent of the reconnaissance survey.

(ii)

The water parameters to be measured should be noted as from the beginning. Such parameters include : (a) Water level; (b) Geological attributes;

(c) Soil conditions (texture, structure and permeability); (d) Water pH, hardness,

alkalinity, chloride, phosphate, ammonia, sulphide, sulphite, dissolved oxygen

etc

SURVEY IN POND CONSTRUCTION

Through topographic survey, the proposed site is inspected and professionally

approved. The water, soil and other parameters are determined. Using levelling

instrument, the topography of the site is ascertained and the area to be dug/

excavated or filled is pegged out with the use of lines. 

LESSON NOTE ON SOME TERMS USED IN LEVELLING OPERATIONS

SOME TERMS USED IN LEVELLING OPERATIONS

1. Bench mark (BM): it is a fixed point on the earth’s surface whose level above ordance

datum is known.

2. Ordnance Datum (OD): it is the mean sea

level to which all other levels are related.

3. Back sight (BS): is the first sight taken after the level has been set up. A sight taken to a point whose height is known or can be calculated.

4. Foresight (FS): The last sight taken. A sight taken to a point whose height is required to carry on the line of level.

5. Intermediate Sight (IS): it is any other sight taken.

6. Reduced Level (RL): calculated level of a point above or below the datum.

7. Height of Instrument (HI): The height of the line of collimation above the datum.

8. Line of Collimation (LM): It is an imaginary horizontal line drawn between two points.

9. Rise and fall: The difference is height or is level between two is referred to as a rise or fall.

10. Change Point (CP): the point at which both a foresight and then a back sight are taken.

LEVELING INSTRUMENTS

These include:

. A Level e.g. theodolite, transit dumpy level(automatic level),e.t.c.

. A staff

. Devices for angle measurements e.g. graphometer, magnetic compass, prismatic compass, orientation compass

. Chain or tape

. Pegs, arrows and ranging poles 

LESSON NOTE ON TYPES OF LEVELLING

TYPES OF LEVELLING

1. Continuous leveling

2. Reciprocal leveling

METHODS USED IN CONTINUOUS LEVELLING

• Collimation method or height of instrument

• Rise and fall method.

In collimation method height of instrument

HI = BS + RL

And reduced level

RL = HI – FS

At the end computation, the difference of the sum of BS and FS must be equal to the difference of first RL and last RL data recorded. Meanwhile in Rise and Fall method, a rise will occur when the staff reading is less than the reading on the proceeding station. The data recorded are also checked for correctness as above, but this time, rise and fall are used instead of BS and FS.

TRAVERSE DURING LEVELLING:

Definition:

A traverse is a continuous frame work of line connecting a number of points, the lengths of the lines and their angular relationship to each other being measured. The lines are known as legs and the points as stations.

USE

Traverse surveys are used where site conditions make the chain triangulation method impossible e.g where the survey is of as large area and details are not required.

TYPES:

1) Closed traverse – when the frame work form a closed figure (or when the traverse connects two stations whose position are known). This type of traverse is used for surveying lakes or other areas across which known check line can be run. Such traverse is easily checked, as the survey starts and finishes at the fixed points.

2) Open traverse – a traverse whose starting and finishing stations do not coined or are not both fixed or known points. This type of traverse is used to survey rivers e.t.c. To enable the work to be checked, sights are taken on to some reference objects, such as well defined landmarks

Note:

a) Chain traverse √

b) Compass traverse √

c) Theodolite traverse √

Terms:

a) Bearing – the term bearing refers to the angle between the line and the north -south line or median.

b) Whole - circle bearing - the bearing from north to the leg is measured in a clockwise direction and the angle from the north line right round to the leg is known as a whole – circle bearing ( as W.C.B)

A N

N N

A

WCB

O Of

WCB OA

O Of WCB

OA O of OA

A

Forward and Back Bearing: with A as the starting station of traverse and the direction of the survey being forward B, the angle between north and AB at A is known as the forward bearing of AB. The angle between north and AB at station B is known as the back bearing of AB, this should differ from the forward bearing by exactly 1800.

The forward and back bearings of a leg will differ by 1800 except there is local attraction. The presence of metal, metallic ores or electric currents will divert the compass needle from the north– south line, and thus cause the readings taken to be inaccurate. Stations should therefore be chosen so that they are beyond the influence of this attraction.

Correction for Effects of Local Attraction:

Line Bearing Diff of FB and BB

AB 600 1800

BA 2400

BC 1200 1800

CB 3000

CD 2100 1780 (-20)

DC 320

DA 3170 1820 (-20)

AD 135

LESSON NOTE ON TACHEOMETRY

TACHEOMETRY

This is the operation of measuring distances by means of stadia hairs.

Measuring the distances using stadia hairs involves setting the instruments at one end of the line being measured and a leveling staff is held vertically at the other end. The points where the stadia hairs cut the staff are read. The difference between the readings is the staff intercept, S. Assuming H is the horizontal distance between the instrument and staff, then

H = KS + (f + C)

Where K = constant multiplier (f +c) = additive constant

Note that K = f/i

Where f = focal length of the objective lens.

i= interval between stadia hairs

The equation above is applied to external focusing telescope, but when an anallactic lens is fitted is the telescope to bring the focal point on the vertical axis and therefore remove the need for additive constant.

H = KS.

But when the ends of the line being measured are on different levels such that the telescope has to be elevated of depressed through an angle of Ө0, the formulae above changes to:

H =KS Cos 2θ`and reduced level:

V = KS Cos Ө sin Ө+ HI – H

HI = height of instrument

h = staff reading

Occasionally, if θ exceeds 45⁰, it is better to tilt the staff so that it is perpendicular to the line of sight. Short sight is therefore attached to the staff to enable this to be done accurately. The method is called normal staffing then the formulae becomes:

H = KS Cos θ+ h sin θ

V = KS sin θ+ HI –– h cos θ

Lesson Note On TYPES OF PLANE SURVEYING

TYPES OF PLANE SURVEYING

Base on the nature of work to be done, we have the following types of the plane survey.

1) Cadastral survey: Involves measuring, delivery, recording the boundaries of precipitate, supplies map plan beyond a parcel of land described in land register. This is kind of plane surveying used in committed areas of land mostly private properties it is mainly used to establish boundary of the precipitate.

2)Engineering surveying: This embraces the survey work require before, during and after a engineering work, it is done for the construction and design of new roads and rails roads.

The type of scale of engineering surveying of archtechtural work drawing are 1 – 50 or

1:50, 1:100, 1:200 for sight plane and civil engineering work, scale of 1:500, 1:1000,

1:2000, 1:2500 for town survey or highway survey, we have scale of 1:2000, 1:2500,

1:5000,

1:10000 etc.

3)Mining surveying: This is a plane surveying used in determining the position and dimension of underground passage of the mine and also the natural and artificial feature of the mine, the data include both horizontal and vertical parts, length direction and slope of the turning and geological and topographic characteristics in a particular vicinity.

We can have open cast mine survey and underground mine survey.

It generally involves establishment of mineral boundaries and fixation of reverence monuments such as locating bore hole, rail roads and constructing geological map.

4)Road surveying: It is a plane surveying carried out for the purpose of locating and constructing cones of transportation and communication such as highways, rail roads, canal pipeline etc. here primary work usually involve topographic survey.

5)Hydrographic surveying: This is the type of plane surveying carried out in relation to considerable body of water such as lakes, rivers, ponds, etc.

The survey aims at determining channel depth for the purposes of navigation, water supply or sub-aquatic construction. In the case of river hydrographic surveying is made for flood control, water storage and apply, navigation and power supply some of the process in hydrographic surveying include (i) topographic survey of shore and bank, leveling to determine underground profile.

Plotting of such profile taking cross section, calculating volume of networks measuring drawings areas and laying out culvert and bridges.

Topographic surveying: This is a plane surveying used in purchasing map’s and plans of natural and mammals features such as relief, elevation, unequal land surfaces. There is no clear differences between a plan and a map of this nature, it is generally accepted that open details are rail drawn to a chosen scale while in map many textile has to be represented in symbol.

Topographic plan survey are used for engineering or design and administrative purpose only whereas topographic map are found useful in navigation, constructional activities.

The second characteristics of plane survey base or equipment are

1)Chain surveying or linear surveying which include the use of chain or tape to measure distances.

2)Compass surveying: Which involves the use of compass I getting bearing.

3)Theoclatide surveying: Which measure angles of elevation and depression

4)Leveling: Which make use of abnormal level, land standard pole; leveling is defined as the process of finding the differences

between in height of any 2 points on the ground.

For the purpose of

a)Tracing contour line

b)Plotting vertical section

c)Establishing point at given any elevation in constructional project.

Lesson Note On How to establish controls in Hydrographic Surveying

How to establish controls in Hydrographic Surveying
	The first step in making a hydrographic survey is to control both horizontal and vertical. Horizontal Controls: In an extensive survey, the primary horizontal control is established primarily by running theodolite and tape traverse before the triangulation station. Tthe traverse lines being run to following the shore lines approximately. In survey of less extent the primary horizontal control only is required and is established by running a theodolite and tape traverse sufficiently close to shore line. For rough work, the control may be established by running a theodolite and staid traverse or plane table trader. Stadia Surveying: The distances are determined by angles there are stadia hairs from which angles and all calculations are determined without change. Vertical Controls: These are based upon a series of bench marks established near the shore line by spirit leveling and these serve for setting and checking tide gages etc to which the sounding are referred.
Shore Line Surveying: Purpose: To determine the shore lines. To locate the shore details, promise topographical feature, light house, pointt of reference etc. To determine the high and lower water lines for average spring. Both in please and elevations in the case of tidal waters. All irregularities in the shore line as well as the shore details are located by means of offsets measured with a tape form the traverse lines, by staid or plane table. The points of reference should be dearly risible form the water and should be near enough such wing mills, flag poles etc. buoys anchored off the shore and light houses are used reference points. The position of the high water line may be judged roughly form deposits an marks on rocks however to locate it accurately the elev of mean high water is determined and point are located on the shore at that elevation. The line connecting these points represent high water level.

RECIPROCAL LEVELING

RECIPROCAL LEVELING

Reciprocal leveling is employed to determine the difference in elevation between two points when it is difficult or impossible to keep backsights and foresights short and equal

In this method, two sets of rod readings are observed, (1) one set is taken with the instrument set up close to one point, and (2) another with the instrument set up close to the other point.

Considering the Figure 1 below, the equations to obtain the difference in elevation are the following

DE_A = (a – b) and DE_B = (a’ – b’)

TDE = (DE_A + DE_B)/2 = [(a - b) + (a’ – b’)]/2

Elev. BM2 = Elev. BM1 ± TDE

where:

   DE_A = the mean difference in elevation between A and B with level at left

   DE_B = the mean difference in elevation between A and B with level at right

   TDE = the true mean difference in elevation between A and B

 

Procedure:

1. Set two hubs either on the 2^nd or 3^rd floors of the Velasco and La Salle Buildings and call these the BM1 and BM2, respectively. The elevation of BM2 is to be determined while the elevation of BM1 is known or assumed to be 10.000 meters above see level. Also, imagine that the football field between the Velasco and La Salle Buildings is an intervening deep ravine or wide river.
2. Set up and level very carefully the instrument at point A at Velasco Building (3^rd floor) near BM1.
3. Take and record a series of three consecutive backsight rod readings on BM1 and six consecutive foresight rod readings on BM2.
4. Move the instrument to point B at La Salle Building (3^rd floor) which is on the opposite side of the imaginary ravine and near BM2, set up, and level the instrument carefully.
5. From the new set up, take and record three consecutive foresight rod readings on BM2 and six consecutive backsight rod readings on BM1.
6. Tabulate observed and computed values accordingly. Refer to the accompanying sample format for the tabulation of field data.

Instrument Set Up Near BM1			Instrument Set Up Near BM2
Station	B.S.	F.S.	Station	F.S.	B.S.
BM1 (a)			BM2 (b’)
BM2 (b)			BM1 (a’)
Sum			Sum
Mean			Mean